Studies in Glacier Mass Balance

Andrew Mercer

Measurement and its errors

Andrew Mercer ©Andrew Mercer, Stockholm University 2018

ISBN print 978-91-7797-205-1 ISBN PDF 978-91-7797-206-8 ISSN 1653-7211

Printed in Sweden by Universitetsservice US-AB, Stockholm 2018 Distributor: Department of Physical Geography, Stockholm University To Wolter Arnberg. For a thesis that never was. The essence of description. What is and what is not. Where does a thing begin? Where does it end? And can we put it in a GIS?

Sammanfattning

Glaciärer har fått av det moderna samhället en ikonisk status och en roll som det främsta exemplet på hur naturen påverkas av klimatförändringar. Denna roll har förstärks av dramatiska bilder på kollapsande glaciärfronter och exponering av dalgångar som tidigare varit täckta av tjock is. Vår förståelse av dessa fenomens betydelse kommer från vetenskapliga studier av hur glaciärer förän- dras med klimatet, hur en glaciärs massbalans (hur mycket snö och is som kommer in och hur mycket som försvinner) påverkas av vinterns snö och sommarens värme. Det vetenskapliga intresset för glaciärer har en lång historia, med rötter i det ökande intresset för naturvetenskap som växte fram under 1800-talet, men också i behovet av att förstå varför vissa glaciärer i Alperna hade börjat sträcka sig allt längre ned från fjällsidorna in i bebodda och uppodlade dalar. Glaciol- ogiska studier från den perioden var, i likhet med andra naturvetenskapliga studier, sällan mer än beskrivande och kvalitativa. Under 1900-talet påbörjades flera försök till mer långsiktiga om- fattande kvantitativa studier, med mätningarna av Storglaciären vid Kebnekaise som det främsta exemplet. Studierna som utfördes vid Tarfala forskningsstation, i regi av Stockholms universitet, är idag världens äldsta kontinuerliga mätserie av massbalans. Det finns numera ett antal liknade mätprogram runt om i världen och alla lider av liknande problem: mätningarna innehåller osäk- erheter och fel. Dessa problem är kända av glaciologer, men ändå svåra att precisera och åtgärda. Många försök har gjorts för att förbättra uppskattningarna av osäkerheten, men med begränsad framgång och vidd. Denna avhandling utgår ifrån ett sådant försök och svårigheterna som belystes under det arbetet. Avhandlingen fortsätter sedan med en närmare granskning av felkällor och hur de inverkar på glaciologiskt arbete. Den första artikeln som presenteras i avhandlingen har sitt ursprung i ett samarbete mellan The World Glacier Monitoring Service och Tarfala forskningsstation. Under detta arbete har två olika metoder för mätning av massbalans förenats: mätning av inkommande och utgående mas- sor (snö och avsmältning) samt geodetiskt mätning av volymförändring hos en glaciär. Studien belyser behovet av nya metoder för datainsamling och förbättrad förståelse av variationer hos processerna som undersöks. Den andra artikeln i avhandlingen behandlar två olika metoder för mätning av snödjup och snödensitet. Resultaten visar att ”Ground Penetrating Radar” (GPR) är ett lovande verktyg som, med vidare utveckling, skulle kunna ge mer heltäckande data och större möjligheter för uträkning av felmarginaler. Metoden löser inte alla problem, men den är relativt lätt att implementera och den kan ersätta manuell snösondering, vilket därmed minskar arbetsbördan väsentligt. De två tidigare nämnda metoderna för beräkning av massbalans kräver en höjdmodell över glaciären i fråga. I avhandlingens tredje artikel redovisas en mätning av Storglaciärens somma- ryta, utförd med Global Navigation Satellite System (GNSS) och prismalös mätning med total- station. Tidigare höjdmodeller har mäts in med hjälp av flygbilder, en mätmetod som är mycket väderberoende och dyr. Att mäta direkt från marken som har gjorts i denna studie innebär vissa begränsningar i omfattning eftersom delar av glaciären är för svåra eller för farliga att beträda. Däremot begränsas mätningen inte av fotogrammetrins behov av igenkännbara punkter i terrän- gen. Det som är gemensamt för båda metoderna, och glaciologiska undersökningar generellt, är hur en glaciär definieras vid sina yttre gränser, framförallt vid fronten. I många fall går glaciärens is in i det moräntäcke som omringar den. Intilliggande moränformer kan innehålla isrester som inte aktivt bidrar till glaciärens dynamik eller massbalans och så kallad “dödis” kan uppstå i glaciären. Hur sådant behandlas beror på sammanhanget och eventuella användningsområden för den slutgiltiga höjdmodellen. För massbalansberäkningar är det av största vikt att den nya höjdmodellen efterliknar de tidigare fotogrammetriska modellerna i sin tolkning av form och funktion. Annars skulle glaciärens yta förändras på ett sätt som inte är konsekvent med de årliga beräkningarna av massbalansen. Problemen med mätosäkerhet och definitionen av vad som faktiskt utgör glaciärens front un- dersöks vidare i ett kapitel i avhandlingen som berör framförallt Tarfala forskningsstations program för mätningar av glaciärfronter, men gäller även andra, liknade program runtom i världen. Mätningar av glaciärfronten använts som en storskalig, logistiskt lätthanterlig substitut för mass- balansmätningar. En glaciärfront antas återspegla glaciärens massbalanstrend; om massan ökar flyttas fronten framåt, om massan minskas flyttas fronten bakåt. I stort kan detta stämma, men tidsskalan för en pålitlig mätning av denna respons är längre än det nuvarande rekommender- ade mätningsintervallet. Detta, tillsammans med förbättrade möjligheter för mätning från satel- litbilder, leder till en rekommendation att årliga fältmätningar av ett fåtal glaciärer ersätts med mätning av många fler glaciärer med hjälp av fjärranalys. Den sista artikeln i avhandlingen behandlar en felkälla som slår till ojämnt och oberoende av glaciologens skicklighet med mätinstrument. Mätningar av ackumulation, d.v.s. hur mycket snö som har fallit under en vinter, utförs så sent som möjligt på vintern. Det finns vissa logistiska begränsningar som att glaciologen måste kunna nå glaciären och att smältsäsongen börjar tidigare på lägre höjder än på högre höjder. År 2012 uppdagades ett stort fel i massbalansberäkningen då resultaten indikerade negativt smältning på sommaren. Källan till felet spårades till en stor mängd nederbörd sent på vintern, efter den sista mätningen för säsongen. Med hjälp av mycket enkla och robusta data, som lufttemperatur och en höjdmodell, kunde en potentiell avsmältning modelleras. Den modellerade smältningen jämfördes då med den uppmätta smältningen för att räkna ut en ny total ackumulation. Liknade fel kunde upptäckas i tidigare års massbalansberäkningar, men var tillräckligt små för att inte ha märkts. Problemet påverkar inte den totala massbalansen som räknas ut oberoende av vinterns ackumulation (vilket är avgörande för den här studien), men har konsekvenser för modellering av glaciärens klimatrespons. Den långa historia som massbalansundersökningar kan stoltsera med ska fortsätta, men glaciolo- gin måste gå vidare. Detta genom att anamma nya metoder, utnyttja ny teknologi och ändra praxis. Markbaserade metoder som GPR och densitetsmätningar kan kompletteras med mer avancerade fjärranalysmetoder, som t.ex. Lidar. Dissertation content

This doctoral compilation dissertation consists of a summarising text and the 4 articles listed below. I Reanalysing glacier mass balance measurement series M. Zemp, E. Thibert, M. Huss, D. Stumm, C. Rolstad Denby, C. Nuth, S. U. Nussbaumer, G. Moholdt, A. Mercer, C. Mayer, P. C. Joerg, P. Jansson, B. Hynek, A. Fischer, H. Escher-Vetter, H. Elvehøy, and L. M. Andreassen, The Cryosphere, 7, 1227–1245 (2013). DOI: 10.5194/tc-7-1227-2013 II A comparison of seismic and radar methods to establish the thickness and density of glacier snow cover Adam D. Booth, Andrew Mercer, Roger Clark, Tavi Murray, Peter Jansson, Charlotte Axtell, Annals of Glaciology, 54(64), 73–82 (2013). DOI: 10.3189/2013AoG64A044 III A DEM of the 2010 surface topography of Storglaciären, Sweden Andrew Mercer, Journal of Maps, 12(5), 1112–1118 (2016). DOI: 10.1080/17445647.2015.1131754 IV Estimating unaccounted, late season snow accumulation on Storglaciären. Im- plications for glacier mass balance programmes Andrew Mercer, Peter Jans- son In preparation

Author contributions

The contributions from listed authors are divided as follows for each article. I All authors participated in workshop, M. Zemp was lead author. A. Mercer and others contributed with data, processing and comments II A. Booth was ﬁrst author. A. Mercer contributed with data collection, data processing and comments. III Field work was designed and performed by A. Mercer. Analysis, study and author- ship by A. Mercer. IV The idea for the study arose in discussion between P. Jansson and A. Mercer. Field work, data processing, model design and modelling was carried out by A. Mercer. A. Mercer was ﬁrst author. P. Jansson was second author.

Contents

1 Introduction 1 1.1 Perspective ...... 1 1.2 Intention ...... 2

2 Glaciers and mass balance 3 2.1 Describing a glacier ...... 3 2.2 Mass Balance ...... 4 2.2.1 Internal mass balance ...... 6 2.2.2 Basal mass balance ...... 7 2.2.3 Surface mass balance and the glaciological method of mass balance measurement ...... 8 2.2.4 The geodetic mass balance method ...... 10 2.2.5 The hydrological mass balance method ...... 11 2.2.6 Energy balance models ...... 11 2.3 From point to surface ...... 12 2.3.1 An alternative ...... 14

3 Glacier front surveys 15 3.1 Tarfala Research Station front survey programme ...... 15 3.2 Glacier front fluctuation surveys ...... 16 3.2.1 Defining the front from a theoretical basis ...... 16 3.2.2 Identifying the front in the field ...... 18 3.2.3 Surveying the front in the field ...... 20 3.2.4 Surveying the front in remotely sensed images ...... 24 3.2.5 Calculating change ...... 25 3.3 Consideration of the Swedish data registered with W.G.M.S...... 26 3.3.1 Data quality ...... 26 3.3.2 Data presentation ...... 26 3.3.3 Trend analysis ...... 27

4 Presentation of papers 35 4.1 Reanalysing glacier mass balance measurement series. The identiﬁcation and classiﬁcation of errors ...... 35 4.2 A comparison of seismic and radar methods to establish the thickness and density of glacier snow cover ...... 36 4.3 A DEM of the 2010 surface topography of Storglaciären, Sweden. A new baseline for surface mass balance calculations ...... 36 4.4 Estimating unaccounted, late season snow accumulation on Storglaciären. Implications for glacier mass balance programmes ...... 37 5 Discussion 39 5.1 Front Survey Programme ...... 39 5.2 Measurement error and geostatistics ...... 41 5.2.1 Technical replicates ...... 41 5.2.2 Entity replicates, stationarity and geostatistics ...... 44 5.2.3 Other work ...... 45 5.3 Surface-wide approaches to mass balance estimation ...... 46 5.4 Accumulation modelling ...... 47 5.5 Concluding remarks ...... 48 References ...... 60

Appendices 61

A A quick overview of a glacier 61

B Glacier front retreat rates 63 1 Introduction

Glaciers as a social construct are regarded as the archetypal representation of climate change but this status derives more from scientific investigation of how glaciers interact with climate (e.g. Zemp et al., 2008; Vaughan et al., 2013) than from dramatic images of glacier front retreat and calving icebergs. This interaction is expressed most directly through mass balance (e.g. Greene, 2005; Raper and Braithwaite, 2009), how much ice is gained or lost. Various glaciological studies measure rates of mass accumulation and ablation (Holmlund et al., 2005; Thibert et al., 2008; Huss et al., 2015; Andreassen et al., 2016), others measure the response of glaciers to changes in these components, often through tracking the fluctuations of glacier fronts (Haeberli et al., 2000; WGMS, 2012). The data from many such studies are the foundation for predictions and models of glacier response to climate change (Hock, 2005; Radić and Hock, 2011; Braithwaite, 2009; Hae- berli et al., 2007). These studies, relying on data collected in the field, are prone to errors of various types and size (Carroll, 1995; Jansson, 1999; Cogley, 1999; Thibert et al., 2008). The work in this thesis is an examination of some of these errors. From surveys of snow depth, melt and elevation to the determination of exactly where a glacier front is, knowledge of what has been measured and just how well is shown to be easy to conceptualise but all the more difficult to attain. The following chapters and papers will describe a glacier from a mass balance perspective, how mass balance surveys are performed, how glacier front surveys are performed and how errors in methodology and calculation enter into all parts of these processes.

1.1 Perspective

It is almost obligatory to introduce a glaciological study with a reminder of some basic facts about how much glacier ice may be found and what would happen to the natural and human environment should that ice melt. There are numerous estimates of just how much of the Earth’s surface is covered by ice but the Intergovernmental Panel on Climate Change (IPCC) gives in Vaughan et al. (2013) a summary table based on a review of previous work in the ﬁeld. Approximately 0.5% of the Earth’s surface is covered by “small” glaciers but 9.5% by the ice sheets of Antarctica and Greenland. Should Antarctica melt it would produce 58.3 m of sea level rise, Greenland would result in 7.36 m of sea level rise and the small glaciers, that is those that are of concern in this work, would give 0.41 m of sea level rise. Clearly, should the ice sheets melt they would have a far greater impact than would other glaciers. But Vaughan et al. (2013) also point out that these small glaciers are currently contributing approximately 50% more to sea level changes than the ice sheets and have, throughout the 20th century, stood for an even greater percentage. The impact of climate change on glaciers and their subsequent retreat leads to many other consequences. Proximal to the glacier, micro-climate is altered and ground cover changes as soils are exposed. But more important, at least from a human perspective, is the eﬀect on hydrology. The storage of winter time precipitation for release during warm

1 summer months is of huge importance in many places, such as the Himalayas, the Alps or the Andes (Jiménez Cisneros et al., 2014). Current melting is also increasing the risk of sudden outburst floods from glacial lakes and moraine dammed lakes (Jiménez Cisneros et al., 2014). These concerns are perhaps modern and have entered the public domain only in recent years but scientific interest in glaciers, their response to climate forcing and the consequences thereof has its roots in the efforts of scientists of the18th and 19th centuries to understand features such as erratics and moraines in green and forested landscapes, evidence in Sweden of uplift of the land and the advance of glaciers into Alpine farm- land (e.g. Lyell, 1835; Agassiz, 1838; Agassiz and Bettannier, 1840; Tyndall and Huxley, 1857). During the 20th century research and monitoring has been more systematic and synoptic, if not panoptic. In the mid 1940s the Tarfala Research Station was established in northern Sweden, where yearly measurements of the surface mass balance of Stor- glaciären have been performed since 1946, constituting the World’s longest continuous mass balance series (Holmlund and Jansson, 1999). Programmes and organisations such as “Global Land Ice Measurements from Space” (GLIMS) and “World Glacier Monitor- ing Service” (WGMS) have allowed researchers to collect together data from across the globe and aid the transition from case studies to a synoptic understanding of systems that affect the planet as a whole (Haeberli et al., 1989; Raup et al., 2007). These programmes have collected direct measurements of surface mass balance but also data on proxies such as equilibrium line elevation (see figure A.1) and fluctuations in glacier front position. This thesis looks at the measurement of the surface mass balance of small glaciers and of their fronts. More specifically, it examines how programmes such as the Storglaciären mass balance programme, WGMS and others gather and unify data that then serve as a basis for models of how the cryosphere may be expected to react to climate change.

1.2 Intention

The work presented in this thesis examines some of the problems, methods and error sources that the study of glacier surface mass balance entails. There is also an examination of glacier front survey methods, which have long acted as a substitute for mass balance surveys when monitoring glacier response to climate change. This study is by no means exhaustive and omits to address many fundamental issues. It does not intend to provide universal nor novel nor unique solutions. Instead, the aim of this work is to improve awareness of basic and fundamental practices which will improve data quality and usability.

2 2 Glaciers and mass balance

2.1 Describing a glacier

In the authoritative glaciological text by Cuffey and Paterson (2010) glaciers are defined as “all ice bodies originating as snowfall”. According to Zemp et al. (2008) a glacier is “a mass of surface ice on land which flows downhill under gravity”. It is generally considered necessary for ice thickness to be at least 30 m for a body of ice to be called a glacier and by this criterion alone many ice bodies, such as the Kebnekaise massif’s “Sydtopp”, are glaciers, but the characteristic trait of flow, brought about by internal deformation of the ice, is essential to almost all glaciological studies and so must, by necessity, exclude these stationary masses. Thus a glacier is a body of ice that is thick enough to deform under its own weight and flow downhill. This thesis begins with this very basic definition because glaciology is the study of the causes and consequences of glacier flow. However, the work herein does not examine ice dynamics nor kinematics directly but instead focusses on mass balance: how much snow and ice goes in and how much goes out, where and how. Glacier front response is itself an expression of ice dynamics and may be regarded as the sum of all processes occurring on, in and under the glacier (Nye, 1952; Paul, 2010; Roe, 2011; Roe and Baker, 2014; Jamieson et al., 2015; Vieli, 2015; Hooke, 2005), over a period of time referred to as the “response time” (Jóhannesson et al., 1989; Bahr et al., 1998). A direct connexion between mass balance and glacier front position does not exist (Hooke et al., 1983, 1989; Hooke, 2005; Roe and Baker, 2014). Factors such as downwasting, kinematic waves and pinning all influence the response of the front (Harrington, 1952; Oerlemans and Van de Wal, 1995; Jansson, 1996; Joughin et al., 2008; Berthier and Vincent, 2012; Muto and Furuya, 2013). But generally fluctuations of front position reflect the long term mass balance of the glacier (Nesje et al., 1995; Holmlund et al., 1996). Returning briefly to the flow of ice, it is driven by an imbalance in the forces acting on it. A quick review of elementary physics gives us:

Force = mass × acceleration If acceleration is that due to gravity then:

Potential Energy = Force × height The immediate cause of ﬂow is the deformation of ice due to an uneven distribution of force and this is in turn brought about by an uneven distribution of potential energy. From the above equations it may be discerned that the distribution of mass, and its position in the landscape, i.e. elevation, drives the motion of glaciers.

Mass balance creates the glacier.

3 Before embarking on a description of mass balance processes it may be appropriate to quickly review the different categorisations of glaciers as these reflect dominant conditions that interplay with mass balance. There are two main ways to categorise glaciers: by form and by process (e.g. Hubbard and Glasser, 2005; Cuffey and Paterson, 2010). Glaciers range in size and form, from hanging glaciers in niches to ice sheets. Small, alpine, valley type glaciers are constrained by the underlying and surrounding topography; they sit in valleys. Ice caps and ice sheets are large accumulations of ice that sit atop and spread out over mountains, valleys and planes. These are, in their central and thick- est areas, largely unconstrained by the underlying topography but at their outer edges, towards their fronts and outlets, flow with the terrain (e.g. Kleman et al., 1997; Hub- bard and Glasser, 2005; Cuffey and Paterson, 2010; Lindbäck et al., 2014; Putnin, š and Henriksen, 2017). Whilst valley glaciers may influence their immediate micro-climate (Jóhannesson et al., 1989; Christensen et al., 1998; Raper and Braithwaite, 2009; Oerlemans, 2010) large scale climate patterns are determined by their surroundings, e.g. topography and distance from ocean waters. Ice sheets, and to some degree ice caps, have a far greater influence on the climate in which they exist. Ice sheets raise surface elevation across large areas, creating highland plateaus isolated from the influences of ocean currents. The interior of Antarctica for example is cold but, in terms of precipitation, dry. A description categorising by process intersects with mass balance processes, but only the categories are introduced here. High polar regions tend to contain cold ice, that is, ice below the pressure melting point, 0◦ C at the surface. Mid-latitude and equatorial glaciers are generally warm or “temperate”. This refers to the ice being at melting point throughout the glacier, with perhaps seasonal exceptions in the snow pack and exposed ice. In sub-polar regions the idealised categorisation places polythermal glaciers between these two (Irvine-Fynn et al., 2011). There are several forms of polythermal glacier but generally they are bodies of temperate ice that contain extended zones of cold ice, either as remnants of a previous regime or as a consequence of ice dynamics and/or local energy balance (e.g. Hutter et al., 1988; Blatter and Hutter, 1991; Pettersson et al., 2007). In reality, most valley glaciers exhibit some form of polythermal regime, if only at certain times of the year (which disqualifies them as truly polythermal, Irvine-Fynn et al., 2011). This thesis focusses on temperate and polythermal alpine glaciers and more specifically Storglaciären, a polythermal valley glacier in northern Sweden, a map of which is shown in figure 2.1. Furthermore, it is the surface mass balance, as explained in section 2.2, its measurement and study that is examined.

2.2 Mass Balance

There have been several attempts to codify both the methodology and the terminology of mass balance. Works such as Schytt (1962), Østrem and Stanley (1969), Mayo et al. (1972), Østrem and Brugman (1991) or Kaser et al. (2003) outlined methods for field studies and calculation of surface mass balance and much of this work is still used to this day. The terminology of glacier mass balance has undergone changes. The work in Anonoymous (1969) attempted to set out a standard vocabulary and shorthand for such work, but after some years it became apparent that the diverse needs of researchers using new and individual solutions to solve specific cases had led to a muddying of terminology usage. It was also clear that Østrem and Brugman (1991) was in need of some updating, if only due to a lack of availability. Therefore the “Glossary of glacier mass balance and related terms” (Cogley et al., 2011) was collectively produced. In this the terminology of mass balance and its usage is defined and standardised and it is this that will be used

4 5

Figure 2.1. Storglaciären and its surroundings. This map is an adaptation of that published in connexion with paper III. The map indicates the locations of ablation stakes and snow density pits as used by the Tarfala Research Station’s mass balance programme. here. From Cogley et al. (2011) we get the following:

C + A = B, (2.1) where C is accumulation, A is ablation and B is net balance (the use of the term “net” here is not entirely consistent with Cogley et al. (2011) in which the term is deemed largely superfluous as balance is generally assumed to refer to the condition after all ad- ditions and subtractions have been made). The terms “accumulation” and “ablation” cover many processes that add and remove mass; snowfall and melt are but two of these. Whether a glacier is growing or shrinking is determined entirely by the net balance (B) but to understand this response to climate forcing (if indeed changes in area or volume are responses to climate, e.g. Roe and O’Neal, 2009; Roe, 2011) the components of accumulation and ablation must be investigated separately. The hydrological response of the glacier, i.e. how much precipitation is stored and released, can only be understood by measuring how much mass has been received and how much is released rather than simply stating that a glacier has grown or shrunk (Jansson, 1996; Skidmore and Sharp, 1999; Dyurgerov, 2003; Harrison et al., 2005; Huss et al., 2008b; Irvine-Fynn et al., 2011; Dahlke et al., 2012). Accumulation and ablation may occur throughout a glacier but tend to vary in their dominant form. Typically mass balance is divided into three types: surface, internal and basal. These receive the subscripts sfc, i and b according to Cogley et al. (2011). Surface mass balance is by far the most dominant part of glacier mass balance, at least for the type of glacier studied here (Kaser et al., 2003; Fischer, 2011; Andreassen et al., 2016). Schneider and Jansson (2004) find internal accumulation within the snowpack to be significant but this occurs often within or at the lower boundary of the layer under investigation. Some glaciers may experience large scale ablation at their bases due to geothermal heating (Beedle et al., 2014; Zemp et al., 2010) but accretion of ice at the base may also occur (Souchez and Lorrain, 1978; Tison and Lorrain, 1987; Cuffey et al., 2000; Bougamont and Christoffersen, 2012). But in general, and for most land terminating, valley glaciers it is surface mass balance that dominates. In paper I of this thesis internal accumulation is, in places, used as a correction to surface mass balance calculations but commonly “mass balance” means “surface mass balance”. This usage is of course discouraged by Cogley et al. (2011) and for good reason. In paper I the geodetic mass balance method is used and this method intrinsically includes internal and basal mass balances, albeit with certain caveats discussed later. The hydrological method also considers mass balance as a whole and is indeed incapable of distinguishing between surface, internal and basal mass balance. In this work the term “surface mass balance” will be used except when referring to specific instances where it is customary to use the briefer form, such as when referring to the Tarfala Mass Balance programme (e.g. Holmlund and Jansson, 1999, and paper II). One shorthand that will be adopted is the use of the word “glacier” to mean mid-latitude and sub-polar, land terminating, polythermal/temperate valley glaciers. The following sections give summary descriptions of mass balance components and the methodologies used to measure them.

2.2.1 Internal mass balance There are various sources of internal accumulation and ablation. They are all diﬃcult or, by all practical standards, impossible to measure. This problem is often dealt with using energy balance models (e.g. Reijmer and Hock, 2008) and according to Oerlemans (2010)

6 is of significance only for colder glaciers or higher elevations on mid-latitude glaciers. A temperate snow pack will not allow refreezing except at the interface with underlying ice, where it may form superimposed ice. In Schneider and Jansson (2004) internal accumulation, as studied on Storglaciären, is restricted to melt water refreezing in snow and firn layers below that measured by the current season’s surface mass balance survey. This water comes from melt occurring at the surface of an otherwise cold snow pack/firn layer. Should this melt water refreeze at the interface with the previous summer’s surface it becomes superimposed ice and is accounted for in surface mass balance measurements. Water that percolates further before refreezing must be estimated from such samples as are available and energy-based theoretical calculations (Schneider and Jansson, 2004). However, work by van Pelt et al. (2016) suggests that water percolating several metres into firn may remain unfrozen throughout the winter. van Pelt et al. (2016) also consider the secondary effects of melt water refreezing in the snow pack, how the process itself alters stratigraphy and thus heat flow as well as albedo. These secondary effects have complex feedbacks into surface mass balance. Other sources of internal accumulation are water entering the system of englacial channels, via moulins and crevasses. Should such water lose enough energy to cold ice it will freeze onto the conduit carrying it. Such accumulation tends to occur below the firn layer and does not feed back directly to the surface. Some ablation may occur just below the glacier surface due to incoming radiation (Bintanja and Van Den Broeke, 1995; Cuffey and Paterson, 2010) but this will generally be recorded as surface ablation. More commonly internal ablation arises due to strain heating induced by ice deformation and by heat transfer from flowing water. Both of these derive their available heat energy from the loss of potential energy due to mass flowing from higher elevations to lower elevations (Cuffey and Paterson, 2010). Melt is dependent on the pressure melting point, the explanation of which can be somewhat confusing. To begin with, temperate ice is ice at the pressure melting point. The temperature at which ice melts is determined (in part) by pressure; as pressure increases the temperature at which it melts decreases (up to a point). A temperate glacier is therefore one in which temperature decreases with depth but at a rate that maintains the ice at pressure melting point. Any heat that might raise the temperature above the pressure melting point goes into melting ice, producing water that maybe held by the ice or move through it, following the hydrological gradient. Temperate ice is there because it hasn’t melted. Note that internal accumulation as used by Schneider and Jansson (2004) is that which is commonly applied as a correction to surface mass balance.

2.2.2 Basal mass balance The first component to mention here is that of geothermal heat flux which can, under typical conditions, be expected to produce ≈ 5 mm a−1 of melt (Cuffey and Paterson, 2010), though this may be significantly higher in geothermally active regions. This component is difficult to measure directly but may be calculated from measurements of heat flux in the surrounding bedrock. Except for rare and small contributions from inflowing streams basal accumulation and ablation otherwise are determined by ice dynamics. There are different specific mechanisms such as accretion and regelation but in essence changes in pressure and heat transfer rates are key. Regelation occurs at the base where ice slides over a small protrusion. The upstream ice experiences an increase in pressure, requiring the ice to either become cooler or melt. The phase transition from ice to water requires energy (heat) thus cooling the ice. Water passes around the protrusion to the leeward side where the ice experiences relatively

7 lower pressures and the water refreezes to the ice (e.g. Lliboutry, 1993; Hubbard and Sharp, 1993; Cuffey and Paterson, 2010). This would not seem to contribute one way or another to mass balance and is generally invoked in discussions on basal sliding and entrainment of debris (e.g. Alley et al., 1997) but cannot be entirely discounted. The scale of this phenomenon is limited. The size of protuberance does not exceed 1 m as heat flow through anything larger would be too slow; under such circumstances the melt and freeze processes become disconnected and modelling the relative scales considerably more complicated. Though in sum the ice mass will have been heated slightly. Accretion at the base of terrestrial ice may occur due to pressure changes experienced by supercooled water (Alley et al., 1998; Lawson et al., 1998). Water that has melted under pressure remains in thermal equilibrium with the surrounding temperate ice, but should the ice overburden pressure reduce, the pressure melting point increases (that is the temperature at which ice melts increases towards 0◦ C) and the water is supercooled, relative to its surroundings. The water then freezes onto the base (Alley et al., 1998), or if it should emerge from the ice near the front form an artesian vent (Tweed et al., 2005). This mechanism, of overburden pressure increase and decrease, is most commonly associated with overdeepenings in the substrate. Ice flows downhill but is then forced to flow uphill, increasing its potential energy and removing heat. More importantly the upper surface generally does not mimic this upward flow, instead it continues to slope downward and thus the ice thickness is reduced and so pressure is reduced (Alley et al., 1998). Water at the base may enter the subglacial system from the surface, via moulins and crevasses and is thus a net accumulation upon refreezing or it may come from melt due to geothermal heating, pressure melting, friction, conversion of potential energy to heat energy or any combination of these. Melting and subsequent sub- and englacial transport from the glacier without refreezing is an ablation component. Its existence is crucial for basal sliding and rates of glacier flow (e.g. Jansson, 1995, for a case study on Stor- glaciären).

2.2.3 Surface mass balance and the glaciological method of mass balance measurement Surface mass balance and the glaciological method of mass balance surveys may effi- ciently be described jointly. The glaciological method is based on estimates of mass balance at discrete points across the glacier. These point balances are given a lower case letter in Cogley et al. (2011) distinguishing them from the glacier-wide upper case form. At a point on the glacier an ablation stake is drilled into the ice or firn (see e.g. Østrem and Stanley, 1969; Kaser et al., 2003; Hubbard and Glasser, 2005, for details of practical implementation). Stakes move with the ice down glacier as the ice mass flows downhill but stakes also submerge into the ice as mass is added at the glacier surface and emerge from the ice as ablation removes mass, a process referred to as “emergence” (e.g. Pope et al., 2016). The top of the stake is a reference height for subsequent measurements of the glacier surface. In figure 2.2 the left hand panel illustrates how mass balance may be estimated from two measurements. The first measurement is performed at the end of the glacial year, the end of the ablation season. The height of an ablation stake above the summer surface is measured. At the end of the next glacial year the measurement is performed again and the height difference gives the volume of change. This volume is combined with appropriate densities for snow or ice, giving mass change, either ablation or accumulation. This single survey is sufficient to provide an estimate of surface mass balance at a point, bsfc. In order to estimate the size of the accumulation and ablation components one additional survey is needed, that for end of season accumulation, csfc.

8 Figure 2.2. Mass balance surveys. Mass balance may be measured by a single survey at the end of the ablation season, referencing the height of an ablation stake above the previous ablation surface. If snow depth is surveyed at the end of the accumulation season then, in combination with the end of ablation season survey, accumulation, ablation and mass balance can be estimated (see eq. 2.2).

Snow depth is typically measured using both the ablation stake data and a denser network of snow probing points. This is done using a tool such as or similar to an avalanche probe (essentially a long, thin metal rod). This measurement does not use the stake top as a reference (which would be rather circular) but instead relies on identifying the previous summer surface by sensation through the snow probe. Snow density is measured either by digging a snow pit and sampling down through the snow or by using a bore and extracting a snow core (e.g. Østrem and Brugman, 1991; Conger and McClung, 2009; Brown et al., n.d.; Cogley et al., 2011). The bore can reach greater depths for less labour but is less precise and less accurate due to losses of material during extraction and compaction of material during boring. From the density measurements a depth–density proﬁle is calculated and this function is then used to transform snow depth readings into mass estimates, or more practically, metres of water equivalent (m w.e.) (e.g. Østrem and Stanley, 1969; Kaser et al., 2003; Cogley et al., 2011). Ablation asfc is calculated by rearranging the point form of equation 2.1

asfc = bsfc − csfc (2.2) These estimates of surface mass balance at discrete points are then inter- and extrapolated to glacier-wide estimates. The method of inter- and extrapolation varies and can significantly affect the result; these issues will be discussed later. For an overview and discussion of some error sources in both surveying and calculation see Jansson (1999). There are further considerations that are relevant, especially with regards to paper IV: the definition of “end of season”. Firstly there is the question of timing; surveys may adhere to one of several systems. In the fixed date system surveys are performed on the same date each year, or corrected to this date. The floating date system is similar but with-

9 out the correction should the survey date not be practical. The stratigraphic system relies on identifying the end of season surfaces and measuring csfc and asfc relative to these. It also relies on surveys being performed as one season transitions to the next. This implies that the period for one complete cycle diﬀers from a calendar year and therefore the use of “annual” to describe the mass balance is discouraged in favour of “net”. The combined system is, as the name suggests, a combination of the stratigraphic with either of the date systems. According to Cogley et al. (2011) it is variously implemented (the authors also imply that it is not in all cases entirely clear just how). The second consideration is that each season has been named after the dominant component but it should be remembered that ablation occurs in winter and some accumulation may occur in summer. For this reason it is generally held that csfc should be replaced by bw and asfc by bs for most surface mass balance programmes. These terms refer to winter balance and summer balance (Cogley et al., 2011).

2.2.4 The geodetic mass balance method The geodetic method of mass balance estimation relies on what may feel like the most intuitively obvious approach: the accurate measurement of elevation change. In the glaciological method stake heights are measured, this height being the distance between the top of the stake and the glacier surface. With modern instrumentation it is tempting to assume that the time consuming job of drilling stakes may be abandoned and the height simply measured with survey quality Global Navigation Satellite System (GNSS). The problem with this is that it takes no account of emergence velocity, the fact that as ice ablates at the surface more mass flows in to balance the loss. In figure 2.2 the stake tracks with this flow of ice and so the distance to the top reflects the lost volume at the surface rather than a change in absolute elevation. The geodetic method however measures exactly this change in elevation (Magnússon et al., 2016; Andreassen et al., 2016). It measures the entire glacier rather than measuring exchanges at the surface. The flow of mass down glacier occurs as forces are balanced; as mass is removed from the surface it is replaced from beneath by the flow of ice from the up glacier (accumulation) areas. In for example Cogley et al. (2011) point mass balance (b) is illustrated as a column extending down, through the glacier, where fluxes in and out of this column are components of the point mass balance. These fluxes are not accounted for by surface mass balance methods but as fluxes are controlled by mass distribution throughout the glacier they reflect internal and basal accumulation. By measuring the elevation of the glacier surface on two separate occasions total volume change can be measured. This volume change must be converted to a change in mass by defining what the volume consists of: ice, firn, snow or air (e.g. Rolstad et al., 2009; Huss, 2013). A glacier retreating at the front towards an unchanged equilibrium line would invite a very simple conversion where volume lost above the equilibrium line is snow and below is ice but this does not take into account the flow of ice within the glacier. More commonly for the geodetic method “Sorge’s Law” is applied. In essence what this law implies is that the density profile of the glacier is entirely depth dependant and that any volume change can be assigned to ice. This assumes that accumulated snow and firn densities and depths tend towards average values (for the glacier in question) with time (Cuffey and Paterson, 2010; Bormann et al., 2013). Its original usage was limited to high polar, cold glaciers with dry snow packs but has been extended for usage on other glacier types for use in geodetic mass balance surveys (Cogley et al., 2011). Without the use of Sorge’s Law field surveys of cover, depth and density would be required. The combination of this simplification with the relatively poor precision of aerial photographic digital elevation models (DEM) (e.g. Rolstad et al., 2009) has meant that the geodetic method

10 has not been used on a year by year basis but instead applied over multi-year measurement periods, increasing the signal to noise ratio.

2.2.5 The hydrological mass balance method As previously stated, one of the most important consequences of changes to glacier size is the effect on hydrology (Fountain, 1996; Arnold et al., 1998; Konz and Seibert, 2010; Dahlke et al., 2012). The connexion between downstream hydrology and glacier size is exploited in the hydrological method of glacier mass balance (see e.g. Sicart et al., 2007; Tangborn et al., 1975; Kaser et al., 2003). In this method, run off from a drainage basin is measured downstream of a glacier. This volume is compared with the theoretical run off attributed to contemporary precipitation and snow melt. The difference between these two is then assigned to mass balance. However, there are complicating factors in this calculation. Modelling precipitation and snow melt of glacierised basins is not trivial (Hock et al., 2005; Dahlke et al., 2012). But the glacier itself causes fluctuations in discharge due to water storage within it (Jansson et al., 2003; Hock et al., 2005). Water may be stored or delayed through various mechanisms and at different time scales ranging from hours to years. For these reasons the hydrological method is generally not the primary source of glacier mass balance data.

2.2.6 Energy balance models Surface mass balance may also be estimated from measurements and models of weather conditions over the glacier. This approach attempts to combine available weather data with physical and/or statistical models of how such weather contributes to accumulation and ablation. Accumulation modelling is a greater challenge as not only must the amount of direct precipitation be modelled but also its redistribution by wind (Dadic et al., 2010; Jaedicke and Gauer, 2005; Réveillet et al., 2016; Huss et al., 2008a). Both direct precipitation and redistribution are chaotic, that is to say they are deterministic but very small perturbations or changes in initial conditions can create large differences in the outcome. Turbulence can be modelled statistically and it is well understood how topography influences air flow but as snow may be added or removed, thus changing topography dynamically, models rapidly diverge from reality. Add to this the problems of predicting weather and then predicting what may happen as a weather pattern passes up, over and down a mountain it becomes evident that accurate modelling is very demanding (Oerlemans, 2010; Matthews et al., 2015). Many mass balance models rely on greatly simplified accumulation components (Oerlemans, 1992, 2010) or field data instead. Ablation tends to be more approachable as it correlates more strongly with available energy and as a major energy source is air temperature, modelling temperature change according to the adiabatic lapse rate can account for a good portion of ablation (Hock, 1999; Hock and Holmgren, 2005; Hock, 2005; Huss et al., 2008a). How detailed this model is varies greatly as do the models’ dependence on data. In general the following from Bamber and Payne (2003) summarises energy based ablation model components:

Q0 = S ↓ (1 − α)+L ↓−L ↑ +QH + QL + QR (2.3)

Q0 is the net energy flux at the surface and determines the total amount of energy available for melt (Pellicciotti et al., 2009). S ↓ (1 − α) is the net incoming short wave radiation, the first term is the total incoming radiation which is then attenuated by the reflectivity of the surface at the wave lengths in question. The term α is albedo, the re- flectance of a surface, hence (1 − α). Surfaces typically have different albedo values for

11 different wavelengths of incoming radiation but it is assumed that only albedo for short wave radiation is sufficiently different from zero to be of importance. More problematic is that albedo varies across a glacier by surface type (snow, ice, debris) and by angle of incidence. L ↓ is the long wave radiation received by the glacier from e.g. clouds and valley walls. All matter at a temperature above 0 K emits radiation and at temperatures found on Earth the wavelength of this radiation is infra-red, that is “long wave”. L ↑ is then the long wave radiation emitted by the glacier, the ice having a temperature above0K.QH is the sensible heat flux from the air and is strongly influenced by turbulence at the boundary between the air and glacier but also in the column of air above. Measuring this is prone to errors and equipment failures (Bamber and Payne, 2003) but modelling also requires data and rather complex calculations (Hock, 2005). Latent heat flux QL is similarly dogged by complications but for both sensible and latent heat fluxes the roughness length of the surface, how uneven a given parcel of air experiences a surface as being, is the greatest error source (e.g. Munro, 1989; Brock et al., 2006; Irvine-Fynn et al., 2014). QR, the heat flux supplied by rain is regarded as insignificant in all but extreme cases. As stated earlier, energy balance models may be able to consider internal accumulation or, at least that part occurring in or near the snow pack, and for this reason may be considered as a corrected surface mass balance. The rather complex and data demanding energy balance model can be replaced by a hugely simplified model that relies on temperature data and coefficients for converting temperature to melt: the degree-day model. From Hock (2003) the following equation is taken: n n + M = DDF T Δt (2.4) i=1 i=1 The term on the left is the sum of melt over the period in question, i.e. n time intervals. Δt is the length of a time interval, defined in days, and T + is the average of positive temperatures in ◦C experienced during a time interval. These temperatures are summed to give “positive degree days” (sometimes known as the “Combs number”, Seguinot (2013)) and multiplied by the degree day factor, DDF. The degree day factor is dependent on surface type, i.e. snow, firn or ice, but varies from case to case. Hock (2003) reviews many previous studies and provides a table of measured values. It should be noted however that these estimates vary greatly, from glacier to glacier as well as through a season but above all from study to study. Despite this the models are considered to be reliable and the simplification actually removes error sources due to the difficulty of modelling turbulent air flow and roughness. Paper IV uses a degree day model for calculating theoretical ablation and then com- pares this with measured ablation.

2.3 From point to surface

Common to all the methods discussed above is the need to inter- and extrapolate data from discrete point measurements to a continuous surface. The term “continuous” is used here in the not entirely mathematically correct sense, but rather a raster grid of high enough resolution to appear continuous for the user’s needs. Much work has been done comparing diﬀerent methods of geospatial data inter- and extrapolation (e.g. Chaplot et al., 2006; Myers, 1994) and there have been several attempts to analyse the relationship between point measurements of mass balance and glacier wide

12 mass balance. Whilst work such as Jansson (1999) looks at errors in point estimates, Jansson and Pettersson (2007) explored the correlation of individual pixels in maps of the surface mass balance of Storglaciären with the glacier wide mass balance. These two approaches are quite different. The first asks how reliable are the field data; the second, how representative can any individual point be? In contrast to work such as Lliboutry (1974); Fountain and Vecchia (1999); Cogley (1999), in which surface mass balance components are determined by elevation only, Jansson and Pettersson (2007) highlight the spatial variability across the glacier. Cogley (1999) however finds that ablation stakes are, spatially, highly correlated and that the effective sample size of the surveys analysed was close to n =1. The analysis focussed on determining standard error rather than the representativeness of any particular stake or distribution of stakes but still suggests that a large number of stakes does not improve performance. In common with Fountain and Vecchia (1999), the study from the outset simplifies its analysis by claiming that surface mass balance is determined almost entirely by elevation and investigates therefore only this variable. This is problematic, for reasons discussed in the description of kriging below. There are many methods available for such work but it would be an unnecessary indulgence to explore them in detail; therefore, the only methods introduced here are: Nearest Neighbour, Triangulated Irregular Networks (TIN), Inverse Distance Weighting (IDW), kriging and Geographically Weighted Regression (GWR). The simplest method of filling in data at an unmeasured location is nearest neighbour, i.e. find the spatially nearest known value and assign it to the point in question. This is similar to the method historically used to assign values according to elevation bands and by expert knowledge of the glacier (e.g. Østrem and Stanley, 1969). A vector format that can reduce data file size, especially for surfaces containing areas of different data densities, is the TIN. This method interpolates linearly between measured nodes and renders a surface as triangular facets; any point on the surface of a triangle is a simple linear interpolation between the three nodes of the triangle. TINs are valued for their simplicity and the fact that interpretation of a value given for any point is straightforward. A major drawback is that it is incapable of extrapolating outside the surveyed area. Another, mi- nor, drawback is that, if the survey data density is not great enough, the surface has an aesthetically less pleasing, angular look. Inverse Distance Weighting solves both of these problems. When calculating a value on the face of a TIN only the values of the three nearest measured points are used; IDW can use many more, sometimes all, measured points, weighting them according to distance from the new point. Points nearer have a greater influence on the outcome than those farther away. IDW tends towards the mean and often gives rise to “Mexican hats” or “funnels” around data points as the interpolated or extrapolated surface moves away from a more extreme value. The degree to which these effects arise is in part due to the number of points used and the rate at which the applied weighting decays with distance. In most implementations of IDW the user can control the maximum search radius for known points, the maximum number of known points to include and the decay rate of the weighting. Kriging is, in essence, an advanced form of IDW where the weights for each known data point are not based only on distance but on the spatial covariance exhibited by the data. Kriging, when it works, produces pleasing, varying surfaces that clearly follow localised patterns in the available data. There are several problems with kriging; however, many of them are problems of interpretation and visualisation. Firstly, it requires a large number of data points, at least 100 to work properly (Webster and Oliver, 2007) which excludes valid usage for all glaciological surveys of ablation. At least, in theory. In prac-

13 tice the method works and produces “pleasing” surfaces. Secondly, the method requires the data to satisfy the intrinsic hypothesis (see section 5.2.2 and Myers (1989); Journel and Deutsch (1998); Journel and Huijbregts (2003)) or at least qualify for use with quasi- intrinsic methods. For some processes, simple trend surfaces may be derived from theory or from the data itself (Universal Kringing attempts this) but mass balance processes at the glacier surface vary in mathematically complex patterns not amenable to detrending. This places constraints on how much of a glacier’s surface may be used for calculating the variogram as the processes of accumulation and ablation vary across the glacier surface. This leads to the final problem, one that afflicts all methods: the areas into which data are extrapolated should, in most cases, be expected to differ considerably from those were data are measured. Areas such as glacier margins exhibit turbulent wind patterns, complex shadowing and long wave emission patterns and topographic irregularities (e.g. Fountain and Vecchia, 1999; Dadic et al., 2010; Oerlemans, 2010). All of these factors mean that processes measured on the central portions of a glacier must be expected to differ in mean, variance and spatial covariance at the periphery, over deeply crevassed areas or other topographic extremes. Whilst this may have a proportionally small effect on ice sheets and large ice caps (e.g. Rotschky et al., 2007), on smaller glaciers, more strongly influenced by underlying and surrounding topography, statistical methods based on data from spatially limited surveys will produce incorrect or at least uncertain results. The final method introduced here is an attempt at dealing with the second problem given above for kriging, that the data may only be valid locally. Geographically Weighted Regression attempts to fit a regression function for each location with constants estimated from local data (Lu et al., 2011). This is similar to “quasi-stationary kriging” (see section 5.2.2) and in some respects similar to splines but allows for a greater range of models. The problem with this method, as with kriging, is data availability; glaciological surveys typically contain too few data points for a valid implementation of this method. In summary, “all models are wrong but some are useful” (Box, 1979). It is therefore common practice to use ordinary kriging to generate maps of surface mass balance components.

2.3.1 An alternative This chapter has introduced concepts and methods used in glacier mass balance surveys. The following chapter concerns the measurement of a proxy for mass balance surveys: front fluctuation surveys. In (Haeberli et al., 2000) large scale surveys of front fluctuations are considered as part of tier 4 in the W.G.M.S. framework, whilst the surface mass balance programme for Storglaciären is given as an example of a tier 2 study. Logistically simpler and conceptually easier to calculate, the glacier front retreat or advance rate is taken as a reflection of the overall mass balance of a glacier. This method does not rely on snow probing, ablation stake measurements or the calculation of a continuous surface and as such is generally considered to be the easiest monitoring method for large scale coverage. The following chapter examines specifically the programme and methods of the Tar- fala Research Station and its contributions to the W.G.M.S. global database on glacier front fluctuations (WGMS, 2012). But it may also be considered applicable to most such programmes and their methods.

14 3 Glacier front surveys

The complexity and logistical diﬃculties involved in surface mass balance surveys lead to the use of glacier front movements as a proxy for the measurement of the long term trend in mass balance. In its publication "Fluctuations of Glaciers" (WGMS, 2012) the W.G.M.S. has attempted to gather such data from all research and monitoring programmes across the globe. The publication contains reports of other measures and proxies, such as E.L.A. and where available, area averaged mass balance. The data reported therein for Sweden are largely the results of eﬀorts by the Tarfala Research Station, part of Stockholm University (Holmlund et al., 1996; Holmlund and Jansson, 1999). This chapter is an assessment of the glacier front monitoring programme at Tarfala Research Station.

3.1 Tarfala Research Station front survey programme

The front survey programme of the Tarfala Research Station has its origins in the 1960’s and an effort to assess the representativity of Storglaciären and its climate response at a regional scale (Holmlund, 1993). A further aim of this initial project was, according to Holmlund (1993), to study the variation in climate types across the mountains, though how this was to be achieved from front data alone is not made clear. The distribution of glaciers in the programme reflects these initial goals. There are two large scale axes: a latitudinal, north-south axis and a west-east, maritime to continental axis. Within this distribution there are several pairs of glaciers, separated by only a ridge or peak, intended to illuminate smaller scale climate differences. In all, 20 glaciers were selected for the programme and are still actively monitored. Many glaciers have front data dating back to as early as the late 19th century. Additionally Kårsajietna has been monitored by other groups but has in the last few years entered into the Tarfala programme (Holmlund, 1993). A full list of Swedish glaciers found in the W.G.M.S. database and in "Fluctuations of Glaciers" (WGMS, 2012) can be found in section 3.3.2 as well as a map (figure 3.1) showing the locations for all glaciers in Sweden and the Tarfala Research Station. The Tarfala programme aims to measure all glaciers in the programme at least once every five years and preferably more frequently than this as a contingency against technical or logistical problems. The interval of five years stems from the publication frequency of "Fluctuations of Glaciers" (WGMS, 2012), though its editorial staff encourage yearly reporting where possible. The periodicity of the surveys will be discussed later but it should be noted now that there exist no generally applicable, glaciological reasons for the five year interval. Surveys occur typically in August, when the glacier front should be snow free, though this is not documented or given in protocol as practice. The melt season and thus glacial front retreat will continue throughout the summer (June to September, the "ablation season") and so August cannot be said to mark the yearly minimum of the glacier extent. However, accessing the fronts is now and has been since the programme’s start, prob-

15 lematic. The wide distribution of the glaciers necessitates helicopter transport, which is weather dependent and considerably more reliable in August than late September; furthermore, September is also when the Tarfala Research Station’s mass balance programme intensiﬁes, requiring increased resources. The survey methods employed throughout the programme’s history have varied and changed with the availability of newer, more accurate tools. The original surveys were performed using a tape measure to measure the straight line distance from a marker to the glacier front (Holmlund et al., 1996). More detailed surveys could be performed with the introduction of theodolites and then Total Stations. In more recent years various types of GNSS have been employed. This technical progression has not excluded older methods being used for some surveys. A more detailed description of the survey methods employed follows in section 3.2.3 and a map of glacier locations can be found in ﬁgure 3.1.

3.2 Glacier front ﬂuctuation surveys

The earliest surveys of glacier front positions, in Sweden and elsewhere, stem from scientific curiosity, aroused perhaps by the advance of many glaciers during the so called Little Ice Age (L.I.A.). The advance of glaciers into areas inhabited by humans gave impetus to the study of glaciers, providing a definable need for understanding. The glacier front seems an obvious place to start acquiring knowledge, both because of the very apparent changes and the relative ease of measuring these changes. Throughout the first decades of the 20th century glaciers in Sweden, as elsewhere, were in rapid retreat as the L.I.A. ended (Holmlund, 1993). This response to a measurable climate signal suggested that glacier front fluctuations could provide information on climate that was otherwise un- available. In Matthews and Briffa (2005) the term and the timing of "the Little Ice Age" are discussed, wherein the distinction between climate and the response of glaciers to climate is central. The sensitivity of glacier response has been shown to be high resolution in some cases responding to weather rather than climate (Oerlemans and Reichert, 2000; Nesje et al., 2000). This response is generally assessed via the fluctuations of glacier fronts, with the response time of valley glaciers being of greatest interest (Jóhannesson et al., 1989; Bahr et al., 1998). Le Bris and Paul (2013) suggest also that glacier length data is a valuable source of verification for climate response models.

3.2.1 Defining the front from a theoretical basis The first step in measuring the change in glacier front position is to actually define what is meant by "front". A simple definition would seem to be "where the glacier ends" and a perhaps more refined version might be "the downslope terminus of the glacier". Neither of these is adequate even if they may summarise the basic concept of what is intended. We may refine our definition further by incorporating some notions of mass balance and rheology. Rates of accumulation and ablation vary across the glacier, mostly due to elevation, shading, topography and wind patterns. The variation in mass distribution and the resultant differential in force drives movement of the ice, pushing ice from accumulation areas to ablation areas. And generally, as the ice moves further from the accumulation zone it progresses into areas of increasing potential ablation. We may therefore want to assume that maximum potential ablation is at the front, after all this is almost always the lowest elevation on the glacier and temperature increases as elevation decreases. But maximum potential ablation may occur at some other location on the glacier, due to other contributing factors both at the front and elsewhere. The front may be heavily shaded by

16 Figure 3.1. The location of the Tarfala Research Station and the glaciers in its monitoring programme

17 surrounding mountain walls, it may be in a cold sink or experience very little air turbulence and the reverse at other locations may apply. Instead the front may be thought of as being where potential ablation is greater than the influx of mass, either through accumulation or through ice flow into that area (Howat et al., 2008). This definition is not perfect as the same conditions apply along the sides of a glacier; however, if we add to this the definition of the front as being approximately perpendicular to the central flow line our definition becomes more specific to that form we intuitively regard as being "the front".

3.2.2 Identifying the front in the field With the above definition in place it may seem that the job of measuring the front becomes simply a question of survey technology; however, before turning to such matters there remain several considerations that must be addressed. Firstly there is the question of timing; as with mass balance surveys, front surveys attempt to capture the state of a system that is in continual flux and has components that can switch sign on time scales of hours, days, months and years. The front position is the sum of the flow of mass to the front from up glacier, plus any net accumulation at the front, minus all ablation terms. It would be convenient to consider the flow in as near constant or at least varying on longer time scales but this is not the case. The interplay of glacial hydrology with rheology and, above all, with basal friction means that ice flow may respond to diurnal changes in meltwater availability (Hooke et al., 1983; Jansson, 1995; Rignot and Kanagaratnam, 2006). This response varies throughout the season as the subglacial and englacial hydrology develops towards a more efficient system, with decreasing interaction between water and ice (Irvine-Fynn et al., 2011; Meierbachtol et al., 2013). This development and the state of the relative contributions of accumulation and ablation to glacier kinematics are driven by the weather and therefore do not follow a fixed schedule (Hooke et al., 1983; Jansson, 1996). In some cases, such as Storglaciären, these responses may be smaller than the long term, yearly averaged flux rate and do not significantly alter the short term response of the front (Nye, 1960; Hooke et al., 1983; Bahr et al., 1998). Ideally surveys of front position should be performed when the rate of change is at an inflexion point, when mass loss at the front is equal to mass flux in to the front (Boulton, 1986). As it is difficult to know exactly when this may occur for each glacier and for any given year, timing becomes an issue of logistics but equally an issue of visibility. Visibility, or access is the second important consideration for front surveys: rarely does the glacier front present itself as a distinct boundary between clean, exposed glacier ice overlaying debris free bedrock, certainly not along its entire length. Snow cover may remain for some time, especially at the very front of the glacier (see the discussion below on snow aprons) and early autumn snow fall presents problems for the timing remote sensing of glaciers. Beyond this ephemeral obfuscation of the glacier and its front there exist several other impediments to glacier front surveys; foremost of these is the state of the front. A calving glacier is one which terminates on water, the lowest part of the glacier held afloat and thus experiencing considerably different forces there than on the land based parts and calving is the process by which vertical blocks of ice detach from the calving front (e.g. Benn et al., 2007a,b). This process is a further addition to the many complicating factors linking frontal position to climate and there is no simple, linear connexion (Bassis, 2013). The calving front position is not generally regarded as an appropriate measure of climate response, at least not in the relative short term. This however is not an issue in Sweden where only one glacier, Salajekna, has a true, calving front. Salajekna’s front is rather complicated, with two distinct parts set almost at a right angle to each other, one land terminating and one calving.

18 Alternatively a glacier may terminate in a lake without the ice detaching from the underlying bed and calving will not occur in these circumstances. Proglacial lakes are a common feature and may obscure some or all of a front, e.g. Suottajekna in Sarek. It is not unusual for the front of a glacier to be covered by a patch of perennial snow that may last several years though not contributing mass to the glacier ice. The occur- rence of such snow aprons is the result of many interacting factors, chief among them is perhaps slope. Surface slope is, like most aspects of a glacier, dynamic; the underlying topography certainly influences surface slope, if somewhat indirectly, but recent mass balance also affects the form of the slope, especially so at the front. Positive net mass balance will increase the flow of mass down from the accumulation area toward the front. Should this increased ice flow make it to the front, rather than being ablated in subsequent negative mass balance years, it may cause the glacier to at first bulge upwards at the front and to then advance the front (Jóhannesson et al., 1989). Similarly, negative mass balance may cause the front to down waste (become thinner) before eventually retreating up glacier. Further complicating the issue is the presence of a cold surface layer in polythermal glaciers (Holmlund and Eriksson, 1989; Pettersson et al., 2003, 2007). Should this layer reach to the base of the glacier, freezing it to its bed it will hinder basal sliding, resulting in surface bulging as well as reduced mass flux through to the down flow parts of the glacier (Bindschadler, 1983; Morland, 1984; Pettersson et al., 2003; Anderson, 2004). Mass fluxes influence the surface gradient, and where relative bottom topography is large when compared with ice thickness so too will this. If the surface slope near the front should favour the creation of lee a greater depth of snow may be deposited at the front than would otherwise be possible at that location. If thick enough this snow may become a snow apron persisting throughout the year, insulating the underlying ice front and masking it from direct observation. Snow aprons will occur on glacier fronts where accumulation is greater than ablation and it may therefore seem abstruse to not consider this snow as part of the glacier when it is in direct connexion with it. The W.G.M.S. published some guidelines for object classification in volume VIII of "Fluctuations of Glaciers" (WGMS, 2005) but do not indicate any treatment for snow aprons. In Müller et al. (1977) guidelines for “The World Glacier Inventory” (Haeberli et al., 1989) indicate that ice cored moraines and perennial snow above the bergschrund should be included in the glacial area; furthermore, perennial snow fields should also be included in the database. There is however no explicit directive for the treatment of snow aprons. If instead we turn to Raup and Khalsa (2010) and “Global Land Ice Measurements from Space” GLIMS (2014) it is suggested that such objects be included in the database but as objects separate from the glacier itself. Further justification for not including the snow apron in a survey of glacier fronts stems from the fact that the lower density of snow as compared to ice means that less energy is required to melt a given thickness of snow and that there is no compensating influx of mass into the snow apron as exists in the glacier proper. This then causes the snow apron to fluctuate in area to a greater extent than ice front and it is thus considerably more sensitive to weather rather than climate. It has therefore been judged best practice to exclude such snow from the Tarfala Research Stations front survey programme. Debris cover and moraine present considerable problems for identifying the front on most glaciers. Should a glacier terminate as a clean, distinct ice margin over exposed bedrock the front may confidently be determined at that point along the glacier margin, at that particular point in time. These conditions do occur but they are far from being representative, rather occurring in a minority of cases (figure 3.2 illustrates such a case). There are several sources of debris that may cover the ice at or near the front but almost all material is derived from moraine, i.e. bedrock ground mechanically eroded

19 Figure 3.2. Debris cover and irregular fracturing of the apparent front from the base and sides of the glacier. Should this material attach to the base of the glacier it may become entrained within the glacier through non-laminar ice flow and subsequently melt out onto the surface of the ice (Alley et al., 1997; Cuffey et al., 2000). Smaller fractions may be forced through crevasses and other channels by pressurised water either at the base or in an englacial channel that feeds into a moraine filled crevasse. This process tends to separate the moraine into fractions and the smaller particles are transported farther and more rapidly than larger fractions. Upon reaching the surface the fractionated debris covers and insulates the underlying ice (e.g. Swithinbank, 1950; Boulton et al., 2004; Goodsell et al., 2005). Rockfall directly onto the surface may also produce localised debris cover; these rockfalls may become buried if originating in the accumulation zone only to re-emerge further down the glacier through surface ablation. As debris cover merges often smoothly into till, glaciofluvial sediment and end moraine the distinction between glacier and foreland becomes blurred (Boulton, 1986; Boulton et al., 2004; Goodsell et al., 2005).

3.2.3 Surveying the front in the ﬁeld The front survey programme of the Tarfala Research Station has employed several methods for surveying front positions. Remote sensing using aerial photography has been applied sporadically, as and when images have been made available through research programmes or national surveys. This method will be discussed in section 3.2.4. Most surveys have been performed "on the ground", initially using tape measure and then theodo- lite or total station and more recently GPS. This progression has not been linear, new methods displacing old upon introduction, but rather piecemeal for reasons of instrument availability and user skill. Most recent surveys have been performed using GNSS in one form or another; however, during the International Polar Year of 2008 (Rapley et al., 2004) a combined dGNSS and total station survey was used to measure fronts and georeference benchmarks used in previous surveys. This work has allowed previous sur-

20 vey data (where available) to be transformed to the SWEREF99 coordinate system and from there to SWEREF99 TM.

Tape Tape surveys are the oldest survey method used in the programme. The method requires an initial survey of benchmarks, in most cases boulders or bedrock where available, painted with a cross and identifying code. This survey was often performed using theodo- lite and Electronic Distance Metre (EDM) or aerial photography. Once established in a local reference system, straight line distances from the benchmarks to the front are used to measure position. These distances are measured parallel to the average flow of the glacier near the front. The method does not allow for detailed surveys and becomes in- creasingly difficult as the fronts retreat away from the established benchmarks. The error sources in this method are multiple. At a range of 100 m an angle error of 1◦ produces an insignificant error in distance of approximately 0.015 m but a 10◦ error in angle results in an over estimation of distance by 1.52 m. At 300 m of range these angle errors give 0.05 m and 4.56 m respectively. These larger angle errors are not unlikely; each survey estimates flow direction and then transfers this to the benchmark in question. It is not the difference between an individual estimate and an absolute true value that is considered here but rather the difference between two separate estimates of flow direction and their transfer to a benchmark. A further error in distance measurement comes from the tape itself not being straight. Snagging is almost unavoidable but sagging is absolutely unavoidable over the distances measured and under the prevailing conditions. These errors are difficult to give an estimate for, especially snagging but values for sagging are estimated in e.g. Ternryd and Lundin (1966) to between 0.03m and 0.05 m over 100m, which would be insignificant for surveys of glacier fronts but these errors represent best case scenarios when practised by experienced surveyors, applying appropriate methods for straightening and tensioning the tape measure. A true estimate is impossible to calculate but 0.5 m of error over the distances commonly found in front surveys does not seem unrealistic, requiring no more than 6◦ divergence from horizontal over 100m.

Total station Total stations and EDM enabled theodolites require more equipment to be taken into the field and more time to establish each survey but are subsequently faster and more detailed. Angles and distances between known points and locations on the front can be measured almost instantaneously. Older equipment requires an instrument operator at the instrument and an assistant with a survey prism at the glacier front. Modern machines can be remotely controlled by an operator at the glacier front or may measure distances directly from the glacier surface. In the case of the Tarfala Research Station survey programme only the older type surveys have been performed. The accuracy of these measurements must be considered in two parts: the accuracy of the instrument’s measurement of the given target and the accuracy of the user’s definition of the target. The accuracy of the instrument contains several components but essentially the angle measurements, horizontal and vertical, and sloping distance measurement are combined, as are their individual errors. A well maintained and serviced instrument can be expected to give an error of no more than 0.020 m over the distances considered here. For many instruments the error is smaller still. A greater problem is the user; firstly the prism must be held exactly over the target by ensuring that the prism pole is plumb. Errors of up to 0.1 m may be expected if the user is

21 not observant. Secondly, the instrument’s position and orientation is determined by reference to benchmarks with well defined coordinates. The markings used are almost always large, crudely painted, often faded and, more often than not, painted on boulders in glacial foreland, i.e. resting upon relatively unstable sediments. If the instrument and back objects are not plumb over their benchmarks and these themselves are poorly defined then errors in positioning are impossible to avoid. These errors are mitigated somewhat if the instrument’s position and orientation is established using a "free station" method to back objects at a greater distance from the instrument than the glacier front. A further source of angular error may be introduced if the tripod upon which the instrument stands is not stable. Should a tripod leg sink or loosen the instrument’s orientation will be altered. The instrument may correct for this error to a certain degree (if it has been serviced and calibrated correctly) but above an instrument specific limit this will no longer be possible. There are warning functions for this error built in to most modern instruments but these are often turned off to reduce disturbance when high precision is not required. In such cases it is expected of the user to perform a control measurement against a back object at the end of the survey to assess the scale of any error. It is questionable whether such a measurement is performed during glacier front surveys. A similar error occurs if the instrument is not fastened correctly to the base plate of the tripod. Turning the instrument on its vertical axis for targeting may cause the entire instrument to slip, perhaps imper- ceptibly, introducing an orientation error. Given observed practice and knowledge of the instruments and methods used it seems that an average error of 0.1 m may be expected. The above factors combine when calculating the position and bearing of the station and can result in considerable errors, as illustrated in figure 3.3 using data from the 2013 survey of Isfallsglaciären . The survey was established using measurements of distance and horizontal angle to four benchmarks, which allows several methods for calculating instrument position and bearing. Trilateration (shown in green) uses only the distances to two known points (Egeltoft, 1996, p. 69) but may produce unstable solutions from poor geometry. Triangulation (shown in red) uses angles to three known points (Egeltoft, 1996, p. 78) and is generally a better method for calculating free station coordinates. With both distances and angles to multiple points a least squares method of optimisation (shown in blue) can be used (Egeltoft, 1996, p. 83). This method iteratively reduces the differences between the calculated angles and lengths and those surveyed in the field. This should provide the best solution; however, if the measurements or the benchmark coordinates do not have similar errors then this method may actually provide a worse solution but this fact may remain unknown without independent verification of the data. From the 2013 data the positions calculated for the instrument differ by up to 8.9 m (triangulation to least squares). At the northernmost end of the front survey line the difference between the data calculated from the triangulation establishment and the trilateration establishment is 10.2 m or 8.5 m from end point to perpendicular intersection. The least squares method lies between these two over the northern part of the front but then shifts to the east, closer to the station. The example above relies on a survey established using distances and angles to four points, i.e. eight measurements, many surveys rely on only three or perhaps four measurements.

Navigational GNSS This type of Global Navigation Satellite Systems (GNSS) is cheap and since May of 2000, when selective availability for GPS was removed, has been able to provide 20 m accuracy. Further improvements to the GPS and more broadly GNSS technology as well as the "European Geostationary Navigation Overlay Service" have resulted in a potential

22 Figure 3.3. Positioning and orientation error of Total Station and their cumulative eﬀect on the 2013 survey of Isfallsglaciären’s front accuracy of 1.5 m (European Satellite Services Provider S.A.S., 2018). This accuracy estimate is, however, a best case value. Surveying glacier fronts in northern Scandinavia pushes the potential of these instruments to breaking point. The geometry of the satellites visible to the GNSS unit is often suboptimal, atmospheric disturbance is greater due to relative atmospheric thickness, multipathing (signals being received after reﬂection from a nearby surface such as rock face) may occur and signal shadowing, whereby the surrounding topography blocks the direct line of sight signal from a satellite is common. These factors result in poor Geometric Dilution of Precision (GDOP) reducing the ability of the GNSS to resolve its position. Commonly the GNSS can be expected to achieve an accuracy no better than 20 m but this is continually changing and should be checked repeatedly.

Geodetic GNSS (differential) Geodetic GNSS, commonly referred to as differential GNSS, dGNSS or dGPS operates in a similar manner to EGNOS enhanced GPS. Whereas the simpler navigational GNSS devices receive only the L1 band, decoding the C/A (Coarse/Acquisition) data, geodetic GNSS receives both L1 and L2 bands, decodes the C/A data and analyses the carrier wave to determine the travel time from satellite to receiver. The travel time is then adjusted for errors induced by atmospheric conditions by comparison with errors registered at a reference station of known position. This reference station must not be too far from the "rover" unit as the validity of the corrections decreases with distance from the reference and satellite visibility may be different for the two receivers if they are geographically distant (e.g. Leick, 2004; Lantmäteriet, 2017). The Tarfala Research Station maintains a GNSS base station and may be used to correct rover surveys as far away as Riukojietna and Mikkajekna; however, SWEPOS (Lantmäteriet, 2017) maintains a network of reference stations in Sweden as well as a post processing utility which may offer better accuracy at such distances.

23 This method can provide an accuracy of better than 0.02 m at the receiver antenna for rapid surveys and even better accuracy for so called "static" surveys. The issue of shadowing is not avoided and may still present problems. In regions without access to the SWEPOS network and its virtual base stations a lack of common satellites between rover and base station is often a problem at least during some part of the day. Uncor- rected dGNSS data is often little better than EGNOS corrected GNSS data and can be considerably worse.

3.2.4 Surveying the front in remotely sensed images There are four main types of remote sensing that may be considered relevant for topographic studies of glaciers: satellite imaging, aerial photography, Lidar scanning and drone photography. The errors in positioning vary greatly between methods and within methods, depending on platform and instrument. For the Tarfala Research Station front survey programme only aerial photography has been used and then only in a few cases.

Satellite imaging Satellite imagery, such as Landsat, Sentinel-2 or Aster, can provide high resolution (10- 20m) snapshots of a large area allowing multiple glaciers to be mapped from one image and from data obtained at one point in time (see e.g. Andreassen et al., 2008; Bolch and Kamp, 2006; Tedesco, 2014; Paul et al., 2016; Kääb et al., 2016). Pixel resolution does diminish the spatial accuracy of the survey but the overview allows features to be traced under debris and snow cover with some degree of conﬁdence. The data also contains information in other wavelengths than the visible which may aid mapping. The timing of the acquisition of data cannot usually be controlled by the glacier survey team but ac- quisitions are repeated regularly, typically every few days to weeks, depending on which platform is used. This may mean that in some years, no usable data can be found for a particular region due to cloud cover but given that the satellite will continue to acquire data this is not a major limitation.

Aerial photography Aerial photography (see e.g. Campbell, 2006) has already been used both for mapping glaciers (Holmlund, 1996; Koblet et al., 2010) as well as for determining the internal relationship between the benchmarks used by the ground based surveys. The method oﬀers a higher spatial resolution than satellite imagery, often better than 0.5 m, and yet still provides the overview that allows hidden features to be traced; however, the area covered by each image is much smaller and the range of wavelengths often much smaller than for satellite imagery. The acquisition of the images is also highly weather dependant but those images acquired are, to a large extent, cloud free. This method does allow the user to order acquisition at speciﬁc times (again depending on weather) but is expensive. The expense may be shared by multiple users but this is rarely possible, especially in glaciology. Given the limited area captured by each image and the restrictions imposed by weather and cost, fewer glaciers can be surveyed with this method than is the case with satellite imagery.

Lidar scanning Lidar scanning is a relatively new method that maps distance to ground from a scanner. The scanner itself has an accurately determined position, ﬁxed using dGNSS, and thus a highly accurate and precise (potentially 2cm accuracy) digital elevation model (DEM)

24 can be made. These surveys are preferentially performed from aircraft (Wehr and Lohr, 1999; Abermann et al., 2010) flying at relatively low altitude, covering an area similar or smaller than that for aerial photography. Thus this method suffers many of the same limitations as aerial photography but the richness of detail and data accuracy make this method superior. This is partly due to the fact that most Lidar surveys include visual wavelength imagery as well. Lidar scanning is, at present, more expensive than aerial photography alone but its cost is coming down rapidly. Terrestrial Lidar scanning (Bauer et al., 2003; Carrivick et al., 2015; Fischer et al., 2016) does not require expensive aircraft or cloud free conditions but does require exten- sive fieldwork for each glacier surveyed.

Drone photography Using small, cheap, unmanned aircraft oblique photographs of terrain can be rectified and used to create 3D models of terrain such as glaciers (Nussbaumer et al., 2015; Holmlund and Holmlund, 2017; Lambiel et al., 2017). This method is inexpensive and under the user’s control. It is still dependent on weather, as are all the methods described here, but more problematic is that it would require workers to go into the field to survey each glacier specifically. This reduces greatly the number of glaciers that can be surveyed per season. It is also prone to data loss due to accidents, i.e. crashes, and may not be viable in all areas due to regulation. Whilst this method is of interest it seems least appropriate for large scale monitoring of glacier fronts. All remote sensing methods require an interpretation of an image representing only a part of the information available on the ground. The problems of determining where the front actually is remain but with the addition of identifying this from limited information. One advantage often available is the ability to view each feature in a larger context than that of its immediate surrounding, the user may be able to trace a feature (the front) from geographically disparate parts.

3.2.5 Calculating change After a satisfactory survey of a front position has been performed the change compared with a previous survey must be calculated. This process can in itself introduce variation, even outright errors into change calculations. Valley glaciers rarely flow in a straight line as the constraining topography is seldom straight. This complicates determining the average flow line along which fluctuations can be measured. Furthermore, the front itself seldom changes evenly along its breadth; melt rates vary with shading and cover, basal sliding varies with bed type, hydrological state as well as ice temperature and topograph- ical constraints vary, changing flow into the front. The WGMS reports a single figure, the straight line distance between one front position and another. Neither Caflisch et al. (1977) nor Haeberli et al. (1989) give recommendations for determining this distance. Others have attempted various methods, often for large scale changes and based on remotely sensed data (e.g. Andreassen et al., 2005) In Moon and Joughin (2008) the area between two surveyed fronts is divided by the average width. This does not constrain change to flow direction and is difficult to apply on partial surveys. Using data from Greenland Lea et al. (2014) examined several methods, including the Moon and Joughin (2008) method. They concluded that the best method choice depends on circumstance but that a variation on the Moon and Joughin (2008) method, called the "curvilinear box method" and the "extrapolated centre-line method" gave the most robust results (see Lea et al., 2014, for details). The potential error introduced at this stage is proportional to the degree of irregularity across the front and Lea

25 et al. (2014) estimate it to be less than 5% for the extrapolated centre-line method. This is in itself somewhat subjective due to the deﬁnition of the central ﬂow line and the irregularity of the front. An examination of the method suggests that it translates the side centroid of the measured front orthogonally to the centre-line (Environmental Systems Research Institute, Inc. (Esri), 2015).

3.3 Consideration of the Swedish data registered with W.G.M.S.

3.3.1 Data quality The survey quality has varied considerably, due to both method and circumstance. Tape measure surveys are imprecise and the errors increase greatly with distance between benchmark and front. As illustrated in the examination of Isfallsglaciären’s 2013 data in figure 3.3, more precise instrumentation does not necessarily imply more precise positioning. For total station surveys errors are identifiable if not always quantifiable. From the field protocol data available it is impossible to tell if post survey checks of orientation have been performed. It is possible that the operator simply read off the apparent bearing without noting the reading if the error was considered insignificant. But the greatest errors induced by the survey method result from the cumulative effect of poor benchmark definition, poor back object alignment and calculation choice. These comments hold for all total station surveys of fronts within the Tarfala Research Station front survey programme. GNSS surveys are free of these types of errors. Long baselines may worsen post processing results but as long as satellite coverage is adequate this imprecision should remain below the accuracy of front definition. Navigational GNSS cannot be expected to provide better than perhaps 10 m accuracy on average, even if individual points may be higher quality. It is not certain that older surveys of glacier fronts followed the same principles of front definition as are applied today. Indeed, it is not certain that individual field workers interpret the conditions identically. The 2014 survey of Salajekna was performed using a navigational GPS held in a helicopter flying over the approximate position of the front as this was actively calving on its western arm and deemed too dangerous along its southern arm. How this data should be compared with other surveys is not easy to answer.

3.3.2 Data presentation

Maps Maps of all glaciers surveyed would not be helpful in this document, especially given the small amount of data found for certain glaciers. Instead, a selection of maps is presented in figures 3.4 to 3.6 to illustrate cases of interest and relevance to the discussion. In figure 3.4 a map of Mikkajekna’s front retreat, the longest data series in Tarfala Research Station programme, shows an almost ideal form for study. The slight curvature does present a small difficulty for calculating distance but the flow line is quite easy to define given the well constrained form of this valley glacier. What is not evident from this map is that the oldest front positions were in fact beyond the constraint of the glacier’s main valley and flow direction may have been different at this oldest front. However for most of the last 100 years this has not been a concern. The rate of retreat is plotted in figure 3.9 (black diamonds) using data from the WGMS. This data contains fluctuations not recorded in the map, early in the 20th century the front appears to have advanced as

26 well as retreated. By the second half of the 20th century Mikkajekna would appear to be in continual retreat of between 10 m and 20 m per year. Turning to figure 3.5 and Storglaciären the front positions date back to 1910 with the addition of a "Little Ice Age" (LIA) maximum front delineated using a distinct terminal moraine (Schytt, 1959). What is perhaps most notable in this map and in figure 3.7 is the stability of the front position during the last 20 years. The front has been snow covered for much of the time, accounting for some of this apparent stability but the front has been pinned to a riegel or bedrock ridge, with flow into the front area restricted by this bedrock. Thus prior to this period of stability the front retreated more rapidly than it otherwise would have. The flow of ice over the riegel was then sufficient to maintain the front at this position. Ruopsokjekna in Sarek illustrates another difficulty in determining front retreat. In figure 3.6 a clear disjoint can be seen in the front caused by the presence of a nunatak. This not only alters the apparent flow direction but also strongly influences the rate of front retreat on either side of it. Mapping around this is problematic, especially in the field, where an overview is hard to gain.

Retreat rates Rates of glacier front fluctuations, calculated from data recorded in the W.G.M.S. database are presented in figures 3.7 to 3.10 and in appendix B. The WGMS database records the amount of front movement since the previous survey rather than a yearly rate. In some cases the data is unclear, such as Vartasjekna 2010, where the previous year, 2009, was registered as snow covered and nothing at all registered in the three years prior to that (WGMS, 2012, p. 143). Does the figure of -12 m refer to 2009 or some year prior to this? In such cases no rate has been calculated and the data excluded. Along with the fluctuation rates first order regression models are shown. The higher orders are not shown as they cannot be expected to be useful or fit the data in a meaningful manner. Additionally the North Atlantic Oscillation (NAO) index averaged for January, February, March & April and June, July & August is shown as well as the June, July & August average temperature as recorded in the Tarfala valley. Correlation with these is indicated in each diagram as well as in table 3.1.

3.3.3 Trend analysis A cursory analysis of the fluctuation rates and their correlation with some assumed drivers reveals moderate correlation with the winter North Atlantic Oscillation index. The correlation is moderate at best and in some cases weakly negative. Tarfalaglaciären lacks enough data for the correlation coefficient of −1.00 to have any meaning, indeed in many cases the data are insufficient for such an analysis to be interpreted. The moderate negative correlation with summer temperature is also subject to similar problems; Stuor Räta shows a weak positive correlation due to the paucity of data and the fact that the retreat has slowed in recent years. The regression models have generally poor R2 values with the exception of Mikka- jekna and Unna Räta. In both cases the data distribution explains this more than the goodness of the model. Unna Räta especially has one cluster of points at a static front, another smaller more vaguely defined cluster and then one point alone. The linear model does not fit this well but a fourth degree model found a reasonable fit due to the cluster- ing. The second and third degree models were poor fits for all the data sets, which may be expected given the poor distribution of the data. The high R2 values for the Mikkajekna

27 28

Figure 3.4. Mikkajejkna’s front retreat, from 1913 to 2013 29

Figure 3.5. Storglaciären’s front retreat, from Little Ice Age to 2013 30

Figure 3.6. Ruopsok’s front retreat, from 1965 to 2013 Figure 3.7. Storglaciären ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate

Figure 3.8. Vartasjekna fluctuation rates together with NAO index and summer temperatue at Tarfala. Re- gression models are not meaningful, correlation coefficients moderate data are caused by the data being divided between two series, one at the start of the survey period and one at the end (note that only the linear model is shown). The regression models are presented here because they are a standard first analysis but, as shown, they are inadequate and cannot be said to describe the data or serve to predict future fluctuations. The correlations with NAO and temperature may be useful and could potentially be improved with better data; the errors in the calculation of front position introduce noise that weakens the correlation. In summary, the front surveys, intended as a logistically simple proxy for long term mass balance (Haeberli et al., 2000) are currently providing noisy data, degrading their potential use. The data do not consistently show changes in mass balance inducing a response at the front to move the glacier into equilibrium. A simplistic model would have the front retreating away from lower elevations and high ablation when mass balance is negative and, conversely, advancing into areas of higher ablation when mass balance is positive. This model may be generally true but the response time and the degree of the response at the front are complicated by ice dynamics, down wasting and perhaps other factors, such as increased debris cover insulating the front from ablation (Nakawo and

31 Figure 3.9. Mikkajekna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Re- gression models are not meaningful, correlation coeﬃcients moderate

Figure 3.10. Ruopsokjekna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate

Rana, 1999; Jansson and Fredin, 2002). The diﬃculty that this rather non-linear connexion between mass balance and front response brings when trying to use front surveys as a proxy is exacerbated by survey errors. The following chapter presents four papers exploring various elements of surface mass balance surveys and many potential error sources therein.

32 Table 3.1. Fluctuation rates and their correlation with assumed drivers

Rate Model NAOJFMA NAOJJA Temp.JJA Glacier Name Min Max Mean σR2 Corr. Coef. Kårsajietna -19 1.5 -6.2 5.0 -0.002 0.593 0.162 -0.364 Riuokojietna -15 0 -6.0 5.3 0.539 0.741 0.176 -0.281 V. Påssusjietna -21.3 0 -8.2 7.9 0.719 0.671 0.084 -0.805 Ö. Påssusjietna -20 0 -7.4 6.5 0.183 0.458 0.089 -0.481 Stour Räita -20 0 -6.3 6.5 0.469 0.486 0.244 0.299 Unna Räita -12 21 -0.3 7.0 -0.396 -0.003 -0.256 -0.398 S.O. -10 5 -1.5 4.1 0.631 0.473 0.183 -0.152 Kaskasatjåkka Tarfalaglaciären -5 14 2.2 6.4 0.098 -1.000 1.000 -0.731 Isfallsglaciären -34 5 -5.4 7.6 0.388 0.503 0.040 -0.163 Rabots Glaciär -26 -1.7 -11.2 4.8 -0.458 -0.095 0.182 -0.268 Storglaciären -22 0.5 -6.7 5.8 0.453 0.495 0.192 -0.331 Hyllglaciären -10 0 -4.4 3.8 0.182 0.440 -0.219 -0.571 Suottasjekna -36.9 6.3 -7.5 10.6 -0.285 0.551 -0.196 -0.434 Vartasjekna -13 0 -2.7 3.8 0.411 0.304 -0.342 -0.526 Mikkajekna -26 9 -9.5 8.9 -0.814 0.443 0.407 0.061 Ruotesjekna -27 0 -13.1 7.0 -0.082 0.417 0.042 -0.115 Ruopsokjekna -27 -0.1 -9.8 7.9 0.224 0.300 0.167 -0.206 Pårtejekna -25.5 0 -12.2 7.1 -0.211 0.187 -0.104 -0.480 Salajekna -22 1.1 -9.9 5.6 -0.334 0.160 0.340 0.051 Kuototjåkka- -17 -10.5 3.8 -8.0 0.355 -0.200 -0.787 -0.929 glaciären

33 34 4 Presentation of papers

This chapter contains short summaries of each of the papers included in this thesis and sets each into context with regard to the themes explored herein.

4.1 Reanalysing glacier mass balance measurement series The identiﬁcation and classiﬁcation of errors

In 2012, the World Glacier Monitoring Service and Stockholm University held a workshop at the Tarfala Research Station on “Measurement and Uncertainty Assessment of Glacier Mass Balance”. One result of this workshop and the work it inspired was paper I in which a standardised method for homogenising mass balance data from different glaciers and, above all, different methodologies was proposed. The need for such work arises primarily from the use of two conceptually different measurements of mass balance: the glaciological method and the geodetic method (see chapter 2, sections 2.2.3 and 2.2.4) but also from the use of the results to model the global response of glaciers to climate change (e.g. Radić and Hock, 2011). Glaciers show a range of specific responses to weather and climate, all generally aligned with the accepted conceptual physical model of glacier-climate interaction but the scale and details of each response vary. This variation stems from hypsometry, geology, response time (“memory”) and what may be called “the glacier itself” but some part of the apparent response stems also from measurement. This paper accounts for some factors introduced into estimate calculations by the necessary limitations of the survey methods by analysing the differences between different model types of the same glacier. Storglaciären is used as a case study, illustrating the proposed algorithm. The uncertainty assessment and validation process central to the work are dependent on correct estimates of measurement error. Error sources for the geodetic method can be divided into several different types: those that may be estimated from instrumentation specifications, those that may be estimated by statistical analysis of stable topography, i.e. surrounding bedrock and those which are transient and essentially unknowable without groundtruthing, e.g. low contrast patches in aerial images resulting in poor elevation estimates. The glaciological method is prone to field survey errors such as in reading stake heights and sampling snow density. But the glaciological method is also more prone to errors similar in character to those discussed in section 2.3 of chapter 2: sparse data must be representative of its neighbourhood but also allow the estimation of the random function1 describing the entire glacier surface. Estimating just how representative a measurement is of a single point is not straightforward and repeat measures are difficult as measurement methods are destructive (snow probing, density sampling), costly (abla-

1A random function is a statistical model that describes the most likely value to be observed at a location. It does not ﬁx the value, it merely speciﬁes an expected value and the variance around that value. A given value becomes less likely the further from the expected value it is.

35 tion stakes) and subject to variation in the measurand of a similar scale to the theorised measurement error of the method under investigation. The paper also highlights the problem of inter- and extrapolation methods (see section 2.3) as well as the diﬃculty in estimating spatially distributed density values. Both of these issues are considered in other work presented in this thesis.

4.2 A comparison of seismic and radar methods to establish the thickness and density of glacier snow cover

The previous paper highlighted issues related to the problem of transferring sparse, point measurements to an entire surface. In paper II some field methods are explored which may, in some part, address these issues. Using Ground Penetrating Radar (GPR) and seismic surveys, snow depth and density were measured over a continuous surface. GPR appeared to offer the most robust solution, estimating snow depth in agreement with depth measured at a snow pit. The depth estimates are reported with an uncertainty of 0.02 m to 0.03 m and agree with depths measured from snow pit walls to within a similar error, though some adjustment is needed for depth hoar. Density estimates from GPR were more problematic and the need for validation against physical samples suggests that this may not be of great benefit. The results suggest that GPR surveys of snow depth may be used to complement a minimal probing network. As the GPR surveys do not offer complete coverage but are instead measured along lines, providing continuous data along track and discontinuous data across track, the data must still be interpolated between survey lines. Furthermore, GPR surveys are still prone to limitations due to safety considerations as well as noise at the glacier boundaries requiring extrapolation beyond the surveyed area.

4.3 A DEM of the 2010 surface topography of Storglaciären, Sweden A new baseline for surface mass balance calculations

In paper III a digital elevation model of the surface of Storglaciären made from field data gathered using Total Station and GPS surveys is presented. This ground based method is labour intensive but provides detailed results. The model is used for both the geodetic and the glaciological methods of mass balance measurement. The glaciological method uses a DEM for inter- and extrapolation of point data and is expected to remain valid for a period of approximately ten years and for such purposes is not acutely sensitive to exactly when during the glaciological year the survey is performed. However, the timing of the survey was chosen for use with the previous aerial photographic DEMs, produced also on an approximately decadal interval (Koblet et al., 2010). The implementation of the survey in the field is not unproblematic as the resultant model should be comparable with those produced by other methods, such as those described in Zemp et al. (2013), e.g. aerial photography. This requires an understanding of how aerial images are interpreted but also of how glacier ice interacts with its boundaries. In many cases a glacier does not simply end but rather merges into and under sediments at the front or becomes a complex pattern of ice filled, lateral moraines. Decisions on what may or may not be active glacier ice are relevant but must also consider how such features may be interpreted without the aid of groundtruthing. The survey methods used also necessarily contribute to errors in model production. Whilst survey quality GNSS equipment was used where possible, many areas of the glacier were deemed to dangerous or at least difficult to reach and were thus measured using a Total Station capable of measuring distances to a hard surface

36 rather than requiring a prism (the method is in principle the same as is used in Lidar). Snow and ice viewed at oblique angles do not always return a strong enough signal for the equipment to register it as significant. This limits the distribution and number of survey points in such areas, which is reflected in the quality of the DEM. In the future manual field surveys of topography may produce high quality results but are likely limited in use due to advances in airborne technology.

4.4 Estimating unaccounted, late season snow accumulation on Storglaciären. Implications for glacier mass balance programmes

The work introduced so far has focussed on measurement error, always with the assumption that what is being measured is correct. Paper IV considers an error arising from the falsity of this assumption. The Tarfala Research Station’s mass balance programme discovered a large error in its survey of Storglaciären for 2012. Calculations of surface ablation suggested that mass was gained during the summer, a highly unlikely situation. Closer inspection of the data indicated that large amounts of snowfall had come after the accumulation season’s final survey. This problem could be detected, albeit on a smaller scale, in data for many previous years. Timing of the final winter survey (and of the final summer survey) is difficult and almost always wrong. There are several reasons for making such a statement. Firstly, weather predictions are limited in scope, reliable only a few days into the future at best; what may appear to be the beginning of the melt season may simply be a temporary change. Secondly, when do such temporary changes become the next season? Rarely do weather patterns switch decisively from being “winter, accumulation weather” to “summer ablation weather”. Periods of snowfall may be interspersed with periods of considerable melt. Thirdly, this mixed pattern applies not only over time but along the gradient of the glacier; higher elevations remain in winter for longer than do lower elevations. From this it may reasonably be assumed that exact timing is impossible, but modelling the theoretical accumulation and ablation during this period of uncertainty would seem to be not only reasonable in years of extreme error but also good practice generally (see section 2.2.3 and the fixed date method). To this end a simple, robust method of correction that relies on minimal data was developed. Modelling precipitation is complex and requires many different data types whereas ablation can be modelled with a reasonable degree of accuracy using only temperature and elevation data (Oerlemans, 2010). Net surface mass balance measurements, that is, end of summer stake surveys, are independent of errors specific to the estimation of accumulation and ablation, allowing a model of theoretical ablation to be subtracted from the net mass balance and provide an estimate of accumulation (see figure 4.1 for an illustration). The model designed here is a degree day model which uses an adiabatic lapse rate to adjust temperature data measured at Tarfala to ablation stakes on glacier. The lapse rate is not linear but rather attempts to take into account the fact that the air at the interface is always at 0◦ C no matter how warm the air above is (provided air temperature is above freezing). The model also attempts to take into account how shading may affect temperature by use of a daily shade distribution model. The degree day factors and lapse rate adjustments are all set by use of the Nelder-Mead simplex algorithm (Nelder and Mead, 1965). The model is intended for use in connexion with the glaciological method and not as a replacement, which it cannot be. Its use retroactively, to identify errors in

37 the winter survey of accumulation was the primary motivation. Further, it may be used to estimate run-oﬀ, which, if measured separately at or near the glacier front may aid models of sub-glacial channel evolution.

Figure 4.1. Modelling accumulation by modelling melt. Firstly, net surface mass balance may be measured independently of accumulation and ablation, as in figure 2.2. In the left panel of the figure above snow depth (co) is measured at the assumed end of the accumulation season by measuring the current height of the ablation stake’s top above the snow level (hc) and comparing this with the height recorded at the previous end of ablation season survey (h0). Following this the first survey of the ablation season records a reduction in snow depth (ha) due to observed ablation (ao). The middle panel illustrates how ablation for the period between the last accumulation survey and the first ablation survey is modelled and the modelled amount adjusted to the level of the observed remaining snow depth (am). The difference between the observed ablation and modelled ablation gives the unobserved ablation (au) which is equal to unobserved accumulation (cu). The sum of the observed and unobserved accumulation gives the final, modelled accumulation (cm). Note that for simplicity the term “height” is synonymous with mass and that all measurements are in practice adjusted to metres of water equivalent (m w.e.).

38 5 Discussion

In the following discussion the reader should bear in mind the concept of “ﬁt for purpose”. Haeberli et al. (2000) places both front surveys as well as surface mass balance surveys into a context of global cryospheric monitoring. Just how these methods have come about and how they are applied may inﬂuence the suitability of the resultant data for such purposes but it will also be necessary to consider what reasonable alternatives might exist.

5.1 Front Survey Programme

The initial aims of the Tarfala Research Station front survey programme were not clearly defined even if the varying scales at which climate, weather and topography may influence glacier kinematics and dynamics was taken into consideration. The choice of glaciers used by the programme was not purely arbitrary but neither was it based on prior knowledge of suitability; these choices have not been revised or reviewed. There seems to have been little discussion on survey frequency beyond that of budget constraints, al- though Holmlund (1993) suggests a decadal interval supported by an initial investigation of mass balance as well as GPR surveys in order to establish a base line and the validity of the front survey frequency. The five year schedule of the WGMS "Fluctuations of Glaciers" (e.g. WGMS, 2012) and the presentation of yearly data therein seems to have been the strongest driver for determining survey frequency otherwise. For a meaningful appraisal of the programme’s current schedule and methods a discussion of what can be measured and with what accuracy must be undertaken; furthermore, the question of why such a survey is even necessary must be addressed. Accuracy is a complex issue and there will be no definitive number but if we begin by excluding the methods of total station based on poorly defined benchmarks and improper usage we may be able to reasonably expect a position estimate of better than 0.1 m for each surveyed point using dGNSS and/or total station. For navigational GNSS the estimation of position is more variable but under optimal conditions 1.5 m of accuracy may be achieved but more realistically 10 m or even 20 m should be expected. Remote sensing methods can be expected to produce results with accuracies within the range of these field based methods. An examination of figure 3.3 shows an apparent retreat of approximately 50 m and more between 2012 and 2014, this then would seem to be a location where navigational GNSS may suffice. However, the retreat rate between 2004 and 2006 was negligible but determining this fact would have been difficult from poor quality surveys. The front itself is more difficult to constrain; as discussed earlier, its position may be difficult to determine, as a distinct ice margin may not be visible or even exist. The matter of timing must also be addressed; at what point in the cycle of kinematic response to mass balance can the front said be at a minimum or maximum? There are no long term, systematic studies of front response, covering more than one entire mass balance cycle but dGNSS surveys of Rabots glaciär’s front for 4th July 2013 and 18th August 2013 show

39 a retreat of approximately 9 m between these dates. In "Fluctuations of Glaciers 2005– 2010" (WGMS, 2012), the only recorded fluctuation rate for Rabots glaciär is a retreat of 63 metres registered in 2007. By comparing with the previous volume (WGMS, 2008, vol. IX) this figure refers to the survey from 2002 giving a retreat of approximately 13 m per year. The years prior to this, in volume VIII (WGMS, 2005), average somewhat less than 10 m per year. Clearly the retreat throughout the summer is of at least the same scale as the long term fluctuations. The 2013 surveys were of a front that had a distinct boundary, with a stream eroding the ice margin to a steep edge. It is entirely possible that active glacial ice continued further out, under the cover of stream bed sediments. Even if we may position a ranging pole or GPS antenna to within a few centimetres what this position represents is still undecided. From here it is perhaps best to consider why front surveys are performed. Surface mass balance programmes are time consuming, require considerable resources and, if simplified incorrectly, can be entirely misleading. The assumption that a glacier’s front reflects its recent mass balance history and thus its local climate is central to the value of front surveys. This connexion is far from simple or direct and certainly cannot, even theoretically, be expected to reflect year by year variations in mass balance (e.g. Jóhan- nesson et al., 1989; Oerlemans and Van de Wal, 1995). If this is so then what reason can there be to survey a glacier’s front every year? The front is a proxy for the long term average of mass balance; any fluctuations on a year by year scale or any larger responses such as those by Mikkajekna’s front, must be considered as partially due to factors other than climate. If these factors are not also investigated then it is difficult to justify measuring year by year variation. This fact can be seen in the weak to moderate correlation of some front fluctuations with winter NAO; it is difficult to say exactly how this correlation comes about but surveying other components of the glacier system would perhaps shed some light. The correlation may even improve if survey quality improves but in the data so far gathered there is too much noise to be certain. This of course ignores the suggestion in Roe (2011) that stochastic forcing may be enough to produce large changes in glacier length and thus front position. Returning now to the phrase "long term", this will vary in size from glacier to glacier. Some theoretical work has been done on the response time of glaciers, including Nye (1965a,b),which test model results against data for Storglaciären. In Jóhannesson et al. (1989) the impact of kinematic waves on response was considered in more detail and revealed a shorter glacier memory length than previously suggested and though "memory" and "response" are not quite the same it does suggest that response occurs only a few years after a mass balance perturbation. Oerlemans and Van de Wal (1995) clearly state that a response to a kinematic wave cannot be expected to be measurable at the front. In Nesje et al. (1995) it is suggested that the response time at the front may be less than five years, though this is for maritime glaciers with large mass turnover. Does this argue for continued yearly surveys? No, because the front surveys on their own do not provide enough information to interpret high frequency fluctuations, should they even be detected. One may try to argue for yearly surveys based on spatial resolution but if we cannot determine front position to better than 10 m then front fluctuations of less than this cannot be measured. This is method dependent as well as being dependent on the nature of the front and perhaps illustrates the difficulty in specifying any single value for survey frequency. If the exact position of the front cannot be determined to less than a few metres due to snow and debris cover as well the rather fuzzy nature of the transition from ice to non-ice then what is it that is represented by the idea of the front position? What is certain though is that reporting fluctuations with a precision of 0.1 m is entirely misleading (e.g.

40 Rabots glaciär in WGMS, 2005) and this practice should be abandoned. There seems little justification for measuring a poorly defined front every year, no matter how accurately this poorly defined position may be surveyed. The validity of only measuring the handful of glacier fronts currently included in the programme may also be questioned. Modern remote sensing methods may have limitations in terms of survey resolution, especially when compared with the theoretical accuracy of dGNSS but this is less problematic when the object being surveyed cannot be determined with higher precision or indeed trueness. Remote sensing has the advantage of being able to provide coverage of many more glaciers, potentially all Swedish glaciers, at one single time point. Checking yearly on the viability of late season remotely sensed images and surveying from these every five years on average, would seem to provide data at least as good as is gathered now but with greater coverage and reproducibility. Such data would provide a more synoptic view of glacier front response, more appropriate to a generalised understanding of glacier response to climate change. Should field surveys be desired then their current form is inappropriate and cannot be recommended. Surveys should be performed at the end of the ablation season, when melt has largely stopped but before dynamic response pushes the front forward again. It should only be performed using dGNSS as total station surveys are too contingent on correct implementation and benchmark quality.

5.2 Measurement error and geostatistics

It is the author’s opinion that the single largest issue in surface mass balance data is that of replication. It is central to understanding both of the problems mentioned above. Replication may be understood to mean two closely related parts of a whole: repeated measurements of the same physical entity and repeated measurements of the same quality in diﬀerent entities of the same kind (Blainey et al., 2014). The ﬁrst is intended to provide an estimate of the variance inherent in the measuring device, the second an estimate of the variance in the quality being measured, termed “technical replicates” and “biological replicates” respectively in Blainey et al. (2014) but in this discussion “entity” will replace “biological”. The sum of these is the total variance of the system, that is, the variance of the quality under investigation, in that particular population and using the chosen method of measurement.

5.2.1 Technical replicates Performing technical replicates using standard glaciological field methods is problematic; snow probing is destructive in that the materials (snow and ice lenses) which influence both the path of the probe and the surveyor’s judgement of when a boundary is met, have been pushed aside and no longer influence subsequent measurements made in the same hole. Repeatedly reading a probe in such a case would not constitute a replicate measurement, it is simply a good practice, helping to avoid an all too common error source, namely reading error. In the case of ablation stake readings the situation is no better. At any one point only one stake may be drilled into the glacier surface. This stake may be measured repeatedly and Østrem and Stanley (1969); Kaser et al. (2003) give advice on how to best estimate true mean surface around a stake but in reality this varies and in many cases is difficult to determine. In this case there may be some value in performing repeated measurements of the stake height but this will provide a technical replicate of the specific conditions around that particular stake. This estimate may be transferable to other stakes exhibiting similar

41 surface conditions, such as micro-topography, ice crystal structure and water content, but these conditions will vary across a glacier. A greater problem is that the stake reading is not the complete measure of ablation but simply a part; in similar fashion to the snow probe creating a path through the snow that destroys the sample, the stake cannot be removed and reinserted in order to repeat the measurement. The trueness with which the stake can measure ablation is also not considered by such a repeat; measurement is a long process, and subject to errors even before ablation begins (see Østrem and Stanley, 1969, for details on how a stake may sink or otherwise fail to track linearly with emergence velocity). One possible way out for both of these issues is to regard a surface of some area as homogeneous rather than restricting measurement to one point. This simple proposition is fraught with technical difficulties and risks encroaching on entity replicates. Beginning again with snow probing, over what distance may snow depth be regarded as the same, at least in terms of glacier-wide surface mass balance? The previous summer surface is, in almost all cases, not a flat, horizontal plane but rather it is undulating, incised and fissured. Surface roughness has been examined in glaciology but often with energy balance modelling and remote sensing in mind. In detailed energy balance models sensible heat flux, Qh from equation 2.3, is influenced by turbulence in the boundary between air flowing over the glacier and the glacier itself. The scale of this turbulence is, in part, dependant on surface roughness (Hock, 2005; Brock et al., 2006; Oerlemans, 2010; Cuffey and Paterson, 2010; Brock et al., 2010). Similarly, albedo (α in equation 2.3) is influenced by surface roughness (Hock, 2005). Air turbulence roughness and albedo roughness are often of a similar scale to that required (centimetre to decimetre in height) but do not reflect the actual roughness, instead they are measures of experienced roughness. Herzfeld et al. (2000) measured surface roughness with a dedicated instrument but at scales not appropriate here. A further problem is that roughness may be expected to vary across the glacier depending on material, slope, hydrology and wind as well as varying with time (Brock et al., 2006, 2010; Smith et al., 2016). The work of Smith et al. (e.g. 2016) suggests that detailed surveys of micro-topography are achievable. This then would appear to allow the identification of homogeneous surfaces in preparation for subsequent snow depth probing. Snow surface roughness may also vary, especially where wind conditions create sastrugi and snow dunes (e.g. Mather, 1962; Li and Pomeroy, 1997; Schlosser et al., 2002), requiring yet further categorisation. If end of ablation season surveys of micro-topography are performed and the subsequent snow surface categorised, plots of snow containing homogeneous upper and lower surfaces, if not approximate thickness, may then be probed repeatedly under the assumption that the same thing is being measured and technical replication is performed. There is, of course, one more caveat in the case of probing; the surveyor performing the probing is, to a very high degree, a part of the measurement. It is the surveyor’s judgement of what constitutes the boundary between new snow and the previous summer surface that determines when probing ceases. Furthermore, the skill of the surveyor to guide the probe vertically into the snow pack is crucial. For these reasons any attempt to measure the variance introduced by probing must consider both the glacier and the glaciologist. This would then provide error estimates for probing a particular combination of upper and lower surface, under the condition that the surfaces are parallel, i.e. snow depth is the same across the test plot. The work in paper II, measuring snow depth with ground penetrating radar, may simplify the preparation of such a study if the summer surface type is more broadly categorised into types identifiable in the radar return signal. The radar determined depth may then be taken as truth and probing error measured against this, summed of course with the error for the radar measurement.

42 Alternatively, snow depth may in future be measured by GPR and truthed against depths measured at density pits or using snow corers, as shown in paper II. For ablation stake errors the problem is somewhat harder. In similar fashion, homogeneous end of summer surfaces should be identified and multiple stakes bored into them. This presents logistical challenges and the experiment is inflexible; should the new snow surface vary in thickness and micro-topography across a plot, variance in the measurement becomes harder to separate from variance in the underlying process, i.e. ablation. Ablation rates may be expected to vary as snow pack thickness decreases due to increased melt water retention and changes in albedo and sensible heat exchange. The capillary pressure of snow is much less than for a soil of comparable grain structure and melt water tends to drain readily through the snow pack (DeWalle and Rango, 2008). As melt water meets a denser, less penetrable surface, such as ice, it may slow and refreeze, releasing energy and warming the surrounding snow pack but also creating ice lenses (Jansson et al., 2003; Schneider and Jansson, 2004). The melt rate at the surface may be expected to change as the structure of the ice crystals changes from dry snow through to strongly metamorphosed, wet snow and ice lenses (e.g. Hock, 1999, 2003, 2005; Hock and Holmgren, 2005; Huss et al., 2008a; Cuffey and Paterson, 2010; van Pelt et al., 2016). For this reason snow depth should be homogeneous across a single test plot and structures such as sastrugi, crevasses and moulins avoided. The difficulty in determining what level in the immediate vicinity of a stake is representative has been mentioned earlier and varies with type of surface (as outlined above). This is not an insignificant error source but becomes more so when measurement is not performed carefully. Recommendations in (Østrem and Stanley, 1969; Kaser et al., 2003) suggest laying an ice-axe on the surface, which in snow helps prevent the rule sinking further and on ice is intended to level micro-topography as well as provide a solid surface from which to measure where often there is a water filled hole. Of course, the surveyor must ensure that the ice-axe does not itself sink too deeply into the snow and that on ice its level is indeed representative. Perhaps the biggest problem when estimating ablation stake errors is the fact that the stake itself interacts with the measurand, influencing the very process it is measuring. The aforementioned hole around the stake is perhaps the best example. It may be hoped that this interaction should be similar across multiple stakes within a “small” area. Investigating the truth of this is a further complication that shan’t be touched on more here. It seems clear that there are many factors to be considered when determining the variance in the measurement method when performing technical replicates. This multitude of factors would seem to limit the applicability of any error estimate and require detailed categorisation of surface types at each probing point and ablation stake for each survey. But there is some hope that a simple ANOVA will be capable of determining if inter- plot variance is greater than intra-plot variance and perhaps allow more generalised error estimates as it is a so called robust method and is usable if the difference in intra-plot variances is no greater than approximately fourfold (Field et al., 2012). Similar work for estimating measurement error in snow density has been performed by Conger and McClung (2009) and Brown et al. (n.d.). The Brown et al. (n.d.) work suggests that bulk density sampling rather than piecewise analysis of density variation is by far the most reliable estimator of bulk density. Repeat measures of snow density are possible if bulk density only is considered. A vertical density profile through a snow pack exhibits changing variance around a value that approaches higher densities with depth but that may suddenly become less dense near the interface with the previous year’s summer surface, due to depth hoar. This profile varies spatially and seasonally, it exhibits large, non random, departures from the depth–density curve due to ice lenses and mass

43 redistribution due to melt, but is spatially non-stationary (e.g. Frezzotti et al., 2005). At what scale stationarity is lost is undetermined. The bulk density measurement however is more stable as the redistribution of mass through the snow pack does not aﬀect the total mass.

5.2.2 Entity replicates, stationarity and geostatistics Replicating measurements of the thing itself, e.g. ablation snow depth or snow density, is similarly dogged by the variability of the measurand. Here the issue of stationarity, mentioned in section 2.3, returns. Restricting the discussion to spatial data, first order stationarity requires that a random process has the same mean and variance everywhere (e.g. Myers, 1989; Journel and Deutsch, 1998; Journel and Huijbregts, 2003; Webster and Oliver, 2007). This does not require that the resultant expression of that random process be the same everywhere but that the expected value (mean) is. The mean at any one point exists only as an expected value and cannot be calculated directly, at least not from a geostatistical point of view (e.g. Journel and Deutsch, 1998; Journel and Huijbregts, 2003; Webster and Oliver, 2007). Replicates may be performed by measuring at different locations as the process is stationary and it is the process which is being measured. This of course is not the case on a glacier; it is expected that the value should change in space, e.g. ablation decreases with elevation. These changes are not the same as the variations due to micro-topography discussed above but they do influence the form of micro-topography present at a particular location. Micro-topographic variations are part of the random error associated with the process. For geostatistical tools such as variogram analysis and kriging, stationarity is relaxed and the concepts second order stationarity or weak stationarity, the intrinsic hypothesis and quasi-stationarity are introduced. The following is based on Journel and Huijbregts (2003). To begin with, stationarity suggests that for any point in space (e.g. on the glacier surface) an expected value exists and is the same everywhere. Furthermore, for any two points separated by a distance called the lag, usually denoted h, the covariance of the expected values at each point exists and is dependent only on h. Additionally, the stationarity of the variance and variogram is implied from the stationarity of the covariance. For practical application to typical geospatial data a further relaxation of stationarity is required. The intrinsic hypothesis states again that the expected value is independent of location; furthermore, the expected difference between two values at separation h has finite variance and that this variance is dependent not on where the two points under consideration are but on h only. Quasi-stationary or quasi-intrinsic, implies that the validity of the assumptions are spatially restricted and that new, locally derived functions must be sought further afield. The above does not quite solve the problem of replication on a glacier, nor does it imply that kriging is a valid tool for surface mass balance studies. Geostatistics accepts from the outset that replicates cannot be made, that the true mean at any one point is not available but that the expected value of the random process may be estimated. The intrinsic hypothesis falls foul directly as it has already been stated that trends exist. The concept of trend, or drift, is dealt with in Journel and Deutsch (1998); Journel and Huijbregts (2003); Webster and Oliver (2007), by extracting linear or quadratic functions describing the drift from the measured data. Furthermore, beyond drift, which implies large scale patterns of influence such as adiabatic lapse rate, other factors such as turbulent wind patterns, complex shadowing, long wave emissions and topographic irregularities add locally variable effects (e.g. Fountain and Vecchia, 1999; Dadic et al., 2010; Oerlemans, 2010). Here it is tempting to invoke quasi-intrinsic methods, i.e. localised estimates and indeed such would be valid but require sufficient data to firstly identify local drift(s) and

44 secondly to estimate the variogram. Typical surface mass balance programmes contain far too few data points, which is true even for the Tarfala Research Station’s programme on Storglaciären, which has always had a high data density as far as surface mass balance studies are concerned (Holmlund et al., 1996; Holmlund and Jansson, 1999). Section 2.3 concludes suggesting that kriging is a useful tool, and indeed it is but it and geostatistics in general cannot provide better estimates of error. In Hock and Jensen (1999); Jansson (1999); Jansson and Pettersson (2007) geostatistical methods are used to map surface mass balance and there is some discussion on accessing error. It is typical that the experimental variogram (i.e. a ﬁtted line through covariance against h, the lag) does not pass through the origin but instead passes through the y-axis (covariance) at some positive value known as the “nugget” (Journel and Deutsch, 1998; Journel and Huijbregts, 2003; Webster and Oliver, 2007). The nugget is variance not explained by the model and is generally assigned to two sources: measurement error and variance at scales smaller than the lag. As the size of the smallest possible lag is determined by sampling density, unless new data become available it is impossible to separate these two sources. Simply using the nugget as an error estimator for point surveys is problematic; the model itself introduces an error that isn’t part of the data and the data errors have multiple sources. This last point is perhaps less relevant if the errors may be considered stationary across the data but as has been discussed earlier, this assumption does not hold true. However, given the apparent lack of alternatives the nugget serves as the ﬁrst best guess.

5.2.3 Other work There have been attempts to quantify error in surface mass balance data, at least for ablation. Braithwaite and Olesen (1989) used a simple linear model, taken from Lliboutry (1974), that attempted to break down a time series of ablation stake readings over a glacier into three parts.

yit = αi + βt + it (5.1) y is annual ablation at stake i in year t, α is the spatially dependent signal at stake i, β is a climate signal and is random noise. It is assumed that βt and it are random stationary processes, that it is uncorrelated across the stakes and uncorrelated with β. β is the climate signal and assumed to be the same across all stakes in a particular year. Both β and are assumed to average to zero over time and averages to zero over all stakes whilst β is the same for all stakes in a particular year. This results in the standard deviation of the ablation signal at a stake being a sum of the standard deviations for the 2 2 2 climate signal and the random noise signal sy = sβ + s . In Braithwaite and Olesen (1989) it is already suggested that non-stationarity may be a problem with longer time series and the influence of climate change both introducing a trend in β. This however is not the only departure from stationarity that the simple model does not consider. The climate signal across a small, valley glacier will vary in size and variance due to shading and topography influences. The random noise cannot be assumed to be stationary as the variance may reasonably be expected to vary with surface type, slope, water content and field worker. Further consideration must be given to the flow of ice and the inherent movement of any stake down glacier. Unless an ablation stake is re-drilled frequently measurements made at the stake will not represent one location but rather a series of locations. What constitutes “frequently” is determined by the speed of surface movement and the rate at which the process under investigation vary along the direction of flow at that particular

45 part of the glacier. Paper I (section 4.1) in this thesis results from the 2012 workshop held at the Tar- fala Research Station on “Measurement and Uncertainty Assessment of Glacier Mass Balance”. A previous workshop in 1998, “Methods of mass balance measurements and modelling”, produced several papers cited in this thesis: Cogley (1999); Fountain and Vecchia (1999); Hock and Jensen (1999); Jansson (1999). Many of the problems discussed above are touched upon in the material stemming from that workshop but the issue of stationarity, whilst mentioned, does not come under closer inspection and, in common with all other glaciological work in this field, discussion centres around either minimising field work (i.e. reduce data points) or finding optimal modelling methods to use with sparse data. Truthing is performed against the most complete available data sets which themselves stem from designs constrained by the needs of long term monitoring programmes or restricted funding. Paper I is an attempt to provide better truthing data, to provide accurate models of net surface mass balance which may guide estimates of errors in the components. It remains to be seen just how effective such an approach can be; geodetic methods can only provide a model of an integrated, multi-year net transport of mass, details of how seasonal responses bring about such change are not captured. Whilst geodetic methods may show the scale of what occurs outside the network of survey points, again the detailed responses are lost.

5.3 Surface-wide approaches to mass balance estimation

There are several studies on sampling density (e.g. Lliboutry, 1974; Jansson, 1999; Foun- tain and Vecchia, 1999; Cogley, 1999; Pelto, 2000; Jansson and Pettersson, 2007) relating to the glaciological method of surface mass balance study but paper III (section 4.3) of this thesis illustrates that sampling density varies in surveys for the geodetic method also. In this case the model was based on data gathered by traversing the glacier and safety issues as well as time constraints strongly influenced spatial distribution. Photogrammatic methods (e.g. Cogley, 2009; Thomson et al., 2017; Andreassen et al., 2016) suffer also from constraints in areas where contrast is poor, limiting the identification of tie-points or due to poor metadata (Magnússon et al., 2016). Alternatives such as ground based, oblique photogrammetry or laser scanning are available for future work but have their own safety and logistical constraints. Airborne laser scanning such as that used in Fischer et al. (2015) is expensive and reliant on favourable weather conditions, which glaciers tend to lack. Terrestrial laser scanning (e.g. Carrivick et al., 2015; Fischer et al., 2016) has great potential but the scanner must be set at a number of stations that maximise their view of the glacier surface, which may entail either a large number of stations and/or stations on surrounding peaks and ridges. The equipment is sensitive, heavy and prone to sinking into snow if great care isn’t taken during set up. But the results of the method are of potentially high quality (Hartzell et al., 2015). Interestingly some work, such as Kääb (2000), attempts to derive mass balance not using the geodetic method but by analysing high resolution images for data on glacier dynamics (velocity and strain) and using this to model mass flux in three dimensions and thus mass balance. Unfortunately such work is also limited by data quality as well as the rather long chain of errors accumulating between ice flux and the expression of this flux in visible features at the glacier surface. Paper II (section 4.2) provides an indication of how field methods might best be altered to maximise data acquisition. The study shows that high frequency GPR may successfully be used to measure snow depth with an accuracy better than 0.03 m. The equipment and method is very well suited to simultaneous differential Global Navigation Satellite System (dGNSS) surveying of the type utilised in paper III, with an accuracy

46 of approximately 0.02 m, indeed by mounting the GNSS antenna on the same sled as the GPR antenna, the irregular vertical errors introduced by the surveyor’s gait may be avoided. Such a combined survey would, in one fell swoop, satisfy the glaciological method’s accumulation survey and the geodetic method’s topographic survey (see Pälli et al., 2002; Previati et al., 2011; Wainwright et al., 2017, for similar applications). The errors stated for each method can be combined. For the specific case of Storglaciären 2 2 sz¯ = sGP R + sGNSS =0.036 m and generalising for GNSS errors increasing with baseline distance sz¯ =0.058 m, assuming an error of 0.05 m for the dGNSS survey. There are of course some caveats: dGNSS is reliant on adequate correction data, i.e. a base station or network of such stations, a direct line of sight to a minimum of five satellites is required and surveyed terrain must be directly accessed. Many countries have established networks of GNSS base stations (e.g. Lantmäteriet, 2017) and base stations themselves are easily established using a second receiver. Processing of the data may be performed post hoc but the surveyor is advised to check satellite availability before surveying. If the glacier in question is within coverage of real time correction signals, so called Real Time Kinematic surveys may allow more rational data collection, triggering a recording at specified distances between data points. The issue of satellite availability on glacier peripheries proximal to high and steep slopes to the south (northern hemi- sphere) is no small problem at higher latitudes such as on Storglaciären. GPS satellites have orbits that make surveying in polar and sub-polar regions more sensitive to signal shadowing; however, the expansion of GPS methods to include other constellations, GNSS, provides greater coverage in the high northern latitudes. Improvements in the Galileo (European Global Navigation Satellite Systems Agency, 2017) system as well as use of the GLONASS (Information and Analysis Center for Positioning, Navigation and Timing, 2017) improve coverage and may soon largely eliminate this problem, at least at certain times of the day. The last problem, that of physically accessing areas of the glacier judged unsafe or inaccessible is perhaps the most difficult to overcome. Winter- time access is generally better than summertime, except with regard to avalanche risk. There is however, no risk free method and in such cases judgement must be exercised but any data losses to the snow depth survey will be no greater than for regular probing. The GPR/GNSS method does not cover the entire glacier surface, even when access to all parts is available. Data will be acquired in lines and these must then be extended to the whole surface. The discussion in section 5.2.2 concerned the sparse data gathered from probing and ablation stake surveys whilst GPR depths can easily provide greater coverage and as noted earlier the method avoids many sampling errors.

5.4 Accumulation modelling

Paper I concludes with a summary of error estimates, both systematic and random. The systematic errors are estimated to ≈ 0.1 m w.e. a−1 whilst the random errors are estimated to several times this amount. The methods used in paper I correct year by year surveys post hoc using geodetic mass balance models of long term trends. This method can correct (partially) for net errors but is largely blind to errors masked by subsequent errors of opposite sign. Such weaknesses are not signiﬁcant for estimates of mid to long term mass balance but are problematic when modelling glacier response to climate signals. Paper IV is the result of such an error being identiﬁed in data that suggested large amounts of accumulation during the ablation season. The error is an inevitable consequence of logistical constraints on mass balance programmes such as that at the Tarfala Research Station but it is also unpredictable and hugely variable, stemming from both variations in the onset of ablation season conditions and variations in accessibility.

47 The need for correction of accumulation surveys is already acknowledged in the fixed date and combined systems of surface mass balance measurement (see section 2.2.3 and Cogley et al. (2011)). The correction method implemented in paper IV accounts not only for specific late season events, such as snow storms, but also for the spatial variations in the onset of the switch between accumulation dominated conditions to ablation dominated conditions. As such, the spatially distributed model of accumulation, achieved by inverting an ablation model, complements existing methodologies. Furthermore, the ablation model itself may be used as tool for quality control during field surveys of ablation. By calculating daily or potentially real time estimates of expected ablation from available temperature data in situ measurements may be checked for reading errors, unnoticed removal of stake extensions, slippage and other localised, non-linear errors.

5.5 Concluding remarks

A central theme of this thesis has been the ability or inability of the glaciologist to estimate errors in surveys. A large part of the problem stems from the inability of most surveys to adequately replicate measurements, due either to the variable nature of the measurand or the practical constraints on measuring such processes. Technological solutions are at hand but, given the nature of the field, even these are limited in their capacity. Airborne laser scanning (Lidar) offers some hope but if seasonal signals are to be measured surveys are required twice a year, in remote locations and over terrain not usually conducive to low altitude flying. In addition, these surveys must be supplemented with ground based measurements of density, which still requires digging snow pits. It would appear that glaciologists are needed in the field; therefore, high frequency GPR suggests itself as a logistically simpler solution for accumulation surveys. If this is performed in conjunction with a GNSS survey, year on year geodetic mass balance may be achieved even without Lidar. However, the details of how such new, combined surveys can be implemented are not yet resolved. For instance, surveying elevation to the previous summer surface instead of the accumulation season snow surface will provide a more accurate and robust measurement of geodetic mass balance as snow pack density (Sorge’s law) must still be considered a significant error source. But uncertainty in density estimates of the snow pack result in errors in the calculation of snow thickness from a GPR survey. Should these issues be resolved, as well as that of access to avalanche prone areas, we may have the best of both worlds: a high spatial and temporal resolution geodetic survey, with its inherent access to aspects of ice dynamics as well as surface mass balance surveys of seasonal components, capable of rendering accurate glacier – climate interactions. Whilst the problems encountered in glacier front surveys are in some respects similar to those for surface mass balance (knowing what is being measured), remote sensing seems to provide a clear and obtainable alternative, one which could not only improve the current front survey programme but could easily expand it. The only “cost” being a potentially lower temporal resolution but this has been shown to be no cost at all in reality. A final concluding remark must be that field work isn’t dead but it will change and so will the glaciologist.

48 Acknowledgement

The staff of the Tarfala Research Station, in particular Andreas, Henrik, Pia, Rafael, To- bbe and Tobbe. The many and various guests and “hantlangare” at Tarfala. Tarfala Lars for skiing instructions and for being Lars. Christian and Susie for support, discussion and agonising laughter. Christian again. A truly great office mate and perhaps the only person who could endure and even appreciate my contributions to office life. Helen, for support, patience, proofreading, patience, discussion, patience, ideas and patience.

Stipends and external funding provide by: Axel Lagrelius Fond Bolin Centre for Climate Research International Glaciological Society

49 50 References

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60 A A quick overview of a glacier

Figure A.1. A very simple model of a glacier. Snow accumulates and is transformed into ﬁrn then further into ice. Ice ﬂows into the ablation zone. The equilibrium line represents where accumulation and ablation are equal and the Equilibrium Line Altitude (E.L.A.) the elevation at which this occurs.

All entries below, except for Snow Apron, are taken from Cogley et al. (2011). Accumulation zone The part of the glacier where accumulation exceeds ablation in magnitude, that is, where the cumulative mass balance relative to the start of the mass-balance year is positive. Ablation zone The part of the glacier where ablation exceeds accumulation in magnitude, that is, where the cumulative mass balance relative to the start of the mass- balance year is negative. Firn, 1 Snow that has survived at least one ablation season but has not been transformed to glacier ice. This sense prevails in the study of mass balance. Snow becomes firn, by definition, at the instant when the mass-balance year ends. Firn, 2 Structurally, the metamorphic stage intermediate between snow and ice, in which the pore space is at least partially interconnected, allowing air and water to circu- late; typical densities are 400˘830 kg m˘3 In this sense, the firn is generally up to a few tens of metres thick on a temperate glacier that is close to a steady state, and up to or more than 100 m thick in the dry snow zone on the ice sheets.

61 Equilibrium line The set of points on the surface of the glacier where the climatic mass balance is zero at a given moment. The equilibrium line separates the accumulation zone from the ablation zone. It coincides with the snowline only if all mass exchange occurs at the surface of the glacier and there is no superimposed ice.

Equilibrium Line Altitude (E.L.A.) The spatially averaged altitude of the equilibrium line. The ELA may be determined by direct visual observation, but is generally determined, in the context of mass-balance measurements, by ﬁtting a curve to data representing surface mass balance as a function of altitude. This is often an idealization, because the equilibrium line tends to span a range of altitudes.

Bergschrund A crevasse at the head of a glacier that separates ﬂowing ice from stagnant ice, or from a rock headwall. From an ice-dynamical point of view the bergschrund is the headward boundary of the glacier, while for hydrological and other purposes, including glacier inventory, the stagnant ice above the bergschrund is part of the glacier.

Front The terminus of the glacier. The lowest end of a glacier, also called glacier snout or glacier toe.

Snow apron An ephemeral layer of snow proximal to the glacier, usually at the front, which may survive throughout the ablation season. It does not feed into nor is it fed by the glacier and may disappear rapidly during warm summers.

62 B Glacier front retreat rates

In section 3.3.2 of chapter 3 some figures illustrating fluctuation rates and a first order regression models were presented for a small number of glaciers in the Tarfala Research Station’s front survey programme. The figures also contain plots of the North Atlantic Oscillation (NAO) index averaged for January, February, March & April and June, July & August is shown as well as the June, July & August average temperature as recorded in the Tarfala valley. Correlation with these is indicated in each diagram. Below are similar figures for the remaining glaciers in the aforementioned programme.

Figure B.1. Kårsajietna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Re- gression models are not meaningful, correlation coeﬃcients moderate

63 Figure B.2. Riuokojietna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate

Figure B.3. Västra Påssusjietna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate to strong

Figure B.4. Östra Påssusjietna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate

64 Figure B.5. Stour Raitaglaciären ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate

Figure B.6. Unna Raitaglaciären ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients weak to moderate

Figure B.7. Sydöstra Kaskasatjåkkaglaciär ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate to weak

65 Figure B.8. Tarfalaglaciären ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients likewise

Figure B.9. Isfallsglaciären ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate to weak

Figure B.10. Rabots Glaciär ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients weak

66 Figure B.11. Hyllglaciären ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate

Figure B.12. Suottasjekna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate

Figure B.13. Ruotesjekna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Regression models are not meaningful, correlation coeﬃcients moderate to weak

67 Figure B.14. Pårtejekna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Re- gression models are not meaningful, correlation coeﬃcients weak to moderate

Figure B.15. Salajekna ﬂuctuation rates together with NAO index and summer temperatue at Tarfala. Re- gression models are not meaningful, correlation coeﬃcients weak