A Novel Approach to Map the Intensity of Surface Melting on the Antarctica Ice Sheet using SMAP L-Band Microwave Radiometry

The polar ice sheets have undergone unprecedented melt events in the recent past years, which have consequences for ice sheet mass balance, stability, and sea level. In this study, we employed L-band (1.4 GHz) brightness temperature observations collected by NASA’s Soil Moisture Active Passive (SMAP) mission to investigate the extent, duration and intensity of melt events on the Antarctic Ice Sheet from 2015 to 2020. Satellite microwave measurements have long been used to detect melt events because of their sensitivity to the presence of liquid water in snow and ice. The observed microwave 15 response depends on the sensor measurement frequency. Our hypothesis for this study is that the relatively long wavelength SMAP observations can detect a wider range of surface wetness conditions relative to shorter wavelength microwave observations that attain signal saturation at relatively lower wetness levels and within shallower surface layers. SMAP provides nearly all-weather surface monitoring over all of Antarctica twice daily with morning and evening overpasses at about 40 km spatial resolution. We applied an empirical threshold algorithm using horizontally and vertically polarized microwave 20 brightness temperature differences to detect surface melt events over Antarctica from 2015 through 2020. The results show that the SMAP empirical algorithm can be used to detect melt extent and duration, and the geophysical model-based algorithm can be used to detect snow wetness, which can be used as an indicator of melt intensity. Analysis of the melt seasons between 2015 and 2020 show that even though the melt extent in 2019-2020 was not as large as during the 2015-2016 melt season, it was significantly more intense, particularity on the West Antarctic Ice Sheet. 25

Antarctic Peninsula, in particular, has experienced several major ice shelf collapses as a result of a significant annual melt cycle (Datta, et al., 2019). 35 Due to their all-weather operational capability and sensitivity to the presence of the liquid water in snow, both satellite microwave radar and radiometer systems are commonly used to detect melt events over Greenland (Ashcraft & Long, n.d.;Mote & Anderson, 1995;Mote, et al., 1993;Wismann, 2000). Past studies reporting on melt events over Antarctica commonly used 19 GHz and 37 GHz frequencies available from several satellite sensors, such as the Scanning Multichannel Microwave Radiometer (SMMR) on the Nimbus 7 satellite or the Special Sensor Microwave/Imager (SSM/I) and Special Sensor 40 Microwave Imager Sounder (SSMIS) from the Defense Meteorological Satellite Program (DMSP) satellites, since the beginning of the satellite era (e.g., (Liu, et al., 2006;Picard et al., 2007;Scambos, et al., 2000;Ridley, 1993;Zwally & S. Fiegles, 1994;Torinesi, et al., 2003).
L-band (1.4 GHz) radiometer systems may provide more comprehensive information on the polar ice sheets because the larger characteristic ice penetration and sensing depth at lower microwave frequencies, which can extend up to hundreds of meters 45 (Jezek et al., 2015), (Leduc-Leballeur, et al., 2020;Jezek et al., 2018;Macelloni et al., 2019;Miller et al., 2020). In this paper, we investigated the response of the L-band radiometer on the NASA SMAP (Soil Moisture Active Passive) satellite, launched in January 2015, to Antarctica melt events (Entekhabi, et al., 2010). The objective of the study was to detect dielectric changes in the surface composition, such as snow wetness percentage, and relate those changes to melt events. Studies have shown that the surface of the ice sheet may warm to depths of about 3 m during melt events (Munneke, et al., 2018). Our hypothesis was 50 that the long wavelength measurements from SMAP are more sensitive to a higher melt intensity and deeper surface snow/firn/ice layers than the shorter wavelength measurements used by more conventional satellite microwave radiometers.
Our approach was to develop an empirical algorithm to detect melt events and a geophysical model-based algorithm to determine spatial and temporal variations in surface wetness over the Antarctica ice sheet using SMAP brightness temperature retrievals. This paper is organized as follows. In Sect. 2, we briefly talk about the SMAP data and our approach to detecting 55 melt events using SMAP microwave observations. In Sect. 3, we introduce our geophysical forward modeling, and Sect. 4 explains our empirical and model-based melt detection and snow wetness retrieval algorithms. Sect. 5 demonstrates the melt detection and snow wetness retrieval results from both the empirical and the model-based algorithms. Sect. 6 presents our conclusions. 60 2 Data and Methods

SMAP Data
NASA launched the SMAP mission on January 31, 2015; the science data production began on March 31, 2015. The L-band radiometer on-board the satellite includes vertically (V) and horizontally (H) polarized brightness temperature (TB) channels.
The SMAP TB measurements have a 38 km spatial footprint (defined by the half-power footprint on the Earth's surface of the 65 radiometer antenna pattern), and the data are gridded on a 9-km polar equal-area projection grid (Chaubell, et al., 2016). The https://doi.org/10.5194/tc-2020-297 Preprint. Discussion started: 20 November 2020 c Author(s) 2020. CC BY 4.0 License. SMAP satellite has a sun-synchronous 6AM/6PM equator-crossing orbit, a constant 40° sensor incidence angle, and an approximate 1000-km swath width (Piepmeier et al., 2017). This enables daily coverage of the Antarctic Ice Sheet with both AM and PM overpasses. The radiometric resolution of the gridded SMAP TB product is less than 0.5 K (Piepmeier et al., 2017). 70

Method
The presence of even a small amount of liquid water in the surface snowpack significantly impacts the electrical properties of snow at microwave frequencies (Ulaby & Long, 2014). This results in large changes in the microwave TB measurements, which permits melt detection and derivation of melt related characteristics (Ulaby & Long, 2014). Our method is composed of detecting melt events from the changes of normalized polarization ratio (NPR) and V-polarized TB with respect to reference 75 values computed during winter conditions, and subsequently, estimating snow wetness for melt events using a snow model. We use snow wetness as an indicator of melt intensity. The NPR is computed as follows: where and ℎ are V-and H-polarized TB, respectively. The advantage of using NPR in addition to is that it does not depend on the physical temperature of the snow and ice, but is a function of dielectric changes, which vary between different 80 seasons. snow conditions or areas that typically experience limited seasonal melting. These areas consist of layered snow and firn, and penetration depths can be up to hundreds of meters (Jezek et al., 2015). The NPR is relatively low in these areas, and Melt events cause the NPR to increase because the presence of meltwater causes a greater V and H polarization difference than under dry snow/ice conditions. The case for the negative NPR change is somewhat more complex. In areas that experience seasonal melting with complex subsurface structures like ice pipes and lenses, the penetration depth is reduced to tens of meters 90 (Miller et al., 2020). The NPR is relatively high for these areas, and the presence of meltwater during the melt events causes the NPR to decrease because it extinguishes signals with a large polarization difference emanating from structures inside the ice sheet.
After detecting the melt areas, we retrieve snow wetness based on a geophysical multi-layer snow emission model. The model relates observed TB changes to the amount of liquid water in the surface layers of the ice sheet. The model is formulated 95 somewhat differently for the increasing and decreasing NPR cases as is detailed in Sect. 3.

Forward Geophysical Modelling
In this section, we calculate the H-and V-polarization TB ( ℎ , ) for a multi-layer medium using the incoherent approach 100 of radiative transfer (RT) theory (Ulaby & Long, 2014;Tsang, et al., 2000). As the increases and decreases during the melt season depending on the location, we developed two separate models for each of these scenarios. One scenario has a three-layer medium (air, wet snow, and dry snow layers) for the case of increasing NPR, and one with a four-layer medium by adding a middle layer between the wet and dry snow layers of the three-layer model for the case of a decreasing NPR.

Three-Layer Model (Increasing NPR) 105
Fig. 2(a) shows the configuration of the three-layer model, which consists of air, wet snow, and semi-infinite dry snow layers with two boundaries at = − 1 = 0 and = − 2 = − 2 , where 2 is the thickness of the wet snow layer. In this schematic diagram, 2 and 3 are the angles of the wave propagation inside layers 2 and 3, respectively, which can be found from the known observation angle, 1 , using Snell's law. The dielectric constant of the wet snow and dry snow layers are estimated as explained in (Ulaby & Long, 2014). 110 Because of the long wavelength of L-band, the model does not include volume and surface scattering, which are critically important at higher frequencies. For simplicity, the model assumes ideal conditions for the environment, and therefore ignores other complicating factors such as radio frequency interference and atmospheric attenuation. The upward and downward traveling components of the TB in the -th layer are given by 2 ( 2 , ) = 2 ( 2 , − 1 ) 2 ( + 1 ) sec 2 + (1 − 2 ( + 1 ) sec 2 ) 0 2 where the subscript = (ℎ, ) stands for the polarization, 0 2 is the physical temperature of the second layer, and 2 = −2ℑ{ √ 2 2 } is the power absorption coefficient of the layer 2, where 2 = 1 (nonmagnetic material), and 2 = 2 ′ − 2 ′′ .
The superscripts and show upward and downward dwelling components of the TB. The boundary conditions at the top 120 and lower boundary are given by 2 ( 2 , = − 1 ) = Γ 12 2 ( 2 , = − 1 ) (4) 2 ( 2 , − 2 ) = Γ 23 2 ( 2 , − 2 ) + (1 − Γ 23 ) 0 3 where 0 3 is the physical temperature of the third layer, and Γ 12 and Γ 23 are the Fresnel reflectivity at the top and lower boundaries, respectively. It is assumed that there is no horizontal variation, and the boundaries are locally flat within the antenna footprint. Using equations (2) Finally, the estimated TB at the radiometer antenna ( ) is given by (8), which is approximately equal to the TB just above the top boundary (air-snow) as the atmospheric attenuation is assumed to be negligible in the SMAP L-band frequency (1.41 GHz). 130 https://doi.org/10.5194/tc-2020-297 Preprint. Discussion started: 20 November 2020 c Author(s) 2020. CC BY 4.0 License.

Four-Layer Model (Decreasing NPR)
shows the configuration of the four-layer model, which consists of air, wet snow, a high absorptive layer, and a semi-135 infinite dry snow layers with boundaries at = − 1 = 0 and = − 2 = − 2 , and = − 3 = −( 2 + 3 ′ ) where 2 and 3 ′ are the thicknesses of the layers 2 and 3. As the medium 3 does not fall into the category of the wet snow or the dry snow models, its real and imaginary parts are considered as two independent parameters in our model.
To streamline the TB estimation, an effective reflectivity Γ ( 2 ) and effective physical temperature 0 are used for a composite medium combining layer 3 and 4 similar to (Tan, et al., 2019). Then, after introducing the top layer 2, the boundary 140 conditions are given by https://doi.org/10.5194/tc-2020-297 Preprint. Discussion started: 20 November 2020 c Author(s) 2020. CC BY 4.0 License.
The Γ ( 2 ) is equal to the Fresnel reflectivity of layered media with electrically smooth boundaries, which also consists of the coherent interactions, and 0 is related to the TB of the composite medium of layers 3 and 4, ( 2 ), as given by (11). The ( 2 ) for this composite medium of layers 3 and 4 can be found using equations (6)- (8), as given in the Sect. 145 Finally, the observed TB can be calculated using equations (6)-(8) similar to Sect. 3.1, as it is now a three-layer medium with the above effective reflectivity and temperature.

Figs. 3(a) and (b) illustrate an example where the simulated TB decreases and the increases with increasing snow wetness 150
(three-layer model). Table 1 shows the layer properties for this three-layer model. In Figs. 4(a) and (b) the simulated TB increases and the decreases with increasing snow wetness (four-layer model). Table 2 shows the layer properties for this four-layer model.

Empirical Threshold Algorithm
An empirical threshold algorithm is used to detect melt events. The algorithm determines that a melt event has occurred if both 165 ) are greater than an empirically found threshold value, as given by (12) and (13), respectively.
where E[] stands for the mean estimator; SD[] stands for the temporal standard deviation estimator; WREF refers to the time 170 period from Oct 17 to Oct 31; All Pixels refers to taking the spatial average over all Antarctic pixels; and and are constant real numbers. This formulation relates the threshold to the variance of the NPR and , while and are used as tuning parameters to determine appropriate threshold levels for each grid cell. A melt event will be detected at time t if both 1 ( ) and 2 ( ) indicate a melt event, which corresponds to a bitwise AND operation (⋀) on 1 ( ) and 2 ( ) binary states. A logic truth table is shown in Table 3, where ( ) is a dimensionless binary state variable designating melt (1) and frozen 175 (0) conditions. The Z parameters dictate how much the NPR and TBV need to deviate from the reference level in order to result in a positive indication for melt. Conversely, the parameter determines the false alarm rate (FAR) which can be defined as (De Roo, et al., 2007;Mousavi, et al., 2018): 180 where erf( ) is the error function (Mousavi, et al., 2018). For example, the FAR will be about 2.2% and 15.8% for = 2 and = 1, respectively. Since the FAR for each day in a melt season is independent of other days, the FAR for all days in a melt season is related to the FAR for a single day, as given by Since the melt detection is based on a bitwise AND operation, the lower value of the parameter will dictate the final FAR.
Using these conditions for the and , the right value for the minimum number of days for the winter reference, , 190 and the parameters can be found by simultaneously satisfying (17a) and (17b).
A spatial average of the over all pixels can be performed to find a unique and fixed number for the required winter reference days for a given parameter. As an example, for the 2015-2016 austral melt season, Figs. Fig. 5(a) and (b) show the region of values that make the inequalities in (17a) and (17b) true (shaded green), respectively. The false region is shown in 195 red. It can be observed that a higher value would require a higher value. Even though choosing a higher value will decrease the FAR, it will decrease the number of melt days, which results in missing days. Our proposed two week interval from Oct 17-31 for the winter reference period has enough samples to satisfy these conditions with = 5 and = 10.
The threshold values for |Δ | and |Δ | using these proposed parameters are 0.010-0.011 and 6.97-7.31 K, respectively, for all the austral melt seasons from 2015 to 2020. 200 Table 3. Logic truth table for the ( ) dimensionless binary state variable. Green is for logic 1 (True), and red is for logic 0 (False). The main purpose of monitoring is to avoid false melt detection, because the may change in some cases due to the 205 changes in the snow/ice vertical structure rather than due to a melt event (because is more sensitive to the vertical structure changes than ), while mainly changes from snow wetness and temperature variations. As an example, Figs. 6 and 7 show and , respectively, measured by SMAP over the Southern George VI ice shelf (

Model Based Snow Wetness Retrieval (SnoWR) Algorithm
The snow wetness retrieval (SnoWR) algorithm uses the microwave emission models explained in Sect. 3 for either decrease  Fig. 2(a) is entirely absent during the frozen season. The LUT-MS-DECR uses the four-layer model, while the LUT-FS-DECR uses a customized three-layer model where the wet snow layer (medium 2) in Fig. 2(b) is absent. The high-absorptive layer is assumed 230 to remain unchanged between the frozen and melt seasons.
The algorithm first separates the pixels for NPR-INCR and NPR-DECR scenarios using the statistics of and and equation (12) and (13)  Next, another LUT is made by sweeping the wetness range of the wet layer ( 2 )   The snow wetness variation is well retrieved during different seasons, as shown in Fig. 11. The estimated snow wetness values are based on the model physical parameters used to match with the SMAP measurements. Because the tuning process includes an empirical adjustment of the layer parameters and in-situ snow wetness values are unavailable for an assessment and comparison, a quantitative accuracy measure of the snow wetness retrieval is not reported in this paper. However, the estimated snow wetness range is similar to measured values reported from previous studies (Willatt, et al., 2010). The retrieved snow 275 wetness in Fig. 11 is the corrected snow wetness as given by (19)

Empirical Threshold Algorithm Results
Fig . 12 shows the most recent Antarctica digital elevation model (DEM) with various ice shelves denoted (Howat, et al., 2019). 290 The Antarctica ice mask used in this study is obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS) for the 2013-2104 (Scambos, et al., 2007;Haran, et al., 2018Haran, et al., , updated 2019. This ice mask matches the outline of the Antarctica DEM in Fig. 12. Table 4 shows the melt seasons and winter reference periods used in this study. The potential melt seasons start on the last day of their winter reference period.   (12) and (13) and Table 3. Fig. A1 and Fig. A2 show that there is very little interannual variability in the and values. experienced more typical melt extent and duration (Tedesco, 2009;Tedesco, et al., 2007). The exceptions are an approximate 315 10-day melt even over the narrow strip along the Transantarctic mountains to the east of the Ross Ice Shelf during MS 2, and the recurring melting on the Amery Ice Shelf.
In comparison, previous melt detected areas with the number of melt days derived using higher frequency SMMR and SSM/I TB retrievals (Munneke, et al., 2012;Picard, et al., 2007;Picard et al., 2006;Anon., 2003) are also shown compared to the SMAP melt detection results for each season in Fig. 13. The melt areas are in general the same across the continent for both 320 frequencies in each melt season. However, the lower frequency of the SMAP L-band radiometer provides additional spatial information due to its deeper penetration depth. Because even a small fraction of surface melt will quickly saturate the higher frequency signals, they exhibit a larger uniform melt area. Columns 3 and 4 of Table 5 show the melt area percentage and median of the number of melt days derived from the empirical algorithm over Antarctica in each MS, respectively. Fig. 18 illustrates the results in columns 3 and 4 of Table 5 in a bar chart format. The melt maps show the melt extent and duration across Antarctica, but they do not convey the intensity of the melt, 330 which we derived using the snow wetness retrieval and discuss in the next Section.

Snow Wetness Retrieval Results 355
Using the SnoWR algorithm, as explained in Sect. 4.2, snow wetness is retrieved over Antarctica for each austral melt season.
Only the pixels with significant Δ and Δ are processed, as explained in Sect. 4.2, while the rest of the pixels did not show a detectable melt event. The melt pixels in the SnoWR algorithm here are the same as the empirical algorithm results, as described in Sect. 5.1. Fig. 16 shows the temporal mean snow wetness percentage retrieved across Antarctica. The figure shows that the Ross Ice 360 Shelf melt event was less intense as compared to the melting of the ice shelves along the periphery of the Antarctic Peninsula.
In addition, these ice shelves experienced more intensive melt in MS 5 compared to the other melt seasons, as shown in Fig.   17. For example, the Larsen C and Larsen D ice shelves experienced intense melting during MS 5 compared to the other melt seasons. Even though MS 1 exhibited the most extensive melt area, MS 5 had the longest duration and most intensive melt events. Column 5 of Table 5 shows the median of the snow wetness percentage over Antarctica retrieved using the SnoWR 365 algorithm in each melt season. Fig. 18 illustrates the results in columns 3 and 5 of Table 5 in a bar chart format. The retrieved wetness of MS 5 was clearly anomalous compared to the other melt seasons corresponding to the exceptional melt events in early 2020 (Robinson, et al., 2020). MS 2 and MS 5 have similar melt extent and duration, but the wetness of MS 5 separates it from the more typical seasonal melt of MS 2. In particular, the Antarctic Peninsula and the Amundsen-Bellingshausen Sea coast experienced very intensive melting, which corresponded to warm temperature anomalies in February 2020 indicated 370 https://doi.org/10.5194/tc-2020-297 Preprint. Discussion started: 20 November 2020 c Author(s) 2020. CC BY 4.0 License. from reanalysis data (Robinson, et al., 2020). There are other satellite-based studies, such as SSM/I, which shows agreement in terms of snow wetness extent over the Antarctica Peninsula (Zheng, et al., 2019), as well as some in-situ wetness measurements on the east Antarctica in the range of 0 to 4.63% with an average 0f 0.75%. These in-situ measurements were collected during September and October 2007 (Willatt, et al., 2010).

Conclusion
The ability of the SMAP L-band radiometry as a powerful passive microwave remote sensing tool to detect ice sheet melt events was demonstrated. We introduced a new way of computing Antarctica melt extent, duration and intensity using the SMAP L-band brightness temperature observations. The approach exploits the effect of the liquid water in the surface layers of the ice sheet on the L-band radiation. The long wavelength allows tracking a range of wetness conditions across the surface 390 layers, which provides additional value compared to shorter wavelength observations that saturate quickly with the presence of liquid water in the shallow layers of ice sheet. The results showed that while the extent and duration of the melt during 2019-2020 melt season was not exceptional, the intensity was substantially higher than in other years observed by SMAP,