Recent Ice Trends in Swiss Mountain Lakes: 20-Year Analysis of MODIS Imagery

Noname manuscript No. (will be inserted by the editor)

Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery

Manu Tom 1,2,3 · Tianyu Wu 1 · Emmanuel Baltsavias 1 · Konrad Schindler 1

Received: date / Accepted: date

Abstract Depleting lake ice can serve as an indicator products. We find a change in Complete Freeze Dura- for climate change, just like sea level rise or glacial re- tion of -0.76 and -0.89 days per annum for lakes Sils and treat. Several Lake Ice Phenological (LIP) events serve Silvaplana, respectively. Furthermore, we observe plau- as sentinels to understand the regional and global cli- sible correlations of the LIP trends with climate data mate change. Hence, it is useful to monitor long-term measured at nearby meteorological stations. We notice lake freezing and thawing patterns. In this paper we re- that mean winter air temperature has negative correla- port a case study for the Oberengadin region of Switzer- tion with the freeze duration and break-up events, and land, where there are several small- and medium-sized positive correlation with the freeze-up events. Addition- mountain lakes. We observe the LIP events, such as ally, we observe strong negative correlation of sunshine freeze-up, break-up and ice cover duration, across two during the winter months with the freeze duration and decades (2000-2020) from optical satellite images. We break-up events. analyse time-series of MODIS imagery by estimating spatially resolved maps of lake ice for these Alpine Keywords lake ice monitoring · machine learning · lakes with supervised machine learning (and addition- semantic segmentation · satellite image processing · ally cross-check with VIIRS data when available). To MODIS · VIIRS train the classifier we rely on reference data annotated manually based on webcam images. From the ice maps we derive long-term LIP trends. Since the webcam data 1 Introduction is only available for two winters, we also validate our results against the operational MODIS and VIIRS snow Scientists around the globe strive to understand the changing climate, to find ways to mitigate the impact of Manu Tom ( ) associated extreme weather conditions, and to protect E-mail: [email protected] the environment for future generations (Rolnick et al., Tianyu Wu 2019). The repercussions of climate change are fore- arXiv:2103.12434v2 [cs.CV] 3 Aug 2021 E-mail: [email protected] seen to amplify in the next few decades. Furthermore, Emmanuel Baltsavias the latest climate models underline the need for urgent E-mail: [email protected] mitigation (Forster et al., 2020). ”Human activities are Konrad Schindler estimated to have caused approximately 1.0◦C of global E-mail: [email protected] warming above pre-industrial levels, with a likely range ◦ ◦ 1Photogrammetry and Remote Sensing Group, of 0.8 C to 1.2 C. Global warming is likely to reach ETH Zurich, 8093 Zurich, Switzerland 1.5◦C between 2030 and 2052 if it continues to increase at the current rate”, said the IPCC special report on im- 2 Glaciology and Geomorphodynamics Group, pacts of global warming (Masson-Delmotte et al., 2018). University of Zurich, 8057 Zurich, Switzerland Many studies have reported on the response of LIP 3Remote Sensing Group, Swiss Federal Institute of Aquatic trends to climate variations (Brown and Duguay, 2010; Science and Technology, 8600 Dübendorf, Switzerland Duguay et al., 2006; Howell et al., 2009; Kang et al., 2 Tom et al.

2012; Sharma et al., 2019; Surdu et al., 2014). Lo- the spatial resolution is moderate (250-1000m Ground cal weather patterns and lake ice formation processes Sampling Distance, GSD). In addition, the global cov- are inter-connected (Brown and Duguay, 2010). Hence, erage is beneficial to eventually scale up to country- or monitoring the long-term LIP trends can provide in- world-wide monitoring. On the other hand, cloud cover tegral cues on the local and global climate. Increasing is a bottleneck for optical satellite data analysis. An temperatures cause decreasing trends in the lake ice important asset is the availability of large time-series, formation process. Air temperature in the vicinity of a e.g., MODIS data is available for the entire period since lake affects the ice formation process within the lake 2000, contrary to other sensor data like airborne or ter- and vice versa. Moreover, there are potential positive restrial photography, webcams etc. This makes it pos- feedbacks, as frozen lakes have higher albedo (especially sible to implement a 20-year analysis and to derive the when covered with snow), and thus lower absorption LIP trends. and evaporation (Slater et al., 2021; Wang et al., 2018). The last decades have seen the rise of machine learn- In addition to its usefulness for climate studies, lake ice ing as a tool for data analysis in remote sensing and monitoring is also crucial to organise safe transporta- the Earth sciences. That is, large-scale statistical data tion especially in lakes that freeze only partially, to con- analysis is used to capture the complex input-output reserve freshwater ecology, to trigger warnings against ice lationships in a data-driven manner. Machine learning shoves caused by wind during the break-up period, and is a powerful tool to recognise the underlying patterns for winter tourism (Hampton et al., 2017; Hirose et al., in data where mechanistic models are lacking or too 2008; Knoll et al., 2019; Mullan et al., 2017). complicated. We leverage it to create a 20 year time- In the present case study, we aim to monitor lakes series of ice cover in Swiss mountain lakes primarily of the Oberengadin region in the Swiss Alps (which using the Terra MODIS (https://terra.nasa.gov reliably freeze every winter) on a daily basis during /about/terra-instruments/modis) data, and show the winter months, to derive the spatio-temporal ex- empirically that the ice formation indeed follows a de- tent of lake ice.1 Specifically, we estimate the four im- creasing trend. We cast lake ice detection as a 2-class portant LIP events: Freeze-Up Start (FUS), Freeze-Up (frozen, non-frozen) per-pixel supervised classification End (FUE), Break-Up Start (BUS) and Break-Up End problem. Class frozen represents both snow-on-ice and (BUE). Using these four dates, we also estimate the snow-free-ice pixels, while non-frozen denotes open wa- Complete Freeze Duration (CFD) and Ice Coverage Du- ter. As part of our study, we compare the performance ration (ICD), refer to Table 1 for definitions. Some pub- of three popular machine learning methods: Support lications have termed FUE and BUS as ice-on and ice- Vector Machine (Cortes and Vapnik, 1995, SVM), Ran- off dates, respectively (Hendricks Franssen and Scher- dom Forest (Breiman, 2001), and XGBoost (Chen and rer, 2008; Tom et al., 2020c). However, other researchers Guestrin, 2016). Additionally, we assess the sensitivity (and the NSIDC database, https://nsidc.org/) con- of these classifiers to the respective hyper-parameters. sider BUE as ice-off (Duguay et al., 2015). Regarding We find that a linear SVM offers the best generalisa- the ice-on/off dates, the Global Climate Observing Sys- tion across winters and lakes for our data, and derive tem (GCOS) requirements are daily observations at an LIP from the resulting time-series by fitting a piece-wise accuracy of ±2 days (https://gcos.wmo.int/en/es linear model per winter. sential-climate-variables/lakes/ecv-requirem ents). 1.1 Operational lake ice / snow products In this work, we focus on estimating the spatio- temporal extent of the ice cover from optical satel- To our knowledge, the only operational lake ice prod- 2 lite data. Compared to other sensors, MODIS and uct at present is the Climate Change Initiative Lake VIIRS satellite data have several advantages such as Ice Cover (Crétauxet al., 2020). A comparison of our wide area coverage, good spectral and fine temporal results with this product is however not possible, since resolution (daily), free availability etc. Additionally, none of our target lakes are included in the list of 250 compared to other optical satellites such as Landsat- lakes covered by the product. A second product, Coper- 8, Sentinel-2 and the like, MODIS and VIIRS offer the nicus Lake Ice Extent (LIE, https://land.coper best spatio-temporal resolution trade-off for the appli- nicus.eu/global/products/lie), is still in pre- cation of single-sensor lake ice monitoring, even though operational stage due to accuracy issues, and coverage only starts in 2017. Though not designed for lake ice, 1 we do not include the ice thickness. the MODIS Snow Product (Hall and Riggs, 2016) and 2 we have previously also used webcams (Tom et al., 2020c; Xiao et al., 2018) and Sentinel-1 Synthetic Aperture VIIRS Snow Product (https://nsidc.org/sites/ns Radar (Tom et al., 2020a, SAR) for lake ice monitoring. idc.org/files/technical-references/VIIRS-sno Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 3 w-products-user-guide-final.pdf) are also possi- and reported delayed FUS (0.58 d/a) as well as BUS ble options for comparison, since lakes in the Alps are (0.09 d/a), and reduced ice duration (-0.49 d/a) trends. typically snow-covered for most of the frozen period. We Another study (Yao et al., 2016) also noted increas- cross check our results with these two snow products, ingly shorter freeze duration during the period 2000– see Section 5.2.4. More details on all the mentioned 2011 when investigating the lakes in Hoh Xil region products can be found in Table 7 (Appendix A). (Tibet, 22 lakes with area > 100 km2), using MODIS, Landsat TM/ETM+, and meteorological data. In addition, that work estimated later freeze-up and earlier 1.2 Definitions used break-up trends. They reported that the FUS, FUE, BUS, BUE, CFD and ICD shifted on average by 0.73, We exclude mixed pixels and work only with pixels that 0.34, −1.66, −0.81, −1.91, −2.21 d/a respectively. Cai lie completely inside a lake, termed clean pixels. Non- et al. (2019) also analysed 58 lakes located on the Ti- transition dates are the days when a lake is either com- betan Plateau during the period from 2001 till 2017 pletely frozen or completely non-frozen, the remaining using both Terra and Aqua MODIS imagery. For 47 days in a winter season are termed transition dates. By lakes, a later FUS was noticed (0.55 d/a) while for the winter season, we denote all dates from September till remaining 11 lakes an earlier FUS was observed (-0.44 May for our purposes. d/a). For 50% of the target lakes, an earlier BUE (-0.69 d/a) was noted, however, for the other half a later BUE (0.39 d/a) was observed. Additionally, they reported a 2 Related work reduced ice cover duration for 40 lakes (-0.8 d/a), while for 18 lakes an increase was noted (1.11 d/a). 2.1 LIP trend analysis studies using MODIS and VIIRS data Yang et al. (2019) used MODIS to estimate the LIP trends for 8 large lakes (106 - 3461 km2) in Northeast- The LIP trends of several lakes with different geograph- ern China from 2003 to 2016. Later FUS (0.65 d/a), ical conditions have been studied and reported in the earlier BUE (-0.19 d/a) and shorter freeze duration (- literature. Though most of them use information from 0.84 d/a) trends were noticed. Qi et al. (2020) used various ice databases (e.g., NSIDC), some studies di- AVHRR, MODIS, and Landsat data to extract the LIP 2 rectly derived the trends from radar and optical satellite of Qinghai lake (China, area of 4294 km ) for the period data. In the following we focus on studies that, like ours, 1980–2018. They estimated a shift of 0.16, 0.19, −0.36, analyse MODIS and/or VIIRS optical satellite imagery and −0.42 d/a for FUS, FUE, BUS and BUE respec- to examine trends over multiple winters. tively, also pointing towards progressively later freeze- Smejkalováetˇ al. (2016) extracted the LIP trends up and earlier break-up. Additionally, they computed (2000–2013) for 13,300 Arctic lakes (area >1 km2) us- the decreasing patterns in ICD (−0.58 d/a) and CFD ing MODIS imagery, and earlier break-up trends were (−0.52 d/a). That study also identified correlations be- noticed. They reported a mean shift in BUS in the tween the LIP and climate indicators like the Accu- range: -0.10 d/a (Northern Europe) to -1.05 d/a (cen- mulated Freezing Degree-Days (AFDD), wind speed, tral Siberia), and BUE in the range: -0.14 d/a to -0.72 precipitation, etc. during the winter season. Cai et al. d/a. Kropáˇceket al. (2013) studied the LIP trends of (2020) used a threshold-based method to extract LIP 59 lakes on the Tibetan Plateau from 2001 to 2010 us- trends from MODIS snow product for 23 lakes (2001- 2 ing MODIS data. However, the estimated LIP trends 2018, Xinjiang Uygur Region, area: 11 to 1004 km ) in varied across the target lakes and it was concluded China. They found that the ICD decreased (-1.08 d/a) that 10 year time span is too short to draw firm con- in 16 out of the 23 lakes and increased (1.18 d/a) for clusion about LIP trends. Gou et al. (2015) analysed the rest. In addition, they reported later freeze-up (0.52 the ice formation trends (2000–2013) in lake Nam Co d/a) and earlier break-up (-0.51 d/a) in 17 and 18 lakes, (Tibet, area 1920 km2) using MODIS and in-situ data respectively. Additionally, they found that the freeze-up and found strong correlations with air temperature and events are more affected by lake-specific factors such wind speed patterns. This study found that high wind as area, mineralisation, etc.; while climatic factors like speeds during winter time could potentially expedite water surface temperature have more influence on the the freeze-up process. Additionally, this work reported break-up events. That work also emphasised that lake a significant reduction of the total freeze duration. Gou surface water temperature has a stronger influence on et al. (2017) later analysed Nam Co for the period 2000 the LIP events than air temperature. till 2015 using multiple MODIS products (MOD11A1, Latifovic and Pouliot (2007) used the historical data MYD11A1, MOD09GQ, MYD09GQ, and MOD10A1) record of AVHRR satellite in addition to in-situ mea- 4 Tom et al. surements to perform long-term (1950-2004) trend anal- used the temperature data from 1901–2006 to study ysis in Canadian lakes, via an automated profile feature eleven lakes in the lower-lying Swiss plateau, none extraction procedure, confirming later freeze-up (0.12 of the target mountain lakes were included. Our case d/a) and earlier break-up (—0.18 d/a) for the major- study focuses on the Oberengadin region, with three ity of lakes that were analysed. They suggested that main lakes: Sils, Silvaplana and St. Moritz (with the their procedure to extract the LIP events is not sensor- latter very small for the GSD of MODIS). Moreover, specific and could be applied to other satellite data, we include another Alpine lake Sihl to check generality. too. Murfitt and Brown (2017) also used MODIS data, Our goal in this work is lake ice monitoring using to extract lake ice trends (2001-2014) for the regions only image data from optical satellites, which provides a Ontario and Manitoba in Canada. However, the discov- direct, data-driven observation not influenced by model ered trends varied across regions. Zhang et al. (2021) assumptions about the ice formation process. We see put forward a new LIP database (4241 lakes with a satellite imagery as an independent information source minimum area of 1 km2) for Alaskan lakes covering and consider image analysis complementary to other the period 2000-2019. Ice-on/off dates and freeze dura- methods of lake ice modelling. Furthermore, compared tion values included in this dataset were extracted from to our satellite-based approach, which can easily anal- MODIS data using a threshold-based method. Addi- yse the whole lake area, it is difficult to effectively de- tionally, they estimated the following LIP trends: later rive the spatial extent of lake ice from the temperature freeze-up (0.29 d/a) and earlier break-up (-0.55 d/a) (point) observations recorded at one or a few nearby were recorded for 289 and 440 lakes, respectively, while weather stations, even if they are situated in the imme- earlier freeze-up (-0.33 d/a) and later break-up (0.75 diate vicinity of the lake (which is not always the case). d/a) were noticed only for 11 and 4 lakes, respectively. This is even more true in the Alpine terrain that we Compared to MODIS, the literature on lake ice target, due to strong micro-climatic effects. monitoring with VIIRS data is limited. Sütterlinet al. (2017) estimated the LIP dates for winter 2016–17 in se- 2.2 Lake ice observation with machine and deep lected Swiss lakes using the lake surface water temper- learning ature (LSWT) derived from visible and near-infrared reflectances, and thermal infrared band (I5) of VIIRS Machine learning algorithms have become a standard data. Later, for winter 2016–17, Tom et al. (2020c) es- tool for several environmental remote sensing research timated the LIP dates of lakes Sihl, Sils, Silvaplana, problems, including our earlier works on monitoring and St. Moritz from VIIRS and MODIS data. To our lake ice cover. In Tom et al. (2018), we already inves- knowledge, no multi-winter LIP trend analysis based on tigated pixel-wise classification of the spatio-temporal VIIRS data has been reported yet. extent of lake ice from MODIS and VIIRS imagery To summarise, most related works reviewed so far with SVM. Each pixel was classified as either frozen have found trends towards later freeze-up, earlier break- or non-frozen in a supervised manner. Though this ap- up and declining freeze duration. The prevalent meth- proach achieved strong results (including generalisation ods are physics-inspired models based on empirical in- across winters, and across lakes with similar geographic dices and thresholds. Most studies focus on large lakes, conditions), the test set at the time did not have a often in the Arctic and sub-Arctic regions. Beyond complete winter of reference data (including the crit- analysing the lakes of the Oberengadin region, in the ical freeze-up and break-up periods), due to technical present work we also show that supervised machine problems. Later, Tom et al. (2020c) presented exten- learning models are able to detect lake ice with high sive experiments on data from two full winters and accuracy, hoping that the outcome may be useful for confirmed the efficacy of SVM for lake ice monitoring future research. To our knowledge, none of the ear- with MODIS and VIIRS. Both these works dealt with lier trend studies applied data-driven machine learning small- and mid-sized Swiss mountain lakes. Xiao et al. methods to identify lake ice. (2018) and Prabha et al. (2020) explored the potential For Swiss lakes, a previous study (Hen- of convolutional neural networks (CNNs) for lake ice dricks Franssen and Scherrer, 2008) verified that detection in terrestrial webcam images (RGB). They the lake ice formation and surrounding air temperature performed a supervised classification of the lake pix- are heavily correlated. They deducted an empirical els using the Tiramisu (Jégouet al., 2016), respectively relationship between sum of negative degree days Deeplab v3+ (Chen et al., 2018) networks, into the four (same as AFDD) and the lake ice formation process, classes: water, ice, snow and clutter. An integrated ap- and modelled the probability of ice cover via binomial proach using both the satellite and webcam observa- logistic regression. Though this approach gathered and tions was discussed in Tom et al. (2019) to estimate Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 5 the ice-on and ice-off dates. Recently, Hoekstra et al. lakes. For each lake, the temperature and precipitation (2020) proposed an automated approach for ice vs. wa- data recorded at the nearest meteorological stations are ter classification in RADARSAT-2 data, combining un- shown in Fig. 2. On the top and bottom rows, we plot supervised Iterative Region Growing using Semantics the mean air temperature and total precipitation (solid (IRGS) and supervised random forest labelling. A deep curves) during the winter months on the y-axis, against learning approach to lake ice detection in Sentinel-1 the winters on the x-axis in a chronological order. Ad- SAR imagery has been described in Tom et al. (2020a), ditionally, in both rows, we plot the linearly fitted trend and achieved promising results, including generalisa- curve (dotted line) for each station. tion across lakes and winters. Very recently, Wu et al. For lakes Sihl and St. Moritz, the nearest meteo- (2021) compared the capabilities of four different ma- rological stations are Einsiedeln (EIN) and Samedan chine learning methodologies: multinomial logistic re- (SAM) respectively as shown in Fig. 1 (see also Ta- gression, SVM, random forest, and gradient boosting ble 8). Lakes Sils and Silvaplana are located next to trees for lake ice observation using the MODIS Top of each other and hence share the same meteorological sta- Atmosphere product. They modelled lake ice monitor- tion: Segl Maria (SIA). The station EIN is located at a ing as a 3-class (ice, water, cloud) supervised classifi- relatively lower altitude and closer to the Swiss plateau, cation problem. The four classifiers were tested on 17 while the other two stations are in the Engadin valley large lakes from North America and Europe with ar- at higher altitudes. This explains why the absolute tem- eas >1040 km2, and achieved >94% accuracy. Random perature is relatively higher for station EIN. Addition- forest and gradient boosting trees showed better gener- ally, the stations SIA and SAM are located within 20 alisation performance on this dataset of large lakes. km from one another, see Fig 1, and hence have similar temperature and precipitation values. Exceptionally high winter temperature was recorded at all three sta- 3 Study area and data tions in winter 2006–07. It can be seen from Fig. 2 that during the past 20 3.1 Study area winters, at all the three stations, the mean temperature follows an increasing trend. On the other hand, precip- We process four small-to-medium-sized Swiss Alpine itation (snow and rain) has a decreasing pattern. While lakes: Sihl, Sils, Silvaplana and St. Moritz, see Fig. 1 Meteoswiss has reported a significant trend of temper- and Table 8 (Appendix B). While most of the earlier ature increase in the Swiss Alps since 1864, they have works (Gou et al., 2015; Qi et al., 2019, 2020; Yao so far not confirmed a significant precipitation trend et al., 2016) on long time-series monitoring of lake ice (https://www.meteoswiss.admin.ch/home/climate with MODIS concentrated on larger lakes, many lakes /climate-change-in-switzerland/temperature-a that freeze are actually small- or medium-sized moun- nd-precipitation-trends.html). Over the shorter tain lakes, especially outside the (sub-)Arctic regions. period of the past 20 winters, precipitation has been The lakes we analyse are relatively small in area (0.78 slightly declining. Warmer winters at higher altitudes - 11.3 km2), representative for this category. in Switzerland could be linked to a decrease in precipi- The lakes were chosen according to the needs of tation, see Rebetez (1996). The pattern of precipitation two projects of the Swiss GCOS office (Tom et al., over the 20-year period differs somewhat between the 2019, 2020b). For the three small lakes in the region station EIN and the two other (similar) stations, e.g., Oberengadin (Sils, Silvaplana, St. Moritz), located at see the winters 2008–09, 2012–13. an altitude > 1750 m, there are long in-situ observation series (important for climate studies), and they are also included in the NSIDC lake ice database (https: 3.2 Data //nsidc.org), although not updated recently. The fourth lake (Sihl) from the region Einsiedeln has been In our analysis, we use the data from Terra MODIS chosen mainly to test generality, as it is relatively larger, and Suomi NPP VIIRS (https://ncc.nesdis.noaa. lies at a lower altitude on the North slope of the Alps, gov/VIIRS/) satellites downloaded from the LAADS and has different environmental conditions, see Table 8. (https://ladsweb.modaps.eosdis.nasa.gov) The three lakes in Oberengadin fully freeze every year, and NOAA (https://www.avl.class.noaa.gov whereas lake Sihl does not (but still freezes in most /) databases, respectively. For MODIS processing, we winters). downloaded the MOD02 (geolocated and calibrated ra- For these four lakes there is no reference freeze/thaw diance, level 1b, Top Of Atmosphere), MOD03 (geolo- data available from the past two decades. Hence, we cation) and MOD35 L2 (cloud mask) products and pre- study the weather patterns in the regions near the processed using MRTSWATH (https://lpdaac.usg 6 Tom et al. ±

EIN

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SIA

0 4 8 Kilometres 0 35 70 140 Kilometres

Fig. 1: MODIS orthophoto map (RGB composite, red: band 1, green: band 4, blue: band 3) of Switzerland (left) captured on 7 September 2016. Red and amber rectangles show the regions Einsiedeln (around lake Sihl) and Oberengadin (with lakes Sils, Silvaplana and St. Moritz, from left to right) respectively. Inside each zoomed rectangle on the right, the respective lake outlines are shown in light green and the nearest meteorological stations (EIN, SIA and SAM) are marked using pins. s.gov/tools/modis reprojection tool swath/, re- each band, the bar width is proportional to the corre- projection and re-sampling) and LDOPE (Roy et al., sponding bandwidth. 2002, cloud mask) software. For VIIRS, we downloaded We analyse MODIS data from all winters since the Scientific Data Record data for the imagery bands, 2000–01 (20 winters), and VIIRS data from all winters IICMO and VICMO products for the cloud masks, since 2012–13 (8 winters). In each winter, we process and GITCO (for image bands) and GMTCO (for cloud all the dates from the beginning of September until the masks) for terrain corrected geolocation. VIIRS pre- end of May on which at least 30% of a lake is free of processing is done using the following software pack- clouds, according to the mask. Fig. 3 displays more de- ages: SatPy (https://satpy.readthedocs.io/) tails of the MODIS and VIIRS data that we use as a for assembling the data granules, mapping and re- stacked bar chart (one colour per lake). For all target sampling, H5py (https://www.h5py.org) for cloud lakes, the total number of cloud-free, clean pixels in mask extraction, PyResample (https://resample.r each winter is shown on the y-axis, against the winters eadthedocs.io) and GDAL (https://gdal.org) for in chronological order on the x-axis. re-sampling of cloud masks. As in Tom et al. (2020c), we use only twelve (five) selected MODIS (VIIRS) bands In Fig. 3, note that some winters are relatively less to form the feature vector. The bands that offer max- cloudy. This explains why the number of pixels vary imum separabilty for the task of lake ice monitoring across winters, even for the same lake and sensor. On were automatically chosen by the supervised XGBoost average there are 16558, 5899, 3972 and 329 MODIS feature selection algorithm (Chen and Guestrin, 2016). pixels per winter for the lakes Sihl, Sils, Silvaplana and The spectral coverage of these bands is shown in Fig. 14 St. Moritz respectively. Similarly, there are 5538, 1901 (Appendix C) where MODIS (M) and VIIRS (V) bands and 1606 VIIRS pixels for the lakes Sihl, Sils and Silva- are displayed as blue and red bars, respectively. For plana respectively. Due to its small size there exist no clean pixel for St. Moritz in VIIRS imagery bands (Tom et al., 2020c), hence we exclude it from the VIIRS anal- Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 7

EIN SIA SAM EIN trend SIA trend SAM trend

Temperature (°C) 2 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter

EIN SIA SAM EIN trend SIA trend SAM trend

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400 Precipitation (mm) 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter

Fig. 2: For the region near the lakes, the mean winter air temperature (row 1) and total winter precipitation (row 2) are plotted (solid curve) on the y-axis against the winters shown in a chronological order on the x-axis. Twenty winter data from the nearest meteorological stations: EIN (Sihl), SIA (Sils and Silvaplana) and SAM (St. Moritz) are used. The corresponding trends (linear fit, dotted curve) are also shown with the same colour. Data courtesy of MeteoSwiss. Winter 00–01 represents the dates from September 2000 till May 2001 (and similarly other winters). ysis. The number of pixels per acquisition is propor- IRS acquisitions from the same day. For all four lakes, tional to the lake area and hence varies across lakes Fig. 3c shows the percentage of non-cloudy days (at even for a given sensor. Additionally, for a given lake, least 30% cloud-free pixels) in each winter season. It the number of VIIRS pixels per acquisition is lower can be seen that ≈40 to ≈60% of all days are not usable compared to MODIS, due to the higher GSD of VI- due to clouds, significantly reducing the effective tem- IRS imagery bands (≈ 375m) compared to MODIS poral resolution. We notice that the data loss is worse (250m). We super-resolved all low resolution MODIS for lake Sihl located near the plateau. bands (500m, 1000m) to 250m using bilinear interpola- tion prior to the analysis. This step is not required for 3.2.1 Ground truth VIIRS as all used bands have the same GSD. It can be inferred from Fig. 3 that in both VIIRS We use the same ground truth as in Tom et al. (2020c), and MODIS plots, the cloud patterns of lakes Sils, Sil- which is based on visual interpretation of freely avail- vaplana and St. Moritz are quite similar, due to geo- able high-resolution webcams monitoring the target graphical proximity (see also Fig. 1). Minor differences lakes. One label (fully frozen, fully non-frozen, partially exist (in few winters) between the two very nearby lakes frozen) per day is assigned. Two different operators Sils and Silvaplana due to cloud mask errors (see also looked at each image, i.e., a second expert verified the Section 4.1). Lake Sihl has a different cloud coverage judgement of the first operator to minimise interpre- pattern compared to other three lakes, due to its lower tation errors. When deciphering a webcam image was altitude and different surrounding topography. Both difficult, additional images were used from other web- MODIS and VIIRS have daily temporal resolution, but cams viewing the same lake (if available), images from the data capture can happen at different times within the same webcam but at other acquisition times on the a day. Consequently, the cloud pattern (and hence the same day, and images of the same webcam for the days cloud masks) can differ even between MODIS and VI- before and after the given observation day. We also im- 8 Tom et al.

Sihl Sils Silvaplana St. Moritz

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NC days (%) 20

0 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter

Fig. 3: First row displays the clean, cloud-free pixels (from transition and non-transition dates) from the four target lakes (Sihl, Sils, Silvaplana, St. Moritz) used in our experiments. Data from both MODIS (20 winters, 4 lakes) and VIIRS (8 winters, 3 lakes) is displayed. Second row shows the percentage of at least 30% Non-Cloudy (NC) days during each winter (derived from the MODIS cloud mask). Winter 00–01 represents the dates from September 2000 till May 2001 (and similarly other winters). proved the webcam-based ground truth using sporadic serves the purpose, in the sense that it has significantly information available from media reports, and by visu- fewer wrongly labelled pixels than the automatic pre- ally interpreting Sentinel-2 images, whenever available diction results. We see no possibility to obtain more and cloud-free. No webcam data is available from the accurate, spatially explicit ground truth for our task. winters before 2016-17. Moreover, the manual interpretation process is very labour intensive. Thus, ground truth is available only for two winters (2016–17, 2017– 4 Methodology 18). 4.1 Pre-processing Even though visual interpretation is the standard practice, a certain level of label noise inevitably remains We perform the same pre-processing steps as in Tom in the ground truth, due to factors such as interpreta- et al. (2020c). First, the absolute geolocation error for tion errors, image compression artefacts, large distance both sensors (0.75, respectively 0.85 pixels x- and y- and flat viewing angle on the lake, etc. Furthermore, the shifts for MODIS; 0.0, respectively 0.3 pixels x- and y- webcams used are not optimally mounted for lake ice shifts for VIIRS) are corrected. The generalised (Dou- monitoring application and hence do not always cover glas and Peucker, 1973) lake outlines are then back- the full lake area (or even a major portion of it), even projected onto the images to extract the clean pixels. for the smallest lake St. Moritz. Still, the ground truth Note that, we discard the mixed pixels and our analysis Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 9 is only based on the clean pixels. Binary cloud masks Also, given the large GSD and limited need for spa- are derived from the respective cloud mask products to tial context, we do not expect deep models to greatly limit the analysis only to cloud-free pixels. We noticed outperform our shallower ones, see Section 5. some errors in both MODIS and VIIRS cloud masks. The most critical ones are false negatives, where an actually cloudy pixel goes undetected. Such cases can cor- 4.3 LIP estimation rupt model learning and inference and introduce errors in the predicted ice maps. In each winter, using the trained machine learning model, we process all available acquisitions that are at least 30% cloud-free and generate pixel-wise classification maps (one per acquisition). To recover the tempo- 4.2 Machine learning for lake ice extraction ral evolution (per winter), the percentage of non-frozen pixels is computed from each classification map and is We model lake ice detection in optical satellite images plotted on the y-axis against the acquisition time on the as a per pixel 2-class (frozen, non-frozen) supervised x-axis. Then, as in Tom et al. (2020c), multi-temporal classification problem. For each pixel, the feature vec- smoothing is performed as a post-processing step us- tor is formed by directly stacking the 12 (5) bands of ing a Gaussian kernel with standard deviation 0.6 days MODIS (VIIRS), see Fig. 14. More details on band se- and window width 3 days. An example MODIS results lection are in Section 3.2. We treat snow-on-ice and timeline for lake Sils from winter 2006–07 is shown in snow-free-ice as a single class: frozen. Class non-frozen Fig. 4a. Results from different months are displayed denotes the open water pixels. The class distributions in with different colours, see the legend. In addition, only winters 2016–17 and 2017–18 are shown in Fig. 15 (Ap- the acquisitions for which the lake is at least 30% non- pendix D). There is a significant class imbalance in cloudy, are displayed. our dataset, since we include all cloud-free dates from In the post-processed timeline, we find all the poten- September till May, of which only a minority is frozen. tial candidates for the following four critical dates: FUS, We have tested four off-the-shelf machine learning clas- FUE, BUS and BUE, see Table 1 for the corresponding sifiers: linear SVM, SVM with Radial Basis Function definitions. Within a winter, it is possible that >1 can- (RBF) kernel [SVM RBF], Random Forest and eXtreme didates exist per critical date which all satisfy the re- Gradient Boosting [XGBoost] to perform pixel-wise su- spective definition. In order to weed out some obviously pervised classification in order to predict the state of a spurious candidates, we enforce the constraint that the lake. four dates must occur in the following chronological or- We recall that SVM is a linear large-margin classi- der: FUS→FUE→BUS→BUE. Then we exhaustively fier, which can be extended to non-linear class bound- search for the optimal set of four dates among the re- aries with the kernel trick. The choice of kernel is criti- maining candidates. To that end, we fit a continuous, cal and depends on the data distribution. In our case we piece-wise linear ”U with wings” shape to the per-day tested both linear and RBF kernels. Random forest is values of percentage of non-frozen pixels, such that the an ensemble learning approach which relies on bagging fitting residuals z are minimised (see example fit in (bootstrap aggregation) of multiple decision trees con- Fig. 4b, shown in cyan colour). In detail, the loss func- structed from the data, using randomisation to decorre- tion for the fit is defined as: late the individual trees. XGBoost is also an ensemble method based on (shallower) decision trees, but itera- N 1 X L = · H (z) (1) tively learns the trees with gradient descent, such that LIP P φ each tree corrects the error of earlier ones. XGBoost is i=1 highly scalable and exploits sparsity. We note that sev- where N is the total number of available acquisitions eral comparison studies exist in the literature for other that are at least 30% cloud-free. applications than ours, e.g., Ogutu et al. (2011); Pham ( et al. (2020); Wainer (2016). z2 |z| ≤ φ Hφ(z) = (2) Note also, while there recently has been a strong 2φ|z| − φ2 |z| > φ interest in deep learning for remote sensing tasks, it is not suitable for our particular application, due to the is the Huber norm of the residual. For the shape pa- scarcity of pixels with reliable ground truth. The lakes rameter φ, we use a constant value of 1.35 which offers that we monitor are small and ground truth is available a good trade-off between the robust l1-norm for large for two winters (see Section 3.2.1 and Fig. 15), which residuals and the statistically efficient l2-norm for small is too little to train data-greedy deep neural networks. residuals (Owen, 2006). 10 Tom et al.

(a) Post-processed results timeline before curve ﬁtting

(b) After curve ﬁtting

Fig. 4: Piece-wise linear (”U with wings”) curve ﬁtting example. NF indicates Non-Frozen. Results are displayed only for the acquisitions for which the lake is at least 30% non-cloudy.

Table 1: Key LIP events.

Event Deﬁnition Freeze-Up Start (FUS) 30% or more of the non-cloudy portion of the lake is frozen and the just previous non-cloudy day should be < 30% frozen Freeze-Up End (FUE) 70% or more of the non-cloudy portion of the lake is frozen and the just previous non-cloudy day should be < 70% frozen Break-Up Start (BUS) 30% or more of the non-cloudy portion of the lake is non-frozen and the just previous non-cloudy day should be < 30% non-frozen Break-Up End (BUE) 70% or more of the non-cloudy portion of the lake is non-frozen and the just previous non-cloudy day should be < 70% non-frozen Ice Coverage Duration (ICD) BUE - FUS Complete Freeze Duration (CFD) BUS - FUE

Per lake, we assume that each critical date occurs The prior probability (P ) is given by: only once per winter, which is always true in Oberen- gadin. Lake Sihl does not always fully freeze. As it lies P = Pfus · Pfue · Pbus · Pbue (3) outside of the target region and is included mostly to ensure generality of the ice classifier, we do not extract where Pfus, Pfue, Pbus, and Pbue are Gaussian nor- the LIP events for Sihl. Moreover, we decide to exclude mal distributions for the events FUS, FUE, BUS and lake St. Moritz since it is too small for the GSD of BUE, respectively. The prior formalises the knowledge MODIS (only 4 clean pixels), making the fraction of that freeze-up normally occurs around the end of De- frozen pixels overly susceptible to noise. We thus prefer cember and takes around three days, and break-up oc- to study only the two main lakes in Oberengadin, Sils curs around the end of April over a similar period, for and Silvaplana, in terms of long-term lake ice trends. both target lakes. In order not to bias the estimation, These two lakes fully freeze every year and typically but only to minimise the risk of implausible results, have a single freeze-up and break-up period. To further we choose very wide Gaussians (σ = 1 month). Fur- stabilise the LIP estimates we include a weak prior for thermore, we impose a constraint that the duration of each phenological date, in the form of a diffuse Gaussian freeze-up (FUE-FUS) and break-up (BUE-BUS) is not distribution. more than two weeks. Inspired by Qi et al. (2020), we additionally compute further indicators that can be derived from the Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 11 four critical dates, namely ICD and CFD, see Table 1 5.1.1 Hyper-parameter tuning for details. We use 30% as the threshold to estimate the four dates. For example, a date is considered as FUS In SVM, the two main hyper-parameters are cost and candidate if 30% or more of the non-cloudy portion of gamma (for the linear variant just the cost) which indi- the lake is frozen. Some studies based on MODIS (Qi cate misclassification cost and kernel width respectively. et al., 2020; Reed et al., 2009; Yao et al., 2016) have used Higher values of cost means the model chooses more 10% as threshold, while another approach (Kropáˇcek support vectors which effectively increase the variance et al., 2013) even employed 5%. All of them monitored and decrease the bias and results in overfitting and vice larger lakes (45 to 4294 km2 in area). We empirically versa. When gamma is set to a high value, more weight found that for our comparatively tiny lakes the above is assigned to the points close to the hyperplane com- thresholds are too strict and a threshold of 30% is pared to the far away ones. Higher gamma values also needed to ensure reliable decisions. To see why, con- result in low bias and high variance thus causing overfit- sider that in the best case (Sils, cloud-free) a lake has ting. For random forest, num trees represents the num- 33 clean pixels, but that number can go down to as few ber of trees in the forest while num variables denotes as 7 (Silvaplana at 70% cloud cover). Note also that the number of predictors (features) to select at random on such small lakes a large portion of all pixels is very for each split. Note that the minimum leaf size is set close to the lake’s shoreline, where the residual absolute to 1 in all our random forest experiments. In XGBoost, geolocation error (in the worst case 0.5 pixel) may have the three most important hyper-parameters are number a significant impact. of trees (num trees), learning rate and the tree specific parameter: colsample bytree. Learning rate shrinks the contribution of each new tree to make the boosting pro- 5 Results cedure more conservative and thus the resulting model more robust. Colsample bytree controls the fraction of In our experiments, we perform a comparison of the features (spectral bands) to be used in each boosting performance of various machine learning classifiers, de- iteration. rive a 20-year time-series of the key phenological dates, For each machine learning approach, the opti- and perform correlation of our results with the re- mal hyper-parameters are first independently deter- gional weather trends. In addition to the overall clas- mined with a grid search. The best-performing hyper- sification accuracy, we report a stricter measure: mean parameters thus chosen are shown in Table 2. We use intersection-over-union (mIoU) for fair reporting of the these parameters in all further experiments. However, results on a dataset with imbalanced class distribution. note that the parameters are dataset-dependent, too. Overall classification accuracy is given by: Overall, random forest, XGBoost and linear SVM ex- TP + TN Accuracy = (4) hibited fairly stable results across a range of hyper- TP + TN + FP + FN parameters, whereas SVM RBF was very sensitive. where TP, TN, FP, and FN represent true positives, true negatives, false positives and false negatives, respectively. For each class, the Intersection-over-Union 5.1.2 Four-fold cross validation score (IoU or Jaccard Index) is given by: In k-fold cross validation scheme, the data is randomly TP IoU = (5) partitioned into k different parts. A model is then TP + FP + FN trained on all but one parts. The trained model is then mIoU is the average of the per-class IoUs. More detailed tested on the remaining part. This procedure is then results can be found in the following sub-sections. repeated k times and the results are averaged. As the first experiment, we combine the data (inde- 5.1 Choice of machine learning method pendently for MODIS and VIIRS) of all the available lakes from winters 2016–17 and 2017–18 and perform We first conduct experiments on the two winters 2016– 4-fold cross validation and report the overall accuracy 17 and 2017–18, for which the ground truth is available. and mIoU, see Table 3. For both MODIS and VIIRS, These experiments serve to compare the performance of the performance of all classifiers except linear SVM is the SVM, random forest, and XGBoost classifiers and more or less the same, with accuracy differences be- determine which one is most suitable for our task and low 1%. While SVM RBF performs marginally best on dataset. We train the models and report quantitative MODIS data, XGBoost scores well on VIIRS. Though results only on the non-transition dates, since per-pixel lower than other three classifiers, the performance of ground truth is not available for the transition dates. linear SVM is also very good on both sensors. 12 Tom et al.

Table 2: Optimum hyper-parameters of each classiﬁer and sensor estimated using grid search.

Method Sensor Hyper-parameters Linear SVM MODIS cost 0.1 SVM RBF MODIS cost 10, gamma 1 Random Forest MODIS num trees 500, num variables 10 XGBoost MODIS num trees 1000, colsample bytree 1, learning rate 0.2 Linear SVM VIIRS cost 0.1 SVM RBF VIIRS cost 10, gamma 1 Random Forest VIIRS num trees 500, num variables 3 XGBoost VIIRS num trees 500, colsample bytree 1, learning rate 0.3

Table 3: Four-fold cross-validation results (in %) on MODIS and VIIRS data. The data from both winters 2016–17 and 2017–18 are used in this analysis. Overall classiﬁcation accuracy and mean intersection-over-union (mIoU) scores are shown. The best results are shown in bold.

Sensor Feature vector Method Accuracy mIoU MODIS All 12 bands Linear SVM 93.4 83.9 MODIS All 12 bands SVM RBF 99.4 98.5 MODIS 10 bands (random) Random Forest 98.9 97.2 MODIS All 12 bands XGBoost 99.3 98.3 VIIRS All 5 bands Linear SVM 95.1 88.4 VIIRS All 5 bands SVM RBF 97.1 93.1 VIIRS 3 bands (random) Random Forest 97.6 94.5 VIIRS All 5 bands XGBoost 97.7 94.5

5.1.3 Generalisation experiments fication is > 82.5% correct. Lake Sihl from the region Einsiedeln is different compared to other three lakes In order to study how well the classifiers generalise from the region Engadin in terms of area, weather, sur- across space and time, we train a model on all except rounding topography etc., c.f. Section 3.1. Hence, the one lake (respectively, winter) and test on the held-out performance on lake Sihl is interesting to assess geo- lake (winter). graphical generalisation over longer distances. It can Fig. 5 displays the results (bar graphs showing over- be seen in Fig. 5 that for lake Sihl the linear SVM clas- all accuracy and mIoU) of the four classifiers for leave- sifier performs best on both MODIS and VIIRS data, one-lake-out setting on MODIS (top row) and VIIRS suggesting that the other (non-linear) models already (bottom row) data. It can be seen that the performance overfit to the specific local conditions of Oberengadin. varies across lakes and sensors. For MODIS, XGBoost As a second generalisation experiment, more im- has, on average, a narrow advantage over SVM RBF portant for our time-series analysis, we check how well and random forest, with linear SVM a bit behind. For the trained classifiers can be transferred across different VIIRS, on the other hand, random forest marked the winters. We train on one winter and test the resulting best performance closely followed by linear SVM, SVM model on the held-out winter (leave-one-winter-out), RBF and XGBoost. see Fig. 6. We only have data from two consecutive win- On both sensors, the best performance (especially ters (2016–17, 2017–18) to perform this analysis. Still, in terms of mIoU) is achieved for the lakes Sils and we believe that the experiment is representative for gen- Silvaplana. This is likely due to them having the most eralisation to unseen years, since the weather conditions similar characteristics and imaging conditions, see Ta- in different years are largely uncorrelated (c.f. Fig. 2). ble 8. I.e., pixels from one of them are representative In particular for the two available winters, 2017–18 was also of the other one, such that the classifier trained markedly colder than the previous year, see Fig. 2. in one of the two generalises well to the other. Lake Fig. 6 (top row) clearly shows for MODIS that lin- St. Moritz (only for MODIS) has too few clean pixels ear SVM adapts best to a new winter, with signifi- per acquisition to draw any conclusions about general- cantly higher generalisation losses for XGBoost, ran- isation. However, we still include it in our processing dom forest, and SVM RBF. For VIIRS (Fig. 6, bottom to study how far lake ice monitoring with MODIS can row), linear SVM also copes best with generalisation be pushed (in terms of lake area) – indeed, the classi- across different years. Here random forest can keep up, Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 13

4 4 . 1 9

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Sihl Sils Silv Mean Sihl Sils Silv Mean

SL SR RF XGB SL SR RF XGB

Fig. 5: Generalisation across lakes results on MODIS (top row) and VIIRS (bottom row) data for the classiﬁers Linear SVM (SL), SVM RBF (SR), Random Forest (RF) and XGBoost (XGB) on lakes Sihl, Sils, Silvaplana (Silv) and St. Moritz (Moritz). Both overall accuracy (left column) and mIoU (right column) are shown. whereas SVM RBF and XGBoost again suﬀer higher 5.2 Experiments on MODIS data from 20 winters generalisation losses. 5.2.1 Test-train split

So far, we have used only on parts of the available ground truth for training, so as to evaluate the method. We now move on to the actual longer-term analysis, where we process MODIS data from all the 20 winters since 2000–01 (inclusive). Details of the training set for Overall, all classifiers exhibit a certain performance each tested winter is shown in Table 5. To avoid sys- drop when having to generalise beyond the exact train- tematic biases in the estimated ice maps due to over- ing conditions. Table 4 shows the detailed performance fitting to a particular year, we proceed as follows: we drops compared to Table 3. Since mIoU is a stricter train the linear SVM model on all non-transition dates measure than overall accuracy, the drops are more pro- of 2016–17 and use it to estimate lake ice coverage for nounced. It is interesting to note that in both gener- all days in 2017–18 (including transition dates). We re- alisation experiments the most robust (least affected) peat that procedure in the opposite direction, i.e., we classifier is the linear SVM. With all other classifiers train on all non-transition days of 2017–18 and per- the drop is much higher for unseen winters than for un- form inference for all dates of 2016–17. Then, we merge seen lakes. We conclude that linear SVM is the safest all non-transition dates from both winters into a new, option four our task, where data from multiple differ- larger two-winter training set, which we further aug- ent winters must be processed, and use it for all further ment with an auxiliary dataset. The latter contains all experiments. Recall, though, that we only have a rel- acquisitions of lakes Sils and Silvaplana captured during atively small dataset at our disposal from few small the remaining 18 years in September (when the lakes mountain lakes over two winters. It is quite possible are never frozen) and in February (when the lakes are that the small volume and specific geographical con- always frozen). The purpose of the auxiliary dataset ditions aggravate the tendency to overfit, and that a is to cover a wider range of weather and lighting con- higher-capacity, non-linear classifier will work best if ditions that might not have been encountered in the a larger and more diverse dataset were available, or if two winters with annotated ground truth, for better the conditions were less variable (large lakes in smooth generalisation. Data of lake Sihl is not included in the terrain). auxiliary set, as it does not freeze reliably, St. Moritz is 14 Tom et al.

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2016-17 2017-18 Mean 2016-17 2017-18 Mean

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2016-17 2017-18 Mean 2016-17 2017-18 Mean

SL SR RF XGB SL SR RF XGB

Fig. 6: Generalisation across winters results on MODIS (top row) and VIIRS (bottom row) data for the classiﬁers Linear SVM (SL), SVM RBF (SR), Random Forest (RF) and XGBoost (XGB). Both overall accuracy (left column) and mIoU (right column) are shown.

Table 4: Generalisation loss (across lakes / winters) encountered by each classiﬁer. Drop (in % points) for overall accuracy and mIoU are shown in black and grey respectively.

Sensor Loss type Linear SVM SVM RBF Random Forest XGBoost MODIS across lakes 3.7/5.1 7.6/16.0 7.3/15.0 7.4/15.8 MODIS across winters 1.3/2.8 12.0/26.6 10.7/23.6 9.9/22.4 VIIRS across lakes 1.1/1.5 3.6/7.4 3.5/7.5 4.3/8.9 VIIRS across winters 2.6/5.7 5.5/12.2 5.1/11.9 6.7/14.5 ignored due to its negligible number of pixels. The two- additionally process the VIIRS data from 8 winters winter and auxiliary datasets are merged and used to (since winter 2012–13, inclusive) and compare the re- train a linear SVM model, which is then used to predict sults to MODIS. Since a pixel-to-pixel comparison is ice cover maps for the 18 remaining winters. not straight-forward due to different GSDs, we fit the timelines per winter for each lake as described before 5.2.2 Qualitative results (Fig. 4a) and compute absolute differences (AD) between the daily estimates for the percentage of frozen Exemplary qualitative results on some selected days pixels. The AD is computed only on dates when both (one per winter) of lake Sihl are shown in Fig. 7. The re- MODIS and VIIRS acquisitions are present, and when spective dates are displayed below each sub-figure. The the lake is at least 30% cloud-free. The ADs are then lake outline overlaid on the MODIS band B1 is shown further aggregated to obtain a Mean Absolute Differ- in green. Pixels detected as frozen and non-frozen are ence (MAD) for each winter. Fig. 8a shows, for each shown as blue and red squares, respectively. The re- lake, the mean and standard deviation of the MAD sults include fully-frozen, fully non-frozen and partially across the 8 common winters. The low mean values (3.5, frozen days. 5.8 and 4.3 percent respectively for Sihl, Sils and Sil- vaplana) show that our MODIS and VIIRS results are 5.2.3 Additional check using VIIRS data from 8 in good agreement, especially considering that a part winters of the MAD is due to the difference in GSD between MODIS (250m GSD) and VIIRS (≈375m GSD). Note A direct quantitative analysis is not possible, since also that, the acquisition times during the day (and no ground truth is available for 18 out of the 20 hence the cloud masks) can differ; and that, although winters. In order to validate our MODIS results, we the absolute geolocation has been corrected for both Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 15

Table 5: Test-train split for the MODIS data from 20 winters.

Test set Training set winter 2016–17 winter 2017–18 winter 2017–18 winter 2016–17 winters till 2015–16, from 2018–19 winters 2016–17 and 2017–18, auxiliary set

(a) 8 Nov 2000 (b) 1 Feb 2002 (c) 29 Apr 2003 (d) 29 Dec 2003 (e) 15 Oct 2004

(f) 1 Jan 2006 (g) 30 Mar 2007 (h) 8 Feb 2008 (i) 9 Jan 2009 (j) 23 Jan 2010

(k) 24 Mar 2011 (l) 2 Mar 2012 (m) 24 Apr 2013 (n) 10 Mar 2014 (o) 28 Jan 2015

(p) 22 Jan 2016 (q) 15 May 2017 (r) 21 Apr 2018 (s) 5 Feb 2019 (t) 20 Sep 2019

Fig. 7: MODIS qualitative classification results (overlaid on band B1 from the respective day) for lake Sihl on selected dates from the past 20 winters using the linear SVM classifier. Blue and red squares are overlaid on the pixels detected as frozen and non-frozen respectively. sensors, errors up to 0.5 pixel can still remain (Aksakal, 5.2.4 Comparison with MODIS and VIIRS snow 2013) and affect the selection of clean pixels near the products lake shore.

We compare our MODIS (20 winters) and VI- IRS (8 winters) results to the respective opera- 16 Tom et al.

MODIS vs VIIRS results MODIS results vs MSP VIIRS results vs VSP 30.0 30.0

22.5 22.5

15.0 15.0 MAD (%) MAD (%) 7.5 7.5

0.0 0.0 Sihl Sils Silv Sihl (M) Sils (M) Silv (M) Sihl (V) Sils (V) Silv (V) (a) Our MODIS vs. VIIRS results (b) Our results vs respective snow products

MSP vs GT VSP vs GT 30.0

22.5

15.0

MAD (%) 7.5

0.0 Sihl (M) Sils (M) Silv (M) Sihl (V) Sils (V) Silv (V) (c) Snow products vs. our ground truth (GT) for 2 winters.

Sihl Sils Silvaplana 100

MAD (%) 20

0 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter

(d) Our MODIS results vs. MSP for 20 winters. Winter 00–01 represents the dates from Septem- ber 2000 till May 2001 (and similarly other winters).

Fig. 8: Row 1 shows the comparison of our MODIS and VIIRS results for the 8 common winters (left sub-figure) and comparison of our MODIS (20 winters) and VIIRS (8 winters) results with the respective snow products (right sub-figure, MSP and VSP represent MODIS Snow Product and VIIRS Snow product, respectively). Row 2 shows the deviations between the two snow products and our webcam-based ground truth. Row 3 displays per-winter MAD (for MODIS) for each lake. tional snow products: MODIS snow product (collec- percentage of frozen pixels per day using our MODIS tion 6, MOD10A1), VIIRS snow product (collection and VIIRS results. Since a pixel-to-pixel registration is 1, VNP10A1F). For the regions of interest, VIIRS difficult in the presence of absolute geolocation shifts snow product has some data gaps, hence the compar- and/or GSD differences, the daily percentage of frozen ison is done whenever it is available. For actual snow pixels is also computed from the snow products and the cover mapping, errors of 7-13% have been reported for MAD is estimated for each winter. See Fig. 8d for our MODIS snow product (Hall and Riggs, 2016). Our find- MODIS results vs MODIS snow product comparison. ings are in line with this: for the two winters 2016–17 For the three lakes, the per-winter MAD is shown on and 2017–18 (non-transition days only) we observe an y-axis against the winters on x-axis. We again exclude error of 14% w.r.t. our ground truth, see Fig. 8c. lake St. Moritz because of its minuscule area.

Similar to the evaluation methodology explained Overall, the 20-year time-series inter-comparison in Section 5.2.3, for each lake, we ﬁrst estimate the (per-lake mean and standard deviation of MAD, Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 17

Fig. 8b) does not suggest large, systematic inconsis- Using the estimated LIP dates from 20 winters, we tencies. On average, our MODIS and VIIRS results de- plot their temporal evolution for lakes Sils (top) and viate by mean MAD values of 14-18% and 12-19% re- Silvaplana (bottom) in Fig. 9. On the y-axis, all the spectively. These deviations are only a little higher than dates from 1 December to 1 June (we skip September the estimated error of the snow products, and relatively till November since no LIP events were detected during stable across different years. these months), while on the x-axis we show the winters It is important to point out that the snow products in a chronological order. In each winter, the non-frozen, are an imperfect proxy for lake ice, because a lake can freeze-up, frozen and break-up periods are displayed in be frozen but not snow-covered, especially near freeze- cyan, red, yellow and dark green colours, respectively. up when it has not yet snowed onto the ice. Also, mixed It can be seen from Fig. 9 that the freeze-thaw pat- ice and water cases go undetected in MODIS snow prod- terns of both lakes vary considerably across winters. For uct (Hall and Riggs, 2016). Fig. 8c shows that the snow lake Sils (Silvaplana), on average, the FUS occurred on products are less consistent with the manually anno- 3 January (5 January) followed by a freeze-up period tated ground truth than our ice maps. In fact, most de- of 3 (3) days until FUE on 6 January (8 January). Ad- viations between our estimates and the snow products ditionally, on average, the lake remained fully frozen occur around the transition dates, mostly freeze-up. (CFD) for 113 (108) days until BUS on 29 April (26 Additionally, MODIS and VIIRS snow products use a April) and the break-up period lasted 1 (1) day until less conservative cloud mask than we do (accepting not BUE on 30 April (27 April). The average number of only confident clear and probably clear, but also uncer- days from FUS to BUE is 117 (112). tain clear as cloud-free). Despite these issues, the inter- The Oberengadin region with lakes Sils and Silva- comparison provides a second check for our results. For plana is a single valley (Fig. 1 and Table 8) and hence completeness, we note that our algorithm has similar the two have similar weather conditions. Silvaplana is issue and thin ice is sometimes confused with open wa- relatively deeper but has smaller area than Sils, mak- ter: firstly, snow-free-ice is rare and underrepresented ing them comparable in terms of volume, too. So simi- in the training set. Secondly, it appears predominantly lar LIP patterns can be expected. However, the clouds near the transition dates (especially freeze-up) when we above the lakes (especially on partly cloudy days), and do not have pixel-accurate ground truth. Thirdly, thin the associated cloud mask errors, can cause small dif- ice and open water are difficult to distinguish, we ob- ferences. In winter 2016-17, the ice-on date of the two served that even human interpreters at times confused lakes, confirmed by visual interpretation of webcams, them when interpreting the webcam images. differ by 7 (low confidence) to 10 (medium confidence) It is interesting to note that, for both sensors, the days, see also Tom et al. (2020c). mean MAD is inversely proportional to the lake area In most of the winters, the LIP characteristics of (see Fig. 8b). This hints at residual errors in the prod- these lakes derived using our approach are in agree- ucts’ geolocation, which would affect smaller lakes more ment, see Fig. 9. However, there are some outliers too due to the larger fraction of pixels near the lake out- (>10 days deviation). A notable outlier is the break-up line. Besides the < 0.5 pixel inaccuracy of our maps, period in winter 2009-10. For Sils (Silvaplana), BUS and inaccurate geolocation of the snow products has been BUE were both estimated as 19 May (28 April). This reported (more for MODIS, less for VIIRS) especially drift primarily happened because of a huge data gap for freshwater bodies, due to uncertainties in gridding, due to clouds and cloud mask errors. During the period reprojection etc. (Hall and Riggs, 2016). from 28 April till 20 May, Silvaplana had > 30% cloud- free MODIS acquisitions only on 28 April, 29 April, 8 May and 20 May, and the lake was detected as non- 5.2.5 LIP trends using MODIS data frozen on all these dates. However, Sils had MODIS acquisitions on 28 April, 29 April, 5 May and 19 May. As discussed in Section 4.3, we fit ”U with wings” poly- On 5 May the lake was detected as 100% frozen due gon to each winter to estimate the four critical dates: to a false negative cloud mask, although break-up had FUS, FUE, BUS and BUE. Sometimes, these phenolog- started on the two earlier dates (75%, respectively 60% ical dates are defined such that a second, consecutive frozen) and the lake was ice-free on May 19. We also day with similar ice conditions is required to confirm the checked the Landsat-7 acquisitions on 20 April 2010 event. We do not enforce this constraint, because, quite and 22 May 2010 and found that both lakes were fully often, the days after a potential freeze-up or break-up covered by snow on the former date and fully non- date are cloudy, and looking further ahead runs the risk frozen on the latter date. No cloud-free Landsat-7 data of pruning the correct candidates. is available in between these two dates. For Sils, the ac- 18 Tom et al.

Non-Frozen Freeze-Up Frozen Break-Up 01 Jun

01 May

01 Apr

01 Mar Date 01 Feb

01 Jan

01 Dec 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter (a) Lake Sils

Non-Frozen Freeze-Up Frozen Break-Up 01 Jun

01 May

01 Apr

01 Mar Date 01 Feb

01 Jan

01 Dec 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter (b) Lake Silvaplana

Fig. 9: 20 winter temporal LIP characteristics of lakes Sils and Silvaplana estimated from MODIS using linear SVM classifier. Winter 00–01 represents the dates from September 2000 till May 2001 (and similarly other winters). tual BUS probably happened on 29 April (> 30% non- In winter 2013-14, our method asserts FUE of Sils frozen) and BUE soon after (likely on 30 April, since on 26 December and of Silvaplana on 6 January. Be- the BUE of Silvaplana was detected as 28 April and Sils tween those dates there were a number of partially was detected < 70% non-frozen on 29 April). However, frozen dates, but with more ice cover for Sils than Sil- both dates went undetected until 19 May, because of vaplana. Additionally, 2-5 January were cloudy, lead- the clouds in combination with the maximum allowed ing the fitting to chose the earlier date for the former, duration of 2 weeks for the break-up. but the later one for the latter. We again checked with In winter 2003-04, the freeze-up periods of Sils Landsat-7 that on 15 December both lakes were fully (FUS on 1 January, FUE on 2 January) and Silva- non-frozen, whereas on and 25 January both lakes were plana (FUS and FUE on 14 January) were also detected fully snow-covered. There exist no cloud-free Landsat-7 far apart, again due to a data gap because of clouds. image in between these two dates to pin down the dates Sils was estimated 68% and 90% frozen on 1 and 2 more accurately. January, respectively, so they were chosen as FUS and In some winters, there is almost no freeze-up and/or FUE. On lake Silvaplana, the sequence for 1-5 January break-up period detected by our algorithm. This is was 4%→13%→0%→21%→0% frozen. Then 14 Jan- partly a byproduct of the relatively loose threshold uary and 21 January were both found 100% frozen, so needed to estimate the initial candidates for our small the fitting chose 14 January as both FUS and FUE. No lakes (see Section 4.3), bringing the start and end dates cloud-free MODIS data exist on the intermediate dates of the transition closer together; and also influenced by 6-13 January and 15-20 January, and we could also not frequent cloud cover during the critical transition dates find any cloud-free Landsat-7 images between 21 De- (often more than half of all days c.f. Section 3c). For cember 2003 and 29 January 2004 (both inclusive) to instance, if a couple of adjacent dates are cloudy dur- check, but could confirm 0% ice cover on 20 December ing break-up (and the real BUS occurred during one of and 100% cover on 30 January. Connecting all the dots, these dates) and on the next non-cloudy day, the lake is we speculate that FUS and FUE of Silvaplana occurred estimated 70.1% non-frozen, then our fitting will choose soon after 5 January. this date as both BUS and BUE. Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 19

We go on to analyse the freeze-up (FUS, FUE) and Mean Winter Temperature (MWT) corresponds break-up (BUS, BUE) patterns, by plotting time-series to the air temperature (in ◦C) averaged over the of the four critical dates over the past 20 winters for whole winter season (September till May). As expected, lakes Sils and Silvaplana, see Fig. 10. Here also, we plot Fig. 12 shows that MWT has strong negative correla- all the dates from 1 December till 1 June in each winter tion with the freeze durations CFD and ICD, negative on the y-axis and the winters in chronological order on correlation with the break-up events BUS and BUE, the x-axis. Additionally, per phenological date, we fit and positive correlation with the freeze-up events FUS a linear trend. Progressively later freeze-up and earlier and FUE. We conclude that, indeed, as winters got break-up is apparent for both lakes. warmer over the past 20 years the lakes froze later In each winter, we also derive the remaining LIP and broke up earlier. For both lakes, the relationship of events (ICD, CFD) listed in Table 1. Their trends are MWT with CFD is shown in Fig. 13 (row 1). Further shown in Fig. 11, with the duration in days on the y- significant correlations are displayed in Appendix E. axis and the winters in chronological order on the x- AFDD represents the cumulative sum (of daily axis. Obviously, ICD and CFD are decreasing for both mean temperature) on the days with average air tem- lakes. perature below the freezing point (0◦C) in a winter sea- Quantitative trend values that we estimated for all son. AFDD is a popular proxy for the thickness of ice the LIP events of Sils and Silvaplana are shown in Ta- cover (Beyene and Jain, 2018; Qi et al., 2020). For both ble 6. As explained above, we correct obvious failures Sils and Silvaplana, AFDD has strong positive correla- of the automatic analysis, and set the following corrections with ICD and CFD, strong negative correlation tions for lake Sils: BUS and BUE occurred on 29 April with the freeze-up events FUS and FUE, and moderate and 30 April respectively in winter 2009–10. Similarly, positive correlation with ice break-up events BUS and for Silvaplana: FUS and FUE occurred on 6 January BUE, see Fig. 12, again indicating that in colder win- in winter 2003–04 and FUE occurred on 26 December ters (higher AFDD) the freeze-up occurs earlier and the in winter 2013–14. For completeness we also fit trends break-up later, leading to longer freeze duration. The without the correction – these differ only slightly and relatively weaker correlation for the break-up indicates confirm that the corrections hardly impact the over- that freeze-up play a larger role for that event. As an all picture. The trend towards earlier break-up (BUS, example, the correlation with FUS is shown Fig. 13, for BUE) is more pronounced than the one towards later further plots see Appendix E. freeze-up (FUS, FUE), for both Sils and Silvaplana. It To study the effect of sunshine on LIP events, we is interesting to note that the decrease in freeze dura- correlate the total winter sunshine (hours) with the tion (ICD and CFD) is stronger for the slightly smaller freeze length events ICD and CFD, total sunshine in the lake Silvaplana. months September to December (S2D) with the freeze- up events FUS and FUE, and the total sunshine from January to May (J2M) with the break-up events BUS 5.2.6 Correlation of LIP events with meteorological and BUE. Here, we assume that the sunshine in the data months after freeze-up has no connection with freeze- up events. Similarly, we assume that the sunshine in the We have also studied the (centred and normalised) cross early winter months (September till December) does correlation ∈ [−1, 1] between the LIP events (corrected not affect the break-up events. We notice strong nega- version) and climate variables such as temperature, tive correlation of the total winter sunshine with ICD, sunshine, precipitation and wind during the 20 win- CFD and break-up events. The more sunshine in the ters. The results are shown in Fig. 12 for the lakes Sils months near break-up, the earlier the ice/snow melts, (top) and Silvaplana (bottom). Air temperature (mea- which also reduces the total freeze duration. An exam- sured at 2m above ground) and precipitation data were ple correlation with CFD is visualised in Fig. 13, further collected from the nearest meteorological station SIA. significant correlations are displayed in Appendix E. However, we used the sunshine and wind measurements We also check the relationship between the LIP at station SAM, since these were not available for the events and the total precipitation (snow and rain) dur- complete 20 winters time span at SIA. We did not use ing the winter months. Similar to sunshine analysis, we the cloud information (number of non-cloudy pixels) correlate the total precipitation during the months from from MODIS data as a measure of sunshine duration, September till December, January till May and Septem- since that would ignore the evolution throughout the ber till May to the freeze-up (FUS, FUE), break-up day, and suffers from a non-negligible amount of cloud (BUS, BUE) and freeze duration events (CFD, ICD) re- mask errors. spectively, see Fig. 12. Notable are the break-up events 20 Tom et al.

01 Jun

01 May

01 Apr

01 Mar FUS FUE BUS BUE Date 01 Feb

01 Jan

01 Dec 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter (a) Lake Sils 01 Jun

01 May

01 Apr

01 Mar FUS FUE BUS BUE Date 01 Feb

01 Jan

01 Dec 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter (b) Lake Silvaplana

Fig. 10: 20 winter ice freeze-up (FUS, FUE) and break-up (BUS, BUE) trends for lakes Sils and Silvaplana from MODIS estimated using linear SVM classiﬁer. Winter 00–01 represents the dates from September 2000 till May 2001 (and similarly other winters).

250 ICD CFD 200

150

100 Days

0 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter (a) Lake Sils 250 ICD CFD 200

150

100 Days

0 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter (b) Lake Silvaplana

Fig. 11: 20 winter ice duration (ICD, CFD) trends for lake Sils and Silvaplana from MODIS estimated using linear SVM classiﬁer. Winter 00–01 represents the dates from September 2000 till May 2001 (and similarly other winters). with good positive correlation. More precipitation in snow), favours later break-up, and vice-versa. Correla- the months January to May (likely to be predominantly Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 21

Table 6: Estimated LIP trends (black). Results before manual correction of the automatic results are shown in grey.

Lake FUS FUE BUS BUE ICD CFD Sils 0.23 0.31 -0.46/-0.47 -0.32/-0.34 -0.55/-0.57 -0.76/-0.78 Silvaplana 0.45/0.37 0.38/0.36 -0.51 -0.45 -0.9/-0.82 -0.89/-0.87

6 6 58 56 . . . . 5 51 0.75 0 0 . 0 . 0 41 0 39 0 . 36 32 . . 0 . 0 0.5 0 2 0 17 . . 0 0.25 0 0

2 2 1 . −0.25 − − 12 14 0 . . 21 21 0 23 10 . 0 − 10 . Correlation . 0 0 −0.5 · · 0 − − 5 5 − 5 − . − 6 6 6 55 55 55 0 − . . − . −0.75 . . . 64 0 0 64 0 0 0 − 66 0 . . . − − 0 − 0 −1 − − − 0 − − − FUS FUE BUS BUE ICD CFD 1

6 58 . 53 . 51 0.75 . 0 47 . 0 44 . 43 0 4 41 . . 0 38 . 0 . . 0 3 0 0 0 0.5 . 0 2 0 . 0.25 0 0

−0.25 2 2 13 − − 17 19 . 22 . 22 . 0 . 26 . Correlation 0 10 0 10 . −0.5 0 0 − · · 0 − − − − 1 − 52 51 53 53 . . 56 55 15 . . . 57 −0.75 . . . 9 62 . 62 0 0 63 0 0 0 . . 0 8 0 . − 0 − − 0 0 − − − −1 − − − − − − FUS FUE BUS BUE ICD CFD

MWT AFDD Sunshine Precipitation Wind

Fig. 12: Bar graphs showing the 20 winter correlation of the LIP events (Sils on top row, Silvaplana on bottom) with climate variables. tion with BUE is shown in Fig. 13 and with BUS in able only from the winters 2016–17 and 2017–18. Us- Appendix E. ing the data from these two winters, we first performed Finally, inspired by Gou et al. (2015), we also looked thorough experimentation with different classifiers. Ad- at the effect of wind on the LIP events, which may ditionally, we did an inter-comparison of the individ- also influence lake freezing. We correlated the mean ual performance of these machine learning classifiers. winter wind speed (km/h) with CFD and ICD, mean For the four-fold cross validation experiment, the high- wind speed from September to December with FUE and est performance on MODIS and VIIRS data were re- FUS, and mean wind speed from January to May with ported for SVM RBF and XGBoost classifiers respec- BUS and BUE. However, we did not find any significant tively, see Table 3. However, SVM RBF, random for- correlations, see Fig. 12. est and XGBoost suffered a significant generalisation loss compared to the linear SVM counterpart. I.e., non- linear classifiers tend to overfit on our relatively small dataset. We emphasise that it does not contradict the 5.3 Discussion findings of Wu et al. (2021) for a dataset of larger lakes with many more training pixels. There, random forest In any machine learning-based system, the variety in and gradient boosting trees performed very well. We the training dataset has a critical influence on the model empirically selected linear SVM as the most suitable being learnt. Our dataset consists of small lakes and classifier for our lakes of interest, and we recommend has significant class imbalance. This is a biased, but to repeat the empirical exercise when moving to dif- realistic scenario, representative of mountain lakes in ferent geographical conditions. Our MODIS and VIIRS sub-Arctic and temperate climate zones. For supervised results validate each other in a relative sense (< 5.6 % classification, proper ground truth information is avail- 22 Tom et al.

MWT CFD MWT CFD

200 200 0.0 0.0

150 150 2.5 2.5

5.0 100 5.0 100

7.5 7.5 50 50 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter AFDD FUS AFDD FUS Jun 30 Jun 30

1000 1000

500 500

0 Dec 1 0 Dec 1 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter Sunshine CFD Sunshine CFD 1400 300 1400 300

250 250 1200 1200 200 200 1000 1000 150 150 800 800 100 100

600 50 600 50 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter Precipitation (J2M) BUE Precipitation (J2M) BUE Sep 30 Sep 30 200 200

400 400

600 600

800 800

1000 Mar 1 1000 Mar 1 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter

Fig. 13: Correlation of LIP events and weather variables: MWT (◦C) and CFD (days) are shown in ﬁrst row, AFDD (◦C) and FUS in second row, total winter sunshine (hours) and CFD in third row, total precipitation (mm) in the months January to May (J2M) and BUE in last row. Results for lakes Sils and Silvaplana are displayed in left and right columns respectively.

MAD in the worst case, lake Sils), but could be sub- lake St. Moritz, our study goes to the limit in that re- ject to a common bias. In the absence of ground truth spect. A further, often-named obstacle for optical satel- there is no way to assess our absolute accuracy, but as lite observation are occlusions due to clouds, which sig- an external check against a methodologically different nificantly reduce the effective temporal resolution and mapping scheme we inter-compared our results against also cause irregular gaps in the time-series. These un- the respective operational snow products. The devia- predictable data gaps are particularly troublesome for tions were in the expected range (MAD < 20 %). ice phenology, because the critical events occur over a short time and at times of the year where cloud cover Besides its advantages, like dense coverage, regular is frequent in sub-Arctic and mid latitudes. time-series and homogeneous observation conditions, satellite data also has disadvantages. The trade-off be- Data gaps due to clouds are the main source of er- tween spatial and temporal resolution makes it difficult ror in our LIP estimation, besides cloud mask errors, to monitor smaller lakes – with 21 MODIS (9 VIIRS confusion between open water and thin/floating snow- pixels) for lake Silvaplana and only 4 MODIS pixels for free-ice, and quantisation effects around hard thresh- Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 23 olds. This makes phenological observations challenging time-series. One solution for the cloud issues of opti- – in particular the uncertainties of our predictions are cal satellites is to complement/replace them with radar largest during freeze-up, because of the frequent, but observations, e.g., Sentinel-1 SAR. We have done pre- short-lived presence of snow-free-ice. Still, it appears liminary research in this direction (Tom et al., 2020a). that our classifier copes better with the reflectance of SAR-optical data fusion holds great promise, particu- ice than simple index-based snow products, and it is larly in view of the GCOS requirement to monitor lake likely that more training data and, if available, addi- ice at daily temporal resolution (with an accuracy of tional spectral bands could further improve its detec- ±2 days). tion. In the future, it will be interesting to cross-check and As said before, a limiting factor for small lakes is validate existing temperature-based models like Hen- the GSD, as decision based on very few pixels become dricks Franssen and Scherrer (2008) against our data- overly unreliable and prone to statistical fluctuations, driven results. Beyond a simple inter-comparison, tem- and even small geolocalisation errors have a large effect. perature measurements could be used to eliminate gross Our work is also on the challenging ends of the spectrum prediction errors, and to bridge temporal gaps in opti- in terms of local weather conditions: in a drier climate cal satellite image-based predictions that occur due to the observations would be less affected by cloud cover clouds or fog. (we process lakes with as little as 30% cloud-free area to obtain sufficient temporal coverage), and fewer clouds We expect that machine learning-based ice detec- also means fewer cloud-mask errors. tion itself could still be further improved with additional training data. I.e., pixel-accurate annotations during transition dates, as well as for more winters and 6 Conclusion a wider variety of lakes. Unfortunately, gathering such data is not only a considerable, tedious effort, but also In this paper, we have reported results from a case poses its own challenges. In most locations and for older study in Southeastern Switzerland, where we have re- data, no corresponding webcam data (or similar regu- trieved lake ice phenology based on MODIS optical im- lar photography) is available; even when available, its age time-series. On the one hand, we have tried to push coverage is almost invariably incomplete; and even with the limits of MODIS data for the analysis of small-to- usable webcam and satellite imagery, manual annota- medium sized lakes, and have shown that even for such tion is not trivial and prone to mistakes exactly in the high-Alpine lakes it is possible to derive meaningful cor- situations that are most critical also for computational relations between the 20-winter lake ice phenological analysis (such as thin, black ice). We speculate that, trends and climate data. On the other hand, we have given the enormous archive of unlabelled satellite data, confirmed that a dedicated machine learning scheme approaches such as unsupervised, semi-supervised or maps lake ice more accurately than classical index- and active learning may be applicable and could improve threshold-based approaches. the lake ice detector. As expected, our results point towards later freeze- up (freeze-up start at a rate of 0.23 d/a for lake Sils, Yet another interesting research direction is to close respectively 0.45 d/a for Silvaplana and freeze-up end the gap between knowledge-driven, model-based top- at a rate of 0.31 d/a for lake Sils, respectively 0.38 d/a down models of lake ice formation and data-driven, for Silvaplana), earlier break-up (break-up start: -0.46 bottom-up machine learning. Introducing expert knowl- d/a for lake Sils, respectively -0.51 d/a for Silvaplana edge about ice formation and associated physical con- and break-up end: -0.32 d/a for lake Sils, respectively straints into machine learning models could also reduce -0.45 d/a for Silvaplana) and decreasing freeze dura- the need for training data, and get the best of both tion (ice coverage duration: -0.55 d/a for lake Sils, re- worlds in terms of accuracy as well as interpretability spectively -0.9 d/a for Silvaplana and complete freeze of the model (Camps-Valls et al., 2018, 2020; Jia et al., duration: -0.76 d/a for lake Sils, respectively -0.89 d/a 2021; Kashinath et al., 2021; Reichstein et al., 2019). for Silvaplana). We also observed significant (but not How to best bridge the gap between statistical machine surprising) correlations with climate indicators such as learning models and physical process models is an open temperature, sunshine and precipitation. question and an active research direction in the Earth Our machine learning approach is generic and easy sciences and beyond. to apply to other sensors beyond MODIS and VIIRS (given training data). Importantly, the VIIRS sensor Acknowledgements We are grateful to Damien Bouffard is projected to ensure continuity well into the future, (EAWAG, Switzerland) for providing advice regarding the opening up the possibility to establish an even longer correlation of meteorological variables and LIP events. 24 Tom et al.

Declarations Change Initiative (Lakes cci): Lake products, Version 1.0. Centre for Environmental Data Analysis. Avail- Funding This work is part of the project Integrated able online: http://dx.doi.org/10.5285/3c324bb lake ice monitoring and generation of sustainable, 4ee394d0d876fe2e1db217378 (accessed 03 August reliable, long time-series funded by the Swiss Federal 2021) Office of Meteorology and Climatology MeteoSwiss in Douglas DH, Peucker TK (1973) Algorithms for the the framework of GCOS Switzerland. reduction of the number of points required to represent a digitized line or its caricature. Cartographica Conflict of interest The authors declare no conflict 10:112–122 of interest. Duguay C, Prowse T, Bonsal B, Brown R, Lacroix M, Menard P (2006) Recent trends in Canadian lake ice cover. Hydrol Process 20:781–801 References Duguay C, Bernier M, Gauthier Y, Kouraev A (2015) Remote sensing of lake and river ice. In: Tedesco Aksakal SK (2013) Geometric Accuracy Investigations M (ed) Remote Sensing of the Cryosphere, Wiley- of SEVIRI High Resolution Visible (HRV) Level 1.5 Blackwell, Oxford, UK, pp 273–306 Imagery. Remote Sens 5:2475–2491 Forster PM, Maycock AC, McKenna CM, Smith CJ Beyene MT, Jain S (2018) Freezing degree-day thresh- (2020) Latest climate models confirm need for urgent olds and Lake ice-out dates: Understanding the role mitigation. Nat Clim Chang 10:7–10 of El Niño conditions. Int J Climatol 38:4335–4344 Gou P, Ye Q, Wei Q (2015) Lake ice change at the Nam Breiman L (2001) Random forests. Mach Learn 45:5–32 Co Lake on the Tibetan Plateau during 2000-2013 Brown LC, Duguay CR (2010) The response and role and influencing factors. Prog Geogr 34:1241–1249 of ice cover in lake-climate interactions. Prog Phys Gou P, Ye Q, Che T, Feng Q, Ding B, Lin C, Zong J Geogr 34:671–704 (2017) Lake ice phenology of Nam Co, Central Ti- Cai Y, Ke CQ, Li X, Zhang G, Duan Z, Lee H (2019) betan Plateau, China, derived from multiple MODIS Variations of lake ice phenology on the Tibetan data products. J Great Lakes Res 43:989–998 Plateau from 2001 to 2017 based on MODIS data. Hall DK, Riggs GA (2016) MODIS/Terra Snow Cover J Geophys Res Atmos 124:825–843 Daily L3 Global 500m SIN Grid, Version 6, NASA Cai Y, Ke CQ, Yao G, Shen X (2020) MODIS-observed National Snow and Ice Data Center Distributed Ac- variations of lake ice phenology in Xinjiang, China. tive Archive Center. Available online: https://do Clim Change 158:575–592 i.org/10.5067/MODIS/MOD10A1.006 (accessed 03 Camps-Valls G, Martino L, Svendsen DH, Campos- August 2021) Taberner M, Muñoz-Mar´ıJ, Laparra V, Luengo D, Hampton SE, Galloway AW, Powers SM, Ozersky T, Garc´ıa-HaroFJ (2018) Physics-aware Gaussian pro- Woo KH, Batt RD, Labou SG, O’Reilly CM, Sharma cesses in remote sensing. Appl Soft Comput 68:69–82 S, Lottig NR, Stanley EH, North RL, Stockwell JD, Camps-Valls G, Svendsen DH, Cortés-AndrésJ, Alvaro´ Adrian R, Weyhenmeyer GA, Arvola L, Baulch HM, Moreno-Mart´ınez,Pérez-Suay A, Adsuara J, Mart´ın Bertani I, Jr LLB, Carey CC, Catalan J, Colom- I, Piles M, Muñoz-Mar´ıJ, Martino L (2020) Living Montero W, Domine LM, Felip M, Granados I, Gries in the Physics and Machine Learning Interplay for C, Grossart H, Haberman J, Haldna M, Hayden B, Earth Observation. arXiv pre-print, arXiv:201009031 Higgins SN, Jolley JC, Kahilainen KK, Kaup E, Ke- Chen LC, Zhu Y, Papandreou G, Schroff F, Adam H hoe MJ, MacIntyre S, Mackay AW, Mariash HL, (2018) Encoder-decoder with atrous separable convo- McKay RM, Nixdorf B, NõgesP, NõgesT, Palmer M, lution for semantic image segmentation. In: European Pierson DC, Post DM, Pruett MJ, Rautio M, Read Conference on Computer Vision,, Munich, Germany, JS, Roberts SL, Rücker J, Sadro S, Silow EA, Smith 8–14 September DE, Sterner RW, Swann GE, Timofeyev MA, Toro Chen T, Guestrin C (2016) XGBoost: A Scalable Tree M, Twiss MR, Vogt RJ, Watson SB, Whiteford EJ, Boosting System. In: International Conference on Xenopoulos MA (2017) Ecology under lake ice. Ecol Knowledge Discovery and Data Mining, San Fran- Lett 20:98–111 cisco, USA, 13–17 August Hendricks Franssen HJ, Scherrer SC (2008) Freezing of Cortes C, Vapnik V (1995) Support-Vector Networks. lakes on the Swiss plateau in the period 1901–2006. Mach Learn 20:273–297 Int J Climatol 28:421–433 CrétauxJF, Merchant C, Duguay C, Simis S, Calmettes Hirose T, Kapfer M, Bennett J, Cott P, Manson G, B, Bergé-Nguyen M, Wu Y, Zhang D, Carrea L, Liu Solomon S (2008) Bottomfast ice mapping and the X, Selmes N, Warren M (2020) ESA Lakes Climate Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 25

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A Operational lake ice products

Details of operational lake ice products are shown in Table 7.

Table 7: Comparison of the operational lake ice / snow products. Note that lake ice extent is still a pre-operational product.

Product Availability Spatial Temporal Input resolution resolution sensor(s) CCI Lake Ice Cover from 2000 250m daily MODIS, VIIRS Sentinel-1,-3 MODIS Snow Product from 2000 500m daily MODIS VIIRS Snow Product from 2012 375m daily VIIRS Lake Ice Extent from 2017 250m daily MODIS

B Characteristics of the target lakes

Details of the target lakes are shown in Table 8.

Table 8: Details of the lakes (primary source: Wikipedia). Last three rows display information about the nearest meteorological stations.

Sihl Sils Silvaplana St. Moritz Latitude (◦N), Longitude (◦E) 47.14, 8.78 46.42, 9.74 46.45. 9.79 46.49, 9.85 Altitude (m) 889 1797 1791 1768 Maximum depth (m) 23 71 77 42 Average depth (m) 17 35 48 26 Area (km2) 11.3 4.1 2.7 0.78 Volume (Mm3) 96 137 140 20 Meteorological station EIN SIA SIA SAM Latitude (◦N), Longitude (◦E) 47.13, 8.75 46.43, 9.77 46.43, 9.77 46.53, 9.88 Altitude (m) 910 1804 1804 1708

C MODIS and VIIRS bands

MODIS and VIIRS band spectrum are displayed in Fig. 14.

V5 V4 V3 V2 V1 M25 M23 M22 M20 M19

Bands M18 M17 M6 M4 M3 M2 M1 0 1 2 3 4 5 10 11 12 13 Wavelength ( m)

Fig. 14: Spectrum of the MODIS (M, blue) and VIIRS (V, red) bands used in our analysis. 28 Tom et al.

D Class imbalance in our dataset

Details on class imbalance in our dataset are shown in Fig. 15.

20,000 Frozen

568 15,000 , Non-Frozen

10,000

598

137 ,

019

5,000 , 345

965 919 , 3 736

, ,

2 051

1 1

, 1 Number of pixels

894

765 739

191 157 0

Sihl (M) Sihl (V) Sils (M) Sils (V) Silv (M) Silv (V) Moritz (M) 20,000

15,000 804

11 10,000

311

5,000 435

, 858

574

2 169 , 005

, 1 , Number of pixels

784 722

621 591

198 124 140 0

Sihl (M) Sihl (V) Sils (M) Sils (V) Silv (M) Silv (V) Moritz (M)

Fig. 15: Bar graphs showing the class distribution in our dataset from the winters 2016–17 (top) and 2017–18 (bottom). The total number of clean, cloud-free pixels from the non-transition dates that are at least 30% cloud-free are shown. M and V denote MODIS and VIIRS respectively. Silv and Moritz represent lakes Silvaplana and St. Moritz respectively.

E Correlation of weather data and LIP events

Correlation of LIP events with temperature variables are shown in. Fig. 16. Similarly, correlations with sunshine and precipitation are displayed in Fig. 17. Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery 29

MWT ICD MWT ICD

200 200 0.0 0.0

150 150 2.5 2.5

5.0 100 5.0 100

0.0 0.0

2.5 2.5

5.0 5.0

7.5 7.5 Mar 1 Mar 1 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter AFDD ICD AFDD ICD 0 300 0 300

500 500 200 200 1000 1000

1500 1500 100 100 2000 2000

2500 0 2500 0 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter AFDD CFD AFDD CFD 0 300 0 300

500 500 200 200 1000 1000

1500 1500 100 100 2000 2000

1000 1000

500 500

Fig. 16: Correlation of MWT (◦C) with ICD (days) and BUS are shown in rows 1 and 2 respectively, AFDD (◦C) with ICD, CFD (days) and FUE are displayed in rows 3, 4 and 5 respectively. Results for lakes Sils and Silvaplana are displayed in left and right columns respectively. 30 Tom et al.

Sunshine ICD Sunshine ICD 1400 300 1400 300

250 250 1200 1200 200 200 1000 1000 150 150 800 800 100 100

600 50 600 50 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter Sunshine (J2M) BUS Sunshine (J2M) BUS Sep 30 Sep 30 800 800

600 600

400 400

200 200

0 Mar 1 0 Mar 1 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter Sunshine (J2M) BUE Sunshine (J2M) BUE Sep 30 Sep 30 800 800

600 600

400 400

200 200

0 Mar 1 0 Mar 1 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Winter Winter Precipitation (J2M) BUS Precipitation (J2M) BUS Sep 30 Sep 30 200 200

400 400

600 600

800 800

Fig. 17: Correlation of total winter sunshine (hours) with ICD (days) is shown in row 1, total sunshine from January to May (J2M) with BUS and BUE are displayed in rows 2 and 3 respectively. Correlation of total precipitation (mm) from January to May (J2M) and BUS is shown in last row. Results for lakes Sils and Silvaplana are displayed in left and right columns respectively.