Cold Surface Layer Dynamics of Storglaciären, Northern Sweden

Examensarbete vid Institutionen för geovetenskaper Degree Project at the Department of Earth Sciences ISSN 1650-6553 Nr 458 Cold Surface Layer Dynamics of Storglaciären, Northern Sweden 2009-2019 Dynamik av det kalla ytskiktet på Storglaciären, norra Sverige 2009 2019 Shunan Feng INSTITUTIONEN FÖR GEOVETENSKAPER DEPARTMENT OF EARTH SCIENCES

Examensarbete vid Institutionen för geovetenskaper Degree Project at the Department of Earth Sciences ISSN 1650-6553 Nr 458 Cold Surface Layer Dynamics of Storglaciären, Northern Sweden 2009-2019 Dynamik av det kalla ytskiktet på Storglaciären, norra Sverige 2009 2019 Shunan Feng

Title page: Kebnekaise and Storglaciären, photo taken by Shunan Feng during the summer fieldtrip 2018-08-27. I came, I measured, I modeled. ISSN 1650-6553 Copyright Shunan Feng Published at Department of Earth Sciences, Uppsala University (www.geo.uu.se), Uppsala, 2019

Abstract Cold Surface Layer Dynamics of Storglaciären, Northern Sweden 2009-2019 Shunan Feng Storglaciären is a sub-arctic polythermal glacier in northern Sweden. Twenty years monitoring of the cold surface layer found that it has lost one third of its total volume of cold ice with an average thinning rate of 0.80 ± 0.24 m a -1 for the period of 1989-2009. This thesis presents the continuous investigation of the thermal structure evolution of Storglaciären using thermistor string measurements and a coupled energy balance-snowpack model. The thickness dynamics of the cold surface layer is derived from both the thermistor string measurement (2018-2019) and the simulation results (2009-2018). The subsurface temperature evolution and the associated cold-temperate transition surface (CTS) dynamics are analyzed at both the thermistor scale and glacier scale. Point study involves installing a thermistor string and extrapolating the measured subsurface temperature to the pressure melting point isotherm depth. The simulated CTS depth changes at the study site was also used for comparison. Glacier scale study aims to simulate the spatial and temporal variations of the thickness of the cold surface layer. Meteorological data was collected from multiple automatic weather stations and the solid precipitation was estimated from the winter mass balance survey. The model was utilized in the study of the cold surface layer dynamics for the first time. Both the point scale and glacier scale study suggest an overall thickening trend of the cold surface layer. The thermistor derived CTS depth exhibits a thickening rate of ~0.9 m a -1 compared to the depth derived from ground penetrating radar survey in 2009. The influence of mass balance, melt and accumulation are also examined by spatial correlation with CTS depth. Keywords: Storglaciären, cold surface layer, cold-temperate transition surface, polythermal glacier Degree Project E1 in Earth Science, 1GV025, 30 credits Supervisor: Rickard Pettersson Department of Earth Sciences, Uppsala University, Villavägen 16, SE-75239 Uppsala (www.geo.uu.se) ISSN 1650-6553, Examensarbete vid Institutionen för geovetenskaper, No. 000, 2019 The whole document is available at www.diva-portal.org

Populärvetenskaplig sammanfattning Dynamik av det kalla ytskiktet på Storglaciären, norra Sverige 2009 2019 Shunan Feng Storglaciären är en subarktisk polytermal glaciär i norra Sverige som har ett kallt ytskikt i ablationsområdet. Tidigare studier av mäktigheten hos det kalla ytskiktet visar att Storglaciären har förlorat en tredjedel av sin totala volym av kall is med en genomsnittlig uttunningshastighet på 0,80 ± 0,24 m a -1 för perioden 1989-2009. Denna uppsats presenterar den fortsatta utvecklingen av det kalla ytskiktet på Storglaciären under perioden 2009 till 2019 med hjälp av istemperaturmätningar och en ytenergi balansmodell koppla till en och en termodynamisk modell för snö och is. Istemperaturens utveckling och djupet till övergången mellan kall och tempererad is (CTS) analyseras både på lokalskala vid en punkt och över hela glaciären. Punktstudien utnyttjar temperaturmätningar vid en termistorslinga för att uppskatta temperaturfördelningen i isen och djupet för övergången mellan kall och tempererad is. Resultaten används också för jämförelse med simulerade resultat. Den rumsliga studien använder en kopplad energibalans och en termodynamisk modell för snö och is för att simulera rumsliga och tidsmässiga variationer av tjockleken på det kalla ytskiktet. Som ingångsdata till modellen användes meteorologiska data från flera automatiska väder stationer och den nederbörden i fast form uppskattades från massbalans mätningar som görs på glaciären. Det är fösta gången den här typen av modell används för att studera det kalla ytskiktets dynamik. Både på lokalskala och glaciärskala tyder på en övergripande förtjockningstrend av det kalla ytskiktet. Uppskattningen av CTS djupet vid temperaturmätningar uppvisar en ökningshastighet av ~ 0,9 m a -1 av det kalla skiktets tjocklek jämfört med markradar undersökningar i 2009. Påverkan och rumslig korrelation mellan massbalans, smältning och ackumulation på CTS-djupet undersöks också. Nyckelord: Storglaciären, kallt ytskikt, kall-tempererad is, polyterrmal glaciär Examensarbete E1 i geovetenskap, 1GV025, 30 hp Handledare: Rickard Pettersson Institutionen för geovetenskaper, Uppsala universitet, Villavägen 16, 752 36 Uppsala (www.geo.uu.se) ISSN 1650-6553, Examensarbete vid Institutionen för geovetenskaper, Nr 000, 2019 Hela publikationen finns tillgänglig på www.diva-portal.org

Table of Contents 1. Introduction... 1 2. Study Area... 3 2.1 Storglaciären... 3 2.2 Cold Surface Layer Dynamics Mechanism... 5 2.3 CTS Survey 1989, 2001 and 2009... 5 3. Method... 7 3.1 In-situ Thermistor Data... 7 3.1.1 Preparation of Thermistor String... 7 3.1.2 Calibration of Thermistor String... 7 3.1.3 Installation of Thermistor String... 8 3.1.4 Deriving CTS from Thermistor Data... 8 3.2 Model... 9 3.2.1 Model Setup... 9 3.2.2 Data Input... 10 3.2.2.1 Preprocessing of Climate Forcing and Mass Balance Data... 10 3.2.2.2 Preprocessing of Mass Balance Data... 11 3.2.2.3 Model Grid... 12 3.2.3 Initial Subsurface Conditions... 13 3.2.4 Deriving CTS from Model Results... 14 4. Result... 15 4.1 CTS Derived from Thermistor Data... 15 4.2 Model Results... 16 4.2.1 CTS Spatial Evolution and Temporal Changes... 16 4.2.2 Correlation Map... 18 4.2.2.1 Cumulative Mass Balance vs CTS... 18 4.2.2.2 Melt vs CTS... 20 4.2.2.3 Accumulation vs CTS... 20 4.3 Time Series CTS Evolution at Study Site... 22 5. Discussion... 25 5.1 CTS at Point Scale... 25 5.2 CTS at Glacier Scale... 25 5.3 Spatial Correlation and Analysis... 26 6. Conclusion... 28 7. Acknowledgements... 30 8. References... 31 Appendix 1 Thermistor Data Conversion... 34 Appendix 2: Annual Evolution of CTS... 36

1. Introduction Glaciers play a critical role in regulating the seasonal water cycle in many mountainous regions and have been considered as one of the best indicators of terrestrial climate variability and response (Kääb et al., 2012). The glacier meltwater is also seen as a major contributor to global sea level rise (Thompson et al., 2011). Retreat of valley glacier can trigger the destabilization of mountain slopes and increase the risk of rockslides and catastrophic outburst floods (Marzeion et al., 2014). Storage of fresh water in the mountainous glacier ice and seasonal snow cover plays a prominent role in irrigation and hydropower production (Huss et al., 2010). The glaciers and ice sheets which exhibits nontemperate thermal regimes occupies a significant proportion (Irvine-Fynn et al., 2011). Polythermal glaciers contain layers of temperate ice at the pressure melting point which coexist with zones of cold ice (Ryser et al., 2013), are commonly found in the Canadian Arctic and the drier side of the Scandinavian mountains (Pettersson et al., 2003). The coldtemperate transition surface (CTS) is the boundary between cold and temperate ice as well as a hydraulic boundary for intra-granular water, separating the water-free region in polythermal glaciers (Gusmeroli et al., 2012; Pettersson et al., 2004, 2003). Water content varies from zero on the cold ice side to positive values on the temperate side (Blatter and Hutter, 1991). Temperate ice is a layer at the pressure melting point (PMP) and can contain up to 9 % of coexisting interstitial liquid and liquid water content (Irvine- Fynn et al., 2011; Pettersson, 2004). The heat balance of a glacier is controlled by the processes of conduction, advection and latent heat transfer (Cuffey and Paterson, 2010; Paterson, 1994). Consequently, the glacier s thermal structure is influenced by the factors affecting those processes (Irvine-Fynn et al., 2011), including ice flow, glacier hypsometry and geometry etc. The dynamics of cold surface layer may affect Arctic and sub-arctic environment by influencing glacial hydrological processes, glacier mechanical properties and landforms etc. (Pettersson et al., 2003). The influence on erosion rates could significantly impact suspended sediment loads as well as nutrient production downstream (Humborg et al., 2002; Pettersson et al., 2003). Storglaciären is a well-studied glacier with a polythermal regime in northern Sweden, and it has the longest (post-1946) continuous mass balance and glacier dynamics observations (Gusmeroli et al., 2012; Holmlund and Eriksson, 1989; Pettersson et al., 2003). Previous studies found that the CTS depth decreased 8.3 m (22% of average thickness) during 1989-2001 (Pettersson et al., 2003) and the thinning of cold surface layer continued. A repeated ice penetrating radar survey in 2009 suggested that Storglaciären has lost one-third of its cold surface layer volume with an average thinning rate of 0.80 ± 0.24 m a -1 (Gusmeroli et al., 2012; Pettersson et al., 2004, 2003). The changes of cold surface layer are the evidence of warming in the Arctic and were cited in the 2007 Intergovernmental Panel on Climate Change (IPCC) report (Gusmeroli et al., 2012). However, the thinning pattern of cold surface layer on Storglaciären is not uniform and the processes were not fully understood (Pettersson et al., 2007). 1

Previous attempts in mapping the cold layer were conducted by ground penetrating radar (GPR) surveys and subsurface temperature surveys by thermistor string measurements (Gusmeroli et al., 2012; Holmlund and Eriksson, 1989; Pettersson, 2004; Pettersson et al., 2003). Dobiński et al. (2017) investigated CTS along the center line using GPR and two short transects with electro resistivity tomography data. Direct geophysical surveys provide us the thickness and distribution of cold surface layer with high spatial resolution while reconstruction of the surface cold layer evolution in time may be logistically challenging. The long time span between the repeated radar surveys restricted the understanding of the temporal changes. The time window of conducting GPR survey is also limited to wintertime due to the presence of meltwater in summertime. The coarse temporal resolution could not reveal the seasonal or annual variations of CTS. Thermistor strings usually monitor a season or several full cycles of accumulation and ablation seasons. Decadal continuous measurement is not practical due to the cost of maintenance. Furthermore, thermistor string measurements at multiple sites alone could not reflect the spatial evolution. Hock and Holmgren (2005) developed a distributed surface energy balance model which proposed a new way of parameterizing the snow albedo. It was applied to Storglaciären, but the subsurface melting is neglected. Pettersson et al. (2007) investigated the mechanism and sensitivity of cold surface layer using a one-dimensional model. The model requires knowledge of emergence velocities which is not available in the study period. Aschwanden and Blatter (2009) proposed an enthalpy method to simulate the evolution of cold and temperate layer and water in Storglaciären along the kinematic center line. van Pelt et al., (2012) developed a coupled surface energy balance-snowpack model and it has been tested to multiple glaciers on Svalbard. The data input requirement is only the basic meteorological parameters, which makes it easy and fast to be implemented. The purpose of this study is to answer the following questions: 1) What are the spatial and temporal changes of CTS on Storglaciären from 2009 to 2019? 2) How mass balance affects the evolution of the cold surface layer? This is done by deriving the thickness of cold surface layer from an installed thermistor string in 2018 and modelling the CTS migration from 2009 to 2018. This thesis compares and analyzed the cold surface layer dynamics at both point and glacier scales. Point study compares the thermistor data derived CTS with both the previous geophysical survey and the simulated temporal evolution of CTS at the study site. Spatial analysis focuses on the thickness of the cold surface layer variations. The simulated spatial extent and temporal variations of CTS are compared to previous geophysical surveys. Different forcing parameters are spatially correlated with simulated CTS to assess the role of mass balance, melt and accumulation. 2

2. Study Area 2.1 Storglaciären Storglaciären (67 55 N, 18 35 E) is a polythermal valley glacier in the Kebnekaise massif, northern Sweden (Figure 1) (Aschwanden et al., 2012; Holmlund et al., 2005). It covers an area of 3.1 km 2 and its elevation ranges from ~1120 to ~1730 m (Hock and Holmgren, 2005). Storglaciären has an average ice thickness of 95 m. The ice flow is supplied from two cirques in accumulation zone where the northern one contributes the most (Aschwanden and Blatter, 2005). The thermal structure of Storglaciären is Scandinavian-type (Svalbard-type) glacier, which exhibits a cold surface layer covering the temperate ice in the ablation zone (Aschwanden et al., 2012; Ryser et al., 2013). Temperate ice occupies ~85 % of the glacier (Gusmeroli et al., 2010b). The glacier is frozen to the bed along its margins and terminus and is surrounded by permafrost, except at the forefield (Holmlund and others, 1996; Isaksen and others, 2001). The geomorphology is mainly shaped by a long-lasting glaciation process (Dobiński et al., 2017). Figure 1 Study Area (The coordinates of Tarfala Research Station, the automatic weather station on the ablation zone (Ablation AWS) and the outline of Storglaciären are obtained from Bolin Center for Climate Research https://bolin.su.se/. Digital Elevation Model (DEM) is provided by Lantmateriet through https://maps.slu.se/. The location of the installed thermistor string is marked in the map.) The climate is influenced by predominant westerly winds (Pettersson, 2004) and is frequently affected by cyclonic activity (Hock and Holmgren, 1996). The glacier is situated on the eastern side of the Scandinavian mountains, therefore experiences lower precipitation and temperature with higher seasonal amplitude than the western side (Pettersson, 2004). The mean air temperature from a 47-year (1965-2011) analysis is -3.5 ± 0.9 (Jonsell et al., 2013). Most of the snow accumulation is brought by storms in later winter or early spring (Pohjola and Rogers, 1997).The mass-balance program at Storglaciären was initiated in 1946 (Holmlund et al., 2005; Holmlund and Jansson, 1999), providing the world s longest continuous direct glaciological measured record of glacier mass balance. Precipitation on Storglaciären is influenced by orography (Pohjola and Rogers, 1997), but the mass balance program had revealed that the accumulation pattern was much more complicated than the 3

ablation pattern, which is strongly elevation dependent (Holmlund et al., 2005). Winter mass balance survey on Storglaciären keeps track of the snow depth probing annually in later April-early May, before the start of melt season (Holmlund and Jansson, 1999). The snow probing has been made at a fixed system of 100 100 m grids, which is 300 possible probing grid points, since 1966 (Holmlund et al., 2005; Holmlund and Jansson, 1999). A various number (5 or 6) of snow density pits are also taken along the center flow line. Winter mass balance surveys prior to 1966 were measured by profiles which is not as homogeneous as the fixed system (Holmlund and Jansson, 1999). The mass balance record shows that the glacier has been retreating steadily since 1910 (Holmlund et al., 2005). The Tarfala Research Station (TRS) (67.9112 N, 18.6107 E) is located on the northeastern side of Tarfala valley (Figure 1). The thermistor string was installed at the southern part of the ablation zone (67.90 N, 18.58 E), southeast of two automatic weather stations (67.9030 N, 18.5726 E) in the ablation area. Various sources of meteorological data are available for Storglaciären, including TRS and Swedish Meteorological and Hydrological Institute (SMHI). a b Figure 2 Bedrock Topography of Storglaciären. a) the bedrock topography of Storglaciären with 30 m contour line interval, the study area is highlighted; b) filled 2D contour map in study area. The reference line shows the bedrock threshold (subglacial topography was surveyed by radio echo soundings (Björnsson, 1981) and is accessed at https://github.com/pism/storglaciaren/). The subglacial topography of Storglaciären is shown in Figure 2a and its valley form ratio ranges from 1.6 to 4 (Björnsson, 1981). This study focuses on the changes of cold surface layer in the ablation zone. The study area is divided into upper and lower two parts by a bedrock threshold south of the kinematic center flowline (Björnsson, 1981; Pettersson et al., 2003) (Figure 2b). The upward slope of which is found to be about five and up to ten times the downward slope of glacier surface (Björnsson, 1981). The threshold is reported to be associated with faster ice flow and consequently steeper slope (Pettersson et al., 2007). As result, thinner snow cover forms over this area as the drifting snow accumulates downward the ice flow in the lee-effect affected area because of steeper slope (Pettersson, 2004). It may also cause the accumulation of water in the center basin (Björnsson, 1981). 4

2.2 Cold Surface Layer Dynamics Mechanism Pettersson (2004) did an elaborate work and provided a detailed description of the physical processes defining the thermodynamics of the cold surface layer at Storglaciären. The schematic diagram of Storglaciären s thermal structure is shown in Figure 3. The CTS depth (thickness of the cold surface layer) is determined by the fluxes of mass and energy at the surface and liquid water content of the ice supplied into the cold ice layer, and velocity field (Blatter and Hutter, 1991; Hutter et al., 1988; Pettersson et al., 2007, 2003). The surface layer in accumulation zone is cold seasonally (Aschwanden and Blatter, 2005) and it becomes temperate because of the latent heat released from refreezing of percolating water (Holmlund and Eriksson, 1989; Pettersson, 2004) at the start of melt season. The surface ice in the ablation zone serves as a transient thermal layer (Irvine-Fynn et al., 2011). In the ablation area, the impermeable ice surface prohibits the percolation of meltwater and limits the refreezing of water to the contact surface, forming superimposed ice (Holmlund and Eriksson, 1989). The glacier surface is warmed by the supplied latent heat until it reaches melting point, but heat conduction is limited by ice. The minimum annual average subsurface temperature was found at approximately 4 m below ice surface at central part of the tongue of Storglaciären (Holmlund and Eriksson, 1989). The temperature of glacier surface is limited to the melting point and all excessive surface energy flux is used to melt ice on the surface. Hence, the cold ice layer remains cold unless ablation melts all ice layers away. The downward migration of CTS is driven by the negative temperature gradient in the cold surface ice (Pettersson et al., 2007). When CTS penetrates the glacier and freezes to the ground, CTS starts to enter permafrost zones and forms permafrost base surface (Figure 3). The stability and long term thickness of cold surface layer is determined by the balance between the downward migration of CTS and net ablation at glacier surface (Pettersson et al., 2007, 2003). 2.3 CTS Survey 1989, 2001 and 2009 Figure 3 Schematic diagram of thermal structure and Permafrost Base (CTS-PB) of Storglaciären, modified from (Dobiński et al., 2017; Pettersson, 2004). Gray shaded area is temperate ice and above is the cold surface layer. Below the ground is the permafrost zones. Ice penetrating radar has been widely implemented in detection of water content within a glacier (Dowdeswell et al., 1984; Kotlyakov and Macheret, Yu, 1987; Macheret and Zhuravlev, 1982; Ryser et al., 2013). CTS is the boundary that separates the impermeable cold ice and wet temperate ice in polythermal glaciers (Gusmeroli et al., 2010b). The hydrological property of CTS enables us to map the extent of CTS with radar (Holmlund and Eriksson, 1989). GPR surveys usually took place in spring (late April to early May) to avoid possible unnecessary noise from meltwater (Gusmeroli et al., 2012). 5

Table 1 Summary Table of Previous CTS Survey Year CTS depth (m) Min Mean Max 1989 23 38 64 2001 4 31 65 2009 1 25 59 Figure 4 Spatially interpolated CTS depth from GPR survey in 2009 (Gusmeroli et al., 2012) Three comprehensive GPR surveys of the cold surface layer in Storglaciären were conducted in the past 30 years. The spatial pattern and differences of CTS from 1989 to 2009 were summarized in Table 1. In the 1989 survey, Holmlund and Eriksson (1989) obtained GPR profiles with an average spacing of ~200 m. The thickest cold surface layer was found along the northern side of local accumulation area and the along the southern side. Additionally, the 1989 survey found a cold surface layer situated above the equilibrium line along the southern cirque margin. The 2001 survey was implemented by following the 1989 profiles (Pettersson et al., 2003). The average CTS depth declined from 38 m to 31 m. Gusmeroli et al. (2012) mapped the extent of CTS in 2009 (Figure 4). The average thickness of the cold surface layer has undergone a gradual thinning process. The mean depth of CTS in 2009 survey was only two meters deeper than the minimum survey result in 1989. The comparison of 1989 and 2001 GPR surveys shows an overall thinning of 8.3 m in 12 years (Pettersson et al., 2003). The northern and southern margins saw an increase in the thickness which were believed to be caused by the poor overlap of the GPR survey (Pettersson et al., 2003). The continuous thinning of cold surface ice had led to an average CTS lost rate of 0.80 ± 0.24 m a -1 in twenty years (Gusmeroli et al., 2012). In general, the spatial pattern in the surveys are similar (Gusmeroli et al., 2012; Pettersson et al., 2003). The deepest CTS was found along the glacier margins and northwesterly part (Pettersson et al., 2003). A shallow cold surface layer was in the lower southern part along the glacier centerline, which was assumed to be affected by the bedrock terrain. The thinning rate is not uniform in space. The cold surface layer along the southern and northwesterly margins saw higher decrease of ~ 20 m or up to more than 30 m (Gusmeroli et al., 2012). In the central part of the ablation zone near the center flow line, however, the thickness differences were within the uncertainty range of the data (Pettersson et al., 2003). 6

3. Method 3.1 In-situ Thermistor Data 3.1.1 Preparation of Thermistor String A 20-meter thermistor string was manufactured using Amphenol Advanced Sensors MC65F103A thermistors. The thermistors were mounted to an electrical control cable with 37 leads (37 0.14 mm²). The cable was labeled with 0.5 m separation for the lower 15 thermistors from the bottom and 1 m for the remaining thermistors at the upper part. In total, 24 thermistors were soldered and sealed with selffusion tape and heat shrink tubes. All 24 leads soldered with thermistors were then connected to one common lead. The threads of the cable leads were wired to a Campbell Scientific CR 10X logger with a multiplexer AM16/32B under a single ended connection scheme. The wiring is following the procedures from Marchenko (2018) and the electric circuit scheme is given in Appendix 1 Figure 17. The excitation voltage (U ex ) was 310 mv and the reference resistance (R f ) of the temperature-stable reference resistor was 100 kω. Both the logger and the multiplexer were placed on a metal plate inside a Pelicase 1450. The logger was powered by two 6 V alkaline batteries inside the logger box. The completed logger box was sealed by silicone glue before installation. 3.1.2 Calibration of Thermistor String The precision of the thermistors was reported to be ± 0.05 by the manufacturer. The thermistor resistance (R t ) changes in response to temperature. The logger measured the voltage of the reference resistance (R f ). The thermistor resistance can be obtained by Eq. 1 according to Ohm s law. The ratio of R 25 /R t is a function of temperature (Eq.3). The calibration was achieved by re-calculating the thermistor resistance at 25 (R 25 ). The calculated thermistor resistance is then used to compute R 25, which will be used to convert the measured voltages to actual temperature. The assembled thermistor string was calibrated in an ice/water bath and a freeze room under the temperature of -25 before installation. However, both attempts failed due to the lack of control over the environment temperature. Sensors were sensitive to the minor temperature gradient variations between the ice water bath and thermistors. Heat from room temperature made it hard to reach equilibrium. The temperature of freeze room was controlled by a thermometer, which was less accurate than thermistors. Taking all the factors into consideration, the calibration was suggested to be done after the installation. The temperature inside the borehole takes time to recover from the disturbance caused by the steam drill. The measured voltage (U m ) curve flattens when the borehole temperature reaches freezing point before it s frozen. The mode of U m when the curve flattened was used to calculated thermistor resistance (R t ) by Eq. 1. The temperature was assumed to be at the melting point when U m became stable. The ratio of R t /R 25 was further updated by Eq. 3. U ex R t + R f = U m R t (1) 7

3.1.3 Installation of Thermistor String Subsurface ice temperatures were measured in a borehole (Error! Reference source not found.) drilled w ith a Heucke steam drill (Heucke, 1999) at the study site in August 2018. The borehole was 14.3 m deep, but the thermistor string was installed to a depth of 13.3 m due to the impediments at the bottom. Before the installation, the selection of the study site aims to drill the borehole at the same location where previous seismic survey and thermistor measurement was conducted (Gusmeroli et al., 2010a). However, the coordinate provided in the article was a typo (67 90 N, 18 57 E). Alternatively, a site where the radar profile had revealed the CTS depth was relatively shallowest (Gusmeroli et al., 2012) was chosen, which was close to the previous borehole and ensured higher reliability of empirical estimates. The logger box was connected to a mast which stood next to the borehole (Figure 5a, b). Three thermistors remained at the surface due to the depth limit of the borehole. The logger box and the data were collected in the winter fieldtrip to TRS in April 2019 (Figure 5c, d) and it was discovered to remain in good conditions. The battery voltage was 11 V and no signs of excessive humidity was found as is indicated by the status of dehumidifier bags with Silica gel inside. a b c d Figure 5 Installation of thermistor string: a): Scheme of installed thermistor string (provided by Rickard Pettersson); b) Logger box installed on Aug 27, 2018; c) the logger box on the retrieval day Apr 15, 2019; d) inside logger box on the retrieval day Apr 15, 2019. 3.1.4 Deriving CTS from Thermistor Data The post-processing of thermistor data first converted the measured voltages to actual temperature. The temperature is a function of thermistor resistance (R t ), which was calculated using Eq. 2, following the instruction provided by the manufacturer of the sensors. The ratio of R t /R 25 was adjusted to the range of temperatures from -50 to 0. Detailed description of the constants and the measured voltage curve is given in Appendix 1. 1 T = a + b (ln R t ) + c (ln R 2 t ) + d (ln R 3 t ) R 25 R 25 R 25 8 (2)

where ln ( R t R 25 ) = A + B T 1 + C T 2 + D T 3 (3) Pettersson et al. (2004) determined position and migration rate of CTS by extrapolating the fitted temperature profile and finding the position where ice temperature reached the melting point. The onedimensional thermal dynamic equation requires vertical velocity at study site, which is not available in this study. Additionally, the installed thermistor string only reached a depth of less than 13.3 m where the bottom thermistor at the depth of 12.7 m, which was still above the CTS in theory. In practice, a linear regression was applied to the temperature of the last three thermistors from the bottom. The freezing isotherm position was estimated by the simple linear regression model. 3.2 Model 3.2.1 Model Setup A coupled surface energy balance-snowpack model was utilized in this study to simulate the evolution of subsurface temperature. The model runs from 2009-04-01 00:00 to 2018-04-01 00:00, which covers nine-year time span since the last comprehensive CTS survey in 2009. The simulation produces the mass balance, subsurface temperature and the associated layer thickness changes etc. with a time step of every three hours. The daily average output is saved for analysis. The model was built by van Pelt et al. (2012) from the surface energy model (Klok and Oerlemans, 2002) and the multi-layer snowpack model (Greuell and Konzelmann, 1994). The model has been implemented to multiple glaciers on Svalbard (Marchenko et al., 2017; van Pelt, 2013; van Pelt et al., 2014). Surface temperature is determined by the net surface energy flux and the excess energy is used for melting when surface reaches melting point (van Pelt and Kohler, 2015). The meltwater production simulated in the surface energy model (Klok and Oerlemans, 2002) provides data input for the multilayer snowpack model (Greuell and Konzelmann, 1994). The subsurface simulation serves to update the liquid water storage, gravitational densification and heat conduction (Marchenko et al., 2017; van Pelt, 2013). Shading effect from surrounding topography will be taken into consideration by the model. The surface energy and mass exchange compute the upper boundary conditions from basic climate forcing data, including air temperature, precipitation, relative humidity and cloud cover (van Pelt and Kohler, 2015). Vertical profiles of subsurface temperature, density and water content are updated by the subsurface model (van Pelt, 2013). Percolating water may be retained as irreducible water held by capillary force in the snow (van Pelt et al., 2014) or stored as slush water if it reaches an impermeable ice layer (van Pelt and Kohler, 2015). The refreezing of liquid water happens when the subsurface temperature is below melting point. The amount of refreezing water is also limited by ice density. The model adds layers at the surface and bottom of each grid points when a layer is completely removed at the surface (van Pelt and Kohler, 2015). Having the Lagrangian type grid that follows the stratigraphical 9

layers, the model is allowed to account for the vertical advection of material downwards in the accumulation zone and upwards in the ablation zone. In this study, the moving grid routine that adds a new layer at the bottom was updated. The temperature of added new layer is set at 273.15 K since the ice layers underlying the cold surface are supposed to be temperate ice only. The water content in the moving grid supplied by the model was also changed to 8 mm w.e. instead of adjusting by the model, which was described in the following chapter of initial subsurface conditions. Furthermore, the ice density was reset to 910 kg m -3, which allows updating the irreducible water within the temperate ice. 3.2.2 Data Input 3.2.2.1 Preprocessing of Climate Forcing and Mass Balance Data The meteorological data input required by the model includes 1) air temperature, 2) precipitation, 3) relative humidity (RH) and 4) cloud cover (van Pelt and Kohler, 2015). Four automatic weather stations (AWS) were established and maintained by Tarfala Research Station (TRS). Tarfala Metrological Station ( Tarfala Met station ) was installed on the northern side of TRS and was replaced by the new weather station ( Tarfala RS AWS ) in 2017 (Tarfala RS AWS METADATA REPORT, 2019). Both AWSs will be referred as TRS AWS in the following chapters. TRS AWS provides the most continuous hourly measurement of liquid precipitation. The other two AWSs stood in the upper ablation zone of Storglaciären (Storglaciären AWS Storglaciären Snow METADATA REPORT, 2019), one of which only measures during summertime ( StorSummer AWS ) while the other one operates all year round ( Stor AWS ). Additionally, the meteorological data from Swedish Meteorological and Hydrological Institute (SMHI) AWS, which stands next to TRS, was also used. Cloud cover from the closest station was reported by a SMHI AWS 24 km south of TRS in Nikkaluokta, Kiruna, All the available meteorological data (Table 2) was analyzed and integrated to a complete time series during the preprocessing. Stor AWS was selected as the main source for it provides the direct measurement on Storglaciären. TRS AWS provided the data for the period (2009-2013) prior to the installation of Stor AWS. All the gaps were detected and filled by the available measurements from SMHI or interpolated by fillmissing (MATLAB) function. The script used for detecting and filling gaps in time series data is available at https://github.com/fsn1995/matlabfsn/blob/master/timeseriesdata.m. Air temperature was extrapolated assuming a constant in time and space lapse rate. The temperature lapse rate calculated from temperature measurement (2013-2018) in Stor AWS and TRS AWS was 0.60 100 m -1 on average. Temperature input is calculated from the integrated time series of temperature measurements by the temperature lapse rate. The attempt to estimate the precipitation lapse rate found no clear relation between the summer precipitation measured by TRS AWS and Stor AWS, which might be explained by the windy conditions on the glacier. TRS AWS was chosen as the only reliable source for summer precipitation without considering the precipitation lapse rate. Winter precipitation could accumulate on glacier surface in solid or liquid form. The amount of liquid precipitation in the 10

accumulation season was assumed to be only fractional and would refreeze in snowpack. Winter precipitation was reconstructed from the snow stake readings in the following steps. Table 2 Data Summary Table Data Date Parameter Source mass balance 1946-2018 Stake measurement Snow density https://bolin.su.se/data/tarfala/tarfalaglaciaren.php TRS AWS 1988-2018 temperature, RH, precipitation, global radiation, https://su.figshare.com/trs wind, air Pressure Storglaciären AWS temperature, RH, 2013-2018 Storglaciären precipitation Provided by TRS at request Snow SLU DEM 2 m resolution DEM https://maps.slu.se/ SMHI AWS * Temperature, RH Cloud cover https://www.smhi.se/klimatdata/meteorologi/ (*: The monitoring time in SMHI varies depending on the station and the parameter. The RT90 and SWEREFF99 coordinates are converted to WGS84 using the script: https://github.com/fsn1995/matlabfsn/blob/master/sweref2wgs84.m) 3.2.2.2 Preprocessing of Mass Balance Data Winter balance surveys are conducted before the start of melt season in each year. The differences in the timing of the separation of accumulation and ablation season were considered as negligible. In the preprocessing of winter balance data, the accumulation season was assumed to start from October in the year before the winter mass balance survey and end in the end of April. The remaining months from May to September were considered as the ablation season. The coordinates of all snow stakes and snow pits were converted from RT90 or SWEREFF99 to WGS 84. Snow metamorphism starts once snow touches the ground. The densification of snowpack is caused by gravity and other metamorphism processes. Snow water equivalent (w.e.) of each snow pit was converted and compared against the sampling depth. The snow pit water equivalent is found to be linearly increasing as depth increases. The linear regression model of the snow pit depth against the cumulative sum of snow w.e. was stored to estimate the snow cover water equivalent in each year (Figure 6). 11

Figure 6 Linear relation between the snow pits depth and the snowpack water equivalent (cm w.e.). Linear fitting regression is applied to snow pits measurement from 2009-2018. 3.2.2.3 Model Grid This step defined the horizontal grids for the model. The integrated time series of climate record was spatially distributed to each grid points. Solid precipitation during the accumulation season was estimated from winter mass balance survey data. Figure 7 shows the general workflow of generating climate forcing for each grid points. Lapse rate Temperature Mass Balance Measurement DEM(Grid) Homogeneous Summer Precipitation, RH, Cloud Cover AWS Meteorological Data Selection and Gap Fill Snow Cover Winter Precipitation Figure 7 Workflow of Climate Forcing Preparation The modelling grids were defined by the DEM provided by Swedish Land Survey (Lantmäteriet: https://maps.slu.se/). The selected DEM covers the whole study area and the surrounding mountain ranges. This is to allow the model to take the shading effect by the terrain. The original 2 m resolution data pixels were resampled to 64 m by a 5 5 window and masked by the outline of Storglaciären. The gap filled complete time series of climate forcing data was spatially interpolated to each grid cell using biharmonic spline interpolation (MATLAB griddata method). RH, cloud cover and liquid precipitation were assumed to be spatially homogeneous over the study area. Temperature was 12

calculated based on the temperature lapse rate using DEM. Water equivalent of snow cover was determined from the mass balance survey. The snow depth readings were spatially interpolated. The snow water equivalent was assumed to be a function of depth and the obtained gradient from the linear regression model was applied to the snowpack depth of each grid cell. The converted snow water equivalent was used to represent the winter precipitation by linearly distributing the snowfall to the entire winter season (October-April). 3.2.3 Initial Subsurface Conditions The vertical model grids in ablation zone can be divided into three layers: snow/firn, cold ice and temperate ice. The initial conditions of the subsurface temperature (subt), density (subd), water content (subw) need to be described before running the model. The initial time step of the full model run was set as 2009-04-01 00:00:00, which is close to the time of the most recent GPR survey of CTS in 2009. The maximum depth of CTS was found at 59 m (Table 1), therefore, each grid points were assigned with a thickness of 60 m, with the thickness (subz) of each subsurface layer of 1 m. This is to make sure all grid points contain enough ice that covers the range of CTS depth. For vertical grids at the depth below the CTS depth, subt was set as 273.15 K (0 ). For vertical grids above the CTS, Pettersson et al., (2004) suggested an exponential equation to determine the position of CTS from thermistors. Yet most of the previous thermistor string measurement (Gusmeroli et al., 2010b; Pettersson et al., 2004) did not investigate the subsurface temperature changes in the snow/firn layers near the surface. In practice, the air temperature at the first time step of climate forcing data was used to represent the glacier surface temperature. The temperature within the layers with cold ice was linearly extrapolated based on the CTS position and surface air temperature. This would introduce large horizontal temperature gradient variation due to the varying CTS depth. We expect the model would readjust the subsurface temperature itself. The initial subsurface density was divided to two layers: upper surface snow/firn layer and lower subsurface ice layer. The spatial distribution of snow/firn density was defined by the spatially interpolated snow depth. The depth of snow/firn layer of each grid cell was given by the winter mass balance stake readings in 2009. The vertical snow/firn density variations were found to be following a linear relation with log-transformed depth (Figure 8). Hence, the linear regression model was used to linearly extrapolate upper layer density. For all ice layers below snow/firn, the density was set as a constant of 900 kg m - Figure 8 Linear Regression Model of Snow depth vs Snow Density (log-transformed) for Model Initialization 13

3. Pettersson et al. (2004) extrapolated water content at CTS from the relative backscatter strength of GPR that was calibrated from thermistor measurement at three boreholes, which was 0.8 % ± 0.26 %. However, the vertical variations of water content in temperate ice remained unclear. The initialization of subsurface water content was done by assigning the same amount of water in each grid cell in temperate ice layer. 3.2.4 Deriving CTS from Model Results The simulation started from 2009-04-01 00:00 to 2018-04-01 00:00, with a time step of every three hours. The daily average subsurface temperature (subt), the associated layer depth (subz), melt and cumulative mass balance were stored and analyzed. The CTS was determined by finding all the layers with temperate ice. This was done by applying a moving filter to all vertical layers from the bottom to the surface. The first encountered layer was marked as the upper boundary of the temperate ice. The direction of the detection process is to exclude the surface layers reaching melting point in the summertime. The model derived thickness of the surface cold layer is the sum of the depth of vertical grid cells in the identified temperate ice layer. 14

4. Results CTS variations were obtained from both the thermistor string and model. The analysis involves point study and spatial analysis. For the point study, the isothermal position was estimated from the extrapolated thermistor temperature profile at study site. The thermistor string profile was analyzed and compared with the simulated subsurface temperature. The thermistor derived CTS depth was used to assess the model-reconstructed cold surface layer thickness. The spatial analysis investigated the spatial pattern of CTS and its temporal evolution. 4.1 CTS Derived from Thermistor Data Three thermistors were left on glacier surface during installation due to the depth limit of the borehole. The measured voltages of thermistors during the monitoring period were shown in Appendix 1 (Figure 18). It had revealed that one more thermistor was exposed to surface after the summer fieldtrip at the end of ablation season in 2018. Hence, the four thermistors at glacier surface were excluded from the data analysis. In total 21 thermistors were used in this study. The retrieved thermistor voltages of the 21 thermistors inside the borehole were converted to actual temperature. The monthly average thermistor string temperature profile is shown in Figure 9a. The negative gradient of temperature profile gradually changed to positive. The temperature curve was bended to the negative side through wintertime and the profile slope became lower. The displacement of temperature profile indicated the seasonal changes of temperature gradient. The temperature gradient became larger as the winter season continues. At the end of the observation period, signs of increasing surface temperature were spotted. The temperature at upper part shifted towards 0 while the cold wave from previous months continued penetrating downwards. The slope of the temperature near the bottom was considered as linear, therefore, the thermistor profile was linearly extrapolated from measurement of the deepest three thermistor. The ice near the thermistors close to the bottom took longer time to refreeze and recover from the warm state during installation. The thermistor string was installed near the end of ablation season. The positive readings of the thermistor at the bottom of thermistor string in first month was caused by the hot water introduced by the steam drill. After three months of refreezing and recovery of temperature field, the thermistor profile finally stabilized. The extrapolation of subt to the isothermal position was done for November 2018 - April 2019 (Figure 9b). The estimated monthly CTS depth was shown in Figure 10. The CTS migration rate was ~1.3 m per month during the first three months. It reached maximum depth of 23.8 m in January, indicating a steeper temperature gradient of the last three thermistors. The thickness of CTS gradually rebounded close to its initial conditions. The reconstructed CTS depth covered almost the entire winter season. The migration of CTS was assumed to be mostly driven by the cold wave penetration and snow accumulation. 15

a b Figure 9 Subsurface temperature profiles measured by thermistor string: a) Monthly average temperature profile; b) Monthly average temperature with extrapolated (dashed line) profile (Note: First three months were discarded for the temperature field in the borehole hasn t recovered). 4.2 Model Results Figure 10 Monthly Average Extrapolated CTS Depth Model results enabled us to investigate not only the spatial extent of cold surface layer but also the temporal variations. The CTS depth were mapped monthly and annually through the whole simulation period. The differences of CTS were obtained by subtracting the consecutive time series of CTS maps with its previous time step. The influence of mass balance and its component (accumulation and ablation) were analyzed by spatially correlating CTS depth with each parameter respectively. 4.2.1 CTS Spatial Evolution and Temporal Changes Monthly CTS depth was mapped and initial month and the last month were displayed: Figure 11a shows the average CTS depth in 2008 (April-December) while Figure 11b depicts the average CTS depth in 2018 (January-April). During the first year of simulation, both the horizontal and vertical extent of cold ice remains similar to the results of the GPR survey in 2009 (Figure 4). Thicker cold ice layer was found in the northwesterly part, southern margin and near the glacier front. The deepest CTS reached 59 m while shallower cold ice layer ranged from 5 to 15 m near the center part of ablation zone. The model results indicated an overall thickening trend of CTS during the simulation period. The model also reduced the spatial variability of the cold surface layer and produced a more flattened CTS map. The general pattern of thicker cold ice in the northwest of Storglaciären and its southern edge was 16

preserved, however, the shallowest CTS near the bedrock threshold became deeper. Similar phenomenon of a net gain of cold ice in that area was found in the comparison of 1989 and 2001 GPR surveys, however, the minor positive values were considered to be within the uncertainty limits of comparison (Pettersson, 2004; Pettersson et al., 2003). Although the cold surface layer above the bedrock separation point was still the thinnest, it demonstrated a 10-15 m increase of its thickness. The cold ice layer was found to have lost ~5 m to the flank of the subglacial bedrock threshold (Figure 11d) after nine year s simulation. In summary, the overall trend of the CTS spatial pattern was becoming deeper and smoother. The thickening rate of the cold surface layer varies spatially and tends to be higher in areas with deeper CTS. Slow thinning rate is only found at the upper and lower side of the bedrock threshold and near the front. a b c d Figure 11 CTS Spatial Evolution and Changes: a) average depth of modelled CTS in 2009; b) average depth of model derived CTS in 2018; c) boxplots of simulated annual CTS depth changes in all grids, the black dashed reference line indicates no change (0 m differences); d) CTS differences between Apr-2009 and Mar-2018. The annual differences of CTS depth are displayed in Figure 11c. The 25 th and 75 th percentile of differences were within the range of -1 to 4 m. The large discrepancy in 2018 is because the last year of simulation did not cover the full calendar year. The annual differences pointed out a clear trend of a gradual thickening of the cold surface layer in general, as the median of all annual boxplots were above zero (2010-2017). The annual differences were normally distributed from 2010 to 2012. The mode of CTS depth shifted to the side of higher differences values after 2012, which is an indication of a slightly 17

accelerated thickening rate. The CTS in 2011 and 2017 were significantly deeper than the previous years. The minimum median of annual differences was 1 m in 2012 while the maximum median was 2.7 m in 2017. The thickening rate slight declined from 2011 to 2013, then rebounded to a higher rate and remained stable. The amplitude of annual differences was stable except for the year of 2014 and 2015. The long tail on the negative side suggested a high thinning rate of cold surface layer at some grids in 2014. Many outliers were found in 2015 as well. The simulation in the last year was not a full calendar year (ends in April). Hence, whether the trend of net gain of cold ice continued remained unknown. 4.2.2 Correlation Map The patterns of spatial and temporal dynamics of the cold surface layer are driven by a complex interactions between different processes (Pettersson et al., 2003). The long term thickness of the cold surface layer is governed by the balance between the downward migration of CTS driven by the freezing of temperate ice and the removal of surface layer driven by the surface melting rate (Pettersson et al., 2007). The relation between annual evolution of CTS and mass balance, accumulation and ablation were investigated by producing the correlation map. The Pearson correlation coefficient (R) and P-value of all grid points were computed by correlating the annual average CTS depth with cumulative sum mass balance and annual melt from the simulation and the accumulation of snow mass from the snow probe readings. 4.2.2.1 Cumulative Mass Balance vs CTS The mass balance of each grid cell is the accumulative exchange of mass due to the mass accumulation and ablation over a period of time (Cogley et al., 2011; van Pelt, 2013). It represents the net effect of precipitation, condensation or riming, runoff and evaporation or sublimation (van Pelt and Kohler, 2015). The model accounts for both the surface and subsurface process and stores the cumulative mass balance in m w.e. for each time step. The cumulative mass balance at the end of each calendar year during the simulation period was extracted and correlated with the annual CTS depth at each grid cell. The correlation map of R and P values and the nine-year average mass balance are shown in Figure 12. The general mass balance pattern was elevation-related: the net mass balance increased from ~ -3 m w.e. a -1 at lower altitude area near the terminus to ~ 0 m w.e. a -1 at the upper part close the equilibrium line altitude. The spatial pattern agreed with the previous mass balance analysis (Pettersson et al., 2007). The ablation zone generally experienced a net loss of ice during the simulation period except at the northwestern and southern margin. The nine-year average net mass balance became positive at the northwestern margin, where the region was associated with local accumulation (Pettersson et al., 2003), and southeastern margin. The area where glacier experienced the fastest mass loss was found in the lower part of the ablation zone where a transverse area located on the bedrock threshold that separates the ablation zone into upper and lower area (Pettersson, 2004; Pettersson et al., 2003). Ice flows much faster above this region and this area is associated with less snow cover and higher ice melting rate. The 18

loss of ice was slower down-glacier from this area was caused by a lee effect due to the accumulation of snow drift from the ice flow break point (Pettersson et al., 2007). Thicker snowpack protects the underlying ice in the ablation season as it takes longer time to remove snow before ice melt starts. The majority of grid cells in the northwest part of the upper ablation area, along the southern margin had shown a strong correlation (R>0.5) with annual CTS depth, indicating a positive correlation between mass balance change with the migration of CTS. The high positive correlation suggests that higher mass balance would lead to a thicker cold surface layer. The excess supply of snow protected the cold surface layer from melting in the ablation season. A contrasting finding is observed in the area where glacier experienced a net negative mass balance, the correlation coefficient become negative (R < -0.5). The indication of a less negative mass balance would result in a thinner could surface layer. In the center of ablation zone, the transition boundary of net mass balance and the lee effect affected area where ninea a b b c c Figure 12 Correlation Map of Cumulative Sum Mass Balance vs CTS Depth: a) nine-year average net mass balance; b) P-value of each grid points; c) Pearson correlation coefficient of each grid point. Figure 13 Correlation Map of Melt vs CTS Depth: a) nine-year average melt; b) P-value of each grid points; c) Pearson correlation coefficient of each grid point. 19

year mass balance was close to equilibrium, the R values were close to zero while the correlation were not significant (P > ~0.2). 4.2.2.2 Melt vs CTS The spatial pattern of the nine-year average melt (Figure 13) coincided well with mass balance (Figure 12) since mass balance is the net mass exchange of accumulation and ablation. The melt rate was lower at high altitude area and higher at low altitude area. The maximum mass loss rate in the ablation season was more than 3.5 m w.e. a -1 while in the upper reaches of the study area the melt rate was less than 1.5 m w.e. a -1. The re-analysis of the mass balance record of Storglaciären had revealed that the summer temperature is directly connected to the melt rate (Holmlund et al., 2005). The average melt rate was elevation-dominated (Ohmura, 2001) as the air temperature input was calculated from temperature lapse rate. Although the melt rate generally decreased from the eastern side towards the accumulation zone, it was not entirely altitude dependent. The latitudinal variation of ablation pattern was higher in the upper part of ablation area and the melt rate is higher along the southern margin. The annual sum of melt produced by the model was closely correlated with CTS depth. All grid cells showed a negative correlation coefficient between melt and CTS. This supported the findings that one of the dominant force of the migration of CTS was melt (Gusmeroli et al., 2012; Pettersson, 2004; Pettersson et al., 2003). It was true for most areas in the ablation zone except for a few grid points at the net equilibrium mass balance transition area (Figure 12). The strength of the correlation enhanced from northwestern and southern margin towards the glacier terminus as the correlation coefficient got more negative (R value decreased from -0.2 to > -0.6). Higher melt rates (> 3 m w.e. a -1 ) were found in the areas that surrounded the lee effect affected area, yet the clusters of high ablation rate were not shown in the correlation map. Some other factors may also play a role in affecting the CTS migration. 4.2.2.3 Accumulation vs CTS The model uses a temperature threshold to determine whether the precipitation was in liquid form or solid. Here the accumulation was taken from snow depth readings done during the winter mass balance surveys using probes. The spatially interpolated and converted snow water equivalent in the preparation of climate forcing was used to correlate with model derived CTS depth. The mass accumulation (Figure 14a) was higher near northwestern and southern edge of Storglaciären. The northwestern and southwestern margins manifested two local high accumulation centers. The snowfall was significantly above average in these two areas, with the maximum nine-year average snow cover was > 2 m w.e. The nine-year standard deviation was higher near the glacier edge, which indicates higher temporal variability of snow accumulation. It might be the result of both orography effect and the poor snow probing data coverage. Snow depth was also higher down-glacier from the bedrock threshold. The spatial distribution of the snow coverage had revealed a belt of shallower snow coverage. The belt stems from the equilibrium line altitude where the average snow depth is about 1 m w.e. and stretches from northwest to southeast along the southern margin. Having 20

reached the mid-point along the southern margin of the upper ablation zone, it turns to northeast towards the bedrock threshold. The accumulated drifted snow accumulates due to the lee effect and the belt joins the other belt that originates from the mid-point along the northern margin of the upper ablation zone. The integrated belt ends to the flank of the high accumulation center in the lower part of ablation area with the thinnest snow cover (< 0.5 m w.e.). The belt of thinner snow cover is also associated with zones of higher ablation rate and more net mass loss (Figure 12-13). a b c d Figure 14 Correlation Map of Snowfall w.e. vs CTS depth: a) average snowfall (m w.e.) from snow stake readings 2009-2018; b) standard deviation of average snowfall (m w.e.) from snow stake readings 2009-2018; c) Pearson correlation coefficient of each grid point; d) P-value of each grid points. Coefficients p1 = -7.645 (-9.239, -6.051) p2 = 18 (13.71, 22.29) p3 = 18.31 (16.1, 20.53) Goodness of fit: SSE: 3.024e+04 R-square: 0.1212 RMSE: 9.077 Figure 15 Robust Fitting Curve of Snow from Winter Mass Balance vs GPR Derived CTS Depth in 2009. 21

The correlation map (Figure 14) demonstrated a negative correlation (R < -0.5) with CTS in the upper northwesterly part of ablation zone, which indicates thicker snow cover is associated with a thinner cold surface layer. The high local accumulation area received more than 1.5 m w.e. of snow fall on average, indicating lower snow accumulation rate would result in a thinner cold ice cover. However, such spatial pattern was not found along the high accumulation area along the southern margin. The week negative correlation was not significant at 95 % confident level in northwestern ablation basin and the cluster of high accumulation rate area down-glacier from the bedrock threshold, the snow cover ranges from 1 to 1.5 m w.e. A large area in the southern ablation zone and along the thin snow cover belt where the annual snowfall was less than 1 m w.e. exhibited a strong positive correlation with CTS. Gusmeroli et al. (2012) found that the CTS changes in the previous GPR surveys (1989, 2001 and 2009) at the thickest and thinnest parts of the cold surface layer correspond to the long-term average snow accumulation pattern well. The behavior of CTS variations agrees with previous assumption of a thinner snow cover is an indication of thinner cold surface layer. 4.3 Time Series CTS Evolution at Study Site Most of previous CTS surveys had a coarse temporal resolution. The modelling of the subsurface ice layers and the corresponding temperature changes enabled us to investigate the cold surface layer changes at a high temporal resolution. The time series of CTS derived from simulated subsurface temperature (subt) evolution at study site covered the time range from 2009 to 2018. The direct thermistor string measurement monitored the period of nearly a full winter season from 2018-2019. The seasonal and annual variation of CTS evolution were analyzed. The extrapolated subt profile from thermistor data was concatenated to the time series of simulated subt evolution at the study site (Figure 16a). The profile of subsurface temperature clearly shows the seasonal variations of temperature gradient and the associated surface height changes. The temperatures of surface layers are sensitive to air temperatures while deeper ice layers normally display a lagged response. The temperature gradient increases during wintertime as cold wave penetrates downward until it reaches CTS. The temperature gradient in the underlying temperate ice is zero since the temperature of temperate ice is constantly at pressure melting point. At the start of melt season, the surface temperature quickly increases and reaches the melting point when all snow is melted. Layers at lower part of the cold surface layer continues to react to the cold wave. The temperature gradient below 10 m to CTS was ~ -1.14 m -1 and evolved to ~ -0.33 m -1 at the end of the simulation. 22

a b Figure 16 Time series of subt evolution at study site: a) Simulated subt Evolution; b) subt measured from thermistor string and extrapolated to CTS. (CTS depth was depicted by black line). The re-adjustment period was masked out. The pressure melting point isotherm was plotted in a black line in the concatenated time series of subsurface temperature, which was also the bottom boundary of the cold surface layer. The simulated CTS depth was close to the initial 13.5 m thickness of cold surface layer as it was defined by 2009 GPR survey. The model derived CTS remained non-stationary during the whole simulation period. The general trend of the cold ice was becoming thicker and the thickening rate accelerated after 2015. The last time step of modelled CTS was approximately 28 m from surface, which is twice as deep as the initial depth. 2018 2019 CTS curve fluctuates seasonally in response to the temperature gradient and ablation. The slope of the curve also changes seasonally. The seasonal variations had a quick response to ablation. The gradient of CTS curve was higher during the melt season. The rapid removal of surface layers led to the thinning of cold surface layer. The loss of ice at glacier surface ceased as soon as the melt stopped. The timing of the CTS migration behaves with a time lag in response to temperature changes. The gradient of CTS curve was lower during the wintertime, which resulted in a slower downward migration rate of CTS 23

compared to the upward movement of CTS in summertime. The effect of the penetration of cold wave persisted the whole accumulation season and reached its maxima near the early stage of melt season. The extrapolation of thermistor data was done by performing a linear regression to daily averaged subt of the bottom last three thermistors. The large CTS displacement in the initial three months (August-October 2018) was masked out for the consideration of the time required by the gradual refreezing and re-reaching equilibrium state for the ice near thermistors. The average CTS depth estimated from thermistor data is 22.41 ± 1.56 m, which was about 5.59 m shallower than the last simulated CTS position. It also suggested that the cold surface layer at study site became thicker with an average thickening rate of ~ 0.9 m a -1 compared to the initial condition of CTS in 2009. 24

5. Discussion 5.1 CTS at Point Scale The point study involves the extrapolation of CTS from thermistor data and extract the time series of subsurface temperature and the associated CTS changes. The thermistor string aims to provide the direct measurement of subsurface temperature for the purpose of extrapolating the depth of CTS. The extrapolated temperature profile showed an unexpected thickening of the cold surface layer with a thickening rate of ~ 0.9 m a -1 compared to 2009 CTS survey. The surprising trend can be affected by many factors. The borehole drilled through a water channel and caused additional intrusion of liquid water inside the borehole. The bottom of the thermistor string did not reach the targeted depth during the installation and stopped at 13.3 m, which was more than 9 m shallower the thermistor estimated CTS depth. The extrapolation of the pressure melting point isotherm was done by applying a simple linear regression model to the temperature of the three thermistors at the bottom. Ideally, the temperature reached the annual minimum at approximately 4 m (Holmlund and Eriksson, 1989). The underlying ice layers were to be less variable. The assumption of a simple linear subsurface temperature gradient makes the derived CTS depth more prone to error. The attempt of calibrating the thermistor string before installation was done in the lab under room temperature and in the freeze room. It has proved to be hard to control the temperature in both environments. The resulted simplification of the calibration after the installation may reduce the precision of the calibrated thermistors. The extracted time series subsurface temperature at the study site provided detailed temporal variations of CTS. The seasonal changes of CTS migration gradient coincided with the driving force. This phenomenon was not captured by thermistor data for it only covered the accumulation season from 2018 to 2019. However, the comparison of CTS depth derived from the thermistor data and model results showed large discrepancy (~5.59 m difference). The overestimated CTS depth might be the limitation of the model, which will be discussed in the next section. The simulated period ended in April 2018, which was nearly a year from the thermistor s effective monitoring period (Nov 2018-Apr 2019). The spatial resolution of model grids is 64 m. The scale of the pixel size that covers the study site might also help explain the large deviation. The accuracy of the extrapolation of thermistor data needs to be further investigated. 5.2 CTS at Glacier Scale The spatial study focuses on modelling the spatial distribution of cold surface layer and its temporal variations. In general, the spatial pattern of CTS matches with previous GPR surveys. However, the annual CTS differences analysis demonstrated a trend of thickening of cold surface ice. This finding is in line with the thermistor estimated result but contradicts the long-term thinning trend of the cold surface layer reported by previous study. 25

In general, the nine-year of simulation estimated an overall thickening trend of the cold surface layer. The thickening trend is supported by the point study. The validation of the model performance is not the primary goal of this thesis. This is also the first time that the model is used for simulating the cold surface layer changes. The accuracy of modelled mass balance is of critical importance to the results as accumulation and ablation are potent factors that affect CTS. Even though the final output of melt rate and net mass balance in study area was in line with the mass balance survey, the general thickening trend contradicts the previous survey and the long-term thinning trend of the cold surface layer. This suggested that some processes on Storglaciären may have not been fully understood by the model implemented in this study, though the coupled model has been tested and applied on multiple Svalbard glaciers. Additionally, the surface albedo after snowfall is a function of time. The total volume of winter precipitation was the sum of accumulated snow water equivalent and it was linearly distributed during the whole winter season. Fresh snow constantly updates the surface energy flux with a high albedo, which may cause a stronger cold wave in the snowpack. Although water content at CTS has been well studied, the water content within temperate ice was not. The initialization of model relies on the homogenous spread of liquid water content in both vertical and horizontal directions in temperate ice layers. All could lead to the overestimated CTS depth. The mapping of simulated CTS revealed that the spatial extent of the CTS morphology was also becoming smoother. The smoothing tendency might be the result of the preparation of climate forcing. The summer precipitation, RH, and cloud cover were homogeneously assigned to model grids. Temperature was spatially distributed to each grid cell based on a linear temperature lapse rate. The homogenous or linear simplification of the complex processes of interaction between glacier and air might be the reason of a smoothed CTS in simulation. Possible errors may also come from the data integration. The meteorological measurements were collected from different AWSs. The inconsistency of data from different sources were reduced by minimizing the time series of integrated data. All the available data from TRS was considered more reliable source, only the gaps were filled from other datasets. 5.3 Spatial Correlation and Analysis The role of the net mass balance in explaining the CTS migrations varies depends on the magnitude of glacier mass change. Areas that experiences high net loss of ice mass tend to have a negative relation with CTS. Positive correlation exists in areas with high positive mass balance. The net gain of cold ice at the surface would lead to a thicker cold surface layer. However, most of the grid points with negative mass balance did not exhibit a thinner cold surface layer. On the contrary, CTS became deeper in most parts of the study area. Previous findings that the ablation is one of the major driving factors in controlling the migration of CTS (Pettersson, 2004; Pettersson et al., 2003). The long term thinning of the cold surface layer occurs when ablation rate exceeds the downward migration of CTS (Gusmeroli et al., 2012). The simulated 26

annual average of melt is negatively correlated with CTS at all grid points. It is more significant at areas with higher ablation rate and is less significant in areas with net positive mass balance. This suggests other factors are also contributing to the CTS changes. CTS was found to be closely related to snowpack thickness (Gusmeroli et al., 2012; Pettersson et al., 2003), particular at the thickest and thinnest snow covered areas. Under a similar ablation rates, thinner snow cover would result in a higher melt rate at cold surface layer compared to thicker snow-covered areas. This is also observed in areas with lower annual snow accumulation (< 1 m w.e.). However, this spatial correlation pattern is reversed at areas with higher annual snowfall (> 1.5 m w.e.). The response of the cold surface layer thickness to snow depth might be explained by the hypothesis of snowpack insulation effect. Thicker snowpack that exceeds the threshold (~1.5 m w.e.) would serve as an insulator of the cold ice, which prevents the penetration of cold wave in the winter. The subsurface thermal structure will be dominated by the ground thermal heat fluxes consequently. The insulation effect might reduce the downward migration rate of CTS by affecting the subsurface temperature gradient. This effect can only be noticed when snow accumulation exceeds a certain threshold. Thinner snowpack could not prohibit the cold wave, therefore only the melt protection effect of snow cover comes into effect. The nine-year average mapping of the mass balance data, together with spatial correlation of simulated cumulative sum of mass balance, melt and measured accumulation with derived CTS depth all confirmed the importance of the bedrock threshold that separates the upper and lower part of the ablation zone. The ice flow accelerates over this area (Pettersson et al., 2003), which may lead to a large difference in the emergence velocity that strongly decelerates the thinning rate (Pettersson et al., 2007). The discovered belt of low snow accumulation is also associated with subglacial topography. It might also be affected by the contribution of ice flow from the cirques in the accumulation zone. However, the subsurface topography, vertical and horizontal advection of ice were not considered by the model. 27

6. Conclusion This study investigated the cold surface layer dynamics by deriving CTS depth from subsurface temperature obtained from both extrapolated thermistor measurements and a coupled surface energy balance-snowpack model. The evolution of the cold surface layer was investigated at different spatial and temporal scales in this study. 1) CTS derived from both extrapolated thermistor string data and model results shows an overall increasing trend of CTS. The thermistor data suggests a thickening rate of ~ 0.9 m a -1 since 2009 GPR survey. The model overestimated the thickening rate at the study site compared to thermistor data. The findings contradict the general trend of cold surface layer thinning in the previous 1989, 2001 and 2009 surveys. 2) The spatial pattern of the cold surface layer thickness from previous surveys were preserved in the model results. The northwesterly and southern margin possesses the thickest cold surface layer but the thinner areas near the bedrock threshold also receives a net gain of cold ice during simulation. The thickening rate is not uniform in space. Areas with thicker cold surface layer in previous survey observe a higher thickening rate. The overall spatial extent of the simulated cold surface layer tends to become smoother. 3) The temporal evolution of CTS migration finds the migration gradient is higher during the ablation season and lower during the accumulation season. In summertime, the rapid removal of surface layer drives the upward movement of CTS. During wintertime, the gradual downward migration of CTS is mainly driven by the temperature gradient. Seasonal variations of CTS migration gradient have a time lag in response to the temperature changes at glacier surface. 4) The spatial correlation of modelled cumulative sum of mass balance, melt and actual measurement of accumulation with model derived CTS finds that all three parameters are closely connected to the cold surface layer evolution. The relation is affected by complicated processes. Different factors account for the CTS variations differently and the strength also changes. 5) Melt is negatively correlated with CTS in the whole study area while mass balance and snow accumulation exhibit a change of correlation pattern. Higher melt rate would cause a thinner cold surface layer and is more significant when ablation rate is above 2 m w.e. a -1. Positive net mass balance has a positive correlation with CTS while negative net mass balance is on the contrary. The influence of snowpack has two contradictory mode. In low annual snow accumulation (< ~1 m w.e.) area, the snowfall serves as a buffer to protect the cold surface layer from melt. Snow water equivalent is negatively correlated with CTS. In high snow accumulation area (> ~1.5 m w.e.), the relation is reversed, and snow depth becomes positively connected with CTS. The hypothesis is that thicker snow that exceeds the threshold would become an insulator that prevents the penetration of cold wave. 28

6) The bedrock threshold is identical on the spatial pattern of CTS and plays an important role in the correlation map experiment. The overall net gain of cold surface layer above this area might be the result of not taking its effect into consideration by the model. 7) The selected coupled surface energy balance-snowpack model needs to be validated before implementing it to Storglaciären. Future work could try to couple the lateral and vertical advection of ice for it plays an important role in the spatial distribution and thickness of cold surface layer. Possible errors have been discussed in discussion. 29

7. Acknowledgements My master s study was supported by the IPK scholarship from Uppsala University. The thesis fieldwork was funded by Linnaeus scholarship and Otterborg stipend. Many thanks to all the staff in the Tarfala Research Station. We received very warm welcome and support from TRS. Torbjörn Karlin guided me the first tour to the glacier. Standing on the glacier for the first time was an amazing adventure. Gunhild "Ninis" Rosqvist and Pia Eriksson helped provide the valuable data and Ninis permitted me to keep the coffee cup from Tarfala. The biggest pity was I could not meet Peter Jansson and join his team during the spring fieldtrip. I would like to thank my thesis reviewer, Sergey Marchenko, for his patience and detailed help through all my thesis work, and for his accompany for my summer adventure to Storglaciären. I learned to build a thermistor string and logger box from beginning. The thesis work cannot be finished without his help. Thanks for Ward van Pelt for building his model and providing me his model script. It s a dream team to work with. Special thanks go to my supervisor, Rickard Pettersson, who dedicated a lot of time and effort in answering my questions at all stages of my master study. His support helped to get used to the study in Uppsala and guided me in two other projects. Without him my two years life in Uppsala would be a completely different story. Rikipedia is always there when I need help and he is the key to my master study. Words cannot express my thankfulness. Thanks to my bachelor supervisor, Wenxia Tan, for her words of encouragement. I am always benefiting the knowledge about RS and GIS that I learned from her in my undergraduate study. Thanks for my best study friends in Uppsala, Felipe de Fileni and Johannes Erikson, who tolerated my poor English and slow learning process at the beginning of study. It s my great pleasure to work with them. We have our moments in the computer lab and at EGU 2019 in Vienna. And thanks for Ragna Orbe s valuable comments. And my good old friend, Haozhi Ma, who is dedicated to science and has always been an inspiring friend to me. Best luck to both of us in the pursuit of science. I would like to thank Chen Chen, who is smart and talks like a book. I will always treasure the time when we shared supermarket coupons, burgers, stories with our study or life (good or bad) and even complaints with each other. Last but foremost, I want to thank my parents. Their support and understanding have always been my strongest backup. They are my heroes. I am glad that I chose to study in Uppsala two years ago. If anyone found that I improved myself and learned to become a better person. I improved and learned in Uppsala University. I improved and learned from my cute teachers and friends. 30

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Appendix 1 Thermistor Data Conversion Figure 17 Electric circuit of the wiring scheme The reference resistor (Rr) and thermistor (Rt) are connected in series using the electric circuit provided by Marchenko (2018). The constants required by Eq. 2-3 are provided by the Amphenol sensor temperature curve guide and are listed in Table 3. The temporal changes of measured voltages of each sensor are shown in Figure 18. Table 3 Constants for calculating thermistor temperature Temperature range ( ) A B C D -50 to 0-1.4122478E+01 4.4136033E+03-2.9034189E+04-9.3875035E+06 Rt/R25 range a b c d 68.600 to 3.274 3.3538646E-03 2.5654090E-04 1.9243889E-06 1.0969244E-0 34

Figure 18 Time series of measured voltage of each thermstor 35

Appendix 2: Annual Evolution of CTS 36

Figure 19 Annual Evolution of CTS from 2010 to 2018 All annual (2010-2018) maps of CTS depth not shown in thesis are plotted here in Figure 19. 37

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