AN Weidong

PALSA FORMATION :MATHEMATICAL MODELLING AND FIELD INFORMATION

Thèse présentée à la Faculté des Études des Études Supérieures de L'Université Laval pour I'ob tention du grade de Philosophiai Doctor (Ph-D.)

FAcULTÉ DES ÉTUDES SUPÉRIEURES UNIVERSITÉ LAVAL QUÉBEC

AVRIL 1997

O An Weidong, 1997 National Library Bibliothèque nationale 14 of,,,, du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395. tue Wellington ûttawa ON K1A ON4 Ottawa ON K1A ON4 Canada Canada

The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or seil reproduire, prêter, distribuer ou copies of this thesis in microfom, vendre des copies de cette thèse sous paper or electronic formats. la forme de micro fi ch el^ de reproduction sur papier ou sur format électronique.

The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur q~ protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des chtssubstantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. ABSTRACT

Palsas are defrned as "Peaty permafrost mounds possessing a core of altemathg laye1 of segregated ice and pt or mineral soi1 material". Although such mounds can be compose exclusively of frozen peat and ice, the overwhelming field evidence shows that the peat i pdsas usuaiiy overlies sonme minera! sediments. When a frost susceptibIe soi1 is subjected : freezing, heave occurs as the result of the growth of ice lenses fed by water migration from tf adjacent unfiozen soil. The ice segregation responsible for the topographie heave of thes landforms takes place dominantly in the freezing sediments, the peat cover pIaying the singl role of an insulating layer tbat does not heave itself.

A theory for the ongin of palsas was published as early as 1910 by Fries an Bergstrom. Since then, for a century, several hypotheses have been proposed to explain t€ inception, growth and degradation of palsas. RecentIy, it has been found that palsas, like oh periglaciai landforms, are signif~cantly affected by climatic changes: aggradation an degradation of the paisas are contemparaneous processes. Studies of the palsas and oth~ permafrost indicators do not have only an interest for geornophology but also for climatic an environmentai changes.

The formation of palsas and cryogenic mounds and their evolution is principal1 controlled by the interaction of thermodynamics processes, ice segregation, frost heave thaw consolidation during decades and centuries. So far, our knowledge was mainly obtaine from field observations and investigations; very few field experiments were reported.

Using the I -Dmodel presented, the long terni aggradation of permafrost, the buiidup ( segregated ice and frost heave that takes place during paisa formation have been numericd simulated with reference to field conditions met near the village of Kangiqsualujjuaq, Northem Quebec. The model suggests th: a) discrete ice Iens aggradation near permafro base is the dominant process of palsa heave, and b) palsas cm form under the present climat conditions under snowfree sites. These results and conclusions generdy agree with fie observations, and the modelling approach wili help increase the understanding of still unsolvt aspects of the processes of palsa formation such as the effect of surface geomophologic changes and climatic variations on pemiafrost. Also, using the 1-D model, a numericd prediction of the influence of dimate cooling 01 the palsas is presented. The predicted resuIts show that the cooling spells lead to formation O small ground ice layers in the palsas or cryogenic mounds. Despite a lack of exact data fron deep drill-hoIes and long-term observation of formation of thick layer of ground ice, thc existing cryostatigraphic information in the literature agrees with our model.

The 2-D modelling sirn~Aatesthe inception of palsas in an open syseem impacted by a the simultaneous effects of the snow cover and snowfree ground conditions, side by side, b the seasonai variations of water content in the peat cover.

The computed results are in agreement with observations from both experimental pals; inception and new natural ones in the field. The modelling results show that, because of th4 insulating effects of seasonal snow cover, the permafrost core fmt foms beneath the snowfrei peat surface and then develops graduaily and yearly in the cross-section. After 6 years O freeze-thaw cycles, the frost heave finally builds up a small incipient palsa 53 cm high. Thi conclusions are that: a) the seasonal snowpack is a major insulating factor directly impacting 01 the soi1 thermal regime for the origin of palsas; b) palsas are not only the product of pas climates, but also forrn in the current climate conditions in discontinuous permafrost regions, i the extemal and internai thermodynamics, mass supply and other relevant conditions are me1 The basic understanding of the origin of paIsas is very useful for studies of cold region climatic and environmentai changes. The conclusions pertaining to palsas should also b applicable to a large array of landforms, such as cryogenic mounds, and to permafrost in fin soils of the discontinuous zone. SHORT ABSTRACT

This thesis presents two mathematical models that reproduce the formation and the aggradation of permafrost in palsas. Three major problems are adressed: 1) A one-dimensional mathematicai model of palsa formation; 2) The influence of climate cooling on palsas; and 3) A two-dimensionai model of the origin of palsas. The numerical modeiiing, assurning a saturated inhomogeneous soi1 medium, provides a basis for the advancement of theorical knowledge relative to palsas. Ground thermal regime, discrete ice lensing and frost heave problems had to be numerically soIved in the process. Cornparison of the numerical results with field data shows good agreement. 1 would iike to express my great gratitude to rny advisor, Professor Michel Aiiard of the Centre d'études nordiques for his wise guidance. encouragements and continuous suppori £rom the inception to the present form of this thesis. He has given me an invaluable help. Comrnents of the two other members of my supernision conmittee, Dr. Jean-Claude Dionne and Jean-Marie Konrad are aiso acknowledged.

I wouId iike to acknowledge the help 1 received from many friends and the staff of the Centre d'études nordiques and of the département de Géographie, Université Lavai, particuiarly Dr. Janusz Frydecki, in charge of automatic data acquisition systerns, Martin Poitras, computer specialist and Serge Caron, research assistant. The contributions to field work by the following persons was also appreciated: Christian Bouchard, Richard Fortier and Éric Ménard.

1 owe a dept of gratitude to the National Science and Engineeering Research Council of Canada and "Fonds pour la formation de chercheurs et l'aide à la recherche" of Quehc for financial support for this project through grants to my supervisor and to the Centre d'études nordiques.

I also want to express rny thanks to professor Wu Ziwang, director of the State Key Laboratory for Frozen Ground of the Lanzhou institute of Geocryology and Glaciology, my mentor in China, who encouraged and supported me to pursue rny doctoral degree.

Finally, my parents and my whole farnily desserve rny full reconnaissance for their Life long support of my education.

4.8 Summary...... 52

Chapter V A ONE-DIMENSIONAL MATHEMATICAL MODEL OF PALSA FORMATION AND GROWTH ...... 54

5.1 Background ...... 54 5.2 Study Site ...... 56 5.2.1 General characteristics of the study site ...... 56 5.2.2 Peat properties ...... ~...... ~...... 58 5.3 Mathematical Modelling ...... 60 5.4 Numerical Computation ...... 65 5.5 Numerical Results ...... 66 5 .5. 1 Themai regime ...... 66 5.5.2 Ice segregation conditions ...... 68 5.6 Discussion ...... 71 5.7 Summary ...... 73

ChapterVI INFLUENCE OF CLIMATE COOLING ON PALSAS ...... 75

6.1 Introduction ...... 75 6.1.1 Background ...... 76 6.1.2 Regional clirnate cooling ...... 77 6.2 Synopsis of Modelling ...... 77 6.2.1 Initial condition ...... 77 6.2.2 Boundary condition ...... 77 6.2.3 Soi1 material and thermal parameters ...... 79 6.3 Thick Segregated Ice Lliyers ...... 80 6.3.1 Effects of climate cooling on ice iensing ...... 80 6.3.2 influence of Segregation Potential (SP)...... 88 6.3.3 Influence of the peat layer ...... 91 6.4 Summary ...... 94 Chapter VII A TWO-DIMENSIONAL MODEL FOR THE ORIGIN OF PALSAS ...... 95

7.1 Background ...... 95 7.2 The Mode1...... 98 7.2.1 Characteristics of snow and peat at the simulated site ...... 98 7.2.1.1 Seasonai snow cover...... 98 7 .2.1.2 The Peat layer ...... 101 7.2.1.3 Clayey silt ...... 103 7.2.1.4 Unfrozen water content ...... 103 7.2.1.5 The parameters of the SP ...... 104 7 .2.2 Thermal energy of soils in keze-thaw cycles ...... 104 7 .2.2.1 Energy equations ...... 104 7.2.2.2 Heat sourceslsink...... 105 7.2.2.3 Frost heave and discrete ice Iensing in palsa system ...... 106 7.3 Numerical Computation ...... 109 7.4 Results and Discussion ...... 112 7.4.1 Thermal regirne ...... 112 7 .4.2 Ice lensing ...... 118 7 .4.3 Ongin of palsas ...... 121 7.5 Summary ...... 126

Chapter VITI CONCLUSION ...... 127

Up to date knowledge on paisas ...... 127 Consideration from rnodelling palsa formation...... 178 Lnfluence of clirnatic cooling on palsas and cryogenic mounds ...... 179 Role of spatial variation in snow cover conditions...... 131 Distributions of ice lensing in cross-section ...... 131 Ongin of Paisas ...... 132 Modification of the conception for ongin of paisas ...... 132

REFERENCES ...... 134 ANNEX 1 ...... 151 ANNEX II ...... 170 ANNEX In ...... 203 NOTATION constant thawcompressible coefficient apparent volumetric thermal capacity (I i3Kt)

volumetric thermal capacities of ice and water (J rnJ KI)

volumetric thermal capacity of soi1 particles (J rn" K.') fringe thickness thermal hydraulic conductivity (m2s" 'C*') pore ratio heave (m) height of peat (m) height of peat top (m) height of peat bottom (m) heave from pore water content (m) heave from water migration (m) depth of snow accumulation maximum depth of snow accumulation energy flux of downweiling short wave radiation hydraufic conductivity, hydraulic conductivity at - 1 "C(m s-') volumetric latent heat of fusion (335 kT kg-') soi1 porosity pore water and pore ice pressures (kg m-') Po, P, overburden and applied pressures (kg m-2)

PIC, pressure in the ice (kg m-2) additional pressure component (kg m.*) pore pressure at the fi-eezing front (kg rn-') water velocity (rn s-') mass water fiow in saturated dry snow heat source portion of incident radiation short wave radiation long wave radiation saturation (96) segregation potentiai coefficient (m' s-' OC-') tirne ternperature (K) freezing temperature of pure water (OC) segregation freezing and frost front temperatures (OC)

lower warm boundary temperature of frozen fringe (OC)

water velocities in soiis and the freezing fringe irn s ! j velocity of soi1 particle movement Cartesian coordinates (m) end of Faii thermodynamic constant thermodynamic constant thermal conductivities of soil sand soil particles (W m-'K-') thermal conductivities of ice and water (W m-'K-')

bulk densities of soil and snow (kg m-3) densities of ice and water (kg m-3) total content of liquid water and ice original water content water content of peat

water content at top of peat surface

water content at bottom of peat

water content of peat beneath the snow free surface

water content of peat beneath the snow cover

air content and soil particle content (m3 nY3)

unfrozen water and ice content

chernicd potentials of ice and water in soils

volume strain of soils

horizontal distance of snow covered peat surface

horizontal distance of snow free peat surface

actual stress

Subscript Ab beginning of fali s f rniddle of surnrner sm snow melting si snow melted wb beghhg of winter we end of winter

Yto end of faü LIST OF TABLES

Table 5-1 Soi1 physical and thermal properties used for mode1 cornputations ...... 65

LIST OF FIGURES

Figure 3.1 Location of Kangiqsuaiujuaq reference site ...... 27

Figure 4.la Conditions controling ice lensing in the frozen fringe ...... 40

Figure 4.lb Heat and mass transfer properties in the frozen fringe ...... 40

Figure 5.1 Actual thermal profiles in the paisa cornplex of Kangiqsualu@aq ...... -57

Figure 5.2 Location of the three frost (and thaw) fronts in a palsa systern ...... -64

Figure 5.3 Evolution of the thermal profile with elapsed theduring aggradation .... -67

Figure 5.4 Distribution and thickness of ice lenses dong a vertical profde after 200 years. frorn simulation...... 67

Figure 5.5 Growth of ice lens and deepering of permafrost with times (SP of 1-29 x 10.~)...... 69

Figure 5.6 Differences in heave and ice lens thickness with depth depending whether only in situ water (A) is used in the process of if there is free succion of ground water (B) ...... 69

Figure 5.7 Ice lens distribution and thickness after a mode1 mn in absence of peat cover. Ice enrichment and several thick ice lenses form in the upper layer of permafrost ...... 70

Figure 6.1 Scenario for the one step clirnate cooling for mode1 test ...... 82

Figure 6.2a Vertical distribution and thickness of ice lenses in the palsa formed during 180 years of steady climate (MAAT=44'C) ...... 83

Figure 6.2b Growth of the sirnulated palsa of figure 6.2a and ice lens thickness and distribution after 35 years of cooling...... 83 Figure 6.2~ Renewed formation of thick ice Ienses at permafrost base during the steady pend followïng cwhg...... 83

Figure 6.3 Time progressive graph of ice lense formation, thickness and distribution in the one step cooling scenario ...... 85

Figure 6.4 Evolution of the temperature profile in the one step coohg scenario for (A) summer situation and (B) winter situation...... 86

Figure 6.5 Scenario for the two steps clirnate cooling used in the second simulation. .87

Figure 6.6 Distribution and thickness of ice Ienses in palsa with climate cooling ...... 89

Figure 6.7 Evolution of temperature profiles in the palsa under the two steps cooling scenario ...... 90

Figure 6.8 Ice lens thickness and distribution following the one-step cooling scenario with an SP vdue of 2.58 x 10" ...... 92

Figure 6.9 Ice lem thickness and distribution foilowing the one-step cooling scenario with an SP value of 1.29 x 18~...... 93

Figure 6.10 Ice lens thickness and ditribution following the two-step cooling scenario with an SP value of 1.29 x 10-6, compare to figure 6.6 (E) ...... 93

Figure 7.2 Initial conditions for the two-dimensional mode1 where SC is snow cover, SB is snow border and SF is snow-free ...... 1 13

Figure 7.3 Evolution of the thermal profile under point SC of figure 7.2, (A) summer profiles and (B)winter profiles...... 1 13

Figure 7.4 Evolution of the thermal profile under point SB of figure 7.2, (A) summer profdes and (B) winter profiles...... 1 14

Figure 7.5 Evolution of the thermal profile under point SF of figure 7.2, (A) summer profiles and (B) winter profiles...... 1 14

Figure 7.6 Cornparison of winter profiles, year 6 vs year 1 ...... 115

Figure 7.7 Progression of the O°C isothem over the six fmt years of palsa growth.. 1 15

Figure 7.8 (A) Thermal profiles and (B) thermal regime from summer of year 3 to early fa11 of year 5, under point SC ...... 1 17 Figure 7.9 (A) Thennal profde and (B) thermal regime from summer of year 3 to early faii of year 4. under point SF...... 11'

Figure 7.10 Ice lens growth and vertical distribution with time under point SF...... 1 l!

Figure 7.1 1 Thickness of ice lenses below the horizontal profde with the ...... 115

Figure 7.12 Comparative vertical distribution and thickness of ice lenses under points SC. SB and SF after 2 years ...... 12C

Figure 7-13 Comparative verticai distribution and thickness of ice Ienses under points SC. SB and SF after 6 years ...... 12C

Figure 7.14 Heave dong the profile during 6 years ...... 123

Figure 7.15 Details of heave from August of year 3 to September of year 4 ...... 123

Figure 7.16 Details of heave. continued until year 6...... 124

Figure 7.17 Yearly heave with SP0=3.25 x 10' m2/h. 'C ...... 124

Figure7.18 YearlyheavewithSPO=L.85x 106rn2/h.aC...... 125

LIST OF PHOTOS

Figure 3.2 (A) The paisa plateau and paisa complex near Kangiqsualujjuaq. in June 1992 during snowmelt . (B) Segregation ice from the palsa cored. 1.1 m below the stratigraphie peadsilt contact ...... 28

Figure 7.1 Pictures of palsas with seasonai snow cover ...... 96

Chapter 1

INTRODUCTION

1.1 THE PALSA: A WIDESPREAD LANDFORM TYPE

Palsas are defined as: "Peaty permafrost mounds possessing a core of alternathg layeri of segregated ice and peat or minera1 soii matenal" (Associate Cornmittee on Geotechnica Research, National Research Councii of Canada (A.C.G.R.) 1988). They are widespreac aiinost everywhere in subarctic and alpine regions. Studies of palsas have been reported nearIj from every regions of discontinuous permafrost: from the northern regions of Finland Norway and Sweden (Lundqvist 1951; han1976; Seppala 1982, 1986), Iceland (Friedmar et al. 197 1; Schunke 1973). from Siberia, Russia (Washburn 1979; Akerman 1982a), frorr North Arnerica where palsas are distributed in Alaska, Yukon, the Rockies (Péwé 1975 Nelson and Outcalt, 1982) and in northern Qu6bec CWashbum 1983~Brown et al. 1983 Lagarec 1982; Allard et al. 1986; Lévesque 1990; Dionne 1984, 1992). Palsas are dsc reported in Hokkaido, northern Japan (Takahashi and Sone 1988; Sone and Takahashi 1993) Observations and investigations have shown that palsas are a more cornmon and widespreac permafrost indicator than earlier realized.

1.1.1 GEOMORPHOLOGICAL CHARACTERISTICS OF PALSAS Palsas are srnaii mounds of frozen peat or peat-covered frozen sediments rising oui mires and fens. Marine, lacustrine or other fine-grained sediments are the dominant mateRa12 in which these landfom are developed. With clirnatic and ground surface condition changes paisas cm undergo inception, growth, maturation and decay. The size and shape of palsas are determineci by a combination of local factors such i Quatemary geology, climate, soii type and vegetatîon cover.

Most palsas show eIiiptic or circular plan shapes in which the diameter usudy rangt from a few meters to tens of meters and more; the height varies from less than 1 rn to maximum of about IO m. Other shapes aiso occur such as peat plateaus (about IOûû mZ), pals ridges (100-20 m2), and palsa strings (10-100 m2) (Ahman 1977; Seppaia 1972). Wii growth, a srnali pillow-like frost body fmt rises above the surrounding tundra surface, the develops steep s!opes and graduaily produces a mature dome-like paisa mound. For instanci the smail paisa formed in a field experiment by Seppdlii (1982) was a 35 centimeters hie pillow-shaped frozen peat mound. Near Kanjiqsualujjuaq (George River) and in tl Ouiatchouan fen, near Richmond Gulf, in northem Quebec, the paisas are in average 2-5 m j height and 13-40 m in diarneter (long axis) (Lagarec 1980). In the Macmillan Pass-Tsich River area, Northwest Temtories, paisa heights range from 0.15 to 9.75 m, averaging 4 m an have diameters from 3.25 to 76.0 m, averaging 30 m. Peat plateaus have maximum heights c 2.5 rn, averaging 2 m and diameters that reach 22.5 m. Relief on top of peat plateau average 1.5 m (Kershaw and Gill 1979).

After reaching the mature stage, some palsas will fluctuate in height, degrade, or collaps along open cracks. Often, most wili coiiapse completely and leave a thennokarst pon surrounded by a rim. This is because of the fact that when the surface insulating layer of pei is damaged, the thermal equilibrium of paisas is changed. The processes are mainiy so: i) th organic material layer, or peat layer, at the top or on the slopes of the paisas is dry and crack! The absorption of solar energy, ground surface water. and rain supply additional heat along th cracked or damaged portion of the peat Iayer into the palsa to erode the underlying frozen cort ii) under warming climatic conditions, thaw occurs at permafrost base and permafrost top du to the increasing thermal energy and the frozen core graduaiiy melts out.

1.1.2 THEORIES FOR THE ORIGIN OF PALSAS Since the rniddle of the XlXth Century, permafrost studics have been performed in col countries. The earliest studies were done in Russia. How to determine the presence c permafrost from related landforms? Many investigations support that palsas are among th most conspicuous and available surface manifestations of permafrost in the sporadic an discontinuous permafrost zones. But although an abundant literature described the geologica geomorphologic and physical features of palsas, only a few comprehensive theoricai work were devoted the explanation of the origin of palsas. In 19 10, a theory for the origin of palsas was fmt published by Fries and Bergstroi Based on their hypothesis, the origin of palsas is mainly conditioned by wind drifting of snoT The winds make an uneven snow distribution in tundra areas, and the drift controls the locatii and thickness of the snow cover on the mire surface. Frost penetration beneatb the snow fi peat surface or below areas with a thin snow cover is rnuch deeper than that beneath the thi, snow drifts. Then, the frozen soi1 beneath the thick snow drift thaws completely in summc but the frozen soi1 beneath the snow free peat surface or thin snow cover remains and develo thicker in the following winter. The developing frozen core wiIi remain permanent and resi in Izther upheave of the ground. This is the inception stage.

Fries and Bergstrom's theory for the origin of paisas was presented nearly a centu ago, but before t!!e 1970is, very few works were concerned with the mechanism again. It h been for long believed that palsas are elevated above the surrounding terrain by the combinc action of peat accumulation on the surface and ice segregation in the underlying mineral sc (French, 1976, Dever et al, 1984). Also, some authors suggested that paisic landforms m; be inherited from past climatic deterioration periods (SeppaIa 1982), without any detaili explmation on formation processes.

Afkr the 1970's. with the wider and sounder studies of permafrost developing wor wide, the approach to pdsa genesis lead again to stress the importance of a thinned snow cov and ice segregation. It was suggested from laboratory experiments that ice segregation is fi by suction of unfrozen water to the freezing front in freezing soils (Taber 1929, Konrad ai Morgenstern 1980). Otherwise, the influence of snow drift on the peat plateau and paisas w further identified by Seppala (1982) with a field experiment of palsas formation. That winc cany the snow away from the exposed surface but accumulate it in surrounding are provoking the orïgin of paisas was further identified as the main mechanism by Seppala (1981 in the northern regions of Finland and by Allard et al. (1986) in northern Que%ec.

It has been proposed that wetland vegetation ceases to grow and is replaceci t xerophytic species when the peat surface is raised above bog level (AUard and Seguin 1987 Only in particularly wet climate cm mat thickening somewhat conmibute to palsa growth afi heave is initiated. Many researchers have agreed that pdsas may occur in a large variety 1 shapes and they are often genetically and spatially associateci with peat plateaus (SaIrni, 197 Schunke 1973; Washburn 1983a). Washburn (1983a) proposed that palsas can originate fro two chahs of different processes: one is by aggradation due to frost heave by growth of ic the other is degradation due to the disintegration of extensive peat plateaus. The two types 1 palsas are Bcult to identify by shape. While the depdational type indicates thermoka processes, the aggradational one indicates the growth of pedostunderneath.

From the field experirnents and investigations, it is now a widely demonstrated fact tl for the ongin of palsas, snow and peat covers, coid winter temperature, as well as watt saturated medium are the major control factors, while ice segregation taking place dorninani in the underlying sediments is responsible for the topographie heave of these mounds (hm 1976; Washbum 1983a; Pissart and Gangloff 1984; Dionne 1984; Seppala 1986; Mard et r 1986). However, many questions still remain to be answered about how these major factc affect on the ongin of palsas. ALmost nothïng is known on the interaction betwec thermodynarnics and mass redistribution under the soi1 system in recuning freeze-thaw cyclc Importance of sediment properties, exact growth mechanisms, sensitivity to climatic variatio are all questions asked about paisas but for which no quantitative estirnates are availabl Formation duration of paisas is not known, except for a few scattered examples.

1.1.3 TERMINOLOGICAL DISCUSSIONS ABOUT PALSAS "What is a palsa (Washbum 1983a)?" This question generated abundant terminologie discussions and debate. Palsas were identifred as "immature pingos" by Porsild in 1945 1951, and they are also cIassified as pingos by Brown and Péwé (1973). However, it is no well-known that one of the fundamental differences between palsas and pingos is the type ice contained in the mounds. Palsas and peat plateau complexes contain segregated ice lensi and mineral materials or peat cores and have at least a surface covering of peat, while pingc are composed mainly of pure ice bodies that were supplied by pressured water.

Palsas were p~cipallyclassifieci into two types: "palsas" in a classical sense, ar "palsa-like frost mounds" .

"classic" palsas

This type of palsas was interpreted as a smaii mound of peat rising out of wetland ar containing a permafrost core of frozen peat, smali ice crystais, and thin segregated ice laye (Seppala 1972; Dionne 1978, Washburn 1983a; Brown et al. 1983). According to th viewpoint, the permafrost core of palsas is lirnited in the peat layer. Usually, the peat layer relatively thin, a few centimeters at the most and, therefore, the naturd phenomena show that Ehe ciassic palsa is small, Le. about 1 m or a little higher, and ii) the classic palsa elapses for relatively short period from the inception to decay, usuaiiy few decades due to the variation ( increase of the external thermai effects on the smaii rnound. "palsa-like frost mounds" Different from the "classic" paisas, the second type of paisas consists of mounds built up of hzen minera1 soils and discrete segregated ice layes underlying a peat layer (Lundqvist 1951; Svensson 1964; Seppala 1972; Ahman 1976). This type of frozen mounds were also called "minera1 palsas" (Pissart and Gangloff 1984; Dionne 1984). They are generally larger in size and as the extemai thermal energy involved is important, the rnounds last much longer.

With rnany field investigations in the entire cold regions and the improvements of study methods, such as using the ground probing radar, '" dating, therrnistor cables, dnU holes and other geotechnical and thermal instruments, the terminological discussions and debate over the processes of palsa formation can be narrowed into more precise tenns. Aithough palsas can be composed exclusively of frozen peat and ice, the majority of field investigations have indicated that the bulk of he landforms usually lies dominantly in the underlying permafrost mineral sediments where ice lenses form Qgarec 1982; Pissart and Gangloff 1984; Dionne 1984; Mard et al. 1986; Doolittle 1992). It is now a widely demonstrated fact that aii the "classic" paisas and "paisa-like frost mounds" are formed by ice segregation which is responsible for ground upheave in freezing soils. Therefore, the both types of mounds mentioned above are al1 defined as palsas (A.C.G.R. 1988).

It was aiso shown that many other mounds of shapes and sizes similar to palsas but without a peat cover also formed through segregation of ice lenses. They are referred to most often as cryogenic mounds (Lagarec, 1982; A.G.C.R., 1988) or mineral permafrost mounds (Allard et al. 1986), or, again, as minerai palsas (Dionne 1978, Pissart and Gangloff 1984). Recently, Harris (1993) proposed the new terme "lithaisa" for such mounds.

Recently it was shown that variations of palsa size and distribution (Le. aggradation or degradation) are significantly linked to environmental and climatic changes (eg Laprise and Payette 1988; Laberge and Payette 1995). Therefore, studies of paisa formation and variation are obviously significant, not only for studies of the problerns of frost heave and thaw sediment in frozen soils, but also for predictions of climatic and environmental changes which are very important issues for cold regions research and development. In order to increase the general understanding and develop new knowledge on hc paisas form, how they evolve and in order to better understand the interpiaying role numerous geological and climatic factors. this thesis presents mathematical modek of pal formation, and of cryogenic mounds as well since the processes involveci (mainiy ice le segregation) are now known to be similar. Mode1 conditions are set according to observc terrain and clirnatic conditions in the palsa region of northern Que'bec.

After a literanire review of freezing and thawing processes in soils and a review pertinent environmental factors in northern Québec, the physical and mathematicai concepts the models are presented. Thereafter follows a chapter on modeliing paisa-growth in oi dimension, then on modelling the effect of climate coohg on the internai structure of pals and, finaily, cornes a two-dimensional mode1 of inception and earIy growth of a pdsa ove1 peat bog. Mode1 results bring new understanding on the factors and the processes involve They will also give way to new and original field measurements and experiments in the futu by proposing new research questions. Chapter II

FREEZING AND THAWING SOLS: LITERAmREVIEW

2.1 ICE LENSING AND FROST HEAVE IN PALSA GROWTH

Ice lensing and frost heave are central processes in the formation of paisas. The: periglaciai landforms are principally dominated by freezing and thawing processes of soi induced by long-term recumng annuai freeze-thaw cycles. Most of existing explanations fc formation of these landforms are incomplete or partial because they are based on broz qualitative descriptions and points of view restricted to generd environmental consideration The thermodynamics involved in their genesis and their environmental controls remain to t tackied appropriately. ObviousIy, in order to adequately understand the origin and ti dynarnics of these widespread mounds, the fundamentai problems of ice segregation ar freeze-thaw cycles in soils are to be approached and mode1 parameters must be as ciose i possible to real field situations. The mechanistic approach to these processes draws from il comprehensive application of different pertinent disciplines: Quatemary geolog: geomorphology, and geocryology, temperature measurernents and appropriate thermal ar mass transfer modelling.

Frost heave resulting from moisture migration and discrete ice lens growth occurs freezing, and thaw consolidation (thaw settiement) derives from ice (pore ice, ice Iens, i( body) melting. Because of phase-change heat transfer in soiIs, opposite processes alterna during the freeze-thaw cycle. If it is considered that soil fkezing is responsible for the energ and mass accumulation which result in frost heave, soii thawing is responsible for the energ and mass dissipation which leads to thaw consolidation. Except for some experimental ar observational measurements and mathematical modeiiing for phase-change temperatu problems. these studies have been mainly htedeither to freezing conditions or to thawin So far, nearly no literature has ben presented describing the whole fieeze-thaw cycle witl mathematical modeliing.

Of particular interest to the phenomena of pedostand frozen ground are the studie! of heat and mass transport and interaction of temperature, moisture and stress during solid. liquid phase change in soils. Generally, frost have and ice formation take place in freezing soils as water migrates into the frozen front hmthe unfrozen zone to form discrete ice lenses.

During thawing, on the one hand, ice melting causes infiltration of excess pore water and, often, excess melting water enveloped in fine-grained permeable soils causes settlemeni and potholes with extemai surcharge. On the other hand, melt water in the thawing layer ir drawn down into the frozen front of the frozen core to fonn ice and induce some fkost heave The important problem for palsa growth, stability or decay is to assess the relative part of ia formation and ice melting. If frost heave dominates the freeze-thaw cycle annually, then thE accumulations of energy and water are pater than the dissipation, the differences of botl- accumulation and dissipation remain in the forms of ice and soil displacement or with stress accumulâtion. The energy and mass storage are responsible for the formation of palsas anc other similar periglacial landforms. On the contrary, the main landscapes of permafrosi degradation, thennokarst and other relevant thermal settiements are the reflection of a situatior; within which energy and mass accumulation are less than the energy and mass dissipation. Because of the influence of seasonal energy-mass storage and release, soi1 components and properties, the mechanistic studies of freezing and thawing processes of soils are very compiicated.

2.1.1 FROST HEAVE IN FREEZING SOILS

When they freeze, either in unsaturated or saturated conditions, fine soils show typical structural deforrnation and water redistribution which result from the formation of pore ice and ice lenses or layers. Ice lensing under freezlng conditions is regulated by soii properties, by rate of freezing, by the availability of water and by appiied loads. Discrete ice lenses grow mainly from water which is drawn to the freezing front through the frozen fRnge from the unfrozen zone of the soil (Konrad and Morgenstern 1980, 1982; An 1987; Nixon, 1987, 1991, 1932; Ishizaki Nishio 1988; Takeda and Nakano 1990; Williams, 199 1).

Owing to the complexity of the soil freezing process, most of the studies of the phenomena of soil freezing have dealt with and fd into only one of the following classes: 1) index tests of samples to establish the degree of frost susceptibility, thaw settlement and other similar properties; 2) fundamental thedynamic analyses; 3) empiricai studies relatin quantitative laboratory investigation to field experiments; 4) mathematical modehg embracin heat and mass transport and including stress combined with observed data from eithc laboratory experiments or field measurements.

During recent decades, especiaüy the 70's. and primarily as a result of oiI exploitatio and pipeline engineering in the cold regions. especialiy in the arctic regions of Norther America, problems of moisture migration and frost heave were important research concem: Those studies can be rnainly divided into two major types of work: experimental analysis an mathematical modelling.

2.1.1.1 Experimental analysis The studies based on experirnentd freezing of soils have ken performed mostly fo observation of frost heaving, ice growth and determination of the process parameters mi relationships with the relevant factors.

Numerous important tests were performed on frost-susceptible soils. The scientifi investigation on segregated ice lenses began in the early 1900's. Taber (1929, 1930) observe{ formation of successive ice layers as a frost front moved downward when a column O saturated clay was frozen from the top down. However, the research climax pend oi permafrost and frozen ground was in the penod of 1970 and 1980's when the mechanistii studies of frost heaving were further developed. The studies involved observations of thi temperature profile, water migration rate, unfrozen water content, segregated ice, tiquid wate and ice pressure, stress and strain of soils, etc., in order to approach the relationship O relevant factors and to establish fundamentai theories (Mageau and Morgenstern 1980; Konrat and Morgenstern 1980; Kay et al 1981; Xu 1985; Penner 1986; Garand and Ladanyi 1987 Nixon, 1987, Williams, 1991).

For frost heave problems, the main purpose is to approach the mechanisrn of the wate migration and ice segregation. Tsytovitch (1 975) quoted earlier Russian studies that recognizer the concept and significance of the frozen fringe. Mageau and Morgenstem (1980) found ir their tests that the thick and warmest ice lem fom behind the frozen-unfrozen interface ir saturated freezing soils. Many researchers have made successful progress in the domain anc provided cheoretical knowledge. The Segregation Poten frai theory Based on freezing experiments under fixed temperature boundary conditions, Konrad a Morgenstern (1980) proposed one-dimensional mode1 of fiost heave, the Segregation Potent theory, temied SP. Segregation potential can be defrned as the ratio of the water intake flux I temperature gradient in the hzen fringe at any instant. It is assumed that Darcy's law a Clausius-Clapeyron equation are valid at the base of the ice lens. The water is transported the ice lens fiom the unfrozen soil through the fiozen fringe. When the rate of coolhg is clc to zero, Le., close to thermal steady state, water is always attracted to the freezing front. T driving force arrives from suction generated at the ice-hge interface, and the fringe irnped the flow to the lens because of its low permeability. Provided that the applied pressure smailer than the real "shutoff' pressure for which no water flow, feeding the growth of the i lens is possible. For a fine-grained soil, this shutoff pressure is too high to be of interest f practical applications. The Segregaiion Potentiai is given as:

V,,= SP. grad T (2. where Vif is water velocity in frozen fringe.

The Segregation Potential predicts frost heave at near steady-state conditions both und a negligible overburden pressure and under a significant overburden pressure. Wht segregation takes place at normal atmospheric pressure, such as in most laboratoi experiments, Segregation Pocential is termed as:

Under the effects of an overburden, the Segregation Potential is affected by pressure and can be termed as:

SP = ~p~e-''" (2.: where a is a constant and pe is the applied pressure (including overburden pressure).

In field conditions, SP can be approximated by the values obtained from the formation c the fmai ice lens using freezing tests with constant temperature boundary conditions. Becaus of the much deeper frost penetration in large soi1 system, the influence of the overburde becomes important, even if no additional surcharges are introduced. Discrete ice tens test

i) Penner (1986) published results of an experimental study for discrete ice let formation and hstheave in an open system.

In Penner's test, the samples were cyiinders 10 cm long and 10 cm in diameter. Tt soil sample was kept in saturated conditions; the sample was freezing from the bon01 upwards, and the temperature bounciary conditions was controlled with linear variation. Pennr measured the growth of ice lenses, frost penetration, temperature variation and frost hm under 50 kpa overburden pressure. His experiments provided a good knowledge of th discrete ice lens formation in laboratory conditions.

ii) Shizaki and Nishio (1988) and Tokeda and Nakano (1990) performed a series c freezing tests on the steady growth of ice layers under step changes in thermal boundar conditions. Their test results on the three types of soils showed that (2.1) the discret segregated ice lenses have a Iayered distribution; (2.2) the steady growth condition of discret segregated lenses is deterrnined by the absolute value of the temperature gradient of th unfrozen part of the soil and by that of the frozen part of the soil under a given hydrauli condition; (2.3) the frost heat rate is in direct proportion with the water intake rate.

It has been concluded that moisture migration and formation of segregated ice lenses i freezing soils result from the application of a temperature gradient.

2.1.1.2 Mathematical mode1 studies Since the 19703, theoretical mechanistic studies of frost heave in freezing soils hav made great progresses mainly for the purpose of engineering applications. An abundar literature on mathematicai modehg of freezing soils was published. Up to now, these mode1 principally focus on theoreticai analyses, semi-empiricai approaches. numerical simulations an' predictions of frost heave in association with i) phase-change heat transfers; ii) coupled he and mass transfers in saturated and unsaturated soils; iii) the segregation potential approact SP, in saturated soils; iv) discrete ice lens growth in saturated soils; and v) stress-strai relations in freezing and frozen soils.

Modelling of the heat and mass transport in freezing soils

In the beginning of the Mid-1970's. arnong the fmt authors to present mathematicé rnodels simulation of coupled heat and moisture transport in freezing soils were Harlan ( 1974 and Guymon and Luthin (1974). Assuming the ice formation at atmospheric pressure and th soil at zero loading, Sheppard et al. (1978) used the Clapeyron equation for the solution of water pressures in frozen soils. A frost heave model for unidirectional freezing in a moist silt with water table was proposed by Guymon et al. (198 1). Nearly aü these models work are unidimensional.

Loch (1979) stressed that the Clapeyron equation was developed based on the static and steady thermodynamic equilibrium, and therefore it wiii result in some deviation if it is employed in transient problem. To the contrary, Kay and Perfect (1988) indicated that even if the Clapeyron equation was developed from the thermodynamic equilibrium, if the surcharge is not too large and there is no restriction to water flow, that equation is valid for the caiculation under the transient condition at atmospheric pressure. But in reaiity the soîl is under flow restriction and overloaded, the stress distribution between soil particles, ice and pore water should be determined and the calcuiating results obtained in the transient situation are affected by the effective thermal conductivity.

With measured air and soi1 surface temperatures as input data, Guymon et al. (1983) employed and reviewed the modelling of the heat and mass transfer to simulate one- dimensional frost and thaw penetrations of the field. The computed frost heave and thaw consolidation agreed weII with ground surface displacement induced from ice segregation and ice lens melting, respectively. He suggested that 1) this niode1 can reasonably estimate field frost heave, provided accurate data on boundary conditions and parameters are available; 2) any complete model of frost heave should require calibration to determine the hydraulic conductivity and account for changes of this and other key parameters due to freeze/thaw cycles. Cary (1987) proposed a model for calculation of frost heave while taking account of solute effects. Neither this model, not any other currently available attempts include the influence of alternate freezing and thawing.

A two-dimensionai problem of moisture rigration and frost heave of saturated freezing drainage canal foundations in naturai conditions was numericdy solved by An et al. (1987). It was found that thick ice Iens forms behind the frozen fringe as the frost front advances to a quasi-steady state and finally reaches a maximum. Additionally, one dimensional moisture migration and fiost heave in an unsaturated freezing canal foundation was simulated by Yie and An (1989) and a similar trend of moisture accumulation were obtained.

In these numencal simulations and predictions, the major diff~cultyis the estimation of hydraulic conductivity at the freezing front in the mass equation. Alttiough an amount of literature has presented data on experimental measurement of hydraulic conductivity of frozen soils, especially in the frozen fringe, there is some dispute on the rneasurement precision of tI coefficient in practicai usage, because it appears to be much sensitive to the caiculated result Apparently, it is necessary to carry further experimental measurements of hydraui conductivity with careful sample preparation and replicate testing in order to get more accurai values (Konrad, 1984).

Williams (1991) fuaher stressed chat large quantities of water that rernain unfrozen i frozen soils sbould be taken into consideration. In even simple themial calculations, whei accurate values of thermal properties are required, the amount of umfkozen water as a functia of temperature rnust be assessed. Actually, the fact is chat fomlation of the them parameters from the experiments for the calculatior~sand maintenance of acceptable accurac are very important for the application of the thermal parameters.

The Segregation Potential method With the Segregation Potential method (SP), Konrad and Morgenstern predicted th frost heave near steady-state conditions in laboratory tests. The predicted results fit well wit the test results in experimental conditions. SP is a semiempkical approach (Nixon 199 1) an the SP parameter involves thermal parameters and further considers the effects of th overburden Ioading in soil systems. With the SP. comparison of prediction of water intak using constant parameters, normal atrnospheric pressure, with actual data, the simulation doe not mode1 the actual shape of the curves in a satisfactory manner, especiaiiy the beginnin period of the elapsed time (test NS-4); the predicted totai heave is relatively close to th rneasured vaiue (about 15% smaller) (Konrad 1982). For long-term problems, this accuracy c computation should be av;iil;ible. On the other hand. when comparing the SP parameter wit hydrauiic conductivtty in coupled heat and mass uansfer applications, the former is les sensitive and much easier to deterrnine.

Either rnodels of the coupled heat and moisnue transfer or the SP method can simuiat, and predict the frost heave. water migration, and the final ice lens growth, as the fros penetration reaches the quasi-steady or steady-state, but these mcthods can't sirnulate th, distribution and Iocation of discrete ice lenses in freezing soils.

The modelling of the discrete ice lensing and frosr heave Some researchers are more interested in studying the frost heave in association with thi location and magnitude of discrete ice lenses, and have presented relevant rnathematica models. Milier (1973, 1978) proposed the theory of "secondary frost heave" to explain how frozen zone of soil behind the freezing front affects fiost heave behavior in soils. In his theory Miller suggested that the suction responsibIe for frost heave is developed withul the hzl fringe of soil behind the 0°C isotherm, and he fomulated a mathematical model to describe t coupling of various water transport mechanism. But this theory remains untested.

Gilpin (1980) developed a mathematicai model of ice lens formation and frost heave saturated, granular, air-free and solute-fke soil conditions, based on the equations develop from the fundamental considerations of heat conduction, Darcy's law and thermodynam equilibrium. His model is supported by lahratory investigations. Many variables whii include temperature, water influx, ice, water and Ioad pressures, thickness and variation of tl frozen f~nge,frost heave, etc. are involved in Gilpin's modelling, with which the frost heti and discrete ice lensing could be computed using the temperature gradient of the unfrozen zor In the model, the simulated water infIux at the beginning of the freezing trends to zero, whii is a rather Iarge deviation. Therefore, in this rnodel, the proper estimation of the initiai value the special arguments are quite important for the prediction,

With the sirnilar assumption of a straight hear temperature profiles in the frozen zoi and a constant thermal conductivity as Gilpin (1980), Nixon (1991) extended and modified ; approximate analytical technique of Gilpin (1980) and accounted for the effects of distribu phase change within the freezing f~gein both the heat and mas-transfer components of tl formulation. Assuming that independent measurements of the hydraulic conductivity of frozc soils can be made, then the model can be used for more fundamental understanding of tl physics of frost heave. Comparison of the numerical results with the test data of Konrac experirnents showed a good agreement. Hereafter, based on the similar assumptions ar fundamentai theory, Nixon (1992) furthes presented a two-dimensional modelling ar: caiculated the axis-syrnrnetry problems for a chilled pipeline. Both Gilpin's (1980) Nixon's (1991, 1992) models employing the numencal iteration method are applicable fi predictions of one-dimensionai and axis-symmetry discrete ice lens formation and frost hea~ within the homogeneous freezing soil. Owing to the assumptions of a straight line temperature profiles both in homogeneous frozen and unfrozen zones of the soil system ar constant thermai conductivities, this model is preferentially applicable for the prediction of one layered homogeneous freezing soils; ii) with the relatively stable temperature bounda: conditions and no large ciifference of the upper and lower boundary conditions, especiaily 5 the temperature timedependent boundaries.

Cornparing with the Gilpin's and Nixon's models, the one-dimensional rigid ice mod proposed by O'Neill and Miller (1985) seems to be more complicated. Perhaps this model more preferabIe for theoreticai exploration than for practical application because it consists of series of nonlinear partial differential equations which describe the temperature, movement a the ice, water, and soi1 particles, stress-stain relation in the fiozen soils. Even if a computatio: sample was given in O'Neill and Miiler's paper, the mode1 is nearly unusable to solve long term practical problems.

2.1.1.3 Analysis of field conditions The studies on frost heave, rnoisture migration and thaw consolidation in the fielc coupled witb numencal analysis, are done mostly for engineering predictions (Johnson et a, 1963; Nixon 1982; Ladanyi and Lemaire 1984; Smith 1984, 1985; Smith and Patterson 1989: As for palsas, most studies untii now have been performed by geophysical methods such a ground probing radar and thermal measurernents at field sites (Arcone et al 1982; AIlard et ai 1988). Many other studies on palsas focus on geomorphologic and stratigraphie description5 pollen analysis of peat, isotopic analysis of water from the segregated ice and radiocarbol dating (French 1976; Dever et al. 1984; Allard and Seguin 1986; Seguin et al. 1989) Modeiiing of ice lens formation and heave was not yet applied to palsa formation.

In the field, frost penetration rates and actual temperature gradients in the frozen zonc near the frost front are smdl. It is suggesced that SP (field) may be approximated by the SI obtained from the formation of the final ice lens using freezing tests in laboratory with constan temperature boundary conditions. The influence of overburden pressure becomes important ii palsas and cannot be negiected. The prediction using constant thermal parameters with the SI showed deviation in the experimental condition in short-term period; however, for the cases O long-term, large amplitude of annual temperature and srnall cooling rate in field, the infiuenci of this deviation employing theoretical mathematical modelling should be considered.

Up to date, most of the studies reported seem to focus on the short-term behavior O frozen ground and permafrost in one dimensional problerns and are performed under Iaboratoq conditions because of Iimitations of the periods of experirnental cycles and various conditioni which can be set and controiied.

Even though models of the basic processes of frost heave and ice segregation whicl dorninates the origin of palsas have made considerable progress in engineering, there an alrnost no report in the Literature of their application to geomorphological problerns in natura permafrost environment. This is probably due to the fact that the temperature, moisture an( pressure interactions involved in the freezing and thawing are more intricately linked in nahm conditions than under controlied laboratory and engineering conditions. The time periot involved is also longer. Another important reason is that although many frost heave and thav consolidation models have been presented, the mechanisrns of ice iens growth, frost heave anc thaw sedement stili remin knotty subjects. Accurate data acquisition on temperature, rnoism and pressure in the field to obtain mode1 parameters and conditions is also difficult to achieve.

Viskanta (1991) suggested that the existing models of ice Iens growth are considered tc be rather compIex (Gilpb 1980; O'Neill and Miller 1985). and neither the hydrodynamic, th€ rigid ice nor the secondary have models can be applied in the fieid because of the high level O: information requirements and the natural vanability in soils. There are complicating factors anc difficulties for the soh.ion of the mathematical problem. Very few studies have been reportec for rhe prediction and simulation of layered ice lens growth and frost heave in nature.

inversely, using mathematical modelhg combined with observed data both from fielc and laboratory, simulation of palsa growth and dynamics is of great significance not only foi understanding the processes of palsa formation and other sirnilar periglacial landforms, but alsc as a feedback for numerous geotechnological and geophysical applications. To be significant such modehg needs to be done in one and two-dimensions and to encornpass recurring freezing and thawing cycles. Therefore, some compiicated but also interesting and original modeliing work is also required.

2.1.2 THAW CONSOLIDATION Thawing of the permafrost and frozen ground with subsequent surface subsidence under both the periglacial geomorphic landforms and coId regions engineering constructions are an important aspect of permafrost related problems. Compared to the iiterature on frosi heave, the studies on the thawing in frozen soils are less abundant, due to the fart that, perhaps, the rate and extent of degradation are less important considerations in geotechnical engineering. Because predictive ability of mathematical modemg is based on identification and qualification of the significantly physical phenomena, the problems of thawing in frozen soiis can be further divided into the problem of thaw consolidation in saturated and in unsaturated soils, and the problem of melting of the ground ice layeribody. The problems of the thaw consolidation in thawing are rather complicated and mainly dependent upon the soil type, thaw rate. saturation, ice content and distribution, bulk density, porosity, ioading pressure, drainage and time. Severai researchers have made much effort both on the experimental approach in laboratory and in the field, and on the establishment of mathematicai models and nurnericai computations of thaw consolidation. 2.1.2.1 Experimental analysis of moisture migration in thawing soils

It is noticed that an interesthg and important phenomenon is the moisture migration i thawing soils. Moisture migration accurs not only in freezing soils but also in thawing soil During thawing, rnoisture is also drawn hmthe thawed zone to the hzen zone due to therm; gradient and suction. But the process is complicated for two rasons: i) thawing rate is greau than the cooling rate, that is, the rate of solid to liquid phase-change is greater than the rate c the liquid phase-change in transient processes, and ii) the arnount of thawconsolidation : greater than the amount of frost heave. the frost heave king swdlowed by the thal consolidation. Thaw consolidation changes the soi1 structure. However, moisture rnigratio during thawing finally enriches ice lenses beneath the upper table of permafrost, increasin ground ice a Iittle. In the long-term, in a cold environment, this phenomenon is significant fc the formation of thick ice lenses and an ice rich layer near permafrost table. This was observe from experimentai tests (Cheng 1983; Cheng and Chamberlain 1988; Harris 1988), and Va Vliet-Lanoï ( 199 1 ), but so far almost no iiterature has ben presented that makes numerici simulation and prediction of moisture migration in tfiawing conditions.

2.1.2.2 Mathematical studies of thaw consolidation in thawing soil

The first studies of this subject were attempted by Tsytovich and CO-workers ( 196( 1966). They concluded that thaw consolidation resulted from the abrupt change in void rati that occurs during thawing of the soil ice; and gradudy resulted in consolidationlsettlemen Consolidation is: i) approximately equal to the thickness of ice inclusions; ii) proportional t depth of thawing, iii) independent of external Ioad, and iv) occurs at a rate proportionai to th square root of time. Frorn a sirnplistic and practical point of view, the one dimensional mode1 were approached also later by Zaretskii (1968) and by Brown and Johnston (1970).

Nixon and Morgenstern (1 97 3) proposed a mode1 for the prediction of thaw settIemer in saturated frozen soils. In their modei, they fmt suggested a moving boundary to treat th thaw plane where the thaw line is assumed to move proportionaliy to the square root of timc employing the simple Stefan formuIa, to caiculate the temperature profde and thaw penetratior thus, the rate of movement of the thaw front controls the rate of liberation of excess pore fluic They aiso used the Terzaghi equation for hear consolidation to govern the dissipation of th resulting pore fluids, and obtained the excess pore pressure distribution in the thawed zone, b~ no flux of drainage water and amount of thaw seniement were reported. In addition, the further introduced the nonlinear compressibility relation into the theory. Because of th limitation of the Stefan formula, this model applies only to one-dimensiond problems. Also, dc~snot apply for the numerical simuIation of the thaw-consolidation of ice-riched soils.

Nixon and Morgenstern (1973) have also proposed the thaw analysis of a compressib soil with discrete ice [ayers. Assuming that the straias in the soi1 skeleton associatecl with ar increase in excess pore water pressure [caused by the extra influx of water into soil) are smi (then the distance between soil surface and thaw plane becornes constant) they numericai solved the problem of a thawing ice layer beneath the thaw plane of soils. From these theor ticd and numericai analysis, they conchded that for a slow rate of thawing, the presence of ; ice Iayer at 1 m depth does not produce pore pressure in the soil that deteriorate simcant with time. In fact, if an ice layer were presented at a depth of 3 m under these thawir conditions, the pore pressure at the soil-ice interface actually diminishes siïghtly with tirne; the result aiso suggested that although the settlement is obviously considerable, the pore pressui condition in the soii above a thawing ice layer may not be as critical as hitherto supposed.

For the anaiysis of a heated oil pipeline buried in permafrost and the andysis of foui dations on permafrost, Sykes et al. (1974) solved 2-D problems by the finite element rnethc to determine the effects of settlement, the significance of variable geomeuy and force convection rather than heat conduction only as done previousiy. Guymon et al. (198: obtained a numerical solution of the model and made cornparisons with experimental vduf from CRREL.

If the models mentioned above for thaw consolidation lay particular stress on tk practical engineering application, the other models of thaw consolidation discussed below pa attention co the nonlinear theoretical approaches to the fundamental mechanisms of thauring i saturated and unsaturated frozen soils. Sykes and Lennox (1976) presented a model whic further considered a nonIinear stress-strain relation for thawing permafrost.

Bear and Corapcioglu (1981) developed a mathematical model for fluid pressurc temperature, and load subsidence due to temperature and pressure changes in a saturate porous medium. The model similady includes the energy balance equation and the equilibriur equation and applies the conservation of mass equation to the unfrozen water, the melting icc and the defonning porous medium for the entire system. The effects of viscous dissipation an compressible work have been comprised in the formuIation of the model which consists of series of the nonlinex ppartiai differentid equations. Later, Corapcioglu and Panday (1983) developed another model describing thai consolidation in an unsaturated and partiaüy frozen porous medium. This model is mol complex than that in the saturated soi1 conditions. Besides the simiIar principles of tb governing equations in saturated soils, this model further involves the infiuence of saturatio and wiii be capable of simulating pressure, saturation, temperature, ice content an displacements in permafrost thaw consoli&tion problems.

Because of the complexity of those nonlinear mathematicai equations and difficulties c numerical computations, even in the short-term problems, so far there have ken nearfy no us employment of these theoretical models for the purpose of application with nurneric; simulation and prediction in practice except an example, which was a more detailed treatment c the subject of unsaturated and partiaily frozen soils, given by Corapcioglu and Panday (1988).

Obviously, mathematical modelling of thaw in frozen soiIs was used p~cipdiyeithe for the numencal predictions in practicai engineering problems or for the theoreticd studies CI the mathematical models themselves. In the field, the distribution of ice layers is rathe different from that in the laboratory.

Actually, for the multi-layered structures of ice lenses in soils beneath the upper table O the permafrost in the palsas, thaw modelling will be a complicated problem. On the one hand from the characteristics of originaily consolidated soils and a reiatively thin active layer in th palsas, the influence of thaw-consolidation in the active layer on the paisa formation anc dynamics is very lirnited and not much significant when the clirnate and geological environmen are relatively stable. On the other hand, because of the history and dynamics of the palsas, it i impossible to use the pure theoretically mathematical model, such as CorapciogIu and Panday' model (1983, 1988) to study the palsas even for one-dimensional problems.

In the light of the previous and present works and reference of the literature on thawinl of permafrost, An et al. (1989) simplified and developed a thaw consolidation mode1 ii saturated partially frozen soils. In this model, the moisnire migration from the thawed zone intc the frozen zone is also considered during thawing because the inversion of the thermal gradien (the frozen core of paisas beneath the thawed zone in permafrost is colder than the uppe thawed zone) promotes heat and melting water transfer into the fiozen substratum. Otherwise this model avoids employing the Stefan formulation and cm numencaiiy compute the two dimensional problems. Of course, this is also relatively difficult to apply for the long-term ant two-dimensional problems. Obviously, the existing studies on thaw consolidation of the fiozen soils have bee concentrated principaiiy either on numericai analysis and predictions for cold region engineering problerns or for theoretka1 approach of nonlinear mathematical models.

2.2 PERMAFROST AGGRADATION VS FORMATION OF PALSAS

The effects of fieeze-thaw cycles on fiost heave and thaw consolidation in pdsas ar dependent of soii properties, clunate and other external and internai conditions of the heai mass and pressure reIated to the pdsas. Freezing, water migration and ice segregation emic the ice content and provoke frost have to result in palsa growth. In turn, thawing, wate outfiltration and consolidation cause paisa settlement. Because the soiis in palsas are originali: undisturbed, and because of the short thawing season in cold regions, the consolidation effec in palsa dynamics is rnuch less than that of frost heave and limited to the active layer.

Based on the background research of the related subjects and present state, oi quantitative studies of paisas in nature, accurate prediction of detailed distribution, variatio~ and complicated shapes of each ice lem, the accurate prediction of location, the magnitude O each differentiy shaped ice lens in a palsa has to be questioned. Simulation must necessarily tu concordant with the current reseârch state in laboratory tests and mathematical rnodeliing. Bu even after simplifications, mathematicai modelling for the nurnencal simulation and predictioi to approach pdsas remains a powerful research tool for the understanding of the inheren processes of palsa formation and variation.

2.3 SUMMARY

The purpose of this chapter was eo provide a brief introduction and review of the mos important developrnents that wcurred during recent decades in the mechanistic studies of fros heave, thaw settlement, heat and mass transfers in freezing and thawing soils which potentiail~ apply to palsas.

These mechanistic studies mainly involve: i) the proposed hypotheses for the origin o. palsas and effects of the major limiting factors on the palsa formation fiom observations anc investigations in the field; ii) the models of frost heave, discrete ice lensing and thau consolidation developed from experimental and mathematical approaches. So far, most of thest rnodels have been applied successfuiiy and are available for the description of hzen soils ir laboratory and engineering conditions. Their application to the formation of palsas and sMai cryogenic mounds under long-term recming fkeze-thaw cycles is new and it has the potenti to make a significant contribution to the dornain of Quatemary geology and periglaci geomorphology . Chapter III

QUATERNARY GEOLOGY, PERMAFROST AND PALSAS IN NORTHERN QUEBEC: A BREF REVIEW

3.1 INTRODUCTION

Palsas, cryogenic mounds and other perigiaciai features in the subarctic regions art related to the various Quatemary suficiai formations and geomorphology. The distributior and the characteristics of pdsas are closely linked to locd geological and climatic conditions and to vegetation cover. These factors have a large influence on the geothermd regime and thr thickness of the permafrost. According to stratigraphie analysis of severai paisas, the age anc the evolution of the permafrost are conditioned by the Quatemary geology of the sites

Permafrost in subarctic regions can be as old as deglaciation in regions which were never forest covered; however, it is probably of XeogIacial age elsewhere (Nard and Seguin. 1987).

Owing to the relationship between paisas, permafrost and Quaternary geology, a review of previous srudies of Quaternary geology history and permafrost development in Nunavik is important for mechanistic studies of pdsa formation. Particularly, the Holocene paieoclimatic context provides elements of thermal history that must be input into models.

3.2 QUATEXNARY GEOLOGY AND PERMAFROST CONDITIONS

It is found that permafrost is tightly related with Quaternary sedirnents and subarctic cii- mate conditions, principally those which prevailed after the deglaciation. Deglaciation of the re- gion started by about 10,000 years BP dong the Hudson Strait coast (Lauriol and Gray 1987; Fulton 1989) and the whole Quebec-Labrador peninsda was ice-free by 6500 BP (Dyke and Prest, 1987). However many radiocarbon dates on sheiis coiiected in raised glacio-marint sedirnents in fjords dong that coast indicate that the ice rnargin lingered close-by inland until a least 7000 B.P. before receeding inland over the continent. As the Laurentide Ice Sheet wz breached over Hudson Bay and replaced by the sea, deglaciation started in the James Bay am Kuujjuaraapik areas by 8000 B.P. (Vincent et al. 1987: Hilaire-Marcel 1976). The coastal re gion between Ivujivik and Inukjuak dong the northern sector of Hudson Bay was deglaciatec between 7700 and 6700 B.P. (Lauriol and Gray 1987), and the coastal area around Ungavs Bay was freed of glacier ice around 7300-7200 B.P. (Allard et al. 1989). By about 7000 B.P. the Labrador dome of the Laurentide Ice Sheet was within the actual lirnits of the Quebec. Labrador peninsula and was rnelting fast (Dyke and Prest 1987). As estirnated by basai dates on lake sedirnent cores, it had finaliy vanished by 6600 B.P. in the Schefferville region (Suavers 1981). in the Caniapiskau lake ma in the center of the Quebec-Labrador peninsula (Richard et al. 1982) and by at least 5300 B.P. in the Ungava peninsula (Lauriol and Gray 1983). These dates must correspond broadly to the probable beginning of permafrosi aggradation in the region as new temtory was gradualiy uncovered from glacier ice and exposed to climate.

Afier the glacial epoch, ice in the region finally disintegrated, the isostaticaily depressed regions around the peninsula were floooed by glacial lakes and invaded by the sea. These events changed the entire coastal regions into a marine environment and the marine limit varies from 280 m in the southeast of Hudson Bay to 100 m on the east coast of Ungava Bay. This entire coastai region was submerged and marine sediments, silts and clays, generally massive, were deposited offshore in the seas, whereas varved clays were laid down in several glacial lakes. After 6500 years BP, these areas experienced uplift from D'Iberville and Tyrreii Seas. As the isostatic uplift and associated sea regression occurred, the sea bed emerged.

Ln the region, bedrock (mostly granitic) outcrops over a very large portion of the land surface. Above the marine lunit, till is the dominant surficiai deposit. The texture, structure, composition, and morphology of the till are variable. Generaliy, denved frorn metarnorphic and igneous rocks, tiiis in the area consist generaiiy of sandy, gravely, and bouldery materiais and are noncalcareous. In regions of ground moraine or fluted ground moraine, till is massive, and found mainly in interfluve areas and in various types of landforms such as Roggen and De Geer rnoraines,and in vast dnirnlin fields. Glaciofluvial sediments are also abundant in the form of sandurs and eskers. A characteristic feature of the eskers is that they commonly cross the grain of the landscape, ascending and descending hilis and ridges. Where the ice retreated in contact with water bodies, eskers consist of subaqueous outwash deposits and may be buried by thick sequences of fine grained sediments. Owing to extensive flooding of coastai areas by the sea during deglaciation. fossiliferous silts and clays, generally massive, were deposited offshore, whereas varved siits and clays were laid down in giacial lakes. Thick, fme, clayey and siity sediments extend in valley bottoms that were formerly marine bains. As the seas or lakes regressed or were drained, near shore facies were produced in places where waves and currents could rework glacial deposits. Around Ungava Bay, large tidal ranges during the postglacial marine episode were responsible for strong currents and wide intertidal zones; this resulted in a variety of sedirnentary facies including intertidal bouldery muds now fonnuig diamictic soils with a fine matrix, sand veneers over deep deposited clays and raised bouider flats. In some regions, the cover of marine sediments is either sparse or consists of a veneer a few meter thick. Today rivers are reworking older, mainiy glacial and marine sedirnents and are depositing materiais on their floodplains and deltas in Iakes and seas (Fulton 1989, Aiiard et al., 1993).

Organic deposits have accumulated on poorly drained glacial and marine plains, Iow relief till areas, and in depressions on bedrock surfaces. The peat cover is widespread in the area. Peat accumulation include a range of biogeomorphic features; the main physical requirement for the establishment of peatlands under northem Quebec climatic regimes is abundant moisture. This cm be satisfied by a rainy clirnate such as that of the east sea coasts and by the poor drainage condition such as bogs, fens, swamps and marshes, and high water tables.

According to the National Wetlmds Working Group (1988) (Fulton 19891, there is a belt of wetlands about 500 km wide stretching from James Bay to the Labrador Coast. The organic sediments that accumulated in wetlands cover more than 50% of its surface. Because clirnate varies from north to south, the type of wetland in which organic deposits accumulates also varies from north to south. At the southem fringe of the Canadian Shield, wetlands are dorninantly domed raised bogs and ladder fens. Farther nonh, organic deposits are being laid down in domed, flat, basin and string bogs and ribbed fens dorninate. In the northern part of the area, peat plateau and pattemeci fens give way to wetlands characterized by low and high centered polygons containing ice wedges and lenses and underlain by permafrost. Palsas are cornmon in coastal and northern bogs and thennokarst depressions are IocaHy cornmon in fens and bogs underlain by fine sediments (Fulton 1989).

3.3 PERMAFROST CHARACTERISTICS

Permafrost formation and aggradation kept step with the emergence on the f~gesof Nunavik Peninsula. As pst-g1acia.i uplife took place graduaily during the Holocene, the exposure of emerging terrain was in a cold atmosphere, and permafrost progressively invaded the newIy emerged land, a process stiii taking place at present dong the coastal areas. Altbough the chnate above the actual tree line was certainIy cold enough to generate permafrost shortiy after deglaciation, many Holocene climatic reconshuctions suggest that permafrost was less abundant during the Hypsithemal and expanded during the Neoglaciai period starting about 3000 B.P. (Ailard and Seguin, 1987b).

Since the permafrost maps of Northem Quebec by Brown (1979) and Ives (1979). extensive new research has been canied out in the regions by the recovery of hzen cores from driuings, hstaliing therrnistor cables, and geophysical methods: vertical and bi-dimensional elecmcal resistivity; induced polarkation profiling in the dipiedipole configuration and ground probing radar profiling. The new regional knowledge on permafrost distribution and charactenstics has ken further discussed (Mard and Seguin 1987a; Dionne 1983; Aliard et al., 1993). Recently, it has ken found by the identification on air photographs that the continuous permafrost zone extends much further southward than previously mapped dong the Hudson Bay Coast south of Inukjuak and southwest of Ungava Bay, between Tasiujaq and Kuujjuaq. The southern limit of the continuous permafrost zone is quite close the forest line.

The arnount and type of ground ice in permaf?ost were found to be closely reiated to the type of Quaternary sediments. In the southern part of the widespread discontinuous permafrost region, tundra polygons are the most widespread perigiacial features over the couse-grained materiais; frost boiis are also abundant over u1l and other diarnicts, and they often pit the interior of the polygons (Jetchick and Mard 1990). In the continuous permafrost region, ice wedge polygons are found on flat terraces where often rnost frost cracks and polygons are still in developrnent. Pore ice dominates in sandy and gravely materiais either of glacial, glaciofluviai, fluvial or beach origin. As the fine sediments are prone to ice segregation, these geological variations lead to numerous lateral and stratigraphie changes in cryofacies. Ice lenses and thick ice layers or massive icy beds are mainly distributed in fine-grained materials, particularly silt and cIay which accumulated in the vailey bottoms and lowiands. Usually, ice nch layers are found from the permafrost table down to 3-4 meters, volumeûic contents varying frorn 50 to 80% (Aliard et al. 1988). More recently, it was aiso found that ice rich layers may also be present at the base of the permafrost with saturated water supply in the discontinuous permafmst zone (Fortier et al. 1991).

In the discontinuous region, maximum thickness of permafrost in both tills under drumlins and silty clays under cryogenic rnounds reaches between 15 and 30 m (Lévesque et al. 1988; Fortier et al., 1991), in bedrock with snow free and windswept surfaces, it reaches 120 m in Schefferville (Thom, 1969) to 180 m depth near Kuujjuaraapik (Poitevin and Gray 1982). In the continuous region pemiafrost depth cari reach over 500 m (Seguin, 1978; Taylo and Judge, 1979).

3.4 REFERENCE AREA AND PALSAS

3.4.1 CHARACTERISTICS OF GEOLOGY

The site of Kangiqsuaiujuaq (65*57'W,58"401N) in Nunavik (the Inuit territory O Northern Quebec) has climatic and geologicai conditions typical of the palsa region of easten Canada (Figure 3.1). It lies at the northern bit of the discontinuous permafrost zone. Thc present-day subarctic chnate of the region is characterized by long winters, short summers and by a mean annual temperature of -5.8'C. The mean annual total precipitation is about 40( mm, of which about 42% falls in the fom of snow (Wilson, 197 1). Due to wind-dnfting snow cover is very uneven, varying from Wluaiiy nothing on wind-swept sites to over 2 n around topographic obstacles. The local cove of George River and the lake near the palsas an ice-covered for a very long period; freezeup and breakup generaiIy occw in early Novembe and Iate June respectively (Québec,1984). The maximum depth of annuai thaw varies gen' depending on the thickness of organic cover, soi1 type and variation of the thawing index. Thr active layer ranges from 30 to 80 cm on the peat plateau, whiie the permafrost thickness varie! between 3.5 and 22 m.

A cornplex of peat plateaus and palsas was used as a terrain reference for the modellini exercise (Figure 3.2A). Located in a topographic basin by a lake at an elevation of 36 m a.s.1. the site emerged about 6000 years ago frorn the d'Iberville Sea which inundated the landscap up to the present-day elevation of about 100 rn (Altard et al. 1989). A Iake larger than th€ present one then occupied the site. Starting around 4500-4300 years BP, peat covered part O: the original lake and started to grow. Radiocarbon dates from samples at the stratigraphie contact between hydrophytic and xerophytic vegetation in the peat cover on the palsas indicab that heave of the fen surface, and thenceforth permafrost aggradation, fmt took place arounc 1800- 1600 BP and wastiIl active in some sectors of the peat pIateau around 800 BP (Gahé e, al. 1987). UNGAVA

BAY

Figure 3.1. Location of Kangiqsualujjuaq reference site. Figure 3.2: (A)The palsa phieüii idpdsn cornplcx nçai- K~ingiqsii;iIr1j~ji1:1~1.in Jiinc 1992 during snowmelt. Airow points to the flac ill-c;i wlicrc the ternial pr-ofilc OF Fig~1i.c5. IA cornes from. The other thernial profiles are froin Iiuniiiiocky relief closci. to ilic plii~[iigr;iplici'spoint of vicv. (Bi Segrtytion icc lrnm the p;ils;i corerl. 1.1 rn lrclow rlic srr;itigr:ipliic pc;li/silt ContaCr. The region of Kangiqsualufiuaq lies within the shmb subzone of the forest-tundra zor This transitionai zone extends between the forest-tundra and the tundra, and is dominated by shnibby vegetation composed p~cipallyof dwarf birch, coniferous trees, and shmb thicb of willows in depressions and on slopes. Lichens dominantly cover the extensive patches tundra terrain (Us,plains. terraces and peat plateaus).

The vdey, 2 km hmthe village, contains a lake that drains to the south. It forms basin where meltwater from snow cover and precipitations can flow and saturate the mari sediments entrapped in the valiey bottom. The flat bottom is poorly drained and is coven with shnibs, spruces and tamarack that grow on the wetland. Sphagnum Fat and fen pe occupy the valley bottom around the lake. The peat plateaus and palsas raising above th wetland level bear a cover dominated by lichens.

A simplified stratigraphy down to the depth of 24 m at the main study site consists three major units:

Unit 1, Peat: The peat layer is relatively thin. On the palsa cornplex, it varies in thickness fro a few centimeters where it has been eroded to over 2.5 rn in hollows where slumping of pe blocks from surrounding slopes occurred. In generai. the peat cover is about 90 cm thic where it has not slided or slurnped and where there is no evidence of surface erosion.

Unir 2, Boulder pavement: Between the peat and the underlying clayey silts. dispersed ii rafted boulders iie at the stratigraphie contact (Allard et al. 1988, 1989), fodng a nez continuous pavement.

Unir 3, Minerai soils: The stratified layers of minera1 sediments underlying the peat consists i saturated clayey silts deposited in a sea basin. They reach a maximum rneasured thickness ( about 24 m at the field site. The permafrost core of the palsas consist of aiternating layers ( ice and silty clays.

Below the deep marine sediments one expects to find some glacial drift, probably til and then, bedrock.

3.4.2 OCCURRENCE AND DISTRIBUTION OF PALSAS

Shce Fries and Bergstrom (1910) fmt investigated the palsas in Scandinavia, near one century ago, many researchers have agreed that segregated ice in the frozen core of pals; is fed by suction of unfmzen water to the freeung front in aggradating permafrost. Palsas ai often geneticaiiy and spatiaiiy associated with peat plateaus (SW 1972; Schunke 1973 Washburn 1983a) and a thin or absent snow cover. The investigation of Quaternary geolog and periglacial geomorphology have focused maïniy on the causes and the conditions of pals evolution, variation. distribution.

In Nunavik (northem Quebec) palsas occur commody in mires, bogs, or lowlanc tundra areas. kwas found that palsas cm take the shape of plateaus, ridges, strings anc mounds, among which the type and the size are more or less related the soil materiais, drainag~ and topography. Size varies from 10 rn' to over 10 000 m2,and shapes vary hmcircular O elliptic rnounds having a diarneter of a few meters to vast piateaus, whereas heights generalk are from 1.O to 5.0 m (Allard et al. 1986; Fulton 1989).

in the reference site ail the palsas have mineral cores (Seguin and Mard 1984; Mard e al. 1986). as observed elsewhere by han,(1976), Seppala (1983a), and others. Generally covered by the relatively thin peat layer, post-glad marine silts are the dominant materials i~ which segregated ice developed. Owing to strong winds and snow drifting, a thin and unever snow cover is a characteristic feature of the forest-tundra in winter. The thermal equilibrium u these landforms is controiled by surface vegetation height and density, by peat and by snov distribution. Should the soil surface be exposed, the wind sweep the snow away. Th{ exposure of the palsa surnmit will annihilate the insulating effect of the snow cover. However snow generally accumulates dong the sides and at the foot of the palsa mounds. Thereby thc insulation effect is locaily present, and the laterai expansion of a paisa is thus restricted. Thi! explains why these growing mounds have ,pdually steep dopes (Payette et al. 1975; Allarc et al. 1986).

3.5 MAJOR LIMITING FACTORS OF PALSAS

3.5.1 CLIMATIC CONDITIONS

The cold climatic conditions are the most basic extemai thermal conditions for pals; formation and existence. Cold temperature in winter results in so deep frost penetration that i can keep a remainder of permafrost core during the following surnmer and then the remaindei wiil grow till reaching a new thermal equilibrium.

Even though the -1'C mean annual temperature isotherm has been suggested as thi extreme upper temperature lirnit for palsa formation (han1977), actuaiiy in different region! it is quite different due to the effects of letitude, altitude, atmospheric currents and loca microclimatic and precipitation conditions, etc (Dionne 1984). For instance, the -1°C me; annual air temperature isothem and an annuai precipitation beIow 400 mm are requirernents fi the southern iimït of the palsa region in FishLapland (Salmi 1970). The zone of tempe& beIow -10'C for 120 days (Lundqvist 1951). and a mmannual temperature of -2°C to -3' are mentionned for the general distribution of palsas in Sweden (Lundqvist 1962). SimiIi observations have been made in northem Norway (&man 1977). In Northern Québec, tf observations have shown ttiat the mean soii surface temperatures is approximately -4.5"C i Kuujjuarapik, about -41°C in Kangiqsualujjuaq, -5.8-C near Nastapoca river and betwee -2.O0C and -5.0°C near Manitounuk Strait. Those vaiues are very close to recorded mean a temperature and refiect the fact that the summit of palsas and cryogenic mounds are snow fre in winter (Allard er al. 1987).

3.5.2 PEAT PROPERTIES

In the climatic conditions of the Subarctic tundra, the surface energy exchanges ofie bdance on marginal values. Sm& changes in thermal properties or in transfers thus have larger effect on a tundra surface than similar changes have in middle latitude climates.

Peat cover is a major factor impacting surface energy exchange. The physicd propertie and thickness generally depend on the history and environment of peat formation, the type O organic materials and water content. Its thickness generally can Vary frorn a few centimetres tc over 2.5 m.

Peat is an accumulation of variably decomposed and compacteci plant debris. Rernain: of peat-fomiing mosses and sedges usuaiIy dominate most peat bogs, dthough other plan rernains and variable quantities of inorganic material may be present.

Peat is a medium with high porosity, permeability and non-surface energy. Owing tc influences of seasonaUy climatic fluctuation, solar radiation and evaporation, as well as grounc surface water suppiy, the thermal conductivity of peat in frozen and unfrozen States m significantiy different and affects the palsas and peat plateau in recuning annuai cycles. T'hi5 property wiii be further discussed in chapter 4.

3.5.3 SEASONAL SNOW COVER Snow is also considered as a porous medium. The pores are completely occupied by either air, liquid water or ice. It is different from mineral soils in that snow grains are not an incompressible and elastic material. Seasonal snow cover varies by accumulation and rnelting which also affect the thema1 conduction, solar radiation, difisive evaporation, and water flc during fieeze-thaw cycles.

Continued accumulation and wind drifting gradually densi@ the snow cover as wint lasts, thereby changing thermal properties.

Compared to accumulation, snow melting is still more complex and dependent upc many major factors such as solar radiation, thermal conduction, vapor diffusion and wat infiitration. The process results in increases of temperature and porosity, decrease of densi and, finally, loss of snow rnass until melt is achieved.

Snow accumuiation and melting is rather complicated, and so far there is no adequa mode1 to describe the entire accumulation-melting process. A simplified approach of tl problem wili be further presented in chapter 7.

3.6 SUMMARY The Quatemary deposits of the Ungava region were emplaced during and sin( Wisconsinian glaciation. Laurentide Ice Sheet first grew in this area, and it is aiso where i last remnants findly disappeared, about 6.5 Ka ago. The characteristics and the distribution ( the Quaternq marine sedirnents and peatlands in Nunavik are a result of the ice shee deglaciation, marine sedimentation and land uplift during and afier the Late Wisconsinian.

Permafrost was less abundant during the Hypsithermal and expanded during the Nec glacial period starting about 3000 BP. But it aggraded in areas uncovered from glacier ice an exposed to periglacid climate. Ln permafrost within coarse sediments, pore ice dominates an excess ice is very scarce. In the region above the marine limit, till is the dominant surfici; deposit. Thick fine, clayey and silty sediments extend in valley bottoms that were formerl marine basins around Ungava Bay and Hudson Bay. As the fine sediments are prone to ic segregation, these geological variations lead to numerous lateral and stratigraphic changes i cryofacies.

It has been found recently that the continuous permafrost zone extends much furth( southward dong the Hudson Bay Coast south of inukjuak and southwest of Ungava Bay, an the southern iimit of the continuous permafrost zone is quite close to the forest limi Permafrost thickness in Quaternq sediments varies from fine-grained sediments to coarsc grained sediments; and the maximum thickness of permafrost varies from 15 and 30 m in th discontinuous permafrost region to 500 m in the continuous permafrost. Lu the reference area near Kangiqsualujjuaq, permafrost aggradation in palsas fmt toc place around 1800-1600 BP and was stU active in some sectors of the peat plateau around 8( BP. A complex of peat plateau and palsas formed. These landfonns have a miner permafrost core with abundant segregated ice underlying a relatively thin peat layer.

Investigation of the Quaternary geology and periglacial geomorphology have focuse mainly on the causes and the conditions of pdsa evolution, variation, distribution and tf description of features. Our knowledge on palsas is mainly limited to qualitative analysis ( environmental information. Chapter IV

MATHEMATICAL MODEL FOR ORIGIN OF PALSAS

Paisas could occur in regions where the annual air temperature is equal to or less than - 1'C (Washburn 1983, Dionne 1984). The existence of such mounds in such a high temperature region cm be explained by the thermal properties of organic materiai and by the formation of the ice lenses in the permafrost core of the mounds.

In the field, ice lens distribution in palsas is very complex. It can take horizontal, vertical, faulted, bending and inclined forms (Rousseau, 1996). Many environmental factors affect the pdsa: soi1 type, vegetation, snow cover, ground water flow. Moreover, we know that palsas result from the displacement of frozen ground under altemathg kze-thaw cycles for a long period, and that the displacement results from the accumulation of discrete ice lenses developed in the permafrost core beneath the upper table of the permafrost. In the light of known characteristics of palsas, the existing works on frost heave, ground thermal regime, moistue migration, discrete ice lens growth and thaw settiernent in the soi1 system should be integrated in the design of a mode1 for their formation. It is necessary to propose a set of mathematical equations. which considers both freezing and thawing in soils, and numerical methods for simulation and prediction of the palsas.

Because of the laboratory limitations of study conditions and of different understandings on the mechanisrns of soii freezing and thawing, the available rnathematical descriptions are different, and the mathematicai results of each modelling dso show differences. In some situations these differences can be important. Second, an important pmblem of mathematical modelling of pdsas is the consideratic not only of the freezing process but aiso of seasonal thawing of the active layer. In other wor the model should comprise the entire freeze-thaw cycles in the soii systern- But currently, fi the heat and mass transportation problems in permafrost and frozen ground, except the phas change temperature problem, nearly al of the models are only available either for freezing for thawing. A theoretical mode1 which involves fieeze-thaw cycles in this domain something new.

Furthermore, the inception, growth and maintenance of palsas elapse over many tens I hundreds years, whereas existing ice segregation and thaw consolidation models encompa short periods of one fieezing or thawing cycle. Finally, in order to be workable, a mathematic model describing palsas should be as simple as possible, run on a short tirne of computatio and be efficient. Most models are a set of the nonlinear partial differentiai equations whic involve many variables, components, and parameters which are generaliy dficult determine.

In 2-D, palsa formation is a typical two-dimensional problem seriousiy affected I: external and internai conditions. A possible reason for the discrepancy between modi predictions and observed data is inefficient existing algorithm to solve practical problem Some new, original solutions are necessary.

According to these requirements and conditions, and based on the background of tt Quaternary geolou and geornorphology in the reference site, the possible modelling rnust t available for the following conditions: a) The model must simulate the ground thermal regirne in both freezing and thawin processes.

6) The model and computation must sirnulate moisture migration and buiid-up of discrete ic lenses which is the principal process responsible for palsa formation, under cyclicai (yearlj freezing (cooling below permafrost table) and thawing (warming) alternances. c) Reproduce frost heave and thaw consolidation. d) Be efficient and run on a short tirne of computation for long-term problem, with a negligible relative deviation of the results after simulation for a long period. 4.2 OBJECTIVE The main objective of our model is to contribute to the understanding of the prirnar geocryological processes goveming the inception, growth, pulsation and decay of palsa! These processes, that operate simultaneously, are moisture migration, ice segregation, fios heave and thaw settlement. A good understanding of these basic processes will ailow to appl them in the geological and climatic conditions under which palsas develop and in th understanding of goveming extemai factors such as snow cover, vegetation and ground watei In addition, the effects of climate change on palsas in the numericai simulations and prediction with mathematicai modelling based on observed data can be attempted. This research provide a new fundamental approach on the phenornena and opens new avenues for further studies a paisas and other comparable periglacial Iandforms.

4.3 BASIC ASSUMPTION

The model is established on the foilowing assumptions:

Darcy's law applies to water migration through snow, peat and both fiozen and unfrozei soils.

The snow. peat and unfrozen minera1 soils are isotropic, homogeneously layered; th unfrozen minerai soils are also saturated.

The peat is a non-surface energy material in the soiI system.

Soi1 particles and water are incompressibk and the volume of soi1 particles remaini constant in the freezing and thawing processes.

Difisive dispersal fluxes of both the water and the gas masses can be neglected.

Moisture transport in both frozen and unfrozen zones occurs only in the liquid phase.

LocaIiy, fluid and solid temperatures are equal.

SoIute concentration is negligible and therefore needs not to be considered in the model. 4.4 GOVERNING EQUATIONS

4.4.1 ENERGY BALANCE

Because of the importance of phasechange from water to ice or ice to water, it i assumed that the ice content is a function of temperature; the volumetric apparent heat capacit can be expressed as:

In frozen soils, the influence of ground temperature on the unfrozen water content iead to variation of ice content. Therefore, ice content is aiso a function of temperature. For a give soil, the relationship between ice content and temperature is determined experimentally. It i given as:

0, = 6,(T) (4-3 de, de, d~

Substituting (4-2) and (4-4) into (4-l'), the equation cm be given as:

The noniinear partial differentiai equations (4-1) to (4-6) are employed efficiently ti calculate problems of the phase-change temperature regime both in freezing and thawing soils. 4.4.2 WATER TRANSFER IN FREEZING SOILS

4.4.2.1 Continuous equations of water migration

If we only consider the moisture transfer hmunfiozen to frozen soils due to the watc pressure gradient, the unsteady water transfer in the saturated or unsaturated anisotropi heterogeneous frieezing soils can be expressed as foiiows (Guymon 1983; Kay and Perfec 1988):

de, p. dei +L-- -v(wP,) T,

Combination of equations (4-7)-(4-9) with (4- 1)-(46) cm describe the water migratio: from unfrozen soils to the frozen front through the freezing fnnge with liquid water pressure.

As the load or overburden is not too large and when it is supposed that pore ic pressure is equal to atmospheric pressure, the Clausius-Clapeyron equation cm be used:

to transform pore pressure into temperature T for solution of a set of nonlinear partia differential equations on coupled heat and rnoisture transfer in freezing soils (Harlan 1974 Sheplar et al. 1978; An et al. 1987)

It is weli known that the rnathernatical mode1 of the coupled heat and mas transfer i successful for description of moisture migration but not for discrete ice lensing in freezinj soils, while the latter is the major characteristics in palsas. 4.4.2.2 Equations of the discrete ice lensing and Frost heave in freezing soi1

Our aim is that the model wiii be made of possibly simple formulations for long-te recurring freeze-thaw cycles and wili be capable of sirnulating temperame, discrete ice lensii and frost have in palsas. Clearly, fmt, the ground temperature regime and phase changes c be described by a set of nonlinear partial differentiai equations (4- 1)-(4-6), given that the s thermal properties are reasonably known. Field data, such as annual air and ground sufz temperature fluctuations, thawing and freezing indexes, snow and vegetation cover, s structures and ground moisture distribution need to be adequately known and representative real palsas.

Second, for the moisture transfer and ice lens formation. the model uses 1 Segregation Potentiai approach and a modification of Gilpin's and Nixon's models to simuli the discrete ice lensing and frost heave. In the two-dimensional probiem, the temperah gradient in the frozen fringe is calculated in normal direction for ice segregation, i.e. parallel heat fluxes. Naturally, as discussed above, the ice lenses in the palsa are very compl because of the cornbined influence of many factors over a long-term period. It is very ciflic. to simulate natural phenornena. Therefore, according to thennodynmics, it is considered tt ice lensing occurs normally to heat flow and suction pressure. even if field peculiarities c generate more complex lensing forms.

In the light of the theory of the heat and rnass transfer, water intake is dong the ht flow direction. In other words, the line e of ice lensing is normal to the heat gradient v (Figure 4.1). Based on this principle of thermodynamics, the equations for mass flow in t one-dirnensiond problems cm be used in two-dimensionai problems. The approach is n only following the physicai principle but aiso significant for simpmcation of mathematic modelling for cornputation. Only is it important to note that the mas velocity V' is found the normal direction of the heat flow which, due to palsa form, is not only vertical. Sim~ vertical (surface to depth) transfers apply only for a one-dimensional problem. Similady, t relative variables, P,, Dr, T, and TI, V', VT, 6' and etc. are ali in the normal flc direction. Ernploying the Segregation Potentiai, SP (Konrad, 1980, 1984) results in a grr simplification of water migration caiculation. -- FROST FRONT

-T O

TEMPERAT URE UNFROZEN WATER CONTENT

Figure 4.1. (A) Conditions controling ice lensing in the frozen fringe. (B) Heat and mass transfer properties in the frozen fringe. The formula of Segregation Potential, SP is giveo as (Konrad and Morgenstern 1980; Konrad and Coutts 1987):

SP is defmed as the ratio of the water migration rate to the thermai gradient in the frozei fringe. The temperature gradient can be written as:

in one-dimensionai problems, and

in two-dimensionai problems.

According to Darcy's law, the water flow through the frozen fringe is

and considering the flow as constant through the fringe, the equation for the continuity of wate flow is given as:

In the normal direction, it is reasonably assumed that a) frozen permeability ii dependent on temperature using a power law of the fom

and b) the temperature change across the frozen f~geis linear; the temperature in the fiozer fnnge wili be satisfied by: Substituting (4- 17) and (4- 18) into (4- 16), the integration of the pore-pressui distribution (4-16) in the fringe is, (Nixon 1991):

It is assumed that the pore-ice pressure at the face of a fonning ice lens must be equal i the overburden pressure. The generalized Clausius-Clapeyron equation at the segregatio freezing front cm be reformuIated to accomodate this pressure factor (Holden et al. 1985 Nixon, 199 1)

Substituting (4-20) into (4- 19) and assuming TI=O'C for simplicity it foiiows that:

Sirnilarly, equation (4-1 1) is derived from the application of Darcy's Iaw and th Clausius-Clapeyron equation at the frozen fringe (Konrad and Coutts 1987). AppIying (4-12 and (4-2 1) at the segregation freezing front at e= O segregation freezing temperature T, , ca be obtained:

The unfrozen water content in the frozen soiis is dependent on the soi1 temperature. Ic content will change with the water migration from the frozen fiinge. It can be written as: Frost heave is fed from two components, original pore water and water migratio given as:

According to the theory of heat and mass transfer, reasonably, ice Iensing is norrnd the heat flow direction. The principle is aiso tenable for the ice Iensing by suction pressur Aithough SP was presented with one-dimensionai experirnentd tests, based on tbis princip and on relation between pore pressure and temperature in CIaiisius-CIapeyron equation at tl segregation freezing front, as long as the water migration is following the nonnd direction I heat flow, the SP method can be extended ta two-dimensional problems.

4.4.3 THAW CONSOLIDATION IN THAWING SOILS

The macroscopic unsteady water flow in a partially saturated heterogeneous thawing porous medium can be written as:

It is assumed that the ice in frozen soils is incompressible and impermeable. In tl - deforming porous medium, the soi1 particle move at a velocity V', it is the specific discharge î the water relative to the moving solid q,, that is expressed by Darcy's Law:

During thawing, both water and ice densities, P,, Piare constant, and if the poror medium is saturated, then the water content 8, can be given as: Substituting (4-28) and (4-29) into (4-27), then it can be reformulated as:

The equation of mass conservation of solid is given by:

The total derivative of the porosity is related to the volume suain and cm be expresse as:

w here:

Assuming vs - Vn «d n / a t . using the relation between porosity n and ratio c pore e,

and substituting (4-311, (4-32) and (4-33) into (4-30), the equation can be rewritten as:

As the load or overburden impacts on the frozen soils, the compression of frozen soi1 is as foIlows

where a * is compressing coefficient, a,actual stress, and e,pore ice pressure. Similxly, a er and the ice keep a balance of the chernical potential as following:

substituting (4-35) and (4-27) into 14-34), the equation is expressed as:

I q =a*(&+ e) (1 + e)'

Because the medium is saturated, the ice content is a function of both liquid wat content and unfrozen water content, the expression is

Supposing the thaw consolidation results only from melting of the ice and liquid wat dissipation, and as soil particles are incompressible, then, the volume main E could 1 estimated with

Combination equations (4-1) to (4-6) with (4-37) to (4-42) in the suitable initial ar boundary conditions cm solve the probiems of thaw consolidation in thawing soil Obviously, even for one-dimensional and short-term probiems, the computation of such a laq set of nonlinear partial differential equations with so many variables remains a very dificl problem. 4.5 SIlblPLIFICATIONS FOR ICE SEGREGATION AT THF, TOP AND AT THE BASE OF PERMAFROST IN A PALSA

4.5.1 ANNUAL THAWING AND ICE SEGREGATION NEAR THE ACTIVE LAYER

The formation and growth of palsas is a long-term process of permafrost aggradation recuning freeze-thaw cycles. It is necessary to analyze the importance and contribution of ti seasonal thaw on the palsas for understanding the thermodynamics and water supply for pal! growth.

Generally, the ground surface is covered by a dense bryophyte cover and peat or 0th organic materials (Harris 1987; Schunke and Zoltai 1988; Williams 1991). The majl characteristics of peat, a medium with high porosity and non-surface energy, is that it providi good insulation when it is dry.

In the subarctic tundra, the active layer of palsas, which usually ranges from little mo than 1 meter to only a few decimeters, is often limited in the peat zone. Even if the tha penetration advances into minerd materials underlying the thin peat cover, the extension of tl thaw penetration in the consolidated marine silt is also litde. Except for marsh wetlands, tl sanirated zone in fine-grained soiis is iocated at the base of the thawed soils as in the peat cov

(Van met-Lanoë 1991). During eariy winter, the fast frost penetration and the effects 1 variable saturation with depth in the active layer lead to almost no segregated ice lenses in tl frozen peat cover. If the peat is thin or absent, only very small segregared ice Ienses and po ice form, even in frost susceptible soils. Consequently, both frost heave and tha consolidation are srna11 in the active layer in normal pressure conditions.

When the permafrost environment is subjected to a regular climate, the active lay remains relatively stable and the frost have caused from ice layes in active layer basical offsets the influence of the thaw consolidation in seasond thawing. In other words, frost heaq and thaw setdement maintain a reIative baiance. Uniess some particular variation of therm boundary condition or chnate change take place, thaw consolidation and frost heave in d active layer. actually, do not contribute to pdsa formation.

Some literature reported that for a slow rate of thawing, the presence of an ice layer at m depth does not produce pore pressure in the soi1 that deteriorates significantly with time. fact, if an ice layer were present at the 3 rn depth under these thawing conditions, the po pressure at the soil-ice interface would actudy reduce siightly with tirne; and it is alsc suggested that, aithough the settiement is obviously considerable, the pore pressure in the soi above a thawing ice Iayer may not lx as aiticai as hitherto supposed ((Nixon, 1973 Corapcioglu 1983; An er al. 1989).

Thus, if climate conditions maintain in a relative steady state, the effects of thav settlement in seasonal thawing in active Iayer on the paisas can be neglected. The functions O thaw compression, pore pressure, and ice content in equation (4-37) and (4-38) can be omim in modelling paisa formation but the effects of thermal energy on water transfer from thc thawing front into the frozen core cannot be ignored. Therefore, for segregation of ice near th top of permafrost in an already existing palsa, equation (4-38) can be written as

Equation (4-43) expresses the water velocity which depends on the thermal gradient Obviously, downward water migration from the thawed and saturated zone of the active laye] into the frozen soil is physically the same as that of the upward water migration from tht unfrozen zone towards the frozen soil; the only difference is the flow direction. The problem of course, cm be treated with the SP theory, for if the influence of the suction pressure of tht medium is incIuded in the coefficient. then the SP can be used instead of the , Thi! treatment is an extension of the usage of the SP theory from freezing soils to thawing soils.

4.5.6 ICE SEGREGATION OF PERMAFROST BASE

For ice Iens formation in the freezing fringe near permafrost base, the Pr parametel needs to be modified for SP as in equation 4-1 1. Thus, the problems concemed can bt simpiified to be made available for mathematical modelling of palsa formation. Suck simplification. no doubt, is particularly significant not only for the mathematicai description ol palsa and permafrost formation but for the deduction of the numericai computation, especialIj in large time-space scale problems.

4.6 INITIAL CONDITION

As reported in the literature (e.g. Seppala 1982; AUard et al. 1986) a paisa can start tc grow in a permafrost free area of a bog or a fen due to an abrupt change of ground surface thermai conditions. Initial conditions are defined as: e(x,y, z, t),=, = fo (x,y9 2) Boundary Condition

The general boundary conditions can be written as foiiows:

The SP values used for silty clay in our simulations are the experimental results O Konrad and Morgenstern (1980, 1984) and Konrad (1988) for very similar soils (Leda clay).

4.7 METHOD OF NUMERICAL COMPUTATION

The mathematicai mode1 for the ongin of palsas presented above is rather simple in thi mathematicai formulations. It includes a set of nonlinear partial differential equations (4- 1)-(4 6),the equations of the Segregation Potential Method (4- 11)-(4- 14), a noniinear equation (4-2 1 and other comrnon, algorithm formulas. The water migration with SP cm be easily calculatec by the simple numericai difference method. The equation (4-21) can be also solved eady usiq an iteration method. The problem is to solve the equations (4-1)-(4-6) which can bc numericaiiy computed by a efficient numericai method, based on difference scheme O conservation, which is given below.

4.7.1 INTEGRAL AND DIFFERENTIAL EQUATIONS

According to the law of conservation of thermal energy, the tirne t increases from t ' tc t ",the fundamental integration equation of heat flow in a domain can be described as: dT Ill (c~)t" du - (CT)t1 dv = 121t dtfl G ddo + jty dt jfl qd v (450 D dn D for aii , [t ',t "1 D C the equation is tenable.

Thus, for al1 [t ', t "1, c fi there is

let t ', r " + t, D tends to a point (x, y, z) the equation (4-5 1) can be written as:

Ln the onedimensional problem, the equation (4-52) can be expressed as:

where fi = [a,b] is a line segment, S is a disconnected point in the ( a, b).

4.7.2 DIFFERENCE SCHEME

The temperature profiles in the freezing and thawing soils can be described with ; nonlinear partiai differential equation which consists, in generai, of the terms of tiea conduction, heat convection and phase-change or non phase-change of solid/liquid phase ir equation (4-1)-(4-6). In a porous soil medium, cornparison of the effects of the heat conductior and convection terms on the ground temperature regirne shows that the function of the forme: term is 2-3 orders (1: 100- 1 :1000) more than that of the latter (Taylor and Luthin 1978) Therefore, it is usual to consider only the heat conduction unless the soil is rather coarse, grained and water saturated under the water table. Otherwise, it is assumed that there is no hea source or sink in the soil system and the thermai and physical properties are the mair parameters. The non-linearity arises due to the dependence on the tempefanire of the them parameters and unfiozen water content.

The implicit ciifference equation in a one-dimensional problern can be given as foiiow (Liu and An 1982; Yogesh and Torrance 1986; Feng 1986):

a) Because of the nonlinear propeny of the partial differential equation (4-1)-(4-6), th€ Prediction-Correction method based on the law of conservation has been used for the numerica calculation of the one-dimensional problerns of phase-change temperature regime in chapter 4.

6) The velofity of water intake vf can be nurnerically calculated by equation (4- 1 1) with temperature gradient VT (4- 13).

C) Equation (4-22) is also a nonlinear equation in which the variable of segregation freezing temperature T, can be computed with the iteration approach. e) The unfrozen water content O,, is from an experhentally obtained statisticai formula (4-23). d) With the fringe thxkness D finding from (4-12), the locations of the frost front, of segregation freezing temperature and of ice lensing are found. f) The pore pressure P,, and discrete ice content oicm be solved by (4-20) and (4-24).

Finally, frost heave is computed by the local rnoving mesh method with the pore water phasechange h, and water migration h,, , determined by equations (4-25) and (4-26). The mode1 is rather simple and easy to cornpute. It can be used to simuiate permafrost fomtion or the influence of climate change on permafrost processes which cover hundreds or thousand of years. Initial condition

Boundary condition

T;+' = (T)

4.7.3 TEE CHARACTERISTICS OF TmDIFFERENCE SCHEME OF CONSERVATION The advancages of the difference scheme of conservation are i) the difference scheme meets the law of consenation strictly, and the naturd boundary conditions are treated in "naturai" but not in isolated form. ii) at the disconnected points in the medium, such as interfaces of snow/peat and peathineral soils, comparison of many other difference schemes of non conservation and usage of the difference scheme of conservation WUavoid resulting in large error in the numencal solutions, the only condition is thai grids of the mesh faii on the interfaces. This characteristic is more beneficial for the cases with inequispaced meshes, disconnected medium and a complex geometrical shape, especially for two-dimensionai problems. In the field, such cases are the nom and this is what should be considered preferentiall y. 4.8 SUMMARY

1) It is weU known that the ice lenses in the palsas form as discrete segregated ia lenses; the mathematical model of coupled heat and water transfer cm not be of efficiency fo the description of dimete ice lensing but is appropriate for water migration and accumulation ii the freezing soils, Evidently, the establishment of a mathematical mode1 which is relativel! simple, easy for computation and efficient in covering both freezing and thawing processes ii significant for approaching the origin of paisas. Considering the Segregacion Potentiai method and modifying the Gilpin's (1980) and Nixon's (1991) model, a mathematical model cru descnbe frost have resulting from water migration, build-up of discrete ice Ienses in thc permafrost core of palsas and thick ice lenses beneath the upper table of permafrost-

2) The model is very simple and requires a short tirne for numerical computation. Thr mathematicai fomulae for water migration are greatly sirnplifred and avoid very comple~ numerical computation of noniïnear partial differentiai equations of mass transfer.

3) The coefficient of SP is less sensitive than the permeability in the frozen fringe.

4) Actually, the water in the active layer does not maintain samrated conditions anc varies discontinuously. Generally, it ranges from unsaturated to saturated from top to the thav front. Establishing calculations for both unsaturated and saturated modelling are cemyveq complicated problems. Using the SP method, the rnodel only considers a requirement that tht frozen fringe is a saturated layer. Because palsas form in peat covered fine-grained soils u bogs or wetlands, this requirement is generally satisfied.

5) Employing the SP method and modiSing the Gilpin's and Nixon's model, oui model can numericaliy simulate the discrete ice lensing in palsas and cryogenic rnounds witi natural temperature conditions without the limitations of quasi-steady and srnail boundaq temperature conditions.

6) Both frost have and thaw consolidation are considered, but the rnodelling is od~ concemed with the results of liquidkolid or solid/'iquid phase-change. It is further assumec that no exceeding pore water results from the thawing process.

7) Ground temperature regime in freeze-thaw cycles is a nodinear problem. Th nonlinearity arises due to the dependence of the thermal parameters and unfrozen water conteni on the temperature. With the difference method based on the law of conservation, this problerr can be numerically solved. The numerical computation rnethods for the mathemticz modelling are stable and convergent.

8) Generally, accurate experimentai constants are difEcult to obtain. Because of th variation of the location and the magnitude of ice lenses, the distance between discrete ia lenses, especiaüy in the transient condition, is too smd, therefore a srnail mesh is required For this reason, much computer memory and time is needed for the two-dimensions computation, particularly in long-term problerns. Chapter V

A ONE-DIMENSIONALMATHEMATICAL MODEL OF PALSA FORMATION AND GROWTH

5.1 BACKGROUND

Although some palsas can be composed exclusively of frozen peat and ice, the majori of researchers report that the peat usuaiiy overlies some mineral sediments, a fact that genem abundant tenninologicai discussions and debate over the processes of their formation (Seppa 1972, 1983a; Ahrnan 1976,1977; Washburn 1983a; Pissart and Gangloff 1984; Dionne 197 1984; AUard er al. 1986). For some tirne it was proposed that palsas are elevated above d surrounding terrain by the combined action of peat accumulation on the surface and ic segegation in the underlying mineral core (French 1976). It is now a widely demonstrated fa that the ice segregation responsible for the topographie have of these landforms takes ph dorninantly in the underlying sediments. Wetland vegetation ceases to grow and is replaced t xerophytic species when the peat surface is raised above bog level (Aiiard and Seguin 1987 Only in particulariy wet climate can mat thickening somewhat contribute to paisa growth afti heave is initiated.

Very few deep coring through the whole permafrost thickness in cryogenic mounds ar paisas are reported except for a few ones in Northern Sweden (Lagerback and Rodhe 198 Akerman and Malmstrr6m 1986). Coring to depths of 5-6 meters was done by Fortier ar Aiiard et al. (1988) in Northem Quebec. These works reveaied that segregated ice is moi abundant just below permafrost table and near permafrost base than in the middle section of tt frozen core. Geophysical works aiso suggest that the permafrost base is the focus of a shar electrical resistivity contras that probably reflects the abrupt transition from icy to non frozen soii (Gahé et al. 1987; Seguin and Mard 1984; Fortier et al. 1991).

Since physical processes goveming ice segregation are now rather weii known and since ice lens formation has been both reproduced in Iaboratory work and simulated by mathematical modelling (Williams and Smith 1989), it is worthy to try the application of segregation and heave theory to cryogenic mound formation with the help of mathematicai modelling.

When a frost susceptible soii is subjected to freezing. heave occurs as the result of the growth of ice lens fed by water supplied to the freezing hge from the unfiozen soii below. Construction and engineering projects (e-g. roads and pipelines, Williams 1986) necessitated the development of fundamentai knowledge of the segregation processes and simulated experimental as weii as modelling work. Many studies use a mechanistic approach supported by laboratory tests (Kay et al. 1981; Konrad and Morgenstern 1980; Xu 1985; Penner 1986; Garand and Ladanyi 1987; Nixon 1987; Takeda and Nakano 1990; Williams 199 1). Others are oriented towards the development of numericd prediction and mathematical modelling (Harlan 1974; Gilpin 1980; Guymon et al. 1983; O'Neill and Miller 1985; Konrad 1988; An et al. 1987; An 1989; Nixon 1982, 1991)

Modelling must take into account variabte phase change temperatures over an array of physico-chernical conditions such as thermal gradients, overburden pressure and solute content of soi1 water. A simple and practical approach is the segregation potential (SP) concept put forward by Konrad and Morgenstern (1980, 1984). Until now SP was applied with good success to freezing soils in engineering projects, for instances underneath road pavements and below cooled gas-lines. The depths involved in such applications are rather shailow and the duration encornpassed is short.

The formation and geomorpholog~cvariations of pdsas and of cryogenic mounds and their evolution are pnncipally controiied by the interaction of thennodynamics, ice segregation, frost heave and thaw consolidation during many years (decades and centuries according to field observations and I4cdating, Mard er al. 1986) of recurring freeze-thaw cycles at the surface of the terrain. A field experiment of palsa formation was reported by Seppala (1982): by keeping a 5 m2 area in a fen fiee of snow over one winter, frost penetration increased sufficiently to form a layer of permafrost and initiate a 0.35 m high palsa. Although ice segregation was invoked to explain the heave of the new Imdfonn, this was not supported by observations on driiied cores or by an attempt at mathematicai analysis. Aithough ice lem growth and frost heave have been a subject of numemus investigatic over rnany decades. most of our knowledge of the process stili derives hmlaboratory tes conducted on small samples of soil. Field situations involve large masses of soil, slow rates fkezing, smd temperature gradients and periods of time of many years (Pemer and Goodric 1981). Pe~er(1986) Indicated that field observations do not support his test consistent aithough they are essential for understanding basic processes, the simple laboratory conditioi can not really sirnulate the compIex conditions that occur in nature.

This chapter presents results of our attem$ at mathematicai modeliing of pal: formation. The model adapts the SP approach to terrain conditions known from a research si in Kangiqsuaiuijuaq, northern Quebec. It is a uni-dimensional model that simulates discrete ic lens formation dong a vertical profile.

5.2 STUDY SITE

5.2.1 GENERAL CHARACTERISTICS OF THE STUDY SITE

The Quatemary geology and permafrost characteristics of the reference site ne; Kangiqsualujjuaq in Northem Quebec (Figure 3.1) has ken briefly inuoduced in a fom{ chaiter. The climatic and geomorphologic conditions of this reference site are ty-pical of ù palsa region of eastern Canada. It Lies at the northern limit of the discontinuous permafro zone. Over the decade 1980-1990 the mean annual air temperature ranged between -4.4'C an -6.7"C, with an average of -5.8'C. For the same period the mean air freezing index w: 3 193'C-days and the thatving index was 1079°C-days. *Mean Januq ternperature is aboi -22°C and mean July temperature about 9.5"C. Total precipitation is about 400 mm, of whc 42% is snow (Wilson 1971). Wind-àrifting makes snow cover very uneven, varying frot virtually nothing on wind-swept sites to over 2 rn on the lee-side of topographic obstacles; it , generally over 1 m thick in forest stands (Black spruce-Picea Mariana, White spruce-Pice glauca and Tamarack-Larix laricina) and bush thickets (dorninantly willows-Salix sp). Tt: extensive patches of tundra terrain are covered by lichens and mosses and retain very iittl snow.

A complex of peat plateaus located in a topographic basin by a lake in the center of valley was used as a terrain reference for the modelling exercise (Figure 3.2). Figure 5.1. Actual thermal profiles in the palsa complex of Kangiqsualujuaq. Figure 5.1 shows temperature profiles hmthermistor cabies in the permafrost. , figure 5.la shows profiles from a 20 m deep hole (HT-301)on a flat area of the peat plate: figures 5.lb, 5. lc and 5. Id show profiles from holes on either the top of higher mounds tl raise above the plateau surface or in depressions. Depresseci sites (Figure 5. lb, 5.1~): warmer because of deep snow accumulation in holiows. According to geophysicai soundinl permafrost thickness in this palsa and peat plateau complex varies hm 3.5 m under sor

depressed areas to more than 22 m under topographie highs (Gahé et al. 1987; Pilon et 1 1992). Maximum elevation on the complex, on top of an individuaiized mound higher than t general plateau surface is 15.4 m relative to the lake level.

5.2.2 PEAT PROPERTIES

Among soils in nature, organic materiais have properties that are unique, and thus are the origin of characteristic features in the landscape. In the subarctic tundra permafrost regior smaii changes in pmperties of the peat cover affect thermal energy exchanges at the tund surface in a more critical way than sidar changes have on the mineral soik

In complexes of peat plateaus and palsas, the mounds in discontinuous perrnafrc areas generaüy rise from 1.O to 10.0 m above their surrounding tundra surface. The maj factors impacting not only on the origin of paisas but aiso on their size and height are ti physical characteristics and thickness of the peat which principaily depends upon I components and its stratigraphie structure, history and environment of peat formation a~ water content. The mineral horizon undemeath is most of the time of relatively fi composition. mainly silt (.h1977). Depending on the thickness of the surface pe stratum, a transition layer of graduaily increasing minerai content may occur near the interfac of the peat and mineral sediments. Silt may appear scattered wichui the peat, in some diffu: contact. Ln other cases the peathineral contact can be very sharp.

Generally, as other requirements are constant in this Iowland, the peat plateaus ar paisas developed in silts overlain by peat suggest that the thinner the peat, the higher the palsa Comparing the classic paisas in the literature with the minerai core palsas, on the average, tl former are lower than the latter.

At the study site, the complex of peat plateau and paisas developed in a topograph basin by a lake. The peat started to grow around 45004300 years BP (Gahé et al. 1987) ar produced mainly from mosses and sphagnum that expanded over a part of the original Id which was larger than the present one. Because of the relatively short history of pe formation, the peat overlying the mineral sediments is relatively thin, an average thickness is oi about 1.0 meter. With col&r climatic conditions, the permafrost core of the palsas mainij developed in the marine sediments, the average height of the palsas in the complex is usuaiij above 3 m.

The climatic basis for paisa formation focuses on two periods of the year, during whict energy fluxes cause resuits of long Iasting effect. These are the mid-summer heating by short- wave radiation, and mid-winter cooiing by long-wave radiation back to the atmosphere. The incoming solar radiation meets, in summer, a shallow vegetation cover over a peat surface oi high porosity and Iow thermal conductivity. The ability of the surface layer to transfer such great energy amounts is Iow. The precipitations in autumn provide excess water available fox the growth of the frost core during the following winter. Since snow cover is negligible, the outgoing long-wave radiation cm be considerable, and surface temperatures down to -20°C or more are observed. Thermal conductivity of icy frozen peat is high, and more thermal energy is released from the frozen body.

Peat, especiaiiy pure peat, is an organic materid with high porosity, permeability and non-surface energy. These physicd characteristics determine storage of water content in the peat. The existing water in pure peat is not bounded but is rather free ground water; capiiiarity does not contribute to water flow. Actudy, in the peat layer of the peat plateau, peat is more or less polluted by mineral soils and there is sorne capillarity, particularly near peat base, but this pIays a very rninor role and cm be omitted in modelling.

Water diffusion in the upper peat Iayer takes place mainly from evaporation. Because of the seasonal fluctuation in precipitation and solar radiation at the reference site, the water content in the peat varies seasondy, especiaiiy near the surface. During surnmer, the combination of relatively less rain, strong solar radiation and evaporation make the peat surface very dry. But at its lower boundary at the end of the auturnn, foliowing the abundant precipitation, ground surface water supply and relativeIy less evaporation, the peat is nearly saturated. This condition maintains itself until the beginning of the foliowing surnmer. The water content varies therefore with the seasons at various depth foliowing recurrent annual cycles.

Based on the observation of natural sites and assuming that the water content at the peat bottom is permanently saturated, 8,,,the fluctuation of the water content at the top of peat surface can be expressed in tirne and space as foliows: In time of the annual cycle,

tA, < t 5 t, [Op - (Op - 'O)(' - 'Ab) '(tyto - 'Ab) is beneath the snow free peat surface and.

The differences in physical properties between organic and mineral soils play a great~ role than elsewhere. In particular, the thermal properties of organic soils show a drast difference between frozen and unfiozen States. In this respect, peat is unique among soi1 Thus the combination of a sensitive energy balance and the extreme thermai properties of pz is capable of creating particular thermal conditions at the surface. In this regard, paIsas ai particularly sensitive features and the study of their thennodynamics offers an excelle] exarnple of seasonal characteristics of energy transfer in permafrost soils.

5.3 MATHEMATICAL MODELLING

The main purpose of this modeiiing exercice with the mathernatical mode1 estabiished i chapter 3 is to simulate the pdsa formation following snow free peat cover conditions. T1: problem of modeIiing palsa formation is mainly to approach ice segregation and frost heave an so, to reproduce the vertical upheaving of a soii profle such as it must occurs in the formatio of a palsa. It takes into account the variable phasechange temperature, build-up of discrete icc lenses, heave and thaw consolidations in order to consider freeze-thaw cycles near the so surface and annual cyclic temperature variations dong the profile. The model is also estabiishe on the assumptions mentioned in Chapter 2. Before, an explanation relative to solutes : necessary.

Our model applies to cases where solute concentration is negligible. For the referenc site, this assumption was verified on cored samples. After melting and extraction b centrifuging, both ice lens water and soii water were tested for salinit. with a hand-hel refractometer. No salt content was detected. This venfication was klieved to be necessary since some salinity was measured in frozen silty clays in cryogenic mounds at other sites near Kangiqsualujuaq. As the paisa site at 36 m a.s.1. emerged about 600 years ago while the cryogenic mounds are only a few meters above sea level and on more recently emerged terrain (Mard et al. 1988), there was most probabIy sufficient time for complete salt leaching hm the soii to occur at the paisa site. a) Discrete ice lens formation and frost heave in freezing soi1

The heat conduction equation is avaiiable for the freezing and thawing soils and it can be written as:

where c, C, Â. are shown in (5-2),(5-5) and (5-6).

Since palsas take many years to grow to thei. fûll size, an active layer exists on their surface during their growth period. This layer which thaws every summer is subjected to thaw consolidation. Two different active layer conditions can happen on palsas:

1- Maximum thaw depth (generaiiy in the range of 0.4 to 1 m) is confined to the surface peat layer, or 2- Due to a thin peat Iayer, maximum thaw depth reaches into the underlying silty sediments.

In most peat types, particulariy fibrous peat, almost no segregation ice form during freezing, a fact observed in many sections in palsas and also observed by numerous drilling in frozen active Iayer at the Kangiqsuaiujjuaq site. Observations aiso demonstrate that ice lenses are scarce and thin in the active layer in siity sedirnents; the most abundant ice region king just below the permafrost table (Fortier et al. 199 1). It is therefore reasonabIe to assume that active layer consolidation at thawing is cyclicaiiy compensated by a srnali amount at freezing and that this factor cm be ornitted in modelling. This reasoning implies stable climatic conditions for a Long period; the situation would be dratnaticaiiy different in the case of climate warrning leading to tbaw penetration deeper in more ice-nch soil.

As the active layer thaws, free ground water in the thawed peat seeps downwards to the thawing front. A perched saturated layer foilows the thawing front downward and some water migrates dong the thermal gradient into the frozen Iayer, and in the permafrost underneath (Smith 1985; Mackay 1983; Cheng 1983). Obviously, in both the fkezing and thawi seasons, the principal mode of water migration is flow from the unfrozen or thawed zone to t fiozen zone through a fieezing fringe. The problem of downward water migration hm t thawing active Iayer is physicaily similar to that of upward water migration to the freezi~ front. Only the flow direction is different. In both cases, the water flow leads to the formatic of segregated ice.

Initial Condition

As reported in the Lterature (e.g. Seppiiia 1982; Mard et al. 1986, 1987), a palsa c;

start to grow in a permafrost fiee area of a bog or a fen when the snow cover is removed 1 reduced by some ecological or climatological process. This induces an abrupt change of gour surface thermal conditions. Mer the inception, the palsa top is kept nearly snow free durir the following winters as it makes a wind exposed topographie protuberance and permafrost a

keep aggrading at the site. The model therefore starts from an unfrozen site at the end 4 Autumn no 1. Peat depth is one meter over silt and the soil materials are water saturated. htii conditions are defined as:

Boundary Condition

The general present-day air temperature conditions are applied. A mean air ternperatu of -5.6"C and the annual temperature cycle integrating freezing and thawing indices is used t solicit the model. The model was run for 200 years keeping these climate conditions constan The top tirne-dependent boundary condition at i= 1 is given as:

T(l,t) = Dr, + f(t) where

Dt, = D, sin in cool season

Dt, = Dcn in warm season in cool season

Conside~gthe actuai depth of permafrost base at the reference site, 22.5 m, the initk temperature at that depth is set as positive. It then gradually drops with elapsed time unti reaching a steady state under the influences of applied clirnate and geothemal conditions. Th lower boundary conditions, at i=M. are defined as:

ei(M, t) = O

Soi2 material parameters

The soi1 thermal parameters used for mode1 computations are presented on table 5-1 These values are typical of such soi1 types (Williams and Smith 1989) and were computed fron laboratory analysis (water content, density of particles) using Kerstern's equauons (Goodricl l98îa).

The unfrozen water content is a temperaturedependent variable. The empirica relationship used in the modelling is:

B-R,(T-T,) Ts

O-R,(T-T,) Ts

I

Frozen \

-----Segregation freezrng front

- - - --Permafrost base ~nfrozenzone

bFq Frozen fringe Ts: Segregation freezing temperature

Figure 5.2. Location of the three frost (and thaw) fronts in a palsa system. Peat 300 76 1900 0.62 4.16~10-7 Clayey silt 1 2025 45 1930 1.92 0.000 1075 Clayey silt 2 2000 49 2080 1.9 0.000 1075 Water 1 O00 4180 0.6 Ice 917 1930 2.22 Table 5- 1 Soi1 physical and thermal properties used for model computations.

The constants are from Fortier (199I) who measured the unfrozen water content from the samples of permafrost in silty clays in northem Quebec and from laboratory experiments (Xu et al. 1985).

The SPo values used for silty cIay are the experimental results of Konrad and Morgenstern (1980) and Konrad (1988) for very similar soils (Leda clay). As proven by the near absence of ice layers, pure peat is not prone to segregation. For example, it is even used as anti-heave foundation fillings underneath some Scandinavian railways (Skaven-Hang 1959). On paIsas, the base of the peat cover may be mixed with silt producing a thin layer with an intermediate SP value, but this would constitute only a negIigible layer (5-10 cm) in the whole permafrost sequence (22.5 rn) and it cari therefore be neglected in the calculations.

Freezing and thawing fronts

At palsa inception in the first winter only one freezing front progresses downumd. During the first surnrncrr, a thaw front propagates from the surface. From the second winter on. a new frost front starts from the surface. These two frost fronts will be cyclically active near the surface while one frost front becomes permanent at the base of permafrost. The model has to consider these three levels of phase change conditions (Figure 5.2).

5.4 NUMERICAL COMPUTATION

In numerical computation of one-dimensional problems, the rnodelling can use a space- time gnd . Because of the nonlinear property of the partial differential equation (4-l), for the numerical calculation of the one-dimensional problems of phase-change temperature regime, the Prediction-Correction method can be used as following (Liu and An 1982; Yogesh and Torrance 1986; Feng 1986; An et al. 1987; An 1989): The frost heave hm, h,, dixrete ice content Bi and velocity of water intake VJ etc. can be solved with the method described in chapter 4.

5.5 NUMERICAL RESULTS

Figure 5.3 illustrates the evolution of the thermal profile as the permafrost base deepem in the palsa and as the ground surface is heaved up to 3 m above the original ground Level. The simulated therrnd profiles compare weii with measured thermal profiles, particularly frorn the flat peat plateau surface (Figure 5.1A).

For the first few years of growth, the thennai gradient is steep. It lowers a( aggradation takes place while the large annual fluctuations keep occurring in the upper 3 rn ol the profile. Under the assurned conditions of constant climatic conditions (-55°C MAAT.,nc snow cover) the mode1 shows fast permafrost aggradation with permafrost base reaching 2 nearequilibrium depth of 16- 18 rn in about 60 years. Thereafter aggradation at the base ot permafrost takes place at a slow pace. However,the mode1 suggests that about half of the total heave is achieved after six decades and that it wdl double in the foilowing 140 years due tc important ice formation near the base of the permafrost (Figure 5.4). Figure 5.3. Ev .oIution of the thermal profile with elapsed tirne during aggradation. A:winter situations, B: summer, C: selected surnmer and winter profiles. One is original ground surface; negative depths above surface represent heave.

-2 2 6 1O 14 18 22 Depth (m) Figure 5.4. Distribution and thickness of ice lenses dong a vertical profile after 200 yeafrom simulation. 5.5.2 ICE SEGREGATION CONDITIONS

With a negligible solute content, the only factor that can depress the freezing point 1 soil water is pressure. As the permafrost base progresses downward, overbwden pressu increases. Added to pore pressure at the freezing front, this results into an ice segregatic temperacure of about -O.1 "C at the depth of 10 m and -0.19°C at 20 m where frost penetratic reaches a quasi-stationary state.

Ice segregation is dependent also on soi1 material and water supply. Texture ar mineraiogy of the soil are important factors of thermal conductivity which is a component ( SP,. For instance an SP, of 3.78x.106 m2/hr."Callows permafrost aggradation to reach a dep of 17.8 m while an SP, of 1.29x1O6 would account for a permafrost base at 19.9 m under ti same long term clirnatic conditions (Figure 5.5). Water supply for ice lens formation comc from soil water contained within the volume of originally unfrozen soil and fiom ground watt below the freezing front that is sucked to the freezing fringe in an open flow system. Fc example, after simulating 200 years of aggradation and assuming that oniy the original sa water content is involved in ice lensing, the arnount of heave is only half in cornparison wil ice lens feeding from ground water flow from the surroundings (Figure 5.6). The difference : heave is greater at depths than near the surface, probably because frost penetration is fasti during the fust decades, thus using alrnost exclusively locdy available soil water. Whe greater depths are reached in the order of 15- 16 rn, the low thermal gradient and slow freezin rate favors the formation of thick ice lenses by drawing water from the surrounding terrai These numerous, thick and close-spaced ice layers near permafrost base should somewhi resemble massive ice seen in other contexts (Mackay 1992) or make thick icy soil layers.

Application of the mode1 shows that, although ice lensing takes place at aii deptk during the process of palsa growth, there shouId be more numerous and thicker ice layers nei permafrost base as well as a zone of ice enrichment just below permafrost table. The lattr results from downward water migration in the upper permafrost zone from the active laye Mode1 runs suggest that the presence or absence of thick ice layers below the permafrost tabl depends on peat thckness. If the peat cover is thicker than the active layer, then very little ic foms; if it is roughly equal, important ice lensing rnay take place dong the stratigraphi contact. If the peat cover is thinner than maximum thaw depth, then ice enrichment takes pIac in near surface permafrost. Ice lens enrichment is very important in silty cryogenic mounc where peat is absent as observed many times by drilling and by geophysical methods (Fortic 1991; Fortier et al. 1991; Pilon et al. 1992; Mard et al. 1996) and as shown by the modc (Figure 5.7). -3.1 0.1 3.3 6.5 9.7 13 16 19 Depth (rn) Figure 5.5. Growth of ice lenses and deepering of permafrost with tirnes (SP of 1.29 x 10*~).

E.;; 0.6 e U, 0.4

0.2

O O 2 4 6 8 10 12 14 16 18 20 Depth (m)

Figure 5.6. Differences in heave and ice lens thickness with depth depending weather only in situ water (A) is used in the process of if there is free succion of ground water I 8 12 Depth (m)

Figure 5.7. Ict lem distribution and thickness after a mode1 mn in absence of peat cover. Ice enrichment and severai thick ice lenses form in the upper layer of permafrost. 5.6 DISCUSSION

Application of our numericd mode1 shows that a new paisa can start to form and gro under the present climatic conditions provided that snow cover is locaiiy absent or significant reduced, a fact supported by the observations by numerous authors of incipient forms in tt actuai landscape of northern Quebec (Aiiard et al. 1986; Dionne and Seguin, 1992; Cummini and Poiiard, 1990; Seguin and Dionne, 1992). A palsa or a mound cm rise 3 m above tt surrounding terrain in roughly six decades. If conditions are maintained long enough, let's sa another 100 years or more, the paisa will continue to grow more siowly as a series of nea massive ice layers WU fom near the permafrost base. Somewhat different types of soi1 wj result in different mound height given the different segregation potentials (SP) iinked i different thermal properties.

At permafrost base beneath a palsa or a cryogenic mound, thermodynamics conditior are such that a quasi-stationary freezuig front is attained. The depth of 20 m obtained with th mode1 is in perfect agreement with permafrost depth at the reference site. It is aIso a dept generaliy found in over 200 surface electrical resistivity soundings in large paisas an cryogenic mounds in regions of Nunavik with the same range of air temperatures (Lévesque c al. 1988; Gahé et al. 1988) and characterized by the presence of comparabIe post-gIacii marine clayey silts. This generd order of depth for permafrost base was aiso found at a fe1 sites by hydraulic drilling and thermal measurements.

The clirnatic controI on palsas focuses on two penods of the year. in surnrner. th incorning solar radiation mets a Iow and bright vegemtion cover on fresh peat of Iow them conductivity, and much of incoming solar energy is consumed in surface evaporation which i turn, creates a strong temperature gradient. The drying of the peat surface further reduces il thermal conductivity. In mid-winter, thermal conductivity of frozen peat is high due to its hig ice content and increased buk density. The outgoing long-wave radiation involves considerable arnount of released heat. Dry peat is an excellent insulator, whereas wet peat is good conductor of heat. The dominance of winter thermal properties over those in summe ensures the negative heat balance over tirne, which is the extemai thermai condition for th repeated seasonal growth of the frost core. Thus, except for snow cover, the energy differenc between thermal absorption in summer season and release in winter season is very important t the formation of paIsas. The seasonai variations of peat water content and peat buk densit seriously condition the thermai properties of the peat layer. The abrupt and considerabl increase of thermal conductivity of freezing peat constitutes the ability of the frozen peat t( loose heat easiiy. Winter conditions have a major influence on the vertical growth of the pals sumrner conditions preserve the results for additional growth during the foilowing winters.

Applications of the mode1 confi a) the widely expressed view that cryosuctic within an open system is a major process involved in the growth of palsa and cryogen mounds (Pissart 1983) 6) the abrupt and considerable ciifference of thermal properties fi frozen and unfiozen peat plays a dominant role in inception, growth, and existence. Ti conditions of surface peat obviously play an essential and characteristic role in preserving tl frozen core of the palsa throughout the sumrner.

The presence of either a series or a single segregated thick ice layer near the base < permafrost has been verified by several authors frorn field coring and observations; but it alc needs to be further substantiated. The presence of such a series of ice layers was reported t Lagerback and Rodhe (1986) who cored throughout some permafrost mounds and by Akermz and Malmstrrom (1986). indication of the existence of such a layer was also found by Fortir et al. (1991) in a cryogenic mound near Umiujaq, Northem Quebec, using diagraph techniques of electrical resistivity (vertical dipole-dipole array) in a hole driiled through tI permafrost. More recently, a palsa which has begun to heave in around A.D. 1830 has bee reported by Sone and Takahashi (1993) in Japan. It was found with coring that the discrete ic lenses and layers developed mostly in underlying silt layers. The thickness of ice lenses variable dong the depth. the smaller ones king in the middie section; but the thicker ones ai in the Iower section near the base of permafrost where they developed into discrete thick ic layers which are almost pure. The author further interpreted that the ice layers are surel formed by ice segregation, because they are parallei to the freezing surface and alternate wii frozen siIt layers.

The formation of a palsa cannot take place in inorganic soils since peat cover is essentii in the thermodynamics on inception. It is a combination of properties and processes unique I organic soils. Palsa formation continues until the equilibrium of thermodynamics is reached ( until coliapsing takes place. However, with the exception of the peat thermodynamics, simili frost heave forms cryogenic mounds.

In its actual form, the mode1 does not explain the existence of palsas and cryogeni mounds higher (over 10 m) than the sirnulated height. An hypothetical explanation would t: that cold clirnatic periods provoke renewed aggradation at permafrost base and further heavc However, non climatic-induced dimensional changes in the iandfom geometcy could also tak place. For instance. it has been shown from thermal measurernents at a few sites (AUard et a 1986) that each mound has its own thermal regime that depends on slopes, vegetation cov and snow distribution on the sides and the tops (such as in Figures 5.1 A, B and C). So, smd feature with only a small surface area outcropping out of the snow cover rnay corne clo, to stabilization for some years whence a few dry winters can change the thermodynam conditions and initiate a new period of ice segregation at permafrost base, eventually leading the formation of more ice rich layers deeper and fùrther growth.

It has aiso ken shown that some palsa fields result fiom the partial melting a~ sectioning of larger peat plateaus by themokarst during periods of chnate warming (Lagan 1982; Ailard and Seguin 1987; Laprise and Payette 1988; Dionne and Seguin 1992; Seguin ar Dionne 1992). Basal thermodynamic conditions in those survival landforms would be changc under a new chtic cooling period. Again, this could reflect in ice layer stratigraphy ne permafrost base.

5.7 SUMMARY

1) The mathematical modelling presented in the chapter simulates the formation r paisas and similar permafrost mounds and other similar perigiacial landforms. It can be use for the numencal study of the effects of clirnate change. alterations of ground surface covei and other reievant conditions in the permafrost environment.

2) Palsas are not only the products of paleoclimatic conditions. They also form undt present clirnatic conditions.

3) The phenomenon of discrete ice lensing forming in the frost susceptible miner; materials underlying the peat is responsible for the frost heave of the palsas. The segregatia potential and saturated upward migrating moisture are dorninantly responsible for the amoui of heave of palsas.

4) Cornparison of the numencal results of the ground temperature profdes an distribution of the discrete ice lenses in the palsas with field data shows a generally goo correspondance.

5) The numerical simulation of palsa formation over 200 years shows that the discrei ice lensing makes smaii lenses, less than 2.0 cm from the top to the middle section of th palsas, but develops thick ice layers and forms a accumulation band of discrete thick ice Iayei in the lower section of the palsa core. 6) Besides a reduced snow cover, the differences of thermal properties between d unfrozen and saturatedfi-ozenpeat are criticai for palsa inception.

7) If the peat cover is thinner than the active layer, then thick lenses wiU form Mo permafrost table in fuie-grained soils. This aspect WUbe Merconsidered in the followir chapters. Chapter VI

INFLUENCE OF CLIMATE COOLING ON PALSAS

6.1 INTRODUCTION

Over the last three decades, many evidences from geothermal measurements, rneteorological observations and geomorphoiogical investigations have shown climatic trend towards cooling over Arctic and Subarctic regions of eastern Canada. This cbtechange is contrary to the trends observed elsewhere in northern regions and is aiso contrary to the climate warming scenario of most atmospheric rnodels. It is not known if this trend wiil rernain so in the future because of the impact of greenhouse gases and other man's activity on climate (PCC) (Houghton et al. 1990).

It is noted ihat a rnarked downturn in temperatures has ken in progress in eastern Canada since 1955 and it has ken speculated that it will be repeated in subsequent years (Hare and Thomas 1974). Interestingly, frorn 1980 to 1992, the mean annuai air temperature coded from -4.4"C to -67°C in Kangiqsualujuaq, which is Our reference site for this mode1 application. h the extreme north of Quebec, this recent cooling has produced permafrost aggradation and ice wedge growth (Allard et al. 1993; Kasper, 1996).

Also, despite the fact that paisas can grow under the present prevailing climate, paleoecologicai information suggest that they are more likely to be initiated and to grow in colder climatic periods (Aliard and Seguin, 1987; Couiliard and Payene, 1982). The main objective of this chapter is to present a fundamentai mode1 descrîbing t impact of periodic steadyltransient climate oscillations on paisa formation. The comput predictive results suggest that periodic chate fluctuations in the process of climate cooling i an important extemai control on the formation of the ice layers during permafrost aggradatic whiie the segregation potential, internai heat flux and soii properties are the internai conu factors in open ground water systems. This significant finding is of fundamental interest sin it leads us to interpret that 1) given senal sequences of ice lenses in palsas and cryoger mounds are the resuIt of heat and mass balance at the base of the growing ice Lenses; 2) li rhythmic sediment cores, geological deposits and tree rings, these ice Iayers could eventual be used as proxy information on past climatic cooling periods reflected in the paisa formatii and aggradation. Applications of the mode1 and the computation resuits wili help to understa how palsas, cryogenic mounds and other sirnilar permafrost landforms respond to past ai recent climate changes.

6.1.1 BACKGROUND

Ground ice forms in nature an important component of permafrost in sediments ai plays a major roie in the growth and decay of periglacial landforms and in the stability engineering structures in Arctic and Subarctic environments. Ice Iensing and frost heave periglacial processes have received considerable attention in the literarure over many decade but most of our knowledge of this type of ice in palsas still derives from field investigatio: (Seppda 1982; AlIard et al. 1986; Dionne 1984; Dionne and Seguin 1992).

Ice-enriched zones are frequently encountered in permafrost. In extreme cases. ii e~~hInentmay approach 100% by volume and the thickness reaches over many meter especially in horizontal layers (Poiiard and French 1980; Outcdt 1982).

The presence of either a series or a single chick segregated ice layer near the base 1 permafrost in paisas and cryogenic mounds was reported by Lagerback and Rodhe (198 1986) from corings throughout permafrost in one mound in northernrnost Sweden. hem; and Malmstrrom (1986) made similar observations in the area around Abisko and Bjorklide Northern Sweden. Conng to depths of 5-6 meters was done by Fortier (in press) and Allard al. (1989) in Northern Quebec; these works revealed that segregated ice is more abunda below permafrost table and near permafrost base but decreases in the middle section of tl frozen core after 2-3 meters. 6.1.2 REGIONAL CLIMATE COOLING In the context of the general clirnatic tenkncy in northeastern Canada hmthe 1950' to the early 19901s,reference conditions for climate cooling used as reference for the modeilin; exercise are those obsemed in the region of Kangiqsualujjuaq (6S057'W,58"40'N) ani Kuujjuaq, Northern Quebec, in the discontinuous permafrost zone at the northern limit of th1 tree-line. The organic cover and soi1 system conditions in the model are the same as th conditions which are used for one-dimensionai mathematicai modehg of palsa formation ii chapter 5.

Since paisas can form under the actuai chmatic regime, it shdi be evident that coohj under these conditions Ieads to permafrost aggradation and mound growth. Over the decadc 1980-90 the mean annual air temperature graduaiiy dropped from -4.4"C to -6.792. One of thc questions that can be asked is what the effects of the cooling on the paisas are, and what effec should this trend have on ice lens formation and distribution in the permafrost within paisas.

6.2 SYNOPSIS OF MODELLING

The unidimensional mode1 designed for simulating palsa formation was aiso used tc test the impact of chate cooling on ice lense distribution in the stratigraphie colunm belov

palsas and growth of paisas. The climatic scenario proposed is one of transient cooling for i few years between stable climatic periods.

6.2.1 INITIAL CONDITION This scenario was preferred to others, such as continuous cooling or warniing-cool in^ oscillations because our main objective is to explain growth processes of paisas and thei resulting cryogenic structures. Pulsations and decay of paIsas WU necessitate furthel modelling, including mechanical failures, slumping and so on which are beyond the scope oi this thesis.

6.2.2 BOUNDARY CONDITION As the application of the model attempts to sirnulate the effects of climate cooling on thr palsa system. two types of ciimate cooling processes with periodic aiternations of steady anc transient climate states were considered. The climatic scenaio used at fmt is: a period oi steady conditions followed by a transient coohg period and, then, another period of steadj climate. We caii it "one step chate cooling" in which a variation of the mean annual ai temperature (MAAT) changes hma steady clirnate state at -4.4'C1 to another steady state a 6.7"C. through a transient period. Ln total the duration spans 275 years.

The second scenario used is caiIed "multiple steps" climate cwling process, in whi, the ciimate cwhg has the sanie pattern as the one step but with three steady states and t~ transient cooiing states aiternateIy. The MAAT changes fiom the steady clùnate states, -4.2'1 to -5.3"C and then to -6.7'C1 two other steady states, also through two transient statr eiapsing a total of 290 years. SimilarIy, the relevant annual temperature cycle integrati freezing and thawing indices is used to solicit the rnodel. The rnodel was run for these tv types of clirnate change conditions to study the responses of palsa systerns.

The upper time-dependent boundary condition can be given as:

T(1,t) = Dr, + f (t) where Dt, = D, sin [n- c J + Dr,

8,(1, t)= 9, are for the cool season, and Dt, = D, f (t)= A, sin [x -

Oi(1, t)= O for the warm season. in the steady chtestate. the coefficients, A,, A,, t,, t, are constant, Ac[, A, t,, , twslbut in the transient climate state, these can be given as:

- LU- *mr - tes (6-1 in equation (6-7) and (6-8), the subscript k is equal to 1 for the one step clirnate cooh process; and equd to 1 and 2 for multiple step chnate cooling process corresponding to t~ transient States.

Lower boundary condition Considering the actual depth of permafrost base at the reference site, 22.5 m, the initi temperature at that depth is set as positive. It then gradually drops with elapsed time uni reaching a steady state under the influences of each applied periodic clirnate cooling ar geothemd conditions. The Iower boundary conditions, at i=M, is defined as:

6.2.3 SOIL MATEIUAL AND THERMAL PARAMETERS

The unfrozen water contents employed are the same as in chapter 5, as following:

for clay silt 1 O-R,(T-T,) T,

The soii thermal parameters and SP values used for mdel computations are presentt on table 5- 1.

6.3 THICK SEGREGATED ICE LAYERS

The an annud air temperature (MAAT) at the reference site over the decade (198( 1990) endured an important cooling of -2.3"C. from -4.4'C to -6.7'C. In 1955 the MAAT Ungava Bay (Kuujjuaq) was about -4.1 "Cand since the 1950s. the climate in these regions h; been cooling continually (Hare and Thomas 1974, Aliard et al. 1995). We used this rate ( climate cooling for simulating the impact of ciimate cooiing on pdsa formation. Further, it necessary for us to consider that the drop of the MAAT is linear in the cooüng penod fc simplification because of the fact that the seasonal rhythm and annual ciimate cycIes do nc occur in the sarne patterns and are rather unpredictable. Sorne summers may lx hotter tha others while one winter may be colder than others; dunng one rnonth the wind frequency ma be high and the air dry but during the sarne month of the following year winds may be cali and precipitation more abundant. The climate fluctuation in each year in the clirnate cooiin period as witnessed can be treated by the smooth seasonal cycle in such phenomena as the a temperature distribution over the reference regions. The whoie ciifference of the MAX -2.3"Ccan be divided into a mean annual increment, for instance, -0.06556"C/year in 35 year

6.3.1 EFFECTS OF CLIMATE COOLING ON ICE LENSING The variable duration of climatic periods and the thermal dynamics of climate coolin are the principal factors which regulate distribution of discrete ice Ienses or segregated ice bed in the palsas.

The periodic climate fluctuation, due to the alternation of steady and transient chme coolin1 dominates the tirnedependent temperature boundary conditions (TBC) of the palsa syster conditioned by MAAT. Such periodic oscillations of the TBC restrict the responses of th palsa system by controlling the interaction of al1 the components involved. The effects ar mainly shown through ice lens growth and location, temperature profile, frost heave and fro: penetration. One step climate cooling Either a steady chteperd or a transient climate cooling pend can maintain itseif fc decades or hundreds years. It is supposed that the effect of the one step climate cooling proce5 is one possible illustration of nahuai variability covering 275 years, in which the cliraai condition undergoes three periods: first, O to 185 years, a steady ciimate period with MAX 44°C; second, covering 186 to 220 years, a transient climate cooling period with PvlAAT fror -4.4 to -6.7"C. then the last steady one elapsing 45 years unrii year 275 at MAAT -6.7"( (Figure 6.1). For the discussion, the numericai tests were run with the SP equai to 3.87~10 M% 'C

The first steady climate period, 0-185 years and MAAT -4.4"C. provides thermc dynamic conditions for permafrost formation with ice lens segregation in the paisa. These fm 185 years of steady climate period can be divided into two intervals defmed by the rate of ic lensing dong the palsa depth. In the fmt interval, the themal gradient is relatively steeF especiaily during the few beginning years; then it lowers gradualiy with permafros aggradation. The frozen core of the palsa advances down following a relatively high rate o frost penetration accompanied by slow ice lens growth untii it reaches about 9.5 m in deptk The mean thickness of ice Ienses is less than 1.6 cm at this depth. The arnount of frost heavl whch results from the palsa growth is contributed dominantly from original pore water phase change and relatively Iittie water migration. The second interval from the depth of 9.5 to 14.1 rn shows that the frost front maintains a very slow penetration rate. In order to keep energy ani mass balances, the lower advancement of frost penetration is compensated by ice lensing whicl grows gradually into segregated ice beds covering the spatiai interval between 10.3 and 14.: m. In the first steady climate period, the paisa grows to a height of 3.0 m, and the maximun ice lens size is about 5.5 cm thick near permafrost base (Figure 6.2A).

Over the following thirty five years of transient cooling period, the MAAT decrease from -4.4 to -6.7"C. The frost front at the base of permafrost, which was quasi stationary a the end of the first steady period, advances again at a rnuch faster speed breaking througl suction obstruction of the water migration. This relative fast advancement of the frost fron results in growth of thin discrete ice lenses. The state of intemal variabihty of the palsa systen will change until it again reaches a new balance of the energy and mas. In response to such , gradual cooling occumng over 35 years, the thickness of ice leasing varies sharply from 5.: cm at the end of first steady period to nearly 2.0 cm and then grow slowly, the maximum O which is only about 2.4 cm thlck. Because of limitation of the water migration, the paisa growi by about 40 cm reaching 3.4 m height in 35 years. (Figure 6.2B). j 4- - -

I 1 50 1O0 150 200 250 300 ELAPSE TIME, years

Figure 6.1. Scenario for the one step climate cooling for mode1 test. formed

Figure 6.2b. Growth of the simulated palsa of figure 6.2a and ice lem thicknes and distribution after 35 years of cooling.

- DEPTH (m) Figure 4.2~. Renewed formation of thick ice ienses at permafrost base during the steady pend following cooling. The third period, another relatively much colder but steady clirna'e period. has a MAA' -6.7-C over fifty years. Such chaie condition provokes the ice lenses to grow further an' increase in thickness. The longer the period, the thicker the discrete ice lenses grow and th more the frost heave deveIops und attaining equilibrium or changing to some other climat condition in the palsa system. In the 1ststeady climate period, the segregated ice beds increas significantly and the maximum thickness is about 11.0 cm. The vertical interval between lense is about 0.45 m. The palsa grows 70 cm higher and reaches a height of 4.1 m. However, th frozen core penetrates Iess than I .O m, the frost heave is dorninantly derived fiom the wate migration in the open system (Figure 6.2C).

Further comparing the distribution of segregated ice in palsa with different chmi periods, it cm be seen that, obviously, steady chmate conditions favor thick ice Iensing as th1 frost penetration reaches a quasi stationary state, whereas transient climate cooling is favorabll to frost penetration (Figure 6.3) and formation of thin interspersed lenses.

The temperature profiles of the palsa (Figure 6.4A and 6.4B. Surnrner and Winter show that the ground temperatures decrease periodicaily with the periodic climate cooling. Thi large annual fluctuations remain in the upper 4.5 m of the profiles.

Multiple steps climate cooling

Climate cooling usually displays multiple periodic changes in dternatively steady anc transient periods. How the palsa system responds to this type of climate cooling in the proces: of palsa formation? Another example has been numerically simulated with two transient climatc cooling penods inlaid between three steady clirnate periods. 1t experiences the MAAT 4.2X to -5.4'C and then to -6.7"C in two periods of cooling. Beginning with a steady climate state 150 years elapse keeping the MAAT at -4.2"C; the following period is a transient cooliq period covering thirty-five years and changing the MAAT from -4.2 to -5.4"C, the secont steady climate penod passes from 186 to 220 years with the MAAT at -54°C;afler this stead! period, the climate changes to cooling again and covers another thirty-five years period tiii 25' years with the MAAT cooling from -5.4 to -6.7"C; the third steady climate period goes unti year 290 with the MAAT at -6.7"C(Figure 6.5).

The computed results, aiso with SP, equal to 3.87 x 10'~rn2/h.'~, show that there an three different size of thick stratified segregated ice layerske beds formed dong a vertica profile in the palsa; they correspond to the three steady clirnate periods, respectively. Fo instance, the fmt one is corresponding to fmt steady clirnate period, 0- 150 years with MAAl -4.20C; and then the second and the third. Two intervals of thin ice lensing arnong the thret 5 1O DEPTH (ml

Figure 6.3. Time progressive graph of ice Iense formation, thickness and distribution in the one step cooljng scenario. DEPTH (m)

S 10 DEPTH (m)

Figure 6.4. Evolution of the temperature profile in the one step cooling scenario for (A) sumrner situation and (B) winter situation. O - -1 - -2

' -3

-5 1

.\ -6 - - \ -7 1 1 50 100 150 200 250 300 ELAPSE TIME, years

Figure 6.5. Scenario for the two steps climate cooling used in the second simulation. thick segregated ice iayers are responses of two transient cooling periods, in which the releva MAAT in the fmt cooling drops from -4.2 to -5.4'C and from -5.4 to -6.7"C, respective1 Figure 6.6A to 6.6E show the ice Iens distribution, in different periods. Figure 6.7A and 6.7 show the evolution of ground temperature profiles correspondhg to the altemately steady ar transient ciimaie States. It can be seen that as both transient cooling penods are of the san duration, 35 years, the advancement of fiost penetration for the pend 150 to 185 year is aboi two times larger than for the 22 1 to 255 year period. Ice lensing is about 2.0 cm in the la transient period, that is nearly half the thickness of the ice layers of the fmt cooling perioc The thickest segregated ice bed is about 18.8 cm thick and is the response to the second steadq climate period.

The rnodeiiing results of ice Iensing distribution in one step and multiple step climat cooling processes mentioned above clearly suggest that the segregated ice layers dong th entire palsa depth have an intermittent pattern distribution. Thin ice lenses inlay betwee. thicker ice layers. The formation of these ice layers in the climate cooling process depend upon the duration of the coolhg period and heat flux intensity of each steady climate perioc affecting on the boundaries of the palsas. The mode1 suggests that: a) if the geologica conditions and physical and chernical properties of the soils and other components are uniform the external thermodynamics in each steady climate condition is the principai control fo formation of ice layers. Surface ciimate controls the rhythrns of the intervals of both thicl segregated ice layers and thin ice lenses. b) frost heave is contributed from both original port water phase-change and water migration in soils, but the contribution of the water migratior plays the major part in the formation of the palsa, particularly as it feeds thick ice layers durini climaticaiiy stable pzriods.

6.3.2 INFLUENCE OF SEGREGATION POTENTIAL (SP) Besides the impact of climate variations, Segregation Potential is one of the main factors for ice lensing in the palsas. It is weii known that SP is primanly dependent on the thermal gradient and the suction gradient of soi1 materials and water supply conditions. Texture and rnineralogy of the soi1 are important factors of thermal conductivity and perrneability which are the components of the SP. 0 5 10 DEPÏH (m)

-5 O 5 10 15 20 DEPTH (m)

$ 0.08 ui 3 0.06 g 0.w C 0.02 a DEPTH (m)

DEPTH (m)

-5 0.14 b O." ", 0.1 z 0.08 g 0.w f "G4 0.02 O

DEPTH (m)

Figure 6.6. Distribution and thickness of ice Ienses in paisa with climate cooling (A) 15 1th year, (B) 185th year, (C)220th year, 0)255th year, (E)290th year. DEPTH (m)

- 290th Yr. W - - - 185th Yr. W - - 255th Yr. W - - - - 15tthYr.W ...... 220th Yr. W

Figure 6.7. Evolution of temperature profiles in the palsa under the two-steps cooling scenario. (A) summer profdes, (B)winter profiles. Figure 6.8 and figure 6.9 show other distributions of segregated ice lenses in the pals in the one step steady-transient chmate cooling as the SP, equals to 2.58~10-~and 1.29~10 m2/hr/hr'C,respectively. Figure 6.10 gives the results in the multiple step chme cooh conditions as the SP, equais to 1.29~10"to m2/hr0~.The latter would apply, for example, t tighter compacted silty clay soils in the palsas.

Comparing resulu in Figure 6.6A-6E, 6.8, 6.9, and 6.10 with different values of th SP,, it is evident thaî the magnitude of SP, dominates the size of the segregated ice lenses an therefore the height of the palsa. When SP, equals 3.78x104, the maximum ice lem is 18.8 a thick and the palsa height reaches 4.5 m (Figure 6.6A-6E); with SP, equal to 1.29~10-~,tfI maximum ice lens is only 7.0 cm thick and the palsa height is restricted to 2.2 rn (Figure 6-10; The Segregation Potential expresses the frost-susceptibility of the soil. The larger the SP, th thicker the discrete ice lens growth and the higher the palsa. On the other hand, if segregatio: potentid is small, water migration will be so little in situ, even under favorable climate con ditions, that oniy thin ice lenses wiU fom. The results are iow palsas and cryogenic moundc However the sequences of thicker and thinner ice lenses in the lower permafrost have the saml pattern.

6.3.3 INFLUENCE OF THE PEAT LAYER Generaily, it is found that ice enrichment exists just below the permafrost table (Macka: 1971, 1983; Rampton and Mackay 1971). The downward migration from the perched wate table in the thawing active layer into permafrost is a fundamental water transfer mechanism fo thick ground ice segrqation when the thaw penetration of the active layer reaches a quas stationary state. But no ice lens fonns in frozen pure peat. When the peat cover is less thm O roughly equd to active layer depth, ground ice accumulates in the frost-susceptible silt near th permafrost table or takes place just dong the stratigraphie contact (Figure 6.6A-6E), otherwise only a smaii arnount of ice is present close to the permafrost table (Figure 6.9 and Figurc 6.10). Similarly, thick ground ice is a significant phenomenon in silty cryogenic mound! where peat is absent as obsewed by drilling and by geophysicd methods (Fortier et al. ir press; Fortier et al. 199 1; Pilon et al. 1992; Allard et al. 1996).

In the study of the influence of climate cooling on palsa formation, palsa responses tc steady state climate condition are called "equilibrium response" studies, and studies of transien clirnate change, climate cooling or ciimate warming, due to a tirnedependent altering of therma dynamics are calied "transient response" studies. In the case of climate variations witl 0.25 S P=2.58 E-6

h 0.2 YE Lu 2 L 0.15 O rn V3 Lu 0.1 Z Y 52 I 0.05 l-

O

DEPTH (m)

Figure 6.8. Ice lens thickness and distribution following the one-step cooling scenario with an SP value of 2.58 x lu6. -5 O 5 1O 15 20 DEPTH (m)

Figure 6.9. Ice lem thickness and distribution folIowing the one-step cooling scenario with an SP value of 1.29 x 10-~.

V) O 0.03 Y 2 0.02 I 0.01

O DEPTH (m)

Figure 6.10. Ice Iens thickness and distribution foiiowing the two-step cooling scenario with an SP value of 1.29 x 10~~,corn~anto figure 6.6 aiternately steady and transient cha& cooling periods or multiple steady-transient-stead states, the response of the palsa system to such chate variations could be caüed "equilibriwr transient-equilibrium" response and the corresponding process of segregated ice bed growt could be caiied "intermittent pattern" process. The evident interrnittent spacing of segregate ice lenses in the paisas deduced fiom the modehg indicates that our understanding of th modelling results and degree of confidence are determined from the recurring cyclic heat an water transfer during the palsa aggradation conditioned by the ciimate change and soil an water properties. The spacing of thick ice Iayers and thin ice lenses dong the vertical profil are the proxy records for the process and intensity of climate variations in steady and transie1 states. Such a proxy record, like other relevant information fiom tree rings, sediment core! geologicai deposits cou1d heIp us in the study of past climates. The field evidence an theoretical understanding of climate changes suggest that we are indeed deaiing, in the pais; with a somewhat predictable system, at least on time scales of centuries.

6.4 SUMMARY

The theoreticai understanding of the modelling results suggests that in the Subarcti discontinuous permafrost regions, the genesis of intermittent intervais of thick segregated ic layers and ice lenses in palsas and in cryogenic mounds can be attributed to the response of th frost-susceptible soil system to the climate cooling process in the permafrost formation an1 aggradation. The intervals consisting of thick segregated ice layers can be the response ti relative steady climate periods, whiie the intervals composed of the thin ice lenses inlai between the thick ones can be the response to transient climate cooling periods. Th1 segregation potential of soils and water supply conditions are also major factors for th1 magnitude and range of the thick segregated ice layers in the palsas corresponding to climat1 cooling process. Ice Iens thickness and distribution dong cores across palsas and cryogenil mounds could eventuaiiy be used as a proxy record of "equilibnum-transient-equilibrium thermal dynamics reflecting climate variations.

Combining terrain studies, particularly by drilling cores through paisas, with thi mathematicai modelling wiil help us to understand how permafrost in the subarctic and alpin1 regions has responded to past and ment climatP. variations and aiso to study the impact O palcoclimates on the palsas, cryogenic mounds and other sirnilar permafrost features in th1 periglacial environment. Chapter VI1

A TWO-DIMENSIONAL MODEL FOR THE ORIGIN OF PALSAS

7.1 BACKGROUND

Among the several hypotheses for the origin of palsas. the most agreed upon theory is the original one by Fries and Bergstrtim which was further studied and confirmed by Seppala (1982, 1986) and Allard et al. (1986). In this explanation, the insulating properties of the seasonai snow cover and the peat layer have been emphasized.

The only field experiment of palsa formation was done by Seppala (1982) who deliberately removed snow cover frorn a peat bog surface during three winters; a 36 cm height palsa formed. Similarly, the influence of snow drifthg on peat plateaus and palsas was fûrther identified by Seppala (1986) and Mard et al. (1986). That wind carries the snow away from the exposed surface but accumulates the thick snow bodies in surrounding areas provokes inception of palsas. Summariung the field experiments, Seppiild (1986) indicated that the insulating snow cover, the low winter temperature, together with the water-saturated medium are the main factors for starting the cyclic palsa evolution. However, many questions still remah to be answered about exactly how these major factors affect the origin of palsas. How do a series of discrete ice lenses form and how ground temperature regime varies? What is the interaction between therrnodynamics and mass redistribution in the soi1 system under recurring freeze-thaw cycles? Figure 7.1 Pictures of palsas with seasonal snow cover. (A) Aenal view and (B) view from the ground; snow accumulation on slopes. (Sheldrake River region. March 1983) Snow has been studied for many decades. An abundant literature deals with tl physical properties of snow and defines reIevant parameters; some works are on the sno. temperature profües and on the influence of snow cover on the ground temperature in freezin soils (Yen 1962; Kojima 1966; Goodrich 1982). Snow melting is a very compIex process i natural conditions and the literature is more concentratexi on thermal regirne and solar radiatic (Wiscombe and Warren 1980; Modand et aL 1990; Yen et al. 1991). A few reports have bee presented on energy and mass balance in snow melting, whith tirne scales of a few daj (Jordan et al. 1989; 199 1).

The problems of frost heave and ice lensing in freezing soils have been successfuU studied in the laboratory, mainly for engineering purposes (Konrad and 1Morgenstern 198. Penner 1986; Karuo Takeda and Yoshisuke Nakano 1990). Sirnilarly, very few theoretici work considered frost heave in field conditions (Nixon 1982, 1992; Konrad and Morgenster 1984; An et al. 1987). A uni-dimensionai modelling approach describes the palsa formatio with snow free and steady chatic conditions (An and Allard, 1995; this thesis, chapter 5: However, mechanistic studies of the effects of insulating snow cover on the orïgin of palsa! discrete ice lensing, with attempts of mathematicai modelling are still lacking.

The uni-dimensional mode[ in chapter 5 presents a sirnplified situation of palsa growt by simulating what takes place below the center of the mound, therefore providing insights t the centrai processes of palsa inception and growth. However, as palsas fonn under patches c snow free wetlands the newly formed mounds main drifting snow around them, which make complex heat exchange conditions around the sides, therefore leading to peculiar conditions fc ice layering. in pdsa systerns the spatid transitions frorn "snow-free permafrost mound" t "permafrost free snow covered flat tenain" are very abrupt. with near vertical contact! Therefore attempting two-dimensionai modeIIhg shall provide further interesthg insights t palsa development.

This chapter mainly presents a two-dimensionai theoreticai model to descnbe the origi of palsas under the influence of seasonal snow drift. Reference climatic and geomorphologi data are the same as in previous chapters. Our model provides the fmt simulation of the effect of neighbouring seasonai snow cover and snow free surface conditions on the ground them regime, ice segregation and frost heave in the process of palsa inception. With a numericl simulation in saturated open system elapsing six years of recurring freeze-thaw cycles. a sma incipient palsa, 49.8 cm high, is forecasted. THE MODEL

The mode1 describes phase-change ground temperature profiles, build-up of discrete ice-lem, and frost heave in a cross-section of the soil system. The.problems are affected by 1, seasonally snow-covered and snow free ground conditions side by side (Figure 7.2), 2, seasonal variations of water content in the peat, and 3) narural climaric conditions in the saturated open system. The simulation involves a) snow accumulation, compaction. densification, vapor diffusion, snowpack melt and water infdtration; b) seasonal and spatial variations of water contents in both peat and soil, transport of liquid water and water vapor; c) solar radiation on aidsnow and aidpeat interfaces, boundary temperature fluctuations, heat and mass transfer, thermal diffusion as well as geothemai conditions.

Obviously, some assumptions and ~imp~cationsare necessary for the simulation of two-dimensional problems elapsing many recurring freeze-thaw cycles: Darcy's law applies to snow, peat and both frozen and unfrozen soils which are considered as isotropic, homogeneously Iayered and saturated. Soi1 particles and water are incompressible, and locdy, fluid and solid temperatures are equd during freezing and thawing. Moisture transport in the snow cover, frozen and unfrozen soils occurs only in the liquid phase and difisive dispersal fluxes of both the water and the gas masses cm be neglected. Snow density is only function of the snow overburden. The effects of chernicai components are negligible and the thickness of the unfrozen peat cover remains constant during formation of the palsa.

7.2.1 CHARACTERISTICS OF SNOW AND PEAT AT THE SIMULATED SITE

7.2.1.1 Seasonal snow cover

Like soils, snow is a porous medium which is characterized by a rnix of solid particles and voids (pore, channel). The void space is completeiy occupied by air, liquid water and mobile ice layers. Being different from particles of mineral soils, snow grains cari grow or melt with heat diffusion or absorption at the normal pressure. The seasonal snow cover is impacted by thermal conduction, solar radiation, difisive evaporation, and water flow during freezethaw cycles. Snow accumulation

Through the winter season, both accumulation and compaction generally characteria snow cover. The compaction results &y from the accumulation and results in mou densifkation.

After snow has falien, on the average, density increases at a rate of about 1% per hou] up to at least an order of magnitude pater after intense snowfaüs of soft snow. Undei blizzard conditions with winds over 17 mk, it was found that the density of new snou increased from 45 to 230 kg/m3 within a 24-hour period (Anderson 1976; MeUor 1977) Generaiiy, after the initial settling stage, densification proceeds at a slow rate, which is largelj determined by the snow load or overburden. The weight of overlying snow results in 2 further, more sustained, compaction of snow cover. Stress from the overburden leads to an increase rate of bond growth which in tum results in a denser snowpack (Colbeck 1972. 1983a).

Without taking into account the effects of winds, Anderson has studied grain growth due to vapor movement and densification from snow fall. His results showed good agreerneni between theory and measurement. Snow densification due to wind compaction is stiii a problem for further study (Jordan 199I), and it does play a role in paisa fields as observed many times in northern Qu6bec.

At the field site, snow accumulation does not result directly from snowfall but is rather dependent on wind drifting. The strong winds carry snow away from the exposed peat fens where pdsas and peat plateaus are developed and accumulate it at the adjacent sides and in shelters where winds are slow (Ailard et al. 1986). After snow reaches a certain height, snowpack thickening slows down and eventually cornes to an end as "topographic saturation" is reached and the excess snow is blown further away (Payette et al. 1972).

The cold temperature, low sublimation and wind drift in winter result in dry snow accumulations. The densification is considered to result mainly from snow overburden, although wind densification is operant dso.

Based on some observations of snow accumulation in northern Quek (Roche 1994), it is assumed in the mode1 that the beginning of snow accumulating is on day 262 (end of September), when the daily air temperature is about -2.4"C. Accumulation continues at a rate set by a natural logarithmic function until day 105 (early April), when a maximum depth of 1.30 rn is reached. The emprcal function of snow accumulation considering the snc compaction cm be written as:

Snow melt

Snow melting is dependent upon many major factors: solar radiation, them conduction, vapor diffusion and water infiltration. Usually, as melt water infilmtes throu the snowpack, capillary forces within snow are 2-3 orders of magnitude less than those gravity as air is at atmospheric pressure (Colbeck 1972), and similady, the inertial, convecti and phase-change terrns are srnall (Morris 1987); the mass water fiow in saturated dry snow a gravity-dependent function and cm be expressed as:

where kW,.hydraulic permeability, is an approximation (Shimizu 1970); p, is the Dynan viscosity of water at OcC(1 -787x10" N slm'); d, the diameter of snow grains (m)

The melting Iayer is a saturated mixture of water and snow. If we further assume tt an infilvating zone is saturated and if the grain size and the porosity of the snowpack are ke constant, then omitting the effects of occasional rain, the mass water flux can be found fro the thickness of melted snow.

In the melting period, water infiitrates through the snowpack. It transfers heat till local thermal regime reaches equilibrium. On the other hand, the percolating water erod original snow grains and structures and even fom some cavities and channels in t snowpack. The process gives way to increases of temgerature and porosity, decrease density and, finally. Ioss of snow mass until d snow has disappeared.

Snow melt is rather complicated and so far there is no adequate mode1 for it. Despi this dficulty, we cm stiii assume that snow is a continuously porous material whose densi varies following accumulation and melting. The thermai properties are mainly dependent ( the idair ratio and the density (Goodrich 1982; Jordan 1991). For simplification of ti problem, it is assumed here that snow density is a linear function of snow thickness. Tl empiricai expression of the snow density can be given as:

7.2.1.2 The Peat layer

As it is discussed in above chapters, peat cover plays a major role in the origin 1 paisas. Its properties and thickness generally depends upon Quaternary geology. vegetatic history, climate and drainage history and water content.

At the study, site. even though the peat overIying the mineral sediments is relative thin (les than 1 m), it is noticed that the ground surface on the complex of peat plateaus reiativeiy flat, and the thickness of the peat layer is rather uniform. However, for palsa especiaiiy high palsas, the thickness of peat varies from a few centimetres at the top to over 2. m in slope hollows, and average thickness is of about 1.0 m. Generaily, at the beginning pdsa formation, both height and dope of the inceptive paisa are small, and furthemore, ti peat surface is covered by vegetation, the peat layer is then rather stable and its thicknei almost uniform. For the simplification of the computation in two-dimensional problen beiow, it is assumed the thickness of the peat during palsa inception maintains constant in ti cross-section.

It is well known that high porosity, permeability and non-surface energy are the ma physical properties of peat. Owing to influences of snow rnelting and ground surface watc supply at the field reference site, the water content near the surface in the cross-section is qui different during the fmt surnrner compared to the foilowing summers. When sumrner begin horizontaily, at the portion of the snow cover, the incoming of solar energy is consumed fc increasing the temperature of the snow cover, for snow surface evaporation and snow meltin; meanwhile, much of the solar energy income at the portion of the snow free peat surface used for moisture evaporation and drying of the peat. The phenornenon continues until tk snow cover is aU melted. Therefore, at the top surface, the variations of water content boi beneath the snow cover portion and beneath the snow free peat surface are not simultaneou On the other hand, the lower boundary of the peat layer, above the marine sediments, reasonably assumed in a saturation state. After the auturnn, foiiowing precipitations, littlm evaporation and ground surface freezing, the peat is neaily saturated. This conditior maintained the beginning of the following summer. The water content is, therefore, functic of the season and deptb in recurring annual cycles. The fluctuation of the water content in tl peat layer can be expressed as the formula in time and space as foliows:

Over the annual cycle, water content is:

[Op - ('p - 'O)(' - 'db ) '(tyto - 'Ab) beneath the snow free peat surface and leO t,, 5 t I t,

beneath the snow cover.

Owing to the Suence of both melting water beneath the snow cover and evaporatic on the snow free peat surface, the water content of the ground surface is variable in horizont; direction and wili be given in the boundary conditions as following:

Within the thickness of the peat, the variation of water content dong the vertical is given as:

= etop - ('mp - 'pb )(HJJ- ~p0) '(~pb - ~p0) Hpo 2 HPC Hpb 7.2.1.3 Clayey silt

The sediments underlying the peat consist of saturated clayey silts deposited in a bas of the postglacial sea. They reach a IllitXimm measured thickness of about 24 m in the stuc site. Permafrost aggradation began around 1800-1600 BP and was still active in some secto of the peat plateau around 80BP. Numerous discrete ice Ienses are present in the marir sediments.

7.2.1.4 Unfrozen water content

If salinity and other chemical components are negligible in the minerai medium, tl unfiozen water content is only a fùnction of the ground temperature in snow, in peat andj mineral materials in frozen ground. The experiments show that the unfrozen water conten within snow and peat decrease sharply with the temperature and tend to zero below the freezin point (Williams 1989; Jordan 1991). The empirical formula can be given as:

and pt for snow and peat, respectively.

Based on other studies in northern Québec (Fortier, in press) and on reports (Xu 198' Tice et al. 1989),the empirical relationship between unfrozen water content and temperature i the siit is:

The thermal parameters of the air, snow, peat and minera1 soils used for modelling a presented on table 5-1. These values are typical of such mediurns and were computed fror laboratory analysis (water content, density of particles) using Kerstern's equations (Goodric 1982a, Williams 1989, Nixon 1990). 7.2.1.5 The parameters of the SP Again, the SP values used for the soils are the experimental resuIts of Konrad (198 1984, 1988) for very similar soils (Leda clay). Pure peat is not prone to segregation due non-surface energy of this type material (Skaven-Hang 1959) and this has been proven by t near absence of ice layes in the reference site. Over the peat bog, the base of the peat cov may be mixed with silt producing a thin layer with an intermediate SP, value.

7.2.2 THERMAL ENERGY OF SOILS IN FREEZE-THAW CYCLES 7.2.2.1 Energy equations

The heat conduction equation for snow and soi1 system in two-dimensional probler cm be written as:

w here

for snow cover, and

for air, peat and mineral soils.

At the air/snow, airlpeat, peatlsoil and soil-llsoil-2 interfaces, the themal paramete concerned are treated by using the average value of the two medium, respectiveiy. 7.2.2.2 Heating sources/sink

The term of heat source or sink Q in equation (7-1 1) includes the solar heating am additional geothermal sources or sink. If there is no such geothennal energy, Q is mai$ hmsoiar incident radiation which generally composes of short-wave radiation Q, and Long wave radiation Q,. .

The portion of incident radiation, Q , is mainly parameterized in term of short-wavt reflectance a,, for short-wave radiation and emissivity e for long-wave radiation. As a f~s approximation the solar energy incident on the snow cover,isassumed to be diffuse anc isotropie. Radiation entering the snow cover is subdivided into near-infrared and visibb components. The energy gain due to solar heating within the snow cover is estimated as

for the top of the snow cover and

for the interior.

The energy flux of downweiiing short-wave radiation 1, in (7- 15)-(7- 16) can Ix eshated with a the-level mode1 (Shapiro 1987) and amPwlm' snow is usually with ; constant equal to 0.78.

Lnfrared radiation for long-wave radiation penetrates the snow cover 5-8 nim and mo O: the infrared component is absorbed at the surface. Snow is neariy a black body with E approaching 1.O; a value of 0.97 is suggested (Jordan et al. 1989). The long-wave flux can Ix estimated approximately with the foiiowing expression where O is the Stefan-Boltzmann (S-B) constant (5.669~10~w/m2k4).

Omitting the second term, with the S-B expression, the equation is the d-wav hemisphericai emitted htensity.

Estimations of the solar radiation are generally of insuffxient accuracy for energ baiance computations (Jordan et al. 1989). It is affected by many factors, such as atmosphen cIear skies and clouds, direct and difise emissions, turbulent fluxes of sensibIe and later heat, and topography, which make determinations rather difficult, especiaiiy for longterr periods. Most of the solar heating is absorbeci at snow top; customady, the solar radiation i regarded as the upper boundary condition. The same approach is used in this two-dimensions modeliing: the term of' the heating source in (7-14) can be removed but considered in the uppe boundary conditions.

7.2.2.3 Frost heave and discrete ice lensing in palsa system

It is well known that, during heat and mass transfer, water intake is dong the heat flou direction. In other words, the line f! of ice lensing is normal to the heat gradient VT. Basei on this principIe of therrnodynamics, it is important to note that in two-dimensionai problem the mas velocity Vg. is found in the normal direction of the heat flow which is not vertica dong the whole profile. The temperature gradient in normal direction can be solved by (4- 14 as following:

Similady. rhe relative variables Vg,P' , Bi,7'' , k and others are aii in the noma direction. This approach is not only following the physicai properties of the problems but dsc a significant simplification of mathematicai modelling for numerical computation. Employinl the mode1 presented in Chapter 4, the frost heave, discrete ice lenses, segregation temperature pore pressure and temperature regime can be numericaiiy solved. Initial condition Approaching an inception of palsas in the field site, the initial condition for th€ modelling starts hma) permafrost free area of a bog or a fen where peat and underlying soi sediments are saturated; b) no snow on the ground surface at the end of Aurunm. The initia conditions can be written as:

The initial conditions of the temperature T ( x, z, 0) and water content 8 (x, z, 0) are generaIiy assumed as steady state and soIved by Laplace's equation as

d2~ +,=O dx' dz

Boundary condition In the horizontd, ground surface is covered by peat in the Sumer season and by seasonal snow-cover and snow free peat simultaneously in the winter season. Water content near the top of peat shows seasonal variations,

The clirnatic conditions used are steady conditions: rnean annual air temperature is -4.8"C covenng 6 years in the modelling. Mean January temperature is about -19.8"C and rnean July temperature about 13S0C. Similady, the reIevant annual temperature cycIe integrating freezing and thawing indices is used to soiicit the modeI- The boundary conditions in x and z directions are: Ln z direction

The upper time-dependent boundaty condition

for air temperature condition (7-2

for snow cover condition (7-2

for snow free condition

are for the winter season, and

for snow cover condition

for snow free condition for the summer season.

Ln the steady climate state, the coefficients, A,, A,, Dm,D,,, ta, t,, are constant.

Lower boundary condition

Considering the actual depth of permafrost base at the reference site, 20.5 m, th temperature at lower boundary is set positive and then pdually and slowly drops with elapse tirne und reaching a steady state under the influences of clirnatic and geothermal condition! The lower boundary conditions, at i =M, is defined as:

7.3 NUMERICAL COMPUTATION

A numerical computation of two-dimensional problerns for the origin of palsas mu2 soIve phase-change temperatures in snow, peat and minerai soils, the discrete ice segregatio and frost heave. A mixture of implicit and exphcit formulations are employed in the solutio procedures. The thermal properties, water content and boundary conditions are variables i space and tirne.

a) The successfu1 numericai computation rnethod of "aitemation-direction an1 prediction-correction" approaches schemed on the Iaw of conservation and control volume ar employed to solve phase-change temperature problems of the two-dimensional nonlinear parti2 differential energy equations. Relative smaii the step usually ensure accuracy due to wea discrete property of the nonlinear phase-change temperature problerns (Yogesh and Torranc 1986; Fen 1986; An 1982, 1989). A ai+1l2---- AT K.,-^^^ r, = -; C'. c2 2h,+112 1.1 2h,-[>2 q, Initial Condition

The initiai ground temperature regirne T (3,q, 0) and water content regime &x,, z, in the cross-section are supposed to be in a steady state and described by Laplace's equatic Generaily, a numerical iteration procedure can be used for Laplace's equation. For exarnp the method of Gauss-Seidel iteration with inequispaced squares for T (xi, z,, O) is given follows:

1

B" = 2(k; + h')I

For computation of the initiai water content regime. we only use variable @(x,, z,, 0) replace T (x,, r,, O) in eq. (745) and solve with the relevant boundary conditions. At t beginning of the freezing season, if the soi1 systern is in unfrozen state. 8(xj, r,, 0) can input with zeroes.

Boundary condition b) In the x-z cross-section of the study system. the water migration V' in equation (4- 1 1) cm be solved with the norrnal temperature gradient (4- 14) in the kzing f~geand in the segregaîion potentiai.

c) Segregation-freezing temperature, T,,in equation (4-22) depends upon the thermal gradient and overburden pressure, which can be iterated with the ground tempemure distribution using an iteration approach due to a nonlinear property.

d) The locations of the segregation freezing temperature and frost front are found in normal direction with the normal temperature gradients in the cross-section.

e) The unfrozen water contents are mainly dependent on the temperature in the medium and they are caiculated with an exponential function obtained from a statistical formula based on field data and experiments (Fortier 1994; Xu 1985).

f) FinalIy, frost heave is computed by the local moving mesh method. First, with the local moving mesh to compte the frost heave at each grid, the arnount of frost heave in the vertical direction is measured by &2.

Beneath the original ground surface the stress in horizontal direction is generally considered as symmetricd and equd in magnitude but in opposite direction. The deformation of the ground surface dong the horizontal is dependent upon ice lensing growing in the normal plane of heat flow.

The numerical rnethod is convergent, stable and relatively simple, and can be efficient1y used for other simiIar problems.

7.4 RESULTS AND DISCUSSION

7.4.1 THERMAL REGIME Because the two-dimensional problem of palsa formation includes a seasonal snow cover, snowpack melting, and ground surface heave, the coordinate point of ground surface in the vertical direction are variabIe. In order to avoid confusion. it is necessary to note that the seasond snow surface at its maximum thickness is given as the starting point in depth for the following ground temperature figures. Except when stated otherwise, the problerns wiU be discussed with SP, equd to 4.37d04m2/h,OC. Peac Layer

Horizontal Figure 7.2. Initial conditions for the two-dimensional mode1 where SC is snow cover, SB is snow border and SF is snow-free. Mineral soi1 1 and 2 are two layers with slightly different properties as in chapter 4.

- - rr.1 - - Yr. 1 ---* Yr.2 -- - - Yr.2 rr. 3 - - . - Yr. 3

-Yr. 4 - Yr.4

---. Yr.S - - - rr. 5 -Yr. 6 ----Yr.6

Figure 7.3. Evolution of the thermal profile under point SC of figure 7.2, (A) summer profiles and (B) winter profiles. - - Yr.1

---- Yf.2

-Yr. 3

-Yr. 4

---Yr. s

-..- Yr. 6

Figure 7.4. Evolution of the thermal profile under point SB of figure 7.2, (A) surnrner profiles and (B) winter profiles.

- - n.1 -- Yr. 1 ---- Yr.2 - - -.Ir. 1 - W. 3 -.- Ir. 3

- Ir. 4 - Yr. 4

-.-. Ir. 5 -.- Yr. 5 - Ir. b --.-Ir. 6

Figure 7.5. Evolution of the thermal profile under point SF of figure 7.2, (A) sumrner profiles and (B) winter profiles. Figure 7.6. Cornparison of winter profiles, year 6 vs year 1.

soi1 surface ------

Horizontal (ml

Y. ----Yr. 4 -Yr. 6 Yr.2 -----Yr.5 ---. U,T.F'.

Figure 7.7. Progression of the O "Cisotherrn over the six first years of palsa growth. Figures 7.3 to 7.5 show the calculated vertical temperature proNes in the soi1 system i the fmt six years of palsa iife. In these figures the temperature profiles are those beneath poir SC, SB, and SF of figure 7.2; they are respectively below the center of seasonal snow covei below the margin of the seasonai snow cover, and below the snow free peat surface.

It can be seen that I) at SC, the insulating snow cover results in a reduction of th thermal energy diffùsing from the ground surface in winter seasons. Consequently, after th fmt year, the ground temperatures decrease more sIowly with the elapse tirne, and the fros penetration advances much slowly. Mer six years, the minimum ground temperature reache only iittie less than O0C, and the lower frost penetration is 4.35 m (Figure 7.3). Th, temperature gradients are very smaii, the temperature profile king dong the OT iine. 2 Beneath the snow free peat surface SF, the situation is quite different. The frost penetratioi advances much deeper and the ground temperame gradient is also much larger. The rninimun ground temperature is -3.8"C, and the lower frost penetration advances to 8.4 m (Figure 7.5) Because of the two-dimensional heat and mass transfer and the combined effects between snov cover and snow free conditions, figure 7.4 indicates the characteristics of the grount temperature regirne beneath the location of the margin of the snow cover. Just by looking a the temperature profiies in mid-winter, the insulating property of the seasonal snow cover cai be further seen clearly from the comparison of frost penetration between the fmt year and thi sixth year (Figure 7.6).

Figure 7.7 shows the progression of the 0°C isotherm over the fmt six years of pals; growth. One can observe that the lateral permafrost contact becomes nearly vertical. Verticaiiy the frost front advances deeper beneath the snow free peat surface, to much shaiiower depth a snow margin. and very little below the snow cover. Obviousfy, the influence of the insularing snow cover on the thermal regime is very significant, and finally results in the differences o. both ground temperatures and frost penetration in the cross-section.

As discussed in Chapter IV, the climatic basis for the origin of paisas is centred on thc differences between the surnrner and winter periods of the year, during which energy fluxe! cause results of long Iasting effect. These are the mid-summer heating by short-wavr radiation, and mid-winter cooling by long-wave radiation back to the atrnosphere. The trenc cm dso be explained by the net effects of snow cover and snow free peat surface. Figure 7.2 and 7.9 show the ground temperature variations during one annual cycle. The results in figure 7.8 are from rnid-August in the third year to Late October in fifth year for SC, and that in figun 7.9 from mid-August in the Fourth year to Late October in sixth year for SF. The result! obtained obviously show that the temperature envelopes beneath the location of the snow fka Figure 7.8. (A) Thermal profiles and (B) thermal regime from summer of year 3 to early fa11 of year 5, under point SC

Figure 7.9. (A) Themal profiles and (B) thermal regime from summer of year 3 to early fall of year 4, under point SF peat condition are much larger and greatly move into the negative temperature zone, whi beneath the location of the seasonal snow cover the temperature envelopes are smii and aroui the 0°C axis.

Snow influence lasts for nearly 8 months (more precisely, 7 months and half). 'il duration is 7 times longer than the melting period (1 month and 13 days). The cold wint temperature in this discontinuous permafrost region keeps the snow dry. The insulating sno porous medium reduces the heat flux from the ground surface during the cold part of the annu temperature cycle.

Water content in the peat layer varies seasonaüy and spatially. In summer, the incornii solar radiation meets a shalIow vegetation cover over a peat surface of high porosity; considerable portion of the heat energy then is consumed in evaporating moishue in the surfa( layers which become dryer, and thereby the thermal conductivity is reduced. The abfity of tl surface layer to transfer such great energy arnounts is low, and a strong temperame gradient created. To a great extent, the paradox is me, that the stronger the heating in surnrner, tl better the preservation wilI be. In consequence of less thaw penetration; once the frozen core initiated, it can be preserved ail through the summer. In auhum the precipitation and meltir snow supply water to the peat. This significantly increases the thermal conductivity and hell the advancernent of the frost penetration in winter.

Differences of the ground thermal energy are derived from the differences of upp boundary conditions. On the snow free peat surface, the heat loss through outgoing long-wa~ radiation can be considerable, and surface temperatures may be down to -20°C or les Thermal conductivity of frozen peat and of its ice content is very high, and thermal energy released from the frozen core. The permafrost core will form and expand rnainly beneath ti snow free peat surface and it will reach into the minera1 soils below (Figure 7.7 to 7.9).

7.4.2 ICE LENSING

The ice lenses mainly grow in the mineral soils below the peat cover. Figure 7.10 to 7.13 sho ice lens distributions in vertical and horizontal. Owing to the properties of nonsurface energ and very high porosity and permeability, suction pressure and coupled heat and mass transfc cannot contribute to water migration to the frost front in the freezing peat. Pore ice is therefoi the main ice component in this frozen zone. In the two-dimensionai problem, ice lenses gro at the frost fronts which are normai to the directions of heat flow and the size ofthe ice lensc is dependent on the suction pressure and segregation potential in the normal direction bol beneath the snow cover and the snow-free peat surface. Even though there are downwards ar Depth

Figure 7.10. Ice Iens growth and vertical distribution with time under point SF.

'r. 6

A a

Horizontal

Figure 7.11. Thickness of ice lenses below the horizontal profile with Ume. Fiare 7.13. Comprative verticai dis"bution and ihiclness of icc lenses under points SC,SB and SF after 6 years. upwards moisture migrations in the process of the paisa growth, the main source of watei supply for the discrete ice lensing is from the lower Wgfront.

Beneath the snow cover, ice lensing is much less important (Figure 7-13), especiaiiy in the beginning years (Figure 7.12), due to the insulating effect of the snow cover and the srnaller frost penetration in winter. Also, thawing in intervening summer seasons reduced and melted ice lenses because of the relatively high ground temperature. Following the second and third recuning freeze-thaw cycles, the frost peneu'ation showed some slow advancement in winter but alrnost complete melting the next autumn, the ground temperature profiles in negative temperature zone king very close to 0°C. The temperature gradients trend towards zero at the Iower freezing front, therefore supplying less thermal energy for water migration and formation of ice lenses.

On the other hand, the ice lenses grow significantiy beneath the snow-free peat surface and gradudIy expand with the permafrost core downwards (Figures 7.10, 7.12, 7.13). Obviously, the frost penetration is more rapid and the temperature gradients are large which supply rnucn energy for moisture migration and ice lense segregation. After the fmt year, with the thermal energy diffusion from the bare ground surface, a permanent frozen core is formed, which wiil grow in Company with ice segregation during the following year.

During the permafrost core growth, pore ice and segregated ice will result in the upheave of ground surface, and the paisa will keep growing und equilibrium is attained or und it starts cracking due to mechanical tention and rhen initiate the degradation part of its cycle.

7.4.3 ORIGIN OF PALSAS Figure 7.14 shows the heave responsible for palsa growth. The numencal results show that paisa inception is p~cipaiiyaccounted for by the vertical component of frost heave. After six years with the SP, equal to 4.37~10-~m2/h;"C, frost heave resuIts in a palsa 49 cm high. From the numerical andysis, the following discussion points cm be brought forward:

a) Alrnost aii deformation is vertical.- This is because of free surface boundary conditions, the advancement of the frozen front in depth, and the absence of soi1 compression beneath the ground surface. b) A cross-sectionai surnmary over the thennal properties of the palsa illustrates, w the ability of various iayers to transfer and store thermai energy, or heat. Because of t dominant effect of snow cover, the frost body in winter is obviously capable of a much mc considerable release of heat in the vertical than in the horizontal direction. The greater t growth of the frost body, the greater the exposure of the pdsa summit where the insulati effect of a snow cover WUnever occur, and, thus, the more the thermal energy releases frc the frost body. On the other hand, the insulation effect of the xcumulated snow dong the fc of the palsa prevents the lateral expansion of the palsa This explains why the big paisas ha steeper walls than the smail ones, which is true aiso of cryogenic mounds.

On figure 7.14 to 7.16, it can be seen that the newly formed pdsa keeps growii during the surnmer. But dong the side and the foot of the palsas where is the seasonal sno cover, the ground surface grows up and settles down around 13 cm. The ground surfa, heaves in winter, but settles back to nearly its original level after the thaw at the end sumer. This is because a reversai of the heat flux in thawing. The ground ice rnelts from tl upper and lower boundaries of the frozen core resulting in subsidence. On the contrary, tl paisa maintains its growth in the section of snow-free peat surface. Ddg the summ season, the paisa grows very slowly at a rather regular rate. This is because ice lenses are th forrning at permafrost base.

With suitable water supply conditions, the arnount of paisa growth is mainly depende on the frost-susceptibility of the mineral soil. Figure 7.17. and 7-18 show other examples pdsa formation with SP,,equal to 3.25~10" and 1.85~10-~rn2/h,"~, respectively. The form -crows to 37 cm and.larter onIy reaches 24 cm. Cornparison of these resutts with figure 7.14 7.18 indicate that for the inception of the palsas the amount of heave changes with SP. But tl growth law of pdsas is respected. Origin of pdsas is coaditioned by the interaction betwet thermal dynamics and mass transfer.

The computed results suggest that 1)In the subarctic tundra regions, the differences physical properties, arnong snow, organic materiais and minera1 soils, play a greater role th; elsewhere. In particuhr, the insulating thermal properties both of snow cover in the wint season and of the peat layer in the surnmer season are capable of creating unique grout thermal regime for the formation of smaii piiiow-like or eilipse shape mounds as palsas. Ti studies of themodynamics and discrete ice lensing offer an exceiient example of season characteristics of energy and mass transfer in permafrost soils. 2) palsa can originate under tl present current climate conditions in cold regions, if externai and intemal thermodynamic mass supply and other relevant conditions are available. These results have been verified t 0.5

0.4 CE .-----ICI.- -g 0.3 a3 0.2

LLe o. 1 Ja*.:s- A/.* - - _C_j O, ...)...I..'l...,...,...,...,...(... O 2 4 6 8 10 12 14 16 18 Horizontal (m)

Figure 7.14. Heave along the profile during 6 years.

0.45 0.4 - 0.35 E 0.3 2 0.25 U =- 0.2 g 0.1s y. 0.1 0.05 O O 2 4 6 8 10 12 14 16 18 Horizontal {ml

Figure 7.15. Details of heave fiom August of year 3 to September of year 4. O 2 4 6 8 10 12 14 16 Horizontal (m)

Figure 7.16. Details of heave, continued until year 6.

O 2 4 6 8 10 12 14 16 18 Horizontal (m)

Figure 7.17. Yearly heave with SPO= 3.25 x 10-6m2/h. OC O 2 4 6 8 10 12 14 16 18 Horizontal (m) - Yr. 1 - - - Yr.3 ----Yr. 5 ...... Yr. 2 - - - Yr. 4 - Yr. 6

Figure 7.18. Yearly heave with SP, = 1.85 x 10-6 m*/h. OC both experimental paisa inception (Seppala 1986) and in new natural incipient ones in the fie (Sone and Takahashi 1993). It was reported by Sone and Takahashi (1993) that in tl Daisetsu Mountains, Hokkaido, Japan, 1) one of the palsas which has been cored began

form around A.D. 1830, or 150 years ago, now is about 1 m high; 2) on the basis 4 comparisons of air photos taken in 1955, 1966, 1971, 1978 and 1982, the paisas and pe plateaus changed in size and areal extent during the period 1955-82. Their total amwi reduced by 36% over 27 years; however, several palsas were hardly reduced (Takahashi ar Sone 1988); 3) the more interesting event is that a new palsa which had been not visible on tl photographs taken in 1955 and 1966 appeared on the photograph taken in 1971; 4) In additioi some palsas seem to be in an early development stage and to be in the growth stage. 1 northem Québec, it has been estimated that some palsas also only 150 years old are over 5 i high.

The cornputed results suggest that two-dirnensionai rnodeiiing cm help interpn efficiently the origin of paisas, while one-dimensional modelling can be used to approach tt palsa growth in steady clirnatic conditions and to simulate the influence of climate change o the paisas.

7.5 SUMMARY

1) The insulating seasonal thick snow cover evidently prevents permafrost COI formation and aggradation, while the initiation and the progression of the permafrost core wit ice lensing results in the inception of paisas under snow-free areas.

2) The computed results suggest that if proper thermodynamics, mass supply and othe relevant conditions are available, palsas form under current climate conditions in cold regions.

3) The significance of this conclusion is that furcher studies of inception and variation of these landforms will be important not only for geomorphologicai knowledge, but also fc studies of clirnatic and environmental changes. Chapter VIII

CONCLUSION

UP TO DATE KNOWLEDGE ON PALSAS

Palsas were studied for nearly a century since 19 10 when a theory for their origin wai Fust published by Fnes and Bergstrom. But the main development period on this subjec begins after 1960. Investigations and observations in the field were made in the permafros regions of the world, from the northwestem parts of Europe, like Finland, Norway an( Sweden, to Iceland, Siberia, Russia and North Arnerica. A great number of evidences havc shown that these periglaciai landforms are more comrnon and widespread than earIier reaiized Palsas are distributed neariy over the entire discontinuous permafrost zone in high latitudt subarctic climate regions. Paisas are dso found in alpine regions.

Perhaps because of the limitations in accessibility of those regions and because of thc difficult environment of paisa growth, the processes of palsa formation gave way more to lonj and abundant cenninologicaI discussions and debates than to gathering in depth evidence Palsas were divided into two main type of rnounds: one was termed as classic or traditions "paisas" and another, "palsa-like frost mounds" which were also caiied "rnineral palsas" "cryogenic mounds", or "mineral permafrost mounds" and recently "lithaisa" With ttic significant improvements and developments of research methods and with abundant fielc evidence from different cold regions of the world, most researchers have agreed that palsas an rarely in frozen peat alone but mainiy in peat and rnineral rnaterials. UsualIy, peat is oniy a thi surface layer. Post-glacial marine and lacustrine sediments, usualiy silt and siity clays, are th dominant material in which these landforms are developed. It is now a widely demonsmte fact that the inception and growth are due to ice segregation which is responsible for groun upheave in freezing soils in generai. Therefore, the two types of mounds mentioned abov klong to the same family. Palsas are defined as: "Peaty permafrost mounds possessing a cor of altemathg layers of segregated ice and peat or minerai soii material. "With climatic an ground surficial condition changes, palsas cm undergo an incepticm. growth, mature anc decay. ûther mounds in fine sediments that do not have a peat cover and that are formeci b frost-heave can be termed differently, for example as cwogenic mounds or pedostmound and plateaus.

CONSIDERATION FROM MODELLING PALSA FORMATION

Numerical simulations of one-dimensional problems of palsa formation provide th, following deductions and conclusions:

1) At permafrost base beneath a palsa or a cryogenic mound. themodynarnil conditions attain and maintain quasi-steady state.

2) The numerical results of palsa formation over 200 years show that i) a paisa or mound 3-m high can raise above the surrounding terrain in roughly six decades. If condition are maintained long enough, the palsa will continue to grow more slowIy as a series of thick icl layers will form near permafrost base. Somewhat different types of soils wiIl resdt in differen mound height given the different segregation potentiais linked ro different thermal properties ii) the discrete ice Iensing grows smali, less than 2.0 cm from top to middie section of th( palsas, but deveIops thick discrete ice layers near the lower boundary of the palsa core.

3) The presence of either a series or a single thick ice segregation layer near the base O permafrost needs to be further substantiated by drilling in many palsas. The presence of sucb ; series of ice layers has been reported and cored throughout some permafrost mounds but 01-11: sporadicaiiy. Some variation might occur in the natural environment. The segregatioi potential and saturated upward moisture migration are dominantly respoasible for the fros heave of paisas.

4) The thermal properties of peat play an essential role in palsa inception in region: where mean annual surface temperature is close to 0°C. The climatic basis of paisa inceptioi focuses on the diffrences of peat behavior in summer and in winter. Both thermal energ] consumption in summer and release in winter from peat create a strong temperature gradien which benefits to the formation and growth of the palsa The dominance of the& propertie in winter over that in summer provides the negative heat balance over tirne. This i signZcantIy important to the understanding of the repeated seasonal growth of the frost core Thus, in snow-free conditions, one of the prerequisites for the palsa inception, growth, ani existence is the abrupt and considerable increase of thermal conductivity of the fiozen pea which releases thermal energy into clear arctic air masses. This reasonning Unplies that thi cryogenic mounds without peat cover require a more severe environment than palsas to form.

5) The downward water migration from the perched saturated water table in thi thawing active layer to the permafrost through the thawing front is a fundamental rnechanisn for thick ground ice segregation, when the seasonal thaw penetration reaches a quasi stationar] state. Ground ice accumulates in the hst-susceptible silt near the permafrost table. As ; consequence, thick ground ice is a sigmficant phenornenon in silty cryogenic mounds whert peat is absent.

6) No ice lens forms in frozen pure peat due to the non-surface energy property of pun peat. This was verîfied by the observations in Kangiqsualujjuaq. As the peat cover is less thar or roughly equal to active Iayer depth, ice lensing takes place just dong the strati,gaphic contact, otherwise, only a small arnount of ice is present close to the permafrost table.

7) In the absence of solutes, the only factor that cm depress the fieezing point of soi water is overburden pressure which increases as permafrost base progresses downward. Ict segregation ternperature drops with the frost penetration of palsa. It is about -O. 1°C by 10 n deep and -0. 19°C near 20 m where frost penetration reaches a quasi-stationary state.

INFLUENCE OF CLIMATIC COOLING ON PALSAS AND CRYOGENIC MOUNDS

Frorn the early 1950's to early 1990's, climate in northeastern Canada trended tc cooling, and the data from observation in the field and in the iiterature suggest that the mear annual air temperature at the reference region over four decades endured a cooling of -2.3" C from -4.4 to -67°C.It is assumed that an aiternation of steady and transient ciimate cooling dominate the tirne-dependent tempera- boundary conditions of the palsa system. Twc examples of numerical predictions, one- and multiple- step climate coohg processes. wert performed to explore the influence of ciimatic cooling on the palsas. The modelling resuits in ice lensing distributions in one- and multiple- step clima

coolhg simulation yield the sarne trends. It can be seen from comparing the dismbution I segregated ice lenses in palsas thai, obviously, steady climate conditions favor thick ice lensir as the frost penetration reaches a quasi stationary state, whereas transient chme cooling favorable to frost penetration and formation of thin interspersed lenses. For exampie, for fro susceptible soils, during a steady climatic period the maximum thickness of segregated ic layers increases simcantly to about 11.0 cm; the palsa grows 70 cm higher. In a transie] cooling period the maximum thickness of the ice lenses is only about 2.4 cm, and Iess wati migration feeds paisa growth which is limiteci to about 40 cm. It ciearly shows that t.l formation of the segregated ice layers aiong the entire paisa depth depends upon the duration c the cool period and heat flux intensity of each period. A long cold period favors paisa grow better than a transient cooling period.

Synthesizing the cases of both one- and multiple- step climate cooling processes, tt theoreticai understanding of the modeiiing results suggests that, in subarctic nindra permafro: regions, if the Quaternary geologicai conditions and the permafrost properties are suitable, tt. extemal thermodynamics in each steady or transient climate condition is the principal contrc

for the formation of ice intervais, that is, the presence of the regular aitemate distribution ( series of thick and thin ice lenses. The sizes of these ice lenses is also related to duration of tk periods. The genesis of these intervais of both thick segregated ice layers and ice Ienses i paisas or in cryogenic mound can be attrïbuted to the responses of the frost-susceptible so system to the clirnate cooling process during permafrost formation and aggradation. TI: intervals consisting of thick segregated ice layers can be the responses to relative steady climai periods, while the intervais composed of series of thice lenses inlaid between the thick one can be the responses to transient climate cooling periods.

The regular alternate distributions of thick ice layers and thin ice lenses aiong th permafrost cores in palsas and cryogenic mounds could eventually be used as proxy record reflecting the process and intensity of climate change in steady and transient States. Such proxy record, like other sediment cores and geological deposits cm help us for the study c past climates. The field evidence and theoretical understanding of the climate change sugge! that we are indeed deaiing, in the palsa, with a somewhat predictable system, at Ieast on timf scde of centuries.

Combining terrain studies, particularly by drilling cores through pdsas, with th modehg wiU help us to understand how permafrost with saturated frost-susceptible soils i the subarctic and alpine regions has responded to past and recent climate variations and aiso t study the impact of paleoclimate on different types of palsas and on other relatai landforms i the perigiacial environment.

ROLE OF SPATIAL VARIATION IN SNOW COVER CONDITIONS

As the upper boundq conditions of both seasonal snow cover and snow free pea surface sirnultaneously regulate the palsa system, insulating properey of the thick snow cove results in a reduction of the ground thermal energy diffushg from the ground surface beneatl in winter seasons. Consequentiy, with elapsed the, the ground erature decrease and fros penetration advances more slowly. Meanwhile, where the snow-fi-ee peat surface is exposei and further cleaned by wind, heat is released easily. The temperature gradient, which generall! decreases with depth, leads to a deper frozen core. Meanwhile, snow accumulates dong th1 foot of the growing palsa slopes and prevents the permafrost core from aggradating an( expanding horizontaiIy. Therefore, laterd expansion is very slow, and walis of growin~ palsas become gradually steeper. Steeper palsa walls. in turn, increase snow accumulation u following winters. The larger the growth of palas and the exposure of the palsa summit, thc more the thermal energy is released from the frozen body. On the other hand, the insulatini effects of the accumulated snow around the sides of the palsas hinders their lateral expansion.

in the cross-section of paisas, the horizontal thermal temperature gradient illustrate! weii the ability of the snow cover and the peat cover to transfer and store thermai energy Owing to the dominant insulating effects of the snow cover, the permafrost core in winter ii obviously capable of a more considerabIe release of heat in the vertical than in the horizonta direction. Comparing the themal regime in the cross-section during six freeze-thaw cycles, th senous effects of insulating snow cover, other variables king kept unchanged, lead tc significant differences of both ground temperatures and frost penetration, and fmaiiy results ir ciifference of the frost heave in the cross-section.

DISTRIBUTIONS OF ICE LENSING IN CROSS-SECTION

In the 2-Dproblem, segregated ice formation at the frost front is nomal to the directior of heat flow in cross-section. The size of the ice lenses is detennined from segregatior potential, suction pressure in the normal direction and elapsed tirne when segregation fron keeps relatively stable. The main source of water migration for ice lensing in the process of th< palsa growth is from below the freezing front. ORIGIN OF PALSAS

The numerical resuits indicate that palsa inception results principaily hmthe vertic component of frost heave. This is &y because of the free deformation at the pur surface, the advancement of the hzen hntat depth, and the limitation of the soil defonnatic fiom the soil compression beneath the ground surface in the horizontal direction.

Palsa growth in the beginning years shows some fluctuations with the altemance ( wïnter and summer seasons. Reversion of both external and intemal heat fluxes in thawk results in melting some ice lenses at the upper and lower boundaries of the frozen core ar some subsidence. After this inception, if the climatic and other relevant conditions are suitabl palsas will grow gradudiy with recurring freeze-thaw cycles in relatively stable clima conditions until they reache a new equilibrium or until they are impacted by some new ciirnat change. GeomorphoIogical processes Like cracking and slumping can also initia desintegration, or permafrost degradation.

MODIFICATION OF THE CONCEPTION FOR ORIGIN OF PALSAS

The computed results suggest that if thermodynamics, mass supply and other relevai conditions are available, paisa cm originate under present climate conditions in cold region Contrary to the belief of some researchers, paisas do not necessarily date back to past col periods.

1) Numerical application of our mode1 shows that a new palsa can start to form an grow under the present chnatic conditions provided that snow cover is locally absent ( suficiently reduced. This significant conclusion is supported by the observations by numeroi authors of incipient forms in the actual landscape of northem Quebec and the other subarcti regions in the world.

2) If suitable water supply is available, either in the one- or two- dimension; problems, the segregation potentiai of soils is a major factor for determihg the magnitude and size of the segregated ice lenses in the palsa corresponding to climate cooiïng process. S is primarily dependent on the thermal gradient and the suction gradient of soil materiais an water supply conditions. Segregation potentiai expresses the fiost-susceptibiiity of the soi The larger the SP, the thicker the discrete ice lens growth and the higher the palsa. On tt other hand, if segregation potentiai is small, water migration wiil be restricted and, even thoug climate conditions are favorable, only thin ice lenses wiii form. The result will be a Iow palsa 3) The significance of these conclusions is that the studies of inception and variation! of these landforms WUnot lead only to contributions in geomorpbology, but dso in studies O the variations of the clirnatic and environmental changes.

4) The one-dimensional mathematicai modeis presented in the thesis can apply to thr formation of palsas, permafrost mounds and other sirnilar perigiaciai landform. They can bi used for numerical studies of the effects of cijmate change, ground surface covers and othei relevant conditions on the permafrost environment in cold regions.

The computed results could give us a suggestion that 2-D modeliing can interpre efficiently the ongin of palsas, while 1 -D modelling can be used to approach palsa growth ir steady clirnatic conditions and to analyse the influence of climate change on palsa evohtion. ~LHMAN,R. (1977). Palsar i Nordnorge (Summary: Palsas in nonhem Norway. Meddelanden fran Lunds Universitek Geografïska Institution, Avhandin~ar,78: 165- 172.

&MAN, R. (1976), The stmcture and morphology of minerogenic palsas in Norther Norway, Biuletyn Peri~lacjdny,26: 25-3 1.

AKERMAN. H.J. and MALMSTRROM, B. (1986), Permafrost mounds in the Abisko ares Narthern Sweden, Geomafïska Annaier, 68A (3): 155-165.

&ERMAN. H.J. (1982). Observations of paisas within the continuous permafrost zone i: east Siberia and in Svalbard, Geoer. Tidskr, 82: 45-49.

ALLARD, M., CARON, S. and BEGNY. (1996), Climatic and ecotogical conml on io segregation and thermokarst: the case histoly of a permafrost plateau in northern Québec Permafrost and Peridacial Processes, 7: in press

ALLARD, M., WANG, B. and PILON, I.A. (1995). Recent cool in^ dong the shore O Hudson Strait. Québec. Canada, documented from permafrost temperature measurement. Artii and Alpine research, 27: 157- 166.

ALLARD, M., TREMBLAY, C., PILON, J.A. and FRYDECKI, S. (19931, Ouaternq geolom and geocryoloq in Nunavik. Canada, Proc. Sixth Int. Conf. Permafrost, Beijing China, 1: 5-10.

ALLARD, M., FOURNIER, A, GAHÉ, É. et SEGUIN, M.K. (19891, Le Quaternaire de 1; côte sud-est de la baie d'Ungava, Queb nordique, Géomuhie physique et Ouatemaire 43(3): 325-336.

ALLARD, M., SEGUIN, M.K. and PELLETIER, Y. (1988), Shoreline prrnafrost U Kaneiasualuijuaa Bav. Ungava. Oue'bec, Proc. Fifth ht. Conf. Permafrost, Norway, 1 113-1 18.

ALLARD, M. and SEGUIN, M.K. (1987a). Le pergélisoI au Quek nordique: bilan e perspectives, Géoma~hie~h~sique et Ouateniain& 41: 14 1- 152. ALLARD, M. and SEGUIN, M.K (1987b), The Holocene evolution of permafrost near th tree line, on the eastem Coast of Hudson Bay (northern Québec), Canadian Journal of Eari Sciences, 24: 2206-2222.

ALLARD, M., SEGUIN, M.K. and LÉVESQUE, R. (1986), Palsas and minera1 pemafro! mounds in Northem Oue'bec, International Geomorphology Part II, 285-309.

AN, W. (1989), Interaction among temmrature moisture and stress fields in frozen soil! Lanzhou University Press, China, 124 p.

AN, W. and ALLARD, M. (1995), A mathematical approach to modelling palsa formatior Insights on processes and growth conditions, Cold Reeions Sciences and Technolop, 23 23 1-244.

AN, W., CHEN, X. and WU, 2. (1987), Numerical simulation of coupled heat and mas transfer beneath canal during freezing, Journal of Glacialow and Geocrycryoloev, 9 (1): 7f 81.

AN, W. and WU, Z. (1987), Numencal simulation of the critical height of Highwa Embankrnent with double medium, Selected Works of the Second national conference O frozen soil, China, 87 p.

AN, W., WU, Z., ZHU, Y. and JUDGE,A. (19931, Influence of clirnate change on hiphwti embankment stabilitv and mrmafrost in the ~emafiostre~ion of the Clinphai-Xizaw Plateau Proc. Sixth Int. Conf. Permafrost. Beijing, China, 1: 11-16.

ANDERSON, €.A. (1976). A ooint enerav and mass balance model of a snow cover, NoAr Technical Report NWS, 19 p.

ARCONE, S.A. SELLMAN, P.V. and DELANEY, A.J. (1982). Radar detection of ic wedges- in Alaska. USA Cold research and Enpineerin Laboratory, CRREL Report, 28 p.

ASSOCIATE COMMIïTEE ON GEOTECHNICAL RESEARCH (1988), Glossaq o permafrost and related mound-ice tems, National research council of Canada, Technia memorandum No 142,60 p.

BEAR, J. and CORAPCIOGLU, M.Y. (1981), A mathematical model for consolidation in thermoelastic aquifer due to hot water injection or pumping, Water Resources Research, 17 723-736. BOOTH, D. B. (198 l), Macroscopic behavior of fieezing saturated siity soil, CoId Re~ic Science and Technology, 15-23.

BROWN, J., NELSON, F., BROCKETI', B., OUTCALT, S.I. and EVERE'TT, K. (1993), Observation on icecored mounds a.Sukapka mountain. south central brooks rani

-9Alaska Proc. Fourth Int. Conf. Permafrost, Fairbanks, 9 1-96.

BROWN, R.J.E. (1979), Permafrost distribution in the southern part of discontinuous zone Quebec and Labrador, Géomaphie ~hvsiqueet Quaternaire, 33: 279-289.

BROWN, R.J.E. and PÉWÉ, T.L. (1973), Distribution of permafrost in North Arnerica a its relationship to the environment: a review. 1963-1973, Permafrost: North Americ Contribution to the Second International Conference, National Academy of Scienci Washington, DC., 7 1-100.

BROWN, W.G. and JOHNSTON, G.H. (1970), Dikes on permafrost: predicting thaw a settlement, Canadian Geotechnical Journal, 7: 365-37 1.

CAMES-PiNTAUX, A.M. (1986), Numencal two-dimensionai study of thermal behavi around a cylindrical cooled underground cavity, VaIidity of an axisyrnmetrical scheme, Cc Regions Science and Technolom, 12: 105-1 14.

CARY,J.W. (1987), A new method for calculating frost heave inchding soIute effects, Resources Research, 23: 1620- 1624.

CHENG, G. (1983). The mechanism of repeated-segregation for the formation of thick Iayen ground ice, Cold Regions Science and Technolo~v,8: 57-66.

CHENG, G and CHAMBERLAIN, E.J. (1988), Observation of moisture mimation in fiozc soils during thawing, Proc. Fifth Int. Conf. Permafrost, Norway, 1: 308-3 12.

COLBECK, S.C. (1983), Theory of metarnorphism of dry snow, Journal of Geoahvsic Research, 88(C9): 5475-5482.

COLBECK, S.C. (1972), A theory of water percolation in snow, Journal of Glaciolog ll(63): 369-385.

CORAPCIOGLU, M.Y. and PANDAY, S. (1988), Thawin~in permafrost simulation ai venfication, Proc. Fifth Int. Conf. Permafrost, Norway, 1: 61-67. CORAPCIOGLU,M.Y. (1983)' A mathematical mode1 for the permafrost thaw consolidation Proc. Fourth Int. Cod Permafrost, Fairbanks, 180-185.

CUMMJNGS, C. and POLLARD, W. (1990), Cryorrenetic cate~orizationof ueat and minera cored als sas in the Schefferville Area Ouebec, Proc. Fifth Can. Conf. Permafrost, 95-103.

DEVER, L., HILLAIRE-MARCEL, C. and FONTES, J.C. ( 1984), Composition isotopique géochimie et genèse de la glace en lentilles (palse) dans les tourbières du Nouveau-Quek (Canada), Journal of Hvdrolos!y, 71: 107-130.

DIONNE, J-C. et SEGUIN, M.K. (1992), Recherches sur le pergélisol dans la région dc Blanc-Sablon. Ouek, dans recherche en cours, Partie D; Commission géologique du Canada Étude 92- 1,59 p.

DIONNE, J-C. (1984), Palses et limite méridionale du pergélisol dans I'hémisphère Nord: Lc cas de Blanc-Sablon. Québec, Géomaphie Phvsique et Ouaternaire, 38(2): 165- 184.

DIONNE, J.C. (1983). Frost-heaved bedrock features: a valuable permafrost indicators Géomaphie Phvsique et Quaternaire, 37: 24 1-25 1 .

DIONNE, J.C. (1978), Formes et phénomènes périglaciaires en Jarnésie, Quek subarctique Géo~tra~hiePhvsique et Ouaternaire, 32: 187-247.

DOOLITTLE, J.A., HARDISKY, M.A. and BLACK, S. ( 1992). A ground-penetrating rada study of Goodream palsas, Newfoundland, Canada, Arctic and Alpine Research, 24(2): 173 178.

DYKE, AS. and PREST, V.K. (1987). Late Wisconsinian and Holocene history of thc Laurentide ice sheet, Géographie uhyiaue et Ouatemaire, 41: 237-263.

ESCH, D.C. (1990), 20 vears permafrost history of fmt insulated roadwav on ~ermafrostir

-1Alaska Proc. Fifth Int. Conf. Permafrost, Norway, 1: 235-243.

FENG, K. (1986). Numerical com~utationmethoci, Industry Press, (Chinese), 289 p.

FORTIER. R. (1994). Étude d'un pe@lisol a Kan~iqsualujuaa à l'aide d'essai! gdotechniques et diagraphies ~éophysiques, Montréal, Département de génie civii, &lr Polytechnique, Thèse de doctorat, 2 Tomes. 6 15 p. FORTIER, R. (1991), Université Lavai. mémoire de maîtrise, 234 p.

FORTER, R., SEGUIN, M.K. et ALLARD, M. (1991), Caractérisation du pergélisol dc buttes cryogènes à l'aide de diagraphies électriques au Nunavik, Que-, Permafrost am Perielacial Processes, 2: 79-93.

FRENCH, H.M. (1976). The _periolacial environment, Longman, London and New York 309 p.

FRIEDMAN, J.D., JOHANSSON, C.E., OSKARSSON, N., SVENSSON, H. THORARINSSON, S. and WILLIAMS, R.S.Jr. ( 197 l), Observations on Icelandic polygor surfaces and palsa areas, Geomaphiska haler, 53a: 1 15- 12 1.

FUS, I., and BERGSTROM, E. (1910), NAgra iakstagelser olver pdsar och deras firi komst i nordligaste Svenge, Geol. Foren. Stockholm forh., 32: 195-2 1 1.

FULTON, R.J. (1989), Uuaternary eoloq of Canada and Greenland, GeoIogy Survey oi Canada, Canadian Government Pubiishing Center. Ottawa, K-1 : 375 p.

GA&, E,, ALLARD, M. et SEGUIN, M.K. (1987), Géophysique et dynamique Holocène de plateaux palsiques à Kangiqsuaiujjuaq, Quek Nordique, Géograhie phvsique ei Ouatemaire, 61( 1): 33-46.

GA&, E., ALLARD, M., SEGUIN, M.K. and FORTIER, R. (1988), Measurements ol active laver and ~ermafrostDamneters with eiecmcai resistiviv. self-wtential and inducec polarization, Proceedings of Fifth International Conference on Permafrost, Norway, 1: 148- 154.

GARAND, P. and LADANYI, B. (1987), Frost susceptibihty testinia of compacted glacial till, Proceedings of 3th International Symposium on Ground Freezing, p. 277.

GILPIN, R.R. (1980), A mode1 for the prediction of ice lensing and frost heave in soils, Watei Resources Research, 16(5): 9 18-930.

GOODRICH, LE. (1982), An introductorv review of numerical methods for mound thermal caiculations, Ottawa, National Research Council of Canada, Division of Building Research. Papa 1061T3Zp. GOODRICH, L.E. (1982), The infiuence of snow cover on the ground thermal regimt Canadian Geotechnicai Journal, 24: 160- 165.

GUYMON,G.L., BERG, R.L. and INGERSOLL, J. (1985), Pratical verification of a thal settlement modei, In freezing and thawing of water systems, ASCE, New york, 18 p.

GUYMON, G.L., W,MX., BERG, R.L. and HROMADKA, T.V. (1983), Field test c a frost heave model, Proceedings of Fourth International Conference on Perrnafros, Fairbanks, 409-4 14.

GUYMON, G.L., BERG, R.L. and HROMADKA, T.V. (1981). A probabilistic-detenninisti anaiysis of one-dimensional ice segregation in a freezing soi1 colurnn, Cold ReiPions Scienc and Technolnv, 5: 127- 140.

GUYMON, G.L. and LUTHIN, J.N. (1974), Accoupled heat and moisture transport modc for Arctic soil, Water Resources Research, 9(5): 995- 100 1.

HARE, F.K. and THOMAS. M.K. (1974), Clirnate Canada, Wiley Publishers of Canad Lirnited, Toronto, 86 p.

HARLAN, R. L. (1974), Analysis of coupled heat-fluid vansfer in partiaüy fiozen soil, !&& Resources Research, 9(5): 13 14- 1323.

HARRIS, S.A. (1993), Paisa-like mounds develo~edin a minerai substrate. Fox lake. Yukoi Territorv. Proceeding, 6th International Permafrost Conference, Beijing, China, 238-243

HARRIS, S.A. ( 1988). Observation on the redistribution of moisture in the active laver mi permafrost, Proceedings of Fifth international Conference on Permafrost, Norway, 1: 364 369.

HARRIS, S.A. ( 1987), Muence of organic layer thickness on active-Iayer thickness at twc sites in the western Canadian, Arctic and Subarctic, Erdkunde, 41: p.275.

HILLAIRE-MARCEL, C. (1976). La déglaciation et le relèvement isostatique sur la côte est d' la baie d'Hudson, Cahiers de !Jéomaphie de Oue'bec, 1976, 50: 185-220.

HOLDEN,J., PIPER, D., and JONES, R. (1985), Some deveio~mentof a ri~id-icemodel O frost heave, Proceedings Fourth International Symposium on Ground Freezing, Japan, 93 p. HOUGHTON, J.T., JENKINS, G.J., and EPHRAUM, J.J. (1990). Clirnate chanee-th PCC scientific assessment, Cambridge University press, New York, 364 p.

ISHIZAKI, T. and NISHIO, N. (1988)- Exmental studv of fiost heavine of a saturata u,Proceedings Fifth international Symposium on Ground Freezing, Nottingham, Jones anc Holden, eds., 65-72.

IVES, J.D. (1979), A proposed history of permafrost developrnent in Labrador-Ungava Géoma~hiePhvsiaue et Ouatemaire, 33: 233-244.

JETCHICK, E. and ALLARD, M. (1990), Soi1 wedge polygons in northern Québec Description of paleoclimatic significance, poreas, 19: 353-367.

JOHNSTON, G.H., BROWN, R.J.E. and PICKERSGILL, D.N. (1963), Perrnafros investigations at Thompson. Manitoba terrain studies, National Research Councii of Canada Ottawa. Ont., Technical Paper No. 158, NRC 7568, 105 p.

JORDAN, R. (199 l), A one-dimensionai temperature mode1 for a snow cover, USA Colc Regions Research and Engineering Laboratory, Special Report 91- 16,49 p.

JORDAN, R., H. O'BRIEN and ALBERT, M.R. (1989), Snow as a thermal backmound Preliminary results from the 1987 field test, USA Cold Regions Research and Engineeriq Laboratory, Speciai Report 89-7, 5 p.

JUDGE, A.S., TUCKER, C.M., PILON, S.A. and MOORMAN, B.J. (199 1). Rernott Sensing of Permafrost by ground-Peneuating radar at two airports in arctic Canada. kctic, 4 4 (SUPP.1): 40-48.

KASPER, J.N. (1996), Geomorphic. geo~hvsicaland Ouatemary studies of ice and soi: wedge features in the Foucault River Vailey. Northern Ouek. Université Lavai, Ph. D thesis, 277 p.

KAY, B.D., FUKUDA, M., IZATA, H. and SHEPPARD, M. (1981), The importance 01 water migration in the measurement of the thermal conductivity of unsaturated frozen soils Cold Reeions Science and Technology, 5: 95- 1 12.

KAY, B.D. and PERFECT, B. ( 1988), State of the art: heat and mass transfer in freezing &, Proceedings of Fifth Internationai Symposium on Ground Freezing, 3 -2 1. KERSHAW, G.P. and GU,D.( 1979), Growth and decay of palsas and peat plateau in th Macmillan Pass-Tsichu River ma, Northwest Temtories, Canada, Canadian Journal of Eart Sciences, 16: 1362-1374,

KOJIMA, K. (1966), Deniçafion of seasonal snow cover, Physics of Snow and ICÉ Roceedings of International Conference on Low Temperature Science, Sapporo, p. 929.

KONRAD, J.M. (1990), Theoretical modeüine of massive ice beds hoc. Fifth Cm. Coni Permafrost, 1990, 3 1-35.

KONRAD, J.M. ( 1989). Effect of freeze-thaw cycles on the freezing characteristics of a claye: silt at various overconsohdation ratios, Canadian Geotechnical Journai, 26: 2 17-226.

KONRAD, J.M. (1988), Influence of freezing mode on frozen heave characteristics, && Regions Science and Techology, 15: 16 1- 167.

KONRAD, J.M. and COUTTS, R. (1987), Procedure for detennining the segregatioi potentiai of freezing soils, ASTM Geotechnical Testing Journal, lO(2): 5-58.

KONRAD,, I.M. and MORGENSTERN, N.R. (1984), Frost heave prediction of chiliinj pipelines buried in unfrozen soils, Canadian Geotechnicai Journal, 21: 100- 1 15.

KONRAD,J.M. and MORGENSTERN, N.R. (1982), Effects of applied pressure on freezin~ soils, Canadian Geotechnicai Journal,, 19: 494-505.

KONR4D, J.M. and MORGENSTERN, N.R. (198 1), The se,qgation poteritid of a freeziq soil: A mechanistic theory of ice lensing in soils, Canadian Geotechnical Journal, 18: 482-49 1

KONRAD, J.M. and MORGENSTERN, N R. (1980), A mechanistic theory of ice leni formation in fine-grained soils, Canadian Geotechnicai Journal, 17: 473 -486.

LABERGE, M.J. and PAYEïTE, S. (1995), Long-term monitoring of permafrost change in i palsa peatland in Northem QueTbec, Canada: 1983-1993, Arctic and Ai~ineResearch, 27: 167. 171.

LADANYI, B. and LEMAIRE, C. (1984), Behavior of a buried pipeline under differentia frost have conditions, Proc. of Cold Regions Engineering Special Conf., Montréai, p. 16 1. LAGAREC, D. (1982), Cryopetic mounds as indicaîors of ~~stconditions. northen Che%, Proceedbgs of Foutth Canadian Permafrost Conference (Roger, J. E. Browi mernorial voIume), 43-48.

LAGAREC, D. (1980), Étude péomorpholopique de als ses et autres buttes cryogènes ei Hudsonie RJouveau-Ouelbec), Thèse de doctorat (Ph.D.), Université Laval, 1980, 308 p.

LAGERBACK, R. and RODHE. L. (1986), Pingos and paisas in northemmost Sweden preliminary notes on recent investigations, Geographiska annaler, 68A(3): 149- 154.

LAPRISE, D. and PAYETE, S. (1988). Évo~utionrécente d'une tourbière à palses (Que% subarctique): analyse cartographique et dendrochronoiogique, Canadian Journal of Botanv, 66 22 17-2227.

LAURIOL, B. and GRAY J.T. ( 1987). The decay and disappearance of the late Wisconsin icr sheet in the Ungava Peninsula, Northern Quebec, Canada, Arctic and Alpine Research, 19 109-126.

LAURIOL, B. and GRAY J.T. (1983), Un lac glaciaire dans la région du lac Minto, Nouveau, Que'bec, Canadian Journd of Earth Sciences, 20: 1488- 1492.

LAURTOL, B. and GRAY J.T. (1987), The decay and disappearance of the late Wisconsin ia sheet in the Ungava peninsula, N. Quebec, Canada, Arctic and Al~ineResearch, 19: 10% 126.

LÉVESQUE. R., ALLARD. M., and SEGUIN, M.K. ( 1988). Regionai factors of permafros' distribution and ehickness. Hudson Bav Coast. Ouébec. Cana&, Proceedings of Fiftl International Conference on permafrost, Norway, 1: 199-204.

LÉVESQUE, R., ALLARD, M., SEGUIN, M.K. et PILON, J.A. (1990), Donnée: préliminaires sur le ré&e- du ~er~élisoldans auelaues localités du Nunavik. Oue'bec, Actes de la cinquième conference canadienne sur le pergélisol, 207-2 13.

LIU, C. and AN, W. (I982), Numericd simulation of flow of a siightly compressible fluic through a medium multi-porosity. Acta Mechanica Sinica, 2: 36-44.

LOCH, J.P.G. (1979), Influence of heat extraction rate on the ice segregation rate of soils Frst i Jord, 20: 19-30. LUNDQVIST. J. (1969), Earth and ice mounds: A terminoloeical discussion. In: Pewé, T.L. (ed): The periglacial environment. Past and present, McGiU-Queen's University Press, Montréal, 203 p.

LUNDQVIST, J. (1962), Patterned ground and related frost phenornena in Sweden, Sveriges Geol. Undersokning, Ser. C. 583, 101 p.

LUNDQVIST, J. (195 1). En palsmyr sydost orn Kebnekaise, Geol. Forhandl, Stockholm, 73: 209-225.

MAGEAU, D.W. and MORGENSTERN, N.R. (1980), Observation on moisture migration in frozen soils, Canadian Geotechnical Journal, 17: 54-60.

MACKAY, J.R. (1992), The Çequency of ice-wedge cracking (1967-1987) at Carry Island, Western Arctic Coast, Canada, Canadian Journal of Earth Sciences, 1992,29: 236-248.

MACKAY, J.R. (1983), Pin~omowth and sub~ineowater lenses. Western Arctic Coast,

-7Canada Proceedings of Fourth International Conference on Permafrost, Fairbanks, AK, National Academy Press, Washington, DC., 762-766.

MACKAY, J.R. (1971), The origin of massive ice beds in permafrost, western Arctic, Canada, Canadian Journal of Earth Sciences, 8: 397-422.

MARSHA, I., SHEPPARD, M.I., KAY, B.D. and LOCH, J.P.G. (1978), Development and testine- of a comuuter mode1 for heat and mass flow in freezing soils, Proc. Third Int. Conf. Permafrost, National Research Council of Canada, Ottawa, 75-8 1.

MELLOR, M. (1977), Engineering properties of snow, JoumaI of Glaciolow, 19(8 1): 15-66.

MILLER, R.D. (1978), Frost heave in noncolloidal soils, Proceedings of 3rd International Conference on Permafrost, National Research Council of Canada, Edmonton, Alberta, 707- 713.

MILLER, R.D. (1973), Soi1 freezine: in relation to Dore water Dressure and temperature, Paper presented at 2nd Intemational Conference on Permafrost, Natl. Acad. sci., Yakutsk, USSR

MILLER, R.D.and KOSLOW, E.E. (1980), Cornputaiion of rate of heave versus load under quasi-steady state, Cold Regions Sciences and Tecbnolo~,3: 243-252. MORLAND, L.W., KELLY,R.J. and MORRIS, E.M. (1990), A mixture theory for a phas changing snowpack, 717: 27 1-285.

MORRIS, E.M., mode il in^ of water flow throueh snowuacks, In 2nd Snow Covers: Physic Chemistry, Hydrology, 1987, 179 p.

NELSON F. and OUTCALT, S.I. (1982), Anthropogenic geomorphology in northem Alask Phvsical Geomauhv, 3: 17-48.

NIXON, J.F. (1992), Discrete ice lens theory for frost heave beneath pipelines, Canadi2 Geotechnical Journal, 29: 487-497.

NIXON, J.F. (1991), Discrete ice lens theory for frost heave in soils, Canadian Geotechnic Journal, 28: 843-859.

NTXON, J.F. (1987), Ground freezin~and frost heave. a review, Northern Enginee 19(3&4. Falilwinter): 8 p.

NIXON, J.F. (1982). Field frost heave predictions using the segregation potential concep Canadian Geotechnical Journal, 19: 526-529.

NIXON, J.F. (1978), The role of convective heat transport in the thawing of frozen soil: Canadian Geotechnical Journal, 12(44): 425-429.

NIXON, J.F. and MORGENSTERN, N.R. (1973), Practical extensions to a theory c consolidation for thawine: soils, In Permafrost-The North Arnerican Contribution to the 2t Intemationai Conference, Yakutsk: Washington, D. C., National Academy of Sciences, 365 377.

OLIPHANT, J., TICE, .4. and NAKANO, Y. (1983), Water migration due to a temperatw gradient in frozen soiI, Proceedirigs of Fourth International Conference on Permafros Fairbanks, 95 1-956.

O'NEILL, K. and MILLER, R. (1985), Exploration of a Rigid Ice Mode1 of Frost Heavt Water Resources Research, 21(3): 28 1-296.

OUTCALT, S.I. (1982), Massive near-surface ground ice in Arctic Alaska: Description an rnodelling analysis, Phvsical Geomaphv, 3: 123- 147. OUTCALT, S.I. and NELSON, F.E. (1984), Computer simulation of buoyancy and snow- cover effects in palsa dynamics, Adcand Ai~ineResearch, 16: 259-263.

PAETTE, S., OUZILLEAU, J. and FILION, L. (1975), Zonation des conditions d'enneigement en toundra forestière, Baie d'Hudson, Nouveau-Québec, Canadian Journal of Botm, 53: 1021-1030.

PENNER, E. (1986), Aspects of ice lens growth in soils, Cold Reoions Science and Technolow, 13: 9 1- 100.

PENNER,E. and GOODRICH, L.E. (1981). Location of segregated ice in frozen susceptible soil, Engineering Geology (Amsterdam), 18: 23 1-238.

PÉWÉ, T.L. (1975), Ouaternary eeolow of Alaska, U.S. Geological Survey Professional Paper 835, 263 p.

PILON, J.A., ALLARD, M. and SEGUIN, M.K. (1992), Ground urobing radar in the investigation of permafrost and subsurface characteristics of surficial deuosits in Kan~iqsualujjuaq. northern Ouebec, Ground Penetrating Radar, ed. J. Pilon; Geological Survey of Canada, Paper 90-4, 165 p.

PISSART, A. (1983)- Pin~oset ualses: un essai de synthèse des connaissances actuelles, dans: H. Poser (ed.): Mesoformen des Reliefs ine Heutigen Periglazealraum, Bericht über ein Symposium. Abhandlungen der Akademie der Wissenschaften in Gottingen Mathematisch- Physikalische masse, Dritte Folge Nr., 48 p.

PISSART,A. and GANGLOFF, P. (1984), Les palses minérales et organiques de Ia vaiiée de I'Aveneau, près de Kuujjuaq. Quelbec subarctique, Géographie Physique et Ouatemaire, 38: 2 17-228.

POITEVIN, S. and GRAY, J.T. (1982), Disiribution de pergélisol dans le bassin de la Grande Rivière de la Baleine, Que'bec, Naturaliste canadien, 109: 435-455.

POLLARl3,W.H. and FRENCH, H.M. (1980), A first approximation of the volume of ground ice. Richards Island, Pleistocene Mackenzie Delta, Northwest Temtories, Canadian Geotechnical Journal, 17: 509-5 16. PORSILD, A.E. (1951), Botanv of southeastern Yukon adiacent to the Cano1 Road, Nation Museums of Canada, Bulletin No.2 1 (Biological Series, No. 4 1). Queen's Printer. Ottaw Ontario, 400 p.

PORSILD, A.E. (1945), The aluine flora of the east slope of Mackenzie Mountains. Northwe Temtories. National Museums of Canada, Bulletin 101 (Biological Series, No. 30). Edmor Cloutier, Printer, Ottawa, Ont., 35 p.

QUÉBEC (1984), Le Nord du que-: Profil &ional, Ministère de l'aménagement et c développement régional, Québec, 135 p.

RAMPTON, V.N. and MACKAY, J.R. (1971). Massive ice and ice sediments throu~houttl Tuktovaktuk Peninsula. Richards Island and nearbv areas. District of Mackenzie, Geologic; Survey of Canada, 16 p.

RICHARD, P., LAROUCHE, A., and BOUCHARD, M.A. (1982), Âge de la déglaciatio finde et histoire post-glaciaire de la végétation dans la partie centrale du Nouveau-Québei Géopvhie phvsique et quaternaire, 36: 63-90,

ROCHE, Y. (1994), Variations du couvert nival et dvnarniaue du ~er~élisolau détroit d Manitounuk. Hudsonie, Thèse de doctorat (Ph.D.1, Université Laval, 186 p.

ROUSSEAU, L. (1996). Études stratima~hiquede paises et de plateaux palsiaues. Rivièr Boniface. Ouek subarctique. Université Laval, Mémoire de maîtrise, 105 p.

SALMI, M. (1972). Present development stage of palsas in Finland, Proc. Int. Peat Cong Helsinki, p. 121.

SALMI, M. (1970), Investigations on palsas in Finnish Lapland, In: Ecology of the Subarcti regions, Proceedings of the Helsinki Symposium, UNESCO,Paris, p. 143.

SCHUNKE, E. (1973). Palsa und Kryokarst in Zentral-Island, Nachnchten der Akademie de Wissenschaften in Gottingen II. Mathematisch-Physikalische Klasse, p.65.

SCHUNKE, E. and ZOLTAI. S. (1988), Earth Hurnrnocks (Thufur), In: Clarke, M. J. (Ed. Advances in Periglaciai Geomorphology, Wiley, Chichester, U.K.,p.23 1.

SEGUIN, M.K. et DIONNE, J.C. (1992), Modélisation géo~hvsiaueet caractérisatio: thermique du pergélisol dans les als ses de Blanc-Sablon. Oue'bec, dans recherche en cour: partie E; Commission géologique du Canada, Étude 92- lE, 207 p. SEGUIN M.K. ALLARD, M. and GAI&, E. (1989). Surface and downhole geophysics fc permafrost mapping in Ungava, Quebec, Phvsical Geomauhy, 10: 201-232.

SEGUIN, M.K. and ALLARD, M. (1984). Le pergélisol et les processus thermokarstiques d la région de la rivière Nastapoka, Nouveau Que%, Géoma hie ~hvsiaueet Ouatemaire, 36 11-25.

SEGüIN, M.K. (1978), Te eIecûicai resistivity rdati0nshiD in continuou permafrost at Purtunia. Ungava p en insu la. Proc. Third Int. Conf. Permafrost, Nation; Research Council of Canada, Ottawa, 137-144.

SEPPALA. M. (1986). The origin of palsas, Geomafiska AnnaIer, 68A (3): 141-147.

SEPPALA, M. (1983). Seasonal thawing of palsas in Finnish La~land,Proc. Fourth In' Conf. Permafrost, National Academy press, Washington, D. C., 1127-1132.

SEPPALA, M. (1982), An experimental study of the formation of palsa, Fourth Canadia Permafrost Conference, Roger Brown Mernorial Volume, National Research Council a Canada, 36-42.

SEPPALA. M. (1972), The term "palsa",Zeitschrift fur Geomorpholo~ie,16: 463-474.

SEPPALA, M. (1972a), Pingo-like rernnants in the Peltojihvi area of finish Laplanc Geografîska Annaler, 54A: 38-45.

SHAPIRO, R. (1987), A sim~Iemode1 for the caiculation of the flux of direct and diffuse sola radiation through the atmos~here, ST System Corporation, Lexington, MassachusettE Scientific Report No. 35. Report AFGL-TR-82-0039,45 p.

SHIMIZU, H. (1970), Air permeabilitv of de-wsited snow, institute of Low Temperatun Science, Japan, Contribution No. 1053, English TransIation (CRREL.9 1- 16), 1 p.

SHIZAKI, T. and NISHIO, N. (1988), Experirnental study of frost heaving of a saturatec soil, Proc. Fifth Int. Sym. Ground Freezing, Nottingham, Jones and Holden, eds., 65 p.

SKAVEN-HANG, S. (1959), Protection against fros t heaving on Norwegian railways Geotechniaue, 9(3): 87- 106.

SMITH, M. (1985). Observation of soil freezing and frost heave at Inuvik, NWT, Canada Canadian Journal of Earth Scienm, 22: 283-290. SMITH, M. (1984), Soi1 freezin~and frost heavinrr. at the Caen exrieriment, Proc. of seminar at Caen, France on pipelines and frost heave, Carleton Univ, p. 19.

SMITH,M.W. and PATERSON, D.E. (1989), DetaiIed observations on the nature of fic heaving at a field scale, Canadian Geotechnical Journal, 26: 306-3 12.

SONE, T. and TAKAHASHI, N. (1993), Paisa formation in the Daisetsu Mountains. Ja~a Proc. Sixth Int. Conf. Permafrost, Beijing, China, 2: 1231- 1234.

STRAVERS, L.K.S. (198 l), Paivnolom and dedaciation historv of the Central Labradc Ungava, M. Sc. Thesis, University of Colorado, Institute of Arctic and Alpine Researc Department of Geological Sciences, 171 p.

SVENSSON, H., Traces of pingo-like frost mounds, Svensk Geogr. kbok, 1964, 40: 9 106.

SYKES, J.F., LENNOX. W.C. (1976), Thaw and seeuape in nonlinear elastic norous medi In: Proc. First Int. Conf. Finite Elements in Water Resources, Princeton: London, Pentec Press. 347-367.

SYKES, J.F., LENNOX,W.C. and UNNY, T.E. (1974), Two-dimensional heated pipeli in permafrost, Journal of the Geotechnical enpineerin~Division, 100: 1203- 12 1 1.

TABER, S. (1930), The mechanics of frost heaving, Journal of Geolom, 38: 303-3 17.

TABER, S. (1929). Frost heaving, Journal of Geolo-g, 37(1): 428-441.

TAKAHASHI, N. and SONE, T. (1988), Palsas in the Daisetsuzan Mountains, Cens Hokkaido, Japan, Geomauhical Review of Japan, 61: 665-674.

TAKEDA, K. and NAKANO, Y. (1990), Quasi-steady problems in freezing soils: Experiment on the steady growth of an ice Iayer, Cold Re~onsScience and Technolog, 11 225-247.

TAYLOR, A. and JUDGE, A. (1979), Permafrost studies in northem Québec, Géomnh- - Phvsiaue et Ouatemaire, 33: 245-25 1.

TAYLOR, F.C. (1982), Reconnaissance ~eoIogvof a part of the Canadian Shield. Northei Ouebec and Northwest Territories, Geological Survey of Canada, Memoir, 399 p. TAYLOR. G.S. and LUTHIN, J.N. (1978), A mode1 for coupled heat and moisture transfi during soi1 freezing, gd, 15: 548-555.

THOM, B. (1969), New permafrost investigation near Schefferville, P-Q, Revue (: ,23:3 17-327.

TICE, A., BLACK, P. and BERG, R. (1989), Unfrozen water contents of undisturbed an remolded Alaskan silt, Cold Re~ionsScience and Technology, 17: 103- 1 1 1.

TSYTOVICH. N.A. (1975), The mechanics of fmzen mound, McGraw-Hill Book Compan! New York, NY., 178 p.

TSYTOVICH, N.A. (1966), Basic mechanics of freezing. frozen and thawing soils, In Technical translation 1239, Ottawa, National Research Council of Canada, 35 p.

TSYTOVICH, N.A. (19601, Bases and foundations on frozen soils, Highway Researcl Board, Special Report 58, Washington, D.C., Nationd Academy of Sciences.

VAN VLET-WOE, B. (1991). Differential frost heave, load casting and convection converging mechanisms: a discussion of the origin of cryoturbations, Permafrost an( periglacid Drocesses, 2: 123- 139.

VINCENT, J.S., VEILLETTE, J.. ALLARD, M., RICHARD, P.J.H., HARY, L. anc HILLARE-MARCEL,C. (1987). The last la ci al cycle and ice-retreat from the upper Ottaw: river vallev to southeaîtem Hudson Bav, XIIth INQUA Congress, Excursion Guide Book C. IO, 311 p.

VISKANTA, R. (1991). Phase change heat transfer in ~orousmedia, Proc. Third Int. Sym, CoId Regions Heat Transfer, 187 p.

WASHBURN, A.L. (1983), What is ualsa? In: Mesofonnen des Reliefs irn heutigen Periglazialraurn. H. Poser and Schunke, E. (eds). Abhandlungen der Akadernie der Wissenschaften in Gottingen Mathematisch- Physikaiische Klasse. Dritte folge Nr, 35: 34-37.

WASHBURN, A.L. (1979), Geocryolom: A survev of penglacial urocesses and environment. Arnold, London. 406 p.

WTLLXAMS, P.J. (1% 1). Thermal prorierties and the nature of freezing soils, Proc. Third Int. Sym. Cold Regions Heat Transfer, 187 p. WiLLIAMS, P.J. (1986), Pi lines and uermafrost. Science in a cold clirnate, Ottaw Carleton University Press, 137 p.

WILLIAMS, P.J. and SMITH, M.W. (1989), The frozen earth. Fundarnentals i -, -, Cambridge University Press, 306 p.

WILSON, C. (197 1), Atlas climatiaue du Oue'bec, Service de l'environnement atrnosphériqi du Canada, Toronto, 180 p.

WISCOMBE, W.J. and WARREN S.G. (1980). A mode1 for the spectral albedo of snow. Pure snow. Journal of the Atmospheric Sciences, 37( 12): 27 12-2733.

XU,X., OLIPHANT, J. and TICE, A. (1985), Ex~erimentalstudv on factors affecting- wati rnimtion in frozen Morin clav, Proc. Fourth Int. Sym. Ground Freezing, Sapporo, 123-128

YEN,Y.C. (1962). Effective thermal conductivity of ventiiated snow, Journal of Geo~hvsic. Research, 67(3): 109 1- 1098.

YEN, Y.C., CHENG, K.C. and FUKUSAKO S. (1991), Review of intrinsic thermo~hvsic~ pro~ertiesof snow. ice, sea ice and frost, Proc. 3th Int. Sym. Cold Regions Heat Transfe 187 p.

YOGESH, J. and TORRANCE, K.E. ( l986), Comptational heat transfer, Hemisphei Publishing Corporation, Washington, 8 1- 143. ZARETSKII, YU.K. (1968), Calculation of the setdernent of thawing soil, Soi1 Mechanics an Foundation Engineering, 3: 15 1- 159. Unidimensional program for heat and mass transfert and ice lense formation (Fortran) $DEBUG * prograrn ANULP 1d * ANULPlD (ZQXHE 1) SEP. 15, I992( Oct.22, 1:2S, 1992) * PERIOD OF COLD SEASON changes 20 days in 10 years * coohg fiam -4.4 to -6.7 C, mean anaual air ternperatures; * AMPLITUDE CHANGES OF BOTH WARMAND COLD SEASONS IN AIR * TEMPERATURE WJTH U.B.C.& L.B.C. * INTEGER I,I2,iqi,IZS,IZ7,EKON,IS,JE,ISNO,IPE, +icly 1,igg,igs,ilzupO,ilzup,IMA,IDTO,ILZO, +jstep,KK,k,ni.n3,Nyr,Nmth,Ndy,nmonth,nv * tjstep,KK,k.ni,ms,n3,Nyr.Nmth,Ndy,nmonth,nv DIMENSION T(3.25 1),CIC(251),stwt(25 1) DIMENSION U(S5 l),V(25 l),FJ l(2S l),gorwfb(4) DIMENSION AS l(25 l),BS l(25 l),CS 1(251),DZ(251),H(25 1),HUL(251) DIMENSION IZKON(4),GRAT(4),KEV(4),Vff(4),PWW(4),PII(4),TZMIN($) DIMENSION HZTf(4),HZïs(4),A 1(4),TS(4),P0(4),D(4),HFI(4),HTMïN(4) * DIMENSION HZTf(4),HEV(4),Vff(4).P0(4),HFI(4) * DIMENSION IZKON(4),GRAT(4),A 1(4),PWW(4),PD(4) * DIMENSION PICE(200),PWATER(400) COMMON /MA/AS 1,BS 1,CS 1 COMMON /Mû/U,V,FJ 1 COMMON iMSTI/CIC,stwT COMMON /MF/DZ/MW/HFI,IZKON,A l,PII,PWW COMMON /SW/STW 1,STWS,Sm,STWSNNA/CT5,CT8NB/BM 1,BM4

+/VCR/RASNWT,RAPTWT,RAS1 WT,RAS2WT,POPT,POS IND/DID 1,DlD2,DIPT,DISN +NF/IDTO,HF,Tff,tzl/VG/ISS,I27/GLAS/GLS 1 ,GLS2,GLPT,GLSN +/VH/IS,IE,ABJWSNO,IPE,ICLY1 ,spO 1,spOuVN/NI,N3,DS +/CBMDT/CWW,Cfl,BMDW,BMDI,CSNW,BMDSN,PHCG +/CNDV/CTa,CTb,CTP,CTNW,CTal,CTb 1.CTP 1.CTNW 1, +Wv 1,Wv2,WPT,WSNW,WvSNP,WvPSl.WvS12 +/FSWWKSW 1,KSW2,KSW3,KSW4,KSWS,KSW6,KSW7,KSWg,KSW9,KSW IO CK,41t4CTER*80 ,M4RKS CHARACTER*20 CNWTLM 1 OPEN(7,FILE='c:\wd\ULSQXMF1.DAT1) OPEN(S,FTLE='c:\wd\ULZQXD1.DAT') OPEN(3,FILE='LPT 1') READ(5,'(A8O)') MARKS WRITE(*.'(a80)')MARKS READ(S.*) CCS l,CCS2,CCPT,CSNW,CWW,CI[I READ(S,*) BMDS 1,BMDS2BMDPT,BMDSN,BMDW,BMDI READ(S,*) CTA,CTb,CTP,CTNW READ(5,*) CTA 1 ,Ci%1 ,CTP 1,CTNW 1 READ(S,*) GMs 1,GMs2,GMpt,GMsNW,GMII,GMWT READ(S,*) SPO I ,sp02,ALPHA,BATA.ACOT,BKO,PU,Psep READ(S.*) NI.N3.KK.IDTO.Tff READ(S;*) CT~.CT~,HF,BCC,TMIN,~~~,~~~1 ,izoron READ(S,*) ILZO.ISNO,IPE,ICLY 1,I2 READ(5,*) CAC0 1,CAC02,CAC03,FI 1,FU 1,crit,dtsd READ(S,*) AMCA,AMCA2,TOTIM,JSTEP read(5,*) STW 1,S'IW2,STWP,STWSN READ(5,*) DID 1,DD2,DZPT,DISN REA.D(S,*) DZD 1,DZû29ZD3,DZD4 READ(S,*) ima,imfb,tbhrdy,grtc2 read(S,*) myr0,myr 1,myr2 read(S,*) ymatdc,bcc2,clbc 1,clbc2,clbc3 1000 PAUSE 'END=1000' WRITE(*,*) CCS 1,BMDS 1,CTA,CTAi ,GMs 1,SPOl ,NI,CT5 WRITE(*,*) ILZO,CACO 1,AMCA,STW 1,Dm 1 ,Dm I WRITE(5, *) CCS 1,BMDS 1,CTA,CïAl ,GMs 1,SPO 1,NI,CT5 WRïIE(5,*) iLz0,CACO 1,AMCA,STW 1 ,DID 1.DZD 1 PAUSE'**** KSWl,KSW2 ,...... ,KSW9 AND KSWlO ? ****' PAUSEt**** EQUAL TO 11,12 ,...... , 19 AND 20 OR NOT ? ** **' READ(*,*) KSW 1,KSW2,KSW3,KSW4,KSWS,KSW6,KSW7,KSWS,KSW9,KSW 10 * ******* Tff IS ALWAYS EQ-TO ZERO,TOTIM, HOURS OF ONE YJ5A.R ***** * ******* ISNOd13 WHICH WAS USED IN ZQX€El, ALSO ISNO-Id14 ******* IZO=rn(Tff) LLl=ll MK=O ilzup=O inut=idtO duba=0.52 DBBO=AC03 TGCN=AMCA/grtc2 * **** CSNP, .....,AND CTAB1 FOR THE INTERFACE OF LAYERS ********* CSNP=(CSNW+CCPT)/2. BMDSNP=(BMDSN+BMDFï)/2. xPS 1=(CCPT+CCS 1)/2. yDPl=(BMDPT+BMDS 1)/2. CCS 12=(CCSl+CCS2)/2. BMDS 12=(BMDS l+BMDS2)/2. WvSNP=(WSNW+WPT)/2. WvPS l=(WPT+Wv 1)/2. wvs 12=(wv 1+Wv2)/2. CTSNP=(CTNW+CTP)/2. CTSNP i =(CTTUW 1+CTP 1jl2. xPSA=(CTP+CTA)/2. xPS A 1=(CTP l+CTA 1)/2. CTAB=(CTA+CTB)/2. CTAB 1=(C'TA 1+CTB 1)/2. xw 1=(STWP+STw 1)/2. STWS 12=(STWl+STw2)/2. GLPS l=(GLPT+GLS 1)/2. GLS 12=(GLS1 +GLS2)/2. CLYPI=(l .O-STwl) ptcly=(l .O-xw 1) cly 12=(1.O-stws 12) clyp2=( l .O-stw2) ptpl=( 1.O-stwp) snwpl=( 1.O-stwsn) pscpl=( 1 .O-(stwp+stw 1)/2.0) * GLPT=STWP-CTF' RASNWT=GMSNWlGMWT FtAFTWï--GMPT'/GMWT RAS 1WT=GMS l/GW dz(i)=dzd 1 STWT(I)= STWSN else if (i.1t.ipe) then dz(i)=dzd2 STWT(I)=S?WP else if (i.eq.ipe) then dz(i)=dzd2 stwt(i)=xw 1 else if (i.lt.icly 1) then dz(i)=dzd3 STWT(r)=STW 1 eise if (i.eq.icly 1) then dz(i)=dzd3 stwt(i)=stws 12 ELSE DZ(I)=dzd4 Srn(Ij=STw2 ENDIF WRITE(*, *) 'I,dz, stwtl,I,dz(I),stwt(i) 270 CONTINUE h( 1)=Tff DO 486 I=2,ni H(I)=h(i- 1)+dz(i- 1) WRïi'E(* ,*) '**I,H(I)',I,H(I) 486 CONTINUE DO 493 K= 1.3 TZMIN(K)=Tff HZTF(K)=TFF 493 CONTINUE TFHV=TFF TFHU I=Tff TFHUZ=Tff TFHD=Tff IE=I2- I * ********JMA,DAY,freezes.;INmCLALICECONTITION******** PP I=FLOAT(TMA)*TMIN PP2=TOTTM-PP 1 * *** PosNW,PoPt,Pos1 ,PRESSURES(CM),SNOW AND SOL LAYERS **** PAUSE'FOR CALL FFI, AND READ lTS= 1 ? TIMES OF THE ANNUAL CYCLES' READ (*,*) rrs is= 1 nzup0=iIzo ie=iizupO CALL fiv(T,FI I ,FU 1) hips=(H(IPE)-H(ISN0)) hilyp=(H(ICLY 1)-H(1PE)) Pos I =RASlWT*hilyp PoPt=RAptWT*hips ~01-ip=(stwp-ctp)*O.O9*hip~ coricy=(stw 1-cta)*O.O9*hiiyp **** Pos2=RAS2WT*(Ha-H(ICLY1))************* *****TIM&tbhrdy, HOUR; THE TIME OF THE FREEZ BEGINNING ******** DS=IDTO NV=ie nyr= 1 nsk=ifx(Tff) tz 1=(Tff+cd)/2. IGS=l IGG= 1 IGI=IMA ********** tim=tbhrdy, the beginning of day input with hour *** tim=Tbhrdy PAUSE1NGS= 10 ? CHECKING THE B0UNDA.YCONDITTON ' READ (*,*) NGs ****************Nmntb=imfb1730

500 DO 450 N=2,2 TIM=TIM+FLOAT(I.DTO) IF(TIM.GT.totim) THEN tim=tirn-totim nyr=nyr+ l IGS=l endif IF(nyr.gt.its) then WRITE(*,*) 'Nyrl,ITS stop'ordinary end' END IF IGG=FIX(tirrJtmin) Nmonth=ifix(ti1n/'730)+Nmntb if(Igg.le.30) then Nsk=O endif Ndy=Igg-Nsk*30 if(Nmonth.gt. 12) then Nmth=Nmonth- 12 else Nmth=Nmonth endif if(Igg.eq.(Nsk+ l)*30) then Nsk=Nsk+ l endif IS=N- 1 * ****** ILZUPO, BEGINNING LOCATION OF THE U. B. C. ****** * IE=ILZLIPO tmt=tim-tbhrdy else tmt=t* endif ******** accumulation of b.c.increment each year ***** if((nyr.ge.myr 1.and.nyr.lt.myr2).and.nyr.eq.myr4) then myr4=myr4+ 1 atcci=atcci+yrnatdc clbcc5=clbcc5+bcc2 pp 1=pp 1+2.0* trnin write(*,*)'myr4,atcci,clbcc5,pp 1',myr4,atcci,clbcc5,pp 1 endif ****** VARIATION OF THE L.B.C. ******* if (nyr.lt.myr 1.and.dbboe.gt.CLBC 1) then DBBOE=dbboe-BCC*2. else if (nyr-lt-myrl.and.dbboe.gt.clbc2) then dbboe-dbboe-bcc else if(nyr.lt.myr1.and.dbboe.le.CLBC2) then dbboe=CLBC2 else if(nyr.It.myr2.and.dbboe.gt.clbc3) then dbboe=cIbcc5+bcc2*trnt/totirn else ...... endif IF (Tmt.LE.PP1) THEN strntin=SIN(3.1415926*tmt/PP1) FI=caco I+(AMCA+atcci)*stmtin

Fï=caco2+(AMCA2+atcci)*SIN(3.14 15926*(trnt-PP 1)/PP2) ENDIF ****&?a# FU=DBBOE FJ 1(NI)=FU T(IS+ 1,NI)=FU T(1St 1 ,iE)=FI FJ 1(IE)=FI IF(ksw 1 .eq. 1 1) then write(*,*) 'Nyr,Nmth,Ndy1,nyr,nmth,ndy,'FI=',FI,'fu=',fu write(*,*) 'cacol,caco3 dbboe,BCC,fu,t(is,ni)' write(*,*) caco 1,caco3,dbboe,BCC,fu,t(is,ni) WRZTE(*,*)'IE',IE,'FJl',FJ1(IE),FJ 1(NI) ENDIF IF(ngs.eq. 10) then GOTO 500 ENDIF N3=NI- 1 ***** * FOR THE THERMAL PARAMETERS. 1SNO.IPE.ICLY 1.ICLY2 IF (LLT-IPE)THEN CALL THERPAR(T,I,CCPT$MDPT,CTP,CTPl,ptpl,STWP) ELSE IF (I.EQ.IPE) THEN * CALL WRPAR(T,I,CCPT,BMDPT,CTP,cTPl,**WPT,ptpl,STlW) CALL THERPAR(T,I,xps 1,ydp 1,xpsa,xpsal ,ptcly,xw 1) ELSE IF (1.LT.ICLY 1) THEN * CALL THERPAR(T,I,CCS 1$MDS 1,CïA,CTA 1,wv 1,clyp 1,Sm i ,*GU1 **) CALL THERPAR(TJ,CCS IJ3MDS 1,CïA,CTA 1,clyp 1,STW 1) ELSE if (i-eq-icly1) then CALL THERPAR(T,I,CCS 12,BMDS12,CTAb.CTAb 1,cly l2,SITWs 12) else CALL THEWAR(T,I,CCS2$MDSZ,CTB,CTB1,clyp2,STW2) ENDIF 4448 CONTINUE DO 470 I=IE,N3 IF(I.EQ.N3) THEN IS5=NI IZ7=I- 1 * write(*,*) 'before aDR DZ 1,DZ2 FJ l(NI)',FJ 1(NI) ELSE IF (1.EQ.E) THEN DZ2=DZ(I)*DZ(I+1) dz 1=dz2 * FJl(IE)=T(IS+l,IE) * IQI=I IZ7=IE IZS=I+ 1 ELSE

DZ~=DZ,STWT(I),hev(k) * CIC(I)=V(I)/( 1 .+HEV(K)* 1-011.00)

1121 CONTINUE DX 1 =Ts(K)/dtsd DX2=D(K)/dtsd PPSO=PO(K)+Psep DZ 1 =0.0 DZ2=0.0 * ******* O.OTO,HF,Tff, +tzl/FSWHfKSW 1,KSW2,KSW3,KSW4,KSW5,KSW6,KSW7,KSW8,KSW9 1. PHCG=DIDT*HF TWv 1=(stwt(i)-uwpr)/(-ct5) T5 l=PHCG*TWv 1 CST=UWPR*UWPR1 T53=PHCG*CST*EXP(UWPRl *Tsv) IF(KSW2.EQ. 12)THEN WRITE(*,*) 'I',I,'CST',CST,'PHCG',PHCG,'DIDT',DIDT WRITE(*,*) 'HF1,HF,'T511,T5 1 ,'T53',T53,'TWV l',TWV 1 ENDJF RE- * *****************END SUBROUTiNE ADV(I) DIMENSION U(25 1),FJ l(2S 1 ) DIMENSION V(25 1),AS l(2S 1),BSl(E 1 ) DIMENSION CS l(25 1),DZ(25 1) COMMON MNAS I ,BS 1,CS 1 COMMON /MDm,V.FJ 1 COMMON /MF/DZ/VB/BM 1,BM4NWIS,E,ABJNG/IZ5,IZ7NNMI,N3,DS COMMONIFSWHIKSW 1 ,KSW3,KSW3,KSW4,KSWS,KSW6,KSW7,KSW8,KS W9,KSW IO IF(1.EQ.E) THEN BS l(I)= 1. CS 1(I)=BM4 U(E5)=-CS l(1) FB J=FJ l(1) V(IZS)=FBJ ABJ=l. AS 1(i)=-aS 10/DD1 CS 1(i)=-CS 1(Q'DD2 bs 1(i)=l .-as 1(i)-cs 1 (i) ABJ=AS 1(I)*U(I)+BS l(1) U(iz5)=-CS 1(T)/AB J

IF (KSW3.EQ. 12) THEN WRITE(* ,*) 'I',I,'IZS',IZS,'U-5',U(IZ5),'V-5',V(IZS) WRITE(*,*) 'AS l',AS l(I),'BS lt,BS l(I),'CS l',CS l(1) WRITE(*,*) 'FJ ll,FJ1 (I),'ABJ',ABJ,'dzl,dz(i),dd 1 ENDIF RETURN END * ...... SUBROUTINE TINT(N,T) DIMENSION T(3.25 1) COMMON /VN/NI,N3,DS/VH/IS,IE,ABJ * WRITE(*,*)NI,IE,N,IS DO 666 I=IE,NI T(N- 1,I)=T(N,I) 666 CONTINUE RETURN * ...... END SUBROUTINE RSTA(t,ndy,NV) DlMENSION T(3,25 1 ),U(25 1),FJ l(î51),CIC(25 1) DJMENSION V(25 l),STWT(25 1) COMMON /MD/U,V,FJ l/MSTVCIC,stwt COMMON /VNINI,N3,DS/VH/IS,IE,ABJ COMMONIFSWWKSW l,KSW2,KSW3,KSW4,KSW5,KSW6,KSW7,KSW8,KS

IF((ksw6.eq. 16).and.(ndy.eq. lO.or.ndy.eq.20.0r.ndy.eq.30))then WRITE(*,*) 'RSTA I',I,'U=',U(I),'CIC',CIC(I),'STWT',STWT(I) ENDIF 777 CONTINUE RETURN * *********************************************END SUBROUTINE FTS A(T,IQI) DIMENSION T(3,25 1),U(251),FJ l(25 1) DIMENSION V(251),AS l(Zl)$S l(î51),CS l(25 1) COMMON /MD/U,V,FJl COMMON WAS1,BS 1,CS 1 COMMON NN/NI,N3,DS/VH/IS,IE,ABJ COMMONIFSWWKSW 1,KSW2,KSW3,KSW4,KSW5,KSW6,KSW7,KSW8,KS W9,KSWlO

WRITE(*,*~II',II.'FJ 1 ',FJ 1(II),'TI',T(IS- 1JI) WHTE(*,*) 'U1,U(II),'V ',V(II),' TI2',T(IS,II) WRITE(*,*)'AS l',AS l(II),' ABJ',ABJ Endif CONTINUE RErn ********************************END SUBROUTINE HTfE(I,K,H,HZTF,crit) DiMENSION DZ(25 1),H(251) DIMENSION U(25 l),V(El),FJ l(25 1) DIMENSION HZTF(4),HFI(4) DIMENSION IZKON(4),A1(4),PWW(4),PII(4) COMMON /MDN,V,FJ 1 COMMON /MW/HFI,IZKON,A 1.PII,PWW COMMON /MF/DZJVF~TO,HF,Tff,tzI/VN/NI,N3,DS +IFSWWKSW l,KSW2,KSW3,KSW4,KSWS,KSW6,KSW7,KSW8,KSW9,KSW10 IF(Tff.LE.U(I).AND.tFF.GT.U(I+1 )) THEN ******* DOWNWARDS, B TYPE,THAWING ********* DZ 1=(U(I+ 1)-U(I))/DZ(I) DZL=(Tff-UjijjiDZ 1 HZTF(3)=H(I+ 1)-DZ2 EKON(3)=I+ 1 ELSEIF (-crit.LE.U(I+ 1 ).and.-crit.GE.U(I)) THEN ********* UPPERWARDS, A C TYPES,FREEZING ******+* DZ 1=(U(It 1)-U(I))/DZ(I) *$*$* DZ2=(Tff-U(I))/DZ1 DZ2=(-Cm-U(I))/DZ1 HZTF(K)=H(I)+DZL IZKON(K)=I WRITE(*,*)'UPWD K,I',K,I K=K+ 1 ELSE GOTO 1212 ENDIF IF(KSW8.EQ. 18) THEN WRITE(*,*) '1',I,'K1,K,'Hi,&i+lt,H(I),H(I+ 1) WRITE(*,*) 'Ui-1,i,&i+l'.u(I- l),u(T),U(I+l),'Tff ,tff write(*,*) 'IZKON 1,2,3',IZKON(K),'HZTFi ,2,3',HZTF(K) ENDIF 1212 RETURN * ***********************************END SUBROUTINE POVFHV (K,ACOT,Vff,HEVQO,GRAT,H,HZTf, +gonivfh,corip,coricy) DIMENSION GRAT(4),VFF(4),HEV(4),HZTF(4),P0(4),H(251),gorwfh(4) COMMON /SW/STW 1,STW2,S~,S~SN/CNDV/CTa,~,CTP,CTNW1 +CTal,CTb l,CTPl,CTNW ~,W~~,WV~,WPT,WSNW,WVSNP,W~PS1,WvS 12 +NI/ISNO,IPE,ICLY 1,SPO 1,sp02NF/IDTO,HF,Tff,tz 1 +NWIS,IE,ABJNCR/RASNWT,RAPTWT,RASlWT,RAS2WT,POPT,POS 1 PosNW=RAsNWT*(H(ISNO)-Hm)) IF(HZTF(K).LE.H(ISNO)) THEN * ********** THE SNOW & 'ZONE ********* * WRITE(*,*)'HZTF(K)

hzy 12=HZTF(K)-H(ICLY1) coriy 13=(stw2-ctb)*O.O9*hzy 12 PO(K)=PosNW+Popt+PosI+RAs2WT*hzy 12 Vff(K)=SPO 1*EXP(-ACOT*PO(K))*GRAT(K) gorwfh(k)~orip-t.coricy+cony12 ENDIF HEV(K)=Vff(k)*FLOAT(IDTO) * WRITE(*,*)'K',K,'HZTFkf,HZTF(K),'Hipe',H(TPE),'HiclyIg,H(ICLY 1 ) * WRITE(*,*)'K',K,'HZTFkrlHZTF(K),'PO,Vff,HEV',PO(K),Vff(K),EV(k) RETUREU' end * **************************findingtS1 ********** subroutine fdts(K,Vff,GRAT,PO,TS,D.ALPHA,BKO,BATA,PU,CRIT) DIMENSION Al(4),TS(4),P0(4),D(4),PWWo,PII(4)lPII(4) DIMENSION IZKON(4),GRAT(4),Vff(4),HFI(4) COMMON /MW/HFI,IZKON,A 1,PII,PWW TSk-CRIT A 1(k)=Vff(K)/(( 1 .O+ALPI-IA)*BKO*GRAT(K)) 236 TS1 =((-Al (K)*(-TsO)**( l+ALPHA)- 1.09*PO(K)+PU)/BATA)/10.0 IF(ABS(TS 1-TSO).GT. 1E-6) THEN TSkTs1 GOTO 236 ELSE IF (Ts 1.GT. 1 .O) THEN WRITE(3,*) A 1(K),Vff(K),GRAT(K),PO(K),TS 1 WRITE(*,*) A 1(K),Vff(K).GRAT(K),PO(K),TS 1 PAUSE'Ts 1 STOP' ELSE Ts(K)=Ts 1* 100.0 D(K)=-Ts(K)/GRAT(K) ENDF F (K.EQ.2) THEN * * mit=-tsl*0.618 ait=-& 1 * **** C--0992 ENDlF * WRITE(*,*)'Kr,K,'A1,PO',A 1 (K),PO(K),'GRAT1.GRAT(K), * +'DV,d(K),'TSI&O',TS 1,TSO RETURN END ANNEX II

Bidimensional program for palsa inception (Fortran) * * { PLSFMT2D includs pls1,main program,&plsS,total subroutines )

* DIMENSION HUL(170),FPW,hztf,HZTs,A1,TSpO,D,TS,PWW,PII( l5O,3)? DIMENSION AS l(l50,2SO),CS l(l50,25O),U( l5O,ZSO),V( 150,250) DIMENSION T(3,150,250),STWT(150,250),FJ1(150,250),HVwm(l50,250) DIMENSION KZ( 150,3),GRAT(l50,2),HEV(150,2),Vff( l5O,2) DIMENSION hztf(15O12),tfhud(150,2).DUBF(lSO),FPW(l50) DIMENSION jze(l50),jpu(l50),jpw(150),hpu(l50),hpw(150),H(250) DIMENSION IXPL(250),XPL(250),IXPR(250),XPR(250) DIMENSION ISNR(250),RRRS(250) COMMON /MW/KZ,GRAT/bccs/bcmi ,snbc,ptbc,cf 1,totirn/bctp/FI,FU, +FIAT,FLPT.FISN/CB~T/ONW,CII,cair,BMDW,BMDI,bmair,PHCG +/CDC/DID 1,DIPT,diair +/CNDV/CTSL,eTP,CTNW,ctair,CTSLl,CTP1,CTNWl,ctairl +/CRC/RAPTWT,RAS 1WT/CSC/STW 1,STWP,STWSN,stair +/SNPRMT/BMDSN 1,CSNW,DISN 1,DISN2,SNJMNAICTS,CT8 +NBINI,J7,18 ,JS,JPSND/BMi ,BM3,BM4$M5,YBNEIDX,DZNF/IDTO,HF,Tff +NGiiZ5,KZ7,IWS,IW7NH/ï 1,Y2,IS,IE,ABJNVspO 1 ,sp02 +NKIACOT,ALPHA,BKO,BATA,HPTTK,HIEH,dtsd,Psep +/FSWH/kw 1,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw10 CHARACTER*80 MARKS CHARACTER"80 CNWTLM 1 * OPEN(7,FILE='D:\wd\ULZQXMF1.DAT') OPEN(7,FILE='D:\wd\pIsf2d.DAT') OPEN(S,FILE='D:\wd\pl2dd1.dat') OPEN(3,FILE='LPT 1') READ(5,'(A80)') MARKS WRITE(*,'(a80)')MARKS READ(S,*) CCS I ,CCPT,CSNW,cair,CWW,CII READ(S,*) BMDS 1,BMDPT,BMDSN 1 ,bmair,BMDW,BMDI READ(S,*) CTSL,CTP,CTNW,ctair READ(S,*) CTSL 1,CTP 1,CTNW 1,ctair 1 READ(5, *) GMs 1,GMpt,GMsNW,pair,GMII,GMWT READ(5,*) SPO 1,spO2,ALPHA,BATA,ACOT,BKO,PU,Psep READIS,*) NI,J8.i5,IDTO,inlar RE AD(^,*) CT~,ET~,HF,BCC,TMIN,~~~,~~~1,izoron READ(S,*) cptcv 1,cptcv2,csncv,ptbc,snbc,bcrni READ(S,*) FI 1,FU1 ,FI2,FU2,dtsd READ(S,*) AMCA 1,AMCAS,TOTIM read(S,*) STW 1,STWPa,STWPb,STWSN,stair READ(5,*) DID 1,DIPT,DISN 1,DISN2,diair READ(5,') DX,DZ,HP?TK,Tff,SNWMX,ferrc READ(5,*) ima,imfb,tbhrdy,nyrj5,snwast,snwaed 1OûO PAUSE 'END= 1000' WRïTE(*,*) CCS 1,BMDS 1,CTSL,CTSLl ,GMs 1,SPO 1,NI,CT5 WRITE(*,*) Cptcv 1,FI1 ,AMCA 1,STW 1,DID 1,DX,ima WRITE(S,*) CCS 1,BMDS 1,CTSL,CTSLl,GMsl,SPO 1,N,CT5 WRITE(S,*) Cptcv 1,Fi l,AMCAl,STWl ,DIDl,DX,ima PAUSEinput myrO & retim; myrû, for saveing data in file; +retim. for kw 1.kw2 ...... kw 10' READ(*,*)iy10,ietim { Tff IS ALWAYS EQ.TO ZERO, TOTIM, HOURS OF ONE YEAR ** ( inipt, init. pt.surf.location, no snow cover; isnr(in1pt) } { HFTTK, THICKNESS OF PEAT as pusi zero,SNWMX,MAX. SNOW THICK ] ( jpu & jpw, EQUAL TO 1, TOP & BOTïOM OF PEAT) { IXPL & XPR, EQUAL TO J, L & R B. OF pt.;ixpl&rxpl&r(dpw)} **** CSNP, .....,AND CTSLl FOR THE INTERFACE OF LAYERS ********* PAUSE' kw l,kw2,kw3 ,....,kw9 & kwl0,is 11,12,13,..,20 or NOT ? ' READ(*,*) kw 1,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw 10 j7=j 8- 1 rzo=IFIx(Tff) { inlar,air range,from 1 to max.sn.cv.,isntk; inlpw.I.b.of pt. 1 iptk=ifu(hpWdz) SNWTKCN=SNWMX/ALOG(snwaed) SNJM=snwmx/dz isntk=ifix(SNJM) jps=jS+isntk+ 1 jps5=jps-j5 inlpt=inlar+isntk+2 jsnmh=inlpt PLSINH=dz*float(idpt- 1) inlpw=inlpt+iptk IZO=IFIX(Tff) LL1=11 EX=1 IXY=l dx 1=dx*dx dx3=dx 1 dzsq=ciz*dz **** CSNP,....., AND CTSLl FOR THE INTERFACE OF LAYERS ********* DISN 1=DISN il1000.0 DISN2=DISNU1000.0 BMDWi=(BMDW+BMDI)I2.0 BMPS l=(BMDPT+BMDS 1)/2.0 CSNP=(CSNW+CCPT)/2.0 CPS 1=(CCPT+CCS 1)/2.0 CTSNP=(CTMrJ+CTP)12.0 CTSNP 1 =(CTNW l+CTP 1)12.0 CTPSk(CTP+CTSL)/2.0 CTPSL l=(CTPl+CTSL 1)/2.0 cwI=(CWW+CII)12.0 DISN 12=(DISN1 +DISN2)/2.0* 1000.0 SWP 1=(STWPb+STW 1)lS.O arsar= l .O-stair CLYP 1= 1.O-stw 1 ptcly= 1.O-SWP 1 ptpl=l .O-stwpb snwpI= 1.O-stwsn RAFTwT=GMPT/GMWT RAS IWT=GMS IIGMWT { inipt,jze(j)=jpu(j), when initial snow thick,zero; Z-D } write(*,*)'snwtkcn,isntk,inlpt,ie,iptk,pp 1,totim' write(*,*) snwtkcn,isntk,uilpt,ie,iptk,pp 1 ,totim do 262 j=lj8 dubf(j)=dz/4.0 jze(j)=inipt jpug')=jze(j) hpu(j)=float(jpu(j)-l)*dz jpw(j)=jpu(j)+iptk hpw(j)=float(jpwCj)- 1)*dz continue iz5=j8/2 write(*,*)'j=j8/2,jze,jpu,hpu,jpw,hpw' write(*,*) iz5,jze(iz5),.jpu(iz5),hpu(iz5),-- +jpw(iz5),hpw(iz5) (IXPL,iXPR(i),left&rightbounders of pt.respectively,in X-D ] do 265 i= 1.ni iXPL(i)= 1 XPL(i)=Tff iXPR(i)=j8 XPR(i)=dx*float(j8- 1) IF (I.LT.jpu(2)) THEN IXPL(i)=99999 XPL(I)=99999.0 else ENDIF write(*,*)'i,IXPL&r,XPL&r1,i,IXPL(i),iXPR(i)%XPL(i),XPR(i) continue do i= 1,ni ISNR(i)=jps end do ( ok initial water content ] DO 293 J=l,J8 DO 304 K=1,3 tfhud(J,k)=Tff hztf(J,K)=TFF CONTINUE DO 294 I= 1,NI HVwrn(j,i)=Tff if (i.lt.JZE(J)) then stwtg' ,i)=stair else IF (i.it.jpu(i)) then STWT(J,I)= STWSN else if (i.lt.jpw(j)) then stwt(j,i)=stwpb else if (i-eq-jpwu))then stwt(j,i)=swp 1 else stwt(j,i)=stw 1 endif continue 293 CONTINUE DO I= 1,NI H(I)=FLOAT(I- 1)*DZ END DO * *** TIM & tbhrdy, HOUR; THE TIME OF THE FREEZ BEGINNING *** PAUSE'SUBR. FIV,ïïS= l? ANNUAL CYCLES;chkT=l or2?,only for temp.' READ (*,*) ITs,chkT call fiv (T,Fi 1,fiS,fu 1,fu2,ferrc,inlpt,AS 1 ,CS 1,FJ 1,V) * **** rsta & htfh for initial KZ( ) **** Cal1 RSTA(T,NV,tim,pdt,jpu,ixx,izoron,U,STTNT) call htffz(hztf,jpu,jze,H,jsnmh,U) JE=I kmnu=jpu(j7) kmxu=kmnu kmxw=jpw(j7) kmnw=kmxw nyr= 1 nsK=ifix(Tff) IGS= 1 igg= 1 IGI=IMA cfl=-bcc tim=Tbhrdy trnid=float(idtO) PAUSE' NGS= 10 ? chECKING THE BOUNDARY CONDITION ' READ (*,*) NGS Nrnntb=imfbff 30 dyp2=pp2/tmin * ******dyp4=dyp2*5.0/6.0 ******* 500 DO 450 N=2,2 IS=N- 1 iF(TIM.GT.totim) THEN tim=tim-totim nyr=nyr+ 1 IGS= 1 IXX= 1 KY=1 endif TIM=TIM+FLOAT(TDTO) IF(nyr.gt.its) then WRITE(*, *) 'Nyr1,1TS stop'ordinary end' END IF igg=IFIX(tim/tmin) Nmonth=ifix(tim/730)+Nmntb if(igg.le.30) then NsK=O endif Ndy=igg-NsK*30 if(Nmonth.gt. 12) then Nmth=Nmonth- 12 else Nmth=Nrnonth endif if(igg.eq.(NsK+l)*30) then NsK=NsK+ 1 endif ****** inlpt, BEGNNING LOCATION OF THE U. B. C. ****** if(nyr.eq. 1) then mit=tim-tbhrdy else tmt=tim endif ( nyr,myrl ,myr2,myr4, climat change. U.B.C.& L.B.C. variations wirh time each year, reference the plstcc-for } *** Here, hpw(j) for modification of U.B.C. & dz(2) *** Cd1 TDZ2M (T,jpu,hpu,hpw,H,U)

( U.B.C.responses (snow accumulation & melting) & peat cover } IF (TMT.LE.PP 1) THEN CALL UBMCT (tmt,T,jze,jpu,AMCA I,csncv,cptcv 1,O.O,pp 1 ,FJ 1) ( EMPIRICAL formula , SNOW ACCUMULATION IN WINTER ) wpsf l=stwpb wpsf=stwpb y2=(tmt-snwast)/tmin if (tmt.lt.snwast) then snwth=Tff else if (tmt.gt.snwast.and.y2.le.snwaed) then snwth=snwtkcn*dog(y2) endif ELSE ( JZE(J),equal to i, increases with SNOW MELTING 1 CALL UBMCT (tmt,T,jze,jpu,AMCA2,O.O,cptcv2,ppI ,pp2,FJ 1 ) *** ( water content variation of peat cover, in summer & winter 1 bd=(tmt-pp 1 )/tmin if (bmS.lt.dypU4.0) then wpsf=stwpb-(stwpb-stwpa)*bm5*4.0/dyp2 else if(bm5.gt.dyp4) then wpsf=stwpa+(stwpb-stwpa)*(bmS-dyp4)/(dypZ-dyp4) else endif do 136 j=ljps if (j~e(j).lt.jpu(j).or.brn5.lt.dyp2/2~0) then wpsf 1=stwpb else if (jze(j)-eq-jpu(j).and.bm5.le.dyp4) then wpsf l=stwpb-(stwpb-stwpb*0.75)*(bmS-dyp2/2.)/(dyp4-dyp2/2.0) else if CjzeCj).eq.jpu(j).md.bm5.gt.dyp4) then wpsf l =stwpb-(stwpb-stwpb*0.75)*(brnS-dyp4}I(dyp2-dyp4) else ****endif if (j-eq-jps)then wpsfl =(wpsf 1+wpsf)/2.0 endif 136 continue ENDIF * **** ( water content variation dong the peat thick } do 147 j=lj8 do 153 i=jpu(j)jpw(j)- 1 if(j.1e.j~~)then stwp=wpsf l+(stwpb-wpsf I )*(i-jpuCj))/(jpwCj)- 1-jpu(j)) else stwp=wpsf+(stwpb-wpsf)*(i-jpu(j))/(jpw(j)- 1-jpu(j)) endif stwtQ,i)=stwp 153 continue 147 continue IF(ngs.eq. 10.or.chkt.eq. l.or.chkt.eq.2) then wrïte(*,*)'Nyr-mth-dy.mt.jze4jpuj7,snwth,T(is, 1,ni),FIAT,FU1 write(*,*)Nyr,Nmth,Ndy,tmt,jze(4)jpu(j7),snwth, +T(is, 1,ni),FIAT,FU GOTO 500 endif * ( Z-D, THERMAL PARAMETERS,dZE, for * air, snow, (snow+peat)R, peat, (peat+soiI)/2., soi1 } if(nyr.1e.n~rj5) then else j5=j8*2000 endif DO 2447 J= 1,J8 if(T(is,j,ni).gt.3.5) then write(*,*)'l st tim,is,j,ni,T,U,fj 1(),ful write(*,*)tim,is,j.ni.T(is,j,ni),U(j,ni),fjlQ,ni),fu stop' 1st Tnb3.5' else endif * {JZE(J)=I, THE LOCATIONS OF SNOW SURFACE IN EACH J } iw5=jze(j) iw7=jpu(j) izS=jpw(j) DO 2448 I=EN if (i.le.jpwG).and.i.ge.jpuCj)) then ptpl=l .O-stwtti,i) stwp=stwt(j,i) endif * ( ok swtw () } IF((I.LT.iw5.and.j.le,ips).or.(I.It.iw7.AND.j.gt.jps))THEN * { no snow cover. air thermo-parameter. } CALL THERPAR(T,j,I,Cair,BMair,Ctair,Ctairl,Arsar,stair,U,V,STVirT) ELSE iF((I.lt.iw7.AND.iw5.LT.iw7).and.j.lt.jps~THEN CALL VMDSN(J,BMDPT,BMDSN,BMDSNP,PU,JZE) CALL THERPARSNW(Tj,I,CWI,BMDWI,BMDSN,U,V) ELSE IF((I.eq.iw7.and.iw5.1t.iw7).anddj.1t.jps)then * { for (snow+peat)/2. bounder } CALL VMDSN(J,BMDPT,BMDSN,BMDSNP,JPU,JZE) CALL THERPAR(Tj,I,CSNPBMDSNP,CTSNP,CTSNP1,ptpl,wpsf,U,V,STWT) else if (i.lt.iz5) then CALL THERPAR(Tj,I,CCPT,B MDPT,CTP,CTP 1,ptpl ,STWP,U,V,STWT) else if (i.eq.iz5) then * ( for (peat+soil)/2. bounder } CALL THERPAR(Tj,I,CPS 1,BMPS 1,CTPSL,CTPSLI ,ptcIy,SWP 1.U,V,SïWï) else CALL THERPAR(T,j,I,CCS 1,BMDS 1.CTSL,CïSL 1,clyp 1,STW 1,U,V,STWT) ENDIF 2448 continue 2447 continue Y2=0. Yl=l. DO 460 J= 1,J8 IWS=J IW7-J DO 470 I=IE,NI IF (1.EQ.Ni) THEN E5=I E7d-1

E5=I+ 1 FJ 1(J,IE)=T(IS,J,IE) IQI=I ELSE IZ5=I+ 1 IZ7=I- 1 * ********ENDIF tsv=T(isj,i) IF((I.LT.JZE(J).and.j.le.jps).or.(I.lt.jpu(J).AND.j.gt.jps))~N Cal1 ddt(j,i,tsv,t5 1.t53,ctair,ctairl ,diair,STWT) ELSE IF((I.lt.jpu(J).AND.JZE(J).LT.jpu(J)).~.It.jps)THEN CALL DDTSNW(j,I,Tsv,TS 1,T53,DISN 12) else if (i.lt.jpw(J)) then CALL DDT(j,I,Tsv,TS 1,T53,CTP,CTP 1 ,DIPT,STWT) else CALL DDT(j,I,Tsv,TS 1,T53,CTSL,CTSL L ,DID I ,STWT) E.WIF if(i.eq.jpu(j)) then dz l=dz*(hpwCj)+dz)/2.O dz2=dzsq else dz 1=dzsq dz2=dz1 endif CALL ADR (TIM,J,I,IQI,T,dzl,dz2,t51,t53,ASI,CSI,FJI,U,V) 470 CONTINUE DO 480 J=Ei ,J8 IF(I.LE.JPU(J).AND.J.EQ.ISNR(I))THEN T(1S ,I,I)=FISN ENDIF * if (tim-gt.8600.and.i.le.kmxu) then * write(*,*)'tim,fi,j,i,ku,ixpl(i)', tim,fi j,i,kmxu,ixpl(i) * endif if((i.le.jpu(j).and,i.eq.IXPL(i)).and. +(rXPL(i).gt.ISNR(i).and.ixpI(i).lt.j8)) then T(IS ,J,I)=FIPT YB=I.O BM4=0.0 else YB=O.O B Mk-1 .O endif W5=J+ 1 * ( x-D,for adv } CALL ADV (I,J,IEI,J,dxl.dx2,AS 1,CS I,FJl,U,V) 480 CONTINUE CALL FTSV (1,T.E 1 ,IQI,AS 1,FJ 1,U,V) 475 CONTINUE * *** X-D, THERMAL PARAMETERS, IZE-jpu-jpw(J)=I *** DO 2557 I=IE,NI if (i.le.kmxw) then ixl=IXPL(i) ixr=iXPR(i) endif DO 2558 J=1,58 if(T(is,j,ni).gt.3.5) then write(*,*)'af ftsv tim,is,j,ni,T,U,fj l(),ful write(*,*)tim,is,j,ni,T(is,j,ni),U(j,ni),fj1(j,ni),fu stop'af ftsv Tnb3.5' else endif if (i.le.jpwu).and.i.ge=ipu(j)) then ptpl= 1.O-stwt(j.i) srwp=stwtCj,i) * ( ok stwtf ) } endif iw5=jze(j) iz7=jpuQ) iz5=jpw(j) IF(i.gt.iz5) THEN * ( soi1 foundation } CALL THERPAR(T,j,I,CCS 1,BMDS 1,CTSL,CTSL 1,clyp 1 ,STW 1,U,V,STWT) ELSEIF ((j.eq.ixr.and.ixr.lt.j8).OR.I.EQ.jpw(j)) THEN * ( for (peat+soil)/2. bounder } CALL THERPAR(T,j,I,CPS I ,BMPS 1,CTPSL,CTPSL 1,ptcly,SWP 1,U,V,STWT) ELSEIF ((j.ge.ixi.and.j.le.ixr).and.(I.ge.i~7~N * ( peat cover} CALL THERPAR(T,j,I,CCPT,BMDPT,CTP,CTP1,ptpl,STWP,U,V,STWT) ELSEIF ((I.ge.iwS.rtnd.i.le.iz7).and.((j.eq.ixl.and.ixl.le. +ISNR(i)).OR.(LEQ.izl.and.j.lt.ISNR(I))))then * { for (snow+peat)/2. bounder ) CUVMDSN(J,BMDPT,BMDSN&MDSNP,JPUJZ) CALL THERPAR(T,j,I,CSNPBMDSNP,CTSNP,CTSNP1 ,ptpl,wpsf,U,V,STWT) ELSEIF ((I.ge.iw5.and.i.lt.iz7).andd((i.1e.ixl.and.ixI.le. +ISMR(I)).or.(i.Ie.ISNR(i).and.ISNR~.lt~)))THEN * { snow cover } CALL VMDSN(J,BMDPT,BMDSNBMDSNPPU,JZE) CALL THERPARSNW(T,j,I,CWI,BMDU?,BMDSN,U,V) else * ( no snow cover, air thermo-parameter. ) CALL THERPAR(T,j,I,Cair,BMair,Ctair,CtairI ,arsar,stair,U,V,SïWï) endif * ~nte(*,*)'tim,kmX~,kmnu,fij,i,stwt()',tim,kmxu,kmnu,Fi, * +j,i,stwt(j,i) 2558 continue 2557 continue IS=N IQI= Lûûû iel=l WRITE(*,*) '4ZQI=',IQI DO 485 I=E,Ni write(*,*)'485,i,ie,ni',i,ie,ni ES=I E7=I DO 488 J=IE1,58 IW5=J+ 1 IW7=J- 1 IF(J.EQ. E 1 ) THEN Mr7=EI ELSE IF(J.EQ.J8) THEN IW5=J8 ELSE ENDIF ** X-D **IXPL,iXPR, LET AND RIGHT BOUNDARIES OF PEAT; J *** tsv=T(isj,i) if (i.Ie.kmxw)then ixl=IXPL(i) ixr=iXPR(i) endif icrt=jpwQ) if (tim.ge.8640) then write(*,*)'489 ddt tim,fij,i,kmxu,jpu,icrt-jpwiji' write(*,*) tim,fi,j,i,kmxu,jpu~),icrt endif IF (i.gt.icrt) THEN { soi1 foundation } CALL DDT(j,I,Tsv,TS1 ,T53,Ci'SL,CTSL1 ,DID 1,STWT) ELSEIF ((j.eq.ixr.and.ixr.lt.j8).OR.I.EQ.icrt) THEN ( for (peat+soil)R. bounder ) CALL DDT(i,I,Tsv,TS 1 ,T53,CTSL,CTSL1 ,DID 1,STWT) ELSEIF ((j.ge.~l.and.j.le.ixr).and.(~.ge.jpu(jd.i.le. CR)) THEN * ( peat cover } CALL DDTQ,I,Tsv,TS1 ,T53,CTP,CTPl.DIPT,STWT) ELSEIF ((I.ge.iw5.and.i.le.iz7).andd((j.eq.ixl.-le. +ISNR(i)).OR,(LEQ.iz7 .md.j.It.ISNR(I))))then * { for (snow+peat)R. bounder } CALL DDT(j.I,Tsv,TS 1,T53,CTP,CTP 1,DIPT,STWT) ELSEIF ((I.ge.iw5.and.i.lt.iz7).and.((j.le.ud.and.ixl.le. +ISNR(I)).or.(j.le.ISNR(i).anddISNR(I).lt.i)))THEN * { snow cover ) CALL DDTSNW(j,I,Tsv,TS 1,T53,DISN 12) eIse * { no snow cover, air thenno-parameter. } call DDTCj ,i,tsv,d 1,t53 ,ctair,ctair 1,diair,STWï) * *********endif CALL ADR (TIM,J,I,IQI,T,DxI,dx2,t5l,t53,AS 1,CS l,FIl,U,V) IF(J.EQ.IE 1) THEN FJ 1(J,I)=T(IS,J+l.I) T(IS ,J,I)=T(IS .J+ I ,I) eIse if (j.eq.j8) then fj l(j,i)=t(is.j- 1,i) T(IS,J,I)=T(IS,J- 1 ,I) ENDIF 488 CONTINUE 485 CONTINUE ****** Y2=1. and Y1=0. for 2-D ****** Y2= 1. y l=O. IS=N+ 1 ***$$$$ is=n BM5=0. IQI- 1 BM3=0. BM4=0. YB= 1. BMl=O. DO 490 J=2J7 IW5=J DO 495 I=IE,NI ES=[+ 1 { hpw(j),from SUBR. TDZ2M, modification of U.B.C. & dz(2) } if (i.eq.jpu(j+l).and.jpuCj).le.jze(j)) then dz l=dz*(hpw(j)+dz)/2.0 dz2=dzsq else dz l=dzsq dZ2=&1 endif write(*,*)'z-d,for adv,j,i,hpw(j)',j,i,hpwCj) { z-D,for adv ) CALL ADV(I.J,IE,I,dz-. 1 ,dz2,AS 1 ,CS 1,FJ 1,U,V) 495 CONTINUE CALL FTSA(J,T.IQI,AS1 ,FJ 1 ,U,V) 490 CONTINUE * *****#######******* do 491 j=lj8 if(T(is,j,ni).gt.3.5) then write(*,*)'af ftsA tim,is,j,ni,T,U.fj 1(),fut wnte(*,*)tim,is,j,ni,T(is,j,ni),UQ,ni),fjl(j,ni),fu stop'af ftsA' else endif DO 496 I=IE,NI VQ,i)=Tff if Q.eq. 1) then T(is, I ,i)=T(is,2,i) else ifU.eqj8) then T(IS,Jg,I)=T(IS,J7,1) else endif T(1S-2j,I)=T(ISj ,I) comm continue CALL RSTA(T,NV,tim,pdt,jpu,ixx,izoron,U,STWT) ( k,omitting U.W.M. in active Iayer for snow melting,k=3; at U.P.T., k=2, L. frost front, k=l } CALL HTffZ(hztf,jpu,jze,H,jsnmh,U) IF(chkT.EQ. 1) goto 500 { normal direction,length & intension of heat & water flow } do 6068 k= 1,2 KZ( L ,k)=KS(2,k) KZ(j8,k)=KZ(j8- 1,k) hztf( 1 ,k)=hztf(2,k) h~tfljti,k)=hztf(j8-1 ,k) do 6050 j=3.j7- 1 jj=j7- 1+3-j if (hztf~,k).lt.hpu(jj))then grat(ij,k)=tff else if (hztf(jj,k).gt.hpu(jj)) then { k= 1, upward, Fig.6; K=2 downward, Fig.7; k=3, sonw melting } CUL fgrac2d (jj,K,hztf,U,NV,Hj endif continue grat(l,k)=grat(3,k) grat(2,k)=grat(3,k) grat(j8,k)=grat(j7- 1,k) grat(j7,k)=grat(j7- 1,k) continue iF(chkT.EQ.2) goto 500 * { 1st pusi,angle of gradient in 2 j coiurnrnns; hpw( ) in z-d } do 238 j=2j8 jj=j 8+2-j y l=abs(hpu(jj)-hpu(ij-1)) pusi=ATAN(y l/dx) * ( for peat thick in z-d & location of the 1.b. of peat cover } hpw(jj)=hpu(j)+hpttk~cos(pusi) 238 continue hpw(I)=hpw(2) CALL ptuwb(hpw,jpw,xpr,ixpr,inlpw-1) * **** Origindhtmin&gratetc. **** * [ 1-d W. m. to u.perm.table & L. fros front, see plstcc } * WRITE(*,*)'**** ICE LENSING AND HEAVE ****' hieh=dz*float(kmnu- 1) DO 1124 K=1,2 do 1127j=lj8 * ******* grat hztfts; CHANGED FPW TO FPW ****** stwp=(wpsf+stwpb)/2.0 CALL POVFHV~,K,Vff,HEV,hztf,hpu,hpw~W,TS,D,krnnu) * ******* hev two front,u.p.t.& 1.f.f. ****** IF (hztf(J,2).GT.Habcd) THEN TF'HUD(J,2)=Tff ENDIF * Habcd=HZTf(j,2) if ((j.eq.6.or.j.eq.20.or-j.eq.35.or.j.eq.j7-l).and. +hztf(j, l ).gt.jpw(j)) then write(*,*)'AfPV j,k,hpu,grat,Vff,HEV,hztf,FPW,TFHUD,kz(i,k)' write(*,*)j,k,hpuu),gratCj,k),Vff(j,k),HEVu,k),hztf(j,k), +FPW(i),TFHUDG,k),KZu,k) endif * **** ICE LENSING V( ) ONLY FORMS FROM THE iWGRATED MOISTURE *** BMS=Tff BMkTff DO 1 121 I=jpu(j),NV IF (I.EQ.KZ(J,k).and.k.eq. 1) THEN HVwm(J,I)=HVwm(J,I)+HEV(J,K) STWT(J,I)=STWT(J,I)+HEV(J.K)/(1 .O+HEV(J,K)) elseIF (I.EQ.KZ(J,k).and.k.eq.2) THEN V(J,I)=HEV(J,K) STWT(J,I)=STWT(J,I)+HEV(J,K)/(1.O+HEV(J,K)) ELSE ENDE BM4=BM4+HVwm(j,i) BMS=BMS+V(j,i) * WHTE(*,*) 'K,j,I,T,HVwm,V,stwt',K,j,I,U(J,I),HVwm~,i), * +V(J,I),STWT(J,I) 1121 CONTINUE * { BELOW CHANGE DDZRU,k),TOTAL HEV.,TO GRAT(j,k),saved mernory ) * ******* hev two front,u.p.t.& 1.f.f. ****** TFHUD(J, 1 )=bm4 TFHUD(J,2)=bmS grat(j,k)=Tff if (k-eq.1) then GFWT(i,k)=(FPW(J)+TFHud(j,k)) endif * if (j.eq.6.or.j.eq.20.or.j.eq.35.or.j.eq.j7- 1) then * write(*, *)'TOTAL hev.;j,k,DDZR,FPW,tfhud(ji'j,k,grat(j,k), * +FPW(j),tfhud(j,k) * endif 1127 continue 1124 CONTINUE Cd1 smthb(l,2j7,grat) Cal1 smthb(2,2,j7,grat) Cal1 smthb(1.î j7,tfhud) * ****####**Caii smthb(2,2 j7,rfhud) * ****TFHV,TOTALF.HV; ADDITiONALLOCATIONOFU.B.C.*** do 1082 j=l j8 do 1084 i=IE,Ni if(j.eq.3.or.j.eq.j5/2.or.j.eq,i5.or.j.eq,i7-2.or.j.eq.j7) then * WRITE(*,*) 'Befor dzl j,i,stwt()',J,I,stwt(j,i) endif if (i.lt.jpw(j).and.i.ge.jpu(j)) then stwp=stwt(j,i) endif if (i-lt-jzeu))then dz l=stwt(J,i)-stair else if (i.lt.jpu(j)) then dz 1=stwt(J,i)-stwsn elseif (i.lt.jpw(j)) then dz l=stwt(J,i)-stwp elseif (i.eq.jpw(j)) then dz 1=stwt(J,i)-SWP 1 else dz l=stwt(J,i)-stw 1 endif fj l(j,i)=dzl/(l.O-dzl) if~.eq.3.or,i.eq.j5/2.or.j.eq.jS.or,j.eq.j7-5.or.j.eq.j7)then * WRITE(*,*) '3rd j,i,dzl,fj l,stwt()',dzl.fj l(j,i),stwt(j,i) endif 1084 continue 1082 continue * ********** VALUE OF F.H.(Vff,t & Tm)*****++es* * ** DDZR(j)=(FPW(J,K)+TFHud(j,I))/DZ * (palsa height, u.b.of peat cover, at each coIummn j } do 549 j=2j7 hpuCj)=PLSINH-GRATG,1) 549 continue * { Finding of U.B.of pt., location,i,grid, & depend vari. T } CALL PTUWB(hpu.jpu,xpl,ixpl.inlpt) heu( 1 )=hpu(2) hpu(j8)=hpu(j7) jeu( 1)=jpu(2) jpu(j8)=jpu(j7) * *** range of grid change for peat cover *** * { 2nd pusi,angle of gradient in 2 j columrnns; hpw( ) in z-d } do 5 18 j=îj8 jj=j 8+2-j y l=abs(hpu(jj)-hpu(jj-1)) pusi=ATAN(y lldx) * { fcr peat thick in z-d & location of the 1.b. of peat cover } hpw(jj)=hpu(ij)+hpttk/cos(pusi) 518 continue hpw(l)=hpw(2) * { mm& min. hpu & hpw( ), cornparsion, for paisa height } * { note: not includes thickness of snow, will rnodify } iwS=jpu(l) iw7=jpu(l) do 627 j=lj7 if (jpu(j).lt.iwS) then [ right portion of pt. cv.; min. pu( ) } kmnu=jpu(j) iw5=kmnu jkmnu=j kmnw=kmnu+iptk else IF (jpu(j).Ge.iw7) THEN ( left portion of Sn. cv.; min. hpu( ) } kmxu=jpu(i) iw7=kmxu jkmxu=j kmxw=kmxu+iptk ELSE endif continue if(kmxu.gt.inlpt) then kmxu=inlpt kmxw=kmxu+iptk eIse if(krnxw.gt.inlpw) then kmxw=inlpw kmxu=kmxw-iptk else endif hvmax=pIsinh-float(kmnu) { max. height of palsa at time t; upper 1.b. of pt. cv. range } Maxplsh=kmxu-kmnu { @ 1 RRRS() tamporarily transfer preventing error ofixpl() } do i=l ,krnxw RRRS(i)=ixpl(i) end do CALL XLRBPT(ixpl,xpl,jpu,jkmnu,jkmxu,RRRS) CALL ptuwb(hpw,jpw,xpr,ixpr,inlpw- 1) hpw( 1)=hpw(2) hpw(j8)=hpw(j7) jpw( 1)=jpw(2) jpw(j8)=jpw(j7) { @2RRRS( ) tamporarily transfer preventing error ofixpr() } do i= 1,kmxw RRRS(i)=ixpr(i) end do CALL XLRBPT(ixpr,xpr~jpw,jkmnu,jkmxtl,RRRS) if(maxplsh.eq.iz0) then ixpl(kmnu)= 1 xpl(kmnu)=Tff endif nptw=kmxu+iptk {Air temp. for no sn.cv.;Sn.B.C.for Sn. surface; Pt.B.C.for pt. surface. Sn.accml.,before j5 sarne hight & between j5 and jps vari. from jze() to jpu() in winte; Sn. melting,vari.,in sumrner} if IFIAT.le.tff) then ** snwth, thickness of Sn. acml.; finding of sn. surface ** zhmn=Tff IZS=Tff do 736 j=2,jS if (abs(hpu(j+l)-hpu(j)).LT.dz) then zhmn=zhmn+hpuCj) iz5=IZ5+1 endif 736 continue zhmn=zhmn/FLOAT(iz5).t0.001 jmnpu=iFix(zhmn/dz+O.00000I) hsnw s=zhmn-snwth jsnmh=ifix(hsnws/dz) * jze(2)=jsnmh do 745 j=2j7 * ( maintain jze( ) on the sarne level for sn. acd. ) jze(i)=jze(2) IF Cj.ge.jS.and.j.1e.jps) then zsn=dz*float((jmnpu-jze(2))*(j5-j))/float(j5-jps) isz=ifix(zsn~dz+û.ûûûûû1) dsz=zsn-float(isz) *dz if(dsz.gt.dd2.0) then jzeg')=jze(2)+isz- 1 else jzeQ)=jze(2)+isz endif ELSE if(j.gt.jps) then j=(i)=jp~Cj) ENDF * ( for problem of no snow cover } if (snwast.gt.pp1) then jze(i)=jpu(j) endif 745 continue endif jze( l)=jze(2) jze@)=jze(j7) * { right b. of Sn.; ISNR(I) only works as jpu(jps)c or =jze(î) } JPZ2=jpuCjps)-jze(2) IF(JPZ2.GT.Tff) THEN XSN=FLOAT(JPSS)*DX BMI=XSN/FLOAT(JPS2) DO i=jze(2)jpu(jps) IZ7=BM 1/DX BMS=BM I -FLOAT(IZ7) if(BMS.gt.dx/Z.O) then IZS=IZ7+I else IZ5=IZ7 endif ISNR(I)=JS+IW*(I-JzE(2)) end DO ELSE ISNR(jpu(JPS))=JPS ENDIF * {modificationof the location of XPL(i) and XPR(i)) do 6030 i=ie,inIpw if (i.le.kmxw.and.i.gt.kmxu) then IXPL(i)= 1 XPL(i)=Tff endif if (i.ge.kmnu.and.i.1e.h~) then iXPR(i)=j8 XPR(i)=float(j8- 1)*dx else if (i.lt.kmnu) then IXPL(i)=99999 iXPR(i)=99999 endif 6030* *********continue do 6034 j= 1j8 if (grat(j, l).gt.dubf(j)) then dubf(j)=dubf(j)+dz do 1085 i=ie,nv- l stwt(J,i)=stwt(j,i+ 1) 1085 continue else endif if (Cj.eq.2.or.j.eq.j5/3.or.j.eq.j5.or=~.eq.j8-10.or. +j.eq.j8).and.hztf(j,l) .gt.jpw(j) ) then write(*,*)'j,grat-total hev,dubf,fpw,tfhud(j, 1)' write(*,*) j,i,grat(j, l),dubf(j),fpw(j),tfhud(j, 1) endif 6034 continue 1424 CONTINUE * ****save & THE COMPUTATION OF THE NEXT TIME SEP************ DO j=l j8 DO K= 1.3 hztf(J,K)=hztf(J,K)*(- 1.O) end do * *********end do IZ7=IFIX (tm tPDT) IF (nyr.gt.myrO.and.IZ7.EQ.IGS)then IGS=IGS+izoron READ(7,'(A40)') CNWTLM 1 WRITE(* ,'(A4O)') CNWTLM 1 WRITE(*,*)'Tim,Nyr,mth.dy',tim,Nyr,Nmth,ndy WRITE(*,+)'fi,fu,jze,jpu,kz,fpw,2&j7'.fi,f~.jze(2).jpu(2), +jpu0'7),W2,1 ),kz0'7,1 ),fpw(2),fpw(j7) WRITE(*,*)'i,isnr()',(i,isnr(i),i=jze(2),jpu(j5)) OPEN(LL 1,FILE=CNWTLM 1,STATUS='NEW',FORM='FORMATTED' ) WRITE(LL 1.55) Nyr,Nmth,ndy,tim WRITE(LL1.54) FLAT,FI,FU,ts,inlpt,inlpw,maxplsh * {***MARKS:STRING***;) write(LL1,44)Q,jze(j) ,jpu(j),FPW(i),GRAT(J, l),tfhud(j, l), +tfiud(j,2),hztf(j,l),hztf(j,2),fjl(j,kz(j, 1)-l),kz(j, l)j=lj8) write(LL 1,46) (i,ixpl(i),XPL(i),ixpr(i),XPR(i),i=kmnu-2,kmxw) write(LL 1,48)(I,H(i).u(3,i),u(jps,i),u(j7-1 ,i),stwt(3,i), +fj 1(3,i),fj 1(jps.i),fj 1(j7- 1,i),HVwm(j7- 1.i),i=jze(2)-4,nxn) 1,53 1 ENDIF do 1002 j=l j8 KZ(J,3)=2 FPW(J)=Tff DO 1001 K=l,2 VFF(J,k)=Tff HEV(J,k)=Tff hztf(J,K)=Tff KZ(J,K)=2 GRAT(J,K)=Tff 1ûû1 continue * ****findingminimumT() **** bmkufi,ni) do 1006 i=jpu(j),ni-! if (U(j,i).GT.T@ then HVWMCj,i)=Tff else endif 1006 continue 1002 continue D=Tff Ts=Tff * * **** DELTATAO IS THE TIME INCREMENT, NEXT TlME STEP ********** GOTO 500 450 CONTINUE close (LL1 ) 50 FORMAT (2X,'k&s',4(I3,FT2.8)) 44 FORMAT (2X,I4,14,I5,F7.3,f8.3,f8.4,F8.4.F8.4lf7.3,fl.4,I4) 46 FORMAT (2X,IlO,lX,iS,F12.3,i1O,F12.3) 48 FORMAT (lX,i4,f6.2,F8.3,F8.3,F8.3,F6.4,F6.4,f7.4,F7.4,fl.4) 52 FORMAT (2X,I4,F6.2,F9.5,f9.5,f9.5,15) 64 FORMAT (1X,I4,i4,FIO.6,F10.6,F10.6,F9.5,F10.6) * FORMAT (2X,'I,WT',6(13,F7.4)) 53 FORMAT (5X,4OH*****H*****1 55 FORMAT (2X,'1D,PLS.Nry,Nrnth,Ndy=',I4,2(13), 1 X,'TIME',F7.1) 54 FORMAT (2X,'F-art,I,U;ts',4(F8.4),'inlpt,inlpw,maplsh',3(i5)) 11 FORMAT (2X,'IGS=',I3,'N=',I2,3X,'TIME,F9.2) * end of part 3 stop 'somereson,pleasestop' END $NODEB UG $DEBUG * program PLSFMTîD * *********** ************ SUBROUTINE FIV(T,fi1 ,fi2,fu l,fu2,ferrc,inlpt,AS1,CS 1 ,FJ1 ,V) DIMENSION T(3.1 SO,25O),AS1 (150,25O),V(150,250) DIMENSION CS l(l5O,25O),FJ l(l5O,25O) COMMON mINI,J7,J8,JS,JPSNE/DX,DZNH/Y1 ,Y2,IS,iE,ABJ +/FSWWkw 1 ,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw10 write (*,*)'NIj7j8,JS,FIl,FI2,FUl,FU2',NI.j7,j8,J5,FIl, +FI2.FUl.FLJ2 DO 100 N=2,2 DO 300 J=l,J8 IF(J.LT.JS) THEN FU-FU 1 R=FI 1 ELSE FU=FU2 FI=FI2 ENDIF do 299 i=IE,ni IF(1.EQ.N) THEN T(N- 1,j,i)=FU ELSE IF(1.EQ.E) THEN T(N- I ,J,I)=FI ELSE T(N- 1,J,i)=(FU-FI)*float((I-E)/(NI-E))+FI ENDIF IF(I.EQ.IE.0R.I.EQ.NI) THEN AS 1(J,I)=O.O V(J,I)=O.O CS 1(J,I)=O.O FJ l(J,I)=O.O ELSE AS 1 (J,I)= 1.O V(J,I)=dx*dx/dz/dz CS 1(J,I)=V(J,I) FJ l(J,I)= 1.O+AS 1(J,I)+V(J,I)+CS 1(J,I) ENDIF * WRITE(*,*)'OKj,i,A-V-CSl,F(J,I)',j,i,ASl(J,I),V(J,I). * +CS 1(J,I),FJ 1(JJ) 299 continue 300 CONTlNuE IG=O IS=N- 1 260 IG=IG+1 WRITE(*,*) 'IG1,IG DO 789 J=2,J7 do 784 i=E+1,NI- 1 T(N,J,I)=T(N- 1,J,I) IF(J.EQ.2) THEN T(N- 1,J- 1,I)=T(N- 1,J,I) ELSE IF(J.EQ.J7) THEN

T(N- 1,J,I)=(T(N- 1,J- 1,I)+as 1(J,I)*T(N- 1,J+ 1,I)+V(J,I)* +T(N-l,J,I+l)+cS l(J,I)*T(N-l,J,I-l))EJl(J,I) 784 continue DO 779 -i=IE+ 1,NI- 1 FIC=T(N,j,i)-T(N- 1 j ,i) IF (ABS(FIC).GT. ferrc) GOTO 260 continue CONTI[NUE DO 888 I=IE,NI T(N- I ,1 ,I)=T(N- 1.2.1) T(N- 1,J8,I)=T(N- 1,J7,I) corn OPEN (9,FILE=PILLE 1,STATUS='NEW',FORM=FORMATTED1) DO 950 J=1,J8 DO 959 I=IE,NI T(N,J,I)=T(N-1 ,J,I) CONTINUE CONTINUE CONTINUE CLOSE(9) format(2~,2hig,i5) FORMAT(2X,'INITIAL TEMPERATURE, THAT IS T(N- 1,JI)') RETURN ***********ENd SUBROUTINE RSTA(T,NV,tim,pdt,jpu,ixx,izoron,U,STWT) *** J. MAXIMUM OF THE FROZEN FRONT, FOR NV **** DIMENSION T(3,l SO,2SO),U( 150,25O),STWT(150,250) ,jpu( 150) COMMON /VBN,J7,J8,JS,JPSNHIY 1 ,Y2,1S7E,ABJNF/IDT0,HF,Tff +/FSWH/kw 1 ,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kwIO ixyz=ifix(tim/pdt) DO 777 J=l J8 DO 788 I=I,IE-1 U(J,I)=O.O 788 CONTINUE DO 790 I=E,NI U(J,I)=T(IS,J,I) IF (U(J,I+l).GT.Tff.AND.U(J,I).LT.Tff)THEN NV=I+ 1 ENDIF if (nv+ 1O.ge.ni) then nv=ni else endif IF (kw6.eq. 16) then WRITE(*,*)'RSTA tim,J,I,T,U,STWT() jpu() ',tim,J,I,T(is,j,i), +U(J,E),sTWT(J,I),jpu(j) ENDIF 790 CONTINUE 777 CONTINUE IF (kw6.eq. 16.and.Ixyz.EQ.I~~)then WRITE(*,*)'RSTA tim,J,I,u,stwt,jpu','ixyz',ixyz IXX=IXX+izoron ENDIF RETURN * ***********END SUBROUTINE HTFET(hztf,jpu jze,H,jsnmh,U) DIMENSION U( 150,25O),KZ( 150,3),hztf( 150,2),H(250) DIMENSION grat( 150,î) jpu( 150)jze(150) COMMON /MW/KZ,GRAT/bctp/FI,FU,FIAT,FIPTflSN +NBINI,J7,J8,JS.JPSNE/DX,DZrVF/IDTO,HF,T~1,Y2,IS ,IE.ABJ +/FSWWkw 1,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw IO do 314 j=l j8 do 3 16 i=ie,ni-2 * ( snow thawing, k=3,H(I+ 1) ) if (fiat.gt.Tff.and.((i.ge.jsnmh.and.i.Ie.jpu~)).and. +(U(j,i).gt.Tff.AND.U(j,i+l).lt.Tff)))THEN k=3 fn=H(I+ 1)-(TFF-u(j,i+ 1))/((u(j,i)-u(j,i+ l))/DZ) kz(j,k)=ifix(fn/dz)+ 1 jze(j)=kz(j,k) ( DOWNWARD to u. perm. table; k=2, THAWING, H(I+l) ) else IF (TFlF.Lt.u(i,i).AND-TFF-GT.uQ,i+1)) THEN k=2 hztf(j,k)=H(I+ 1)-(TFF-uCj,i+ l))/((u(j,i)-u(j,i+l))/DZ) kz(j,k)=I+ 1 write(*,*)'2,HTffZ DWD i,KZ, hztf ,i,kz(j,k),hztf(j,k) ( UPWARD to 1.frost front; k=l, FREEZING, H(1) ] ELSE IF (TFF.Lt.u(j,i+l).and.TFF.Gt.uCj,i))THEN k=l hztf(j,k)=H(I)+(TFF-u(j,i))/((u(j,i+ 1)-uCj,i))/DZ) kz(j,k)=I write(*,*)' 1,htffz UPWD i,KZ,hztf ,i,kz(j,k),hztf(j,k) ELSE ENDIF continue if (FIAT.gt.Tff.and.U(j,jpu(j)).GT.Tff)THEN jze(j)=jpu(j) endif IF(kw8.EQ. 18) THEN write(*,*)'J,KZ 1,2',J,kz(J, l),kz(J,2), +'hztf l,2;,hztf(~,1),hztf(J,2) ENDIF 3 14 continue RETURN * ***********END Subroutine TDZ2M(Tjpu,HPU,HPW,H,U) DIMENSION T(3,150,250),U( 150,250) DIMENSION jpu(150),HPU(150),HPW(150),H(250) cornmon NB/NI,J7,J8,JS,JPSNE/DX,DSNWYl,Y2,1S,E,ABJ +/FSWWkw 1,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw 10 * *** iIPW(), modification of the U.B.C.& dz(2), location *** do 100 j=l@ iw7=jpu(j) iwS=jpu(j)+1 iz5=jpu(j)+2 do 102 i=iw7,iw5 ( ddhv, palsa growth incre. from top to following gridJig.4 ] ddhv=H(I)-HPU(j) if (ddhv.lt.dz.and.ddhv.gt.dz/5.0) then { preventing of overfiow, condition is ddhv>0.0 for u(j,i) } u(j,iw5)=u(j,iw7)+(u(j,iz5)-u(j,iw7))*ddhv/(dz+ddhv) t(is,j,iwS)=u(j,iwS) HPW(j)=ddhv else HPW(j)=dz endif IF(kw3.eq. 13.and.(I.eq.jpu(j).or.i.eq.jpu(j)+l)) then write(*,*)'j,I,ui- 1,i,i+l ,ddhv'j,I,U(j,i- l),u(J,I),u(j,i+l),ddhv write(*,*)'HPW*$,jp~,HPU',HpW(j)~jpu(j),HPU(j) endif 102 continue 100 continue return end SUBROUTINE UBMCT(tmt,T,jzejpu,AMCA2,csncv,cptcv 1,pp 1 ,ppZ,FJl) DIMENSION T(3,150,250),FJ1(150,250),JZE(150),jpu(150) COMMON /bccs/bcmi,snbc,ptbc,cf 1,totim/bctp/FI,FU,FIAT,T;rPTIFTSN +NH/Y1 ,Y2,IS,IE,ABJNBMI,J7,J8,jSïJPS +/FSWH/kw 1,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw 1O DO 464 J= 1,J8 if(ptbc.gt.bcrni.and.tmt.ge.totim) then ptbc=ptbc+cf 1 snbc=snbc+cf 1 else endif EU=snbc-(snbc-ptbc)*j/j8 DO 466 I=IE,jpu(J) IF((I.LT.JZE(J).and.j.le.jps).or.(i.lt.jpu~).md.j.gt.jps))THEN * { both sumrner and winter, for air temp. } DCCOE=O.O ELSE IF((I.EQ.JZE(J).AiYD.JZE(J).LT.jpu(J)).and.j.lt,jps)THEN * { WINTER, for snow cover surface } DCCOE=Csncv ELSEIF ((I.EQ.jpu(J).AND.jpu(J).EQ.JZE(J)).and.j.Ie.jps)then * { Sl-ll4MER snow melted, for peat cover surface } DCCOE=cptcv 1 else if ((i.eq.jpu(j).and.j.gt.jps).OR. +(I.EQ.JPU(J).AND.JPU(J).LT.JZE(J)))then * { WINTER SNOW ACCUML.,for peat cover surface } DCCOE-C- ptcv 1 else goto 466 ENDIF * ( further consider the 1. b.c. decrease in x-D from Z to j8 } ffb=SIN(3.14 15926*(tmt-PPl)/PP2) FIAT=AMCA2* ffù Fi=(dccoe+AMCA2)*ffb FiPT=(CPTCV 1+AMCA2)*ffb FiSN=(CSNCV+AMCA2)*fTb FJ 1(J,NI)=FU * write(*,*)'~t,j,i,dccoe,~~~~~,tmt,j,i,dccoe,~~~~,~~ write(*,*)'tmt,j,i,FIAT,FUt,tmt,j,i,FIAT,ELJ write(*,*) 'U.B.;jze,jpu()~fjit,jzeO,jpu(j),fj 1(i,i) write(*,*)'T(is,+l ,+Z,ni)',t(is,j,ni),t(is+l j,ni),T(is+2j,ni) write(*,*)'fj 1(j,i),snbc,ptbc,cfll,fj l(j,i),snbc,ptbc,cfl endif 466 continue 464 CONTINUE RETURN * ***********END SUBROUTINE THERPAR(Tj,I,CCS 1,BMDS 1,CTSL,CTSLl dyp1 ,STW 1, +U,V,STwT) DIMENSION T(3,150,250),stwt(150,250) DIMENSION U(l50,25O),V( 150,250) COMMON /CBMDT/CWW,CII,cair$MDW&MDI,bmair,PHCG +NAKT5,CT8/VFIIDTO,HF,TffNH/YI ,Y2,IS,IE,ABJ +/FSWH/kw l ,kw2,kw3,kw4,kw5,kw6,kw7,kw8~kw9,kw10 TSV=T(IS j ,1) IF(TSV.LT.Tff.AND.TSV.GE.CT5)THEN WVl=(STWT(J,I)-CTSL)/(-CT5) STU=STWT(J,I)-WV1 *(Tff-TSV) CICn=STWT(J,I)-STU SIS= 1.O-(CICn+STU)

U(J,I)=CCS 1*SIS+CWW*STU+CII*CTCn V(J,I)=BMDS1 **SIS*BMDW**STU*BMDI**CICn ENDIF * *** WïïH CWW,CII,BMDW,BMDI FOR THE U,V, OK *** IF(kw7.EQ. 17) THEN WRITE(*,*)'J,I,Tsv',J,i,Tsv,'CCS1,BMDS 1',CCS 1,BMDS 1 WRITE(*,*)'STU,SIS',STU,SIS,'ctSL,STWT(J,I)',ctSLl,STWT(J,I) WRITE(*,*) 'U,V,CICn',U(J,I),V(J,I),CICn,'Wvl',wvl ENDIF RETURN END * ************ SUBROUTINE VMDSN(JBMDPT$MDSN,BMDSNP,JPU,JZ) DIMENSION JPU(15O)JZE(I5O) COMMON /SNPRMT/BMDSNl ,CSNW,DISN 1,DISN2,SNJM +/FSWH/kw 1,kw2,kw3Jrw4,kwS,kw6,kw7,kw8,kw9,kw IO * ( FOR BMDSN VARIATION WïïH DEN VARIATING WITH SNOW THICK } DISN=DISN l+(DISN2-DISN 1)*(JPU(J)-JZE(J))/SNJM BMDSN=BMDSNl *DISN*disn BMDSNP=(BMDSN+BMDPT)/2.0 IF(kw7 .EQ.17) THEN WRITE(*,*)'J,BMDSN,BMDSNP,DISN,JPU,JZE' WRITE(*, *) J,BMDSN,BMDSNP,DISNJpU(J),JZE(J) ENDIF RETURN END * *********** $DEBUG SUBROUTINE THERPARSNW(T,j,I,CWI,BMDWI,BMDSN,U.V) DIMENSION T(3,150,250) DIMENSION U(l SO,ZO),V(150,250) COMMON /VA/CT5,CT8lWlIDTO,HF,Tff/VWY1,Y2,1S,IE,ABJ +/CBMDT/CWW,CII,cair,BMDWBMDI,bmair,PHCG +ICNDV/CTSL,CTP,CTNW,ctair,CTSL1,CTPl ,CTNW 1 ,ctair 1 +/SNPRMT/BMDSN 1,CSNW,DISN 1,DISNS,SNJM +/FSWH/kw 1,kw2,kw3.kw4,kw5,kw6,kw7,kw8,kw9,kw 10 * **** melted snow'll be infrietration; no U&V() ***** * wnte(*,*)'j,if j,i TSV=T(IS,j,I) F(TSV.LE.Tff.AND.TSV.GE.CT5)THEN STU= 1.O-( I .O-cTnw)*TSV/CTS SIS= 1 .O-STU U(J,I)=CSNW*SIS+CWI*STU V(J,I)=BMDSN**SIS*BMDWI**STU else if (tsv.lt.ct5) then stu=cTnw sis= 1.O-stu u(j,i)=~snw*sis+cww*stu v(j,i)=bmdsn**sis*bmdw**stu else u(j,i)=cair v(j,i)=bmair ENDIF * *** WH(CWW+CII)/2.(BMDW+BMDI)/2- *** iF(kw7.EQ. 17) THEN WRITE(*,*)'J,I',J,i,'Tsv1,tsv,'CSNW,CW~',CSNW,CW WRITE(*,*)'STU,SIS',STU,SIS,'U,V',U(J,I),V(J,I) ENDIF RETURN END $NODEBUG* ************ SUBROUTINE DDTIj,I,Tsv,TS 1,T53 ,UWPR,UWPR 1,DIDT,STWT) dIMENSION STWT(250,150) COMMON /CBMDT/CWW,CIl,cair,BMDW,BMDI,bmair,PHCG ÏF(ÏW~.EQ.12)THEN . WRITE(*,*) 'j,I',j,I,'CST',CST,'PHCG',PHCG,'DIDIDTv,DIDT ENDIF RETURN * **********END $DEBUG SWBROUTINE DDTSNW(j,I,Tsv,TS 1 ,T53,DISN 12) COMMON NA/CE,CT8IVF/IDTO,HF,Tff +/FSWHkw 1 ,kw2.kw3.kw4.kwS,kw6,kw7,kw8,kw9,kw10 F(TSV.LE.Tff.AND.TSV.GE.CT5)THEN STU= 1 .O-TSVICTS T5 l=DISN 12*STUfHF T53=TFF ELSE t5 1=Tff t53=Tff ENDIF iF(kw2.EQ. 12)THEN WRITE(*,*) 'DDTSNW j,I,STU,TS 1 ',j.E,STU,TS1 ENDIF RETURN END $NODEBUG* ********** $DEBUG SUBROüTDiE ADR(TIM,J,I,IQI,T,DZl,DZ2,t5 1 ,t53,AS 1 ,CS 1 ,FJl,U,V) DIMENSION T(3,150,250),AS 1( 150,25O),CS1( l50,25O),FJ1 ( 150,250) DIMENSION U( 150,25O),V(150,250),KZ(i50,3),grat(i SO,2) COMMON /MWIKZ,GRATNAICT5,CT8NB/NI,J7,J8,J5,JPS +NFmiTO,HF,Tfflvgliz5,iz7,iwS,iw7/VH/Y1 ,Y2,IS,IE,ABJ +/FSWH/kw 1 ,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw10 if((i.eq.kz(J,l).or,i.eq.kz(J,2).or.i.eq.,3))) then AA l=(u(IW7,iz7)+ulj,i))12.0+tS 1 AA2=(u(i,i)+ü(IWS,iz5))/2.0+T51 else I~(T(IS.IWS,IZ~).I~.~~~.~~~.T(IS,IW~,IZ~).~~.C~~)then AA 1=(u(IW7,iz7)+u(j,i))/2.0+t53 AA2=(u~,i)+u(IW5,iz5))/2.~b3 else AA 1 =(u(IW7,iz7)+u(j,i))/2.0 AA2=(u(i ,i)+u(rWS,i25))/2.0 endif BB l=(V(TW7,iz7)+V(j,i))I2.0 * *********BBZ=(V(j ,i)+V(IWS,iz5))/2.0 25 IF(I.EQ.IQ1) THEN E5=I+ 1 FJ 1(J,I)=FN- ENDIF IF(kw2.EQ. 12)THEN WRITE(*,*)'TIM',TIM,J,I,'FJ1,T',FJl(J,I),T(IS,J,I) WRITE(*,*)'AS 1,CS l',AS l(IW7,IZ7),CS l(IW5.IZ5) WRITE(*.*)'AA 1,BB l.dz 1 ',AA l,BB l,dzl,'BBN,BBpl,bbn,bbp ENDIF RETURN END $NODEBUG * ******Y**** SUBROUTINE ADV(I,J,IEl ,IP,dzl,dz2,AS 1.CS 1,FJl ,U,V) DIMENSION U( l50,2SO),V( 150,25O),FJl( 150,250) DIMENSION AS 1( I SO,ZO),CS 1( 150,250) COMMON IVB/NI,J~,J~,JS,JPSNHIYI,Y~,IS,E,ABJ +/VD/BM 1,BM3,BM4,BMS,YBNG/IZ5,1Z7,IWS,lW7 +/FSWH/kw l,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kwIO IF(IP.EQ.IE1) THEN CS 1(J,I)=BM4 u(rws,~zs)=-CSI (J,I) V(iw5,iz5)=BM5+YBfFJ I (J,I) FJ 1(J,I)=BMS+YB *FJ 1(JJ) AB J= 1. ELSE IF((Y 1.EQ. 1 .O.AND.IP.EQ.J8).0R,(Y 1,EQ.O.O. AND. +IP.EQ.NI)) THEN AS l(J,I)=BMl fj l(j,i)=(BM3+Y3)*FJ I(J,I) ABJ= l+AS 1(J,I)*U(J,I) ELSE AS 1(j,i)=-AS 1(J,I)/dz 1 CS l(j,i)=-CS 1(J,I)/dz2 ABJ=AS l(J,I)*U(J,I)+l .O-asl(j,i)-csI(j,i) U(iwS,izS)=-CS 1(J,I)/ABJ V(iwS,izS)=(FJ 1(J,I)-AS 1 (J,I)*V(J,I))/ABJ ENDIF iF (kw2.EQ. 12) THEN WRITE(*,*) 'J,I,AB J',J,I,abj,'U,V',U(J.I),V(J,I) WRITE(*,*) 'AS 1,CS l,FJl',AS l(J,I),CS l(J.I),fj l(j,i) ENDIF RETURN END * *********** SUBROUTINE FTSV(I,T,IE 1,IQI,AS 1,FJ 1,U,V) DLMENSION T(3,150,250),U( 150,250) DIMENSION FJ 1(150,25O),V(l50,250),AS1(150,250) COMMON NB/NI,J7,J8,JS,JPSNH/Y 1,Y2,IS,IE,ABJ +îFSWH/kw l,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw10 DO 100 J=IEI,J8 JJ=J8+IE 1-J IF (JJ.EQ.JS) THEN

T(1S ,JJ,I)=U(JJt 1,I)*T(IS,JJ+l ,I)+V(JJ+l ,I) ENDIF IF(kw4.EQ. 14) THEN WRITE(*,*)'JJ',JJ,'I',I,'FJl',FJ l(JJ,i),'TJ',T(IS,JJ,I) WRITE(*,*) 'U1,U(JJ,I),'V ',V(JJ,i),'T2 ',T(IS,JJ,i) WRITE(*,*)'AS l',AS 1(JJJ),' ABJt,ABJ ENDIF 100 CONTINUE RErn * ***********END SUBROUTINE FTSA(J,T,IQI,AS 1,FJ 1,U,V) DIMENSION T(3,150,250),U( 150,250) DIMENSION FJ 1( 15O,XO),V(l50,25O),AS 1( 150.250) COMMON IVB/NI,J7,J8,JS,JPSNWY l,Y2,IS,IE,ABJ +/FSWH/kw 1,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw 10 DO 100 I=IE,NI II=NI+IE-I IF(II.EQ.NI) THEN T(IS.J,II)=(FJ 1(J,II)-IQI*AS l(J,IT)*V(J,II))/ABJ ELSE T(XS ,J.II)=U(J.II+ 1)*T(IS,J,II+ 1)+V(J,II+ 1) ENDIF IF(kw5.EQ. 15) THEN WRITE(*,*)'J'lJ,'II',II,'FJlV,FJ1 (J,II),'TI',T(IS- 1,J,II) WRITE(*,*) 'U1,U(J,II),'V ',V(J,II),' TI2'.T(IS,J,II) WRITE(*,*)'AS 1 ',AS l(J,Ilj,' ABJ1,ABJ Endif 100 CONTINUE RETURN * ***********END $DEBUG subroutine fgratZdQj,k,hztf,U.NV,H) DIMENSION U(150,250),KZ(15013),GRAT(150,2),hztf(lSO,S),H(25O) common lmw/KZ,grat/VE/DX,DZNFmTO,HF,Tff +NH/Y1 ,Y2,IS,IE,ABJ +/FSWH/kw I,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kw10 * { differences of OC isotherm, normal-D angles of temp. gradient } y l=abs(hztf(ij+2,k)-hztfU,k)) pusi=ATAN(y 1/(2.0*&)) * { lengths of normal distances ktween Tff and closest point in * frost front; dltl I : beginning point (BP) of dltl 1 located in * x-D,between 2 colurnrnns } DO 100 I=IE+ 1,NV U2 1=U(JJ+2,1+1) U20=U(J J+2,I) UI=U(JJ,I+ 1) Uû=U(JJ,I) * { dltxl: Iength fmm colummn jj to j+1. to BP of dltll } IF( y 1 .GT.Tff) THEN dltl 1=y 1 *cos(pusi) ELSE F(y1 .EQ.Tff.AND. +(H(i).GT.HZTF(JJ,K).AND.H(I-l).LT.HZTF(JJ,K)))THEN DLTL 1=HZTF(JJ,K)-H(1-2) ENDIF * { TEMP.AT DLTLl IN FREEZING ZONE IN NORMAL DIRECTION } * ****K=;l IF ((KEQ.1 .AND.HZTF(JJ+2,K).GT.HZTF(JJ,K)).AND. +(H(i+i).GT.HZTF(JJ,K).AND.H(I).LT.HZTF(JJ,K)))THEN UD=U21 -(U2 1 -U20)/DZ*(H(I+ 1 )-HZTF(JJ,K)) ELSE IF ((K-EQ.1 .AND.HZTF(JJ+2,K).LT.HZTF(JJ,K)).AND. +(H(i+I).GT.HZTF(JJ+2,K).AND.H(I).LT.HZTF(JJ+2,K)))THEN UD=U 1-(U 1-UO)/DZ*(H(I+ 1)-HZTF(JJ+2,K)) ELSE IF ((K-EQ.1 .AND.HZTF(JJ+S,K).EQ.HZTF(JJ,K)).AND. +(H(i+l>.GT.HZTF(JJ,K).AND.H(I).LT.H2TF(JJ,K)))THEN UD=U(JJ,I-1) ELSE ENDIF * ****K=2 IF ((K.EQ.Z.AND.HZTF(JJ+Z,K).GT.HZTF(JJ,K)).AND. +(H(i+ 1 ).GT.HZTF(JJ+2,K).AND.H(I).LTTHZTF(JJ+2,K)))THEN UD=U 1 -(U 1 -UO)/DZ*(H(I+ 1 )-HZTF(JJ+Z,K)) ELSE IF ((K.EQ.2.AND.HZTF(JJ+2,K).LT.KZTF(JJ,K)).AND. +(H(i+l).GT.HZTF(JJ,K).AND.H(I).LTHZTF(JJ,K)))THEN UD=U:! 1 -(U21-U20)/DZ*(H(I+ 1)-HZTF(JJ,K)) ELSE IF ((K.EQ.2.PLND.HZTF(JJ+2,K).EQ.HZTF(JJ,K)).AND. +(H(i).GT.HZTF(JJ,K).AND.H(I-l).LT.HZTF(JJ,K))) THEN UD=U(JJ,I+1 ) ELSE * *******ENDF IF(Tff.GT.UD.and.dltl1.gt.Tff) THEN grat(jj,k)=(tff-UD)/dltl 1 ELSE IF (Tff.LT.UD.and.dltl1.gt.Tff) THEN grat(jj,k)=(UD-tfT)/dltll ELSE

100 CONTINUE if (kw9.eq.19) then write(*.*) 'jj,i,k,KZ,HZTF,H,GRAT,y 1 ,PUSI,DLTL 1 ' writel l2,*) jj,i,k,kz(JJ,K),HZTF(JJ,K),H(i),GRAT(JJ,K),y1, +PUSI,DLTLl write(*,*)'U 1- 1 ,I,I+l',u(jj,i- l),u(jjyi),u(jj,1+l) endif 12 FORMAT (lX,I4,14,I3,I4,F7.3,F7.3,F1OS,F8.4,F8.4,F8.4) remm end $NODEBUG * ******** $DEBUG SL'BROUTINE POVFHV(j,K,Vff,HEV,hztf,HPU,HPW ,FPW,Ts.D,kmnu) DIMENSION VFF(150,2),HEV(150,2),tiztf(150,2),FPW(ISO) DIMENSION grat( l50,2),KZ(l50,3),HPU(l5O),HPW(l50) COMMON /MW/KZ,GRAT/CNDV/CTSL,~,CTNW,ctair,CTSLl,ml, KTNW 1,ctairl/CRCk4PïWT,RAS 1WT +/CSC/STW 1,STWP,STWSN,stairNE/DX,DzNF/DTO,HF,TfflV 1,sp02 +/VK/ACOT,ALPHA,BKO,BATA,HPTTK,HIEH,DTSD,Psep +/FSWWkw 1,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,h 10 IF (hztf(j,k).LE.HPU(i).or.grat(j,k).LE.Tff)THEN * ( AIR ZONE & SN. CV., SNOW FLUCTUATION WITH SEASONS } PO=Tff Vff(j,k)=Tff HEV(j,K)=Tff FPWCj)=Tff Ts=Tff goto 101 ELSE IF (hztf(j,k).gt.HPU(j).and.hztf(j,k).Lt.HPW(j))THEN * { PEAT COVER, shape VARIATIONS WITH FROST HEAVE } hzsn=hztf(j,k)-HPU(j) PO=RAP?WT*HZsn Vff(J,K)=SP02*EXP(-ACOT*PO)*GRAT(J,K) ELSE if (hztfCj,k).gt.HPW(j)) then * ( SILY CLAY, ICE LENSING * FROST HEAVE } hzsn=HPW(j)-HPU(j) hzyp=hztf(J,K)-HPW(j) PO==RAPTWT*hzsn+RAS1 WT*HZYP Vff(J,K)=SPO 1*EXP(-ACOT*PO)WRAT(J,K) ENDIF HEV(J,K)=V ff(J,k)*FLOAT(IDTO) * { finding ts 1 & gorwth beneath the point of max-frost bev ) if(k.eq. 1.and.(hztf(j,k).gt.HPUCj).and. ihztf(j,k).le.HPW(j))) then hzsn=hztf(j,k)-HPU(j) FPW(j)=(stwp-ctp)*O.O9*hzsn ELSE if(k.eq. 1.and.hztf(j,k).gt.HPWCj)) then * ( SILY CLAY, ICE LENSING * FROST KEAVE } hzsn=HPW(i)-HPUQ) hzyp=hztf(J,K)-HPWCj) FPW(J)=((stwp-ctp)*hzsn+(stw 1-ctSL)*hzyp)*0.09 else endif * ( FPW(j) ok } Ts=-0.00000 1 goto 101 if (k.eq. 1.and.j.eq.kmnu) then TSO=Tff pu=hztf(j,k)-hieh A l=Vff(J,K)/(( 1.O+ALPHA) *BKO*GRAT(J,K)) 236 TSl=((-A 1*(-TsO)**(l+ALPHA)- 1.09*PO+PU)/BATA)/lOO.O write(*,*)'pO,pu,hieh,A 1,TsO,Ts 1,Vff,grat,hztf write(*,*) pO,pu,hieh,Al ,TsO,Ts I ,Vff(j,k),grat(j,k),hztf(j,k) IF(ABS(TS 1-TSO).GT. 1E-5) THEN WRITE(*,*) V~~(J,K),GRAT(J,K),TS1 PAUSE'Ts 1 STOP' ELSE Ts=Ts 1* 100.0 D=-TdGRAT(J,K) ENDIF DX 1=Ts/dtsd DX2=D/dtsd PPSO=PO+Psep DZ 1=0.0 DZ2=0.0 ******* O.O

100 CONTINUE grat( l ,k)=grat(î.k) grat(J7+ 1,k)=grat(J7,k) RETURN END SNODEBUG subroutine Ssfgrat2d(jj,k,hztf,U,h'V) DIMENSION U( l5O.XO),KZ(l~O,3),GRAT(l5O,2),hztf(150.2) cornrnon lmw/KZ,gra~X,DZNF~TO,HF,Tff +NW1,Y2,IS,IE,ABJ +/FSWWkw 1 ,kw2,kw3,kw4,kw5,kw6,kw7,kw8,kw9,kwIO * { differences of OC isotherm, normal-D angles of temp. gradient } y l=abs(hztf(jj+l,k)-hztfCij,k)) pusi=ATAN(y I/dx) * ( lengths of normal distances between Tff and closest point in * frost front; dlti 1: beginning point (BP) of dlti 1 located in * x-D,between 2 colummns } DO 100 I=E+ 1,NV DFl=dz*float(i- 1) DF2=DZ*FLOAT(I-2) IF(K.EQ. 1.AND.(DFl .GE.HZTF(JJ,K).AND.DF2.LE.HZTF(JJ,K)))THEN dit1 l=(hztf(jj,k)-DF2)*cos(pusi) ELSE iF(K.EQ.2.AND.(DFI.GT.HZTF(JJ,K).AND.DF2.LT. +HZTF(JJ,K))) THEN ditil =(DFl -hztf(jj,k))*cos(pusi) ENDF if (dltl 1 .gt.Tff) then * { dltxl : Iength from coIummn jj to j.t-1, to BP of dit1f } * dltx l=dltl I/sin(~usi)

GRAT(JJ,K)=Tff endif 100 CONTINUE if M9.eq.19) then write(*,*) jj,i,k,KZ,HZTF,HI,GRAT,y1 ,PUSI,DLTL 1' write( l2,*) jj,i,k,kz(JJ,K),HZTF(JJ,K),DFl.GRAT(JJ,K),y1, +PUSI,DLTL 1 write(*,*) 'U 1- 1 ,IJ+ l1.u(jj,i-l),u(jj,i),u(jj,I+l) endif 12 FORMAT (lX,I4,14,13,14,F7.3,F7.3,F10.5,F8.4,F8.4,F8.4) return end ANNEX III

AN, W. and ALLARD, M. (1995), A mathematical approch to modelling palsa formation: Insights and growth conditions. Cold Regions Science and Technology, 23: 231-244. cold regIons science and techno

Cold Regions Scieme and Tédiwlogy 23 ( 1995) 23 1-244

A mathematical approach to modelling palsa formation: Insights on processes and growth conditions Weidong An, Michel Allard * Centre D'é& Nordiquu. Univenit6 Lavai Québec. GmanbGl K 7P4 Rmived 19 August 1993; arrcpad after revision 1 1 May 1994 bUiU iGyiUi 13 science and technology €ditor Editorw~ RokrtF~ng J. Brown (USA) J-C. Leiva (Argenîina) Cold Regions Engineering Program GO. Cheng (China) M.P. mnen(Finhnd) 1n-e for Mechanical Engneering DA. m (UK) LW. Morbld (UK) National Research Couna1 of Canada EO. ERhov (Ruçsia) T.E. Osterkamp (USA) Ottawa. Canada K1A OR6 TM. Jacka (AusEralii) B. Salm (Smtzeiland) B.D. Kay (Canada) il. Sasaki (Japan) K Kohnon (Germany) P. Wadhms (UK) f M. Kopilgorodski(Ruççia) W.F. Wcdu (USA) B. (Canada)

CûLD REGIONS SCIENCE AND TECHNOLOGY is an international journal dealing mth the scieritific and technical problem cdd emrirwiments. inâuding both natural and arüfiaal emrironmentç. The primary conœm is with probiems related 10 the fre ing of water. and espedaliy wiîh the many fmof ice. çnow and frozen grwnd. The pumal is intended to serue a wide mgr specialii. mding a medium for interdisciplinary cammunicaiii and a convenient source of reference. Emphasis is given to applied science. mainfy in the physical sciences. with broad mverage of Vie physics. chemistry i rnechanks of ice. -ter systemç. and iœ-bonded çoilç. Relevant aspects of BBMIscience and mateMls ~Üenceare a primary concems. The techndogy content stresses msearch, deveiopment and professional practice in engineenhg. This inciudes &adilional ma malizaîions of engineering (militaiy. uvil, mechanical, mining. electriml). together wiih oîher engineering subdiiions (E hydraulic, agncultural, highway, sanitary, petrdeum, ocsan. airport). Coverage also ernbraces engineering geology, archinectu meteordogy. hydroiogy. foresûy, exploraîion geophysics. naval archite@ure. and so forth. In addition to original papers. technical reviem and short mmrnunications, the journal includes ietters. book reviewç. repoa meetings and cornmittees. and professimal announœmenk. Submiited papers are pmcessed for publication with a minimum delay.

Publication information Cdd RegmScim and Tedmology (ISSN 0165-232x1. For 1995 Volume 23 is scheduled for publication. Sumption pric are avaibMe upon request frorn he publisher. Subscriptions are aœepted on a prepald basis only and are entered on a calent par basis. ISSueS are Sent by surface mail except to Ihe klbwing countries wtiere air delïvery via SAL is ensured: Argentii Ausûalia, Brazil, Canada. Hong Kong, India. Israel, Japan. Malaysia. Mexico. New Zealand. Pakistan. PR China. Singapc SauVI Africa. çouth Korea. Taiwan. Thailand. USA For al1 other anintries aidlrates are availaMe upon requeçt. Claimç missing issues rnust be made maiin six mon* of our pubkation (mailing) date. Pl- address al1 your iequesls regard orders and subscription queries to: Elsevier Science B.V., Journal Department. P.O. Box 21 1. 1000 AE Rmsterdam. T Neaiem. Tel.: 31-20-4853642, fax: 31-20.4853598.

U.S. mailing notice - Cdd Regi'ons Science and Tanology (tSSN 0165-232X) is puMished quarterly by Elsevier Science B (Molenwerf 1, P.O. Box 21 1, 1000 AE Amsterdam). Annual subscription pnce in the USA Usa311 (valid in North. Centrai a South Arnerica). including air sped delivery. Applicaüon to mail at second dass postage rate is pending al Jamaim, NY 1 14: USA POSTMASTERS: Send address changes lo Cdd Regions Science and Technology, Publications Expediting, Inc., 2 Meacharn Avenue. Elmont. NY 11003. Aimeight and mailing in the USA by Publications Expeaing.

Advatüsing information Advetiiing orders and enquiries may be sent to: Elsevier Science B.V., Advertising Department, P.O. Box 21 1. 1000 1 Amsterdam. The Netherlands. tel.: 41-20-4853796, fax: +31-2û-4853810. In the UK TG. Scott 8 Son LM., attn. Vanessa Bi Portland House. 21 Narbomugh Road. Cosby. Leicestershire. LE9 5TA. U.K.. tel: 01 16275052112753333, fax: 01 16-2750522. the USAand Canada: Wesîon Media Associates. atm. Daniel Lïpner. P.O. Box 11 10. Greens Fam. CT 06436-1 110. USA. I 203-2612500, fax: 2û3-2610101.

O 1995. ELÇMER SCIENCE B.V. U RIGHrS RESERMD 0105-2- 09 ~op~dmtrpb(icwai~ybe~ri~c~dnaro~iev;ilryslomor~nwyfomiocb~~mesm.ececuonic.~.photocogriig.~~ 0-W. *mar ho plar wnnon d me Mi.Etfevcor SdoncP B.V.. Coqynph( 4 Pennirwns Dspamnsnt. P.O. Bas 521. 1000 M4 AmneIUmn.

PSNEIY IN THE NETUERLANDS cold regions science and technolog) Cold Regions Seieaa and Tedinolugy 23 ( 1995) 23 1-244

A mathematical approach to modelling palsa formation: Insights on processes and growth conditions Weidong An, Michel Allard * Cenrre DPé& Nordi'es. UmUwrsitiLPvoLQvibrc, GyipdrrGl K 7P4 Received 19 Augun 1993: aaeped afba misioa 11 May 1994

A one-didonai heat and mass îransfer mode1 was designed to sirnulaie UIC long tenn aggradation of permaFrost and the buildup of segregated icc that take place chiring the formation of palsas. nie soi1 and cüma6ic conditions used in mode1 nias are che same as those obscrvcd in the field ncar the Village of Kangiqsualujjuaq. in Northem Québec. The mode1 shows clearly chat palsas can form undcr the present ciimatic conditions under snowfm sim. Wich assumai sleady climatic conditions. mode1 nuis indicatc chat bthm can producc a palsa a fëw meters high in about 60 ywrs. Aher Lhis initial growih priod. the palsa can pwhigher but at a slower rate until a quasi-stcady slate is mched afk15iL2ûû ytars. The mode1 suggcsis that ice conœntrafions ;iggregate acar permafrost base. The- conclusions gcncrally agrct with field conditions laiown hmdrilling and geophysics, and the timing is consistent with knawn aga of radiocarbon datd landfomis. Dcveloprncnts of the modelling approach used in Lhis study will help increase ihe understanding of stül unsolved aspects of rtrt proctsses of paisa fomtion sucb as the effiof surface geomorphologic changcs andctimatic variations on hmand mas ixansfcrin pemiafrost.

1- Introduction generates mounds in minera1 sediments without a peat cover thus fonning landforms comparable in dimen- Paisas are dehed as "Peaty permafrost mounds pos- sions and shape to paisas. Such mou& were caüed sessing a core of alternathg layers of segregated ice "mineral palsas" (Essart andGangloff, 1984; Dionne. and peat or minerai soi1 material" (Associate Com- 1984). "minerd permafrost mounds" (Allard et al., mittee on Geotechnical Research, 1988). ïbey can be 1986), "cryogenic mounds" (Lagarec, 1982; ho- composed exclusively of frozen peat and ice. However, ciate Cornmittee on Geoicchnical Research, 1988). In the rnajority of field researchers report that the peat in most cases, the sedirnents arc silty and are of lacustrine palsas usually overiies some mineral sediments, a fact or glaciernarine or@. that generated abundant tenninological discussions and Since physical proceses goveming ice segregation debate over the processes of theu formation (Seppal& are now rather welI hown and since ice lens formation 1972; Washburn, 1983; Allard et al., 1986). It is now has ben both reproduced in Iaboratory work and sim- a widely demonstrated fact that the ice segregation ulated by mathematical modelling, it is wocthy to bry responsible for the topographie heave of these land- the application of segregation and have theory to the forms takes place dominantly in the underlying sedi- fonnation of palsas and cryogenic mounds with the ments. It has been shown that ice segregation also help of mathematical modelling. When a htsusceptiblesoil is subjected to freezing. heave occurs as the result of the growth of ice lenses

0165-232X/95/$0950 Q 1995 Elsevi~rSa- B.V. AU ri@ SSDlOl65-232X(94)O00 15-P 232 W. An. M. Alkd/ Cold RegimScience adTcciuiology U (19951 231-244 fed by water supplied to the freezing fringe ftom the iment was reporteci in the literanire, by Seppala ( 1982: unfrozen soil. Many studies approach the fundamentai by keeping a 5 m2 area in a fen free of snow over on mechanisms of fiost heave through laboratory tests winter, îiost penetration increased sufficientiy to fon (e.g. Konrad and Morgenstern, 1980; Penner, 1986; a layer of permafrost and initiate a 0.35 m high pals Takeda and Nakano, 1990). Others are orientcd Although ice segregation was invoked to explain hem towardç Ihe development of mathematical modefing of the new landfonn, this was not supporied by obsei and numerid prediction (e.g. Hahn, 1974; Gilpin, vations on dnlled cores or by an atternpt at mathema 1980; An et al., 1987; Nixon, 1991). idanalysis. The formation of palsas and of cryogenic mounds This paper presents results of out attempts at matl and their evolution are principally controiied by the ematical modelling of the formation of palsas and cq interaction of thermo-dynamics,ice segregation, bst ogenic mounds. It uses a unidimensional mode1 hi have and thaw consolidation during rnany years of simulates discrete ice lens formation dong a vertici recurring freeze-thaw cycles at the surface of the ter- profile. Bidimensiond modelling simulating larm tain (decades and -centuries wcording to field obser- variations is at the deveiopmentai stage. vations and 14C dating, Allard et ai.. 1986). 'Ihe dimensions, time deand complexity of conditions in the nahüal environment are much larger than in labo- ratory tests which are conducted in controlled condi- tions on small volume of soils. Yet, the basic .The climatic conditions and the geomorphologici knowledge obtained from such experiments should be setting tised in the mode1 art those met at the study si1 tentatively applied to field conditions in order to gain of Kangiqsualujjuaq. in norrhern Quebec (65O57'H insighis on the terrain processes. Only one field exper- 58"4OrFi) (Fig. 1 ) where conditions are typical of th -

Rg. 1. Location of Kangiqsiralujuaq and photopph of the pcar platcait-pala complu. W.AR M. AM/Coid Rrgiau Science and T~iogyLil(1995) 231-244 2

Fig. 2, (A) nie paisa plaieau a~dpais curnplex near Kangiqsuaiuüuaq. in Jnne 1992 during snowmelt hwpoints io the Rat area where the Ihemial profile of Fig. 3a cornes hm The otfier thenrial pmiïles art from hummocky relief closer to the phoiographer's point of new. (B) Sqrcgation iœ hmthe palsa cDnd 1. I m below ihe siratigqbic pcat/silt con- palsa region of eastern Canada. The site is at the north- and - 6.TC with an average of - 58°C. For the sarne ern limit of the discontinuous perrnafiost zone (Seguin period the mean air freezing index was 3 193"Cdays and Allard, 1984). Over the decade 198&1990 the and the thawing index 1M9°C-days. Mean January mean annual air temperature ranged between -4.4"C temperature is about - 22'C and mean July tempera- W. An. M. AIIardf COURcgionr Scirnce and Tcchnology 23 (1995) 231-24d

Fig, 3. Tempaanin profiltr hmthe peat plaicau: (a) hma fiat are& &ph 20 m; (b) and (d) from deprrssed a~ascovered with sna winla; (c) üom a ptruding moudova the plateau level. turc about 9.S°C. TotaI precipitation is about 400 mm, terraces and peat plateaus) retain very linle snow. of which 42% is snow. Kowever due to winddrifting, A complex of peat plateaus and palsas by a lak the extensive patches of hindra terrain (hills, plains, km ftom the vilIage was used as a terrain reference W. An. M. Allord / COUfigions SCLNe and Tcclrnolog).23 (1995) 231-244

ihe modeiiing exercise (Fig. 2A). 'Lhe peat layer on The latter assurnption was verïfied at the refa the Iarger peat plateau varies in thickness hma few site on cored samples. Afkr melting and extractic cenumeters where it has been eroded to over 25 rn in cenuihging, both ice lens water and soi1 water hollows where slumping of peat blocks hmsurround- tested for salinity with a refractometer. No salt CO hgslopes occud. In general, the peat cover is about was detected. 90 cm thick where it has not slided or slumped and where there is no evidence of surface erosion, Marine 3.1. Discrete ice lemformation andfiost heave i silts rich in segregated ice lies below the peat layer fieezing soil (Fig-î3 ) . Fig. 3 shows tempetanire profiles hmtherrnistor The heat condwtion equation can be written a cables in the pennahst. As Fig. 3a shows profiles hm a 20 m deep hole (iïï-301) on a Bat area of the peat plateau, Figs. 3&d show profiles hmholes on eirher the top of higher mounds that rise above the plateau surface or in depressions. Depressed sites (Figs. 3b and d) are warmer because of deep snow accumulation in hoIIows. According to geophysical soundings, penna- hst thichess in this palsa and peat plateau complex varies from 3.5 m under some depressed a&as to more than 22 m under topographie highs (Gahé et ai., 1987). Maximum elevation on the complex, on top of an indi- viduaiized moud higher than the general plateau sur- Employing the segregation potential (SP) ,dei face is 15.4 m relative to the lake level. as the ratio of the water migration rate to the the gradient in the hzenhge. the formula can be g as (Konrad and Morgenstern. 1980, Konrad Coutts, 1987): 3. The mathematicai mode1

The model simulates ice segregation and hstheave and so reproduce.the vertical upheaving of a soil According to Darcy's law, the water fiow thrc file such as it must occurs in the formation of a palsa the hzen fiinge is It takes into account the variable phase-change tem- perature. build-up of discrete ice-lens. heave and thaw V,=k-gmd P, to consolidations in order consider freezeuiaw cycles V, aear the soi1 surface and annual cyciic temperatme var- and considering as constant through the fringe iations dong the profile. The mode1 is also established equation for the continuity of water flow is given on the following assumptions: The soi1 porous medium is isotropie and homogeneously layered, and soi1 par- ticles and water are incompressible; the volume of soi1 For a one-dimensional problem, it is reason particles ternains constant in the fieezing and thawing assumed that (a) hzen penneability is depender processes. Darcy's law applies both in fiozen and temperature using a power law of the form unfrozen soils. Moistue îransport in both frozen and k=h/(Tf-T)" unfrozen zones murs ody in the liquid phase. Dfi- sive dispersal fluxes of both the water and the gas and (b) the temperatwe change across the frozen fr masses cm be neglected. Locally. fluid and solid tem- is lin*, the temperature in the frozen fringe wil peratures are equal. Finally, soluteconcentration is neg- sacistied by: ligible and iherefore needs not to be considered in the madel. 236 W. An. M. AlM/Cold Regimr S&rue and Tdtwlogy 23 (1993 231-Ze4

Substituting (9) and ( 10) into (8), the integratioa is subjected to thaw consolidation. Two diffcrentaci of the porepressure distribution (8) in the fringe is Iayer conditions cm happen on palsasr (Nixon, 1991): 1. Maximum thaw depth (generdly in the rang4 0.4 to 1 m) is confined to a thick surficial 1 layer. or 2. Due to a thin peat layer. maximum ttiaw de reaches into the underlying silty sediments.

in most peat types, particularlyfibrous peat.:aln The generalized Clausius-Clapeyron equation at the no segregation ice form during kzing. a fact oker segregation fieezing hntcan be written as: in many sections in palsas and also observed by nun ous drilling in hzen active layer at the Kangiqsui jjuaq site. Observationsalso &monstrate that iœ lem substituting ( 12) into ( 1 1) and assuming T'=K for are scarce and thin in the active layer in dtysadime simplicity it follows thac the most abundant ice region being just bdow pen Gost table (Fortier, 1991). It is therefore reasonabl~ assume that active layer consolidaion ac rhawiq cyclically compensahi by a sudi amount at he2 Similady, Eq. (5) is derivexi from the application of and that this factor can be omitted in modelling. 1 Darcy's law and the Clausidlapeyron eqwtion at reasoning impties stable clicconditions for a Ii the frozen hge(Konrad and Coutts 1987). AppIying period, for the situation would be ciramaticaily difi (6) and ( 13) at the segregation freezing fiont at x = 0, in ihe case of climatc warming Ieading to îhaw pe the segxegation fkezing temperature T, cari be tration deeper in more ice-rich SOLAs the active la obtained: thaws, a perched saturateci layer follows the thaw fiont and some water migrates into the hzen la: and even~aiiyin the perrnafhst underneath (Macfi 1983; Smith, 1985) dong the thermal gradient. 1 can be expressed as: The unfrozen water conient in the hm sds is dependent on the soi1 temperature. Ice content will change with the water migration from the hzenfringe. where q, is water flow. It can be witten as: Downward water migration fiom the thawing ac layer is physically sirnilar to îhat of upward W. migration to the freezing hntOnly is the flow di tion different nie SP can apply and its mathemat Frost heave is fed hmhvo components, original expression can be used in Eq. (20) instead of ca pore water and water migration, given as: cient Dr This treatment simpIifies the numerical cc putation of the mode1 and constitute an extensioi the use of the SP method in permaiioçt science.

3.3. Numerical computation

3.2. Thaw consolidation and ubwnward wufer in numerical computation of 1-D problems, tûe m migrOhOhon elling can use a space-time grid on which points t,) (i= 1.2.3,---M,n=0,1,2,3.--SN) are fixed. Since palsas take many years to grow to their hl1 Note that (a) Eqs. (1)-(4) are the nonhearpai size, an active layer exists on their surface during theu differential equations for solving the phase-cha . growth period. This layer which thaws every sumrner temperature problem. The convection term in Eq. W. An. M. Alkyd/ColdRcgians Scimcc Md Tc~hnology23 (1995) 231-244

TaMe 1 Sdphygcal and thermal propcrtia usdfor model compDtations

Mrype P (ks/m3) e (m3/m3) c (w/d K) A (whK) SP, (mmfls 7

a==1.13.fi= 12450cm. a= 1.17x IO-'. h-247X cm/s. TheT,irO.O;lheain~~aatrD~D~~ltO.6I.~d3..respectivdy.Theciw~spaasccpsusedf0~thecompu~~11waeA~4.0h;Az= 0.10 rn Tbt chicimss of peat covcr is 1.1 m hmibc ground surface; nie &pth of the daycy silt 1 ranger from base of dr pcat covcr to 45 n that ofthe dayeysilt 2 liom 45 rn ta 2û m.

is so small that it is ornitteci (Nixon. 1978). Eq. (5) is - dependent upon the phase-change temperature prob- lem. Because of temperaturedependent thermal prop erties, the prediction

3.4. Initinl condition where Dt, = D$n(dr,) +D, in cool season As reported in the titerature (e.g. Seppaii, 1982; Dt, = D, in warm season . Allard et al., 1986; Ahrd and Seguin. 198ï), a palsa can start to grow in a permafrost free area of a bog or f(r) =A$in(dt,) in cool season a fen when the snow cover is removed or reduced by some ecological or climatologicai process. This induces an abrupt change of ground slrrface thermal conditions. After the inception, the palsa top is kept nearly snowfree during the following winters as it Considering the actual depth of permafrost bas makes a wind exposed topographie proniberance and the reference site, 225 m, the initial temperature at permafrost cm keep aggrading at the site. 'Lhe model depth is set as positive. It then gradually drops i tfierefore starts from an unfinzen site at the end of elapsed time until reaching a steady state under Autumn no 1. Peat depth is one meter over silt and the influences of applied climate and geothermd coi soi1 materials are water saturateci. Initial conditions are tions. The lower boundary conditions, at i= M, detined as: defined as: W-An. M. Abd/ Cold Rcgim Science and T~chnology23 (1995) 231-244

Unfrozen zone Frozen fringe Ts: Segrqation freezing temperature

for clay silt 2

The constants are fiom Fortier ( 1991 ) wha mea ured the unfrozen water content from Ifie samples permafrost in silty clays in northem Qukbec and fm laboratory experiments (Xu et al., 1985). nie SPo values used for are the expei The soi1 thedparameters used for mode1 com- silty day mental results of Konrad and Morgenstern (1980) ai putations are presented in Table 1. These values are Konrad (1988) for very similar soils (Leda clay). i typicai of such soi1 types [Williams and Smith, 1989) proven by the near absence of ice layes. pure peat adwere computed fiom labontory andysis (water not prone to segregation. For example, it is even us content, density of particles) using Kerstem's equa- as ami-heave foundation fillings undemeath son tions (Goodrich, 1982). Scandinavian railways (Skaven-Hang, 1959). On pi The unhzen water content is a temperaturedepend- sas, the base of the peat cover may be mixcd with s ent variable. The empicicd relationship used in the producing a thin layer with an intermediate SP valut modeliing is: for clay silt 1 3.7. Freezing and thawùtg fronrs

At palsa inception in the tirst winter anly one h ing front progresses downward. After the first winb a thaw front propagates downward to perma6ost table 4. Namerid dtsand discossion each suerand a new Freezing front does simiiarly each wintet A freezing front is permanent at the base Fig. 5 illustrates the evolution of the thermal profi of permafrost, So the model has to consider these three as the permafrost base deepens in the palsa and as tl levels of phase change conditions (Fig. 41.

Fig. 6. Dimibution and thichs of iœ lenscs ahg the vutical pmfile accmding to model. nie duratiai simuliittd is 200 yoars dg aSP,of l.29x IO-" d.h"*"C-'. IV An. M. Allard/ Cold Regions Sn'mcc Md TechnoIogy 23 119951 231-244

Fig. 8. Amount of hveoccuning at various depths dia200 yean hmsimulatiilioa. (A) Myhm using local sMI pon water- (B) With fia aymudion hmgnnindwattr. ground surface is heaved up to 3 m above the original ence or absence of thick ice layers below pennafros ground level. The simulated thermal profiles compare table depends on peat thickness. if the peat cover ii weii with measured thermal profiles, particularly hm thicker than the active layer, ihen very little ice form the flat peat plateau surface (Fig. 3a). Under the if it is roughly equal, important ice Iensing may taki assumed climatic conditions ( - 5.6"C MAAT, no place dong the stratigraphic contact if the peat cove snow cover) the modelling resulis show that ( 1) large is thinner than maximum thaw depth, chen ice enrich annual thermal fluctuations keep occurring in the upper ment takes place in near surface pemahxt Ice Ien: 3 m of the profile; (2) fast permafrost aggradation takes enrichment below pemiafrost table is very important ii place and permafrost base reaches a near-equilibriurn silty cryogenic mounds where peat is absent ai depth of 16-18 m in about 60 years. Thereafkr aggra- observed many times by cirilting and by geophysica dation at the base of permafrost takes place at a slow methods (Fder, 1991; Pilon et al., 1992) and ai pace. However, the model suggests ihat about h-f of show by the model (Fig. 7). the total heave is achieved after six decades and that it Water supply for ice lens formation cornes from porr will double in the following 140 years due to ice for- water and hmground water below the freezing hn mation near the base of the permafrost. that is sucked to the freezing fnnge in an open system With a negligible solutecontent, the only factor that After simulating 200 years of aggradation and assum can depress the freezing point of soi1 water is pressure. ing that ody the onginai soi1 water content is involvec As the permafrost base progresses downward, over- in ice lensing, the amount of heave is only half ir butden pressure increases. Added to pore pressure at cornparison with ice lem feeding fiam ground watei the freezing fiont. this resu1i.s in an ice segregation flow hmthe surroundings (Eg. 8). . temperature of about -O.l°C by 10 m deep and Application of our numerical mode1 shows that t -0.19"C near 20 m deep where frost penetration new palsa can start to lonn and grow under the presetr reaches a quasi-steady state. climatic conditions provided that snow cover is locall~ Although ice lensing takes place at al1 depths during absent or significantIy reduced, a fact supported by ihc the process of palsa growth, the= should be more observations by numerous authors of incipient fonn: numerous and thicker ice layen near permafrost base in the actual landscape of norlhern Québec (Allard el as well as a zone of ice enrichment just below perma- al., 1986; Cummings and Pollard I990). A palsa or e frost table (Figs. 6and 7). The latterresults ftom down- pemafrost mound 3 m high can rise above the sur. ward water migration in the upper permafrost zone rounding terrain in roughly six decades. If conditions from the active layer. Mode1 mns suggest that the pres- are maintaineci long enough. let us Say another 10C W. An. M. Allard / Cold Regions Scimc and Teehnology 23 (1995) 231-244

-1.7 1.4 4.5 7.6 10.7 13.8 16.9 20 Depth (rn) 242 W. An M. Alhd/ Cold Regions Science and TechnoIogy 27 (1995) 231-244 years or more, the palsa wiff continue to grow more surface characteristics change. the uansfer of heat ani slowly as a serÏes of ice layers will form near the per- water will be altered within the landforms and meltin mafrost base. Somewhat diferent types of soi1 will or ice Iensing will occuragain. The model will be usefu pmduce different mound heights given the different to test hypotheses of the impact of climatic and no] segregation potentials îinked to different thermal prop climatic-induced changes on the dynamics of palsa erties (Fig. 9). and cryogenic mounds. At the permafrost base beneath a paisa or a cryogenic mound. thermo-dynamics conditions are such that a quasi-stacionary freezing front is attained. The depth of 20 rn obtained with the model is in perfect agreement at with pennafcost depth the reference site where palsa Although a wealth of new information and concepi growth started many hundreds of years ago according came out of observation, dating, geophysical work an1 to I4Cdating (Gahé et al., 1987). It is aiso an average expenmenfs in the Iast 1&I 5 yean, further studies a depth measured in over 200 surface electncalresistivity palsas and cryogenic mounds. using modelling to te! soundings in large paisas and cryogenic mounds in hypotheses and propose new ones are still necessary t regions of Northern Qukkwith the same range of air achieve a better understanding of these landfoxms. A temperames (Lévesqueet al., 1988) and characterized palsas and cryogenic mounds are cypical features of th by the presence of comparable post-glacial marine subarctic regions. coring through hem and cornparin clayey silts. This general order of depth for the per- ice layersequences with modelling. will help to undei mafrost base was also found ai a few sites by hydraulic stand how permafrost in the discontinuou zone ha dtilling and thermal measurements. responded to past and recent climate changes. The presence of either a series or a single thick ice segregation layer near the base of pemafiost needs to be Furthersubstantiated. Such abundant ice layers wg-e reported by Lagerbiickand Bodhe ( 1986) and by Aker- 6. Notation man and Malrnstrr6m ( 1986) wbich cored throughout sorne permafkost mounds in Northern Sweden. hdi- constant cation of the existence of such a layer was alsa found apparent volumetric thermal capacity (J by Fortier ( 1991) in a cryogenic rnound near ~miujaq, m-3 K-') Northcrn Qudbec. using diagrapbic rechniques of elec- volumetric thermal capacities of ice and trical resistivity (vertical dipole-dipole array) in a hole water (J m-' K") drilled through the permafrost. mis work reveaied that volumefric thermal capacity of mil particIe segregated ice is more abundant just below permafrost (J m-' K") table and near permafrost base than in the middle sec- thermal hydraulic conductivity (mZs - ' tion of the hzen core. Oc-') In its actual fonn. the mode], that applies steady volumetric Iatent heai of water (335 W climate condition. does not explain the abundance of kg-') palsas and cryogenic mounds much higher (over 10 pore water and pore ice pressures (kg m -2 m) than the simulated height. A hypothetical expla- overburden and applied pressures (kg m-' nation would be that cold climatic penods provoke pressure in the ice (kg rn - *) renewed aggradation at permafrost base and further additionai pressure component (kg m-2) heave. Also. non clirnatic-induced dimensional pore pressure at the Freezing front (kg changes in the landforni geomehy can take place. For m-') instance, it has been shown from thermal measurements segregation potentiai coefficient (mZs - ' at a variety of sites (Allard et ai., 1986) that each Oc- ' ) mound has its own thermal regime that depends on temperature ( K) sIopes, vegetation cover and snow dismbution on the temperature of the kingpoint of pure sides and the tops (similarly in Figs. 3M).Shall these water (OC) segregation freezing and frost hnt AkdM. Seguin. MX, and Lhtsqut. R. 1986- Phand a tempetames (OC) pamaCrostmoundsin~~~ooPIGc phlogy Part Ir. pp. 2Ssm. lower warm boundary temperature of frozen Allard. M, SeguiR M.K., 1987. The HoIocent evolution of 1 Fnnge (OC) hiDstaearthetrttIkonthccastcrncoastofHudso water velocity in frozen fringe (m s- ') (Nonhern Qiitbte). Can. J. Eanh Sa. 24: 22û6-2222 fringe thickness (m) An. Weidong Qitn. Xiaobo and Wu, Ziwang, 1987. Nun soif pomsity sunuliitim of mqltd lits, and mass mmfix baie& faa (m) ing fraepng. J. Glacia GtDcry.. 91 1) :76-85. heave An. Wudong. 1989. In&aion among tunprahire moishi heave from pore water content (m) sims fieids in frozen soifs Laruhou University b,,Ch heave from water migratian (m) Arsociaie Commiaet on Geoccauiid Resauci~Nationai Re hydraulic conductivity at - 1°C (m s- ') Couneil of th ad^^ 1988. Glossa~yof Pennafmst and A wam velocity (m s - ' ) Gmund-ice Tuns. Tsbnid mcmomdm No. 142.60 1 thermody narnic constant Cumiaiags. C and Pollatd W, 1990. CryoguAc mcgwï~ peat and nnwral med paisas in tlac ScheffmilleArta Q thermodynarnic constant (m) Roc. 5th Cas Pamafrast Conf.. pp. 95-103. chaw-compressible coefficient Dionne, J.C. 1984. Palses et Iimiœ méridionak du prgfli thermal conductivities of soils and soit ïbçmispheie Nord: Le cas de Blanc-Sablon. Québec t particles (W m-'K-') Php. Quat, 38(2): 165-[W. thermal conductivities of ice and water (W Fedg. 1986. Ndcal Cornputarion Method. hdustry pp. 28%365 (in Chaese). rn-' K-') Fortia.R, 1991. ~hWgéophysiqucsdu~Iisot~Un bulk density (kg rn - 3, Nunavik Univasitt Lavai. ïhhe de Maîî. 234 pp. ice and water densities (kg GaM E. AUarrl. M. and Ségirin. M.K. 1987. Géophysique e! unfiozen water and ice contents (m-' m-') mique holoche de plaicaux paIsiques à Kangiqsualujjuaq total content of liquid water and ice (m3 aC Nordique Géogr. Phyt. Quat.4l(l): 3M. Cilph, RR.. 1980. A mode1 for the prediccion of ialensir m-3) frostkavcinsoils. WataResour.Res, 16(5):918. Cartesian coordinates (m) Mch.LE. 1982 An hoductory mvitw of numerical m tirne (s) for ground thermal calculatioi~~.National Rgearch Cou Canada Division of Building Research. ûuawa. Paper 32 pp. Harlan. RL. 1974. Analyçis of coupled kat-3uid tr~isferi tially frorea dl.Wata Resour. Ra.. 9(5): 13144323. Konr;iQ JMand Morgennan N.R. 1980. A mcdianisac ch iœ lem fdonin fine-gcahd soils. Can. Geotedi. 4M6. . . The authors acknowledge *e help of Dr. Janusz Fry- Korind, LM. and CoutIs, R, 1987. Roœdurc for deumnni detki, in charge of automatic dam acquisition systems segrcgation potcatial of Mgsoils. Geotech Testi at Cenm D'études Nordiques. The contribution to field lO(2): 5 1-58. LM, of on work by the following persons was also appreciated: KonroQ 1988. iduena hirzing mode fmzen char;ictenstics. Cold Reg. Sci. TethnoL. 15: 161-167. Christian Bouchard, Richard Fortier and Eric Ménard. Lagarec. D.. 1982 Cry@c mouds as indiCatan of pem The fnendly coIlaboration of the community of Kan- conditions. Northm Québec Roc. 4th CULPcrmafros! giqsualujjuaq was essential for the success of our work pp. 43-48. in this region. This project was supported by gram Lagabadc. R and Rodhc. L. 1986. Pingos and palur in m from National Science and Engineering Research mat Sweden pretiminary no= on ment investigations, t AIUL. 68 A(3): 149-154. Council of Canada and "Fonds pour la formation de Uvesque, R.. Aliard. M, and Séguin. M.K. 1988. Regional I chercheurs et l'aide à la recherche" of Qu-. ofptrmafmst distniuiion and thickness. Hudson Bay aasl bec. Canada Roc 5th int Conf. Permafrosf Norwny. 7 pp. 199-209. References Mackay. J.R.. 1983. Pingu growth and subpingo water lenses em Arctic CwsL Canada Roc. 4th lnt. Conf. Prrmafrosi ~km.HJ. and MaImsm6m, B.. 1986. Padmtmounds in the b;iaks. AK. Nationai Acadmy Ress, Washington. DI Abisko ama. Notthern Sweden. Geogr. Ann.. 68 A(3): 155-165. 762-766. Language The offcial language of the Journal is English. but occasbd artides in French and Gemian will be ainsidered for public Such artides shooki statt with an abstract in English, heaW by an Engliih translalion of the title. An abshcî in the lang~ the paper shouiâ foilow the EngTî abçiract. Englii tmnslatiw af the figure and table captions should abbe given.

Preparath of ths teai (a) The manuscript should preferably be prepared on a word procesçw atM printed with double spacing and wide rnargin indude an abstract of not more than 500 words. (b] Authors should use IUGS teminokgy. The use of S.I. units is a& reoommended. (c) The title page should include: the Me, the name(s) of the author@)and their affiliations. faand e-mail nmbers. In a more Vian meauthor. please indicate to whorn the correspondence should be addressed.

Refefences (a) References in fhe text consist of the surname of the author(s). fdlowed by the year of publication in parentheses. All enœs cited in the tex! shouid be given in the reference list and vica versa. (b) The reference list should be in alphabew order.

Tables Tables shwld be compiled on sepamte sheets and should be numbered according to îheir sequence in the texL fables cai be sent as glossy prints to avoid errori in typesetting.

t~histrations (a) Ail illustrations should be numbered consecuîively and referred to in the text. (b) Drawings shwld be Ieitered thraughout, the size of aie lettering king appropriate to mat of aie drawings, but takin account the possible need for reduction in site. The page fomiat of the journal sbould be considered in designing the draW (c) Photographs mus1 be of good quality, printed on gloçsy paper. {d) Fgure captions çhould be supplied on a separate sheet (e) ti contributors wish to have îheir original figures rehrred this shwld be requested in pmof stage at the latest (0 Calour fgures can be acceptecl providing the repmduch'on costs are met by the author. Please consuit the publisher for t information.

Pageproofs One set of page proofs will be sent ta the correspanding author. to be checked for typeseiîin4/ediing. The author is not ertp to make changes or corrections that constiMe departures hom the arb'de in its accapted fonn. Prmfs should be retumed 3 days.

Reprints Fnty reprints of each artide are supplied free of charge. Additional reprints can be ordered on a reprint order form which i sent to the wmsponding autbor upon r8ceipt of the accepted arüde by the publisher.

Subm0;Sion of manwuipts Contributions Io aie journal should be sent to the Editw, eaher direcily or through a rnember of the Editorial Board. Ideally, i butions should be understandable and interesting to a wide range of the ioumal's readen. Presentations shoutd lx dear and unpretenliow. avoiding pondefOUs style, laborious description and unnecessaiy jargon. The indication of a fax and mailnurnber on subrnissii of the manuscript muld assiçt in çpeeding ~mmmunicafions.Ti number for the Amsterdam office is +31-204852696. Submiiior, of an artide is undentocad to imply ihat ihe artide is original and unpuMished and is not being considered for cation elsewhere.

Submission of eiectmnic tex! Authors are requested to submil the final text on a 3.5' or 5.25' diskette. &th double density (DO) and high density diitles are acceptable. Make sure. hovuever. lhat the diskettes are fonnaîted according to their capauty (HD or DD) I copying the files onlo them. As with the requirements for manuscript submission, the main text, Iist of references. tabies ai ure -ans should be stored in separate texi files with dearty identifiable file names. The fomt of these fihi depends r word procesçor used. Texîs written wiîh Display Write. MuIoMate. MiisoR Word. Sarnna Word. Sprint, TEX. VoMter. PC. WoidMARC. WordPerfeci and Wordstar or supplied in OCCVRFT or DECiDX format can be readily processed. In al1 cases the preïerred format is DOS texi w ASCII. It is esçenIial that the narne and version of the word pmcesçing prograi type al mputeron which the text was prepared. and the lomat of the tex1 files are dearfy indicated.

Authors are requested to ensure that the cantents of the diskene conespond eraclty to the contents of the hard copy manu Discrepancies mn lead to proofç of the wrong version being made. The word procesçed text shouM be in single cdwnn fi Keep aie layouf of the text as simple as possible; in paticular, do not use nie word processat's opo6ns to justify or to hypb the words.

If avaiiable, electronic files of the figures çfioufd also be induded on a separate iioppy disk Glossary of Geology Third edition

by R.L. Bates and J.A. Jackson

A superb volume ... eveiy Approximateiy 150 The authority of this new serious garai scientist ml/ references have ben edition - like that of its havie to possess his or her added to the 2,ûW in the predecessors - rests on the omWY- second edition. Literatuie expertise of geoçcientists €OS cited ranges from aie eady from many walties, who 1790s to 1986. New havemviewed definitions, added new terms, and Thsape of hc glossary is numerous in fields of cited referenœs. Their geology and geophysict in ihr carbonate- sedimentology. contributions make the broadest annoration and hydrogeokgy, marine Gloçsary an essential reaches rhc Uircrfaces wich geology, mineralogy, ore reference work for aii in the archeoiogy. astrogeology, deposits, plate tectonics. geoscienœ cammunity. clunatoiogy, oceanogrqphy, snow and iae, and . and soi1 science. stmtigraphic nomendature. €OS Many of the definitiork provide baek round A huge book.. if whtu you infornation. ahus the wantroknowurrcnnsof reader will leam the &fÜu*rions or even shtm d ifference betwwn uplM(11wns ir not kre. fhen sylvanite and qivinite, and if is probabiy of svch many other look-alike pairs; minisculr ùriporrance chat it the orïgin of such ternis as Elsevier Science Publishers really doun' r mnrter chamockite and lottal; the P.O. Box 1930 an ywuy... Qhly meaning of BHP, LVL. 1000 EX Amsterdam recommen&dd MORB, and more than 100 The Netherlands Geophysics other abbreviations naw cornmon in the geoscienœ This is cui indispensible work vocabulary; and the dates Published and distributed that tes~ifksro riil when many terms were first in the USA & Canada by rhorvughss orpersirrence of used, tha rneaning of the Amencan Geological tkediron and rheir 150 certain cornmon prefixes, Institute. collaborators. and the preferred terni of The lnstitute of Mining 8 two or more synonyms. The Dutch Gui& (LM) Metallurgy pln=es quoied iqp& workiwide. US $ pds quoted may be subjecî to This third edition of the emfrange raie fluctuations. Glossary of Geology Custorners m ihe European contains approximately Communiîy shouid add îhe 37,000 terms, or 1,000 appropnate VAT rate more than the second applicable in their w unùy sdition, as well as 650 to tfre pm. emendations and corrections. In addition, il ncludes for the fiffit time ELSEVIER the division of cited terms SCIENCE PUBLISHERS n syllables. with accents to iid in pronunciation. APPLIED 4 IMAGE.lnc

O 1993. Wied Image. 1%. AO Rihts Resarved