Water temperature, mixing, and ice phenology in the arctic–alpine Lake Darfáljávri (Lake Tarfala), northern Sweden

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Introduction
Proglacial lakes exist at high altitudes in the Scandinavian Mountains.Their inflow consists largely of glacial meltwater that, together with the low air temperature, keeps the lake water temperature low all year with the potential to delay the warming observed in other Arctic lakes.
The lake water balance follows the glacial mass balance with maximum volume in late summer.Most of the year, these lakes are frozen, and due to the low temperature, they are mixed or weakly stratified.Water balance and the lengths of the open water and ice seasons are related to the local and global climate.
The primary motivation of recent research of Arctic lakes has been to better understand their climatology and ecology (Salonen et al. 2009) and interaction with the atmosphere (Kirillin et al. 2012;Y. Yang et al. 2013).It is challenging that most data are from the ice-free seasons of these lakes and that reports and data from under-ice processes make only a small part of the published literature on freshwater systems (Hampton et al. 2017;Block et al. 2019;McMeans et al. 2020;B. Yang et al. 2020).In past decades, most mid-latitude lakes have experienced a withdrawal in ice phenology; that is, later ice-on in the fall and earlier ice-off in the summer (e.g., Magnuson et al. 2000;Sharma et al. 2019Sharma et al. , 2022)).Highlatitude lake-ice phenology and lake thermal states are expected to be influenced not only by pronounced seasonal solar radiation changes but also by faster atmospheric warming in the Arctic compared to lower latitudes (Lei et al. 2012;O'Reilly et al. 2015;Šmejkalová, Edwards, and Dash 2016;Woolway and Merchant 2017;Previdi, Smith, and Polvani 2021;Rantanen, Karpechko, and Lipponen et al. 2022).Climate scenarios continue to project shorter ice seasons and thinner ice cover in Arctic lakes (e.g., Brown and Duguay 2010;IPCC 2021) and hence raise questions as to how physical and associated ecological and biogeochemical lake processes may change in response.
Darfáljávri (Lake Tarfala) is a proglacial lake in the Scandinavian Mountains.It is small but deep, ice-covered most of the year, and acts as a temporary storage of the meltwater from local glaciers and snowfields.Pioneering investigations of Darfáljávri's bathymetry and thermal state were conducted by Larje and Nyberger (1960) and Björklund (1967).With modern bathymetric mapping and initiation of long-term thermal state measurements in 2016 (Kirchner et al. 2019(Kirchner et al. , 2021)), Darfáljávri has recently also been included in ensemble investigations of proglacial lakes in Arctic Sweden (Dye, Bryant, and Rippin 2022).
The aim of this work is to examine physical lake processes, with a focus on water temperature and ice phenology, at Darfáljávri.The study is based on observations between 2019 and 2022, including wintertime and under-ice processes, complemented by meteorological data from nearby Tarfala Research Station (TRS).The results show the annual evolution of the state of the lake and some of its forcing factors, as well as their interannual variability, and the specific thermal and physical characteristics of a glacier-proximal alpine polar lake as compared with what is known of polar tundra lakes, here exemplified by Lake Kilpisjärvi, Finland.

Regional setting
Darfáljávri is situated in an arctic-alpine environment at 67°55′ N, 18°35′ E in Darfálvággi (Tarfala Valley) in the Kebnekaise Mountains, northern Sweden, at an elevation of 1,162 m.a.s.l. and above the local tree line with sparse vegetation (Figure 1).Darfáljávri's natural outflow is located in the southeastern corner of the lake, discharging into the stream Darfáljohka (Tarfalajokken).Darfáljávri is a freshwater lake with low electric conductivity (1.33-1.75mS/m, measured in 2017, available from fieldsites.se n.d.) fed by meltwaters from several surrounding snowfields and glaciers, as well as by precipitation and groundwater springs located mainly alongside the mountain flank above the northeastern lake shore.The total area of the catchment is c. 8.5 km2 .Darfáljávri has an area of c. 0.56 km 2 , a maximum depth of 49.6 m, and a volume of c. 11.7 × 10 6 m 3 .The glacial landforms at its floor can be connected to the dynamics of Kebnepakte Glacier, once terminating in Darfáljávri, over decennial scales (Kirchner et al. 2019).Darfáljávri is dimictic (Kirchner et al. 2021), and the timing of mixing processes is inherently related to lake ice phenology.Darfáljávri is ice-covered for most of the year (often from October to July/August); however, ice phenology has only been recorded systematically since 2020 by means of time-lapse photography.Weather data are collected by two automated weather stations placed at TRS, c. 1 km from Darfáljávri, at 1,135 m.a.s.l.There, the mean annual air temperature, averaged over the past twenty years, is −2.43°C and during that period was lowest in 2012 (−4.6°C) and highest in 2003, 2006, 2015, and 2020 (−1.8°C).

Lake water temperature and water level
Lake water temperature data were acquired from 7 September 2019 to 14 September 2020 using six HOBO Water Temp Pro v2 profilers and two Seabird Scientific SBE56 temperature sensors.The sensors were attached to a mooring line at 2, 4, 6, 8, 18, 28 and 38-m depth below the lake surface (bls), anchored at 67°55′28″ N, 18°35′22″ E, in a water depth of 46 m (Figure 1a).The instruments logged, time-stamped, and saved the water temperature every 30 minutes.When the mooring was retrieved on 14 September 2020, it had collapsed and was retrieved with all sensors and the mooring line bundled together and with lake sediments on the mooring line.After downloading from the sensors, an initial data check revealed that the sensor moored at 6 m bls had already malfunctioned before the collapse as it rendered physically unrealistic values that were hence excluded from further analyses.Data were processed and visualized with MATLAB R2022a (MathWorks, Inc. 2022).Lake temperatures acquired during 2019 to 2020 imply an extension of Darfáljávri's temperature record, acquired since September 2016 (Kirchner et al. 2021).The mooring was redeployed on 15 September 2020 but was never recovered-its only remains were a HOBO sensor that was found in Darfáljohka, between the lake outflow and TRS (Figure 1b), on 5 August 2021.Thus, lake water temperature data from 2020 to 2021 were irreversibly lost.
Data acquisition was resumed on 14 September 2021, when a new mooring was deployed at the same position as the previous one.It included the following sensors (depth bls is given in parentheses): HOBO Water Temp Pro v2 (2,4,6,20,30 m), HOBO U20 Water Level (pressure at nominally 3 m bls), Seabird SBE56 Temperature (10, 40 m).The water level logger records total pressure; that is, air pressure plus water pressure.With air pressure available from the TRS automated weather station (AWS; see section "Automated weather stations"), water pressure can be isolated under the assumption that it is approximately the same at Darfáljávri and TRS (but due to the altitude difference 3 mbar higher at TRS, which corresponds to a 3-cm water layer; Figure 1b).The sensors acquired measurements every 15 minutes, except for the water level logger, which had a sampling interval of 30 minutes, and all were retrieved on 14 August 2022.Reading of the HOBO datalogger at 6 m bls failed because of bad battery status.

Time-lapse photography
A SiFar Willfine Trail Camera 4.0CG-W was set up on 19 June 2020 on the mountain flank along Darfáljávri's northeastern shore to capture the timing of ice-on and ice-off events at Darfáljávri.This camera location is c. 600 m from the central part of the lake where the mooring is placed and 59 m above the lake surface (Figure 1a).Iceon is here defined as the first day during autumn on which the lake is completely ice-covered and remains so for the rest of the winter.Ice-off is defined as the first day during summer on which the lake is completely ice-free.The days from the first freezing before ice-on is completed are referred to as the ice-on period, and the time span between the first lake ice melt and initial breakup and the final ice-off is referred to as the ice-off period.The camera was mounted on a tripod (and was therefore elevated 1.8 m aboveground) and powered by a 12 V lead acid battery.The camera position was chosen such that almost the entire lake was captured on the images, except for two small bulges in the southeastern (corresponding to the left margin in the time-lapse images) and northern (corresponding to the right margin in the timelapse images) corners of the lake.The camera operated until September 2021, when it was replaced by a Hunter Orion Trail Camera 4 G.Since June 2020, a picture of Darfáljávri has been taken every 2 hours.The view of the lake can be obscured by weather conditions such as fog, rain, and snow and by darkness during the polar night.

Automated weather stations
Two AWSs are located c. 1 km from Darfáljávri, at TRS (Figure 1b): one operated by the Swedish Meteorological and Hydrological Institute (smhi.se,referred to as SMHI AWS Tarfala A) and one by TRS (referred to as TRS AWS).SMHI AWS Tarfala A provides hourly measurements of air temperature, and TRS AWS records air temperature, wind speed, liquid precipitation, and air pressure every 10 minutes.Data from TRS AWS were used by default; however, when the records suffered from data gaps (October-December 2022), these were filled with data from SMHI AWS Tarfala A.

Degree-day model for ice-on and ice-off dates
A degree-day model to calculate the ice-on and ice-off dates for Darfáljávri was created by using daily mean temperatures of the years of interest.Following Thompson et al. (2005) and Weckström et al. (2014), for ice-on in the autumn all days that had a daily mean temperature <0°C were summed until their sum was less than −30°C•d, and that day determined ice-on.In spring/summer, all days that had a daily mean temperature >0°C were summed until the sum was larger than +130°C•d, and that day determined ice-off.The degreeday model was tested by Thompson et al. (2005) on three different data types with a typical root mean square error value of four days for all three data sets.The modeling was applied to the period 1965-2022 for which weather data were available.

Water temperature indicator for ice-on and ice-off
To infer estimated ice-on and ice-off dates for years where no time-lapse imagery is available, water temperature characteristics are used as follows: When water temperatures in the water column have stabilized to their steadystate winter values, ice-on is assumed to have taken place because ice cover dampens wind-driven turbulence.When the deep-water temperatures have started to depart from their steady winter values (e.g., caused by buoyancydriven turbulence and the beginning of deep convection), it is assumed that the ice-off period has been initiated; however, the final ice-off date cannot be inferred using temperature fluctuations as the criterion.This is because ice-off is defined as the date when the lake is free from all ice, and considerable time can elapse between the initiation of ice-off (which is visible in the temperature fluctuations) and its completion.

Results
The timing of ice-on and ice-off as captured by the timelapse camera is shown in Figures 2 and 3.In section "Darfáljávri's thermal state, mixing processes, and ice phenology", results are detailed for the three occasions where both water temperature and time-lapse data are available; that is, during ice-off 2020, ice-on 2021, and ice-off 2022.These are then compared to modeled and inferred ice phenology in section "Observed, modelled and inferred ice phenology at Darfáljávri".

Darfáljávri's thermal state, mixing processes, and ice phenology
September 2019-September 2020 Continuing the multiyear water temperature record in Darfáljávri (Kirchner et al. 2021), Figure 4 displays the temperatures acquired between September 2019 and September 2020.Lake water temperatures through the water column display the seasonal cycle of cooling, fall overturning (completed by 24 September 2019), winter stagnation and inverse stratification, warming, and summer overturning (completed by 9 August 2020).Fall and summer overturning are detailed in Figure S1.During winter stagnation, attained in early October 2019, with deepening of the thermocline, the near-surface water temperature (2 m depth) started to drop from the steady value in the beginning of February, whereas temperatures at greater depths remained at their steady winter low of about 2.5°C.The near-surface temperature decreased during winter due to heat leakage through ice cover until June and then reached its minimum during solar-induced convection while Darfáljávri was still ice-covered, around the end of June/beginning of July.It is noted from Figure 4 that water temperatures at all depths were nearly equal after 15 July 2020 and did not show a pronounced warming in the near-surface waters or deep convection.This is attributed to the collapse of the mooring (section "Lake water temperature, and water level").
Daily air temperature (Figure 4) from TRS indicates subzero (°C) values from 1 October 2019 to mid-May 2020 and an average temperature of −2.4°C during the period from 7 September 2019 to 14 September 2020 when water temperatures were acquired.In early September 2019, air temperatures still reached up to 8° C but dipped below zero on a few occasions in mid-September before returning to 4°C to 6°C during 25 to 28 September 2019.Notably, the cumulative temperature sum (the sum of the daily temperatures) during 14 to 30 September 2019 amounted to −1.5°C•d.In spring 2020, daily average air temperature rose above the freezing point on 22 May and reached up to 14°C (on 22 June).Wind speeds prior to ice-on are shown in Figure 4 and are addressed in the Discussion section.
Shortly after the installation of the time-lapse camera on 19 June 2020, the ice-off period was initiated.Important events detected in the time-lapse imagery (for a link to the full data set, see Data Availability  Figures 4 and 5).Statement) are combined with the water temperature record and wind speed data (cf.Figure 5).Then, convection due to solar heating of the under-ice water started and affected the temperature profile.First, a decrease in near-surface water temperature (2 m bls) took place, coincident with observations of a growing number of meltwater ponds at the lake-ice surface (21-25 June; Figure 3a) and high surface air temperature recorded at TRS (Figure 4).After 25 June, temperature at 2 m bls increased again with deepening of the convection.At 4 and 8 m bls, temperatures remained at their winter stagnation values until a large number of surface meltwater ponds had formed on 24 June and dropped afterwards until 5 July to then increase again.Very low-salinity meltwater may first form a thin, stable layer just below the ice to be mixed deeper later because near 4°C the sensitivity of water density to temperature is very low.5 July marks the onset of pronounced lake-ice melting along the distal (southwestern) lakeshore, along the foot of Norra Klippberget (Figure 1a).At 18 m bls, small temperature fluctuations are observed from 1 July and onward, followed by a drop in temperature around 8 July, after which the temperature increased again.Water temperatures in the deeper water column (28 and 38 m bls) remained at the winter stagnation values until after 25 July.On 22 July, lake ice retreated from the proximal (northeastern) lakeshore in a few hours, and initially large floes drifted vigorously across the lake from 23 July onwards, eventually disintegrating into smaller pieces.This coincided with increasing wind speeds, culminating at c. 8 m/s in the early hours of 23 July 2020.On 25 July, time-lapse imagery evidenced a drift of ice floes into the northwestern lake corner (where Kebnepakte Glacier terminated previously).After 25 July, water temperatures at all depths increased steadily and in a very similar manner, likely because of the collapse of the mooring (section "Lake water temperature, and water level").Final disintegration of the season's last drifting ice floes was observed between 31 July and 7 August.7 August 2020 marked the day of ice-off (Figure 3b).During the period from 1 to 9 October, the water body was nearly isothermal with slightly decreasing temperature.9 October marked the day when the fall mixing appeared to be completed, with the warmest temperatures recorded at 40 m bls.Completion of the fall overturning also coincided with wind speeds dropping to very low values prior to 9 October.After 9 October, Darfáljávri cooled slightly through the entire water column, and overall wind speed decreases despite daily variability.From 14 October, when overall wind speed increased again, water temperatures were found to fluctuate, with the total range of temperatures increasing to more than 1.5°C for a few days before decreasing to 1.0°C.Furthermore, the largest variations in temperature were found in near-surface water layers.
In the time-lapse imagery, 19 October 2021 marked the first occasion of a clearly identifiable ice cover across the entire lake surface (Figure 3c), which then became snow-covered.At the same time, water temperatures at all depths approached their distinct winter stagnation values.Notably, these values ranged over a wider temperature span than observed during winter 2019/2020.Post-iceon, a patchy patterning of snow cover on the frozen lake surface was observed (e.g., 20-21 October) before the snow cover thickened substantially (23 October).
Events detected in the time-lapse imagery during iceoff 2022 are combined with the water temperature record and wind speed data in Figure S3.Shortly before the ice cover was observed to melt (24 June) in the northwestern corner of the lake, near-surface water temperatures (2 and 4 m bls) started to rise as sunlight started penetrating through the ice.Wind speeds between 25 June and 1 July were low and rarely exceeded 5 m/s.From the end of June until mid-July, due to convection, temperatures at greater depth started to fluctuate and depart, on a cooling trajectory, from their steady winter values, whereas near-surface temperatures continued to increase.In the beginning, fluctuations were small and coincided with observed retreat of ice cover from the camera-proximal (eastern) shoreline and the formation of surface meltwater pond-like features (1-7 July).From 8 July onward, at the same time as wind speeds exceeding 10 m/s were recorded, cracks formed in the southern part of the lake ice cover.These cracks extended to the central parts of Darfáljávri by 15 July, coinciding with larger fluctuations in water temperatures.The water temperature record shows that 18 July marked the completion of summer overturning, at a time when time-lapse imagery showed that lake-ice cover had completely disintegrated and ice floes were drifting across the lake.Wind speed was generally low during mid-July, with the exceptions of 23 and 28 July, when it peaked at 12 to 14 m/s.After 18 July, temperatures at all depths increased steadily, with large fluctuations in the near-surface layers, increasing in amplitude after ice-off on 27 July 2022 (Figure 3d).The fluctuations showed developments and breakages of instabilities, increasing toward 4°C when the sensitivity of water density to temperature was lowest.
Prior to ice-off in July 2022, a drainage basin-related melt-on ice event (Figure 7) was observed from the water pressure time series (acquired during September 2021 and August 2022; cf. Figure 6) and the time-lapse imagery.Figure 6 shows that water pressure at 3 m bls fluctuated between 22 and 26 kPa during October 2021 and February 2022, after which it gradually increased until June 2022 when it reached 30 kPa.Between 1 and 13 June, a rapid increase by 13.8 to 43.8 kPa was recorded (equivalent to a 140-cm-high column of water).This increase in water pressure coincided with observations of large amounts of water accumulating on the lake-ice surface after 1 June 2022, predominantly in the northern lake corner.It also followed a period of little precipitation and elevated air temperatures (around +5°C) observed during 20 to 31 May when, at the same time, a cooling of the uppermost water layers (2-4 m bls) was recorded.Water temperatures attained their lowest values as water pressure peaked in early June due to the cold inflow.After 13 June, water pressure dropped again to fluctuate around 25 kPa, and timelapse imagery no longer showed evidence of notable water accumulations on the ice surface (Figure 7).

Observed, modeled, and inferred ice phenology at Darfáljávri
In section "Darfáljávri's thermal state, mixing processes, and ice phenology", ice-on and ice-off periods and dates are presented for which both water temperature data and time-lapse imagery are available (ice-off 2020, ice-on 2021, ice-off 2022).Though water temperature data from 2020 to 2021 were irreversibly lost, time-lapse imagery was acquired during this time, providing dates for ice-on 2020, ice-off 2021, and ice-on 2022 (Figures 2 and 3).
All observed ice-on and ice-off dates since 2020 are used alongside degree-day modeled dates of ice-on and ice-off at Darfáljávri (cf.section "Degree-day model for ice-on and ice-off dates") for the period 1965 to present (cf. Figure 8).The year 1965 marks the beginning of yearround weather observations at TRS, which are required as input to the degree-day model.A linear fit to degree-day modeled ice-off dates shows that the timing of modeled ice-off has shifted from July to June.Similarly, the present timing of modeled ice-on occurs in late October, as opposed to early October decades ago.With observational data for the years 2020 to 2022 at hand, it is noted that observed ice-off dates in 2020, 2021, and 2022 match the modeled ones poorly but that the observed beginning of the ice-off period (identified from the time-lapse imagery) matches the modeled ice-off better.For ice-on, differences between modeled and observed dates in 2020, 2021, and 2022 are small.The trend for modeled ice-on and ice-off is steeper when comparing the past two decades with the period 1965 to 2002.This implies that the predicted shifting of modeled ice-on to later times in the year and of modeled ice-off to earlier times in the year is accelerated when based on information from the recent decades.
Water temperature characteristics linked to ice-on (such as in 2021) can also be used to infer approximate ice-on and ice-off dates for years where only water temperature data are available, namely, from September 2016 to September 2019 (Kirchner et al. 2021).If ice-on is indicated by water temperatures below the surface layer approaching their steady-state winter values as ice cover dampens turbulence, then data presented in Figure S4 suggest that ice-on during 2016 to 2019 occurred on the following dates: 6 October 2016, 5 October 2017, 24 October 2018, and 10 October 2019.Here, we considered water temperatures to have reached a steady state when their fluctuation was in the range of at most 0.04°C; this is twice the range of the measurement accuracy of the HOBO temperature sensors (0.02° C ± 0.21°C).Similarly, the departure of water temperatures at depth from the steady winter values indicated that the ice-off period had been initiated; however, no ice-off date can be deduced.Based on water temperature data presented in Figure S5, it is suggested that ice-off periods during 2017 to 2019 were initiated around the following dates: 20 July 2017, 8 July 2018, and 13 July to 3 August 2019.Note that these are not ice-off dates.A comparison of observed, inferred, and modeled dates for the years 2016 to 2022 is presented in Table 1.
Based on the summary of ice-off and ice-on dates for the years 2016 to 2022 in Table 1, observed/ inferred ice-off occurs around 20 July (day 203 ± 4.5) and ice-on around 15 October (day 290 ± 3.2), which implies 87 ± 5.4 ice-free days (24 percent of the year) and 278 ± 5.5 ice-covered days (76 percent of the year).The modeled estimates yield a considerably earlier ice-off date around 18 June (day 170 ± 2.5) but a very similar ice-on date around 13 October (day 287 ± 3.4), implying a longer ice-free season of 117 ± 3.4 days (32 percent of the year) with 248 ± 3.4 days of ice cover (68 percent of the year).Based on the modeled estimates for 1965 to 2022, ice-off days were on average slightly (7 days) later (25 June, day 177 ± 1.3) and ice-on slightly (8 days) earlier (6 October, day 280 ± 1.2) than the recent period 2016 to 2022, which implies an approximately two-week (15 days, ~14.6 percent) shorter ice-free season (103 ± 1.8 days, 28 percent of the year).

Darfáljávri's stratification patterns and the interannual variability
Comparing Figures 4 and 6 with a focus on winter stagnation temperatures at depths greater than 4 m bls (exemplified for 1 January and 8 June in 2020 and 2022), the following is observed: In January 2020, the winter 2019/2020 water temperatures between 4 and 38 m bls differed by less than 0.2°C, and this small difference was maintained until June.In January 2022, the winter 2021/ 2022 water temperatures between 4 and 40 m bls differed by more than 1.2°C, and this difference increased to c. 2° C by June.Regarding previously published data (Kirchner et al. 2021) with a focus on winter stagnation  For dimictic lakes, cryostratified conditions have been associated with small, deep, and calm lakes that have strong stratification near the surface so that there is a very thin surface mixed layer (B.Yang et al. 2021).Darfáljávri is a small and deep lake but in a potentially very windy environment.Indeed, the highest wind speed ever recorded in Sweden (81 m/s, in December 1992) is from Darfálvággi.Though ice-on is predicted fairly well from the degree-day model (cf.Table 1) without accounting for wind speeds, wind conditions prior to ice-on play a crucial role in determining the characteristics of the winter stratification.
For instance, in 2021/2022, relatively high average wind speeds of c. 3.5 m/s during two weeks prior to ice-on were recorded alongside a strong stratification and a depth-averaged water temperature of c. 2.5°C.In 2018/2019, even stronger average wind speeds (exceeding 4.2 m/s) prior to ice-on were recorded alongside a strong stratification and markedly colder depth-averaged water temperatures of c. 1.3°C (Figures 6, S4, and  S6).Furthermore, low average wind speeds of c. 1.7 m/s prior to ice-on in 2017/2018 were observed to coincide with high depth-averaged water temperatures (c.3.2°C) at ice-on (after which, however, in contrast to 2018/2019 and 2021/2022, a weak stratification prevailed).This indicates that wind speed prior to ice-on affects winter stagnation water temperatures, where higher winds speeds imply colder water temperatures, in line with B. Yang et al. (2021).Yet, in 2019/2020, depth-averaged water temperatures comparable to 2021/2022 were recorded at ice-on despite calmer winds and also in the presence of lower average air temperatures prior to iceon as compared to 2021/2022.Also, stratification was weak in 2019/2020, in contrast to the strong stratification in 2021/2022 (Figures 4, and 6).Further, prior to ice-on 2016/2017, average wind speeds comparable to those recorded prior to ice-on in 2018/2019 were observed and would hence suggest similar water temperatures at ice-on for both winters, if the former depended only on wind speed.Depth-averaged water temperatures at ice-on were, however, c. 2°C higher in 2016/2017 than in 2018/2019 (Figure S6).This suggests that wind speed is not the only factor affecting cryostratification patterns at Darfáljávri, and it is noted that during pre-ice-on 2016/2017 and 2018/2019, average air temperatures were c. 3°C higher in 2016 compared to 2018.It is emphasized that the above-described relations prevail during a two-week period prior to ice-on, thus excluding not only parts of the longer pre-ice-on forcing history but also details of the forcing conditions right before ice-on.Both are known to be relevant for complex winter stratification patterns but for which important data (such as cloud cover, snowfall, radiation, atmospheric heat fluxes, turbulent losses across the lake surface, etc.) are not available at Darfáljávri.
Interannual variability is further evidenced by different dates when near-surface waters (2 m bls) depart (on a cooling trajectory) from their steady winter values.Cooling of the under-ice water takes place due to heat loss through ice and heat conduction from lake waters to the ice bottom.Snow cover and eventual high surface temperature of ice limit the heat flux in ice.With a sharp thermocline, there is slow heat loss from the deeper waters to the cold surface layer and to the ice; in 2019/ 2020, this loss was seen at 2 m depth only in February 2020 (Figure 4).However, the departure already occurred in November during winter 2021/2022 (Figure 6), when a thick thermocline prevailed, with temperature differences causing more heat conduction upward than in the previous case.Heat was lost through the ice or redistributed via lateral advection.Large meltwater inflow as a source of cooling can be ruled out at least for 2021 because any such inflow would been seen in the water pressure, which remained rather stable during November 2021.In both winters, however, minimum near-surface water temperatures were attained in early June.The difference between these (2.1°C in June 2020 compared to 0.08°C in June 2022) evidenced once more the interannual variability of the stratification strength.Also, the 30-to 40-m temperatures show interannual variability (c. 3.5°C in 2016/2017and 2017/2018, c. 1.8°C in 2018/2019, c. 2.5°C in 2019/ 2020, and c. 2.8°C in 2021/2022;cf. Figures 4, 6, and S5) and where the cold winter conditions in 2018/2019 have been proposed to have been caused by inflow of cold glacial melt water in response to the record warm summer 2018 (Kirchner et al. 2021).It is likely that the cold glacial meltwaters draining into Darfáljávri contribute significantly to its cooling, as indicated by the fact that surface lake water temperature usually is colder than air temperature; however, this remains speculative because inflow into Darfáljávri is unknown.
When water temperature is below 4°C, stratification is stable and even very short cold and calm periods can freeze the surface.After the stratification is established, and in the absence of solar radiation during the polar night, heat conduction into ice (affected by snow depth on the lake ice) and lateral advection are the main processes continuing under the ice, before solar-driven convection starts in response to radiation penetrating the ice again in the spring, causing water temperatures to rise again (Figure 6).Polar night takes about three weeks at the site and even there is diffuse blue light around noon.At other times solar altitude is low (maximum 45° in midsummer), and although partly shadowed, there is always incident diffuse light on the lake surface.
Surface heat loss and mixing prior to ice-on is complex, as illustrated, for example, in Figure S2 for late September 2021 when near-surface water temperature fluctuated for several days, perhaps caused by a series of (local) transient hydrostatic instability developments and breakages, or advection effects; cooling is influenced by snowfall (cf.section "September 2021 -August 2022"), evaporation, and long-wave radiation losses.The former option is supported by the fact that instabilities no longer exist when water is colder (October 2021) and density is more sensitive to temperature (Carmack and Vagle 2021).Note that we cannot rule out the possibility that chemical stratification (Kirillin et al. 2012) also plays a role, because no such data are available at Darfáljávri.Near 4°C the water density is very weakly sensitive to temperature so that even low conductivity differences can cause stratification.Under ice it is known to occur at ~10 mS/m when low-conductivity meltwater is available.Here the conductivity is c. 1.5 mS/m, and in calm, open water chemical stratification is possible but not likely.

Basin-wide melt of snow cover and partial discharge onto the lake ice surface
After 1 June 2022, meltwater accumulation on the frozen lake surface was observed from the time-lapse imagery at the same time as a peak in water pressure built up, culminating on 13 June.This peak corresponded to an additional pressure of 138 kPa, or a water column of 140 cm.Possible sources for this additional water are precipitation and meltwater from the snow-covered Kebnepakte Glacier and Norra Klippberget (Figures 1a,  1b).Precipitation in the last week of May 2022 was low, and even if a total of 20 mm is used for approximate calculations, this precipitation would be able to cause an increase of 3 kPa (resulting from the entire drainage basin, which is c. 15 times larger than the surface of Darfáljávri).It is therefore clear that precipitation is not the main driver of the observed accumulated meltwater on the lake surface.Melting of lake ice or snow on lake ice does not influence the water-level elevation when the ice is floating (which applies to Darfáljávri with the possible exception of a few shallow regions along the shorelines).However, because air temperatures are above zero from mid-May, water from the melting of snow that accumulated on Kebnepakte Glacier and the flanks of Norra Klippberget during the winter is suspected to accumulate on the still-frozen lake surface.Part of it may have percolated through the lake ice, cooling the uppermost water layers, as observed in Figure 6.Accumulation in turn can only be explained by assuming that the shallow natural outflow of Darfáljávri (Figure 1a and left corners of panels in Figure 3) is largely frozen and blocked on the surface by accumulated ice and snow.Field notes taken during the deployment of the temperature sensor mooring in earlier years (when maintenance was occasionally done during the spring) confirm that melt accumulation events appear to have happened before; for example, in 2019, when the following layering was encountered: snow on top of a layer of lake ice, followed by a layer of what we speculate was non-lake meltwater, followed by a layer of lake ice and then liquid water to the lake floor.

Observed, modeled, and inferred ice phenology
Observed ice phenology at Darfáljávri during 2020 to 2022 showed short open-water seasons, between seventy-five and ninety-nine days as recorded by the time-lapse camera.In contrast, the modeled ice-free season is approximately one month longer, at 123 to 128 days (cf.Table 1).These differences may be attributed to the degree-day model (section "Degree-day model for ice-on and ice-off dates"), which is based solely on mean daily temperatures and has been shown to render, despite its simplicity, fairly good results for small low-altitude mid-latitude lakes in a wide range of geographical regions (Thompson et al. 2005).The model, however, might have shortcomings at higher elevations and latitudes and in glacial environments where variables other than air temperature can have a strong impact on ice phenology, especially during the ice-off process.In particular, continuous solar radiation during the polar summer has a major impact on the melting period.Ice melting has a degree-day term and latitude-dependent radiation term that brings a bias to pure degree-day ice-off models as used here, as shown in a study comparing Tibetan and North European lakes (Leppäranta and Wen 2022).Also, heat is first needed to melt snow, and ice melts typically 2 to 3 cm per day, so that the more snow and ice there is, the longer the ice-off period is (e.g., Leppäranta et al. 2019).
For air temperatures, an elevation lapse rate can be accounted for (for standard atmosphere cooling of 0.65° C/100 m elevation, which represents the mean troposphere; see, e.g., Glossary of American Meteorological Society, glossary.ametsoc.org(American Meteorological Society 2020)).To illustrate the effect of this, we compare Darfáljávri with Lake Kilpisjärvi, located 1° latitude further north from Darfáljávri (and hence receives approximately the same solar radiation) at an elevation of 490 m in the Finnish part of the Scandinavian Mountains.The elevation difference between the two lakes is thus 670 m, translating to c. 4.4°C colder temperatures at Darfáljávri compared to Lake Kilpisjärvi.From several lake studies conducted in the Scandinavian Mountains, it has been reported that the sensitivity of lake freezing and lake-ice melting to air temperature is five to seven days per 1°C change (e.g., Lei et al. 2012).Combined, this implies that ice-on and ice-off at Darfáljávri can each be expected to have an offset of twenty-two to thirty-one days as compared to Lake Kilpisjärvi.
At Lake Kilpisjärvi, the mean length of the ice-free season  is 143 days, which would suggest that Darfáljávri is ice-free for c. 81 (=143 -2 × 31) to 99 (=143 -2 × 22) days, which fits well what was observed.This implies that the lakes possess the same major drivers -local air temperature and solar radiation-determining the length of the ice-free period.It should be noted, however, in this comparison that Darfáljávri only has three years of observations, whereas Lake Kilpisjärvi has fortyfour years and that the observational periods do not overlap.It is also noted that ice-off at Lake Kilpisjärvi usually occurs between 3 June and 1 July, at a critical degree-day threshold of 200 to 250°C•d, thus with an increase of this threshold compared with the model of Thompson et al. (2005) based on which 130°C•d are used at Darfáljávri (where it results in a too early ice-off).The model relation is not universally applicable; for example, in extreme glacial environments, such as in Antarctica, where melting of icecovered supraglacial lakes has been reported for very low degree-day thresholds and is attributed mainly to the impact of solar radiation (Leppäranta, Lindgren, and Arvola 2016).
By definition, the length of the ice-free season is determined by the timing of ice-off and ice-on.Shorter ice-free seasons hence require a later ice-off and/or earlier ice-on, with regional variation.Regarding ice-off, for instance, Weyhenmeyer, Meili, and Livingstone (2004) showed that an increase in air temperature by 1°C caused ice breakup to occur approximately seventeen days earlier in warmer regions in southern Sweden but only four days earlier in the cooler northern parts.At Darfáljávri, we suggest that ice-off is delayed also in response to processes in its glacial environment, particularly spring snowmelt (transitioning into glacial melt later in the season).Spring snowmelt is likely to be associated with some inflow of cold meltwater onto and into Darfáljávri, potentially delaying ice-off.That specific local processes are responsible for this delay is supported by the fact that the observed beginning of iceoff at Darfáljávri is very similar to the modeled one (Figure 8), whereas the final ice-off day is considerably later.Another factor that influences ice-off is seiche, which may cause turbulent mixing and heat flow from below thermocline to ice bottom with increased melting and ice breakage (Kirillin et al. 2018).In principle, seiche can break the ice in autumn (after ice-on); however, it will not lead to ice-free conditions.There are no ice and snow thickness measurements for this Darfáljávri, but in general the region has large snow accumulation, easily 2 m, and based on that and the air temperature data, the lake-ice thickness is expected to reach 1 to 1.5 m in a winter (Kirillin et al. 2018).
Regarding ice-on, which is strongly driven by air temperature and the initial freezing of a lake and often happens within a few days after the air temperature has fallen below the freezing point, the correlation between the predicted ice-on day by the degree-day model and the initial ice-on day observed by the trail camera at Darfáljávri is good (Figure 8).We thus suggest that the differences regarding the length of the ice-free period at Darfáljávri obtained from observation versus the degreeday model are related to a later ice-off, caused in turn by the lake's cold glacial environment.
We also suggest that the day when water temperature below surface layers arrives at its steady winter value is a good proxy for ice-on (see Figure S4).In contrast, the departure of water temperature from its steady winter value is not a good proxy for ice-off unless water temperatures are above 4°C, but it does indicate that, for example, summer convection due to solar melting is initiated, triggering melting of the ice at its underside and hence rendering an indication of the beginning of the ice-off period (Figures 5 and S2) but leaving its duration and culmination in a specific ice-off date undetermined.A large part of the overturn process may take place under ice when the surface is not interacting with atmosphere.Thus, exchange of matter (e.g., oxygen) is blocked, and if summer stratification sets up fast, a memory of the winter remains (Salonen et al. 2009;Dugan 2021).

The role of meltwater during ice-off
Ice-off has here been defined as the first day when Darfáljávri is completely ice-free.This is practical when comparing to other lakes where the same definition of ice-off is applied.However, at Darfáljávri, it would be interesting to study the potential impacts of cold meltwater influx of glacial origin on the dynamics of the ice-off process.Because meltwater effects can have a great impact on the final ice-off day, a different definition of ice-off day that better reflects local conditions could be considered for arctic-alpine lakes.So far, different environments have been accounted for using an elevation lapse rate (Leppäranta and Wen 2022).Nuancing the role of meltwater during ice-off, cold water influx from Darfáljávri's glacial surroundings can impact lake water temperature at least in two ways: meltwater accumulating on top of lake ice, prior to iceoff, decreases albedo and increases radiation absorption and is hence expected to accelerate ice-off.At the same time, if ice-off has been initiated partly already such that cold meltwater can percolate into the lake, it is likely to decrease water temperature and therefore also bottom melt, hence decelerating ice-off.
The cascading effects of climate warming in such a glacial environment also imply that the modeled ice-off and ice-on dates (Figure 8) need to be interpreted with care.Specifically, during the very hot summer of 2018, considerable melt occurred in the Kebnekaise Mountains where Darfáljávri is located: For the period 2017/2018, the glacier Storglaciären had a negative mass balance amounting to −1.6 m water equivalent, the highest loss since 2007 and about five times higher than the average mass loss during the years 2007 to 2022.Cooling effects on Darfáljávri from snow and ice melt from the surrounding glaciers can, however, only be expected while the glaciers are still in place.Predictions inform, however, that it is very likely that 80 percent of the Scandinavian glaciers will have either vanished completely or diminished considerably by the year 2100 if greenhouse gas emissions (and associated global warming) continue along their current path (IPCC 2019).

Limitations
Two limiting conditions must be noted when interpreting results from this study: Firstly, our analysis is hampered by a data gap, caused by the loss of the water temperature sensor mooring during ice-off 2020.When the mooring was retrieved on 14 September 2020, all sensors and the mooring line were found bundled together (cf.section "Lake water temperature, and water level"), and the mooring line was stained with sediment, and it appeared that it had been in contact with lake floor sediments for some time.It is unknown when the mooring collapsed, but water temperatures at all depths were very similar after 25 July (cf. Figure 5).From the time-lapse imagery, heavy ice floe movement across the entire lake surface was observed during 23 to 25 July as part of the final phase of the ice-off period.It is therefore plausible to assume that the uppermost buoy of the mooring, attached to the mooring line (just above the temperature sensor at 2 m bls) to keep the sensor chain in a near-vertical position, was dragged out of place by one (or several) of the rapidly moving floes, implying collapse of the mooring.Secondly, we have limited means to attribute heat loss, and subsequent characteristics of winter stratification, to all of their potential drivers because some (e.g., solar radiation, lake-ice thickness) are not yet measured at Darfáljávri.For these reasons, our interpretation of the drivers of physical lake processes requires further evidence.

Conclusions
Results concerning physical lake processes at Darfáljávri were presented with a focus on water temperature and ice phenology.Because they include wintertime data, they can be a valuable complement to more easily studied summertime lake processes.Our conclusions are as follows: (1) Darfáljávri's existing all-year water temperature record (2016-2019) has been extended by records for 2019-2020 and 2021-2022.(2) Different winter cryostratification patterns are observed at Darfáljávri: During winters 2018/ 2019 and 2021/2022, a thick thermocline prevailed in which quasi-steady winter water temperatures ranged from ~0.2°C in the near-surface layers to ~3°C in the near-bottom layers.In contrast, during winter 2019/2020, a sharp thermocline was observed, with lake water temperatures of c. 2.5°C throughout all depths.(3) Ice phenology at Darfáljávri as observed from time-lapse imagery during 2020-2022 indicates that annual ice-off occurs between mid-July and early August, and annual ice-on takes place between 19 and 27 October.Modeled ice-on dates match observed ones reasonably well, but observed ice-off dates in Darfáljávri's cold glacial environment occur much later than modeled ones.(4) Prior to ice-off 2022, cold water drainage onto, and accumulation at, the frozen lake surface was observed from time-lapse imagery and lake water pressure records.(5) Mixing processes and lake ice phenology in glacier-proximal lakes are complex, as also highlighted by the observation that spring overturning can be completed after ice-off (such as in 2020) or before ice-off (such as in 2022).( 6) Despite the new insights into lake processes at Darfáljávri, a complete picture of winter-and summertime processes at this polar alpine glacial-proximal lake cannot be given.This is because crucial data from Darfáljávri, such as inflow, discharge, and evapotranspiration (needed to close the lake's water balance); lakeice thickness and depth of the snow layer on top of it; and light penetration into the lake (to better explain lake processes in general) are not yet measured and included in the study.

Figure 2 .
Figure 2. Ice phenology during 1 July to 31 October 31 for years 2020 to 2022, as observed from time-lapse imagery.Grey: Darfáljávri is ice-covered.Dark blue: Darfáljávri is ice free.The first blue bar marks the date of ice-off, and the first grey bar in the autumn marks the date of ice-on.Number of ice-free days is also indicated for each year.Dark yellow circles indicate that both time-lapse imagery and water temperature data were available during ice-off and ice-on, respectively.Light green arrows indicate periods for which water temperature data were available (see Figures 4 and 5).

Figure 3 .
Figure 3. Darfáljávri, captured by a time-lapse camera (see Figure 1a).Blue star: approximate position of the temperature sensor mooring.(a) At installation of the time-lapse camera, 20 June 2020.Red boxes indicate the nearshore regions where melting was already initiated.Red arrows point to isolated features mimicking meltwater ponds on the lake ice surface.(b) Ice-off, 7 August 2020.(c) Ice-on during 2021, attained on 19 October.(d) Ice-off during 2022, attained on 27 July.For pictures of ice-on 2020, ice-off 2021, see published data sets (Data Availability Statement).

Figure 4 .
Figure 4. Water temperature at various depths (for color coding, see legend) in Darfáljávri during September 2019 to September 2020.Grey boxes marked "S1" indicate periods of fall overturning 2019 and summer overturning 2020 and are detailed in Figure S1.Dotted vertical lines mark dates of notable events (from time-lapse imagery) during the ice-off period 2020, detailed in section "September 2019 -September 2020".Red box labeled "5" is detailed in Figure 5. Top panel: Data from Tarfala Research Station (TRS) (cf. Figure 1b for location).Pink solid line, daily air temperature.Black line, daily wind speed until 15 October 2019.

Figure 5 .
Figure 5. Changes in water temperatures across depth during ice-off 2020.Detailed from Figure4.Dotted vertical lines mark dates of notable events during the ice-off period, from time-lapse imagery, described in section "September 2019 -September 2020".Note the very similar water temperatures at all depths after 25 July, which may be attributed to the collapse of the mooring; see section "Lake water temperature, and water level".Blue solid line in top panel: Wind speed (sampled at 10-minute intervals) at Tarfala Research Station (TRS) during week highlighted by yellow-filled box in water temperature panel.

Figure 6 .
Figure 6.Water temperatures at various depths (for color coding, see legend) in Darfáljávri during September 2021 to September 2022.Dotted vertical lines mark dates of notable events (from the time-lapse imagery) during the ice-on period 2021 and the ice-off period 2022, described in section "September 2021 -August 2022".Grey boxes labeled "S2" and "S3" are detailed in Figures S2 and S3.Panel above water temperature panel: Pink line, water pressure in Darfáljávri at 3 m bls.Black bars, solid precipitation.Top panel: Blue solid line, daily average air temperature.Precipitation, air temperature, and air pressure (for correction of water pressure) are from Tarfala Research Station (TRS) AWS (cf. Figure 1b and section "Automated weather stations").

Figure 7 .
Figure 7. Changing surface conditions at Darfáljávri, between 1 December 2021 and 13 June 2022.Note the large amounts of meltwater accumulating on the northern lake corner in early June and then disappearing (13 June 2022).

Figure 8 .
Figure 8. Modeled ice-off (blue solid line and stippled blue trendline), modeleld ice-on (red solid line and stippled red trendline) for the period 1965-2022.Blue solid dots: Observed ice-off in 2020, 2021, and 2022.Light blue dots with dark blue edge: Observed beginning of the ice-off period in 2020, 2021, and 2022.Red solid dots: Observed ice-on in 2020, 2021, and 2022.Light-red dots with dark-red edge: Inferred ice-on in 2016, 2017, 2018, and 2019 based on water temperatures only.Stippled black lines: Trendlines for ice-on and ice-off until 2180 if trend is based on the period 2002−2022.

Table 1 .
Summary of observed/inferred/modeled ice-on and ice-off dates and related number of ice-free/ice-covered days per year.
Notes.Year 2019 is based on a date interval for ice-off date.Inferred ice-off dates represent the beginning of the ice-off period rather than completed ice-off.Inferred data are from water temperature oscillations; modeled data obtained using the degree-day approach.Ice-free days and ice-covered days are reported as observed/inferred/modelled.