Snow depth product over Antarctic sea ice from 2002 to 2020 using multisource passive microwave radiometers

Snow over sea ice controls energy budgets and affects sea ice growth/melting, and thus has essential effects on the climate. Passive microwave radiometers can be used for basin-scale snow depth estimation at a daily scale; however, previously published methods applied to the Antarctica clearly underestimated snow depth, limiting their further application. 10 Here, we estimated snow depth using passive microwave radiometers and a newly constructed, robust method by incorporating lower frequencies, which have been available from AMSR-E and AMSR-2 since 2002. A regression analysis using 7 years of Operation IceBridge (OIB) airborne snow depth measurements showed that the gradient ratio (GR) calculated using brightness temperatures in vertically polarized 37 and 19 7 GHz, i.e., GR(37/7), was optimal for deriving Antarctic snow depth, with a correlation coefficient of -0.64. We hence derived new coefficients based on GR(37/7) to 15 improve the current snow depth estimation from passive microwave radiometers. Comparing the new retrieval with in situ measurements from the Australian Antarctic Data Centre showed that this method outperformed the previously available method (i.e., linear regression model based on GR(37/19)), with a mean difference of 5.64 cm and an RMSD of 13.79 cm, compared to values of -14.47 cm and 19.49 cm, respectively. A comparison to shipborne observations from Antarctic Sea Ice Processes and Climate indicated that in thin ice regions, the proposed method performed slightly better than the previous 20 method (with RMSDs of 16.85 cm and 17.61 cm, respectively). Comparable performances during the growth and melting seasons suggest that the proposed method can still be used during the melting season. Gaussian error propagation found an average snow depth uncertainty of 3.81 cm, which accounted for 12% of the estimated mean snow depth. We generated a complete snow depth product over Antarctic sea ice from 2002 to 2020 on a daily scale, and negative trends could be found in all sea sectors and seasons. This dataset (including both snow depth and snow depth uncertainty) can be downloaded from 25 National Tibetan Plateau Data Center, Institute of Tibetan Plateau Research, Chinese Academy of Sciences at http://data.tpdc.ac.cn/en/disallow/61ea8177-7177-4507-aeeb-0c7b653d6fc3/ (Shen and Ke, 2021, DOI: 10.11888/Snow.tpdc.271653).


Introduction
Snow is a basic element in the Antarctic sea ice system and it changes the surface albedo of sea ice (Petrich et al., 2012), 30 controls energy exchanges between the atmosphere and ocean (Kwok and Untersteiner, 2011) and affects sea ice growth and melting (Maykut et al., 1971;Sturm et al., 2002). Thus, it has essential climatic effects (Webster et al., 2018). Because snow depth is a fundamental property of snow cover, knowing how it changes is crucially important for understanding rapid changes in the Antarctic climate. Snow depth is also an essential input for sea ice thickness estimation (Giles et al., 20082007;Kwok et al, 2020), and its accuracy will greatly affect the reliability of sea ice thickness estimates. Hence, from 35 the perspectives of climate and sea ice thickness estimation, basin-scale snow depth products in Antarcticain the Antarctic, especially over long times a long time period, are urgently needed.
Although in situ measurements of snow depth over Antarctic sea ice have very high accuracy and precision, their spatial and temporal coverage are quite limited. Airborne snow depth measurements can cover regions of thousands of square kilometres, but they are cost intensive and represent only limited regions. Only satellites can obtain snow depth at the 40 hemispheric scale, and individual and multisource satellites have been applied for snow depth estimation, e.g., passive microwave radiometers (Markus and Cavalieri, 1998;Comiso et al., 2003;Maaß et al., 2013), satellite radar altimeters (Guerreiro et al., 2016;Lawrence et al., 2018), satellite laser altimeters (Kern et al., 2016), and a combination of satellite radar and laser altimeters (Kwok et al., 2019;Kacimi and Kwok, 2020). Given both the basin-scale coverage and the temporal resolution requirements, passive microwave radiometers are the best tools to derive a long data record of snow 45 depth in Antarcticain the Antarctic with daily coverage.
The theoretical basis of snow depth estimation from passive microwave radiometers is that the volume scattering of upper uploading snow cover affects the radiation signal emitted from the underlying sea ice and reduces the observed brightness temperatures (Markus and Cavalieri, 1998). Thus, the observed brightness temperatures are related to the observation frequency and snow depth, and the snow brightness temperature increases as snow depth decreases or observation frequency 50 increases. Based on this principle, Markus and Cavalieri (1998) used correlation analysis for the measured snow depth and brightness temperatures observed from the Special Sensor Microwave/Imager (SSM/I) in Antarcticain the Antarctic. They found that the gradient ratio (GR) calculated from vertical polarized brightness temperatures at 19 GHz and 37 GHz had the highest correlation with measured snow thickness with a correlation coefficient of -0.60. An empirical linear regression equation was then derived for snow depth estimation, and the regression coefficients were updated for the successor passive 55 microwave ratiometers (i.e., Advanced Microwave Scanning Radiometer for EOS (AMSR-E), Comiso et al., 2003).
Although this method can derive basin-scale snow depth, due to the snow penetration depth when 37 and 19 GHz frequencies (i.e., higher frequencies) are used and the strong influence liquid water in the snow layer has on the observed radiation from passive microwave ratiometers, this method is limited to dry snow less than 50 cm thick and thus may underestimate the snow depth in some regions of the Antarctic, which is clearly less than the snow cover over Antarctic sea 60 ice (Kwok et al., 2014). Given these influences, this method obviously underestimates snow depth thickness by a factor of 2.3 (Worby et al., 2008a) or between 2 and 4 (Kern et al., 20162011). Since 2002, successful launches of AMSR-E and its successor Advanced Microwave Scanning Radiometer 2 (AMSR-2) have provided a chance to estimate snow depth with lower frequencies. Lower frequencies are sensitive to deeper ice layers, are less affected by liquid water in the snow layer and weather conditions (Rostosky et al., 2018) and have been used to improve snow depth estimation over Arctic sea ice 65 (Rostosky et al., 2018;Braakmann-Folgmann et al., 2019;Kilic et al., 2019;Winstrup et al., 2019). Compared to the Arctic, snow depth over Antarctic sea ice is usually thicker (Kern et al., 2016), more heterogeneous (Massom et al., 2001) and less affected by surface melting; hence, lower frequencies tend to be more suitable for retrieving Antarctic snow depthreliable for estimating snow depth. However, these methods have not been tested or applied to Antarctic snow depth estimation until now. 70 In the present study, we attempt to construct a new and effective method to estimate snow depth over Antarctic sea ice.
For the potential improvement of snow depth estimation using low-frequency signals, AMSR-E and AMSR-2 were used to derive new regression coefficients in the estimation equation. A detailed introduction to these data is shown in Section 2.
Section 3 describes the methods for snow depth and uncertainty estimations, and the accuracy evaluation is shown in Section 4. Section 5 shows the spatiotemporal variation in the derived Antarctic snow depth between 2002 and 2020. Section 6 75 discusses the uncertainty sources of the proposed method, Section 7 gives the data availability and Section 8 concludes this paper.

AMSR-E, AMSR-2 and SSMIS brightness temperature observations
To generate a complete time series of snow depth data over Antarctic sea ice, multiple passive microwave radiometers were 80 used, including AMSR-E, AMSR-2 and the Special Sensor Microwave Imager Sounder (SSMIS). Between 1 June 2002 and 30 September 2011, AMSR-E data were used. With an observation angle of 55°, AMSR-E can provide daily brightness temperature observations in the whole Arctic and in Antarctica Antarctic. Six frequency channels were applied, i.e., 6.93, 10.7, 18.7, 23.8, 36.5 and 89.0 GHz, and each channel had both horizontal and vertical polarizations. Here, the AMSR-E/Aqua Daily L3 25 km Brightness Temperature and Sea Ice Concentration Polar Grids (Version 3) product from the 85 National Snow and Ice Center (NSIDC) were used, and pre-processing, bias correction and quality control were all applied (Cavalieri et al., 2014).
Between 2 July1 June 2012 and 31 May 2020, AMSR-2 data were used. Compared to AMSR-E, AMSR-2 has the same observation angle and frequency channels but has an additional frequency at 7.3 GHz. Here, the NSIDC AMSR-E/AMSR-2 Unified L3 Daily 25 km Brightness Temperature and Sea Ice Concentration Polar Grids (Version 1) product was used, and 90 pre-processing, bias correction and quality control were also applied (Markus et al., 2018).
Brightness temperature observations from SSMIS were used to fill the gap in AMSR-E and AMSR-2 data between 1 October 2011 and 1 JulyMay 2012. The DMSP SSM/I-SSMIS Daily Polar Gridded Brightness Temperature (Version 4) product was used here because it has the same spatial and /temporal resolutions and spatial coverage as the two brightness temperature products mentioned above, pre-processing, bias correction and quality control were also applied (Maslanik et al., 95 2004). All three passive microwave radiometers can provide the daily brightness temperature observations for the whole Antarctic. The temporal coverage of this dataset is from 14 December 2006 to 31 March 2019, hence it can be used to fill the observation gap between AMSR-E and AMSR-2 data and has a long overlapped time period with AMSR-E/2. However, SSMIS does not have lower frequency channels (lower than or equal to 19 GHz) than AMSR-E and AMSR-2; hence, the corresponding snow depth estimation equation was adjusted accordingly, as shown in Section 3. 100 To generate consistent brightness temperature observations from 2002 to 2020, a consistency correction should be applied in to the three passive microwave ratiometer datasets. The SSMIS brightness temperature observations were calibrated based on theto AMSR-E data based on the method from Wentz (2013), and we calibrated the AMSR-2 data to AMSR-E based on the correction parameters from Du et al. (2014). These brightness temperature observations from AMSR-E, AMSR-2 and SSMIS were also used to obtain the full time (2002-2020) sea ice concentrations by using the ARTIST Sea Ice (ASI) 105 algorithm (Spreen et al., 2008).

Operational IceBridge airborne snow depth measurements
The initial aim of the Operational IceBridge (OIB) airborne mission is to fill the observation gap between ICESat and ICESat-2. This mission provides annual measurements of snow depth over sea ice, elevation and thickness of sea ice, and information on sea ice types in the Arctic and Antarctica. Due to the large coverage of measurements, it was suitable to 110 evaluate satellite-derived parameters. In the OIB airborne mission, Airborne Topographic Mapper (ATM), a laser altimeter, is used to measure the elevation of the sea ice surface. Its footprint depends on the observation angle of the pulsed laser and flight altitude. The size is approximately 1 m (Kurtz et al., 2013, Schenk et al., 1999, and the location and elevation measurements accuracies for individual measurements are approximately 1 m and 0.1 m (or better, Krabill et al., 1995;Schenk et al., 1999), with a vertical precision of 3 cm (Martin et al., 2012). 115 The measured elevations were used to derive the total freeboard. Following Zwally et al. (2008) and Kern et al. (2015), the lowest 2% elevations in a 50 km segment along the track were regarded as the sea surface heights, and the mean value was calculated as the mean sea surface segment height (MSSH). Other points were taken as sea ice measurement points, and the corresponding total freeboard was calculated by subtractingmisusing the local MSSH from the sea ice surface heights.
Snow Rradar is used to measure the snow depth in the OIB airborne mission. However, for snow cover over Antarctic sea 120 ice, the snow-ice interface is hard to distinguish (Giles et al., 2008;Willatt et al., 2009) due to the complicated snow morphology often found in Antarcticain the Antarctic (Massom et al., 2001). Accurate snow depth detection needs more in situ investigations and in-depth studies. Considering these influences, snow depth was derived from the total freeboard as described in Ozsoy-Cicek et al. (2013). The corresponding linear equations were constructed in six individual sea sectors in the Southern Ocean, with correlation coefficients ranging from 0.81 to 0.99. These have been widely used in previously 125 published studies to obtain Antarctic sea ice parameters Kern et al., 2016;Li et al., 2018). OIB ATM data collected in 2009, 2010, 2012-2018 were used, and no data could be obtained for the missing yearsyear of 2015. OIB data in 2011 were not used for the derivation of snow depth estimation equation to reduce the potential effect of the inter-mission calibration between SSMIS and AMSR-E/2, but they were used for the independent evaluation of SSMIS-derived snow depth in 2011. In each year except 2013 the OIB ATM data were acquired in both 130 October and November, for the 2013 OIB campaign only measurement data in November were obtained, more details about the time information of OIB data are available via https://nsidc.org/data/ILATM2/versions/2. The spatial distributions of the used OIB ATM spatial distribution data (after data filter, see Section 3.1)used are shown in Fig. 1a. Most of the OIB ATM data came from the western of Antarctica sea ice region and one track covered the Ross Sea sector. These measurements covered both the thicker snow in the Weddell Sea sector and the thinner snow in the Ross Sea sector and provided 135 comprehensive measurements for the development of satellite-based snow depth estimation methods. For comparison purposes, the OIB snow depth measurements were averaged in the overlapped passive microwave radiometer grid cells (at the spatial resolution of 25 km) in the same day. Although the sea ice is continuously drifting, the time differences between the OIB and passive microwave ratiometer data were always less than one day, which can cause the sea ice drift of several kilometers. Comparing to the coarse spatial resolution of passive microwave ratiometers (i.e., 25 km), this effect can be 140 ignored. More details can be referred to Section 3.1, this processing method was also applied for other data sets as listed in Sections 2.3 and 2.4.

AADC in situ measurement data
We used in situ snow depth measurements from the Australian Antarctic Data Centre (AADC) to evaluate the proposed method. AADC in situ data include measurements of sea ice and snow from 1985 to 2007. This dataset provides records of 145 snow depth, sea ice freeboard and sea ice thickness. Here, AADC data between September and October 2003, between September and October 2007 from 2003 and 2007 were used to compare our snow depth estimation results, which were mainly located in eastern and western Antarctica of the Antarctic sea ice region (Fig. 1b, only the used AADC data (after data filter, see Section 4.2) are shown), more details about the time information of AADC data can be available via https://data.aad.gov.au/metadata/records/sea_ice_measurements_database. Although in situ measurements are relatively rare, 150 AADC has measurements of both thick and thin ice, which provide a comprehensive and accurate evaluation of estimated snow depth.

ASPeCt shipborne observation data
We also used snow depth observations from the Antarctic Sea Ice Processes and Climate (ASPeCt) mission to evaluate the estimated snow depth. These data (including observations of snow depth, sea ice thickness and ice type) were obtained every 155 hour within a 1 km radius of the ship. We followed the Worby et al. (2008b) method to reduce the sampling bias caused by temporal data collection and variable ship speed by removing observations within 6 nautical miles of previous observations. This method ensured the independence of each record. As the passive microwave ratiometer observes both undeformed and deformed sea ice, the 'averaged snow depth' record was used to compare to the passive microwave ratiometer-derived snow depth. This record considers the undeformed thickness, ridge height, and ridge coverage, which are the overall estimates of 160 observed snow depths. According to the error analysis in Worby et al. (2008b), ± 20% bias of ASPeCt data is found for undeformed ice thicker than 0.3 m, and ± 30% bias is found for deformed ice.
This dataset contains snow depth measurements from 81 cruises between 1981 and 2005. Here, we used ASPeCt data from individual months (except for February, May, June and July) between 2002 and 2005, which covered various types of sea ice and most sea sectors in the Southern Ocean (Fig. 1b, only the used ASPeCt data (after the data filter, see Section 4.3) 165 are shown), more details about the time information of ASPeCt data are available via http://aspect.antarctica.gov.au/data.

ICESat-2 data
ICESat-2 data were used here to estimate the snow depth over Antarctic sea ice and the estimated snow depth was compared to estimates from the proposed method. Kern et al. (2016) found that satellite laser altimeters can be used to estimate snow depth over Antarctic sea ice with a low level of uncertainty, and these snow depth measurements agreed closely with both 170 shipborne and airborne data. Considering the potential reliability of satellite laser altimeter-derived snow depth, following Kern et al. (2016), we estimated the Antarctic snow depth in a complete year (January 2019 to December 2019) from ICESat-2 using a linear equation based on total freeboard (Ozsoy-Cicek et al., 2013). The ICESat-2 ATL10 sea ice product (Kwok et al., 2019a), which contains total freeboard estimates, was used for snow depth estimation. The along-track resolution of the total freeboard estimates is variable and is determined by the number of pulse footprints to aggregate the 175 150 photons. For strong beams, this along-track resolution varies between ~10 m and 200 m, and it varies between ~40 m and 800 m for weak beams. An averaged bias of 2-4 cm for ICESat-2 ATL10 total freeboard was found based on assessment in Kwok et al. (2019b). The detailed algorithm for the ICESat-2 total freeboard estimates can be found in Kwok et al. (2019c). ICESat-2 ATL10 sea ice product for the Antarctic sea ice between January and December 2019 were used in the present study. 180

The selection of optimal frequency channels
Although lower frequencies tend to better estimate snow depth, we used all frequencies to find the optimal frequency channels. All available combinations were compared to the OIB airborne snow depth measurements, and only VV 190 combinations were used, since they had better performance than the HH combinations (Rostosky et al., 2018). To reduce the effect of uneven OIB measurement distributions within the passive microwave ratiometer grid cells caused by their resolution difference, on the same day, one passive microwave ratiometer grid cell (i.e., 25 km × 25 km) should contain at least 2500 OIB measurement points. To reduce the influence of outliers, only OIB snow depth data between the 5th and 95th percentiles were used. In order to minimize the potential influence of sea ice concentration, only grid cells with ≥ 75% sea 195 ice concentration were used. After these data filters, OIB data in November 2010, November 2016 and October-November 2018 were removed. Since Antarctic OIB airborne missions are launchedthe used OIB data were obtained in October or November each year, air temperatures could be higher than the melting point and cause surface melting. To reduce the influence of the snow layer's liquid water on brightness temperatures observed by passive microwave radiometers, we excluded brightness temperatures that were assumed to be affected by liquid water based on the 2 m air temperature (T2m) 200 data from ERA5 reanalysis data. If the T2m in a single grid cell during one day or during at least 5 of the 10 preceding days, is higher than 0 ℃, the brightness temperatures were removed (Rostosky et al., 2018). The GR was calculated as follows (take GR(37/7) as an example): Where C is the sea ice concentration, k 1 and k 2 are correction terms for the open water contribution when the sea ice concentration is below 100%. Tb 37,OW and Tb 7,OW are the brightness temperatures over open water at 37 and 7 GHz, the brightness temperatures over open water for the different frequencies can be referred to Ivanova et al. (2015). Table 1 shows the correlation and root mean square deviation (RMSD) between OIB snow depth measurements and 210 individual GRs (including both AMSR-E and AMSR-2 GRs). The combination of GR (37/19) and GR (19/10) was also applied here, since it was considered optimal for Arctic snow depth estimation (Markus et al., 2006). Different weightings (i.e., 3:2 and 2:3) had no obvious influence on the estimation result, and a weighting of 1:1 was used here.  Fig. 2a shows the scatter plot between the OIB snow depth and GR (37/7), detailed temporal information for these data can be found in Sections 2.2 and 3.1, the spatial coverage is shown in Fig.1a. To reduce the influence of outliers, only OIB snow depth data between the 5th to 95th percentiles were used to derive the equation coefficients. The corresponding regression 225 equation can be derived as follows:

The derivation of new snow depth estimation equation
SSMIS frequencies were not as low as those of AMSR-E/2, meaning GR (37/7) could not be used with SSMIS data.
Because of this, we used GR (37/19), which was the best combination among frequencies no less than 19 GHzranked next to 230 GR (37/7), as shown in Table 1 To maintain the consistency of snow depth estimates based on two equations above, we compared their snow depth estimates during the OIB period (the same data for the derivations of Eqs. (4) and (5) were used). The snow depth estimations derived from the two equations agreed well and had an RMSD of 1.89 cm, and we corrected their original 240 difference based on an empirical linear regression equation: The snow depth from 1 October 2011 to May 1 July 2012 was estimated based on Eq. (25) and Eq. (36), the snow depth for the remaining time periods was estimated from Eq. (4). Only valid snow depth estimates (> 0 cm) were allowed..

The estimation of snow depth uncertainty 245
The snow depth uncertainty was estimated from the uncertainty of individual input variables using Gaussian error propagation. Brightness temperature and sea ice concentration uncertainties were assumed to be 0.5 K and 5% (Rostosky et al., 2018). Uncertainties of the intercept and slope for Eqs. (4), (5) and (6) were 0.44 and 18.09, 0.57 and 27.95, 0.65 and 0.02, respectively. In addition, uncertainty due to the limited sample size of the OIB data should also be considered. A sensitivity analysis was performed to quantify the interannual variability (caused from the limited sample size) of the 250 regression coefficients (see Section 4.1), the standard deviation of the regression coefficients deriving from different samples were assumed as the uncertainty value. These were ±3.23 cm for intercept and ±158.69 for slope. The uncertainties in the regression coefficients were summed to combine the uncertainties from linear fitting and limited OIB samples. Detailed calculation steps can be found in Rostosky et al. (2018). (October-December), summer (January-March), autumn (April-June) and winter (July September) (Zwally et al., 2002). The snow depth uncertainty in summer (an average of 4.5232.50 cm) was larger than that in the other seasons due to the effect of liquid water in the snow layer. In autumn, winter and spring, the average snow depth uncertainties were approximately 3.6620.76 cm, 3.3317.85 cm and 3.7423.79 cm, respectively. The averaged annual snow depth uncertainty was 23.73 cm.
Spatially, smaller snow depth uncertainties were found in the sea ice interior, while larger uncertainties were found in the sea 260 ice marginal region, which may be due to complex surface conditions there. As the sea ice concentration is the dominant factor affecting the observed brightness temperatures (and thus the GRs, Markus and Cavalieri, 1998), the influence of the open water is greater in the sea ice marginals and thus causes larger snow depth uncertainties. The averaged snow depth uncertainties accounted for approximately 13%, 12%, 12% and 11% of the averaged snow depths in spring, summer, autumn and winter, respectively, and depended on the snow depth. 265

Self-evaluation of the proposed method
To prove the robustness of the proposed method, we calculated 7 pairs of regression coefficients (for Eq. (14)) based on each 6-year combination of OIB snow depth data between 2009 and 2018 ( Table 2). Only regression coefficients calculated from 275 more than 80 matched points were used for sensitivity analysis to ensure reliability. The uncertainty of the individual coefficient was estimated as its standard deviation. The estimated slope ranged from -474 to -349 with an uncertainty of 42.85, which caused a bias of <1 cm for the snow depth estimation; furthermore, the intercept varied from 25.4 to 28.3 with an uncertainty of 1.14. No obvious interannual variations could be found for either the slope or the intercept values.
280 Here, the OIB snow depth data in October 2016 were used to self-evaluate the snow depth estimation based on the equation derived from data in the remaining years (equation coefficients are shown in Table 2). The method proposed in Comiso et al. (2003) (hereafter called the Comiso method) was also applied for comparison, this is the commonly used snow 285 depth algorithm for Antarctic sea ice by using passive microwave radiometers, which modified the algorithm coefficients of the Markus and Cavalieri (1998) method to match the frequencies of AMSR-E. Data from October 2016 were chosen randomly, and the large size of this dataset ensured that the evaluation was comprehensive. In addition, the OIB data in individual years were independent, which also ensured the evaluation's objectivity. The result showed that the proposed method obviously outperformed the Comiso method with a mean difference of approximately -1.55 cm, while the latter had 290 an average difference of -19.15 cm, which greatly underestimated the snow depth (Table 3). In addition, the snow depth derived from the proposed method had a narrower numerical distribution when compared to the OIB data (Fig. 4a). A peak of 30 cm could be found in both the proposed method and the OIB snow depth distributions; however, the Comiso method had a peak of 10 cm. This result confirms the conclusion of Worby et al. (2008a) that the Comiso method underestimates snow depth by a factor of 2.32. The snow depth estimated from the proposed method ranged from 20 to 60 cm, which was generally consistent with the OIB distribution. However, the OIB data had more snow depth 300 values of < 20 cm (Fig. 4a). A quadratic fitting equation was assumed to improve this situation; however, the uncertainties of the derived equation coefficients were usually larger (Rostosky et al., 2018).
Approximately 79% of the snow depth differences between the proposed method and OIB data had absolute differences of <10 cm, while the Comiso method showed that only 15% of the absolute differences were less than 10 cm, and 80% of the absolute differences were greater than 10 cm (Fig. 4b). Although the snow depths estimated from the proposed method and 305 the Comiso method had almost the same variation pattern as the OIB snow depth data (here, Eq. (14) was used), the Comiso method obviously underestimated the snow depth by a mean difference of -17.3 cm at the interannual scale, nearly equal to the minimum OIB snow depth (Fig. 4c). Hence, compared to OIB snow depth measurements, the proposed method not only had a closer snow depth distribution but also showed a consistent temporal variation pattern, which demonstrated its reliability for estimating Antarctic snow depth. 310 Here the OIB snow depth data in October and November 2011 were also used to evaluate the snow depth estimates. On 320 the one hand, OIB data in 2011 were not used for equation derivation (i.e., Eq. 4) and thus were suitable for an independent accuracy evaluation. On the other hand, in this case SSMIS-derived snow depth can be evaluated, which provides a reference for the performance evaluation of the Eqs. (5) and (6). The result showed that the proposed method still outperformed the Comiso method with a mean difference of -7.93 cm, while the latter still underestimated the snow depth with a mean difference of -24.65 cm (Table 4). 325

Comparison to AADC in situ measurements in growth season 330
As mentioned previously, liquid water in the snow layer affects observed brightness temperatures and causes larger uncertainties in estimated snow depths. The proposed method was thus mainly used for snow depth derivation during the growing seasonin cold seasons, i.e., autumn, winter and spring. In this subsection, we focus on evaluating the performance of the proposed method during the growth season in winter and spring. 1418 AADC snow depth measurement points were used for evaluation, and all AADC snow depth measurements within one passive microwave ratiometer grid cell were averaged 335 and compared to passive microwave ratiometer-derived snow depth (from the proposed method and Comiso method, respectively) in the same day. Each grid cell contained approximately 95 ± 36 AADC measurement points. All AADC data used were collected during the growth season (i.e., November and December). The used AADC data were collected between September and October 2003 and between September and October 2007 (Fig. 1b).
The result showed that the proposed method performed better than the Comiso method across all evaluation indices (Table  340 45) with a mean difference of 5.64 cm, which was clearly less than the 14.47 cm value obtained using the Comiso method.
Although the number of AADC measurements were limited, the high accuracy and uneven distribution ensured the accuracy assessment was reliable and objective.

Comparison to ASPeCt shipboard observations in melting season 350
Although the AADC in situ data were more accurate, their amount was still limited. To evaluate the methods at larger spatial and temporal scales, ASPeCt shipboard observations were used for evaluation. More importantly, ASPeCt data include snow depth measurements during the melting season, which enabled us to test the applicability of the proposed method during this season. All ASPeCt snow depth observations within one passive microwave ratiometer grid cell were averaged and compared to passive microwave ratiometer-derived snow depth (from the proposed method and Comiso method, 355 respectively) in the same day. The operational periods of used ASPeCt data are listed in Table 6, no data can be obtained in the missing periods. All ASPeCt data as listed in Table 6 were used here, and the spatial distribution is shown in Fig. 1b. Overall, the proposed method performed slightly better than the Comiso method, which was clearly different when compared to AADC data (Table 45). ASPeCt snow depth data are usually obtained from thin ice regions, as ships tend to avoid thick ice; hence, the observed snow depth was with modal depths ranging between 0 and 10 cm (Worby et al., 2008b).
In addition, the snow depth estimation equation from the Comiso method was derived from ASPeCt data, which might be unfair for the proposed method. Nevertheless, the proposed method still outperformed the Comiso method, and the similar 365 performance demonstrated the reliability of the proposed method to estimate thin snow depth.
To show how the methods performed in different seasons and test the applicability of the proposed method during the melting season, in Fig. 5 we compared the passive microwave ratiometer-derived snow depth to the ASPeCt snow depth observations during four seasons. The performances of the two methods during the four seasons were different. The proposed method was most accurate during autumn with an RMSD of 0.10 m (13 grid cells, the same hereinafter), followed 370 by summer with an RMSD of 0.15 m (73), winter with an RMSD of 0.18 m (65) and spring with an RMSD of 0.18 m (113), which were nearly comparable. For the Comiso method, accuracy was highest during winter with an RMSD of 0.10 m (65), followed by autumn with an RMSD of 0.14 m (11), summer with an RMSD of 0.15 m (77) and spring with an RMSD of 0.22 m (119). A larger bias was found in spring than in the other seasons. Overall, the proposed method was better than or comparable to the Comiso method during spring, summer and autumn. However, it should be noted that, the amount of data 375 may also affect the performance comparison.
A clear overestimation for the proposed method can be found by comparing to the ASPeCt data in all seasons (Fig. 5), we attribute this to the underestimation of ASPeCt snow depth observations. The thickness of level ice and snow cover, and estimates of surface ridging were recorded in the ASPeCt data, the latter was used to correct the level ice thickness based on the mass of ice in ridges (Worby et al., 2008b). However, this correction was not be applied on snow depth observations, 380 hence the ASPeCt snow depth data only represented for the level portions of ice floes (Worby et al., 2008a) and deformed ice with thicker snow cover was not included (Worby et al. ,2008b). As only thinner snow cover on level ice was included, it is obvious that these data underestimated the true snow depth (Worby et al., 2008a), which explains why the snow depth estimates from the proposed method were overall higher than these from ASPeCt data. In addition, the proposed method also tends to overestimate the snow depth, as discussed in Sections 4.4 and 5. Bellingshausen-Amundsen Sea: 230°-300°). It should be noted that in some sea sectors, we could not construct the evaluations during all four seasons, due to the limited distribution of ASPeCt data. Both methods have lower accuracies in the Weddell West sector, which may be due to the thicker snow there, as the Weddell West is dominated by multiyear sea 390 ice and it has similar emission signals to snow covermost of the multiyear ice is in the Weddell West. Comparatively, the Comiso method underestimated snow depth in all sea sectors and seasons. Some negative correlation coefficients in Tables 7   and 8 can be found even in areas with comparably many grid cells, this is due to the observation bias of the ASPeCt data (± 20% bias was found for undeformed ice thicker than 0.3 m, and ± 30% bias for deformed ice, Worby et al. (2008b)). Due to the limited accuracy of ASPeCt samples, the evaluation may be biased, but ASPeCt shipborne data can still provide be 395 assumed as a proxy for performance evaluation due to its large spatial-temporal coverage. More importantly, no obvious differences could be found during different seasons in individual sea sectors, and the proposed method achieved a comparable or better performance in summer than in other seasons. Hence, the proposed method can still estimate snow depth during the melting season.   Kern et al. (2016) found that satellite laser altimeters can be used to estimate snow depth over Antarctic sea ice with a low 410 level of uncertainty, and these snow depth measurements agreed closely with both shipborne and airborne data. Considering the potential reliability of satellite laser altimeter-derived snow depth, fFollowing Kern et al. (2016), we estimated the Antarctic snow depth in a complete year (January 2019 to December 2019) from ICESat-2 using a linear equations based on total freeboard, monthly snow depth estimates from ICESat-2 were then posted onto the 25 km grid cells and compared the results to estimates from the proposed method, as shown in Figs. 6 and 7. Generally, the spatial distribution patterns of snow 415 depths estimated by the proposed method agreed closely with those derived from laser altimeters. Both snow depth datasets showed deeper snow cover mainly in the Weddell West and Bellingshausen-Amundsen Sea sectors.

Comparison to satellite laser altimeter-derived snow depth data in both spatial and temporal scales
As satellite laser altimetry is independent of the snow properties, satellite laser altimeters can better reveal snow depth evolution. Fig. 8 shows the monthly snow depth evolution in 2019 based on the two methods. Overall, the two snow depth time series were highly consistent and have an RMSD of 3 cm and a correlation coefficient of 0.86. Although the snow depth 420 ranges from the two datasets still have some differences, the overall variation patterns were similar (except in summer). The existing differences in snow depth range and variation pattern were due to sensor and method differences. In clod seasons (i.e., spring, autumn and winter), Hhigh consistency between the two datasets on both spatial and temporal scales implies the reliability of the proposed method.
An obvious snow depth overestimation for the proposed method can be found comparing to these from ICESat-2 in all 425 months of 2019. Empirical linear regression models were used to compute snow depth from ICESat-2 total freeboard measurements. These empirical models were constructed based on the local sea ice measurements from 15 cruises in the Southern Ocean over a time period of about 22 years . The limited coverage of this data set and the variable nature of snow cover over sea ice reduce the representativeness of this data set, which may contribute to the underestimation of snow depth estimates from ICESat-2, more local sea ice observation data (including snow depth, sea ice freeboard and sea 430 ice thickness) are needed to improve the snow depth estimates from ICESat-2 in recent years (e.g., 2019). Snow depth retrieval based on passive microwave radiometers is sensitive to grain size (Markus and Cavalieri, 1998) and ice type. For example, at microwave frequencies multiyear ice has a similar influence on the brightness temperatures as snow cover (Rostosky et al., 2018), and thus the snow depth over multiyear ice is overestimated in this case; in late winter/spring the grain size growth leads to a stronger reflected radiation and a reduction of the brightness temperature (Markus and 435 Cavalieri, 1998). Both of these can influence the GRs and then increase the snow depth estimates. While satellite laser altimeters are independent of the snow properties and thus suffer less from the variable snow properties than passive microwave radiometers. Thus, the difference between snow depth estimates from the passive microwave radiometers and ICESat-2 is due to their sensor and methodology difference, more observations of snow cover (including thickness, ice freeboard and snow properties) are needed to quantitatively explain the difference between these two snow depth estimates. 440 Figure 6. The spatial distributions and probability density functions (PDFs) of snow depth based on the proposed method and ICESat-2 between January and June 2019. The averaged snow depth value and its standard deviation value are shown in the upper right corner of (c), red for snow depth estimated from the proposed method, i.e., based on passive microwave ratiometer (PMW), green for ICESat-2 snow depth. 445

Spatio-temporal variation of Antarctic snow depth from 2002 to 2020 470
Although the proposed method was initially applied for snow depth estimation during the growing clod seasons (i.e., autumn, winter and spring), comparable performances were still found during the melting seasonsummer; hence, we estimated the snow depth for all seasons from 2002 to 2020 and analysed the spatiotemporal variation pattern. The averaged Antarctic snow depth distributions from 2002 to 2020 showed obvious seasonal patterns (Fig. 9). In all four seasons, thin snow covers were seen in the marginal sea ice and thicker snow was located in the Weddell West and Bellingshausen/Amundsen Sea 475 sectors, which was more obvious in summer. In winter, sea ice expands, and thicker snow cover could be found.
In Antarctic, cyclical thaw-freeze event can occur at all times (even in winter, Markus and Cavalieri, 1998); in summer due to this event the microwave signal changes rapidly within one day, and thus the brightness temperatures have large diurnal variations (Wankiewicz, 1993). This biases the snow depth estimates when daily averaged brightness temperatures are input to the snow algorithm. In summer the Antarctic is dominated by multiyear sea ice. Markus and Cavalieri (1998) 480 found that in the Western Weddell Sea where perennial ice was present, daily variations of snow depth were higher in summer (January/February). As the thaw-freeze event can lead to larger grain sizes of snow cover, which can further result in an overestimation of snow depth, this event can cause large temporal variations in the snow depth estimates (Comiso et al., 2003). Due to the larger fluctuations of snow depth estimates in summer (Markus and Cavalieri, 1998), we infer that the thaw-freeze event frequently occurs in summer and thus causes higher snow depth estimates in summer than in spring. This 485 explains why snow depth increased from spring to summer during a melting period, and also explains why the thickest snow depth for the East Antarctic and Bellingshausen-Amundsen Sea is (where has a large amount of multiyear ice) in summer.
In addition, the emission signal of multiyear sea ice in microwave region is quite similar to these from snow (Rostosky et al., 2018), hence the snow depth on multiyear ice estimated from passive microwave radiometers is indeterminate and this algorithm is more suitable for dry snow conditions (Comiso et al., 2003). Considering these, we suggest that it should be 490 cautious when applying the proposed method for summer snow depth.
In particularly, we can find that the snow depth in the Weddell West sector decreased from autumn to winter during a growing period. As we mentioned before, the variability of grain size affects the brightness temperatures, in winter the grain size increases and thus results to a stronger radiation scattering. This effect can cause a reduced brightness temperature (Markus and Cavalieri, 1998) and is stronger for higher frequencies (Rostosky et al., 2018), which leads to the 495 overestimation of snow depth. The regression coefficients in proposed method were based on snow depth measurements in October and November (i.e., winter), considering the influence of the grain size on the microwave emission (Rostosky et al., 2018) these could lead to an overestimation of snow depth in autumn with smaller grain sizes. In the other sea sectors, this effect was not obvious, hence the proposed method still has the capability in estimating the snow depth distribution in autumn. The above discussion indicates that in order to accurately retrieve snow depth over Antarctic sea ice in all seasons, 500 more in situ observations of snow cover (including thickness and properties) with comprehensive spatio-temporal representativeness are needed to derive a more robust snow depth algorithm based on passive microwave radiometers, in the meantime the detailed understanding of the influences of snow properties (e.g. grain size and wetness) on brightness temperatures are also needed.
Antarctic snow depth showed significant a decreasing trends of -0.13 cm/yr from 2002 to 2020 (Fig. 10aTable. 7). This 505 snow depth trend of Antarctic sea ice is the combined result from the six sea sectors, and the trend of snow depth may be "enhanced" or "offset". Hence, it is necessary to analyse the trend for individual sea sectors. All six sea sectors showed decreasing trends (Fig. 10), and these trends were decreasing across all four seasons.

The uncertainty from estimation methods
Growth and melting of the snow layer will change the observed brightness temperatures; hence, the numerical relationship between brightness temperatures and snow depth is not fixed. When the snow layer starts to melt, its emissivity greatly differs from that of dry snow, which causes some biases in the snow depth estimation (Willmes et al., 2014). Hence, it is 540 suggested that the proposed method in this study is limited to clod seasons (i.e., autumn, winter and spring).In the present study, we still estimated the snow depth during the melting season with the following assumptions: 1) surface melting in Antarctica is not as strong as that in the Arctic, and 2) the evaluation shows the performance of the proposed method is comparable during the growth and melting seasons. The latter may be due to the application of Although the used lower frequenciesfrequency, as they suffers less from the volume scattering caused by the seasonal variation in the snow layer 545 (such as densification or grain size increase, Rostosky et al., 2018). However, because lower frequencies are, it is less sensitive to thin snow there may be some biases for snow depth in early winter. This result explains why the proposed method performed only slightly better than the Comiso method when compared with thinner ASPeCt snow depth. Since the snow depth over Antarctic sea ice is thicker than that in the Arctic and lower frequencies are more sensitive to thicker snow (Rostosky et al., 2018), this influence is assumed to be limited. 550 In addition, at the end of winter or early spring, the top snow layer melts during the day and refreezes at night. This forms an ice layer in the snow. This ice layer will enhance the scattering intensity and lead to overestimated snow depth. In Antarctica This forms an ice layer in the upper layer of snow cover. These ice layers usually have large grains which can contribute to the increase in scattering, and thus lead to overestimated snow depth (Markus and Cavalieri, 1998). In the Antarctic, the ice-covered snow layer may be covered by new snow (Willatt et al., 2009) and this melt-refreeze cycle will 555 result in further overestimation. In additionBesides, the relationship between brightness temperatures and snow depth is affected by snow density, snow grain size, flooded sea ice and weather conditions. However, because in situ measurements of these snow and ice properties are infrequently collected, their influences cannot be quantified and are thus not considered in the existing method. This issue can be solved with future in situ measurements. Lower frequencies are less affected by these factors and are more sensitive to deeper snow. Thus, they can improve the current Antarctic snow depth estimation. 560 However, they are also more sensitive to roughness on the sea ice surface (Stroeve et al., 2006), and the spatial differences in snow emissivity derived from snow metamorphism in Antarcticain the Antarctic are rather small (Willmes et al., 2014).
Nevertheless, similar performances of estimated snow depth with those derived from ICESat-2 at both spatial and temporal scales still demonstrate the reliability of the proposed method and imply that the snow depth uncertainties caused by the factors mentioned above are relatively small and acceptable, as satellite laser altimeters are independent of snow properties. 565 Although the inclusion of low frequencies can reduce these influences, the linear regression equation may be too simple for some situations, e.g., very thin or thick snow. Some complex methods, e.g., polynomial fitting equations (Kilic et al., 2019), random forest regression models (Winstrup et al., 2019) and neural network models (Braakmann-Folgmann et al., 2019), may improve these situations. However, all these methods require more snow depth samples and much more training data if complex machine learning or deep learning technologies are used. Antarctic samples are quite sparse. Considering 570 these potential limitations and the lack of a better operational snow depth product, we assume that the linear equation can estimate Antarctic snow depth more robustly in the current stage.

The uncertainty from OIB data
Since the derivation of the regression coefficients in Eq. (14) and Eq. (25) directly depends on the applied OIB samples, the uncertainty from the OIB data has a direct influence on snow depth estimation. Most of the OIB airborne measurements were 575 taken in West Antarcticathe western of Antarctic sea ice region during October or November, and their spatiotemporal representativeness was hence limited. Nevertheless, it was the most situatable data source for equation derivation considering its large spatial and temporal scales. The comparisons to ASPeCt and AADC data both demonstrated that this equation could be used in all different seasons and sea sectors. Limited by the extreme climate and oceanic conditions in Antarcticain the Antarctic, in in situ Antarctic sea ice measurement data are still limited. When more in situ data can be 580 obtained, the corresponding algorithm can be further improved.

The uncertainty from sea ice types
It is still difficult for passive microwave radiometers to estimate snow depth over multiyear ice because multiyear ice scattering properties are similar to snow. On the one hand, reliable sea ice type data in Antarcticain the Antarctic was not accessible until now, and we still cannot derive snow depth estimation equations for different ice types. On the other hand, 585 Antarctic sea ice is mostly young, first year ice. Multiyear ice is mainly located in the Weddell West sector. No obvious overestimations could be found when comparing the ASPeCt data in the Weddell West sector to data from both methods (as shown in Tables 5 and 6). In most cases, thickness was underestimated, which indicated that the underlying ice did not affect the ratiometer signals. Hence, the influence amount of multiyear ice in the Antarctic is on snow depth estimation was assumed to be limited, and bias was mostly introduced by snow properties. This will be further improved when accurate 590 Antarctic sea ice type data and in situ measurements are available.

The uncertainty from applied spatial resolution
Coarser spatial resolutions cannot obtain a detailed spatial pattern of snow depth. Although optical or SAR images have fine spatial resolutions, they still cannot estimate Antarctic snow depth on a daily scale. The passive microwave radiometer is one of the most effective sensors for daily Antarctic snow depth derivation. Although the current spatial resolution of the passive 595 microwave radiometer is relatively coarse (25-50 km), considering the relatively flat surface of Antarctic sea ice and the urgent need for snow depth over Antarctic sea ice, the uncertainty caused by the coarser resolution is acceptable.

The uncertainty from the different spatial resolutions of satellite, airborne, shipborne and field datasets
Since the spatial resolutions of used data in this study are vastly different (i.e., satellite, airborne, shipborne and field data), the scale effect needs to be considered. Zhou et al. (2021) compared the snow depth values in various spatial grid cell 600 spacings using OIB data, and found that the limited footprint of airborne data still caused the offset of snow depth values even when the coverage of these airborne measurements is overall good. Hence, the difference of spatial resolutions will further affect the comparison and evaluation of snow depth data. As the in situ measurements (including airborne, shipborne and field data) were not extensively obtained, i.e., the spatial coverage of these data in one satellite footprint is limited, investigation of how the spatial resolution of in situ data on snow depth comparation still could not be carried out at present. 605 The reason is that airborne and shipborne data were usually obtained along the tracks, and the field measurements were spatially sparse. This effect will be quantified in future work when much more in situ data are obtained. However, considering the sea ice cover in the Antarctic is relatively flat, the uncertainty caused by data sets with different spatial resolutions should be limited and smaller than that for Arctic sea ice. 7 Data availability 610 Snow depth product (including snow depth uncertainty) over Antarctic sea ice can be downloaded from National Tibetan Plateau Data Center, Institute of Tibetan Plateau Research, Chinese Academy of Sciences at http://data.tpdc.ac.cn/en/disallow/61ea8177-7177-4507-aeeb-0c7b653d6fc3/ (Shen and Ke, 2021, DOI: 10.11888/Snow.tpdc.271653). A short summary and some auxiliary information (including file naming, required software and etc.) are also provided. 615

Conclusions
Our study updates the regression equation for estimating snow depth over Antarctic sea ice using passive microwave ratiometers. By comparing 7-year OIB snow depth measurements, we found that the GR calculated from both lower and higher frequencies, i.e., GR(37/7), was best for deriving the Antarctic snow depth. It had an RMSD is of 8.92 cm and a correlation coefficient of -0.64. The derived equation based on GR(37/7) was applied at to consistent brightness temperatures 620 from AMSR-E and AMSR-2. To fill the observation gaps between AMSR-E and AMSR-2, we used SSMIS data with a new equation based on GR(37/19) with a correction applied for consistent snow depth estimation. The estimated snow depth uncertainty analysis used a Gaussian error propagation. The mean uncertainty of the micrometer passive microwave ratiometer-derived snow depth was 3.8123.73 cm, with an average ratio of 12%, dependent on snow depth.
The self-evaluation based on the combination of OIB data in different years showed that no obvious interannual variations 625 could be found in the regression coefficients. The uncertainty of slopes from different combinations of OIB data was 42.85, which resulted in a snow depth estimation bias of <1 cm. The proposed method agreed well with the OIB data, showing a mean difference of -1.55 cm, and there was a similar snow depth variation pattern at the interannual scale. The Comiso method underestimated snow depth, with an average difference of -19.15 cm.
AADC data provided a comprehensive and unbiased assessment because they include measurements of both thick and thin 630 snow layers. In comparison to AADC in situ measurements, the proposed method outperformed the Comiso method, with a smaller mean difference of 5.64 cm and an RMSD of 13.79 cm. The Comiso method underestimated snow depth with a mean difference of -14.47 cm and an RMSD of 19.49 cm.
We suggest the proposed method be used during the growth season; however, the comparison to ASPeCt shipborne observations implied that this method could also be used during the melting season. The comparison to ASPeCt data showed 635 that the proposed method had slightly better performance than the Comiso method (RMSDs of 16.85 cm and 17.61 cm, respectively) because the ASPeCt shipborne observations were focused on thin ice. The evaluation may be somewhat biased due to the observational accuracy of ASPeCt data (a mean bias of 20% or 30%). Nevertheless, comparable accuracies could be found during both the growth and the melting seasons, suggesting that the proposed method could be applied in all seasons. 640 Acknowledgments AMSR-E brightness temperature data are derived at https://nsidc.org/data/AE_SI25/versions/3; AMSR-2 brightness 660 temperature data can be derived at https://nsidc.org/data/AU_SI25/versions/1; SSMIS brightness temperature data are derived at https://nsidc.org/data/NSIDC-0001/versions/4; OIB airborne data can be derived at https://nsidc.org/data/ILATM2/versions/2; ASPeCt Data are derived at http://aspect.antarctica.gov.au/data; AADC in situ data can be derived at https://data.aad.gov.au/metadata/records/sea_ice_measurements_databasehttps://nsidc.org/data/G10011/versions/2. We 665 thank all the data providers for their data.

Financial support
This work is supported by the Programs for National Natural Science Foundation of China [grant numbers 41976212, 41830105].