Correlation and interaction between temperature and freeze-thaw in representative regions of Antarctica

ABSTRACT As the most sensitive and direct indicator of global climate change, the freezing and thawing of the Antarctic ice sheet is of great significance for research on surface mass and energy balance. In this study, four representative regions in Antarctica were selected and correlation analysis, Granger causality testing, and cluster analysis were applied to comprehensively analyze the correlation and response of spatiotemporal variation in freeze-thaw and temperature. The conclusions are as follows. (1) In the Antarctic Peninsula, a phenomenon was demonstrated that the summer shifts rearward. Hotter December and colder March temperatures were observed in the Amery Ice Shelf and Queen Maud Land. (2) The Antarctic Peninsula featured the most severe degree of melting among the four regions, with the largest melt area in the past 30 years appearing during the 2015/2016 season. However, the number of melt days in most areas of the Antarctic Peninsula was observed to have decreased. (3) There is a strong correlation between the freeze-thaw state of the Antarctic ice sheet and temperature, as well as spatial differences among regions, but the data were clustered at different time scales.


Introduction
The Antarctic ice sheet is the largest on Earth and a critical area for studying global climate change because it is sensitive to minor changes in the global temperature. Meanwhile, Big Earth Data has provided useful information in global climate change research and has promoted the field's development on a global scale (Guo, Zhang, and Zhu 2015;Guo et al. 2021Guo et al. , 2022. Greenhouse gases are one of the most important factors affecting climate change in the Antarctic ice sheet (Laurance 2019). According to data released by the National Oceanic and Atmospheric Administration (NOAA), global atmospheric CO 2 concentrations have continued to rise since the 1980s, with the global average monthly concentration reaching 412.35 ppm in August 2021. These enhanced greenhouse gas emissions are leading to global warming (Bongaarts 2019) and are bound to cause increased melting in the Antarctic ice sheet. The melting of the ice sheet can lead to changes in ice flow and result in the collapse of edge ice shelves, while the runoff generated by melting has been linked to uncertain changes in the ice sheet and sea levels (Tedesco 2009). It is therefore important to study the long-term temporal and spatial variation in the freeze-thaw state of the Antarctic ice sheet and its driving factors due to its sensitivity and its relevance for global climate change research (Guo, Fu, and Liu 2019).
In 2019, the Special Report on the Ocean and Cryosphere in a Changing Climate, released by the Intergovernmental Panel on Climate Change (IPCC), noted that global warming led to mass loss on the ice sheet. Between 2006 and 2015, the Antarctic ice sheet lost an average of 155 ± 19 Gt/a (0.43 ± 0.05 mm/a) (Meredith 2019). Research in 2019 also noted that between 1979 and 2017, Antarctic glaciers melted about five times faster than 40 years ago and directly caused the global average sea level to rise by about 13 mm (Rignot et al. 2019). According to the real-time data released by NASA's Global Climate Change, the Antarctic ice sheet mass loss was 2522.8 Gt between 16 April 2002, and16 October 2021, andreached 3029.9 Gt by 15 January 2021 (https://climate. nasa.gov/vital-signs/ice-sheets/). The main drivers of mass loss in the Antarctic ice sheet have been identified as rising atmospheric and oceanic temperatures (Slater et al. 2021). In-depth discussions have appeared in Science (Smith 2020) regarding the geological processes of the Antarctic ice sheet's formation, the interaction mechanisms between the ice sheet and ocean, and the Antarctic ice sheet freeze-thaw trend. Antarctic ice sheet mass loss is increasing and a failure to act will lead to an acceleration in global sea-level rise (Pattyn and Morlighem 2020).
The Antarctic ice sheet is covered in snow and ice year-round, and the surface melts after absorbing enough heat, changing from solid to liquid (Liang et al. 2021b;Zhao et al. 2021). The melting of the Antarctic ice sheet is mainly caused by solar radiation, though the warming effect caused by foehn winds can also lead to local melting (Datta et al. 2019;Liang et al. 2021c). The melting of the ice sheets mainly occurs during summer (i.e. from December to February in the Southern Hemisphere), and melting begins earlier and ends later at lower latitudes. Generally, melting begins in the northern areas and parts of the Antarctic Peninsula and then gradually advances to higher latitudes. In late December and early January, temperatures peak and parts of the Antarctic ice sheet melt rapidly, so that melt water accumulates and forms glacial lakes. As the melting weakens and the melt area shrinks by the end of summer, the melt water re-freezes in the snow layer. During winter, the temperatures in Antarctica are generally low and therefore there are rarely any melting events, except for local melting caused by foehn winds around the Antarctic Peninsula. The melting of the Antarctic ice sheet is affected by latitude, elevation, and a variety of other factors. Solar radiation is more concentrated and intense at lower latitudes, so the Antarctic ice sheet at lower latitudes melts more than at higher latitudes. Additionally, local topography and circulation are also important factors affecting the melting of the Antarctic ice sheet (Gardner and Sharp 2010;Liang, Li, and Zheng 2019).
The freeze-thaw cycle has an important impact on the mass balance of the Antarctic ice sheet (Shepherd et al. 2018). The meltwater generated by ice sheet melting has three main effects. (1) The meltwater forms runoff and causes ice sheet thinning. (2) The melt water is transmitted vertically and moves deeper into the ice, changing the thermal and hydrological state of the bottom of the ice sheet. (3) The melt water accumulates in ice cracks resulting in further fracturing when the water refreezes. The ice lakes formed by meltwater create pressure on the ice shelf, causing the ice shelf to bend and crack and eventually disintegrate (Hanna et al. 2013). Additionally, the surface albedo of the wet snow is much lower than that of dry snow, facilitating absorption of solar radiation and consequently leading to further melting.
Antarctica has undergone regional changes in surface temperature since the mid-twentieth century. The temperature rise in West Antarctica and the Antarctic Peninsula has been observed to be over two times faster than the global average rate, while there was a slight decline in East Antarctica (Bell and Seroussi 2020). The surface temperature of Antarctica has fluctuated due to the strength and location of tropical forcing and circumpolar westerlies, together with the invasion of mild and humid oceanic air masses along the coast. With global warming, the response of surface melt to climate forcing means that the melting area will increase by approximately 2×10 6 km 2 per day on average, with a 1°C increase in the average surface temperature during melting seasons (Meredith 2019). Therefore, quantitative evaluation of the response relationship between freezethaw and temperature is crucial to understanding the mechanism of ice sheet mass balance.
Though previous studies have focused on specific aspects independently in limited areas, such as the accuracy of radiometric data in inversing ice melt (Liang et al. 2021b) and statistical analysis of correlations between freeze-thaw and temperature (National Remote Sensing Center of China 2020), there is a lack of research measuring the spatiotemporal characteristics of temperature and freeze-thaw in representative Antarctic regions. This study focuses on the correlation and interaction between temperature and ice sheet freeze-thaw to reveal the response of the Antarctic ice sheet to global changes, using freeze-thaw information measured by microwave radiometer and temperature data derived from automatic weather stations while comparing data and trends between different selected regions.
The paper is outlined as follows: the study area, datasets, and research methods are listed in Section 2; Section 3 discusses the spatiotemporal characteristics of temperature variation and the freeze-thaw cycle in regions of Antarctica; Section 4 gives an analysis of the correlation; and Section 5 concludes the study.

Study area
At the southernmost point of the globe, Antarctica is a large landmass with an approximate area of 14.051 million km 2 covered in snow and ice consisting of glaciers, ice shelves, and islands. Antarctica has a cold, dry, mostly continental climate, though the climate in the Antarctic Peninsula is comparatively mild. Antarctica accounts for 9.4% of Earth's land area, while 98% of the Antarctic continent is covered by snow and ice throughout the year at an average thickness of 2000-2500 m and a maximum thickness of 4200 m. The Antarctic ice sheet is generally divided into three parts, the East Antarctic and West Antarctic ice sheets and parts of the Antarctic Peninsula ice sheet. The east and west are divided by the Transantarctic Mountains, and the area of the East Antarctic ice sheet is twice the area of the West Antarctic ice sheet. The latter is a fold belt composed of mountains, plateaus, and basins. Inter-annual cyclic freezing and thawing of the Antarctic ice sheet occurs mainly in areas near the coastal zone and on ice shelves. This study was carried out at four selected geographical locations: the Antarctic Peninsula, Queen Maud Land, Amery Ice Shelf, and Victoria Land ( Figure 1). Each of these regions has a unique climate and freezethaw characteristics.

Temperature data
More than a hundred automatic weather stations (AWS) have been deployed in different regions of Antarctica to study near-surface weather, climatic conditions, and physical micrometeorology processes. They enable long-term unmanned observations in remote areas and areas with severe weather conditions. The temperature data used in this study were mainly derived from the AWS temperature data provided by the British Antarctic Survey (BAS) and the United States Antarctic Program (USAP). The station information is shown in Figure 1 and Table 1.
Monthly mean temperature data from five meteorological stations were selected to represent the Antarctic Peninsula. Faraday station had the best data quality and provided continuous monthly temperature data from 1950 to March 2020, followed by Marambio and Rothera stations, which had four and six months of missing data, respectively. Poor data quality was observed at O'Higgins station since the start of its operation in 1963. The station had only one month of missing data by the end of 1987, but eleven months of data were missing in 1988. Since then, missing temperature data gaps were found on a yearly basis from 2003 to 2020, except for 2012 and 2018. Data were also The monthly mean temperature data from three meteorological stations were selected for Queen Maud Land. Syowa station was missing data from February 1958 to January 1959 and no observation data were provided from February 1962 to January 1966. The station provided high-quality observation data from February 1966 to November 2021 with no missing periods. Novolazarevskaya and Neumayer stations provided satisfactory data with only one month of missing data in October 2009 and January 1987 during the observation period, respectively.
The monthly mean temperature data from three meteorological stations were selected to study the Amery Ice Shelf. Mawson station provided high-quality data during the observation period from February 1954 to March 2020, with data only missing in October 2018 and July 2019. Davis station provided observation data from February 1957 until October 1964 and no   1987, 2004, 2006, and 2008, and small gaps on a yearly basis from 2010 to 2013. Cape Philips station featured large data gaps in 1992, 1997, and 2006, with a missing rate of over 50% since it began providing temperature measurements in January 1991. A sporadic amount of data was found to be missing in some years.

Freeze-thaw data derived from microwave radiometer
Microwave remote sensing techniques can be used for the inversion of the dynamic states of melting in the Antarctic ice sheet under all weather conditions. The microwave brightness temperature is extremely sensitive to changes in physical characteristics such as snowfall, snow age, the quantity of snowmelt, snow density, and densification of the ice sheet surface. However, the time scale for the emergence of liquid water affecting brightness temperature is much shorter than other factors. In such cases, a distinct feature is that sharp increases in brightness temperature can be detected by microwave sensors when the frequency is above 10 GHz, which can be found in the transition from dry snow to wet snow (including liquid water, ice, and air). The changes in melting regions and their duration in ice sheets can be effectively detected using SMMR, SSM/I, and SSMIS brightness temperature data (Liang et al. 2021a).
This study used the surface freeze-thaw data of the Antarctic ice sheet downloaded from https:// snow.univ-grenoble-alpes.fr/data.html. The freeze-thaw dataset consists of imagery with pixels representing a surface area classified as frozen or thawed (liquid). The dataset was produced by using microwave radiometer data (SMMR and SSM/I) with a 25 km spatial resolution and the algorithms developed by Torinesi, Fily, and Genthon (2003) and Picard, Fily, and Gallee (2007). It was recorded almost continuously at a 2-day temporal resolution from 1979 to 1988 and a 1-day resolution since 1989. In the dataset, 0 indicates no melting, 1 indicates melting, and −10 indicates data that is not available.

Correlation analysis
The time series of freeze-thaw area and temperature in selected Antarctic regions was analyzed to summarize the spatiotemporal variation in the freeze-thaw of the ice sheet and to analyze regional temperature variations. Moreover, the relationship between temperature changes and ice sheet freeze-thaw was also examined according to the correlation between Antarctic freeze-thaw and temperature data using Pearson's correlation coefficient.

Granger causality test
Granger causality is a statistical method for hypothesis testing that can be used to measure the mutual influence between time series by testing whether one set of time series x is the cause of changes of y in another set of time series. It has been widely adopted in fields such as economics, meteorological sciences, and neuroscience. Let x and y be the generalized stationary series. To begin, a p-order autoregressive model is established before the augmented regression model with the introduced lag period, that is: where c 1 and c 2 are constant; a (i) st (s, t = 1, 2) is the lag autoregressive coefficient of the i period; u 1t and u 2t are error terms; and x t−i and y t−i (i = 1, 2 · · · p) are the values of the ith period of x and y, respectively. Taking y t as an example, the Granger causality does not exist when the autoregressive coefficient satisfies:

Cluster analysis
Clustering is the process of classifying data into different classes or clusters, so objects in the same cluster have greater similarities, while objects in different clusters have greater differences. The ice sheet freeze-thaw and temperature time-series data were analyzed using the k-means++ algorithm, which can replace random initialization with an initialized cluster center. The clustering process is composed of two steps, first determining the optimal number of clusters (k) using the elbow method and then dividing the data into k clusters according to the k-means++ algorithm. The elbow method was adopted to determine the number of clusters, as they were not known beforehand. The main idea of the elbow method is to continuously increase the number of clusters (k) according to a step length and determine the optimal number of clusters by executing clusters on a varied k and determining the SSE (sum of squared errors). For a level of the divided clustering results, a smaller SSE between its center and the sample in the same cluster leads to a higher degree of aggregation for samples in the same cluster, and vice versa. The aggregation of samples in the cluster becomes tighter as the number of clusters (k) increases, with the SSE gradually decreasing. When k reaches a certain value, the decreasing magnitude of SSE will drop suddenly and then slowly reduce with the rising value of k. The k value corresponding to a sudden slowdown in SSE represents the optimal number of levels.
The number of clusters (k) was set from 1 to 8. The relationship between the number (k) of different levels and SSE is shown in Figure 2. When the level number was k = 2, SSE decreased greatly and the declining rate of SSE dropped when k = 3. In this case, k = 3 was selected as the optimal number of clusters.
3. Spatiotemporal characteristics of temperature and freeze-thaw 3.1. Temperature Table 2 shows the highest and lowest monthly mean temperatures and the time observed at five stations. The monthly mean temperatures at each station during the observation period are shown in Figure 3. According to Figure 3, all stations in the Antarctic Peninsula recorded an extremely low temperature just prior to 1990, except for Marambio, which had lower average temperatures due to its elevation but did not experience the same anomaly. The minimum temperature showed an increasing trend every winter. The highest monthly mean temperature varied slightly over time on a yearly basis, falling in December or January of the following year, or in February in a few years. The highest monthly mean temperature was above 0°C for years with statistical records in most years except Marambio. Table 3 shows the highest and lowest monthly mean temperatures and the time observed at three meteorological stations in Queen Maud Land. Figure 4 shows the time series of monthly mean temperature at each station during the observation period.

Queen Maud Land
As can be seen from Figure 4, the monthly mean temperature at Neumayer, Novolazarevskaya, and Syowa stations showed periodic variation with no significant rising or falling trend. The temperature varied on a yearly basis. The highest annual monthly mean temperature fell in December and January of the following year or additionally in February in a few years, while the lowest temperatures appeared in June, July, August, or September, and additionally in May and June in a few years. Table 4 shows the highest and lowest monthly mean temperatures and the time observed at three meteorological stations in the Amery Ice Shelf. Figure 5 shows the time series of monthly mean temperatures at each station during the observation period.

Amery Ice Shelf
Apparently, the temperature in Davis, Mawson, and Zhongshan varied on a yearly basis with no significant warming or cooling trend. The highest monthly mean temperature was generally observed for the month of December or January of the following year, and also in February during a few years. The lowest temperatures were observed in May, June, July, August, or September. Of particular significance was finding the temperature at these stations varied according to a w-shape trend within one year.  3.1.4. Victoria Land Table 5 shows the highest and lowest monthly mean temperatures and the time observed at three meteorological stations in Victoria Land. Figure 6 shows the time series of monthly mean temperature for each station during the observation period.
As shown in Figure 6, data quality was poor in Cape Philips, with frequent missing data. In these three stations, the temperature varied yearly with no significant trend. The highest monthly mean temperature was recorded only in December or January of the following year in all years. The lowest temperatures were observed in May, June, July, August, or September.

Variational trends for monthly mean temperature in December and March
The Antarctic ice sheet mainly melts during summer months. December and the following March are the beginning and end of the Antarctic summer, respectively. Therefore, December and March were selected to study the changes in Antarctic summer temperature trends, and identify any changes to the duration of summer in these regions. Inter-annual variations in the mean temperature were analyzed for the months of December and March from each selected station to identify the variations in trends. The change rate is shown in Table 6.   Although the rates of temperature change at each station in December and the following March were obtained, they were statistically insignificant. Faraday station in the Antarctic Peninsula and Manuel station in Victoria became increasingly warm during December, while Mawson station on the Amery Ice Shelf showed the opposite trend. In March, all stations in the Antarctic Peninsula experienced a notable rise in temperature, as the region became warmer and warmer during March, indicating that the duration of summer is increasing. Cape Philips station in Victoria Land showed a clear rise in temperature during March, while Neumayer station in Queen Maud Land showed the opposite trend. Therefore these results suggest that the temperature changes are not dramatic in Antarctica overall, unlike the Antarctic Peninsula. Currently, the phenomenon associated with the summer's rearward shift cannot be deduced from the temperature data in the other three regions.

Freeze-thaw characteristics
The melting of the Antarctic ice sheet takes place during the summer, which in the Southern Hemisphere is from December to February of the following year. Therefore, this study defined a melting year as the period from July 1 of a single year to June 30 of the following year. Figures 7-10 respectively display the melt extent, the total number of melt days, the number of days in each melt year, and the variations from 1989 to 2020 in the Antarctic Peninsula, Queen Maud Land, Amery Ice Shelf, and Victoria Land.
The total surface melt area of ice sheets in the Antarctic Peninsula, Queen Maud Land, Amery Ice Shelf, and Victoria Land reached 1.1 million km 2 from 1989 to 2020, with 288,700 km 2 , 499,300 km 2 , 212,500 km 2 , and 60,000 km 2 in each region, respectively. Surface melting was widely distributed, mainly in the Antarctic Peninsula and the ice shelf areas at low latitudes and elevations. The total number of melt days decreased with increasing latitude and elevation. The melting of the Antarctic ice sheet was characterized by seasonal patterns. The melting process was severe during the Southern Hemisphere summer and featured a rapid increase in melt area. It peaked in December and January of the following year concurrently with the highest mean temperature. The melt area gradually decreased and refroze in late summer. As winter began and the temperature dropped to the lowest level, melting was rarely seen except at low latitudes in the Antarctic Peninsula. The Antarctic Peninsula, which had the most severe melting among the four regions, was the 'hardest-hit area' in terms of ice sheet melt. The situation varied slightly from year to year. For example, 2015/2016 recorded the worst melting in 30 years, when the melt area reached approximately 1,096,900 km 2 under the influence of the El Niño effect. The most severe melting in the Antarctic Peninsula ice sheet, according to the melting degree (or the number of melt days), was recorded during 1992/1993, 1997/1998, and 2019/2020 time periods as shown in Figure 9. The Antarctic Peninsula experienced rapid local warming in the second half of the twentieth century, with an intensified degree of melting in the eastern and northern areas. Then, the region entered an intermittent stage of warming in the early twenty-first century. A more prominent cooling trend was observed in the eastern and northern areas, with the degree of melting showing a decrease, and the melting variation remaining consistent with surface temperature. The sudden and intensified surface melting of the Antarctic Peninsula ice sheet in the 2019/2020 period may have been associated with the temperature rise caused by sea ice and ocean circulation in the surrounding seas (Bintanja et al. 2013).
The Amery Ice Shelf is the largest ice shelf in East Antarctica and the third largest ice shelf in Antarctica. The number of melt days increased when moving from the outside of the ice shelf to the inland areas. The most severe melting in 30 years appeared during the 1997/1998 period, with a melt area of 271,875 km 2 , followed by 1989/1990, 1990/1991, and 2018/2019. In terms of the number of melt days, the Amery Ice Shelf experienced significant melting in 1989/1990, 2003/2004, 2004/2005, and 2005 Trend analysis was conducted on the number of melt days in the four Antarctic ice sheet regions. The results in Figure 10 show a declining trend in the number of melt days in most areas of the Antarctic Peninsula. This is consistent with the conclusion that surface melting in the Antarctic Peninsula and the recession of glaciers and ice shelf edges were reduced (Zheng, Zhou, and Liang 2019). An increasing trend was observed in most of the low-latitude areas in Queen Maud Land, together with a decreasing trend in areas at slightly higher latitudes. A slight downward trend in the number of melt days was observed in most areas of the Amery Ice Shelf, with a slight increase observed in

Results and discussion
The rising temperature under the trend of global warming is a contributor to Antarctic ice sheet melting, and consequently is a significant factor in global climate change (Liang et al. 2021c). This study analyzed the relationship between changes in the Antarctic ice sheet's different areas and the atmospheric system against the background of global climate change with freeze-thaw and temperature as two indicators in the period from 1989 to 2020.

Correlation analysis between freeze-thaw and temperature
The melt area was counted in terms of the number of melt pixels and the pixel size. Figure 11 shows the results of correlation analysis between the melt area and temperature. The monthly mean data for the melt area and temperature were used. When the temperature was lower than −10°C, the melt area was always smaller. In order to more accurately show the relationship between temperature and melt area, only the data with a temperature higher than −10°C were used to construct the regression relationship. It should be noted that Figure 11 shows all temperature data, including those below −10°C, in order to fully display the data distribution.
Meanwhile, a significance test of the univariate regression model indicates the linear regression is significant at the confidence level α = 0.05 in the four regions.
Results suggest that the correlation between the melt area and temperature in the four regions ranged from 0.65 to 0.78, indicating a strong correlation.

Analysis of Granger causality test results
Granger causality tests were performed on the selected representative regions of Antarctica to understand the relationship between temperature and the freeze-thaw of ice sheets. Monthly means were adopted to represent the freeze-thaw of ice sheets and temperature used in this study. Moreover, the dataset was also used to understand the sensitivity of ice sheet surface melting to temperature changes. In this case, the maximum lag order was 1. The freeze-thaw data were converted into the monthly mean melt area (km 2 ) with monthly mean temperature used as temperature data (°C). Two hypotheses were designed for each region. Hypothesis 1 proposes that the freezethaw was not the Granger cause of temperature. Hypothesis 2 proposes that temperature was not the Granger cause of freeze-thaw. Hypothesis 1 was accepted if P was greater than 0.05 and rejected if less than 0.05. The same condition was true for Hypothesis 2.
The freeze-thaw-temperature Granger causalities in various regions and in the entire Antarctic continent are shown in Table 7. Test results show that temperature was the cause of freeze-thaw in the Amery Ice Shelf and Queen Maud Land, while freeze-thaw was the Granger cause of temperature in the Antarctic Peninsula. Furthermore, freeze-thaw was the Granger cause of temperature in Victoria Land, and the temperature was also the Granger cause of freeze-thaw. Freeze-thaw and temperature were Granger causes in Antarctica, indicating that both were mutually influenced. Figure 11. Correlations between melt area and temperature in the Antarctic ice sheet between 1989 and 2020. The outer extension of the Amery Ice Shelf accounted for merely 1.7% of the whole Antarctic coastline, with ice flow accounting for 14% of the East Antarctic. The low-elevation area near the grounding line of the Amery Ice Shelf was frequently affected by persistent canyon winds from the inner ice sheet. Canyon winds have been observed to mix with and warm the air, which can cause the near-surface temperatures in the summer to be 3°C higher than in areas on or under the ice, thus leading to a doubled yield of meltwater near the surface compared to other areas (Lenaerts et al. 2017). Ice sheet surface melting leads to a reduction in surface albedo, while increased solar absorption accelerates melting. In this case, the melt area was affected by factors other than temperature variations. A study pointed out that rapid climate change was observed in Queen Maud Land, especially in the western area (Medley et al. 2018). Its annual average temperature was 0.9°C-1.0°C higher than before the Industrial Revolution. However, snowfall was observed to have increased by 25%. In Queen Maud Land, a 'snowfall anomaly' was a possible cause of the freeze-thaw response to temperature variations, which differs from other regions.
Freeze-thaw variations in the Antarctic ice sheet had temperature effects according to the results of the Granger causality test. In other words, rising temperatures were observed together with the melting of the ice sheet surface, and surface freezing was observed with falling temperatures, indicating mutual influence. The ice sheet surface will melt when the temperature rises, leading to a reduction in the surface albedo of the melted ice sheet. Consequently, the greater absorption of radiation may result in the melting of the ice sheet surface. The albedo is greatly increased when the ice sheet surface freezes, causing a decrease in the absorption of solar radiation and ultimately leading to a drop in temperature. A positive feedback mechanism is then formed between freeze-thaw and temperature. In addition, the bi-directional effect between freeze-thaw and temperature is also affected by factors such as sea ice density, thermal flux, and atmospheric circulation anomalies.

Analysis of freeze-thaw-temperature-time clustering results in different regions
The monthly freeze-thaw-temperature-time clustering results were analyzed and are shown in Figure 12 at the inter-month scale. Similar trends were present in the four regions. The summer (April to October), winter (December to February of the following year), and transition months (March and November) were considered three clusters. The average melt area and temperature are shown in Table 8. From April to October, the melt area in the winter months was small and stable due to the low temperatures in winter and the stable surface state of the ice sheet. The ice sheet surface experienced an increase in melt area along with rising temperatures in November during the transition from winter to summer. The melt area continued to increase along with rising temperatures in the summer months from December to February and began descending with lowering temperatures in March during the transition from summer to winter.
The annual freeze-thaw-temperature-time clustering results were analyzed and shown in Figure 13 at the inter-annual scale. Although the average annual temperature and the average annual melt area changed steadily, the Amery Ice Shelf, Queen Maud Land, and Victoria Land showed an obvious phenomenon: when the average annual temperatures were higher, the average annual melt area was also observably large at the same time. The average annual melt area and average temperature in each regional category are shown in Table 9. Among them, the average temperature of Amery Ice Shelf decreased to −10. 76°C in 1992, 1999-2000, and 2006, and the average annual melt area also decreased significantly to 67,031 km 2 . In 1992In -1995In , 1997In -2001In , 2006In -2009In , 2015In -2016, the average temperature dropped to −12.24°C, and the average annual melt area also decreased significantly to 307,461 km 2 . The average temperature in Victoria Land fell to −17.76°C in 1992, 1996, 2000, and 2017, and the average annual melt area also decreased significantly to 22,188 km 2 . In the Antarctic Peninsula, the largest melt area did not occur during the years when the average temperature peaked, but it was observed that the smallest melt area in the year occurred when the average temperatures were at their lowest. Therefore, on the annual time scale, the melt area values of the four representative regions of Antarctica were consistent with the change in temperature.
Furthermore, freeze-thaw differentiation characteristics were also studied at different longitudes and latitudes. The latitude of Antarctic melt ranges from −77.711°to −63.117°. The freeze-thaw of the Antarctic ice sheet features spatial differences at different latitudes. Overall, the amount of Antarctic ice sheet melting increased with the decrease in latitude, according to the spatial distribution of the average melt pixels at different latitudes in Antarctica, as shown in Figure 14. This is because the solar elevation angle decreased with the increase in latitude. In other words, the decrease in solar radiation and the increase in latitude led to a decrease in temperature. A previous study also found  that surface melting (1989-2020) was widely distributed, but the study focused on the Antarctic Peninsula and ice shelf areas at low latitudes and low elevation (Liang et al. 2021c). When the temperature rises, the ice sheet surface melts, leading to a reduction in the surface albedo of the melted ice sheet. Moreover, melting may occur when the ice sheet surface absorbs more radiation. The average melted pixel reached its maximum value in the longitude range of −75°to −50°and remained stable in the longitude range of −10°to 170°( Figure 15). The melting range from −10°to 170°longitude is mainly distributed in latitude between −73°and −69°. Due to the small latitude   1991, 1995, 1997-1998, 2001-2005, 2010-2012, 2014221,696 −10.23 1993-1994, 1996, 2007-2009, 2015-2018, 2020157,760 −10.42 1992, 1999-2000, 200667,031 −10.76 Antarctic Peninsula 1993, 1997-1998, 2004, 2006, 2015-20161,033,393 −4.47 1994, 1996, 1999-2003, 2005, 2010, 2020815,385 −4.40 1991-1992, 1995, 2007-2009, 2011-2012, 2014, 2018670.250 −4.84 Queen Maud Land 1991, 1996, 2004, 2011690,156 −11.81 2002-2003, 2005, 2010, 2012-2014476,937 −12.08 1992-1995, 1997-2001, 2006-2009, 2015-2016, 2020307,461 −12.24 Victoria Land 1991, 1993, 1998, 2002-2005, 2007, 2010, 2015, 202098,571 −17.62 1994-1995, 1997, 1999, 2001, 2006, 2008-2009, 2014, 2016, 201853,438 −17.66 1992, 1996, 2000 span at this range, insignificant temperature variations may have caused a stable melting trend in the longitude range. Finally, the seasonal distribution characteristics of freeze-thaw were studied. The Antarctic region features a special climate, with only winter (from March to November) and summer (from December to February) seasons. Figure 16 displays the multi-year average melted pixels for the four representative regions in different months. It was observed that the melt area began to increase rapidly in October, or the transition from winter to summer, and began to decrease in March during the transition from summer to winter. As shown in Figure 17, the data featured the same variation trend as temperature. When winter begins in March, the average temperature drops below −10°C with no melting on the ice sheet surface, thereby maintaining stability. When summer begins in October, the temperature will gradually rise with the increasing melt area. This shows that the melting of the Antarctic ice sheet surface is characterized by prominent seasonal patterns, indicating the close relationship between freeze-thaw and temperature.
Previous studies have revealed that the Antarctic Peninsula and West Antarctica are two of the most rapidly warming regions of Earth (Smith and Polvani 2017). Historically speaking, sporadic spikes in air temperatures have been reported in the Antarctic, with melting and freezing cycles in both the sea ice and the neighboring ice shelves during the summer season (Drinkwater and Liu 2000), but this phenomenon has been more severe and widespread over the Antarctic Peninsula (Noble et al. 2020). The Antarctic Peninsula is therefore the 'hardest-hit area' in terms of Antarctic ice sheet melting (Liang et al. 2021c; National Remote Sensing Center of China 2020). It is  predicted that the Antarctic continent will observe climatic changes similar to the prevalent changes along the Antarctic Peninsula. However, unlike the interior of the continent, which will likely continue to experience temperatures well below zero, the coastal regions are likely to experience major changes due to rising temperatures that are already close to thawing (Convey and Peck 2019).
The strong relationship exhibited between freeze and thaw cycles and temperature in this study supports the argument made in recent simulations: changes in melt water and ice discharge from the Antarctic ice sheet as a result of anthropogenic global warming will have regional and global implications for climate change in the future (Sadai et al. 2020). Surface melt water in its various forms (supraglacial lakes, subsurface lakes, surface streams and rivers) have the potential to alter the Antarctic ice sheet mass balance by accelerating ice shelf disintegration and increasing drainage of ice into the ocean (Noble et al. 2020).
In the West Antarctic ice sheet, previous research has also reported a large volume of fresh water discharged into the Amundsen Sea, which likely caused a mass loss of 250 Gt/year between 2009 and 2017 (Convey and Peck 2019), while others reported extensive and active surface lake formations in East Antarctica during the 2017 peak melt season (Drinkwater and Liu 2000).

Conclusions
The Antarctic ice sheet is changing dramatically in the context of global climate change. The accelerated loss of the Antarctic ice sheet stated in the Special Report on the Ocean and Cryosphere in Climate Change, released by the United Nations Intergovernmental Panel on Climate Change (IPCC) in September 2019, has made it a popular research focus for countries worldwide. As the freeze-thaw state of the ice sheet surface is sensitive to global climate change, studying the relationship between freeze-thaw and climate change can contribute to a better understanding of the evolution of the ice sheet and ecosystem in Antarctica.
Hence, this paper presents the spatiotemporal variation in temperature and freeze-thaw in representative Antarctic regions (Antarctic Peninsula, Queen Maud Land, Amery Ice Shelf, and Victoria Land) using field temperature observations and a microwave radiometer freeze-thaw dataset. It also provides a comprehensive analysis and comparison of the available data from multiple regions in Antarctica. On this basis, the relationship among the Antarctic ice sheet surface melt, climate, and environment was also studied through correlation analysis, Granger causality testing, and cluster analysis. The following conclusions were reached. According to the analysis of the inter-annual variation in melt days, the number of melt days in most areas of the Antarctic Peninsula was observed to decrease. Moreover, a rising trend was observed in other areas at low latitudes and elevations, and a falling trend was observed in high-latitude and high-elevation areas. (iii) The correlation between the freeze-thaw state of the Antarctic ice sheet and temperature was analyzed using Pearson's correlation coefficient. The results prove that there was a strong correlation between melt area and temperature. The correlation between freeze-thaw and the temperature of the Antarctic ice sheet and its four representative regions were analyzed using the Granger causality test. The results show that freeze-thaw and temperature were highly correlated and mutually influenced in Antarctica. Spatial differences may be caused by the influence of wind direction (Van den Broeke and Van Lipzig 2004), snowfall (Medley et al. 2018), or other non-temperature factors in different regions. Furthermore, freezethaw-temperature-time data were clustered at different time scales to investigate the differences and consistency between freeze-thaw and temperature in different regions. The results show that a steady monthly melting state in winter was present in the four regions at selected inter-monthly scales. The freeze-thaw began in the transition months between seasons and reached a maximum area during the summer months, which was consistent with the variation in temperature, as well as with the seasonal pattern and high mass loss in the summer (Velicogna et al. 2020). Moreover, at the annual time scale, it was observed that the Amery Ice Shelf, Queen Maud Land, and Victoria Land exhibited a phenomenon where the average annual melt area increased with the increase in average temperature, and the overall melt area showed the same trend as the temperature. The strong correlation between freeze-thaw and temperature was further demonstrated by the consistent changes in freeze-thaw area and temperature at two temporal scales.