Melt in Antarctica derived from SMOS observations at L band

Melt occurrence in Antarctica is derived from L-band observations from the Soil Moisture and Ocean Salinity (SMOS) satellite between the austral summer 2010/11 and 2017/18. The detection algorithm is adapted from a threshold method previously developed for 19 GHz passive microwave measurements from Special Sensor Microwave Imagers (SSM/I, SSMIS). The comparison of daily melt occurrence retrieved from 1.4 GHz and 19 GHz observations shows an overall close agreement, but a lag of few days is usually observed by SMOS at the beginning of the melt season. To understand the difference, 5 we performed a theoretical analysis using a microwave emission radiative transfer model that shows that the sensitivity of 1.4 GHz signal to liquid water is significantly weaker than at 19 GHz if the water is only present in the uppermost tens of centimeters of the snowpack. Conversely, 1.4 GHz measurements are sensitive to water when spread over at least 1 m and when present at depth, up to hundreds of meters. This is explained by the large penetration depth in dry snow and by the long wavelength (21 cm). We conclude that SMOS and higher frequency radiometers provide interesting complementary 10 information on melt occurrence and on the location of the water in the snowpack.


Introduction
Melt occurs in coastal Antarctica and on ice shelves during the austral summer. Its duration and extent are useful climate indicators due to their connection to surface temperature and surface energy budget (e.g. Liu et al., 2006;Picard et al., 2007).
Moreover, intense melting event has been identified as a precursor of some major ice shelf collapses (Scambos et al., 2000). 15 Thus, monitoring of the melt season contributes to characterize the seasonal and inter-annual climatic variations in Antarctica and is important to assess the future stability of the ice-sheet (Golledge et al., 2015).
Remote sensing offers a particularly relevant means to obtain information over the entire Antarctic continent and over long-term periods, given the very rare in situ measurements related to melt or liquid water (Jakobs et al., 2019). Microwave frequencies have been widely used to detect melt in polar regions exploiting the marked variation of the signal due to the high 20 absorption of microwaves by water relative to that of dry snow. Various detection algorithms have been developed for active sensors (e.g. Nghiem et al., 2001Nghiem et al., , 2005Ashcraft and Long, 2006;Kunz and Long, 2006;Hall et al., 2009;Trusel et al., 2012;Zheng et al., 2019) and passive sensors (e.g. Mote et al., 1993;Ridley, 1993;Zwally and Fiegles, 1994;Abdalati and Steffen, 1997;Torinesi et al., 2003;Liu et al., 2005Liu et al., , 2006Tedesco, 2007;Tedesco et al., 2007) and applied in the Greenland and Antarctica ice sheet. 25 1 In the case of radiometer, studies have mainly used 19 GHz and 37 GHz frequencies available since 1979 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 Microwave Imager Sounder (SSMIS) from the Defense Meteorological Satellite Program (DMSP) satellites. Since 2009, the Soil Moisture and Ocean Salinity (SMOS) satellite has provided radiometric observations at L band, a frequency capable of penetrating much deeper in the ice sheets, on the order of several hundred 30 meters at 1.4 GHz (Passalacqua et al., 2018) compared to only a few meters for the higher frequencies (Surdyk, 2002). This suggests that L-band observations could offer new information on melt.
The aim of this study is to retrieve melt in Antarctica from daily SMOS observations, and to investigate the similarities and differences with melt detected at 19 GHz. Section 2 introduces the data sets. Section 3 describes the method to detect melt and Section 4 compares the daily melt occurrence obtained with 1.4 GHz and 19 GHz observations. Section 5 presents a 35 modeling study to assess the liquid water sensitivity of brightness temperature (T B ) at 1.4 GHz and to discuss the differences with 19 GHz.
2 Data sets

SMOS observations
The SMOS mission was developed by the European Space Agency (ESA) in collaboration with the Centre National d'Etudes 40 Spatiales (CNES) in France and the Centro para el Desarrollo Tecnologico Industrial (CDTI) in Spain. This satellite is operated by CNES and ESA and carries on board a L-band interferometric radiometer operating at 1.4 GHz (21 cm) with an averaged ground resolution of 43 km (Kerr et al., 2010). The radiometer provides multi-angular fully polarized T B (Kerr et al., 2001).
The SMOS Level 3 product delivers multi-angular T B at top of the atmosphere in the antenna polarization reference frame (Al Bitar et al., 2017). The product is georeferenced on the Equal-Area Scalable Earth version 2.0 grid (EASE-Grid 2; Brodzik  The land-ocean mask used comes from the Land-Ocean-Coastline-Ice classification associated to the EASEGrid 2.0 map projections and derived from the MODIS land cover product by Brodzik and Knowles (2011) (available on https://nsidc.org/data/nsidc-55 0609).
2 2.2 Observations at 19 GHz and daily surface melting Satellite observations at 19 GHz were acquired by the Special Sensor Microwave/Imager (SSM/I) and Special Sensor Microwave Imager Sounder (SSMIS), processed by the National Snow and Ice Data Center (NSIDC, Maslanik andStroeve (2004, updated 2018)).

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Daily T B observations at H polarization are processed according to Picard and Fily (2006); Picard et al. (2007) to derive daily surface melt from 1979 to 2018 (data available from http://gp.snow-physics.science/melting). This data set provides daily melt status, i.e. presence or absence of liquid water, for every grid point on the Southern stereographic polar grid with a grid spacing of 25 km 2 . The effective resolution of the product is coarser, of the order of 40 km, close to that provided by SMOS.
To compare SMOS and SSMIS datasets, the SSMIS observations and products are collocated within the SMOS grid using 65 the nearest neighbour method. If the nearest neighbour is not flagged as "land" in the SSMIS grid, the pixel was removed from the analysis to avoid the error of comparison between the two frequencies. In this way, about 50 pixels are excluded, which doesn't affect the statistical significance of the comparison results.

Melting detection method
The algorithm to detect melt occurrence from the 1.4 GHz observations is inspired by the work at 19 GHz of Torinesi et al. 70 (2003), itself based on Zwally and Fiegles (1994). The algorithm determines an optimal threshold for every year in every pixel, and considers that any daily T B H over this threshold indicate melting occurrence. T B is measured at large observation angle (above 50 o ). In this configuration, the H polarization is favored because the emissivity of dry firn is usually significantly lower at H than at V polarization, while the emissivity of wet firn is always close to 1 at both polarizations. It results that the increase in T B from dry to wet snow is more significant at H polarization, and easier to detect.

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The algorithm uses an adaptive threshold T in each grid point and for each year given by T = M + aσ, with M the time average and σ the standard deviation of T B when snow is dry. According to the analysis of daily air surface temperature, Torinesi et al. (2003) found a suitable value of a = 3 so that most melting events correspond to daily maximum temperatures above -5 o C. This value is also typical for outliers detection (e.g. von Storch and Zwiers, 2001).
To solve the circular problem of computing M and σ for non melting days in order to detect melting days, the initial step 80 consists in calculating M in each grid point on a fixed period of one year -from 1 April to 31 March -and in setting aσ to a first-guess fixed value. Previous studies for 19 GHz used aσ = 30 K. However, we found it unsuitable at 1.4 GHz, because of the weaker sensitivity to liquid water (Section 5). We instead propose a lower first guess value of aσ = 15 K.
With these assumptions, a first guess melt time series is detected and new estimates of M and σ are computed by removing melting days from the T B series, still limiting the period from 1 April and 31 March. Melt is then detected once again using 85 the updated threshold. The process is iterated three times to ensure stable estimates. The algorithm returns a binary indicator for each day and each grid point, 0 for the absence and 1 for the present of liquid water.
This algorithm needs further correction for some false alarms found on the Antarctic Plateau where melt is known to never occur. These alarms are likely due to variations of T B H of the order of several Kelvin that were reported by Brucker et al. wind storms. Noting that these changes do not impact T B V, although melt does, we consider here that the areas with low annual standard deviation of T B V are not subject to melt. We estimated a threshold standard deviation of 2.8 K based on the fact that it excludes 95 % of grid points with surface elevation higher than 1500 m. Thus, as a final step of the algorithm, the grid points with a T B V annual standard deviation lower than this threshold are masked out that year. The beginning of the melt season detected usually largely differs between both frequencies as illustrated in Figure 2. On average, the first melting day can be detected as early as September at 19 GHz, while it is rare to detect melt earlier than  Peninsula as previously reported for 19 GHz (Tedesco, 2009;Kuipers Munneke et al., 2012;Datta et al., 2018Datta et al., , 2019Scott et al., 2019). The largest differences are observed in Filchner and Ross ice shelves where melt is detected to occur a few days every year at 19 GHz, but is insufficient to be detected at 1.4 GHz. The difference is certainly explained by the difference of sensitivity. Indeed, as these ice shelves only experience limited melt, the liquid water is likely concentrated in the uppermost few centimeters of the snowpack.
115 Figure 3 and 4 highlight that 19 GHz is more effective to detect short melting duration than 1.4 GHz. Indeed, more than 55% of the pixels where melt occurs remain wet for less than 10 days in a year according to 19 GHz observations, and about 20% remain wet between 11 and 20 days. At 1.4 GHz, the duration of the melt season is usually longer, in only 20% of the pixels subject to melt, the season is 1-10 days, it is 11-40 days in 55% of the pixels. This hints that SMOS is only sensitive to long and intense melt seasons.

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However, it also happens that some melting days are detected with the 1.4 GHz observations but not with the 19 GHz observations. This case is illustrated with the example of the Antarctic Peninsula provided by Figure 5 for the three summer seasons from 2013 to 2016. This area is known to be submitted each year to a long melting season, but an interannual variability    strong El-Niño event (Nicolas et al., 2017), this could suggest that 1.4 GHz provide another information than 19 GHz in the case of intense melting events. In this way, Wiesenekker et al. (2018) showed that a stronger than normal foehn wind, which is   ± 23 days on average, i.e. at the end of summer season. Conversely, over 225,000 melting days detected by 19 GHz during the 145 same period, 66% are not concurrently detected at 1.4 GHz.

Sensitivity to liquid water content
The sensitivity to liquid water at 1.4 GHz is investigated in order to understand the signal variations observed in Antarctica and to investigate the observed differences with the 19 GHz melt detection.

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T B is simulated with the multi-layered Dense-Medium Radiative Theory model (DMRT-ML, Picard et al., 2013), available online http://gp.snow-physics.science/dmrtml. This model is based on the radiative transfer theory (Tsang and Kong, 2001). The snowpack is represented by a stack of snow horizontal layers defined by their thickness, temperature, density, grain size, and liquid water content (LWC). Simulations are performed at 1.4 GHz and 19 GHz with an incidence angle of 55 o .
A synthetic snowpack is assumed to run simulations. Its has a total thickness of 1000 m, and is divided in layers of 5 cm 155 from the surface to 500 m and 50 m below. Temperature is 273 K from the surface to 5 m depth, then constant at 263 K up to 500 m depth and finally, linearly increasing to reach 273 K at the bottom. Density linearly increases from 300 kg m -3 at the surface to 917 kg m -3 at 100 m in depth and is constant below (Leduc-Leballeur et al., 2015). Grain size is constant at 1 mm. Picard et al. (2013) showed that grain size has an effect on the sensitivity to LWC at 19 GHz. Nevertheless, it is not expected at 1.4 GHz because the wavelength is much larger than grain size and scattering by grains can be neglected (Mätzler, 1987). (d) Daily winter SMOS observations distribution (cf. text for details) with mean (white solid) and standard deviation (white dashed).

Effect of snow density vertical variability
By modeling L-band emission at Dome C on the Antarctic Plateau, Leduc-Leballeur et al. (2015) highlighted that layering must be considered to obtain reliable T B estimation. To assess if this is also the case for wet snow, the simulations are performed with a smooth density profile and two density profiles with an added Gaussian noise of standard deviation of 10 kg m -3 and 20 kg m -3 , respectively, between the surface and 300 m depth. Figure 7 shows the DMRT-ML simulations at both 1.4 GHz and 165 19 GHz as a function of LWC, and for various thicknesses of wet snow.
For the dry snowpack (LWC = 0 kg m -2 ), the layering significantly decreases T B H from 248.1 K for the smooth density profile to 231.8 K and 196.9 K for the density profiles with standard deviation 10 kg m -3 and 20 kg m -3 , respectively. In wet snow condition, the layering effect becomes weaker as the LWC increases and is insignificant (< 4 K variations) for LWC larger than 1 kg m -2 or when water is spread over a large thickness. Thus, between dry and wet conditions, T B H difference 170 increases with the layering. The histogram only includes pixels where melting has been detected at least once and where ice thickness is 1000±50 m to match with the snowpack configuration used for simulations. The SMOS T B H average is 206.9±8.9 K. This suggests that simulations with a density variability lower than 10 kg m -3 overestimate the dry T B H and thus underestimate the variations 175 between dry and wet snow at 1.4 GHz. We thus now consider the case of a density variability of 20 kg m -3 only.
The simulations show that T B H at 1.4 GHz increases from dry to wet by 19 K when the wet snow layer is 0.25 m and 53 K when it is 5 m (Figure 7c). While in both cases, the change is high and detectable, this highlights that not only the total column amount of liquid water is important but also the distribution in depth. Additionally, Figure 7c shows that the maximum of increase of T B H is reached for LWC of 0.75 kg m -2 and 0.15 kg m -2 , respectively for the 0.25 m and 5 m thick wet snow 180 layers. This means that the LWC sensitivity of 1.4 GHz T B H is weaker when liquid water is confined in the uppermost tens of centimeters of the snowpack. This is rational for choosing a lower first guess aσ for the detection algorithm at 1.4 GHz than at the higher frequencies (Section 3).
Additionally, Figure 7c shows that regardless of the wet layer thickness, T B H reaches a maximum at a certain LWC value, which decreases when the wet layer becomes thicker. Thus, an increase in LWC is not detectable because of the T B saturation.

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This jeopardizes the possibility of using microwave observations to estimate LWC values or even the wet layer thickness.
By contrast, at 19 GHz, the density variability has no effect and the T B H variations are mainly driven by LWC. A sharp increase of 54 K is observed and the maximum is reach for LWC of 0.15 kg m -2 . The thickness of the wet snow layer has no effect (not shown in Figure 7c).
As a conclusion, these simulations show that 19 GHz is more sensitive to liquid water than at 1.4 GHz and that other 190 factors such as the vertical distribution of the water or the layering have a lesser influence. This indicates that detection of melt occurrence at the surface is more robust at 19 GHz.

Effect of the wet snow depth
We explore here the situation when the wet snow layer is buried under a layer of dry firn. This corresponds to the end of summer when the snowpack freezes up from the surface, or on the ice shelves where melt water enters the crevasses and accumulates 195 at depth. The simulations are performed with a wet snow layer (0.2 kg m -2 ), progressively moved down from the surface to 400 m depth. The wet layer thickness is 1 m at 1.4 GHz and 0.1 m at 19 GHz to moderate the sensitivity effect presented in the previous section. Results highlight that T B H is maximum when wet snow is at the surface for both frequencies and decreases within a few meters at 19 GHz and more gradually at 1.4 GHz (Figure 8). T B H is still more than 10 K higher than in dry conditions when the wet layer is at 60 m depth at 1.4 GHz. Deeper than 100 m, the difference between dry and wet T B H is 200 lower than 3 K, i.e. lower than the noise level with SMOS.
At 19 GHz, the simulation shows a T B H variation of 2 K between dry and wet when the wet snow is at 5 m depth. Thus, the sensitivity to liquid water is relatively quickly lost at this frequency if the water percolate deep into the firn. However, observations at 19 GHz should still be suitable for the detection of remnant liquid water at the end of the season, and when the snowpack is continuous, i.e. without crevasse.

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These results suggest that despite a lower sensitivity at 1.4 GHz, liquid water could be detected with SMOS up to several tens of meters at depth and this is a new information compared to that provided by existing melt product derived from 19 GHz and higher frequencies observations. The difference observed between 19 GHz and 1.4 GHz could be exploited to determine if the melt event was limited to the few first centimeters of snowpack or if water has percolated over a sufficient thickness to be detected by SMOS.

Conclusions
The L-band brightness temperature (T B ) from SMOS satellite has been explored to retrieve information about the melt season in Antarctica. Daily melt occurrence can be retrieved using previously developed algorithms for higher frequencies (Zwally and  (Picard and Fily, 2006) shows a lower rate of detection at 1.4 GHz. In particular, SMOS 215 misses short, probably weak, events, which are in contrast perfectly detected at 19 GHz.
A theoretical analysis has been performed using a snowpack emission radiative transfer model (DMRT-ML) in order to estimate the sensitivity of T B at 1.4 GHz and 19 GHz to liquid water content (LWC) and water distribution in the snowpack.
As expected from previous studies, a clear increase in T B happens when snow becomes wet. However, the simulations clearly demonstrate that 1.4 GHz is less sensitive than 19 GHz, especially when liquid water stays within the first centimeters of the 220 snowpack. A thick wet layer (> about 0.5 m) is required to trigger a sharp and detectable T B increase. Despite this limited sensitivity, the simulations show that 1.4 GHz is suitable to detect wet snow buried under a dry surface. For instance, an increase in T B higher than 10 K with respect to a dry snowpack can be observed with liquid water at up to 60 m depth according to the simulation configuration.
An avenue is a combined use of both frequencies to determine if a melt event was limited to the surface of snowpack or if Data availability. Daily occurrence of melt retrieved from SMOS available at www.catds.fr/Products/Available-products-from-CEC-SM/

CryoSMOS-project
Competing interests. The authors declare that they have no conflict of interest.