TmIMPACT OF GLACIERRECESSION UPONTHE DISCHARGEOF THE BOW RIVER ABOVEBANFF, ALBERTA. 1951-1993

Christopher Hopkinson B.Sc., Manchester University, 1995

THESIS Submitted to the Department of Geography in partial fulfilrnent of the requirements for the Master of Environment Studies degree Wilfnd Laurier University 1997 " Christopher Hopkinson, 1997 National Library Bibliothèque nationale of Canada du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395, nie WelIingtori OttawaON K1A ON4 OttawaON K1AON4 Canada Canada Yaw a@ V& réfckmœ

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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 sell reproduire, prêter, distribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfichelfilm, 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 qui protège cette thèse. thesis nor substantial extracts fkom it Ni la thèse ni des extraits substantiels may be printed or othefwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. This niesis is dedicated to rny brother Michael and dl the mernories we never bad a chance to share. Three methods have been used to explore the volumetric change of glaciers in the Bow Basin above Banff for the years 1951 to 1993. Using aerial photography, the extent of glacier covers for the two years were mapped at a scale of 1:50,000. The first volumetric calculation of glacier loss was based on inventory criteria; the second a hypsographic curve method based on Young's investigations in Mistaya Basin (1991) and the third stereo air photogrammetry and DEM cornparisons using computer software. These methods were applied to the highly glacierized Hector Lake catchment within the Bow Valley and then extrapolated up to the whole basin above Banff. Reasonable agreement was achieved between the methods and the magnitude of glacier loss is estimated to be between 930 and 1400 m3xlo6 w.e. for the entire 42 year period.

The bulk glacier "wastage" estimate was divided into proportions using the Peyto Glacier mass balance record. Unfortunately, the record began in 1966 and a back-cast to 1952 was necessary. The mass balance model proposed by Letreguilly (1 988) was considered inappropnate for this task due to it not adequately representing the observations of recession on Peyto for 1952 to 1965. A new model utilizing Banff maximum summer temperature and Lake Louise snow course data was constmcted. The proportions of seasonal wastage contributions to river flow were estirnated using a multiple regression model of monthly average temperature and precipitation with snow course data as the antecedent condition determinant. This model was used to predict the shape of the glacier (ice and firn) melt hydrograph from June to September.

An estimate of the temporal variation of glacier recession inputs to the Bow River hydrograph at Lake Louise and Banff was facilitated by comparing known basin yields with the modelled "wastage" values. For 1952 to 1993 at Banff, the average annual wastagehasin yield ratio is found to be around 2.3%; for 1965 to 1992 (years of available data) at Lake Louise the same ratio is 4.5%. For the extremely low flow year of 1970 these ratios increase to 12.5% and 16.2% respectively. The proportion of flow derived fiom glacier recession in August of this year is estirnated to be around 53% for Banff and 84% for Lake Louise. It is thought that the basin scale extrapolation may lead to under- estimations of wastage but the mass balance back-cast is more likely to preferentially weight wastage contributions toward the latter part of the time series. Many thanks to everyone that helped, especially my parents,

Gordon Young, Mike English, Sophie Gaborit, Scott Munro, Grant Simpson, Gordon Gracie, Richard Tychansky, Ken Hewitt, Alexi Zawadzki, Andrew Gould, Dr Bell, Dr Donahey, the nurses at Bow Valley General, Dave the "Performance Guy", my piranha; Adele, Alberta Environment; particularly the operational guys and holders of "purse strings", Mike Demuth of National Hydrology Research Institute, Tim Davis of Water Survey Canada, the nice National Air Photo Library people, the Whyte Museum of the Canadian Rockies, CRYSYS, Atmospheric Enwonment Service, Parks Canada, Alpine Club of Canada, Dave Collins, RTS; my faithful steed, Yeuval; the Israeli army officer chappy, Beth, the Num-ti-ja Lodge staff and, of course, Mark Saunders; the philanthropie folk singer.

And, hally, the greatest th& of dl go to the mountains and glaciers; for being there and providing me with inspiration and the impetus to spend as much time as 1 am able within theû comforting embrace. A~STRACT III

CWTER ONE:INTRODUCTION 1 1.1 PREFACE 1 1.1.1 Glacier Recession 1 1.1.2 Bow River as a Resource 4

2.2 OVERVIEWOF MOUNTAIN HYDROLOCY 2.2.1 Precipitation 2.2.2 Slow Hydrological Transfer Mechanisms 2.2.3 Hydrological Outputs

3.2 STEREOAIR PHOTOGRAMMETRY 3.2.1 Introduction 3.23 Stereoscopic ParaUar 3.2.3 Ground Control and Image Scale 3.2.4 Stereoscopic Plotting 3.3 DIGITALELEVATION MODELS 3.3.1 Introduction 3.3.2 Irregular Method 3.3.3 Grid Method 3.4 VURFER*@ SOFTWARE 3.4.1 Introduction 3.4.2 Grid Creation and Blanking 3.43 AnalyticaI Functions

4.2 ESTIMATIONOF GLACIERVOLUME LOSS, 1951-1993 4.2.1 Sumrnary 4.2.2 Obtaining the Aerial Imagery 4.23 The Glacier Coverage Map for Hector Lake Basin, 1951 & 1993 42.4 Inventory Method 4.2.5 Hypsographic Curve Method 4.2.6 Photogrammetrical Method 4.2.7 Extrapolation up to the Bow Basin Above Banff and Lake Louise 4.2.8 Glacier Volume Water Equivalence 4.3 ANNUALGLACIER WASTAGE ESTIMATIONS 4.3.1 Peyto Glacier Mass Balance 43.2 Back-cast of Peyto Glacier Mass Balance Record 4-33 Calculating the Annual Wastage Proportions 4.4 SEASONALGLACIER WASTAGE CONTRIBUTIONS 4.4.1 Introduction 4.4.2 Peyto Glacier Seasonal Melt Hydrograph 1967-74 4.43 Multiple Regression Model

5.2 GLACIERVOLUME LOSS 1951-1993 5.2.1 Inventory Method 5.2.2 Hypsographic Curve Method 5.2.3 Photogrammetrical Method 5.2.4 Summary of Volume Calculations and Water Equivalence

5.4 MONTHLYPROPORTIONS OF GLACIERWASTACE 5.4.1 Idealised Ice Melt Hydrograph 5.4.2 Multiple Regression Model Using Meteorological Variables

6.1 REVIEWOF THE TECHNIQUESUSED 6.1. 1 Mapping Glacier Extents 6.1.2 Volume Calculations 6.13 Validity of Extrapolating up to the Scale of the Bow above Banff 6.1.4 Annual Wastage Proportions 6.1.5 Monthly Wastage Proportions

6.2 THEIMPACT OF GLACIERRECESSION ON THE FLOWOF THE BOWRIVER 6.2.1 1952 - 1993 6.2.2 Time Lags 6.2.3 Evaporative Water Losses 6.2.4 The Future 6.2.5 Ciimatic Interactions CEUPTERSEVEN: CONCLUDING REMARKS 7.1 KEYFINDINGS 7.1.1 Glacier Loss in the Bow vaiiey 1951-1993 7.1.2 Impact of Glacier Wastage on the Bow River Hydrograph at Banff, 1951-1993 7.13 Implications for Future Water Avaiiabiiity in the Bow at Banff 7.2 EVALUA~ONOF METHODS 7.2.1 Volumetric Change 7.2.2 Annual Weighting of Glacier Wastage 7.2.3 Seasonal Wastage Hydrograph 7.2.4 Summary of Errors

7.3 SUGGESTIONSFOR IMPROVEMENT REFERENCES APPENDICES Table 4-1 Estimated Average Glacier Depths (Stanley. 1970) ...... 41 Table 4-2 Peyto Glacier surface melt figures for 1966-89 (Young. 1991) and extrapolated for 1952.1993...... a..m.~~*m.~mmm~~~~~~*~~a~..*m*.~~~*~.*~*~~~~*~~.~43 Table 5-1 Hector Basin glacier volume estimation, 1951 ...... 65 Table 5-2 Hector Basin glacier volume estimations, 1993 ...... 66 Table 5-3 Areal extents of glacier cover per lOOm elevation band ...... 68 Table 5-4 Glacier volume loss using hypsographic and surface melt data ...... 70 Table 5-5 Ground control points used in photogrammetrical analysis ...... 70 Table 5-6 Surfer grid file summaries with volume cornputetions ...... 79 Table 5-7 Summary of the glacier wastage estimations...... 80 Table 5-8 Peyto mass balance figures, actual and modelled ...... 81 Table 5-9 Estimated annual proportions of glacier wastagehasin yield for Banff and Lake Louise...... 83 Table 5-10 Estimated Peyto Glacier melt 1967-74 (after Young, 1982) with average monthly proportions ...... 86 Table 5-11 Ideaiised monthly glacier volume loss / basin yield for Bow above Banff and Lake Louise...... 86 Table 5-12 Modelled monthly gtacier volume loss 1 basin yield for Bow above Banff and Lake Louise...... 88 Table 6-1 Glacier volume error estimations using the Inventory Method ...... 92 Table 6-2 Annual & monthly summary of wastagehasin yield at Banff ...... 112 Table 7-1 Volume calculations of glacier wastage for Hector Lake Basin with areal extrapolation up to Banff ...... 126 Table 7-2 Summary of systematic errors in the analysis ...... 130 Figure 1-1 Twentieth century glacier recession within Bow Valley ...... 2 Figure 1-2 Map showing study area and precipitation zones ...... 8 Figure 1-3 Bow Vaiiey above Banff, showing glacier covers and IEID sub basin boundaries ...... 9 Figure 1-4 Hypsographic curve of ground cover types for the Bow Valley above Banff ...... 9 Figure 1-5 Average temperature and precipitation figures for Banff. 1895-1991 ..... 10 Figure 16Hypsographic curve for Hector Lake Basin ...... 11 Figure 4-1 Partial aerial photograph coverage of glaciers above Hector Lake...... 39 Figure 4-2 Trapezoidal glacier volume estimation method ...... 43 Figure 4-3 Location of points where parallax should be removed ...... 48 Figure 4-4 Chart to indicate the presence of tilt in the stereo models ...... 54 Figure 5-1 Glacier Extents in Hector Lake Basin, 1951 and 1993...... -64 Figure 5-2 Elevation bands of glacierization...... 67 Figure 5-3 Hypsographic curve of glacier extents for Hector Basin. 1951 & 1993 .... 69 Figure 5-4 Relative locations of UTM grid and DEM Cartesian grid ...... *71 Figure 5-5 Crowfoot Glacier DEM surfaces created in Surfer ...... 72 Figure 5-6 Crowfoot Icefield DEM surfaces...... 73 Figure 5-7 Waputik Icefield, Balfour and Vulture Glacier DEM,1951 ...... 74 Figure 5-8 Waputik Icefield. Balfour and Vulture glacier DEM, 1993 ...... 74 Figure 5-9 Crowfoot Glacier surface change, 1951-1993 ...... 75 Figure 5-10 Crowfoot Icefield surface change, 1951-1993 ...... 76 Figure 5-11 Waputik Icefield surface change, 1951-1993 ...... 78 Figure 5-12 Annual basin yield and glacier wastage for the Bow above Banff ...... 84 Figure 5-13 Yield / Wastage ratio for Bow above Banff ...... *.85 Fipre 5-14 Observed hydrograph for Bow above Banff 1969.1972. with rnodelled wastage flow super-irnposed ...... 87 Figure 6-1 Idealised glacier cross-section indicating how the Inventory Method estimates volume...... 1 Figure 6-2 Peyto Glacier mass balance, measured 1966.93, back-casied 195245... 104 Figure 6-3 Bow River hydrogrnph at Banff with and without wastage yields ...... 109 Figure 6-4 Monthly wastage proportions for Bow River at Banff, 1952-1993 ...... 110 Figure 6-5 Monthly wastage proportions at Banff, 1970 ...... 113 Figure 6-6 Banff precipitation and temperature during the summer of 1970 ...... 114 Figure 6-7 Specifc mean monthly yield 197401976 for the Bow River ai Banff, Hector Lake and 40 Mile Creek ...... 0121 Within literature of a glacial hydrological nature some of the tenninology in common use is found to contain a level of arnbiguity. To increase clarity and avoid confusion, a glossary of some of the key hydrological ternis, with their meanings as defined for the presented analysis, is listed below:

Basin yield The total volume of river runoff leaving the basin in question during the tirne penod of interest.

Glacier melt The melted ice and fim drainhg from a glacier basin. For the purpose of the analysis presented here, glacier melt does not include melted snow that has fallen ont0 a glacier's surface within the same hydrological year.

Glacier recession The apparent visual shrinkage of glacier dimensions.

Glacier wmage The volume of glacier loss measured over a period of the. Wastage is considered analogous to a net negative mass balance for the glacier or suite of glaciers being studied. Thus for any given year, wastage occurs if the glacier shrinks in volume and water leaving the glacier system is in excess of the net income of hydrological inputs.

Wastage yield The total volume of water derived fÎom glacier wastuge within the basin in question during the time period of interest. "Travellers will cross many rivers and climb rnany rnountainr. Plainsmen may always live within a single valley ' But only those seeking huth will ever reach the summit."

11 " century Indian saying, Anon

1.1 Preface

1.1.1 Glacier Recession

The "Little Ice Age" that persisted over much of the earth fiom around 1550 up until a little over a century ago (Barry & Chorley, 1992) resulted in an advance of ice sheets and of glaciers in high mountain regions, sometimes by several kilometres (Sugden & John,

1993). (The timing of the Little Ice Age varies between locations and may have commenced as early as 1060 AD in the Canadian Rockies (Luckman, 1993)). During this time of margin growth, glaciers gouged out vast quantities of rock and boulder clay, which today Leave us moraines and the evidence of their previous dimensions (Luckman,

1990). Since the middle of the nineteenth century, an irregular but general rise in global temperatures has been recorded (?PCC, 1990) and many mountain glaciers have responded by retreating to higher elevations (see figure 1-1) . Whether the cwent trend of wamüng is just part of a cyclical natural climate process or the result of anthropogenic carbon emissions into the atmosphere has not been fully determined. It is known, however, that global average temperatures are continuing to rise (Bany & Chorley, 1992) Bow Glacier & Wapta Icefield 1902 (Vaux family collection, picture number 145.

Bow Glacier & Wapta Icefield 1996

Figure 1-1 Twentieth century glacier recession within Bow Valley and it is highly likely that fbrther increases in atmospheric CO2 will only aggravate this

situation (Meehl & Washington, 1990). Therefore, it is likely that glacier recession will

continue in most regions. Although the possibility of glacier advances resulting fiom

increased atmosphenc moisture content and precipitation in some areas cannot be discounted.

Observations of glacier recession in the eastem frontier range of the Canadian Roches have been recorded since 1887 (Meek, 1948). Despite the continued diminution of glacier extents they are still perhaps considerably fiuther advanced than during the Hypsithemal penod that occurred over 3000 years ago (Luckman, 1996). Evidence of this is found in tree log and stump samples discovered in the outwash plains below and, indeed beneath, some glaciers (Luckman, 1993). Therefore, it could be argued that if the glaciers are merely retuming to previous and possibly more stable extents at higher elevations, then we could expect a lot more recession in these mountaim.

A consequence of glacier wasting in mountain regions (in addition to raishg global sea level (see Meier, 1984)) is that river basin yields are augmented more than the net income of annuai precipitation. Therefore, during a warm and dry year when flows might otheMrise be low, glaciers act like reservoirs topping up the supply just when it is needed most. Naturally, it is to be expected that the warmer and drier the year coupled with a low winter snow cover, then the more glaciers will recede and more important is their rote in flow augmentation. It is estimated that mountain glaciers globally, have lost on average

1 1% of their total masses during the last 100 years (Meier in Mcimis, 1995). However, as glaciers retreat to higher elevations, their areal extents and volumes diminish and their

snouts approach the average 0' isothenn. Thus, even though toe recession may continue

at a similar or even accelerated rate for a long time to corne, the potential to shed large

volumes of ice through melting will gradually diminish.

1.1.2 Bow River as a Resource

The Bow River is regionally important as a water resource for both the permanent and transient populations that live within the basin. It has been suggested that development in the Bow Valley could not have reached such a high level without the assured supply of melt from glaciers (Collier, 1958). The river is the main source of supply to many domestic usen, the volume of which increase greatly in the summer due to the influx of tourists. in Banff the permanent population numbers less than 10,000, however during the sumrner months of June to Septernber of 1995-96 over 5 million people visited Banff

National Park (McMahon, 1997, persona1 communication). This not only increases domestic usage but ais0 acts to reduce water quality downstream of urban drainage and sewer outfalls (Bow River Water Quality Task Force, 1991) a problem which is heightened during periods of low flow.

Downstream of Banff" the Bow River is considerably more important to non-domestic users. The limestone aggregate and concrete industry is one example. However, by far the most important of al1 users are fmers in the precipitation deficient prairies, needing vast quantities of water for the imgation of crops (Saskatchewan Water Corporation, 1986).

Abstractions fiom the river resource for imgation purposes are naturally at their highest during hot dry spells when evaporation fiom the soi1 surface is accentuated. During the low flow and high demand year of 1977, approximately 95% of water consumption widiin the Bow Basin was for irrigation purposes with 4% municipal and 1% industrial

(Alberta Environment, 1984). Another important consideration is the provincial govemment agreement that States at least 50% of the natural flow leavhg Alberta via the

South Saskatchewan River must be maintained to serve Saskatchewan's needs.

In a region of intense water usage, where demand can sometimes exceed supply (Young,

1995a), a knowledge of the relative proportions of contributing hydrological sources is essential. Also, how these sources Vary through tirne and with climate must be researched in order to predict fhture resource availability. This knowledge can then be used to aid with short term management decisions and, perhaps more importantly, long term policy initiatives. In the Bow Valley, annual river flow is dominated by snow melt, however, it is apparent that during the summer months when demand for water is hi& the flows derived from glacier melt are at their most influential. Therefore, more learned decisions regarding river management issues will be facilitated if the timing and magnitudes of glacier recession flows (past, present and future) can be ascertained. The need to study the implications of glacier wastage to river flow in this region has long been prevalent (see

Meek, 1948).

1.2 Aims & Objectives

There are two broad aims to this thesis: 1. to provide a better understanding of the relationship between glacier recession and the

river hydrograph within the Bow Valley above Lake Louise and Banff. It is hoped that

this aim will be achieved by targeting the following specific objectives:

i. map glacier cover and calculate volume change within a highly giacienzed sub-

basin using aerial photography collected in 1951 and 1993, and apply the

results up to the Bow Valley above BanE

ii. convert the glacier volume change into water equivalence and estimate the

annual proportions for the time period investigated.

iii. estimate monthly glacier melt proportions for each year of study and use as a

mode1 for the seasonal glacier wastage hydrograph.

iv. compare the modelled glacier wastage yields with the actual basin water yields

at both the annual md seasonal scales.

2. using the aerial photography, identik conduct and compare various methods of

analyses to measure the volumetric change experienced by a suite of glaciers within

the theperiod of study.

The first stage of the analysis involves digitizing the extents of the chosen suite of glaciers into a computer mapping application. Following this, volume change of the glaciers between the dates of irnagery is calcuiated using three techniques:

1. the "Glacier Inventory Method" which utilises inventory criteria to estimate

glacier volume;

2. the "Hypsographic Curve Method" which apportions depths of glacier melt

through time based on elevation of the glacier surface; 3. the c'Photograrnmetrical Method" which directly measures glacier volume

change by enabling the construction of surface digital elevation models

@EMS). Surface change between the models is then compared using cornputer

software.

The annual proportions of glacier wastage are estimated using the Peyto Glacier mass balance record for 1966 to 1993 and back-casted to 1952. Peyto does not drain into Bow

River but it is just across the watershed boundary. It is a contiguous part of the Wapta

Icefield which is partly within Bow Valley and also straddles the provincial border with

British Columbia. Seasonal wastage contributions are modelled using multiple regression of the 1967-74 Peyto Glacier meltwater hydrograph (generated by Young, 1982) with climatic variables being independent. Comparisons with actual basin yields are facilitated by superimposing the estimated glacier wastage discharges ont0 measured river hy drographs .

1.3 The Study Area

The area chosen for the analysis is the Bow River Basin upstrearn of Banff, Alberta in the

Canadian Rockies. An excellent overview of the general study area is provided in the

"Handbook of the Canadian Rockies" by Gadd (1995). Figure 1-2 illustrates the approximate location of the Bow River headwaters on the Alberta British Columbia border. This map also highlights the rapid reduction in total annuai precipitation yields as one travels east fiom the Eastern Frontier range of the Rocky Mountains. It is evident that the Bow River flows fkom a very high precipitation zone into the comparatively far more arid prairies of southern Alberta. Shortly before crossing the Alberta / Saskatchewan border the Bow joins up with the Oldman and flows into the South Saskatchewan River.

Figure 1-2 Map showing study area and precipitation zones

Banff lies at latitude 51°10'N and longitude 1 1S030'W with the Bow River Basin upstrearn of this point being around 2200 km2. Glacier covers within the basin were mapped by Young (1995b) using the 150,000 national topographical maps (sheets 82N

1-9) which were updated fiom aerial photography taken in 1977 (Department of Energy

Mines and Resources, 1979). Young estirnated a proportional glacier area of approximately 3.3% within the Bow Basin above Banff., see figure 1-3 for the spatial distribution of glacierization. The basin has an elevation range fiom around 1200m up to

3400m on the summit of Mount Hector, and is underlain predominantly by limestone.

The average annual temperature at Banff is approximately +3OC but temperatures in this part of the Rockies can dip down to as Iow as negative 3S°C in winter and up to positive

35OC in summer (Gadd, 1995). Naturally, the mountain temperatures will tend to be significantly lower due to lapse rates. A sumrnary of the basin ground covers and accornpanying elevations is provided in the hypsographic curve in figure 1-4.

Figure 13 Bow Valley above Banff, showing glaciers and sub basin boundaries

Hypsographic Curve for Bow Basin Upstream of Banff

Figure 1-4 Hypsographic curve of ground cover types for the Bow Valley above Banff This area is ideal for the kind of study being undertaken due to Iow level of development

within the basin upstream of Banff and the long the series availability of

hydrometeorological data. Figure 1-3 shows the sub basins in the Bow Valley that have

some additional strearn discharge data collected during the International Hydrological

Decade (IHD), 1965-74. Extensive meteorological data are available from Banff, Lake

Louise and Peyto Glacier, with snow course data having been collected fiom various locations within the basin. Figure 1-5 is a summary of the annual temperature and precipitation values for Banff' over the last cenhiry. In-siream discharge has been collected at Banff since 1910 (gauge number BB001) and fiom Lake Louise since 1965

PA001). A summary of the meteorological and hydrological data collected for the Bow

Valley (that is relevant to this study) is given in appendix 1. Peyto has been studied extensively since 1965, when a mass balance monitoring program was initiated as part of the IHD (Qlstrem, 1996) and is still in operation today.

Mean Annual Temperature and Annual Precipitation at Banff

Figure 1-5 Average temperature and total precipitation figures for Banff, 1895-1991 Of al1 the sub bains in the Bow Valley, Hector Lake is the most northerly and contains the highest proportion of both lake and glacier cover (see figure 1-6). It is approxknately

276km2 (or 12.5% of the Bow above Banff) and makes up a very large portion of the

Lake Louise Basin (426km2).The glaciers are found to lie mainly dong the western side, in the Waputik Mount- which begin just north of Lake Louise and continue on into

Mistaya Discharge data were collected for this basin during the summer months of 1973 to 1976 and extensive aerial photography missions have been undertaken over the

Waputik Mountains fiom the 1930s up to the present. In addition, the glaciers in question were the subject of an inventory in the Iate 1960s (Stanley, IWO).

Hypsographic Cuwe for Bow Basin Above Hector Lake Gauge

Figure 1-6 Hypsographic curve for Hector Lake Basin 1.4 Thesis Outline

The research presented in this thesis is arranged into seven chaptea with appendices. In the second (following) chapter some background into hydrological interactions within mountainous basins is discussed. In chapter three, the construction and application of digital elevation models is uivestigated and the capabilities of the software used in this analysis, Surfer, are explained. Chapters four and five Iist the methods and present the results of the investigation. A discussion of the findings and probable causes of error is given in chapter six, with conclusions and suggestions for future study in chapter seven. 2.1 Introduction

The impact of glacier recession upon basin water yields in this region of the Canadian

Rockies has been explored previously (for example: Collier, 1958; Henoch, 1971 and

Young, 1991). Collier observed that glacier coverages for 1955 in the Upper North

Saskatchewan Basin (13 18km2) and the Mistaya Basin (247km2) were 24% and 16%, respectively. Using observations of glacier recession, and area loss, photogrammetry and mass balance, Henoch calculated that the glacierized area within the Upper North

Saskatchewan Basin diminished by 10% between 1948 and 1966. This change in cover was estimated to represent 4% of the total discharge for the 18 year penod.

Young's paper studied glacier recession between 1966 and 1989 in the Mistaya Basin, a sub basin of the Upper North Saskatchewan and just north of the Bow valley. Young calculated that total glacier area reduced nom 12.1% of total basin cover in 1966 to

10.8% in 1989, and the corresponding average volumetric glacier loss equated to 6% of annual basin yield. For the low flow year of 1970 it was estimated that the water yield of the Mistaya Basin was augmented by up to 25% as a result of glacier wastage. Young also noted that regional average moff is around 0.0 12 rn3s%f2 with the relatively highly glacierized Mistaya yielding approximately 0.026 rn3s~lkm-*.

A similar but longer term study investigating volumetric glacier loss in the European Alps during the last century has been carried out by Chen and Ohmura (1991). Although no comparison with total basin yields were possible, it was estimated that Alpine glacier areas diminished by 33% fiom 4368km2 around 1870 to 2909krd during the 1970s. This was thought to equal a glacier volume îoss of around 57km3.The volumes in this analysis were computed using an empirical volume-area relationship and the World Glacier

Monitoring Service (WGMS) database of the Alpine glacier inventory. A more complex derivation of volumetric change for the same region during the penod 1850 to the mid

1980s (Haeberli and Hoelde, 1995) suggested that more than 130km3 of ice had been lost.

Clearly, glaciers play an active and very important role in river basin hydrology within mountainous environrnents. This has led to numerous attempts at modeîling basin wide glacier melt. Both empirical (for exarnple: Kasser, 1969; Lang, 1969 and Collins, 1989) and more conceptual models (for example: Quick and Pipes, 1977; Gottlieb, 1980; Lang,

1986 and Moore, 1993) have proven usefid for assessing and forecasting glacier melt discharge. A problem common to most hydrological models with glacier melt components is the under-prediction of peak flows (Fountain and Tangbom, 1985).

Mthough it is out of the scope of this thesis to discuss glacier melt flow modelling in detail, an oveMew of the hydrological components and interactions within a mountain basin such as the Bow above Banff will be provided in the remainder of this chapter. 2.2 Ovewiew of Mountain Hydrology

2.2.1 Precipitation

The pattern and form of precipitation varies both in areal location and with change in altitude. In mountainous regions air masses forced up and over high terrain are compressed and cooled, and if containhg sufficient moisture, precipitation will occur.

Precipitation falling on the windward side of rnountain slopes generally increases with altitude up to some ceiling elevation, where the volume of input diminishes. In addition, the form of precipitation changes with temperature. Above around +3S°C there is no snowfall and below -7S°C there is usually no rainfall (Bagchi, 1982). The approximate environmental lapse rate of temperature with altitude is between -0.6 and -0.7OC per lOOm rise in elevation. Therefore, while rainfall can be expenenced in valley bottoms, it is quite possible that snow is falling higher up in the basin. Although temperature inversions caused by noctumal radiative cooling, large scaie subsidence in an anti cyclone or advection of a warm air mass over a colder surface (Barry, 1981) can sometimes occur.

When a storm moves into a valley, much of the min falling nins off the surface within a short space of the and it, therefore, has a distinct signature super-imposed onto the river hydrograph. The track of the storm, i.e. up valley, down valley, or across valley is also usually evident in the shape of the hydrograph. The path taken by the rainfall upon reaching the ground, depends on the nature of the surface it encounters; impervious, frozen and satuntted ground will lead to very rapid overiand flow, more porous media, such as snow and soi1 will lead to a slower form of "interflow" and vegetated areas will iacrease off ground cbinterception'yand delay the passage of water to the ground via processes of "sternfiow" and 'kanopy drip"

2.2.1.3 Snow Accumulation and Redistribution

The increased volume and likelihood of snowf'aii at higher elevations, naturally, leads to greater potential for snow accumulation nearer the mountain tops. However, the magnitude and incidence of wind also increases with altitude, leadhg to redistribution and higher losses through sublimation (Pomeroy and Gray, 1995). Although the redistribution of snow by aeolian processes can Lead to very specific snow features and patterns, for example cornices, the force of gravity tends to preferentially redistribute snow downwards. Thus, hollows, gdleys and slopes on the leeward side of ridges tend to accumulate deep snow packs, while high level plateaus cm be stripped almost bare of snow.

The ciramatic variation of relief at high elevations, therefore, results in highly variable snowpack depths. However, studies of snow distribution patterns dong exposed mountain ridges in Switzerland (Fohn and Meister, 1983), suggested that high level ridge systems, although highly heterogeneous in terms of observed snow depths, accumulate similar average quantities of snow as adjacent level terrain. A Merconsideration, which is particularly relevant in the Bow Valley, is the geologic construction of the mountain region in question. The sedimentary beds underlying the Bow Basin generally dip to the southwest and have east facing scarp faces. The wide terraces that result from different erosion rates between adjacent layers, lead to greater snowpack accumulation rates than on the surrounding steeper slopes. This can therefore lead to a stepped snow accumulation profile.

The valley bottoms of the Bow Basin above Banff have a predominant coverage of forest and therefore it is necessary to outline some of the effects of forest cover on snow accumulation. Snow falling ont0 a forest canopy can either fall straight through or be intercepted. The snow that passes through is redistributed by turbulent air flow within the canopy and accumulation patterns are dependent largely upon tree spacing and species

(Pomeroy and Gray, 1995). Any snow that is intercepted, either falls to the ground later

(as snow or melt water) or is lost to the atmosphere through sublimation (Pomeroy and

Gray, 1995). The accumulation of snow within densely forested areas is generally found to be lower than in open areas but enhanced accumulation is found near tree line (Gray and Male, 198 1).

2.2.1.4 Snow Melt

The heat sources involved in the snow melt process are net radiation, sensible heat transfer from air to snow, latent heat of vaporisation by condensation from the air, conductive heat transfer and the heat content of rainwater (Gerrard, 1990). In mountainous regions the snow pack does not melt out over a short tirne, as may be expected in more level and low lying terrain, but is spread out over much of the year. The average snow line elevation on mountain sides rises following the onset of spnng, as snow is melted out at lower warmer altitudes. This gradua! progression of snow melt acts to flatten out the muai hydrograph and ensures a substantial supply of snow melt water well into the season. However, the steep sided mountain slopes tend to cornpress diurnal hydrograph limbs due to rapid channel flow velocities.

Around May and June the snow surfàce albedo cm be as high as 0.75 to 0.80, this reduces to between 0.55 and 0.70 by July and August, leading to enhanced melt later in the season (Meier, 1969). The snow melt process is far fiom unifom within mountainous bains; depending on ground cover, slope angle, aspect and shading. Snow melt progression on a glacier surface is observed to be slow and fairly uniforni, with snow line movement on surroundhg mountain slopes being faner and more irregular (Young,

1982). Any snow covered slopes with a northerly aspect or directly shaded by surface features will tend to melt out slower than open southerly facing slopes of conesponding altitude. Further dom valley, however, the influence of forest cover cm act to delay melt runoff due to the "insulating" effect of the canopy.

2.2.2 Slow EIydroIogical Transfer Mechanisms

2.2.2.1.1 Formation

At high elevations, snow accumulates in hollows through processes of snowfall, wind redistribution and avalanche (Meier, 1973). These deep accumulations can persist for an indefinite length of time and the average end of ablation season snowline altitude for a number of years within a region is known as the "climatic snowline" (Bstrem, 1966). A

continued inter annual accumulation of snow above the clhatic snowline leads to

gravitational compression of the snow pack and eventual transformation into ice. In

temperate regions this tmnsformation is relatively fast, sometimes just a few years

(Sugden and John, 1993), with the transitional state known as '%m" (snow that is older

than one year but not yet tumed to ice). An ice mass of suEcient weight moves down

valley by processes of "intemal deformation" due to shear stresses (described by Glen,

1955 and Nye, 1957) and "basai sliding" of the glacier over its sub-sole. Downward

progression of the glacier is kept in check by ice ablation in the lower elevations. Changes

in the winter accumulation or summer ablation regime lead to temporal fluctuations in

glacier total size and mass. The response of glaciers to changes in climate has been

studied by Oerlemans (1 989).

2.2.2.1.2 Mass Balance

The "mas balance" of a glacier is the net gain or loss of mass over its entire surface within a hydrological year and is usually expressed as a depth of water equivalence. It can be defined as the sum of the winter positive balance and summer negative balance or as the sum of total annual accumulation and ablation (0strem and Brugman, 1991). (It should be noted that hydrological and glacier mass balance do not aiways agree (Stanley,

1975; Tangbom et al., 1975 and Meier, 1973)). A net positive mass balance implies that the glacier has grown and water that entered the basin as snow fa11 has gone into temporary (perhaps long tenn) storage. A net negative balance, however, is an indication of glacier loss or "wastage" and thus water has lefi long term storage in the glacier

"reservoir" and augmented river basin yields in excess of the annual hydrological balance.

2.2.2.13 Melt

During the earlier part of the ablation season, melt inputs rise quite steeply as the

snowline moves up glacier and exposes greater areas of glacial ice. Ice is more readily

melted than snow due to it typically having a Iower aibedo of around 0.3 to 0.4 and

greater capacity to transmit radiation. Surface melt usually travels short distances in

"supra-glacial" streams before disappearing into the "englacial" and "sub-glacial"

systems via "crevasses" and ccmoulins"and then out of the glacier and into the river system. Melt above the snowline percolates through the snow pack and into the firn water aquifer, f7om where it plays a very important role in maintMg and increasing base flows throughout the melt season (Rothlisberger and Lang, 1987). Therefore, not al1 of the melt for any given day drains f7om the glacier during the same day, leading to a delay in passage of some of the seasonal melt hydrograph. Some time after the peak of sumrner solar insolation, the base flow begins to drop again.

Super-imposed onto the seasonal base flow are pronounced dimal fluctuations of melt water discharge. Peak daily Bows are normaily experienced a few hours after maximum solar insolation for the size of glaciers found in the Rockies. The diurnai range of melt discharge reduces with cloud cover, rainfall and following snowfall. Fresh snow on the glacier surface raises dbedo and temporarily slows down the melt process until it is melted off. 2.2.2.2 Groundwater

Snow melt and rainfall occurring over porous ground will infiltrate, provided the surface layers are not saturated or fiozen. Glaciers located over zones of recharge can also potentially contribute to groundwater storage. Water entering the ground will either go into "interflow", where it is detained for a relatively short period of the within the surface soil layea; or into deep groundwater storage where the residence time is much longer. Water intiltrating soil layers on a hiIl dope is transported dom dope by a variety of mechanisms, for example: darcian flow, macropore flow, pipe flow and soil matrix

80w (Anderson and Burt, 1990). If the soil water is not discharged into the surface runoff system, it may continue its downward migration to recharge deep groundwater aquifers.

The residence time of water in deep groundwater storage may be a few days or it may date back to the geologic past (Silar, 1988). Therefore, water discharging to the surface fiom groundwater storage may be a remnant of a totally different hydrological cycle and complicate simple annual water balance calculations. During winter, groundwater is the predominant source of river flow in many mountain basins. Sumer base flows are also maintained by a seasonally variable groundwater discharge. During the melt season groundwater base flows rise in response to the extra inputs from earlier snow melt.

2.2.2.3 Lakes

Water motion through lakes is generated by various mechanisms; such as streamflow cross currents, wind circulation, wave action (Starosolszky, 1987) and density currents

(Hutchinson, 1957). Lakes are subject to wind induced circulation but thermal stratification may develop in deep lakes which will act to reduce this circulation process

(Starosolszky, 1987). Therefore, affecthg the overall residence or tumover tirne of lake waters, with the possibility that c'ancienty'water rnay persist at depth. The water detention capacity of lakes leads to a flattening of river hydrographs and delay in peak flow passage.

In the Rockies, the surfaces of lakes tend to fieeze over during winter and reduced runoff fiom surrounding dopes and melt streams leads to low lake water levels. Following the spring melt and ice break up, the levels begin to rise again and some temporary storage of incoming water occurs. The presence of aquifers in the lirnestone beds suggests that there may be some ground / lake water transfer mechanisms operating in some parts of Bow

Valley.

2.2.3.1 River Runoff

The single largest hydrological output fiom a mountain basin within a temperate region is usually the river leaving the basin at its lowest ground surface point. Water held within the basin streams and rivers is an amalgam of ail the upstream flow components and therefore, the hydrograph observed at any point is the sum of countless hydrological pulses. In stream discharge is found to be a function-ofchannel cross-sectional area, water surface dope, length of wetted perimeter and channel resistance which can be approximated ushg the "Manning" roughness coefficient 'h" (Newson, 1994). Flow velocity can be estimated nom discharge calcdations or measurements by dividing by the

average area of chan.net cross-section.

2.2.3.2 Evaporation, Transpiration and Sublimation

Water evaporation occurs when molecules attain sufficient kinetic energy to overcome

surface tension and escape fkom the main body (Newson, 1994). Within a large mountain

basin there are several opportunities for the loss of water through evaporation:

1. Areas of open water, such as lakes heated by solar radiation or turbulent streams.

2. Ground surface moisture, such as water held in upper soi1 layers or held on exposed

rock surfaces.

3. Different types of vegetative surface can increase the potential for overall basin

losses through processes of evaporation, bioIogical transpiration and sublimation.

Law (1956) discovered that afforestation of grassland led to a significant reduction in

basin runoff. Also, losses of water to the atmosphere due to sublimation of

intercepted snow in forested areas can account for up to one third of the total

snowfàll (Pomeroy and Gray, 1995).

2.2.3.3 Groundwater Flux

The hydrological boundaries of a groundwater system and a surface catchment are not likely to be coincident. Thus, water entering the surface basin fiom a groundwater source may have originated within a different wateahed and, conversely, water entenng into groundwater storage may be transported many miles outside the parent basin. The flux of groundwater in and out of a basin will depend on underlying geological form, the Location of discharge zones and the relationship between zones of recharge with precipitation and melt inputs. It is quite possible, therefore, that a basin may lose appreciabie quantities of its hydrological input via groundwater linkages with surro unding bains. 3.1 Introduction

Most topographicd maps, covering glacierked regions are created without the

glaciologist in mind (Schytt, 1966), resulting in such problems as ice margin mis-

representation with insufficient detail of surface features and morphology. In addition,

glaciers are generally fomd in relatively remote locations in difficult terrain, therefore,

making direct ground surveys costly and sometimes potentially dangerous. It is found that

remote sensing techniques are more suited to glacier cover mapping. In terms of man

hours and overail cost, terrestrial stereo photograrnmeûy is probably the most economical

option, with aerial photograrnmetry providing far greater accuracy but at a slightly higher

cost (Konecny, 1966). A classic problem of glacier mapping above the equilibrium line is

the inability to distinguish surface relief due to the high albedo and homogeneity of snow

cover. This leads to increased errors in surface elevation assessrnent and contour line

plonùig when using stereo photogrammetrical techniques.

In this chapter, an overview of the aerial photogrammetrical methods adopted for the purpose of glacier mapping will be presented. Following this will be a discussion of the techniques used in the construction and analysis of digital elevation models (DEMs). The capabilities of the computer software "Surfer ", which has been used for DEM analysis and glacier volume change calculations within this project, will also be investigated. 3.2 Stereo Air Photogrammetry

3.2.1 Introduction

Photogramrneûy is frequently defined as the science, art and technology of obtaining reliable information from photographs. An excellent introduction to the topic is provided in Elfick et al. (1995). There are two broad sub-disciplines within photogrammetry: interpretation and metric analysis. The former is more concerned with object recognition and the latter three dimensional surface representation. These two disciplines use stereoscopic and non-stereoscopic techniques on both terresûial and aeriai derived imagery. However, the majonty of photogrammetrical analyses performed in this thesis utilize stereoscopic techniques on aenal images and therefore discussion will be confined to these topics.

3.2.2 Stereoscopic Parailar

Stereo models of surface relief can be constructed using overlapping aerial photographs by virtue of stereoscopic pamllax. "Parallm is defined as the apparent displacement of the position of an object with respect to a fiame of reference due to a shift in the point of obsentation, " (Elfick et al., 1995). The forward motion of an aircraft taking successive photographs, therefore, induces parallax between adjacent images. Objects closer to the camera lens will have greater parallax than those at a greater distance. This can lead to increased difficulty in aligning high elevation surface features, such as mountain peaks, when viewing overlapping images through a stereoscope or a plotting instrument. The endlap between successive photographs is usually around 60%. If overlapping aerial photographs are placed side by side, aiigned in the direction of t5e flight path taken, X, Y and Z co-ordinates of surface features cm be calculated due to model parallax behg a fùnction of relief. The direction of flight is taken as the Iine joining the principle points of successive images. These points are the ground location of the photographic axis and are located by intersechg the lines made by joining opposing fiducial marks centred dong the edge of the images. The flight line is the effective X axis of the mode1 with the Y axis running perpendicular to this. The height difference between two points can be calculated by measuring the relative distances of each point fiom the X and Y axes on both overlapping images. Detailed explmation of the mathematical fomulae and techniques used in manual relief calculations fiom image parallax are provided in Lillesand and Kiefer (1987) and Elfick et al. (1995).

32.3 Ground Control and Image Scale

In order to cars, out photogrammetrical analysis using stereo aerial imagery, it is necessary to be able to scale the model in the X, Y and Z directions. Image scale is determined by the altitude and focal length of the photographic camera (Lillesand and

Kiefer, 1987). Scaling of the stereo model is facilitated using ground control points

(GCPs) of accurately known latitude, longitude and elevation. These must be located on the ground surface within the bounds of the model. GCPs can be of the basic or photo control type. Basic control refers to surveyed points, such as triangulation monuments and bench marks, already in place pnor to image acquisition. Photo control points are well defined surface features easily identifiable on the aerial photographs that are usually sweyed in fiom basic control points following the photography. The generd mie regarding the number of control points needed for an absolute orientation (stereo model scaling and levelling) is that more is always better. However, the practical minimum when using stereoscopic plotting instruments is three for horizontal scaling and four for vertical levelling (Elfick et al., 1995). Ideally the control points shouid be located near the corners of the model and at a range of elevations.

3.2.4 Stereoscopic Plotang

3.2.4.1 Introduction

Mechanical stereoscopic plothg instruments allow relatively fast and accurate measurement of ground surface locations in three dimensions without the need for manual calculation. Adjacent overlapping photographs, exposed fiom different locations are introduced into the instrument in the same relative position as when they were taken.

This causes pairs of rays fkom the same ground points on both images to intersect. The net of al1 the intersections is the stereo model.

The model is viewed through magniwng binoculan, with each ocular aimed and focused onto one of the photographs. The ground surface cm be browsed dong the X and Y axes using parallel motion gears generally attached to a plotting table or CO-ordinatedisplay.

Relative elevations of features in the model are ascertained using floafing marks. These are usually bright dots of light, sharply focused down vertically ont0 the images, parallel with the camera mis. When the marks are coincident and directIy above the object of interest, the localised parallax has been removed and the instrument is trained onto this three dimensional point. The floating marks are brought together or moved apart by adjusting the distance between the aerial photographs. This movement is controlled using a third '2"motion. Therefore, to adjust the positions and coincidence of the floating marks ,al1 three motions @,Y and

2) must be rnanipulated. A plotting table comected to the motions via gearing mechanisms will draw points or lines which represent the location of floating mark coincidence. Thus, analogue elevation contours cm be drawn if the surface terrain is followed without the floating marks flying apart. Alternatively, digital elevation model data can be collected by moving the marks fkom point to point and reading off the three dimensional CO-ordinates.

3.2.4.2 Model Orientation

Before any surface plotting or CO-ordinatereading of the stereo model can commence, the images mut undergo an inner and outer orientation. The inner orientation simply reconstnicts the exposure rays in the instrument camera. The focal length is set to match that of the photographic camera and the images are centred perfectly in the photo carriers to redore the position of the principle points.

The outer orientation consists of a relative and absolute procedure. The former is the removal of al1 residd vertical parallax in the model due to distortions. This results in a stereo model identical in shape to the ground surface. The first step is the introduction of an approxirnate horizontal scale by adjusting the base line distance (Bx) between the photo carriers. This minirnizes scale corrections Iater on during the absolute orientation.

The next stage of the relative orientation is to remove the parallaxes due to aircraft swing (K), fore and aft tip (cp) and wing tilt (a).Stereoscopic plotting instruments have small gears which facilitate the adjustment of each of these distortion induced parallaxes for both the lefi and nght images. The absolute orientation is the scaling and levelling of the mode1 to conform to real world dimensions.

3.3 Digital Elevation Models

3.3.1 Introduction

There are various techniques available to represent surface relief. Shading using hachures to approximate sudace slope is a qualitative and very old technique that is still in use today. Analogue contouring provides a more quantitative surface representation and therefore a degree of empincai analysis can be performed using topographical contour maps. Although calcuiations of volurnetric change have been facilitated using contoured surface plots of glaciers mapped at different Mies (Brandenberger and Bull, 1966;

Haumann, 1960; Kick, l966), such analysis is manually and mathematically intensive and therefore inconvenient (Burrough, 1986).

Digital elevation models @EMS) (sometimes referred to as digital terrain models) descnbe ground terrain using Cartesian style XYZ grid CO-ordinatesof surface points.

DEMs are ideal for al1 kinds of surface analysis due to the ease with which they cm be input, stored, recreated and manipulated in a cornputer environment and have been used for a variety of glaciological investigations (for example: Ebner, 1987; Rienhardt et al.,

1988 and Rentsch et al. 1990). There are two basic contigurations of DEMs; irregular or grid (Elfick et al., 1995). 3.3.2 Irregular Method

The irregular method of DEM construction can also be termed the controlling point

method, where hi&, low and slope change points are detennined. A DEM created from

an irreguiar array of control points is known as a triangulated irregular network (TIN)

model. AU the points are joined by lines and the surface is described by the triangular

planes that lie between the model nodes. The integrity of points used to construct the

DEM is rnaintained and therefore care must be taken when field surveying or stereo

plotting the control points to be used in the model. Points need to be digitized at the top and bottom of slopes, as well as slope change points and break lines to avoid relief over generaiisation.

3.3.3 Grid Method

In the grid method of DEM construction al1 surface nodes lie on a predetermined regular horizontal grid with equal line spacings. The ground surface is therefore described by the trapezium plane that lies between adjacent grid nodes. This format is useful for computational analysis due to the regular data architecture. However, real world terrain does not conform to regular patterns, resulting in the possible "smoothing" out of high and low points and the mis-placement of break lines and dope change points. Therefore, finer grid spacing leads to better surface representation. Unfortunately, when operating in a personal cornputer environment, the increased data volume due to speciwg fmer grid spacing and more nodes may slow down or even prevent analysis. 3.4.1 Introduction

Surfier is a cornputer software application that converts irregular digital XYZ data into a reguiar rusfer grid format for the purpose of terrain rnapping and sdace analysis. Two or three dimensional surface maps can be created at a variety of scales and projections.

DEM surfaces of the same area can be compared to facilitate the estimation of areal, depth and volurnetric changes. The normal format for CO-ordinatedata being input into the Surfer environment is three column ASCII text, with the first column containing castings, the second northings and the third the elevation attribute of the surface point. In depth explmation and instruction in the use of the Surfer software can be found in the

"User's Guide" (Golden Software, 1995).

3.4.2 Grid Creation and Blanking

A number of steps have to be followed when interpolating a raster DEM from irregular

CO-ordinatedata in Surfer:

1. the grid file containing the raw data must be specified;

2. the limits of the X and Y axes need to be set;

3. a grid spacing must be chosen and;

4. the Ndding procedure to be used identified.

Surfr has nine interpolation procedure options to choose fiom when gridding irregular points. The decision as to which method to use depends somewhat on the number and density of digitized surface points, confidence in point accuracy, speed of the gridding process and the need to maintain point integrity. A summary of the interpolators and their characteristics is provided below (adapted nom Golden Software, L 995).

Inverse Distance is fast but has a tendency to generate "bulll's eye" patterns of

concentric contours around the data points.

Kriging is a flexible method and is usefid for gridding almost any type of data set. For

larger data sets Kriging cmbe rather slow.

Minimum Curvature generates smooth surfaces and is generally quite fast.

Nearest Neighbour is usefbl for converting fairly regularly spaced XYZ data sets to

grid files.

Polynomial Regression processes the data so that underlying large scale trends and

patterns are shown. This is very fast but local details are lost in the generated grid.

Radial Basis Functiom is quite flexible and is sirnilar to Kriging.

Shepard's Method is similar to inverse distance but generates less of a "bull's eye"

pattern.

TrianguZation with Linear Interpolation is fast and preserves break lines in the data

file provided there is sufficient density in the points digitized. Small data sets generate

distinct triangular faces.

If the shape of the ground surface being studied is irregular, then a boundary file will be needed to "zero" al1 Z values that lie outside the study area but within the bounds of the rectangle generated by the maximum and minimum X and Y grid axes. A blanking boundaty file is similar in format to the input CO-ordinatedata file used for gridding, except that it only has two columns for eastings and northings and the first pair of values are repeated at the end of the file to close the boundary loop. The procedure of grid

bZank»tg simply involves specifj6ng the input and output grid names dong with the

corresponding boundary file.

3.43 Analytical Functions

3.4.3.1 Introduction

Surfer possesses many sub-applications or tools for the display and analysis of surface characteristics. It can also be used to investigate temporal changes in surface shape, growth or loss provided grid files of the same region are constnicted for each theslice of interest. However, only those applications of direct relevance to the study at hand will be discussed here.

3.4.3.2 Grid Function

The Grid Function tool enables the construction of an artificial surface generated from a mathematical fiuiction of the form Z = fsn. This tool can be used (in conjunction with the Grid Math tool) to correct a DEM surface that is known to be warped or tilted, such as cm happen with aenal photograph stereo models. To create a mathematically generated grid file, the fiuiction, grid dimensions and spacing need to be specified.

3.4.3.3 Grid Math

Grid Math enables two grid files (a and b) of corresponding dimensions to be compared by using a mathematical hction to relate the two and create a third output file (c). The function takes the form c = f(a. b). Altematively, a single grid file can be mathematically manipulated to constmct a new surface. For example, this option can be used to adjust the height of a surface if it is considered to be in error or the differences between new and

old elevations can be compared to gauge surface growth or loss through time.

3.43.4 Volume Change

Volume calculations are performed on a solid defined by upper and lower surfaces.

These surfaces can either be grids or planes defined by a constant Z level. Before performing the volume calculation the upper and Iower surface must be defined. When specimg two grid files, the dimensions and grid spacings need to be identical (ie. have the same number of rows and colurnns with the same X, Y limits). The output given by

S&r is broken down into Positive Volumes (Cuts), Negative Volumes (Fills) and Net

Volumes.

There are three methods used to determine volumes: Trapezoidal Rule, Simpson's Rule and Simpson's 318 Rule. The differences in the values computed between these three methods provides a qualitative measure of the accuracy of the volume calcdations. If al1 three values are reasonably close, then the true volume between the two grid file surfaces is close to the values given. For more discussion of the volume calculation methods see

Press et al. (1 986). 4.1 Introduction

The analysis undertaken in this study can be divided into four categories:

1. the estimation of bdk glacier volume loss for Hector lake basin during the

time period 195 1 to 1993, with extrapolations up to the scale of the Bow Basin

above Bd,

2. weighting of the glacier wastage for each year within the shidy period;

3. weighting of the glacier wastage for each month of each year within the study

period;

4. comparison of total basin water yields with glacier wastage yields at the

annuai and monthly scales.

For each category outlined, several different analytical procedures, of varying sophistication, have been undertaken. This has facilitated a comparison of the techniques employed and, indeed, enabled greater confidence in the fiai concIusions.

4.2 Estimation of Glacier Volume Loss, 1951-1993

4.2.1 Summary

Three distinct methods were used to amive at a value for the Ioss of glacier volume within the Bow Bssin, upstrearn of Banff. The adopted procedures were similar only in that each was confined to estimating glacier wastage within the Hector Lake sub-catchment utilising glacier extent maps compiled fiom aerial photography. Extrapolations were then

made to estimate total glacier loss for the entire basin.

The ht and simplest of these procedures (referred to as the Imentory Method), used

glacier inventory data compiled in the late 1960's (Stanley, 1970) to estimate average glacier depths within the Waputik Mountains. The area of each glacier was measured

fiom maps created using aend photography taken in 195 1 and 1993. Then a value for the total glacier volume in each image was calculated by combining these depth and area estimations. Finally, the 1993 volume was subtracted nom the 1951 volume and the result was the assumed loss.

The second procedure is refemed to as the Hypsographic Curve Method (der Young,

199 1). It is significantly more sophisticated than the previous in that hypsographic Cumes and rates of ice melt were used to mode1 volume loss per elevation band.

The final procedure (referred to as the Photogrammehica~Method) used stereo pairs of the 1951 and 1993 imagery of the Waputik Mountains in the Hector Lake Region to physically mesure glacier surface change. The computer package Surfer enabled a calculation of the total glacier volume change over the 42 year tirne span.

4.2.2 Obtaining the Aerial Imagery

A search was undertaken at the National Air Photo Library, Ottawa, to identiQ and procure suitable imagery for the analysis. Ail of the flight line maps covering the Bow Valley north of Banff nom the 1930s to the present were investigated to establish what was available. After the flight line and ûame numbers of potentially useful images had been identified, the archived photographs were browsed. The flight lines A13233,

A13253, A13321 (1951) and A27988, A27991 (1993) appeared to offer the highest quality imagery with total basin coverage at a scale of 150,000 (see appendix 2 for a surnmary of the fiame numbers and quality of imagery obtained). Thus, al1 the images on these flight lines containing some glacier coverage were purchased in paper print form.

Not al1 of the imagery procured has been used in the analysis presented but it did aid in establishing the suite of glaciers upstream of Hector Lake as being worthy of Mer scmtiny. To this end, the stereo pair diapositive images A 13233 (189, 190) and A2799 1

(19, 20) (see figure 4-1) were obtained to facilitate photogrammetrical glacier surface modelling. It was decided to purchase a set of optically corrected diapositives for the earlier, 1951, images to prevent any inaccuracies due to lens distortions.

4.2.3 The Glacier Coverage Map for Hector Lake Basin, 1951 & 1993

The topography within the Hector Lake Basin is fairly complex and, as such, has many permanent features which are identifiable on both the 150,000 National Topographical

Series (NTS) map (sheet 82 N9) and the aerial imagery of 195 1 and 1993. Thus, it was quite straight fonvard to translate the glacier margins fiom the two sets of images to the map using the eye and hand only. The resultant map displays the pattern of glacier retreat fiom 195 1 to 1993 within the Hector Lake Basin. Figure 4-1 Partial aerial photograph coverage of glaciers upstream of Hector Lake Following translation of the glacier margins to the 150,000 topographical map, the glacier covers were digitized using a digitizing tablet and Mapinfo Professional software.

The fÏrst procedure conducted during digitking, was to register the map on the tablet using several ground control points (GCPs). Intersections of the UTM grid were considered adequate for this task. Following registration, three Iayers (or tables) were added to the map; the first was the Hector Lake Basin boundary, then two Merlayers of glacier cover for the dates of acquired imagery were constructed.

The glacier covers were digitized in discrete units based on individual watersheds. This was carried out so that reference could be made to the Inventory of Glaciers in the

Waputik Mountains conducted by Stanley (1970). Areas of individual glacier extents for

195 1 and 1993 were measured automatically by the software using Mapinfo's query function. The area estimations generated within Mapinfo were found to compare very closely with area measwements taken fiorn the paper map using a Planimex digital planimeter. More in depth discussion of Mapinfo procedures and huictions can be found in the "Mapinfo Users Guide & Reference Manual" (Mapinfo Corporation, 1994).

4.2.4 Inventory Method

4.2.4.1 Glacier Depth Estimation

Individual average ice thicknesses for twenty three glaciers within the Hector Basin were estimated using the criteria adopted in the Waputik Mountain Glacier Inventory (Stanley,

1970). These criteria assume that depth varies approximately with areal cover and considers whether the glacier in question is of the mountuin or vailey type. For this study the same classifications have been applied to the twenty one glaciers that were investigated in the Inventory. The two glaciers that were not included in the Inventory but lie within the Hector Lake watershed, namely "Hector" and "Molar" are found at high elevation on the eastem side of the basin and clearly fa11 within the mourztain ghcier classification. The average depths applied in this mode1 are estimated by cornparison with depths measured for alpine glaciers in other parts of the world (Stanley, 1970). Table 4.1 summarises the critena for depth apportionment based on spatial extent and type factors.

Valley Glaciers 0-2.5 50 .pP...... 3---, ---.-.-..-.----..P..*----*., 2.5-5 70 .- ULW__l..___l...*-.-.--...... 5- 1O 100 .---____U__ ...... -...* ...... CC__I"--.~-----*---. 10-25 150 Mountaiu Glaciers 0-0.5 10 .-ri-*.rurr+.ir..-~-...--...--, --..-..------.---..--,

Table 4-1 Estimated Average Glacier Depths (Stanley, 1970)

4.2.4.2 Glacier Volume Change Estimation

To calculate a value for the wastage of glacier volume between 1951 and 1993 it was fust necessary to estimate total volumes of glacier ice within the Hector Basin. A volume for each individual glacier was computed by multiplying its measured area and assumed average depth. The volumes of al1 twenty three glaciers were summed for both dates and the 1993 figure subtracted fkom that obtained for 1951. The resultant value was the estimated bulk glacier wastage within the Hector Lake Basin for the forty two year penod. 42.5 Hypsogrnphic Curve Method

4.2.5.1 Division of Glacier Areas into Elevation Bands

in order to create a hypsographic cuve of glacierized regions within the Hector Lake

Basin, the areas of glacier cover, previously traced onto the NTS map, were divided into

1OOm elevation bands. (The 1:50,000 NTS map is imperid and the contours drawn at

lOOft intervals, therefore, some interpolation was necessary). The elevation bands of

glacier cover for 1951 and 1993 were added to two new layers within the digital rnap

using Mqinfo. Elevation range attributes, fiom 2000m upwards, were assigned to each of

the bands on al1 glaciers for both layers. (NB. Glacier covers in the region are not very

accurately dernarked on the 1:50,000 NTS rnap and even the most recent revision displays some gross errors in glacier murgin placement and surface contouring.)

The total area of glacier cover within each elevation band was calculated fiom the map by selecting dl regions with the same elevation atfxibute and adding them together. The hypsographic data of glacier cover for the two years were then entered into a spreadsheet and the curves plotted.

4.2.5.2 Estimation of Vertical Melt Rates Per Elevation Band

The rate of surface lowering observed on Peyto Glacier from 1966-89 (published in

Young, 1991) was linearly extrapolated both fonvards to 1993 and backwards to 1952, see Table 4.2. This rate was then wdas the mode1 for elevation dependant melt for each band of the Hector Basin glacier hypsograph. Elevation Range Surfsce Lowering 1966-89 Extrapolated Surface (tu) (m) Lowering 1952-1993 (in) 28-2900 5.0 9.1 ..-L__.-.-..______n P..- . .--/.---UI- 27-2800 7.5 13.7 >-- >-- ---W.-.- 26-2700 8.8 16.1 .____I....- ...-- 25-2600 15.4 28.1 ItWIUIUII-UP 24-2500 21.1 38.5 .__. - .- ---P...... *- 23-2400 42.8 78.2 .-.--..______II.~. .- .- P 22-2300 55.4 101.2 _f------. --______I_ P >--- -.....-P-.-.... 21 -2200 25.0 45.7 ,---...... - .p.- -.p.-- -.-.--.+..... 20-21 O0 10.0 18.3 Table 4-2 Peyto Glacier surface melt figures for 1966-89 (Young, 1991) and extrapolated for 1952-1993

4.2.5.3 Volume Change Calculations This method differs fiom the previous in that it was not necessary to estimate total glacier volumes within the basin. The volume change was approximated by assuming a trapezoidal cross-section for glacierized regions (see fig. 4-2):

Glacier surface 195 1 (elevation band "A")

\ Glacier surface 1993 (elevation band "A")

Figure 4-2 Trapezoidal glacier volume estimation method Where:

Vr = volume of glacier ice directly above the 1993 surface within elevation band "A";

V2= volume of glacier ice melted out dong the edges, not directly above 1993 surface;

Vchm, = estimated total volume of glacier melt within elevation band "A";

H = depth of ice melt attributed to elevation band "A";

Asi = area of glacier cover in 195 1 for elevation band "A";

Ag3= area of glacier cover in 1993 for elevation band "A".

These calculations were camied out for each 1OOm range and the volumes sumrned to provide an estimation of the total glacier wastage within the Hector Lake Basin.

4.2.6 Photogrammetrical Method

4.2.6.1 Introduction

Of the methods for calculating glacier volume used in this study, this is by far the most sophisticated. Due to the complexity and time taken for stereo photogrammetry and the volume of digital data involved it was irnpractical to cary out this technique for more than a relatively small suite of glaciers. Thus, this section of the andysis was only performed for the region of glaciers directly upstrearn of Hector Lake in the Waputik

Mountains. This area was considered the most appropriate within the entire Hector Lake

Catchment due to the high proportion of glacier coverage: approxirnately 59.5% of its parent basin; and also the range of glacier aspects: over 180' fiom north through east to south facing (few glaciers have significant westerly facing slopes within the Bow Valley). 4.2.6.2 Ground Control Points

A search for ground control points lying withh the bounds of the chosen air photos was undertaken. GCP lists for the Waputik Mountains, archived witbin the Cold Regions

Research Centre, and in the 'Wational Geodetic Database", on the World Wide Web, were browsed. Although two reasonabiy well defined control points were found: one on the suniniit of Balfour Mountain and the other on the eastern corner of Hector Lake, this was insufficient for absolute orientation of the stereo model. It was sufficient, however, for an approxhate scaling of the model.

According to the GCP lists (see appendix 2), one Mer control point had been established between Bow Peak and Crowfoot Mountain in the past but it was not visible on the 1951 and 1993 air photos. Field work was undertaken to install GCPs in and around the Hector Lake Basin but the planned linear survey traverse fkom Bow Peak to

Balfour Glacier using a Tl600 Total Station failed due to breakdown of the Electronic

Distance Measuring unit.

4.2.6.3 The Stereoscopic Plotter

The main piece of equipment used for the analysis was an East German constnicted

"Topocart Bu stereoscopic plotter with mechanical projection instrumentation. The

Topocart was comected directly to a plotting table via various gearing mechanisms to enable point and contour plotcing of the stereo model surface at a range of scales. Three digital scales are located on the fiont of the instrument which provide very precise CO- ordinate read outs in the X, Y and Z planes. The scale precision is 0.01 mm in any plane of the stereo model. Thus, for 150,000 imagery with a 1 :1 scale factor on the base line

adjustment, a real worId vertical precision of SOOmm is theoreticdy possible. If' the

vertical model scale is enlarged by lengthening the instrument base Iine (the Topocart has

a range of O to 240mm in Bx), the precision can be increased by more than a factor of

two. Therefore, for the same 150,000 imagery a vertical precision greater than 250mrn is

theoretically obtainable. However, in practice the scale can fluctuate by up to O. lmrn with

little discemible movement of the floating marks. Thus, the effective instrument precision

is reduced by approximately a factor of ten.

4.2.6.4 Orienting the Stereo Mode1

It was decided to perform photogrammetrical analysis on the 1993 imagery est due to this being of a higher quality. Hence, if the procedure proved of little value on this model there would be no advantage in continuhg with analysis of the poorer quality 1951 images. It was also easier for the operator to become familiar with the instrument using better imagery.

Pnor to orienting the diapositives, the principal distances of the two carnera carriers in the

Topocart were set to the focal length of the aerial camera used dunng photo acquisition

(15 1.1 7mm for 195 1 and 1Sî.85mm for 1993). The first stage of the inner orientation was to lifi the photo carriers off the instrument and place them on a light table. The glass plate covers were removed and the diapositives positioned in the carriers with the emulsion down and the zone of image overlap facing inwards. After an approximate centring of the diapositives, the glas plates were replaced and loosely clamped. Precise positioning was carried out using a cross-fiame with magrifjing aligning Zenses attached. Each lem was placed over the centre of an edge on the carrier plate and the diapositive mauipulated slightly until al1 fiducial marks were in alignment. The photo carriers were then re~med to the Topocart.

With the Topocart, it is possible to adj- the vertical scaiing using gears so that a reading in real world dimensions is possible. This was decided unnecessary in this case due to the lack of ground control available for an absolute orientation of the model. Thus, any scaling would be erroneous. An approximate and relative scaling could be achieved far more simply by mathematical manipulation of the CO-ordinatedata in a spreadsheet.

Therefore, this was the method adopted.

Before carrying out the relative orientation of the model the photo base between t principle points of each exposure was approximately measured using the paper prints and the 150,000 NTS map. It was found that the ground base between successive images was approximately 90mm (1951) and 76mm (1993) on the paper prints or 4.5km and 3.8km respectively on the ground. By using the equation: Bx = photo base x stereo rnodel scale

(or photo scale) the model base length (Bx) was increased to 145mm for the 195 1 stereo pair and 11 9.7mm for 1993. This increase in base length produced an approximate rnodel scale of 1 :30,000.

Whilst conducting the relative orientation, al1 of the drive gears controlling the carrier plate motion were disengaged to enable rapid movement between each of the corners of the model. The Independent Pair procedure was used to remove model parallax, as it is one of the simplest methods for an inexperienced operator. This procedure involves removing pamllax in a set rotation around the model and then continuing the iterations until al1 parallax has disappeared. Basic procedure (refer to figure 4-3):

1. Eliminate Y parallax at point 1 using KR.

2. Eliminate Y parallax at point 2 using KL

3. Elirninate Y parallax at point 4 using p~.

4. Eliminate Y parallax at point 3 using

5. Overcorrect Y parallax by approximately 50% at point 6 using a~.

6. Repeat 1 to 5 until al1 points are fiee of Y parallax.

r 03 @4 1 - 6 = Approximate location points.

a1 e2 es a6 Diapositive frames.

ppppp Figure 4-3 Location of points where parallax should be removed

4.2.6.5 Manual Co-ordinate Digitising

Following the inner and relative orientation procedures it was then possible to begin manually digitizing CO-ordinateson the model surface. Due to the lack of ground control points within the bounds of the model it was necessary to identiQ small but obvious features that were discernible on both sets of imagery. These reference points, dong with the known GCPs, were needed so that the Cartesian grids of the two models could be brought into coincidence. The features had to be "permanent" i. e. considered to have been stationary during the 42 year period between image acquisition. Such features included prominent crack lines in cliffs and edges of rock outcrops. Water courses and glacial features were not used due to their ability to change position and form within a relatively short space of the. The X Y and Z CO-ordinatesof fifieen well dehed features located around the areas of glacierization were noted for each of the models.

In order to separate the areas of glacier cover into discrete units, it was necessary to digitize the X and Y CO-ordinatesof the 1951 glacier edges. These data could then be used later when defining the sizes and boundaries of the individual glacier grids in Surfer.

The 1993 glacier margins were not needed due to them always being located within the bounds of the 195 1 glacier extents.

The final step during the photogrammetrical analysis was to digitize the X, Y and Z CO- ordinates of surface points. Only glacier surface was modelled for 195 1 but for 1993 the areas of ground that were previously glacierized were also inciuded so that the models could be directly supenmposed. An atternpt was made to preferentidly digitize al1 the major and minor change points and break lines on the areas of glacier and ground so that the shape of the surfaces in the DEMs would be as near reality as possible. For the 1993 stereo pair 768 sets of CO-ordinates(including reference features and boundaries) were manually digitized. However, for the 1951 photos only 365 points were obtained due to a

low snow line on the glacier surface with reduced image resolutioa and quality.

4.2.6.6 Transforming the Co-ordinate Data

The X Y and Z CO-ordinatesfor each of the models were manually typed into the

spreadsheet "ExceP' to enable mathematical manipulation. The first task performed was to mesh the aerial CO-ordinatesystems of both models. They couid not be aligned with the

UTM grid due to the limited ground control. However, the fifteen reference points on both models enabled a nibber sheet transformation which converted the CO-ordinate system of the 1951 data to that of 1993. It was considered appropriate to use the 1993 grid system for both years as it was generated from optically better irnagery and thus should be less prone to warping.

The software used to carry out the georeferencing process was Idrisi. The two CO-ordinate files were converted from Excel to text fomat so that they could be imported into Idrisi.

Within Idrisi these files were then converted to vector format so that the analytical capabilities of the software could be utilised. A correspondence text file was then created which held the X and Y CO-ordinatesof ail the reference points for both datasets

(Appendix 3). The correspondence file is the link between the two CO-ordinatesysterns which enables the rubber sheeting process. To initialise the georeferencing procedure in

Idrisi, the input and output file names and locations must be specified dong with the minimum and maximum input and output CO-ordinatevalues (see Eastman, 1992). After completing these steps, the file produced was in a vector format which is meadable in any other software. There was no facility to convert this file into a simple X, Y and Z text

file so it was decided to convert it to Mapinfo Interchange Format (ME) and then manually edit it to a usable three column format This file was then irnported back into

Excel.

The next step was to convert the models kom the arbitraiy mm scale CO-ordinatesystem of the Topocart instrument to a real world grid with units in metres. Areal scaling was facilitated using the Pythagorean law of right angled triangles in conjunction with the easting and northùig values of the ground control points to calculate the actual horizontal distance between them. The same methods were used to estimate the mm distance between the GCPs in the models and the ratio between the two values was the scale factor. Vertical scahg was achieved by calcdating the height difference between the two

GCPs in both the real world and the models and then ratioing the results.

4.2.6.7 Creating the DEM Grid Fües in Surfer

The text files of surface CO-ordinatepoints for each of the years were imported into Surfer and converted to raster Grîd files. The minimum X and Y value was Om and the maximums were 4500m and 8500m respectively. The method chosen for the gridding procedure was Trianguiation with Linear Interpolation because it maintains the integrity of the data points better than any other and is relatively quick. For this analysis it was important to maintain point integrity and not smooth out the surface too much due to the abundance of cliE edges in the area and the effort made to digitize al1 the major break lines on the glacier surfaces. The grid spacing chosen was Sm. This is much lower than the horizontal precision of the

data point CO-ordinatesbut spec@ng a liner grid Ied to problems with the computer

hardware that was being used: A grid spacing of lm Ied to a file size for one DEM of

greater than 50 megabytes. Thus, when analysing two DEMs of this sue the 486 and

Pentium cornputers that were available sirnply crashed due to insuficient memory. The

Sm spacing was only just possible because the DEM files were subsequently made

smaller during the glacier boundary blanking process. However, Sm was considered fine enough for this analysis and should not reduce the accuracy of the volume cornputations.

The lack of surface CO-ordinatesin the areas outside the glaciers meant that these regions were very poorly represented and inaccurately rnodelled. Thus, any volume computations using the 195 1 and 1993 preliminary grids would have resulted in very large errors. Three smaller DEMs needed to be extracted fiom the fust. The X and Y boundary CO-ordinates of Crowfoot Glacier, Crowfoot Icefield and Waputik Icefield (containing Vulhire and

Balfour Glaciers) were used to create "blanking" files. The three new DEMs were constnicted by specifjmg the input grid dong with the "blanking" file and a narne for the output grid. This was carried out six times, once for each glacier region of the 1951 and

1993 models.

4.2.6.8 Tilt Correction

From examination of the variation in differences between Z values for the 17 reference points over both models it was apparent that they did not quite mesh in either the X or Y plane. There was insuficient range of control in the X direction to fit a regression line through the differences in Z values. However, the control in the Y direction covered

almost the entire width of the models and a line of best fit was plotted (see figure 4-4).

Although, the scatter of data points in figure 4-4 is quite considerable and the square of

the residuals is ody 0.16, the presence of tilt between the two models was cobedby

subtracting the first 1993 grid file from that of 1951 using the Grid Math tool in Su$er. A contour map of the newly created grid appeared to indicate approximately 10 to I5m of growth around the glacier edges on the north side of the study area (Y approaching 8500), with a shilar depth of downwasting on the southem side (Y approaching O). Change at the glacier rnargins should, nahually, be very close to zero. Therefore, this anomaly was attnbuted to tilt in the Y plane, with the pivotal ais being in the region of Y = 4500. A

Mer tilt, in the X plane, was identified using grid subtraction which suggested approximately no change in Z for high values of X but almost 15m of surface growth

(195 1 to 1993) approaching X = O. (These values are in addition to any Y-tilt).

The Y-tilt was corrected by creating a new grid with a surface of '2 = -0.0028Y + 12.9"

(the best fit straight iine for the 6ZN data) using the Grid Function tool in Surfer. The grid size parameten were set equal to the grid file covering the Vultwe Glacier and

Waputik Icefield area. The newly created grid was then subtracted fiom the 1993 DEM of this area using the Grid Math tool. The 1993 DEMs for Crowfoot Glacier and Crowfoot

Icefield were both fairly small in extent and, therefore, could be adequately corrected in X and Y by simply subtracting the combined average influence of both tilts. For the Glacier 54

this approximated to 25m and the Icefield around 15m. The influence of the X-tilt was

considered negligible for the Vulture and Waputüc DEM.

Difference in Z Elevations in the Y axis of the DEMs

Y axis of 1951 DEM t Figure 4-4 Chart to indicate the presence of tilt in the stereo models

4.2.6.9 Volume Change Calculations

At this point the DEMs were considered as tnie and meshed as possible given the lack of ground control and, therefore, ready for analysis. The first task undertaken was to produce contour maps and three dimensional surface plots of the DEM grids using Surfer to allow visual inspection. Each 1993 grid was then subtracted from its corresponding 195 1 grid so that maps of surtàce change could be produced to indicate regions of downwasting and growth. Finally, glacier volume change computations were carried out automatically within SMer. This procedure is very simple and only requires that the operator specify the grid files for the upper and lower sdaces. Each of the 1951 grids were specified as

the upper surfaces due to it being downwasting that was of interest.

The output provided by Surj4er indicates positive volumes, known as mts, negative

volumes, known asfills and the sum of the two combined. Whether or not the negative

volumes, which suggest a surface growth, were included was decided after studying each

of the surface change models; i. e. if any region of growth indicated on the models was

considered anomalous it was not included in the cdculations. The fid volumes for each

of the glacier DEMs were summed and then applied to the whole Hector Lake Basin by assuming that the amount of glacier wastage should increase proportionally with glacier extent.

4.2.7 Extrapolation up to the Bow Basin Above Banff and Lake Louise

All volume caicuiations for the Hector Lake catchment are extrapolated up to the scde of the Bow above Banff and Lake Louise based upon areal glacier coverage. The glaciers within the boundary of the Hector Lake catchment make up approximately 45% and 74% of the total cover within the bas& upstrearn of Banff and Lake Louise, respectively

(Young, 1995b). nius, multiplication factors of 2.19 and 1.36 are used for the upward extrapolations. Discussion of the validity of up-scaling volume based upon areal extent is provided later. 4.2.8 Glacier Volume Water Equivalence

If glaciers comprised of pure blocks of ice the water equivalence of any volume lost would be around 91%. However, this conversion factor is considered too high for two reasons:

1. Glaciers are not solid; they contain many voids in the form of crevasses, moulins and

englacial/subglacial conduits;

2. Within the accumulation zone of glaciers there can be several metres depth of fim with

a density between 40 to 80% that of water (Sugden and John, 1991).

A conversion factor of 0.85 glacier volumelwater equivalence was, therefore, considered more reasonable and has been adopted in this shidy.

4.3 Annual Glacier Wastage Estimations

4.3.1 Peyto Glacier Mass Balance

Glacier mass balance data are ideally suited to the task of "weighting" the annual proportions of wastage yield calculated over a long time senes. The data indicate directiy which years did and did not undergo a loss of mass and, also, the relative proportions for each year contained within the dataset. Therefore, the rationale used in this section of the analysis was to assume that the record of net annuai mass balance for Peyto Glacier, just outside the study basin (obtained fiom Demuth, 1996, persona1 communication), would be representative of al1 glacierized regions of the Bow Valley. For the years prior to 1966, when no records were kept, some method of back-casting the mass balancelwastage proportions was necessary. 4.3.2 Back-cast of Peyto Glacier Mass Balance Record

The htoption considered for a mass balance back-cast was the model proposed by

Letreguilly (1988), which demonstrated a strong correlation with mean minimum May to

July temperatures at Jasper. Upon Merscrutiny, it was considered that this model was inappropriate for this application. For 1952 to 1965 Letreguilly's model suggests a thirteen year net positive mass balance of approximately 0.02m depth of water equivdence over the entire Peyto Glacier surface. Aithough this is not altogether impossible, it is considered extremely unlikely when observations made by Brunger et al.

(1967) are taken into account. Their study indicated that the toe of Peyto Glacier receded by alrnost 450m between 1952 and 1965. ïkerefore, a much more negative net mass balance for this period would intuitively be expected.

It is fortunate that within the Bow Valley, long time series of clirnate and winter snow course data exist for a variety of sites (meteorological records and snow course data previously obtained by the Cold Regions Research Centre from Alberta Environment and

Water Swey Canada). Thus, an attempt was made to correlate dl the long term April 1st snow course data fiom each site in the basin with the winter mass balance record for

Peyto Glacier. It is known that summer air temperatures correlate well with melt water yields fiom highly glacierized basins (Collins, 1988). nierefore, various combinations of average monthly temperatures at Banff were correlated with summer balance. (The Lake

Louise temperature record was not used, despite it being located very close to the region of maximum glacierization in the Bow Valley, because the meteorological station was moved during the study period). The Mirror Lake snow course for April 1": located near Lake Louise at 2030m, was found

to have a correlation of around 0.66 with the 1966 to 1993 Peyto winter mass balance

record. The correlation improved to 0.8 1 if only the earlier period up to 1980 was tested

(The mass balance trend appears to change between the mid to late 1970s). It was

therefore considered that the 1951 to 1965 winter balance / snow course relationship

would be reflected better in the 1966 to 1979 data rather than 1966 to 1993; i.e. the relationship between in valley snow accumulation and glacier winter mass balance is not stable through the. Declining winter mass balance is considered to play a major role in the overall net balance reduction observed at Peyto since the late 1970s (Demuth, 1996).

A regression model of the Mirror Lake snow course and winter mass balance for Peyto was calcuiated and plotted in fice1 and then nui backwards to the winter of 195 1/52.

A correlation of 0.70 was obtained between the summer balance and the maximum daily mean temperatures for June to August for 1966 to 1993. Other combinations of months were explored but this provided the best relationship. Again, if the earlier period up to

1979 were tested the correlation improved to 0.81. Therefore, as with the winter balance, the sumrner balance was back-casted using a simple linear regression model. The estimated summer and winter balances were sumrned for each year to give the back- casted net balances for 1952 to 1965. The net thirteen year balance for Peyto Glacier, using this method was - 1.24m depth of water equivalence, which is considered to be a more adequate reflection of the recessional observations than Letreguilly's model. The correlations and regression models used in this section of the analysis can be found in appendix 4. 43.3 Calculating the Annual Wastage Proportions

The recorded Peyto mass balance record was amalgamated with the modelled data to give a continuou dataset fiom 1952 to 1993 (balance years). At this stage of the analysis the balance figures were still expressed as a depth. To adequately represent wastage inputs, the changing area of Peyto Glacier during this time rnust be considered and the depths converted to volumes. The balance volumes were calculated by multiplying the annual balance depths by the changing area of the glacier. In 195 1, the area was approxirnately

14.5km2 and this was assumed to Iinearly decrease to 1 1km2 by 1993.

The annual proportions of glacier wastage were calculated by summing ail of the net balance volumes and dividing each year's balance into the total. Thus, the sum of dl the proportions wouid, naturally, be one. In years where the net balance was positive, it was assumed water was being with-held fiom the system by going into glscial storage and, therefore, the proportions assigned to these years were not included in the "weighting" process. This being for the reason that the sum of al1 years wastage yields must, of necessity, be equivalent to the net wastage for the forty two year period. The glacier wastage water equivalence was then multiplied by each of the positive proportions within the forty two year time series to give the aanual glacier wastage yields for the entire basin.

4.4 Seasonal Glacier Wastage Contributions

4.4.1 Introduction

For the purpose of this analysis it was assumed that seasonal glacier wastage contributions wodd coincide with and be in proportion to the combined ice and fun melt hydrograph derived from glacierized regions. It could be argued that glacier wastage flows do not commence until the exact tirne when the winter accumulation and swnmer ablation are in balance. Any melt water leaving the glacier after this point in time is effectively "shrinking" the glacier. This is a logical argument but is unredistic as it does not consider the factors causing the excess glacier los; For exarnple, if the ablation season of any given year had an exceptionally hot and dry June but a cool and damp

August it would not be fair to suggest that the conditions late in the season were responsible for this year's wastage. Further, such an assumption would predict that a high proportion (if not dl) of this year's September melt was due to glacier wastage. However, the observed wastage of a glacier is the result of melt throughout the entire season, it is not the cause of melt water discharge at the end of a season. If, then, the monthly proportions of a basin wide glacier melt hydrograph could be generated, the seasonal variation in wastage yield can be estimated.

4.4.2 Peyto Glacier Seasonal Melt Hydrograph 1967-74

Al1 hydrogmphs display the amalgamatiol of their upstream flow components. Therefore, separating the observed discharge into its contributhg aiiquots requires complex measurement using tracer techniques or some form of modelling. It was assumed that the shape of the glacier melt hydrograph at Peyto should be very sirnilar to that of the whole

Bow Basin. A study carried out by Young (1982) investigating the nuioff characteristics within Peyto Basin for the sumrner seasons of 1967 to 1974 was used as the starting point for this section of the analysis. In this paper, he describes the monthly flow components and explains the mode1 used to generate the hydrograp h sepration. Hypsographic cwes of ground cover types were used in comection with climatic and snow line elevation data to predict the relative hydrological inputs denved £kom ice, fim, snow and precipitation.

The monthly proportions calculated fiom this model for the years 1967 to 1974 are applied directly to the estimated wastage yields for these years. Outside this time period it was impossible to run the model again due to a lack of data. One method adopted to address this problem was to simply average out the monthly glacier melt proportions for the eight year period and create an "idealised" seasonal wastage hydrograph. This was then applied to all yean for which glacier recession was thought to have occurred.

Unfortunately, the variance in the monthly melt proportions for the sample was high and therefore, could in al1 possibility, predict wastage values that were far fiom the tnith, ie. years with unusual climatic conditions would not be represented.

4.4.3 Multiple Regression Mode1

The data for snow 1ine progressions, which could facilitate a re-run of the melt model, were not available, therefore, a less conceptual model was formulated. Using the Mirror

Lake snow course as the antecedent ground condition detexminant and Banff temperature and precipitation data as the seasonal climatic deterrninants, a multiple regression was executed in Ercel with Young's monthly melt values as the dependant variables. Sirnilar multiple regression techniques have been carried out with some success in the

Aletschgletscher and Rossegletscher basins (Lang, 1969) and in the Upper Rhône catchent, Switzerland (Collins, 1989). The new model was computed fiom June through to September for the eight year sample period. It was found that the model

worked better for the month of September if the snow course data were not included.

The iinear fiinctions generated for each month were of the form :

Mm= klS + (kA+ k3Tm+ ...... -.) + k (4-4)

where:

Mm= melt for month rn (June to July); k,, = constants;

Pm = total depth of precipitation for month rn;

Tm= average temperature for month m.

S = April 1" snow course depth at Mirror Lake.

The adjusted square of the residuals (calcuiated in Excel) between the regression modelled monthly glacier melt volumes for Peyto and those predicted in Young's model ranged between 0.90 for June and 0.99 for September. Therefore, this empirical model was used to estirnate the monthly melt figures in Peyto Basin for the remainder of the study period. The melt values were converted to monthly proportions by the method of summation and division and applied to the entire Bow Basin for each year of estimated wastage. See appendix 5 for the data input, the regression model output fiom Excel and the monthly parameter values.

4.5 The Impact of Glacier Recession on Basin Water Yield

Cornparisons of the estimated hydrologicd glacier wastage yields with actual basin runoff within the Bow Valley were facilitated using average daily discharge data for the Bow

River at Banff, Lake Louise and Hector Lake gauge (provided by Water Survey Canada). The river flow record at Banff extends back to 1909 and thus wastage and moff yields for the entire basin could be compared. The proportional significance of glacier loss to the river flow resource was assessed at a variety of temporal resolutions, ranging fiom the decadal and inter-annual down to the rnonthly scale. Some summer discharge data exist for the Hector Lake Sub-basin but it ody spans the years 1973 to 1976 and therefore only a linited cornparison could be perfonned. However, the discharge record for Lake

Louise, Iess than twenty km downstrearn of the Hector Gauge site, has been in existence since 1964 and could be investigated. 5.1 Areal Extent of Glaciers, 1951 & 1993

1 Hector Lake Basin with Glacier Extents for 1951 and 1993 Glacier encnt 1% 1

Glacier extent 1993

4 Hector Lake Basin gauge on Bow River

1 -21 Glacier id number according to inventory

Figure 5-1 Glacier Extents in Hector Lake Basin, 1951 and 1993 5.2 Glacier Volume Loss 1951-1993

5.2.1 Inventory Method

The results of the glacier volume calculations using the Inventory Method are presented below in tables 5.1 and 5.2. The areas given are those computed automaticdy nom the

Mapinfo software, and the depths estimated using the criteria adopted in the glacier inventory of the Waputik Mountains (Stanley, 1970).

Slacier name & number Planimetric Depth Glacier voIume iccording to 1967 irea estimation estimations. estimation nventory. (km2) (rn) (m3x1 06) 1951 1 Pulpit Glacier 0.33 10 2 Waputik Glacier 0.39 10 3 Balfour Glacier 6.94 100 4 Waputik Icefield 4.20 70 5 Vulture Glacier 5.28 1 O0 6 Crowfoot Icefield 2.42 50 7 Crowfoot Glacier 0.50 25 8 0.07 10 9 Crowfoot Glacier 2.03 25 IO 0.17 10 1 1 Crowfoot Icefield 0.80 25 12 0.1 1 10 13 Wapta Icefield 2.50 25 14 0.20 10 15 0.18 10 16 Bow Glacier 4.26 70 17 O. 10 10 18 0.50 10 19 0.45 10 20 0.29 10 21 0.05 10 Hector Glacier 0.50 10 Molar Glacier 0.17 10 rotals for sample Table 5-1 Hector Basin glacier volume estimation, 1951 Jlacier name & number Planimetric are2 Depth Glacier vo Iume lccording to 1967 estimation estimations. estimation nventory . (km2) (m) (m3x1 06) 1993 l Pulpit Glacier IO 2 Waputik Glacier 10 3 Balfour Glacier 1 O0 4 Waputik Icefield 70 5 VuIture Glacier 70 6 Crowfoot Icefield 50 7 Crowfoot Glacier 10 8 10 9 Crowfoot Glacier 25 10 10 1 1 Crowfoot Icefield 25 12 10 13 Waptakefield 25 14 10 15 10 1 6 Bow Glacier 70 17 10 18 10 19 10 20 10 2 1 10 Hector G tacier 10 Molar Glacier 10 rotals for sample

Table 5-2 Hector Basin glacier volume estimations, 1993

The Hector Lake Basin covers approximately 276km2, as calculated in the Mapinfo software. The areas of glacier cover for 195 1 and 1993 are approxirnately 32.4km2 and

24.3km2 respectively. These figures equate to areal gound covers of 11.7% and 8.7%; indicating that approximately 3% of the Hector Lake Basin plan changed from glacier cover to barren land between 1951 and 1993. The estimated glacier volumes within the catchment are 2 1 16 m3xlo6 for 195 1 and 1550 rn3x106 for 1993. The bulk glacier 67

wastage for the 42 year period within the basin is therefore estimated at 566 m3x106

using the Inventory Method.

5.22 Hypsographic Curve Method

Figure 5-2 Elevation bands of glacierization

The areas of glacier coverage per elevation band within the Hector Lake Basin are shown above (figure 5-2). The calculations of area cover for each lOOm range per glacier are given below (tabie 5-3). The hypsographic curve generated from this data is aiso presented (figure 5-3). N m :m oo im N ig N jin - is i 0 g i; x ig q*qqzio i O oio oio 0:o oio 0:o i

------,---4-.---(---.-+~___t___t___t___t_Y-~.--i--i--i.--i4i. W.- % cg:* 3:.mi0 8"0:o zig0:- sia: O o:o o:o OIO oie oi p-- ....y------...*---- I ]a-- I Area of glacierization (km3 Elevation I ranges (m) O I above 2900

------Figure 5-3 Hypsographic curve of glacier extents for Hector Basin, 1951 & 1993

A summary of the glacier covers per elevation band with the corresponding estimated depths of melt and volume Ioss are presented in table 5-4 (below). Elevation Area iepth of glacier glacier volume Range (m) rurface melt (m) IOSS (m3x 106) above 2900 0.0 0.0

28-2900

27-2800

26-2700

25-2600

24-2500

23-2400

22-23O0

2 1-2200

20-21 O0

Total catchment

Table 5-4 Glacier volume loss estimation using hypsographic and surface melt data

5.2.3 Photogrammetrical Method

5.2.3.1 Surface Co-ordinates

Control Point UTM Easting UTM Northing Elevation (m.a.s.1.) L Balfour Mountain 537088.9 712601.3 327 1.72 1 Hector Lake 1 541496.6 1 715491.7 1 1739.19

Table 5-5 Ground control points used in photogrammetrical analysis The UTM CO-ordinatesof the ground control points used in the analysis are presented in table 5-5 (above). The raw and rescaled metre grid (non UTM) CO-ordinatesof the digitized surface points fiom each of the stereo models for both years can be found in appendix 6-1 and appendix 6-2 respectively. Once referenced to one another, the grid that both models confonned to had an X range of O to 6500m and a Y range of O to 8500m.

The X axis of the grid increased along a south westerly transect with an approximate bearing of 250'. The Y axis increased along a south easterly transect of approximately

160' (see figure 5-4).

NTS Map 82 N 9 UTM Grid (x 1000)

Region of DEM coverage

GCP locations

-. --. - . . . . Figure 5-4 Relative locations of UTM grid and DEM Cartesian grid. 5.23.2 The Glacier DEMs

On the following pages, contour maps of the Crowfoot Glacier and Icefield DEMs created in Surfer are presented (figures 5-5 and 5-6). On these plans the contours have been filled to enable faster interpretation of slope shape and aspects of the glacier surface. The

Waputik Icefield DEM showing Balfour and Vulture Glaciers is displayed as three dimensional surface plots (figures 5-7 and 5-8). Al1 grid lines shown are the X and Y axes of the rescaled, georeferenced and tilt corrected DEMs; they bare no relationship to UTM

CO-ordinates.The scales show in al1 figures are in metres.

Figure 5-5 Crowfoot Glacier DEM surfaces created in Surfer.

Figure 5-7 Waputik Icefield, Balfour and Vulture Glacier DEM, 1951 (100m grid)

Figure 5-8 Waputik Icefield, Balfour and Vulture Glacier DEM, 1993 (100m grid) 5.2.3.3 Gracier Surface Change

The surface change plots of each of the three glacier regions studied were intended to indicate which zones of the glacier surfaces had undergone downwasting and which had not. GeneraIIy most downwasting occurred in the lower regions of the glaciers (as would be expected), with the greatest depths of surface loss being located in the central to upper parts of the glacier tongues. Each glacier grid displayed relatively small regions of surface growth (negative values on surface change plots).

400

2 Axis

1000

1600 -.A 2000 1400 X Axis O 200 400 600 800

Figure 5-9 Crowfoot Glacier Surface Change, 1951 - 1993 In figure 5-9 it can be seen that the maximum depth of downwasting on Crowfoot

Glacier, according to the DEM subtraction, is approximately IOOm, with be~een30 and

60m of loss al1 dong the centre line. Clearly, there is some error in this model: On the east side of the glacier there is shown to be between 10 and 20m of downwasting and dong the western edge considerable surface growth is displayed. In reality there should be zero change at the glacier margin; possible reasons for these anomalies will be discussed later. When computing the volume change in Surfer, this zone of surface

"growth" (considered to be a 'Yill") was not included.

400

Y Axis

1200

2400

X Axis

Figure 5-10 Crowfoot Icefield surface change, 1951 - 1993 Downwasting in the central area of Crowfoot Icefield (2400 to 2600m elevation) appears to be in the region of 100m (figure 5-10), with a maximum depth of loss up to 150m long the northem edge. Around the icefield margins there is generally very little change in surface elevation. This suggests that the two DEMs for Crowfoot Icefield were quite well meshed. The ody real anomaly is dong the lower western edge, where a growth of up to

60rn is indicated. The "fill" volume associated with this srnall region of growth was not included in the analysis.

The first major observation when studying the surface change of the Waputik Icefield

(figure 5-1 1) is that most of the glacier wastage appears to be on the Vulture glacier side.

The maximum depth of surface loss is approximately lOOm at an elevation between

2400111and 2500m. It is to be expected that the majority of wastage should be on this side of the model due to its southerly aspect. Proof that south westerly facing glaciers are most likely to undergo recession has been provided by Kasser (1980). Even high up on Vulture

Glacier (above 2700m), it is suggested that a large area of downwasting has reached a depth of about 70m. On the south side of the model (NE facing), the changes appear to be more erratic with large areas of little change. On much of the tongue of Balfour Glacier, a zone of marked recession, the model indicates that over 50m of glacier depth has been lost. In the accumulation zone patches of surface growth up to 60m are shown. It is thought that these areas of growth are due to errors in the DEMs but the possibility of increased snow depth accumulation at these elevations can not be discounted. Therefore, the positive volumes have been included in the calculations for this model. 1O00

3000

Axis

5000

7000

4000 2000 X Axis

Figure 5-11 Waputik Icefield surface change, 1951 - 1993 5.23.4 Glacier Volume Change

, .

-- - --VOLUMES ' VOLUMES 4!2.!!.!- ---- Approximcd Volume by l App-matai Volume by ---- Approximatcd Volume by

Trapaoidal Rule: 8.û9E+06! .Trapaaidal Ruk 1 .OSE+081 Tropaoidal Rub: __ Simpson's Rule: 8.09E+û6 ISimpson's Rulc 1 .OSE481 ~Simpson's Rule:

Simpson's 318 Rule: 8.08E+06 1 ISimpson's 318 Rule: 1 05E48i Simpson's 38 Rule: , _ . E~%E~.FIUVOLUMES ,CüT&F7LL VOLUMES CUT& FILL VOLUMES - - Positive >lume [CulSI: 1 .ûûE+07' !?witivc Volume fcuts]:! 1 .06E+ût Positive Volume [Cut! 3.07E-- Negative Volume FilK 1.93E+û6 , Ne& Volume [FillsI 752165 Ntgativc VoIume FiII 5.67EM; Cuts minus Fills: 8.û9Ec06 'Cuts minus Fillr 1.05E+08! Cutr minus FilIr: 2.5 1 E4F I

Table 5-6 Surfer grid fie summaries with volume computations.

The volume calculations for each of the grid areas determined within Surfer are dispiayed

above (table 5-6). After summing the approximated volumes, it was found that the results provided were the same down to four significant figures for each of the three calcdation methods used by Surfer. The total estimated glacier loss volume for the suite of glaciers examined is 366 m3x106.Extrapolating this value up to the total catchment above Hector

Lake gauge gives 616 m3x106. 5.2.4 Summary of Volume Caïculntions and Water Equivalence

The volume loss of glacier ice and fim for the Bow River at Hector Lake with extrapolations up to the basin above Banff and their corresponding estimations of water equivalence are presented below (table 5-7). The values taken on to the next stage of analysis were those generated in the stereo photogrammetrical method as this involved direct measurement of volumetric change, rather than interpolation. It is also considered to be reasonable due to the volume estimations fiom this method fdling mid-way between those of the other two. Discussion of errors will be provided later.

Basin Wastage (m3x1 06) Hector glacier ice 566 Lake water equivalence 48 1 Lake glacier ice 770 Louise water equivalence 654 Bow at glacier ice 1240 Banff water equivalence 1053

Glacier volume change estimations 195 1-93 using the Inventory Method

Basin Wastage (m'x 1Ob) Hector glacier ice 695 Lake water equivalence 590 Lake glacier ice 945 Louise water equivalence 802 Bow at glacier ice 1521 Banff water equivalence 1292

Glacier volume change estimations 195 1-93 using the Hypsographic Curve method

Basin Wastage (m3x1 06) 1 Hector glacier ice 616

Lake , water equivalence 524 Lake glacier ice 838 Louise water equivalence 713 Bow at glacier ice 1349 Banff water equivalence 1148 ------

Glacier volume change estimations 195 1-93 using the Photogrammetrical Method ------Table 5-7 Summary of the glacier wastage estimations 5.3 Annual Proportions of Glacier Wastage

Ycar Banff Jun-Aug Mimr Lrkc Modelled balance (cm W.&) Mutsurcd bn (cm W.C.) 1 av IMX ttmp April 1st snow I I Running Running

(OC) course (cm W.C.) bw bs bn totml total 1952 19.5 10.7 143 -123 20 1953 19.7 8.4 121 -129 -7 1954 18.7 14 174 -97 77 1955 20.8 9.1 128 -167 -39

Table 5-8 Peyto mass balance depths with comparative mnning totals, actual and modelled. In table 5-8 the measured and back-casted mass balance values for Peyto Glacier fiom

1952 to 1993 are presented. The 1991 value is, unfortunateiy, estimated based on the

equilibriurn line altitude (ELA) for this year (Demuth, 1996 personal communication) and

1992 is an average of the 1967 to 1991 series. An average value was used for this year so that it would not bias the proportional weightings in any way. These two years currently have no record and could not be modelled due to a lack of data. They are not thought to significantly affect the outcome. The nuuiing totals of modelled and measured net mass balance are given to illustrate the significant divergence between the values der 1979.

The proportions of wastage assumed to be entering hto river flow for each year within the study period above Lake Louise and Banff are presented in table 5-9 (below). For

Hector Lake there was ody one year where net negative mass balance coincided with available discharge data; this was 1 975, a low flow year. The volume of glacier wastage for this year is calculated at 17.2 m3 x 106 (w.e.). The annual yield for the sub-basin could not be determined as only summer time discharges were measured and therefore the annual wastage I yield cornparison could not be achieved.

The annual proportions of glacier wastage to basin yield reach a maximum value of

16.2% for Lake Louise sub-basin and 12.5% for the Bow above Banff. (For the Mistaya basin (247km2),just north of and very similar in character to the Hector basin, Young calculated a 25% wastage/yieId proportion for the same year). These hi& wastage input values occur during the lowest flow year of the study penod, 1970. The number of years not displaying wastage early in the time senes reflect the apparent trend in the Peyto mass balance record to become continually negative after the mid seventies. Year bn volume Annual Wastage (rn3x10') Yieid (rn3xl0? Wastage 1 yield (m3x 106) weigbts Banff Louise Banff 1 Louise Banff Louise 1952 1246 1 1 953 -1.07 0.0049 5.7 1249 1 0.45% 1954 1605 1955 -5.53 0.0254 29.2 1176 2.48% - - 1956 1252 1 957 1098 1958 -728 0.0335 38.4 1262 3.05% 1959 1334 1960 -5.8 1 0.0268 3 0.7 1135 2.70% 196 1 - 14.59 0.0672 77.0 1359 5.67% 1962 1180 1963 -4.54 0.0209 24.0 1293 1.86% 1964 -2.3 7 0.0 109 12.5 1337 0.93% 1965 -1.98 0.009 1 10.4 7.6 1457 599 0.72% 1.27% 1966 1508 599 1967 1539 776 1968 1186 580 1969 -5.20 0.0239 27.5 20.1 1249 615 2.20% 3.26% 1 970 -21 -96 0.101 1 1 16.0 84.7 92 7 523 12.50% 16.18% 197 1 -5.26 0 .O242 27.8 20.3 1230 56 1 2.26% 3.62% 1972 -3.19 0.0147 16.8 12.3 156 1 1.08%

Table 5-9 Estimated annual proportions of glacier wastagehasin yield for Banff and Lake Louise. Italics = Banff yield < 1100 1n~x10~, shaded = wastage > 50 m3x106, Bolded = wastage 1 yield > 5%. It can be seen in table 5-9 and figure 5-12 that years of low yield tend to coincide with

substantial wastage. Lowest yield and highest wastage years are highlighted to illustrate this. However, it is a weak trend (figure 5-13) and two years in particda. deviate significantly fiom this pattern. The year 198 1 is one of both high yield and estimated hi& wasiage with 1957 displaying a low yield and no glacier volume loss.

I Annuai Bow River Yield 1

Figure 5-12 Annual Basin yield and glacier wastage for the Bow above Banff. Yicld (m'x 1o6) 1700 -

le00 " 0 1500 R' = 0.2 e* 1- " 1981

1300

I 1200 I il00 41 1957 1 0 . ! 1000 '. 1970 900 - :

800' 1 O 20 40 60 80 100 120 Giacicr wucigt rbove ~ialt(rn'x10~)

Figure 5-13 Yield I Wastage for Bow above Banff

5.4 Monthly Proportions of Glacier Wastage

5.4.1 Idealised Ice Melt Aydrograph

A summary of the combined Peyto ice and fim melt discharges for 1967-74, as calcdated by Young (1982), are given in table 5-10. The averages of each year's monthly proportions, used to generate an idealised seasonal melt hydrograph are also provided.

Idealised monthly glacier wastage / basin yield ratios are presented in table 5- 1 1.

Table 5-10 Estimated Peyto Glacier melt 1967-74 (after Young, 1982) with average monthly proportions. Ideaiised monthly wastage / basin yield b Bow above Banff Bow above Lake Louise Year June July Angust l~e~temberJune July August September 1952 1 1953 0.03% 0.39% 1.80% 1 1.24% da da da da 1954 1

Table 5-11 Idealised monthly glacier volume loss / basin yield for Bow above Banff and Lake Louise. Shaded cells = months with greater than 20% ratio. Blank cells = years of positive mass balance. 5.4.2 Multiple Regression Mode1 Using Meteorological Variables

The monthly glacier loss / basin yield ratios for the multiple regression modelled melt are

given in table 5- 12. August 1970, is the most notable period of the study. It is estimated

that over 50% of the flow upstream of Banff was derived fiom glacier losses in excess of

the net mual equilibrium. The value increases to almost 85% for the highly glacierized

sub-basin above Lake Louise. The significance of seasonal glacier wastage distribution to

the hydrograph at Banff for the years 1969 to 1972 is illustrated in figure 5-1 4. The

monthly melt proportions used for these years were calculated directly fiom Young's

Peyto Glacier meIt volumes (1982), and were not idealised or modelled using multiple

regression.

Figure 5-14 Observed hydrograph for Bow above Banff 1969-1972 with modelled wastage flow super-imposed. Modelled monthly wastage 1 basiu yield Sow above Banff Bow above Lake Louise Year June 1 July 1 Augiist 1 September June 1 Juiy ( August 1 September 1952

1953 0.03% 0.42% 1.46% . 1.72% da da da nia 1954

1955 - 18.07% ria da da da 1956 1957 1958 0.68% 3.78% 16.48% ria da da nia 1959 1960 1.53% 8.18% 14.36% da nia da da 1961 1.14% 0.00% -39.50'?!. da da da nia 1962 1963 0.45% 227% 7.70% 1.61% da nia da n/a 1964 0.04% 0.53% 2.25% 7.14% da da n/a nia 1965 0.07% 0.92% 3.08% 0.24% 2.65% 6.81%

1974

1975 5.46% 14.39% - nia 35.40%

Table 5-12 Modelled monthly glacier volume loss I basin yield for Bow above Banff and Lake Louise. Shaded cells = months with greater than 20% ratio. Blank ce& = estimated zero glacier wastage. "We cm never have hue knowledge of unything that is in a constant stute @change. " Plato, 4h Centuy BC

6.1 Review of the Techniques Used

6.1.1 Mapping Glacier Extents

The interpretation of glacier boundaries on the aerial photography and transfer to the

1:50,000 NTS map was quite straight forward. The abundance of surface features identifiable on both the imagery and rnap enabled reproduction of the glacier boundaries with reasonable integrity. However, the 1993 boundaries underlay the glacierized areas plotted when the map was created, therefore, resulting in few surface features within close proximiv to the 1993 ice margins. In some cases it was not possible to draw the margins to an accuracy better than +/- 1Smm on the map or +/-75m on the ground.

During the digitization process errors could occur if the glacier boundary lines were not followed accurately or if curves were over generalised by not having enough nodes. Mer the NTS map had been registered to the digitizing tablet, a test was performed. Using the knowledge that the distance between each grid line on the map is 1km, a selection of grid squares were digitized and the areas calculated using Mapinjo's "query" capability. The results suggested that area calculations were accurate down to the third significant figure or within 10m2. However, the areas to be digitized were not uniform angular grids and a

boundary line error margin of +/- 0.5mm (+/- 25m ground) was thought reasonable.

The maximum glacier boundary location error is, therefore +/- lOOm on the ground.

Applying this error factor to small areas leads to a substantial range between minimum

and maximum possible areas, whereas for large glacier covers the range is less

significant. Fortunately, then, it is the glacier covers that have less impact on the analysis

that are most prone to error. It was impractical to calculate the range of possible areas for

each individual glacier unit, therefore, the margin errors were applied to a rectangular

region with sides of 2km and 15km in length. This roughly approximates to the

dimensions of the icefields region in the Waputik Mountains. If each side is relocated by

+/- 100m then the area of the rectangle fluctuates by up to 10%. The perimeter length of a

perfect rectangle is, naturaily, much less than that of irregular shaped glaciers of a similar

total area and, therefore, this comparison may be considered unredistic. However, it is in

the zones of retreat where the lowest confidence in boundary location is found, with the

higher elevation glacier margins not displaying much change. Thus it is a relatively small

length of penmeter that is subject to the greatest errors.

6.1.2 Volume Calculations

6.1.2.1 Inventory Method

The Inventory Method was the simplest of those adopted to investigate glacier losses and provided the lowest estimate of volumetric change. Within this section of the analysis the only new source of potential error was the allocation of average glacier depths based solely upon areal extent. There is no discussion of errors for the estimated ice depths in the Lnventory, or even of the sample used for determination of the values. Therefore, the usefiilness of this mode1 must be viewed with caution. Another, related, cause of concem? is that the average depth estimation for a glacier can rernain *tic through time if the area does not fa11 below a threshold value, see figure 6- 1. A constantly vaiying volume-area relationship, such as discussed by Chen and Ohmura (1990), would be more suitable.

Also estimates can be irnproved if dope angles of glacier cover are known (Paterson,

1970 and Omanney, 1980). However, adequate knowledge of the glacier and ice sheet dopes for each set of imagery was not available.

/ 95 1 assumed cross-section Bedrock

1993 assumed cross-section

195 1 glacier surface

, Average depth

Figure 6-1 Idealised glacier cross-section indicating how the Inventory Method estimates volume.

For the purpose of error evaluation, it will be assumed that depth estimations are the means of normal distributions, with the first +/- 3 standard deviations containhg values within +/- 50% of the mean. For a 68% (or 1 standard deviation) confidence in the depth estimation, given this criteria, maximum and minimum lirnits shouid be set at +/- 17%. The maximum and minimum volume calculations using the Inventory Method and the above criteria are presented in table 6-1.

Total Glacier Volume (m' x 109 . Year min mean max. I 1951 158 1 21 16 2723 1993 1158 1550 1995 1951 - 1993 423 566 728 Table 6-1 Glacier volume error estimations using the Inventory Method

Theoretically, the maximum possible glacier loss would be to take away the minimum

1993 volume fiom 1951's maximum, Ieaving a value of 1565m3 x 106. However, it is thought reasonable to compare only alike maxima and minima due to the Iikelihood of caqing the same kind of errors fonvard; i.e. if areas and depths were overestimated in one set of imagery, then it is probable that they would be for the other.

6.1.2.2 Hypsographic Curve Method

6.1.2.2.1 Hypsographic Curve Construction

For the purpose of this analysis it was assumed that ared glacier coverage diminishes within each elevation band as glaciers recede. This rnay not always be the case in reality due to the surface of a large glacierized terrace downwasting into a lower elevation band that previously held little glacier cover. However, the static nature of the ice surface contours on the NTS map fiom 1951 to 1993 prevents such occurrences being registered.

Thus the boundaries of each elevation band on the 1993 glacier cover map were directly super-imposed on to the 1951 map. It is impossible to quanti@ the errors produced by super-imposing elevation band boundarïes but they are thought to be small. This is because the impact of applyhg a slightly incorrect melt rate to a small volume of ice would not affect the results significantiy.

6.1.2.2.2 Mett Rates

It is not known if the melt rate for 1966-89 is absolutely representative of the 1952-1993 time period. However, study of the rate of recession of the toe of Peyto Glacier (Bninger et al., 1967) appears to suggest that the recession rate for the 1952-1 965 period rnay have been greater than during 1965 to the present: Brunger's observations indicate a total recession of the Peyto Glacier tongue of 445m fkom 1952 - 1965, or an anoual rate of

34.lm per year. Cornparison of the Peyto Glacier Map, produced by the Inland Waters

Directorate (1975), and observations made in the field during the summer of 1996, suggest that nom 1966 - 1996 there was approximately 600m of toe recession. This equates to around 20m per year, which is substantially lower than the recession rate observed during the earlier time period. However, this change in recession rate may be more attributable to a change in the ground topography immediately surrounding the glacier tongue during its backwards progression, rather than a change in rnelt rates.

Evidence suggesting that 1966-89 melt rates are representative of the earlier period is found when the results obtained in Henoch's paper (197 1) investigating volurnetric glacier change in the Upper North Saskatchewan Basin are compared with Young's research

(1 99 1) in the Mistaya Basin. Henoch estimated that the glacierized area within the Upper

North Saskatchewan diminished in size by approxirnately 10% between 1948 and 1966

(1 8 years). Young calculated a similar figure (1 1%) for the change in glacier area within the Mistaya for the time period 1966-89 (23 years). The Mistaya is a large sub-basin of the Upper North Saskatchewan and thus, if the above estimations are reliable, it would be reasonable to assume that average melt rates for each of the two time periods were of

similar magnitude.

6.1223 Volume Calculation Technique

It was impossible to compare contours of glacier surfaces nom one time to the next due to the contours on the NTS map belonging to oniy one point in time and being unreliable.

Therefore, the Finsterwalder or Haumann methods (descnbed in Brandenberger & Bull,

1966) could not be employed in this analysis. The trapezoid method was probably the simplest for this kind of calculation and does not take account of glacier surface morphology. The three dimensional trapezium block assumes that the corresponding glacier surfaces are parallel, perfectly flat and that the 1993 surface is the same length of that for 195 1 only narrower. These are extremely over generalised assumptions and bear only an approximate relationship with reality.

The assumptions made are perhaps most invalid in the lower elevations, where glacier surface change is most pronounced. In these zones the two surfaces will, in dl likelihood, not be parallel in either longitudinal or lateral cross-section and are more likely to be convex than flat. In addition, the valley sides that bound the glaciers will not be straight, as suggested by the trapezoid but rather concave with steepening gradients at the top.

Evidence suggesting that the cross section of a glacial valley can be descnbed by a second degree parabola was put forward by Omstein (1980). However, given the spatial variability of surface and cross section morphology within the mountain glaciers and ice sheets of the shidy region, a more suitable profile than the trapezoid was not found.

6.1.2.2.4 Cornparison with Photogrammehical Observations

The melt rates applied to the entire Hector Lake Basin were the averages of observations on Peyto glacier surface. Although some concession to slope aspect may have been made over a narrow sweep of azimuth, the more general variation of glacier aspect within the basin is not considered. The preferedal wastage of glacierized dopes that face south was observed in the glacier DEMs constructed using photogrammetrical analysis (see figure 5-

10). Vulhire Glacier, south facing, has undergone greater downwasting and recession than the north facing Waputik Icefield directly opposite.

A Meritem of interest is that the maximum depth of surface downwasting predicted using the extrapolation of Young's observations on Peyto for 1966-89 (1 99 l), was a little over 100m. This value is very similar to the maximum depths calculated using DEM cornparisons of Vulture Glacier, Crowfoot Glacier and Crowfoot Icefield. However, in the Hypsographic Cwe Method, this depth is applied to the 22-2300m elevation band ody. The elevation contours of the DEMs are not absolutely dehed but it would seem that the zones of maximum depth are generally higher and not linear across the width of a glacier. Rather, they are centrally Iocated (with reference to the 1951 glacier outlines) and oriented approximately longitudinally with the glacier centre line. It is thought that, although the potential for substantial downwasting did occur in the 22-2300m band, this was not observed because there simply was not sufficient depth of glacier ice at this elevation. It should be noted that greater downwasting can occur at higher elevations due to gravitational mechanical ice flow in addition to ice melt.

6.1.2.2.5 Confidence

It is difficult to place a valw on the confidence in the results derived fkorn the

Hypsographic Curve Method for a variety of reasons:

1. the raw melt data of the Peyto Glacier surface, fiom which the depths of

downwasting were estimated, were not analysed for their statistical variance;

2. the melt depths were extrapolated back through time. Thus, no sample of

surface melt depths exist for venfication purposes;

3. it is very difficult to quanti@ how representative Peyto Glacier is to the

population of glaciers within the entire Bow Valley;

4. the contour height and shape information in glacierized areas of the NTS map

cannot be tnisted when constructing hypsographic curves.

However, this is thought to be a much more usefùl analytical tool than using inventory data alone, as it only concerns itself with glacier losses and not total volumes. The average depth of a glacier is irrelevant when using this technique. If reasonable estimates of melt depth and glacier cover per elevation band are available, this method should potentially provide more reliable results than using the critena adopted in the Inventory

Method. 6.1.2.3 PhotogrammetricaI Method

6.1.23.1 Introduction

Although the Photogrammetrical Method of measuring glacier volume change was b! the most sophisticated and the oniy one that dealt with direct observation of change it was also the most open to subjective interpretations and operator error. Whilst an attempt to explain and jus* aU the steps taken was provided in the methods, various procedures could have been carried out differentiy. Even the sample of glaciers chosen for the analysis could have been different. It may have been more appropriate to use irnagery that had more ground control. However, the decision made was considered econornical due to the greatest proportion of glacier cover on any stereo pair within the Bow Basin being found above Hector Lake.

6.1.2.3.2 Surface Change Anomalies

It was noted during the DEM surface cornparisons that there were some regions which displayed peculiar characteristics. On Crowfoot Glacier the surface of the western side has apparently grown by up to 70m. This can not be the case and is thought to be the result of mis-representing the steep cliff line that nins dong the edge of the glacier and up to Crowfoot Mountain. Warp in this part of the mode1 is thought to be significant as it is near the edge of the stereo models. Also, there were no reference points around Crowfoot

Glacier, probably leading to this area being the least "meshed" in X and Y. The fil1 volume associated with this glacier was omitted fiom the analysis but the lack of coincidence in the surfaces has probably led to an underestimation of the net volume loss.

The high values of surface downwasting, indicated at the northem edge of both Crowfoot Glacier and Icefield could be due to glacier thinning dong the catchment watershed but

are more likely the result of digitization errors at the mode1 edge. However, these areas

are very small and possibly act to even out the discrepancy caused by the small zones of

apparent surface growth.

On the Waputik Icefield DEM, it could be argued that the zones of surface growth are more likely the result of DEM surface mis-representation due to a lack of surface points in the accumulation zone of the imagery. The most distinct features in these areas were rock outcrops and in the absence of other identifiable points the tnangulated mode1 would assume straight flat surfaces linking them. Often the rock outcrops are the hi& points in any locality (this why they protrude) and therefore the general surface elevation would be overestimated. If this is the case, then the decision to include the fil1 volumes may have been invalid. If' these negative volumes had been omitted from the analysis the total change of glacier volume for the studied suite of glaciers would be 423m3x106 or

7111n~x10~for the entire Hector Lake Basin.

On the Vulture Glacier side of the DEM the suggested depth of wastage in the accumulation zone could be slightly exaggerated for the same reasons as discussed above.

It is Iikely, therefore, that this assumed area of wastage compensates for some of the modelled surface growth on the Waputik side. However, on aggregate it is thought that this method tends to underestimate rather than overestimate the vo1u.e change in the suite of glaciers studied. 6.1.2.3.3 Further Errors in DEM Construction

During the construction of the DEMs efforts were continually made to minimize erroa, however, various sources can be identified. The error values listed below are cumulative and therefore increase with the method progression:

instrument precision, estimated to be +/- 30cm horizontaily and vertically (CO-

ordinate scale reading);

floating mark coincidence precision, approximately 10 x instrument precision = +/-

3m horizontally and vertically;

operator enor, unknown value but thought to be less than 5m in al1 directions;

the combined errors due to tilt and warp between the two models are unknown but

could be very high, perhaps of the order +/- 1OOm at any point on the DEMs. This

error is, however, drastically reduced as a result of the georeferencing and tilt

correction procedures which act to mesh the models. Although absolute errors in

elevation and planimetnc location may still be high, the models should be relatively

coincident. Apart fiom residual tilt errors the only significant factor preventing a total

mesh of the models should be polynomial warps across the stereo imagery. Three

dimensional rubber sheeting would have to be carried out to correct for warps and the

computer software needed to carry this out (if any exists) was not available.

in the high albedo and low contrast areas of the accumulation zone it is more difficult

to digitize surface points. Therefore, the DEM surfaces in the upper reaches of the

glaciers are progressively more genemlized. This was particularly the case with the

1951 imagery, as in 1993 the photograph quality and resolution, combined with less

snow cover, enabled better surface reconstruction. 6. errors associated with converting the CO-ordinatedata to a raster grid are considered to

be very small due to the 5m line spacing and the use of the "Triangulation with Linear

Interpolation" surface mapping procedure to maintain point integrity.

Maximum relative errors betweea the 1951 and 1993 models are considered to be around

+/- 30m with perhaps slightly greater values in the accumulation zone and much higher confidence at lower eievations. If this enor is applied to the total planar area of the glaciers, then lirnits of +/- 483m3 x 106 are set. This value is greater than the calculated volume change of 366m3 r 106. However, individual surface errors will be slightly smoothed out by the grid spacing of the raster DEM in Surfer and the abundance of other points in close proximity. Thu, the influence of any anomalous individual points will only be localised.

It is difficult to quanti@ adequately the errors in volume estimation given the possible vertical error of some points on the glacier surfaces. However, given that the three methods used to estimate glacier volume change in the Hector Lake Basin have provided similar results there can be good confidence that the true value is between 500 and

750rn~x10~.It is likely that the true value lies near the middle to upper lirnit of these values.

6.1.3 Validity of Extrapolating up to the Scale of the Bow above Banff

The glaciers within the Hector Lake region of the Bow Basin are considered an appropriate sample to study due to the density of glacier cover, their variety of aspects and range of elevations. However, the validity of a linear extrapolation in volume losses based simply on proportional spatial coverage is perhaps questionable. It was observed in the photogrammesical analysis that wastage volumes can Vary significantly fiom one side of a valley to another. It therefore needs to be ascertained whether or not these large scale variations over short distances are enectively smoothed out when applying the results to a larger area.

This was tested by taking a small sample of glaciers from within the Hector Lake region population and extrapolating volume losses up to the entire sub-basin based on areal covemge. The extrapolation was then compared with sub-basin volume losses, estimated using the hventory and Hypsographic Curve Methods, to check its validity. (The results of the photogrammetrical analysis could not be used as these were already taken fiom a sample population.) The glaciers directly upsîream of Hector Lake were chosen as the sample. The average arcal proportion of this suite of glaciers compared to the rernainder of the sub-basin is approximately 59.5% and therefore the areal extrapolation factor is

1.682.

In the results of the hventory method, the sample of glaciers selected were responsible for 84% of the estimated total catchent wastage. This is significantly more than their areal coverage would suggest. However, this is largely the result of Vulture Glacier reducing its area to just below a depth criteria threshold value which has led to a large volume change estimate relative to other glaciers. Another factor is that many of the glaciers outside the sample are smdl independent units and, therefore, apportioned shallow depths. For these reasons it is felt that the Inventory Method is not suited to investigating small regions of glacierization where individual glaciers can drastically affect the result.

Using the Hypsographic CweMethod it was estimated that the sample of glaciers were responsible for 62% of al1 wastage within Hector Basin. This is very close to the 59.5% areal proportion but still suggests that when extrapolating to a larger scale it could be possible to over-estimate the total glacier wastage. The sample of glaciers tested contain relatively large areas of contiguous ice sheet, whereas much of the rest of Hector and indeed Bow Basins, contain larger proportions of dispersed glaciers and glacierettes. This test indicates, then, that applying glacier volume losses from one glacierized region to another may be invalid if the two areas have different densities of areal coverage.

However, the test itself may not be appropriate. The Inventory Method estimates negligible volume changes in areas of srnail glaciers due to the very shallow depths apportioned. Also, the Hypsographic Curve Method applies shallow depths of melt at the higher elevations where many of these smaller glaciers reside. It was noted in the DEM comparison results that surface downwasting at high elevations was found to be considerably greater than the estimations in the Hypsographic Curve Method. Thus, both of these methods will probably systematically under-estimate the volume losses of glacial ice fiom small glacier areas. Intuitively, this makes sense when one considers that small glaciers and glacierettes rnay be more prone to wastage per unit area than larger ice sheets due to extra longwave radiation and advective inputs fiom nearby surrounding ground features.

In addition to the possibility that more dis-contiguous glacier cover leads to greater wastage, the glacier hypsographic cuwe for the entire Bow Valley indicates that there is a slightly higher proportion of glaciers at lower elevations than in the Hector Basin alone

(figures 1-4 and 1-6). The potential for melt lower down in the basin shodd therefore be greater due to slightly warmer temperahues. The linear extrapolation of glacier volume loss up to the scale of the Bow above Banff, although possibly quite reasonable, is thought more likely to lead to under rather than over-estimation. The limits on basin wide glacier wastage upstream of Banff are around 1100m3x 106 to 1640m3 x 106 (glacier ice) or 930m3x 106 w.e. to 1400m3 x 106 w.e. with increased confidence that it is within the upper half of this range.

6.1.4 Annual Wastage Proportions

6.1.4.1 Peyto Glacier Mass Balance Record

It is intereshg to note that wastage inputs are apparently higher in the second half of the tirne series, after the mid-seventies. This is intuitively not what would be expected if the climate were stable or at least changùig in a linear fashion. Observations do not indicate a decline in magnitude of the net balance values despite the rapidly shrinking dimensions of

Peyto Glacier. Winter positive balance figures show some tendency to reduce through time (Demuth, 1996) but no discernible trend is apparent in the summer negative values

(see figure 6-2). This can indicate one of two things: 1) the Peyto data set is unreliable or 2) there has been a change in climatic regime. There is some evidence to support the

second prernise; a shifi in the atmosphenc circulation pattern at the 700mb level was

observed around the mid 1970s (Fountain and McCabe, 1996).

250 / n winter balance 1 surnrner balance

1 Measured

Figure 6-2 Peyto Glacier mass balance (depth cm), measured 1966-93, back-casted 1952-65.

It is known that for the early period of the Peyto mass balance data series, the area factor

was not changed for at least thirteen years (Young, 1981). More recently the area factor

has been updated regularly, perhaps every third year or so (Demuth, 1997 personal

communication). The application of this dataset to long term glacier wastage estimations

would be improved if it were thoroughly re-examined. The raw field book measurements,

for the earlier time period (if available), should be reviewed and the mass balance values recalculated with adjusted area factors at regular time intervals. 6.1.4.2 Peyto Mass Balance Back-cast

The decision to use a backcasting method which has a correlation with measured mass

balance that is slightly lower than Letreguilly's method, may seem a little subjective.

However, this decision was made based on the chosen model's ability to concur with field

observations not statistical correlation coefficients. Intuitively, local winter snow course

and summer maximum temperatures should provide reasonable surrogates for winter and

summer balances. Maximum temperature is probably a more usefid estimator of summer

melt than average or minimum temperature because it provides some insight into whether

a day was cloudy or very hot. If the maximum temperature for a day is Iow, then it would

be assumed to be cloudy or wet with low melt, conversely a high maximum temperature

suggests high melt potential. It is more difficult to make the same inferences with only

average temperature data.

Continuing the mean minimum Jasper May to July temperature model backwards to 1952 led to a positive mass balance of 0.02m compared to -1.24m for the snow course 1 maximum temperature model. The negative value better represents the observations of recession on Peyto during 1952-65 (Brunger el al, 1967) but it could still be significantly conservative. There are several individual years in the Peyto mass balance dataset that show negative balances of over 1.0m. Therefore, to suggest that the glacier can undergo

445m of recession and only lose 1.24m depth of total water equivalence seems highly unlikely . If it is indeed the case that the annuai wastage proportions for the penod up to 1965 have

been under-estimated then tbis will lead to a systernatic over-estimation of the

proportions after this date. Therefore, it is quite possible that annuaI volumes of wastage

cdculated for Iow flow years such as 1970 are too high. Hypothetically, if the 1952-65

balance was acnially Sm more negative than cdculated (-6.24m), then the annual ratio of

wastage to discharge at Banff in 1970 would be below 10% as opposed to 12.6%. The

August ratio would dso decrease fiom over 50% dom to around 40%, still a highly

substantial proportion. It is difficult to put any confidence bits on the annual mass balance weights except to Say that îhey are best estimates.

An improvement of the back-casted mass balance data senes could be facilitated if air photos dating back to the early 1950s were used to map the Peyto Glacier surface. This would enable a comparison with the previously mapped 1966 surface (Inland Waters

Directorate, 1975) and an estimate of the volume change between the two dates. The volume change could then be converted to the net balance figure in water equivalence.

Monitoring glacier mass balance using aenal photography and sequential mapping has been widely practised with much success in Norway (astrem, 1986).

6.1.5 Monthly Wastage Proportions

6.1.5.1 Idealised MeIt Hydrograph

Using the idealised melt hydrograph to weight the monthly wastage proportions for each year assumes that melt charactenstics are invariant fiom year to year and has resulted in the months of some years displaying unlikely charactenstics. In table 5-9 the monthly glacier loss / basin yield ratio for September 1970 at Lake Louise is almost 99%. This value appears far too high and illustrates that it is inappropriate to apportion the same rnonthly weightings nom one year to the next. This method assumes 2 1.7% of any year's wastage will be in September. However, Young's calculations (1982) suggest that only

4.2% of 1970's glacier melt occurred during this month, probably due to the melt system shutting off rapidly der a substantial snowfall.

6.1.5.2 Multiple Regression Melt Hydrograph

There is a slightly lower tendency for high ratios during September using the multiple regression model method, with some of the bias being transferred to July for a few years.

This simple model does attempt to consider the climatic parameters that are driving the melt process and for this reason these resdts are considered of slightly more value than those denved fiom the idealised wastage hydrograph. However, for some summer seasons the model suggests that melt does not occur during al1 four months £?om June to

September. For 198 1 and 1955 this has led to the entire year's estimated wastage being

Iumped into the month of August. It is thought unlikely that only one month would contain al1 of a years wastage but this may simply reflect that some months can be substantially more dominant than others.

Although the regression model is considered to provide a more realistic reconstruction of the summer melt hydrograph, the proportions calculated should be viewed as a rough guide only. The sarnple of years used to calibrate the mode1 contained only eight values for each month (six for September) and they themselves were the product of another model. It was also found that for the month of September a better fit was obtained if the

April snow course data were not factored in. It would seem to make little sense to leave out the antecedent conditions for any month, however, it is logical that the ground conditions at the beginniog of the suerwould have progressively less impact on glacier melt volume later in the season.

A Merapparent error in the multiple linear regression is that some of the monthly temperature / melt functions are negative, implying some aspects of this simple model have little grounding in reality. A svnilar problem was also found by Collins (1 989) when attempting to correlate and model basin discharges with temperature and precipitation in the Rhône Valley, Switzerland. A more conceptually based and data intensive model would therefore be required to recreate Bow Valley sumrner glacier melt hydrographs with any degree of certain@. An abundance of hydrochemical tracer data has been collected on the Bow River at Lake Louise since 1975 and could be utilised to attempt such a hydrograph separation.

6.2 The Impact of Glacier Recession on the Flow of the Bow River

6.2.1.1 Annual Variations

In figure 6-3 the impact of glacier wastage to the Bow River hydrograph fiom 1952 to

1993 is dramatically illustrated. The top of the "ribbon" being the observed basin yield with the bottom being the average annual yield without the influence of excess hydrological inputs fiom receding glaciers. In summary, it is estimated that the average

basin yield above Banff is reduced by 27 m3x106w.e. f?om 1244 to 12 17 m3x106w.e. if

the influence of glacier recession is omitted. For 1970, the same drop is 927 to 81 1 m3x106w.e. The low flow years of 1970, '79, '83-85, '87-88 and '93 al1 show relatively hi& wastage inputs with most of the high flow years displayhg very little or no glacier wastage. 1961, '8 1 and '90 are interesting for they al1 show above average basin yields but also a high proportion of flow derived from glacier loss. (No conclusions can be drawn for 1991-92 as the measured mass balance data for these years were not available.)

This demonstrates that, although glacier recession is hydrologically at its most influentid during years of low flow, it can still be an important component of river flow even during some high flow years.

t-* Average Buin Y idd wiîh mstage = 1244 rn'x l Cf)

Figure 6-3 Bow River hydrogtaph at Banff with and without annual wastage yields 6.2.1.2 Monthly Variations

When looking at the annual scale, the influence of glacier recession is not adequately

appreciated. Comparing annual yields with annual wastage totals does not account for the

temporal variability of glacier meIt inputs. Thus, when investigating summer month wastage proportions the significance increases. In figure 6-4 the relative proportions of wastage and yield estimated for Banff, 1952 to 1993 are presented for the months of July to September respectively. The average monthly basin yield for Juiy during the 42 year penod is 288 111~x10~w.e. and the wastage proportions are rarely very substantid, with the highest being around 18% in 1970. The August figures show a dramatic rise in wastage contributions with average basin yield dropping to 175 m3x106w.e. August is, therefore, the most critical month with regard to glacier inputs to the river. Figure 64Monthly wastage proportions for Bow River at Banff, 1952-1993 1 -- Proportions of glacier wastage/discharge for the 5 lowest fïow years (%) 1 Year Annual June Jury August Sept 1970 12.5 2.0 18.1 52.6 7.6 1979 5 -2 3.1 16.5 26.5 1975 3.7 5.5 14.4 1985 4.9 0.3 7 .O 19.9 10.0 1977 1.3 0.3 2.2 5.0 1 Proportions of glacier wastagddischarge for the 5 highest glacier volume loas years (%) 1 Year Annual 1 June July August Sept 1970 12.5 1 2.0 18.1 52.6 7.6

Proportions of glacier wastage/discharge for the 5 years with the highest ratio (%) Year Annual June July August Sept I 1970 12.5 2.0 18.1 52.6 7.6 1988 5 -3 2.3 8.2 23.6

Average proportions of glacier wastageldischarge for al1 years in study period (%) Year Annual June July Augus t Sept 1952-9 1 2.3 0.3 2.4 9.8 3.7 Table 6-2 Annual and monthly summary of glacier wastage 1 basin yield at Banff.

It is interesting to note that three years display exceptionaily high August wastage inputs:

196 1, '70 and '8 1. Although 1970 has the highest ratio of wastage I yield, August of 198 1

is estimated to be the month of greatest glacier volume loss. However, this is due to the

multiple regression model Iumping al1 of 198 1's wastage into the month of August. For

September, the relative wastage / yield proportions &op significantly as temperatures drop and snow begins to fa11 at higher elevations. The model suggests, however, that

September can still produce large volumes of glacier loss in some years. 1978, '79, '80 and 1982 al1 show fairly high wastage contributions with September 1978-9 having basin yield proportions of around 27%. The significance of glacier recession inputs to river

80w cm continue into September because more glacier area may be exposed and basin

wide snow melt inputs are reduced due to Iower temperatures and higher snow lines. The

average September basin yield at Banff, 1952 to 1993 is 100 m3x106 w.e. For a sumrnary

of annual and monthly wastage contributions during low flow and high wastage years see

table 6-2.

6.2.1.3 The Low Flow Year, 1970

.A .. .. asin in yield without wastage input) -., -. .:..:;,$+$y -- . ... i..-.- - 4:. - -. 2.. .- ,L +;:, . .:. .+ C -1 - . . . .-.. - . , <- .. -. ._. _,... .- component of basin yield)

- - -- Figure 6-5 Monthly wastage proportions at Banff, 1970

The 1970 basin yield and modelIed monthly wastage contributions for the Bow River at

Banff are shown in figure 6-5. The light section of the bars displays the hydrograph without glacier wastage, the total yield is represented by the entire bar. 1970 produced a high proportion of wastage to yield due to little winter snow fall, low summer precipitation and high temperatures (see figure 6-6). August of this year had the lowest rainfall of any August during 1952 to 1992 and the average temperature of 15.5 OC was considerably higher than the average August tempenihue of 14.4 OC. If the climatic regime that persiçted duriog 1970 were to repeat but without any glacier cover, the basin hydrograph would be sirnilar to the graph shown in figure 6-5 with a srnaller wastage component. The difference between July and August yields would be enhanced with

August and September being almost identical. However, the timing and shape of the hydrograph would probably be a little different due to an earlier snow melt peak from more rapid melt of snow in areas that were previously glacier covered and less flow retardation of water draining through glacier systems.

Figure 6-6 Banff precipitation and average temperatures during the summer of 1970

It is not known exactly what the proportional glacier coverage was in 1970, but it has been show that the areal cover reduced from approximately 1 1.7% to 8.7% in Hector Basin from 1952 to 1993. 1970 is near the middle of this the senes and (using Brunger et al S. observations (1965)) it can be assumed that approximately half of the recession had occurred derthis date. Therefore, fiom 1970 to 1993 glacier cover reduced between

10 and 15%. If areal coverage is considered a reasonable surrogate for the ability of glaciers to augment river flows then the foiiowing conclusion can be made: If a climatic scenario equivalent to that pnor to and during 1970 occurred today, then the amount of flow in the Bow River derived from glacier wastage could be reduced by 10 to 15% of that estimated for June ?O September, 1970. Therefore, the annual yield could be reduced fkom 927 to 9 10 m3x1 o6 and the overall flow for August depleted by up to 7.5%.

6.2.2 The Lags

In the analysis presented, the upstream glacier wastage and downstrearn total basin yield were considered to be temporaily coincident. No lags due to in stream travel tirne and temporary lake storage have been factored in. If these lags are significant (greater than one week for example), the direct super-imposition of glacier and basin yield is invaiid. In addition, a delay in the passage of glacier melt derived nuioff wodd increase the proportional significance of wastage flows to the seasonal recessional limb of the Bow

River hydrograph at Banff.

If it is assumed that in stream average flow velocity is of the order 0.5 m s-' (estimated from personal observations in the field, 1996) then the majority of water entering the river system within the Hector Lake Basin will reach Banff in about three days. When looking at monthly basin yields a tirne lag of this Iength is quite inconsequential. Therefore, if the above assumption is valid, any glacier wastage yields estimated to have melted out of the upper region of the Bow Basin within any month may be considered approximately coincident with total hydrological basin yield at Banff for the same month. However, there is around 15km2 of lakes within the Bow Basin above Banff? and many of these lie directly doWIlStream of the highly glacierized mountain areas feeding into the Bow River.

These lakes act to slow dom flow through velocity of river waters and could potentially significantly impede the progress of glacier wastage flow downstrearn.

In order to quanti@ the tirne lag effect induced by lakes in the river basin, the hydrodynamic and thermal properties within the lakes mut be explored. The classic text on limnology, provided by Hutchinson (1957), provides insight to some of these processes: Any water entering a lake via a surface stream input will tend to remain near the surface provided the new and old water masses are of indifferent stability with no density gradients. Even the momentum of turbulent water with high potential energy is soon dissipated upon entering a large lake. However, the temperature variations within lakes, resulting from surface heating and stream inputs, lead to density gradients and sometirnes complex patterns of convective mixing. A thermocline separating deeper dense water (water is at its most dense at around 4OC) fiom more turbulent and buoyant surface waters is often established.

Although it is possible to make many generalisations about the flow of water through a lake, temperature profiles distributed over the surnrner melt season, would be needed to ascertain density curent patterns of the glacial melt strearns through the lakes. Such data are not available. However, field observations of Peyto Lake during the summer of 1996

would suggest that early in the season, around June, sediment laden melt waters sùik shortly after entering the lake. As the season progressed more of the sedirnent plume was observed to fao out over the surface of the lake until it was totally dispersed, blending with lake waters over 500m fiom its point of entry. If melt waters do, indeed, skim across lake surfaces, then their passage may be delayed due to reduced flow velocity but not significantly detained due to temporary storage.

However, as with the monthly apportionment of glacier wastage flows, it may not be necessary to physicdly identify and follow the progress of actual aliquots of melt water. input and output volumes to and fiom a lake will rarely be identical at any point in time.

Tiny fluctuations in lake level will always be occurring. Shortly after ice break up on the mountai. lakes in question, the water levels are low with output discharges being small.

Daily inputs fiom groundwater, rainfall, snow and glacier melt tend to be greater than lake discharges for much of the surnmer season and the water level naturally rises until average temperatures begin to drop again and surface moff inputs recede. Rising melt water volumes during the sumrner lead to an increase in lake water level and a concomitant but lagged nse in outflow. Thus, a parce1 of water leaving a lake does so by virtue of a discrete and possibly distant parcel of water entering the lake at an earlier time.

It is irrelevant, therefore, to this investigation that new lake water could enter into semi permanent storage and the water being displaced out of the system could be of relatively ancient origin. It is the effective time lag for the melt water input to be translated to a an outfiow that is of interest. During a typical summer day, melt waters will probably be filling the lakes in Bow Valley

faster than they can drain. At night, however, the converse would be me. If a diumal

discharge regime is apparent at lake outflows, it can be concluded that some of the melt

water input is being translated into an output in less than one day. The proportion of input

passing through such a lake in one day would be a detemiring factor in the relative

hydrograph shapes at its input and output. It should be noted, however, that the system descnbed above can be Mercornplicated by the occurrence of lake level changes

induced by up and down valley winds: Katabatic winds, drifting down valley due to radiative cooling of air masses over glacierized areas, may act to preferentially drain lakes at night, with day theupslope anabatic winds raising lake levels at their input, leading to a possible retardation of hydrological throughput. Unfortunately, no quantitative hourly discharge data were available for this study in the Bow Valley (or at Peyto) that wodd indicate the relative hydrographs above and below any of the lakes. Some qualitative but non conclusive evidence of diumal flow fluctuation at the outflow of Bow Lake was observed during the sumer of 1996: Whilst undertaking river crossings downstream of

Bow Lake on three separate occasions, it was found that moming crossings were easier than later in the day due to a rising volume of flow.

No tirm conclusions can be made regarding the time lag of glacier melt water progress fiom high up in the Bow Basin dom to Banff. It is possible that the actual glacier melt and wastage flows could be detained for long penods of time. However, it is thought that the effect of glacier wastage inputs should be transmitted to the downstream hydrograph at Banff within a matter of days. If this is the case, directly super-imposing estimated monthly wastage ont0 basin yield will not lead to large errors. If any error is present it will lead to an under-estimation of the significance of glacier wastage to basin yield in the later months of August and September.

633Evaporative Water Losses

Differences in temperature and stream turbulence of water nom discrete surface and ground sources will lead to varying potentials for evaporation. Evaporative losses are enhanced when water is turbulent and spray is sent into the air or in large areas of open water (Raudkivi, 1979). The lakes in the Bow Valley are quite small but they should have a high potential for evaporation due to the fairly rapid replacement of overlying air with less saturated air (Starosolszky, 1987). The incidence of lakes and more turbulent river water is greatest higher up in the basin and it could be argued that evaporative losses will therefore be greatest nearer the river headwaters. However, the warmer air temperatures experienced lower in the basin may offset this somewhat.

It should be noted that even if the rate of nverine evaporative losses were constant nom the Bow headwaters down to Banff, this would lead to greater overall losses of the water derived upstream, whatever the source. These waters have Mer to travel and are therefore subjected to the evaporation process for a greater length of tirne. This has not been accounted for in the analysis and al1 of the estimated glacier wastage that originated high in the basin has been considered to reach Banff without loss. nius, omitting this process from the analysis will lead to a slight over-estimation of the glacier wastage component of flow at Banff. No atternpt has been made to quantify the influence of evaporative losses to the results but it is thought to be quite small.

6.2.4 The Future

Over the 1st fifty years and indeed probably the entire century, glaciers within Bow

Valley have acted as flow regdators, delivering water late in the surnmer and during dry years when it has been needed most. As glacier areas and volumes shrink, their ability to augment flows in the future will naturaily dirninish. If the glaciers were to continue receding indefinitely in this part of the Rockies, then it will not be long before they are gone altogether. Hypothetically, if it is assumed that the rate of glacier diminution is linear, then the life expectancy for glacier cover can be calculated from the total volume figures estimated using the Glacier Inventory Method. Approximately one quarter of total glacier volume in 1951 is estimated to have been depieted by 1993. Therefore, extrapolating fonvards would suggest that there is between 100 and 150 years of cover left. However, this is an extremely unlikely scenario, as rates of recession should reduce as glaciers reach higher and colder elevations. It is far more plausible that the glacierized regions will shrink until they reach a new equilibrium line, possibly somewhere near their extents prior to the Hypsithermal advance of around 3000 years ago.

If glaciers were to disappear, then the impact on the downstream hydrograph would be substantial. Runoff patterns for highly glacierized basins such as Hector Lake Basin may become more similar in character to nearby non-glacierized basins such as Forty Mile

Creek (see figure 6-7), leading to significantly lower specific yields. Dry months and years would no longer be augmented, leading to a reduction in magnitude of low flows and increasing the occurrence of such events. In addition to reducing late summer discharge the absence of glacier cover wodd lead to more rapid melt of snow cover with no temporary flow storage within the englacial environment, therefore, increasing river flow in spring and possibly leading to a higher incidence of flood events. Summer flows would become more precipitation dominant than they are at present. However, as pointed out, this is an extreme and, hopefully, distant situation. If glaciers reach a new equilibrium, about which they fluctuate little over long periods, then their role in flow regulation will continue for a long time to corne. They will continue to provide water in times of low inputs and hold it back when excessive quantities of snow fdls in winter. It is the magnitude of augmentation that will change.

mecfor Lake (- 1 1% glacicrizcd)

Bow at Banff (-3% glacicrizcd)

.4O Mile Creek (CE% giacicrizcd)

Figure 6-7 Specific mean monthly yield 1974-76 for the Bow River at Banff, Hector Lake and 40 Mile Creek. The annuai basin yields experienced within the Bow Valley have, for the most part. been greater than the net input due to precipitation (inter basin groundwater exchanges and evapohanspiration are accounted for in the "net" input). The increases of basin yield due to glacier recession input have been fortuitous from a water resource point of view and should not be taken for granted.

6.2.5 Climatic Interactions

A greater understanding of the rates of future glacier recession and the implications to down Stream river flows would resdt if more effort were put into investigating climate change I glacier extent relationships. Predicting friture glacier masgins in the Rocky

Mountains may then be possible. Although it is out of the scope of this thesis to research climate change interactions with glacier recession and river flow, the possible impact of

El Nifio events upon the system being studied was bnefly investigated. Between 1952 and

199 1, there were three major El Niiios: 1957-8, 1972-3 and 1982-3 (Barry & Chorley,

1992). The corresponding basin yield hydrograph at Banff and estimated wastage yield figures for these years, do not appear to display any patterns. The yield figures for each of these times are quite different and show no relationship to years of either high wastage or zero wastage. It must be concluded, therefore, that if El Nifio events have any impact on this system it is very weak or over shadowed by other operational clirnatic systems. "Glaciers may be the most sensitive climatic irdicators in

nature, both of current climate and of secular changes. " Valter Schytt, 1966

7.1 Key Findings

7.1.1 Glacier Loss in the Bow vaiiey 1951-1993 in 1993 there was approximately 25% less total glacier area in the Hector Lake Basin than in 1951. The reduction from 32km2 to 24km2 translated to a total basin cover change of

3%. It was estimated that this areal change in glacier cover equated to around 524m3x106 of water equivalence. Extrapolating this up to the Bow above Banff gave a total basin glacier wastage yield of approximately 1150 m3x106 of water equivalence. This is an average glacier wastage input to the river systern of 27 m3x106w.e. per year (or 2.3%).

7.1.2 Impact of Glacier Wastage on the Bow River Hydrograph at Banff, 1951-1993

The Peyto Glacier mas balance annual weighting of the bulk wastage suggests that most of the glacier losses occurred Iater in the tirne series, particularly &er the mid 1970s.

This corresponds with observed lower winter snow accumulations (Demuth, 1996), which could explain why the lowest flow years are also prevalent during this time period. It is found, therefore, that years of high wastage have a tendency to coincide with Iow annual basin yields. However, the years 1961, 198 1 and 1990 dl display above average basin yields at Banff with high westage components also. Thus demonstrating that although low flow years tend to be those most significantly augmented by glacier losses, wastage can make up an important part of basin yield even in a year of above average flow.

1970 was the lowest flow year during the study period and is also estimated to be the year of greatest glacier volume loss. The month of August for this year displayed a particularly low yield at Banff as a resdt of very low precipitation and high temperatures. Therefore, most of this month's flows were made up glacier melt and groundwater base flows.

Groundwater input was probably depleted for this year due to the very low winter snow accumulation. It is perhaps not surprising, then, that approximately 50% of the August basin yield for the Bow above Banff is estimated to be made up of glacier wastage.

7.1.3 Implications for Future Water Availability in the Bow River above Banff

If glacier recession were a linear process that could be extrapolated forwards in tirne, then the glaciers in Bow Valley wouid disappear in around 125 years. However, this is unlikely and it is thought that the augrnentation of basin yields during low flow years at

Banff will continue for quite some time beyond this. However, the magnitude of flow augmentation mut diminish if glacier extents and volumes reduce and their snouts retreat to higher and cooler elevations. The fortuitous augmentation of river flows expenenced over the past century or so should not be relied upon when planning for future water demands in the Bow River Basin.

It has been calculated that a similar climatic scenario to that witnessed in 1970 occurring today, would result in a reduced annual basin yield of approximately 2%. For the month of August this translates to a monthly yield 7.5% lower than that measured in 1970. If the

glacier component is taken out of the hydrograph altogether, then the &op in flow

between July and August flows will be very pronounced, with August approaching the

flow volume experienced in September. A Merconsequence of a zero or negligible

glacier component is the timing of the river hydrograph. Overall basin snow melt may be

more rapid, thus, speeding up and increasing the magnitude of spring melt events and

leading to an increased hazard of flooding. Summer precipitation events will also move

more quickly through the basin if the temporary storage facilitated by glaciers and high

elevation snowpack is diminished. Therefore, as glaciers recede the system will become

increasingly snow melt and precipitation dominant.

These scenarios are based on the assumption that glaciers will continue to retreat as a

resuit of further climatic warming. However, increased air temperatures could lead to a

change of the precipitation reghne also. It is not inconceivable that at some point in the

future the %inter accumulation of snow in these glacierized mountain regions could

increase. Indeed, a recent advance of some maritime glaciers in Norway due to greater winter accumulation has been observed while the majonty of continental Norwegian glaciers have been receding due to increased summer ablation (Bogen, et al., 1989).

7.2 Evaluation of Methods

7.2.1 Volumetrie Change

There was good corroboration between the glacier volume change calculations using the three methods (see table 7-1). There are two values given for the Photogrammetrical Method; one with the inclusion offil volumes in the Vulture and Balfour DEM and one without. The original andysis was carried out with fil1 volumes due to the possibility of surface growth in the accumulation zone. However, there is a strong possibility that these areas of surface growth are more likely due to DEM enors fiom digitizing inaccuracy in regions of high reflectance on the stereo imagery.

Volumetric Change Basin (m3x1 06) w-e. 1 Method Glacier Inventory 48 1 1053 Hypsographic Curve 590 1292 Photogrammetncal (withfills) 524 1148

------Table 7-1 Volume calculations of glacier wastage for Hector Lake Basin with areai extrapolation up to Banff

It is also thought that the Inventory and Hypsographic Methods tend to under-estimate the importance of small hi& elevation glaciers to total glacier volume losses due to the shallow depths of melt apportioned them in these two methods. hcreased advective and longwave radiation inputs could, in theory, increase melt rates in such areas. In addition, the importance of glacier aspect to surface change was highlighted in the DEM comparisons. South facing areas undenvent substantially more wastage than north facing.

Thus, any method constructed to estimate glacier loss through time must factor in a glacier slope aspect component. The linear extrapolation of glacier wastage up to the Bow above Banff is thought systematically under-estirnate the total wastage for the entire basin. This is again due the higher incidence of small glaciers within the basin above Banff and also because there is a slightly higher proportion of glacier cover at lower elevations than experienced in the

Hector Lake Basin. There is reasonable confidence that the true volumetric glacier Ioss for the Bow Basin is between 930 and 1400 m3xlo6 w.e. but the possibility of volume under-estimations in the methods and the linear extrapolation suggest that the tme value is likely to be toward the upper end of this range.

7.2.2 Annual Weighting of Glacier Wastage

The Peyto mass balance data for the early part of the series may contain some error due to glacier area change not being factored into the calculations. If this is the case, then the annual weightings of wastage for this tirne will also be slightly out. This is thought to be a very small source of error. Peyto Glacier was chosen for mass balance measurements, in part, because it was considered to be representative of this region. The analysis has highlighted the considerable variability of wastage characteristics between adjacent glaciers due to aspect and size and therefore many of the glaciers in the study area may deviate from the balance pattern observed at Peyto. However, it is relative inter annual net balance relationships, rather than absolute balance values that are of interest. Thus, the relative balances at Peyto are expected to be similar to other local glaciers that are being driven by the sarne climatic regirne. The back-casting procedure using Mirror Lake April ln snow course and Banff maximum

June to August temperature to predict wuiter and summer balance respectively, was felt

more appropriate than Letreguilly's model (1988) for the 1952 to 1965 time period, due

to it better representing the observations of Peyto recession during this tirne. However,

the net -1.24m balance modelled for this tirne period is still thought to be quite

consemative. If a larger negative balance is more appropriate for the earlier period then

the total net baiance for the 1952 to 1993 the series will be altered. This would result in

apportioning more of the bulk wastage into the pre 1966 period, therefore increasing the wastagehin yield ratio for years such as 1961 (already a high wastage year) with a cornmensurate reduction in ratio for the years following 1965.

7.2.3 Seasonal Wastage Hydrograph

The idealised wastage hydrograph constructed using an average of Young's modelled glacier melt values for the summer months of 1967 to 1974 at Peyto (1982), was not considered appropriate for this analysis, due to anomalous years (perhaps of most interest) being mis-represented. The multiple regression model using Mirror Lake snow course data, monthly average temperatures and total precipitation at Banff to estimate

Peyto melt volumes and hence monthly melt proportions for the entire basin was considered more useful than the idealised hydrograph. It better accounted for the climatic factors drïving the monthly melt proportions but could lump al1 of a summers melt and therefore wastage into one month. In table 7-2 a summary of the systematic erroa introduced and their impact to the analysis at key stages is presented. It is thought that the systematic errors introduced during the volume change calculations and upward extrapolation to the Bow River Basin above

Banff are more likely to lead to an under-estimation of the true glacier wastage value. The mass balance back-cast, on the other hand, is thought to under-estimate the glacier losses early in the time senes and over estimate later on. It is anticipated that these two areas of unquantified error will act to lessen the impact of one another in the second half of the time series, when lower flows are more evident. For example, if total glacier loss has been under-estimated, then a higher wastagehasin yield ratio would be expected in 1970.

However, if the mass balance back-cast has effectively apportioned more of the bulk wastage to the later time period after 1965, then this sarne ratio for 1970 should be reduced as more of the wastage is moved to the period pnor to 1965. Analytical Process Impact to Result Volume Change v--* Glacier Imentory Probable under-estimation If an area threshold value is of total volume change. crossed for a particuiar glacier the This method is unsuitable depth cnteria is altered and a large for small regions of glacier glacier volume change results. cover, where individual Also, melt nom small glaciers is glaciers can drastically always low due to shallow depths affect the remit. aeportioned them. -.. m.---.. Possible under-estimation Melt rates at high elevations rnay be greater than assumed in this method. Possible under-estimation DEMs are inaccurately modelled in the accumulation zone, and apparent surface growth is observed. This is thou& unlikelv. Probable under-estimation More srnall glaciers, and higher proportion of glacier cover in the basin above Banff than is evident in Hector Lake Basin. pp - -p - - Probable over-estimation The back-casting method is der 1966 and under- thought to provide a conservative estimation prior to this estimate of the net negative date. balance for 1952 to 1965. Surnrner Melt Relative timing of summer Multiple regression mode1 used is Hydrograph Mode1 wastage flows could be very empincal and was trained wrong and this mode1 can using a sample data set of eight predict al1 wastage to years only. occur within one rnonth. 1 Natural Processes 1 Flow Lags small delay of wastage Wastage flows mut transcend the flow to downstream by up river system and large lakes, to a few days where they may be detained over-estimation of total The majority of glaciers are found wastagehasin yield high up in the Bow Basin and have proportion farther to flow than most other basin water sources. In addition, water high up in the basin is more turbulent and passes through more lakes; it is therefore probably more prone to evaporative loss. Table 7-2 Summary of systematic errors in the analysis 7.3 Suggestions for Improvement

Naturally, the methods applied in any research project cm be improved. Below is a list of those areas of the analysis where steps could be taken to facilitate such improvement.

They are ranked in order of maximum benefit for minimal effort/cost (in the opinion of the author):

1. Based on the glacier volume change results cdculated in this analysis a neur set of

criteria should be developed relating glacier size, elevation bands, aspect, slope angle

and local climatic parameters to construct an alternative method for assessing volume

change of glaciers in this region through tirne.

2. The Peyto mass balance record should be re-examined to account for the omission of

an area change factor in the early pari of the time series. The new data could then be

used to re-assess the annual wastage proportions used in this study.

3. A method of relating recessional observations and net mass balance could be

investigated to better mode1 the Peyto mass balance back-cast. The aerial photography

covering Peyto Glacier in 195 1 should be stereoscopically analysed to create a DEM,

which can then be compared with the 1966 map. This should be a fairly straight

fonvard exercise, considering the amount of ground control in the area, and could

provide a reasonable idea of the net balance for the 1951 to 1966 time period.

4. The glacier depth estimations used in the Inverttory Methocl could be improved and

re-applied using the depthlslope angle relationship proposed by Paterson (1 970).

5. Seasonal glacier melt components within the river could be investigated using

isotopic tracers. If a hydrograph separation could be achieved for one summer season, a model could be created sirnilar to that above but also utilising in stream

hydrochemical tracers monitored at Lake Louise going back to the early 1970s. Such

an investigation is currently in progress.

6. Greater confidence in the timing of glacier wastage inputs wodd be provided if the

glacier extents were mapped and the analysis conducted for a time intermediate to

1951 and 1993. There is extensive aerial photography coverage of the Bow Basin in

1966. This would be an excellent year to map because it corresponds to the start of the

Peyto Glacier mass balance and Lake Louise discharge records. However, it was not

used in this analysis due to the relatively poor image quality of the photographs.

7. Investigation into improving the seasonal melt hydrograph and using a less empirical

model could be undertaken. A more conceptual model (similar to Young's (1982))

could be generated using lapse rates calculated from Banff to Peyto, snowlines

estimated using calculated melt rates, antecedent snow pack depth, hypsographic

cuves of ground cover and a glacier aredelevation component.

8. As with any analysis performed on a sample population, significant irnprovements

and greater confidence in the results would have resulted from increasing the study

area For exarnple, it would have been very useful to have carried out the volume

change calculations for the Basin above Lake Louise. This would have reduced the

extrapolation factor up to Banff fiorn 2.19 to 1.61 and would have enabled direct

cornparison with basin yields after 1965 (the start of the Bow at Lake Louise

discharge record). However, it is considered that the investment in time and resources

to cany out such a detailed study would only provide minimal retums. 9. Although the glacier extent maps for Hector Lake Basin 1951 and 1993 are felt to

have been fairly holistically reproduced, they codd have been improved if a

photogrammetic plotter had been used.

10. The photogrammetrical analysis would have been greatly improved and the DEMs

more accurately constructed if more ground control had been available. However, this

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Mean Monthiy Temperature and Total Precipitation at Banff, 1890 - 1940

4 Temperature 1 1'1 1

Mean Monthly Temperature and Total Precipitation at Banff, 1941 - 1991 A-1-2 Mirror Lake April 1" Snow Course data A-2-1 Aerial photograph data obtained covering the glacierized areas of Bow Valley above Banff, Alberta

Y& Date Fiight Line Height Lens (6") Frames 1951 3,9,51 Al 3233 20-35k' CS3705 164-5,183,185,!87-8. A 13252 163

A 13253 _i 42,47,99,103. A13321 1 32,356.

A-2-2 Air Photo coverage of Hector Lake sub-catchment

Year Da te Time Flt Line 1 Height Lens (6") Frames 1947 5,l 1,47 12:33 - A10909 1 20k' 195608 257 w I - - - 195 1 3,9,5 1 1034 A13233 20-3 5 k' ~~3705 189 1966 22,8,66 , 19:05 A19685 30k' RCSA 3 1811 5AG99 130 1971 23,9,71 18:08 A22443 44 k' RC8 AG128 6 1973 24,7,73 16:32 A23408 20k' RC8 1060 20 1977 17,8,77 20:49 A24783 34,33,42k' Rc8 UAG 310 85 1991 4,9,9I 1656 A27790 33k' RC20 47 1994 18,9,94 16:36 A27991 33k' RC30 19

A-2-3 Summary of Quality and Observed Changes Between Subsequent Images Covering the Waputik Icefield above Hector Lake.

It is difficult to discem ice extents on this image due to significant snow cover. 1951

Good image quality with ice extents well defined. Slight recession of Balfour Glacier is

apparent from cornparison with 1947 image.

Good Mage quality, ice extents generally well defhed with a littie uncertainty at the

terminus of Vulture Glacier. Ice recession is visible in ail areas of Waputik Icefield,

particularly at the snout of Balfour with a roche moutinée becoming exposed.

1971

Image quality fair but snow and haze make definition of ice extents difficult. Recession of

Balfour Glacier is noticeable as the glacier splits into two tongues either side of the roche moutinée. It is possible to distinguish slight recession in other areas of the icefield.

1973 image quaiity fair but snow and haze hamper definition. Very linle change between 1973 and 1971 imagery is evident.

1977

Good image quality but snow on 1973 image makes it difficult to gauge the ice extent change. A little recession is evident on the upper (western) side of Vulture Glacier. 1991

Good image quality but definition between ice and natural ground sornetimes difficult, particularly in the north of the image. Recession of the ice extents around Balfour,

Vulture and the Waputik ice tongue are apparent.

1993

Very good image quality with excellent ice edge definition. No real change observed since 1991 image was acquired.

A-24 Ground Control Points Around the Study Area.

Name Easting Northing Elevation (m) Hector 5522 15.29 571 1653.13 2969.36 Blaebury 5 15504.83 5725 1 03 -92 2938-27 Mcarthur 528026.34 5709800.28 30 12.03 696 127 538627.62 5729945.07 293 1.75 696 126 54 1664.39 57 193 15.00 2376.04 6961 18 546793.80 5728459.44 2709.55 6961 18b 55 1650.37 572 1264.89 2431.18 6961 19 557 154.12 5724774.30 2666.24 696 120 553933.71 5707 123.66 2455.38 Wap 547783 -28 570490 1.83 2640.24 Devon 551383.40 5 729262.60 3008.07 Willingdon 55 1892.90 5733984.70 3372.92 - - Bow 543 102.50 57 1943 1.60 2867.86 Hector Park 55 13 87.90 5713768.50 3397.9 1 Hector Lake 54 1496.60 5715491.70 1739.19 Balfour 537088.90 571260 1.30 327 1.72 Baker 52789 1.90 5723 690.50 3 172.05 Peyto Joan 53 1622.49 5726 132.49 2239.40 Peyto Kari 532053.00 5725642.80 2285.70 Peyto Liv 530450.0 1 5725024.8 1 2562.00 Peyto Nha 53248 1.40 5722533.40 2784.65 Peyto Marg 531326.17 5723948.26 2486.90 Peyto Qutn 5290 19.15 5722325.33 2982.80 A-3-1 Correspondence text fde used to georeference the 1951 and 1993 glacier DEMs in Idrisi. A41 Correlations of Peyto summer and winter mass balances with various local potential surrogate data sets. (AU snow course data were coiiected around ~ptilPt).

icoire .ation of Bow River snow course and Peyto winter balance 7 corre .ation of Chateau lawn snow course and Peyto winter balance -corre ation of Mirror Lake snow course and Peyto winter balance carre ation of Mirror Lake snow course and Peyto winter balance up to 1979 corre ation of Pipestone snow course and Peyto winter balance --- corre ation of Jasper min may jul temp and Peyto summer balance corre ation of Jasper min may jd temp and Peyto net balance (Letreguilly, 1988) corre ation of Mior lake SC & specific 2 1-2200m Peyto winter mb (1966- 199 1) -corre ation Banff av Jun- Aug max temp / summer balance corre ation Banff av May Jul max temp / summer balance corre ation Banff av Jun Aug max temp / summer balance upto 1979 corre ation Banff av annual max temp / net balance corre ation of Mistaya Q / Peyto net balance corre ation of Mistaya Q / Peyto summer balance corre ation of Mistaya Q / Peyto winter balance corre ation of Mistaya Jun av Q / Peyto winter balance corre ation of Mistaya Jun av Q / Peyto summer balance -- - - corre ation of Mistaya Jul av Q I Peyto winter balance corre ation of Mistaya Jul av Q / Peyto suIllIllet balance ---- -0.1919lcorrelation of Mistava Aue. av O/ Pevto summe~balance A42 Mirror Lake April 1" snow course / Peyto winter mass balance, 1966-1979. Correlation = 0.81. R~= 0.66.

Mhrhkt mm course &ta [mm W.&)

A43Banff average maximum June to August temperatore I Peyto Glacier summer mass balance, 1966 to 1979. Correlation = 0.81. R~= 0.65.

Lnffman mir ternp (Jun-Aug) 1 Pcyto summer baiance 1966- 1979 A-5-1 Peyto Glacier melt yields 1967-74, as modeiled by Young (1982)

- - 1 Year 1 ~ieldm 3 xlO 3 w.e. 1 - - June Juiy Aupst 'September 1967 16.3 1391 4799.1 6 144.7

A-5-2 The drivuig variables in the multiple regression melt mode1

June Julv Au ust Se tember xTemp. * A-5-3 Multiple regression output of Peyto Glacier melt yield / meteorologicai variables, for 1967-74 calculated in ExceL

'~egressionStatistics for June

,.*-- ...... ,P... p.-~~--d-~.A*.-rrr-ri---.---..i-.r-...-i idf hmofsgu--~~>qoare~~lpi~e~ _*-*--*----*--+, .ri-+------.-.-----...--.-~__.L_~..~ 0.0 1 ...... Regression-----~.------3 962034.32; 320678.1 1 r--.-.--.-.-....-..-..--..-~f 23.08 : ResiduaI 4; 555843.- 13896.07i ,.------d.-.-....--- --A---*.-----.--.-.-.---.-.*-,

...... Total 1017618.60i $oericients :Standard Error-t Statistic___ -.: iP-value iLower 95% {Upper---.-.-.-..---.95% Intercek -88227: -1.61: 0.15: -24062I- 64 1 -7 W..... --*---.----*-.-.--..--.--.-.--.. Mhor snow course i -4.56f 1.54i -2.95; 0.02; -8.9: -0.3 ,------,------.--+..------..---~-.---.*-~-,--.-...-&--.-.-.-.---. Sune ~anffTemd 76.26;- 46.77: 1.63: 0.15: -53.6 I 206.1 .-P..------.--Pd--*---~---..-,.-*.------...... -.. June Banff Preci~ 10.41 ! 2.66 i 3.91i 0.0 1 i 3.0: 17.8

Regression Statistics for JuIy ,

.- 0.99 ..--Multiple .-.----*---.---**.-..- R ...... i ...... R Square 0.99 ,.*. 4 -*----....*---.---* f ~-~*-----*t.tttttt,-.~--.---- ...... Adjusted R Square 0.97: ,- ---... -uru...... rrr~~.-__C1--__~1.__C1__C1__C1__C1__C1---.------.------..~~*~.--*~.----*-~,I.11~I--1-.*-.**-**.: Standard Error i 29 1.77: ...... ,.-~...+..--.-*-..*--*. ....~-..*...... +..--.-.-*.----~~-_..-_..--_.._..-----*-... ----*-*- ~,."..*.II.-..-...-* Observations 8: ...... l~egressionStatistics for August (without June precipitation data)

...... * 'Observations .. 8f -n*-.--+--*r..--

,-p.. ,. ..&.--.?.p- -... :----; --.--. z .....-...... id f i-F ...... --IL---:-- .--IL---:-- .-i%zmF *....-.---. 6i ,-.... Rege---:. .--7____ 57857720: 9642953-o...--- ! 217: - -.)...... -...-..-.--..-.0.05i .--+. Residual 1 i 44443------44440 j ,__.-C_C_-- ---*-.-..-*-. ' - ...... -...... Total 7i 57902 160; -4------.------a.-*-.--.*-..-* ....

August.. Banff temp i 499.52: 1 15.29: 4.33; 0.00; -965.42; 1964.46 ------. .--.--.-.-.-...----..- ~--.-~rr)rr)rr)-rr)*t.tttt--*-.--.-~----...--.- ...... August Banff ~recio i -0.20; 13-98; -0.01; 0.99; - 177-84; 177.45

Regression Statistics for September (using al1 Aug & Sep data with July precip)

Multiple R 0.99; .... --.. .- .------4 ...-*...-.---.-..*..*------*-•-*---., 0.99: !!29!E 4...---. . , .W.. -A-. Wlr....***~--.-..---.--..- ....-.--*.- Adjusted----.---. R Square i 0.99; ...... --I-....------.-.--~---*~ .-*-...---- 4 ...... ;-.----W1..----.--.*..-..-- **-.-*---. Standard Error 75.5 1 !

Sept Banff- i 1842.9 1 i 35.25; 52.29: 0.00: 169 1.26; ...... i---i------.-~___U1___U1___~1-___~1-___~1*.---.----.-.-.*- -1.. lllllll..ii.- ...... Se~tBanff D~CD ! 221.75; 6-48; 34-20; 0.00; 193.85: 249-65 A-6-1 1951 Raw stereo mode1 and re-sealed metic grid DEM data.

195 1 DEM data 195 1 DEM data Raw uncorrectcd I~etregrid co-ords Raw uncorrected l~etregrid cwrds

A-6-2 1993 Raw stereo mode1 and re-scaled mehic grid DEM data

1993 DEM data 1993 DEM data Raw uncorrectcd Raw unmmcted