Accelerated decline of Svalbard coasts fast ice as a result of climate change

In the Arctic, it is the Svalbard Archipelago that has experienced some of the most severe temperature increases in the last three decades. The temperature rise has accelerated de-icing along the archipelago’s coasts, bringing changes to the local environment. As the fast ice distribution along Svalbard coasts before 2000 is mainly unknown, we use in situ observation data of the ice extent for the period of 2005-2018 to create a new geographic random forest model in order to predict daily ice extents using freezing and thawing degree days and time of ice season. This allows one to reconstruct the ice extent in the past 10 and predict it in the near future from standard meteorological data with an accuracy of 0.95. The mean, at least two-month ice extent of fast sea ice along Svalbard coasts was about 12,000 km between 1973 and 2000. In 2005-2018, however, the same ice extent declined to 8,000 km. Comparison of the periods 2005-2018 and 2014-2019 shows the accelerating decline of fast ice: the two-month fast ice extent is now only 6,000 km. A further increase in mean winter air temperatures by two degrees will result in a two-month fast ice extent of 2,000 km. 15

hispida), the principal prey of polar bears (Ursus maritimus) (Krafft et al., 2006;Smith and Lydersen, 1991). Moreover, for as 30 long as it persists, fast ice protects coastal areas from erosion by wave action.
The precision monitoring of local sea ice conditions in the fjords and coastal waters of Svalbard began just under 20 years ago (Hanssen-Bauer et al., 2019) using new technology of high and medium resolution satellite images, mainly from C-band Synthetic Aperture Radar (SAR) sensors, and GIS-based automatic or semi-automatic systems for sea ice classification (Zakhvatkina et al., 2019). Previously, ice conditions used to be assessed mainly from in situ observations made as part of 35 various ice-monitoring programmes; they revealed a general trend towards a smaller ice extent and a decrease in ice thickness compared to a few decades earlier (Gerland et al., 2008;Hanssen-Bauer et al., 2019;Zhuravskiy et al., 2012). From 1974From to 1988, analyses of the total number of days with fast ice before 1 st April (the ring seal pupping date) were based on satellite data: a strong interannual variability ranging from 0 to 155 days was detected in the fjords of northern Spitsbergen (the largest island of Svalbard) and from 38 to 107 days on the western coast (Smith and Lydersen, 1991). Most of the ice monitoring 40 projects were carried out on the west coasts of Svalbard. Between 2000-2014, analysis of the temporal changes in the ice cover in Isfjord and Hornsund using SAR and optical images revealed a significant decrease in the extent of fast ice in both fjords in that period (Muckenhuber et al., 2016). Systematic observations in Kongsfjord since 2003 initially detected, as in the 1970s and 1980s, substantial interannual variability in fast ice extent with intervals of 2-3 years or more. More recent observations have indicated that the ice extent is less in most years and that the fast ice season is becoming shorter (Gerland and Hall, 2006;45 Gerland and Renner, 2007;Alexey K. Pavlov, 2019). There has been less fast ice -off the northern coasts of Svalbard, although occasional observations have shown that the fast ice cover can last from November until July (Wang et al., 2013). Since 2005, ice charts of the Svalbard area have been produced almost daily (Monday-Friday) by the Norwegian Ice Service. As the charts are based on current data, it has been possible to gradually improve their accuracy.   (1975 -2018). The solid lines show the annual mean, and the dashed lines the winter (December -May) mean. Eight-year smoothing using a rolling yearly mean was used. Isfjord -Barentsburg meteorological station (78.1, 14.3), Kongsfjord -Ny Alesund meteorological station (76.5, 25.0667), Hopen meteorological station (78.923, 11.9331).
The duration of fast ice cover around Svalbard has become perceptibly shorter in the last ten years (Alexey K. Pavlov, 2019), so a knowledge of the mean temporal distribution of that fast ice is essential to many projects. Unfortunately, this distribution 55 in the last quarter of the 20 th century is unknown. If we had this knowledge, we would be able to compare the two distributions so as to obtain a picture of the changes in the coastal environment due to the increase in air temperature (Nordli et al., 2014).
Hence, the primary aim of the present research was to characterize the spatial distribution of the mean temporal difference in the presence of fast ice between 1975-2000 and 2014-2019 at the archipelago scale and the fjord scale. The second aim was to quantify the changes in the fast ice surface area in different time periods, i.e. in the two periods mentioned above, and in the 60 near future, assuming the forecast increase in temperature.

Datasets of in situ observations.
Meteorological data for 1973-2019 were acquired from the Global Historical Climate Network (GHCN) for the Hopen, Barentsburg and Ny Alesund stations as daily summaries in text file format (Menne et al., 2012). Scans of operational ice 65 charts produced by the Norwegian Ice Service in 2005-2018 for the Svalbard Archipelago were downloaded from the archive dataset of the Norwegian Meteorological Institute. The 900 map scans, created using different methods, were automatically covered by ice in 1973-1998 were acquired (by courtesy of the U.S. Geological Survey). The GIS vector and raster layers with The next step was to calculate for each day the freezing degree days (FDD) and thawing degrees days (TDD) at Isfjord employing Stefan's Law (Lepparanta, 1993): 85 where t is time, Tf is the freezing temperature (0 ⁰C according to the Polar Science Centre) and T0(t) is the average daily temperature. The formulas usually use one day as the unit of time. The FDD is also called the sum of negative degree days and is used to simplify the formula for estimating ice thickness (Lepparanta, 1993): it sums the below-zero temperatures for each 90 successive day. TDD is similar but for temperatures above 0 ⁰C. It was assumed that the ice season starts on 1 st September and lasts for 300 days, until the end of June. The definition of the ice season allows the number of ice seasons (ICESN) and the day number of a particular ice season (ICESD) to be assigned to each day. As a result, a text file was created for 13 794 days   (Lutz et al., 2018;Mutanga et al., 2012;Rodriguez-Galiano et al., 2014, 2015. In this method, random decision trees are created by bootstrapping data in which the samples are drawn with replacement. Then the majority vote or average predictions of all trees is used to generate results. The main advantages of the RF model are that overfitting can be reduced by averaging several trees, and that no statistical assumptions regarding normal distribution and data linearity are necessary. The model also 125 allows one to measure the relative importance of each feature for the prediction. It is easy to apply, and the few default hyperparameters usually give good results. One of the model's shortcomings, however, is that extrapolation beyond the range of values in the training set is not possible. The typical workflow is to use a training set (containing the dependent variable and the independent variables) to learn the RF model, and then to validate the results using a test data set. One can also validate the results using Out of Bag (OOB) error estimation. We performed the RF modelling using the Python Scikit-learn package 130 (Pedregosa et al., 2011). The first step was to build the RF regression model in order to predict the percentage ice cover in Isfjord (ICESUM) using FDD, TDD and ICESD. The aim was to evaluate the importance of particular features and the overall accuracy of the ice cover modelling. Two measures were applied: the feature importance, implemented in Scikit-learn, which yielded results of 67% (FDD), 18% (ICESD) and 15% (TDD), and the permutation importance, implemented in the eli5 library, with results of 75% (FDD), 21% (ICESD) and 5% (TDD). The accuracy was evaluated using the RMS error: the mean RMS 135 was 0.06 (range 0.052 -0.074) for 50 random test data sets, each containing 30% of the original data (for the range of ice cover 0-1). These results of ICESUM predictions for Isfjord were regarded as satisfactory. The results of this model for three  with the cell's ID to the output file. As each model generates information on the errors arising when using the test data set, 145 these errors can also be saved. The data from this file can be added as a new field to the attribute table of the vector layer of the net to the spatial mapping of ice distribution. The results of the modelling and observations are summarised as vector layers in GeoRF_ICE_MODELS [].zip files containing the Geo File Database and Geo Package formats. The models are built iteratively and the whole process, which we have called Geo Random Forest, is presented in Figure 5. Modelling local variables in a complex environment using a simplified set of features, which is effective for these variables averaged in space, requires taking local peculiarities into consideration. Local ice cover depends, among other things, on the 155 water depth, wave action, water circulation and local microclimate. In the machine learning process, all these features are irrelevant if the dependent variable (target) represents just a single location. The model uses only basic features from one location, which correlates well in space, but gives a prediction only for that particular location. Figure 6 illustrates the results of error evaluation for the Svalbard Archipelago model as a histogram of errors, calculated for each cell using an independent validation set containing 20% of the original values. The model is created on the assumption that for any net cell, the formation 160 and duration of the ice are determined by the same temporal processes over time. This is probably true for large FDD values, where the difference in external environmental conditions over different periods may not be important. However, their role in young ice cover (less than one month) may be much bigger. In Figure 5 these processes probably increase errors to 20 -30%.
As a result, the errors of predictions for a temperature increase of 2 or 4 °C may be as high as 50%; this, however, does not alter the anticipated trend of dramatic de-icing in this area in the near future.

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The AI geographic Random Forest (GeoRF) method was used in this work: it disaggregates the classic method of machine learning (Random Forest) into geographic space in the form of local sub-models. It is an alternative solution to the Geographically Weighted Random Forest (Georganos et al., 2019). Using raster maps of the daily fast ice distribution from 1975 to 2018 and the daily mean temperature, GeoRF sub-models were built to predict the local presence or absence of fast ice as a function of three variables -Freezing Degree Days (FDD), Thawing Degree Days (TDD) and day number of the ice 175 seasonwhich can be calculated from standard meteorological data containing the mean daily air temperature. Comparison of the raster maps used in this project (ice charts produced by the Norwegian Ice Service) with accurate data for Isfjord (Gerland et al., 2008) shows their reliability to be satisfactory. 669 sub-models organized in a 4 km 2 hexagon net for Isfjord and 4782 sub-models in a 16 km 2 net for the whole Svalbard Archipelago were used. The mean accuracy of the GeoRF sub-models was R 2 = 0.95 (from 0.84 to 1). The model allows one to predict the presence of fast ice in a hexagon on the basis of mean daily air 180 temperature, which has been measured on Svalbard since the beginning of the 20 th century.  seasons. On the other hand, FDD was lower than the minimum (from 1000 to 1500 ⁰C day) in 9 seasons. Interannual variability still occurs, but the evidently decreasing trend in FDD now applies to both mean and minimum values. Because of the relatively small number of observations, the above analysis is entirely speculative, but it does reflect the general tendencies confirming earlier results (Gerland and Hall, 2006;Gerland and Renner, 2007;Alexey K. Pavlov, 2019).    Between 1973Between -2000 at least half of the surface area of the fjords in west Spitsbergen was covered by fast ice for 4 to 5 months, while the fjords in north Spitsbergen were completely covered by fast ice for the same length of time. The north-west Spitsbergen coasts had fast ice cover for 2-3 months. The east coast, where there are no fjords, was covered by fast ice mainly in the bays. Between 2014-2018 the distribution and duration of fast ice cover changed dramatically; in the fjords of west Spitsbergen, fast ice persisted for 4 months only at their heads, whereas those in north Spitsbergen were covered by fast ice for less than half of their lengths, 205 usually for 2 months and only locally for 3 months. Figure 9 summarizes the changes in the periods under scrutiny for the observed and modelled areas. The scale of the analyses is fixed by the size of the hexagonal cell, which is 16 km 2 for Svalbard and 4 km 2 for Isfjord. The maps show the differences in fast ice duration. The biggest differences are in the fjords of Spitsbergen, the greatest being in the northern ones. In the whole of this area, the duration has been reduced by 3-4 months. In the other fjords, such dramatic changes have occurred only 210 locally; the reduction there has usually been from 1 to 3 months. In northern Svalbard, the duration of fast ice has decreased by 2 months; elsewhere, the changes are no greater than 1 month, and locally no more than 2 months. Figure 4b clearly shows the spatial variation revealed by the larger-scale analyses performed for Isfjord, while the temporal variation is from zero to 4-5 months. This implies that along the coast of this fjord there are some sites where the changes have been significant and others they have been negligible. The significant changes relate mainly to the fjord's branches, where the fast ice cover before 2000

Conclussion
The summary of the project results in the shape of quantitative analyses is shown in Figure 10 were obtained from satellite images from the years 1973-1998. The replicated data generated under the model look similar to observed data (2005-2018, 2005-2018 model) with R 2 accuracy of 0.95. In this time fast ice cover was 8000 km 2 with at least 2 months duration and a bit above 5000 km 2 with at least 3 months duration. This model was also applied for years 2014-2019, when the rapid reduction in fast ice cover was observed to 6000 km 2 for two-month ice, to test its stability for other conditions (2014-2019, 2014-2019 model). The model performs well for longer fast ice cover but worse for ice cover with a shorter 230 duration than 2 months. As well modeled as observational data show 2 months duration fast ice cover reduction by 25% and 50% reduction for ice with 3 months duration compare to 2005-2018. For the time before 2000 and predicted temperature rise of 2 and 4 ⁰C presented results are based only on the models. Assuming that the model error is proportional to the deviation of data used to prediction from the data for which it was originally created some measure of uncertainty may be deducted from  In years 1973-2000 at least 2 months lasting fast ice cover was 12000 ±250 km 2 , and at least 3 months lasting 8000 ± 150 240 km 2 . The reduction of fast ice cover in 2005-2018 comparing wits 1973-2000 is therefore 30-40%. The prediction of the consequences of further air temperature rice has only a speculative character. The temperature rise of 2 ⁰C will reduce the 2month lasting cover to 2000 km 2 which is a 60% reduction comparing to the current situation. The maximum fast ice cover will be only 20% of these in the years 1973-2000. The rice of 4 ⁰C will reduce it further to 10%.

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Author Contributions: J.U. designed the study, analysed the data and was responsible for writing the manuscript. D.L. prepared the data for the project and edited the manuscript.

Competing interests: 250
The authors declare that they have no conflict of interest.