Energetics of Surface Melt in West Antarctica

We use reanalysis data and satellite remote sensing of cloud properties to examine how meteorological conditions 10 alter the surface energy balance to cause surface melt that is detectable in satellite passive microwave imagery over West Antarctica. This analysis can detect each of the three primary mechanisms for inducing surface melt at a specific location: thermal blanketing involving sensible heat flux and/or longwave heating by optically thick cloud cover, all-wave radiative enhancement by optically thin cloud cover, and föhn winds. We examine case studies over Pine Island and Thwaites Glaciers, which are of interest for ice shelf and ice sheet stability, and over Siple Dome, which is more readily accessible for 15 field work. During January 2015 over Siple Dome we identified a melt event whose origin is an all-wave radiative enhancement by optically thin clouds. During December 2011 over Pine Island and Thwaites Glaciers, we identified a melt event caused mainly by thermal blanketing from optically thick clouds. Over Siple Dome, those same 2011 synoptic conditions yielded a thermal blanketing-driven melt event that was initiated by an impulse of sensible heat flux then prolonged by cloud longwave heating. The December 2011 synoptic conditions also generated föhn winds at a location on 20 the Ross Ice Shelf adjacent to the Transantarctic mountains, and we analyse this case with additional support from automatic weather station data. In contrast, a late-summer thermal blanketing period over Pine Island and Thwaites Glaciers during February 2013 showed surface melt initiated by cloud longwave heating then prolonged by enhanced sensible heat flux. One limitation thus far with this type of analysis involves uncertainties in the cloud optical properties. Nevertheless, with improvements this type of analysis can enable quantitative prediction of atmospheric stress on the vulnerable Antarctic ice 25 shelves in a steadily warming climate.

3 cover, and föhn winds. Scott et al. (2019) identify the large-scale meteorological drivers of West Antarctic surface melt, and the approach presented here considers their application to specific locations using available satellite and surface data. If successful, then this approach can be used to assess future risk to the vulnerable West Antarctic ice shelves. For example, if melt events occur frequently under common polar meteorological phenomena such as optically thin clouds that produce the all-wave radiative enhancement, then the stress on the ice shelves might be perennially constant. Conversely, if melt events 70 occur mainly under optically thick clouds only associated with strong atmospheric rivers (e.g., Wille et al., 2019), then one might expect more of a long-term risk in a warming atmosphere. Ultimately multi-year assessment of melt event mechanisms would need to be understood in terms of the large-scale meteorological drivers (Scott et al., 2019) to make such a risk assessment. Here we demonstrate with case studies that each of the above three melt-inducing mechanisms can be identified in satellite and reanalysis data. 75

Data and Methods
Over the cryosphere the surface energy balance (SEB) can be expressed in terms of the melt energy ME (W m -2 ): where the individual energy components are the downwelling and upwelling shortwave (SW) and longwave (LW) radiation, 80 the sensible heat flux (SH), the latent heat flux (LH) and the ground conduction G. The sum of the four SW and LW fluxes is the net radiation. The sum of SH and LH fluxes is the net turbulent flux, and here we use the European Centre for Medium-Range Weather Forecasts (ECMWF) convention where a positive sign signifies energy going into the surface. Advection of air warmer than 0 º C appears in the ME as positive SH flux, whose magnitude depends on both the air temperature gradient and the wind speed. Strictly speaking equation (1) is valid when the snow surface temperature T s is at or above the melt 85 point. If T s is below the melt point and the SEB doesn't close (i.e., the net radiation is not balanced by the sum of the other energy components), it is likely due to ground conduction. Local radiative heating of a snowpack can induce melt at temperatures as low as -2 º C by internal scattering and absorption (e.g., Nicolas et al., 2017). If T s is at or above freezing a positive ME maintains surface melting while a negative ME represents a surface cooling that if sustained will reduce the surface temperature below freezing. A negative ME also represents a phase change (i.e., refreezing of the surface, if the T s is 90 at the melt point. The actual cooling happens through LW radiation and ground conduction. On daily timescales, G over Antarctic firn is usually an order of magnitude smaller than the individual radiative and turbulent flux components (e.g., van Fisher et al. 2015), though it can become somewhat important on sub-daily timescales (i.e., warming of the snowpack in the morning, and cooling it at night, after potential refreezing).

4
If the ME remains positive across at least two diurnal cycles, then this condition combined with skin or 2-m air temperatures at or just below freezing is often associated with a surface melt that is detectable in satellite passive microwave (PMW) data (Nicolas et al., 2017). This does not mean that surface melt is occurring throughout those diurnal cycles. Melt occurs only when T s is between -2 º C and 0 º C, depending on surface microphysics. At colder T s , the positive ME goes into warming the snowpack but does not cause detectable melt. The PMW data are instantaneous observations made twice daily (morning and 100 evening overpasses). If the PMW-measured brightness temperature (T b , section 2.1 below) is consistent with a significant increase in surface emissivity as compared with the previous observation, this signifies a moistening of surface firn layer and/or accumulation of meltwater in response to a positive ME at T s ≥ -2 º C. Identification of a time interval in the ME time series that remains positive across two or more diurnal cycles should therefore be regarded as a strong indicator of satellitedetectable melt at some point during the interval. 105 The largest individual terms in (1) are the upwelling and downwelling radiative fluxes, and they are strongly modulated by cloud cover, which is extensive over West Antarctica . Therefore the net (downwelling minus upwelling) radiative fluxes are just as capable of driving ME > 0 for extended time periods as a strong impulse of positive SH flux. The result is that three distinct mechanisms for inducing surface melt can be at play over West Antarctic ice sheets, either 110 individually or in conjunction reinforcing each other.
One mechanism is thermal blanketing. If an airmass contains overcast cloud cover within a few hundred meters of the surface having liquid water path (LWP) > 50 gm -2 , this cloud cover will radiate in the LW as a blackbody at very close to surface temperature, while also attenuating the net SW flux. The result is a surface net LW flux close to zero, and sometimes 115 even positive, along with a constantly positive net SW flux that has a diurnal cycle of relatively small amplitude. If the net turbulent flux is also positive such that the ME remains positive over two more diurnal cycles, this will usually induce surface melt, if the starting skin temperature is warm enough (e.g., Trusel et al., 2013). This situation prevailed during the large-scale January 2016 melt event over West Antarctica (Nicolas et al., 2017). Wille et al. (2019) have correlated most Antarctic surface melt events with the presence of atmospheric rivers (ARs). If ARs impinging on the Antarctic continent 120 tend to bring mainly large cloud LWP, then thermal blanketing would be a widespread source of stress on the ice shelves.
A second mechanism involves an all-wave (SW plus LW) radiative enhancement by optically thin clouds. Bennartz et al. (2013) discovered this cloud radiative effect and showed that is extensive over the Greenland Ice Sheet (GIS) during warm summers that drive surface melt. When overcast or broken cloud cover has LWP between 10-40 g m -2 , generally very 125 common in the Antarctic atmosphere (e.g., Bromwich et al., 2013;Scott & Lubin 2014;, this cloud cover will radiate substantially toward the surface in the LW while still allowing large SW fluxes to reach the surface. In combination with a mostly positive net turbulent flux, these clouds can often prolong a positive ME over multiple diurnal cycles, causing surface 5 melt. Van Tricht et al. (2016) found an additional role for optically thin low cloud cover, in slowing down the refreezing of meltwater, and this effect may also appear in one of our case studies. 130 A third mechanism very common throughout Antarctica is a föhn wind (Elvidge and Renfrew, 2016). The föhn effect occurs when an airmass crosses high terrain such as a mountain range. As the airmass is forced upslope it expands and cools, and the moisture condenses and may form clouds or precipitation, releasing latent heat. Adiabatic descent on the lee side of the high terrain warms the air even more substantially than the latent heat release and, combined with turbulent mixing upon 135 reaching the lower terrain, brings a large positive turbulent flux input to the surface, potentially great enough to initiate surface melt. Föhn winds are especially prevalent on the lee side of the Antarctic Peninsula, causing stress to the Larsen C Ice Shelf (e.g., Elvidge et al., 2015;King et al., 2017;Datta et al., 2019). However, due to widely varying high terrain over Antarctica, in particular the Transantarctic Mountains, föhn winds can occur and impact an ice shelf depending if the prevailing synoptic conditions yield airflow perpendicular to mountainous terrain (e.g., Zhou et al., 2018). 140

Melt Detection
We identify the Antarctic surface melt events with a standard PMW technique using the Defense Meteorological Satellite Program Special Sensor Microwave Imager/Sounder (SSMIS), but with a new NASA-supported Making Earth System Data Records for Use in Research Environments (MEaSUREs) data product archived at the National Snow and Ice Data Center 145 (NSIDC). We use the Equal-Area Scalable-Earth Grid version 2 (EASE-Grid 2.0) Level-2 PMW brightness temperature (T b ) at 19.35 GHz with horizontal polarization (19 GHz-H; K-band) from the evening overpass at 25-km grid spacing (Brodzik et al., 2016(Brodzik et al., , updated 2020. We base our melt detection technique on an algorithm originally proposed by Zwally & Feigles (1994) and subsequently refined and validated by Torinesi et al. (2003) and Tedesco (2009). For a given grid cell, surface melt is detected when the PMW T b measurement exceeds the prior cold season average by 30 K. The cold season average is 150 constructed by averaging daily T b measurements from 1 April of the prior year through 31 March of the given year. This average is then repeated twice, each time after removing daily values >30 K above the previous average. This technique is generally used to detect and map surface melt over large areas and on seasonal timescales. Here we examine monthly T b time series in the three regions depicted in Figure 1. The Pine Island and Thwaites Glacier region 155 presents the greatest concern for West Antarctic Ice Sheet (WAIS) loss (e.g., Alley et al., 2015). Siple Dome is a site at an intermediate elevation on the WAIS (607 m above sea level) that has a multi-decadal automatic weather station (AWS; Lazzara et al., 2012) record and a US Antarctic Program (USAP) summer field camp that has been used for some field work on the physics of snowmelt (Das and Alley 2005;. Siple Dome is considered here because it is accessible by the US Antarctic Program for future field work. In addition to the AWS, the University of Wisconsin Antarctic Meteorological 160  Research Center archives manual surface weather observations from numerous field camps and expeditions, and some of these are available for our case studies, over Pine Island Glacier and Siple Dome. We choose a third location on the Ross Ice Shelf (RIS) near the Transantarctic mountains that contains two AWS, Tom (84.430°S, 171.455°W) and Sabrina 84.248°S, 170.044°W), whose data have suggested the presence of strong föhn winds. 175 In the AWS measurements, a föhn condition can be inferred from an increase in wind speed along with a south to southeasterly wind direction from the Transantarctic mountains. Each of the regions depicted in Figure 1 contains between 800-1300 25-km EASE-Grid cells. This gives us an opportunity to examine local-scale spatial variability resulting perhaps from varying topography or differential melting and refreezing frequency across the local domain, in addition to time variation. In the monthly T b time series, we identify melt events of short duration (<5 days) by comparing the daily mean, 180 median, and range with the prior cold season average and the 30-K melt detection threshold. Short duration melt events provide relatively straightforward case studies in which we can readily identify the changing meteorological conditions and shifts in individual ME components that lead to melt onset and subsequent recovery. Such case studies allow us to observe the basic physics and develop an understanding of what is driving these surface melt events at a local spatial scale.

Surface Energy Budget Analysis 185
For our SEB analysis, we use the fifth-generation ECMWF meteorological reanalysis data (ERA5; Hersbach et al., 2020).
Previous studies have shown better agreement between ECMWF data and Antarctic in situ data than other reanalysis models (e.g., Lenaerts et al., 2017). The ERA5 model physics includes prognostic determination of cloud water and ice, cloud fraction, rain and snow (Hersbach et al., 2020), more modern atmospheric radiative transfer schemes than its predecessor ERA-Interim (Dee et al., 2011), and a sophisticated snow component in the land surface model (Dutra et al. 2010). We 190 compute ME using the surface radiative and turbulent fluxes on a 0.5°x0.5° latitude-longitude grid with hourly time resolution. Other ERA5 fields we analyse include the near-surface (2 m) air temperature, skin temperature, and 850 hPa wind components.
Because of known errors in polar cloud microphysics simulated by ERA5 and other reanalysis and regional models (e.g., 195 Silber et al., 2019), we found it necessary to supplement the ERA5 ME calculations with satellite-retrieved cloud properties.
We therefore use satellite data products from the NASA Cloud and Earth's Radiant Energy System (CERES) program; specifically, the synoptic 1-degree (SYN1deg) data product. Here CERES top-of-atmosphere (TOA) fluxes, surface fluxes, cloud masking and cloud properties are interpolated to hourly time resolution using geostationary satellite data and gridded to 1° in both latitude and longitude. The SYN1deg product contains NASA A-Train retrievals of cloud LWP and IWP based 200 primarily on the Moderate-Resolution Imagine Spectroradiometer (MODIS) data from the Aqua spacecraft (Rutan et al., 8 2015). Radiometric calibration uncertainty with the MODIS sensor itself is generally taken to be 5% in all bands, for the purpose of evaluating retrieval uncertainties (Platnick et al., 2017). In the MODIS radiative transfer-based retrieval algorithms that use an independent homogeneous pixel approximation, uncertainty in cloud optical depth is of order 10% in the range 3-20 (Platnick et al., 2004;2017), and increases for both smaller and larger cloud optical depths. Over polar 205 regions, Khanal and Wang (2018) have identified additional uncertainties and biases resulting from mixed-phase cloud effects, large solar zenith angles, and cloud spatial inhomogeneity. For the purpose of this study, MODIS-based cloud property retrievals have shown consistency with ground-based remote sensing data from West Antarctica (Wilson et al., 2018), sufficient to discriminate between optically thin and optically thick clouds associated with the distinct mechanisms that induce surface melt. 210 We analyse our case studies by calculating the ME with ERA5 radiative and turbulent fluxes, and then examine the CERES SYN1deg cloud LWP and IWP as a separate check on the realism of cloud properties simulated by ERA5. Justification for this approach is given in Appendix A.

Results and Discussion 215
We organize this work into four case studies, the first three of which involve synoptic conditions that drive surface melt events lasting several days at one location. The final case involves synoptic conditions that drive surface melt over the entire Amundsen Sea Embayment (ASE), with contrasting mechanisms at each of the locations considered herein.

Siple Dome January 2015
Our first case study reveals evidence of an all-wave radiative enhancement by optically thin clouds, which led to satellite-220 detected surface melt on Siple Dome between 5-7 January 2015. As seen in Figure 2, during these days a low-pressure system over the Ross-Amundsen Sea experienced blocking by a weak ridge of high pressure. This synoptic set-up drove a warm, moist marine air intrusion over Marie Byrd Land, which subsequently descended over Siple Coast, causing adiabatic warming and drying of the airmass. This descent may have reduced the optical thickness of any previously thick clouds into the Bennartz et al. (2013) thin cloud range (LWP = 10-40 g m -2 ). 225 Figure 3a shows the daily T b statistics throughout the Siple Dome region depicted in Figure 1. The surface melt detected by the satellite, using the 30 K threshold, begins in some of the region on 5 January and extends through most of the region over the next two days. This is seen in the relative number of T b data points above and below the 30 K threshold as depicted by the daily box plots. Figure 3b shows estimates of the surface emissivity sampled from five grid cells with T b values ranging 230 from the 5th to 99th percentiles on 6 January. These grid cells were chosen from within the Siple Dome region with the 235 criteria that they have a fully overlapping ERA5 grid cell, and span a range of 5 to 99th percentile referenced to the max T b observed in the region. Here surface emissivity is approximated as the ratio of the satellite-measured T b to the ERA5 skin temperature. Before this short melt event, and also beginning four days after it ends (after the 12th), the surface emissivity appears to be spatially uniform. During the melt period the surface shows large variability in emissivity throughout the 10 240

Figure 3. (a) Time series of daily evening overpass SSMIS brightness temperatures T b over the Siple Dome region
during January 2015 as daily statistics, with the box denoting the first to third interquartile range (Q 1 to Q 3 ), the horizontal line in the box denoting the median, the green dot denoting the mean, the whiskers denoting the distance

K above the prior cold season mean (Tedesco 2009). (b) Five estimates of surface emissivity sampled throughout
the region with percentiles referenced to the maximum T b value in the region on 6 January. 11 region, possibly reflecting differential surface properties resulting from non-uniform snow accumulation or refreezing from prior melt periods. Examples of spatial variability in the satellite-measured T b , on the day when the surface melt is most 250 pronounced, are shown in Appendix B. Figure 4 presents time series of the individual ME components. The shaded period of interest contains the melt onset, peak and decrease to when most pixels show no satellite-detected melt. Cloud cover reduces the net SW flux to a monthly minimum on 6 January, while at the same time the net LW flux rises from < -50 W m -2 to ~ -25 W m -2 ( Figure 4a). The total 255 net radiation is at a monthly maximum on 6 January ( Figure 4b). SH flux is small but mostly positive between 5-9 January (Figure 4c), resulting from warmer air just above the surface but this is largely cancelled by mostly negative LH flux so that the net turbulent flux (Figure 4d) does not remain positive over more than one entire diurnal cycle between 5-9 January. The ME remains positive over two full diurnal cycles 6-7 January (Figure 4e), but at no other time in January. This corresponds with a monthly maximum in 2 m air temperature and skin temperature ( Figure 4f). 260 Cloud LWP and IWP ( Figure 5) show discrepancies between ERA5 and CERES SYN1deg, but overall suggest the presence of optically thin cloud cover. ERA5 predicts very low LWP but an impulse of high IWP on 6 January. This may be unrealistic, as Silber et al. (2019) show that ERA5 often produces too much cloud ice water and too little cloud liquid water over West Antarctica. In contrast, CERES data indicate low IWP but an impulse of elevated LWP that briefly reaches a 265 maximum of 49 g m -2 on 6 January. Throughout 5-9 January, the CERES average LWP is 21.2±13.7 g m -2 . We note that the ERA5 radiative transfer algorithm uses the high IWP values when computing the SW and LW fluxes in Figure 4a Examining the vertical profiles in cloud water content over 5-9 January, we find that maximum liquid water content occurs mainly in the pressure range 850-950 hPa, while maximum ice water content occurs in the more vertically extensive pressure range 700-850 hPa (figure not shown). Although the ERA5 IWP values exceed 80 g m -2 on 6 January, they are still likely to 270 manifest as an optically thin cloud in the radiative transfer calculation if the effective cloud particle size is in the range 40-50 µm observed for Antarctic clouds (e.g., Scott and Lubin, 2016). In this case, the cloud optical depth would most likely be less than 5, as opposed to a liquid water cloud that, with effective droplet radius of order 7-10 µm, would have an optical depth of order 10-15 and would therefore radiate in the LW as a blackbody at a temperature characteristic of the pressure range 850-950 hPa. The higher and more vertically extensive range of the ERA5 cloud ice water content on 6 January also 275 signifies colder radiating temperature and therefore smaller LW flux emitted to the surface. This case study underscores the need for improvement in mixed-phase cloud microphysics used in reanalysis models. Gilbert et al. (2020) have demonstrated how surface SW and LW fluxes governing surface melt on the Larsen C Ice Shelf are sensitive to cloud vertical profile as well as thermodynamic phase, and the same considerations apply to West Antarctica. We also note that CERES data show a second impulse in cloud LWP on 9 January. Being absent in the ERA5 cloud simulation, its effect does not appear in the 280 radiative fluxes in Figure 6a-b. However, it may help to explain the satellite T b signals of partial surface melt in the region  Field camp observations between 5-9 January indicate mostly broken and overcast cloud cover with cloud bases between 900-1800 m and unrestricted visibility, occasionally dropping to ~250 m in reduced visibility with freezing fog or mist and light fog during 8-9 January. On 5-6 January the observer remarks "Sun dimly visible" through the overcast. These observations are qualitatively consistent with optically thin cloud cover. 300 14

Pine Island and Thwaites Glaciers January 2012
We next investigate a melt event that is clearly driven by clouds, during synoptic conditions that normally don't favour surface melt. Early January 2012 experienced strong positive Southern Annular Mode (SAM) conditions, as evidenced by the anomalously low geopotential heights over Antarctica in Figure 6. Such conditions, accompanied by strong circumpolar 305 westerly flow, are associated with reductions in meridional heat exchange with lower latitudes. Therefore, this scenario is typically not conducive to melting on the ASE region (Scott et al. 2019). However, during the brief period of interest, a highpressure ridge developed over the northern Amundsen Sea, off the tip of South America (not shown). This briefly diverted the large-scale flow toward the ASE region and provided an impulse of heat and moisture to the area.
Our period of interest shows a modest melt signal (Figure 7a), with the mean satellite PMW T b reaching the standard 30 K 310 detection threshold only on 6 January. However, we note that throughout January 2012 the upper bound of the T b sample is near or slightly above the 30 K detection threshold. In Figure 7b we see that all the sampled surface emissivity estimates are larger than 0.8, in contrast to the lower values observed over Siple Dome outside of melt periods.
During our period of interest 4-8 January, the radiative fluxes show a strong modulation by cloud cover (Figure 8a), with net 315 SW flux attenuated by nearly a factor of two relative to most of the rest of the month, and with net LW driven to nearly zero.
The result is that the net total radiative flux remains positive across three diurnal cycles. The SH and LH fluxes (Figure 8c) are much smaller in amplitude and the net turbulent flux drops below zero every day (Figure 8d). It is primarily the radiative flux terms that keep the ME positive across nearly four diurnal cycles (Figure 8e). The corresponding 2m air and skin temperatures rise steadily during this interval to a monthly maximum on 7 January (Figure 8f), which is the second strongest 320 day in the satellite melt detection signal (Figure 14a). We note that two other short periods, 16-17 January and 20-21 January, show ME > 0 across two diurnal cycles. However, the 2m air and skin temperatures are well below freezing during these periods, and satellite melt signatures are barely detectable (Figure 7). During 4-8 January the 2m air and skin temperatures approach freezing, which is generally necessary for melt onset even when the primary energy input is from a cloud radiative impulse. 325 The cloud LWP estimates (Figure 9a) show consistency between ERA5 and CERES during 4-8 January, although ERA5 appears to underpredict LWP for most of the rest of the month. ERA5 again appears to overpredict IWP during the melt period of interest, by more than a factor of two compared with CERES. During 4-8 January the CERES LWP is mostly within the thin cloud range (10-40 g m -2 ) associated with the Bennartz et al. (2013) all-wave radiative effect. CERES IWP is 330 almost as large as the LWP, which again may reflect errors in MODIS-based phase discrimination. Considering the CERES combined LWP and IWP, it remains unclear if the cloud radiative impulse (Figure 8a,b) is due to the Bennartz et al. (2013) all-wave effect or to thermal blanketing by optically thicker cloud cover. And the ERA5 radiative transfer algorithm produces the fluxes in Figure 8a using the large cloud IWP values that are almost certainly in error. This case study clearly shows the role of clouds in altering the ME to enhance surface melt, but also underscores the need to improve both satellite 340 retrieval and reanalysis cloud microphysics to obtain a complete understanding.

350
The field camp on Pine Island Glacier recorded broken to overcast cloud cover with bases 300-600 m on 4 January, with ceilings dropping to 150 m on 5 January. On 6-7 January at least two cloud layers were observed, with variable ceilings mostly below 2000 m. Throughout 8 January sky coverage steadily reduces from broken to scattered/few. Light snowfall is the most consistent present-weather condition between 4-8 January, but there are also episodes of mist, freezing fog, drifting snow and blowing snow. Qualitatively these observations might suggest optically thicker cloud cover. 355

Pine Island and Thwaites Glaciers February 2013
We now examine a late summer melt event driven by thermal blanketing on Pine Island and Thwaites Glaciers in February, when climatological surface and lower tropospheric temperatures are typically several degrees cooler than in January.
During late February 2013, an amplified ridge of high pressure developed and remained stationary over the Amundsen-Bellingshausen Seas (Figure 10). At the same time, a low-pressure system formed and deepened over the Ross Sea. This 360 365 resulted in strong and sustained meridional flow of heat and moisture into West Antarctica, which lasted for 5 days. Such synoptic conditions are highly conducive to surface melting along the West Antarctic coastline and were likely critical for 20 causing the observed late-summer melt. This synoptic pattern is a signature of the Amundsen Sea Low Clem et al. 2017), and is representative of frequent surface melting in the area (Scott et al., 2019).

370
In Figure 11a, satellite PMW data show a three-day, partial-surface-melt signature in the Thwaites and Pine Island Glaciers region from 20-22 February 2013. Surface emissivity (Figure 11b) has relatively large spatial variability throughout this local region. For our melt period of interest between 19-21 February, the radiative fluxes ( Figure 12a) show a clear signature of thermal blanketing by optically thick cloud cover. The net SW flux is attenuated by a factor of three compared with the earlier weeks in February, such that its diurnal amplitude is only ~20 W m -2 . The LW flux is positive, signifying optically 375 thick clouds that are warmer than the surface. The net radiative flux (Figure 12b) is positive over the diurnal cycles 20-21 February. We also find positive SH flux (Figure 12c) that yields positive net turbulent flux (Figure 12d) across the entire melt period of interest. This positive turbulent flux is comparable in magnitude if not greater than the net radiative flux between 19-21 February. Then between 21-23 February, as the cloud radiative effect diminishes such that the net radiation drops below zero each day, the SH flux doubles in magnitude to sustain the positive ME until 23 February (Figure 12e). The 380 result is a steady rise in 2m air and skin temperatures from 20 February, when the satellite melt signature is first detected, to nearly the freezing point by 21 February and staying this warm for another four days. Even though these temperatures remain close to the freezing point for several days, the satellite melt signature decreases as the ME decreases and resumes a diurnal cycle that drops below zero.

385
The cloud properties during this melt period ( Figure 13) are mainly consistent with large optical thickness. The CERES average LWP and IWP are 34.9±25.8 g m -2 and 47.8±27.4 g m--2 , respectively. While this larger IWP may reflect errors in phase discrimination, the suggested total cloud water content is higher than that associated the Bennartz et al. (2013) allwave effect, and instead indicates primarily a longwave surface warming where a low cloud radiates as a blackbody, with a muted SW diurnal signal. ERA5 LWP and IWP are significantly larger than the CERES retrievals, and may be overestimated 390 due to microphysical errors, but their timing is consistent with the CERES detection of optically thick clouds. In this case study, we therefore see a thermal blanketing effect that is initiated in the first two days by a cloud radiative warming, and then sustained for another two days by elevated SH flux.

West Antarctica and Ross Ice Shelf December 2011
We now consider a meteorological event that triggered surface melting at all three regions considered in this study. In late   (Figure 15), and on 20-21 December most satellite T b measurements are consistent with unambiguous surface melt (also see Appendix B). Examining the surface emissivity samples (Figure 15b) we see considerable spatial variability throughout the month. Between 2-18 425 December some of the grid cells show surface emissivity in the "dry snow" range (<0.80), while others are in a range (>0.80) that may signify wet or otherwise altered firn (e.g., Mätzler, 1987). We notice in Figure 15a that the top of the T b range in all days between 1-18 December is near or slightly above the standard 30 K melt detection threshold. In Figure 15b the sampled percentiles are referenced to the maximum T b on 21 December. We notice that the sampled grid cells reaching the 75th and 99th percentiles had very low surface emissivity earlier in the month. Figure 15b therefore illustrates complexity in local-430 scale surface properties at these low elevation locations near the coast. This complexity might arise from repeated melting and re-freezing episodes, combined with more intense episodes of precipitation, as well as varying topography especially near Pine Island and Thwaites Glaciers.

At Pine Island and Thwaites Glaciers the melt period of interest is between 19-25 December
Over Siple Dome this synoptic condition led to several satellite T b measurements in the > 30-K threshold melt detection range between 22-26 December 2011 (Figure 16), a less pronounced melt signature than in January 2015 but nevertheless 435 detectable. In Figure 16b, we again see spatial uniformity in sampled surface emissivity throughout the prior three weeks; then during the melt period of interest, some surface emissivity values remain low and within the "dry surface" range (e.g., Mätzler, 1987)     Examining the SEB components at Siple Dome, we see that cloud radiative effects (Figure 19a,b) do not substantially alter the SEB until late in the melt period of interest (22)(23)(24)(25)(26). This melt event instead appears to be induced and dominated by an impulse of SH flux that begins on 19 December (Figure 19c), associated with the warm air intrusion, and causes the net turbulent flux (Figure 19d) and the total ME (Figure 19e) to remain positive through two diurnal cycles before 470 the satellite PMW data show signs of surface melt. During the satellite melt detection period, the ME actually drops below zero at the lowest Sun elevations, even as the ERA5 2m air and skin temperatures rise steadily (Figure 19f).
At the RIS location the relevant energy inputs appear to precede the satellite melt signature detection by approximately two days (similar to Siple Dome). For the SEB components ( Figure 20)  Kuipers Munneke, 2012b; 2018; Datta et al., 2019;Elvidge et al., 2020). The maximum in ME on 21 December corresponds with a local maximum in 2m air and skin temperatures (Figure 20f), which increased by nearly 10K until they are close to freezing. The ERA5 daily maximum in 2-m air temperature continues to rise to above freezing on the 24 th and peaking on the 25 th , before returning to sub-zero temperatures.
The cloud properties at Pine Island and Thwaites Glaciers (Figure 21) show impulses of high LWP and IWP simultaneously 485 detected in CERES remote sensing data and simulated by ERA5. The LWP simulated by ERA5 is twice as large as that retrieved by CERES, and the radiative transfer model providing the fluxes in Figures 18a,b responds to this high LWP. The IWP is consistent between ERA5 and CERES, but we note that both could be artefacts: the ERA5 values might be an overestimate per Silber et al. (2019), and the CERES retrievals could also be an overestimate based on occasional difficulties in phase discrimination when using MODIS spectral reflectances (e.g., Platnick et al., 2017). Nevertheless, the information 490 within the melt period of interest in Figure 13, specifically the total cloud water path (liquid plus ice), is highly consistent with optically thick clouds that provide most of the thermal blanketing effect in this case study. A field camp on Pine Island Glacier recorded mostly few and scattered clouds between 20-27 December. The timing of the two periods of increased sky coverage is consistent with the maxima in LWP and IWP of Figure 13. Late on 20 December and early on 21 December, the sky became broken to overcast with cloud base 1800 m. During 24 December the visibility dropped to 100-800 m in freezing 495 fog and blowing snow. These observations do not definitively indicate optically thick clouds, and it is possible that this specific field camp location had lighter cloud cover than average for the entire region considered in this case study.  We now examine the local-scale meteorology at the RIS location in more detail, to illustrate the föhn wind effect. Figure 24 shows ERA wind speed and direction at the surface and at 850 hPa. Between 9-19 December winds are light to moderate, 535 and have a variety of directions but are mostly northerly between 9-14 December and 18-19 December. During the melt period 23-25 December, surface and lower troposphere winds strengthen and their directions become more spatially uniform, mainly easterly to southeasterly, consistent with descent into the region from the Transantarctic mountains. speed is consistently stronger and wind direction is more consistently southeasterly at both AWS than in the ERA5 reanalysis data, although the 2m surface air temperatures compare well. A possible cause of this discrepancy might be the coarse spatial resolution in ERA5, yielding an underprediction of föhn winds (e.g., Trusel et al., 2013). The ERA5-based analysis (Figures 20 and 23) suggests that the initial föhn wind onset combined with a cloud radiative enhancement gradually set up the conditions starting on 20 December that lead to satellite PMW melt signature detection on 23 December. Absent 555 the cloud radiative enhancement after 22 December, the AWS data suggest that persistent föhn winds alone can sustain the surface melt conditions for several more days. We do note that the underprediction of föhn winds in ERA5 might be offset by larger LWC and IWC that are retrieved in the CERES data ( Figure 23).
Finally, we note that between 1-9 December there are strong surface and lower troposphere winds from a southeasterly 560 direction, seen in both ERA5 and AWS, that induce consistently positive SH flux and positive net turbulent flux over at least three diurnal cycles. These observations would also be consistent with föhn winds from the Transantarctic mountains. Skin temperatures and 2 m air temperatures are also 3-5 K warmer than during the subsequent time interval 9-19 December.
However, cloud cover appears to be consistently light in both the ERA5 simulations and CERES retrievals (Figure 23 allows for LW cooling (Figure 20a), and the total ME remains mostly negative before 19 December. Early in December the synoptic conditions discussed above have not yet set up the warm air intrusion that brings moisture and cloud cover to all 570 three locations. A downslope wind by itself may not be sufficient to cause a detectable surface melt event (e.g., King et al., 2017), but may need to operate in conjunction with additional conducive atmospheric conditions.

Conclusion
In this study we demonstrate that readily available climatic data, including meteorological reanalysis and satellite remote sensing, can be used to examine and diagnose individual episodes of surface melt over Antarctic ice sheet and ice shelf 575 locations that are of significant concern in a steadily warming climate. We demonstrate examples for each of three thermodynamic mechanisms that induce surface melting. The case study from January 2015 over Siple Dome very likely involves the same all-wave cloud radiative enhancement discovered over the GIS (Bennartz et al., 2013;Van Tricht et al., 2016).  Bell et al. (2017) show that local-scale variability on Antarctic ice shelves influences whether surface meltwater filters into the ice as a source or hydrofracturing or runs off in temporary rivers. Local-scale spatial inhomogeneity on the ice 590 shelves probably requires further investigation to make reliable projections regarding multi-year stress.
Two limitations stand out with the present level of analysis. First, improvements are needed in cloud microphysics and related optical properties in both the reanalysis models and in the satellite remote sensing retrievals. AWARE ground-based remote sensing data have fostered some progress in this respect, in providing confidence in MODIS retrievals of cloud 595 microphysical properties (Wilson et al., 2018), and in providing unique data for modelling case studies (Hines et al. 2019;Silber et al., 2019;Lubin et al., 2020). Presently throughout the ASE, although the presence of cloud in a case study is reliably detected, the microphysical uncertainties sometimes prevent a full diagnosis of the melt event mechanism. For example, in the January 2012 case study over Pine Island and Thwaites Glaciers, a cloud radiative effect is clearly indicated but it is not clear if this is a thin cloud all-wave effect or an optically thick thermal blanketing effect. In atmospheric models, 600 the use of double-moment cloud microphysical parameterizations makes noticeable improvements over Antarctica (e.g., Hines et al., 2019). However, these more rigorous parameterizations are found mainly in global climate models. Numerical weather prediction models, which are used to generate reanalysis data, must run on an operational forecast schedule and may not be able to accommodate the time-consuming rigorous parameterizations.

605
We mention that one regional model is known to be useful for this type of work. This is the European Regional Atmospheric Climate Model second version (RACMO2; van Wessem et al., 2018). Lenaerts et al. (2018) have used RACMO2 to accurately simulate West Antarctic melt events between 1979. In RACMO2, van Wessem et al. (2014 addressed the common cloud LWP deficiency over Antarctica by altering the model cloud microphysics to allow for more extensive cloud liquid water transport. This is done primarily by making simple but defensible adjustments to the threshold for ice 610 supersaturation (Tompkins et al., 2007), and the critical cloud content for efficient precipitation (Lenaerts et al., 2018).
While these simple alterations allow for sufficient cloud liquid water to contribute radiatively to positive ME and surface melt onset, the simulated LWP values have yet to be thoroughly validated against other data such as SYN1deg. It is therefore not clear if RACMO2 simulations by themselves can discriminate between the mechanisms involving optically thick versus optically thin clouds, and supplementing RACMO2-based analysis with SYN1deg data is therefore recommended. 615 In the MODIS-based retrievals contained in the CERES SYN1deg data product, we suspect that some of the higher IWP values may actually be liquid water clouds. Chylek et al. (2006) suggest that cloud phase discrimination that relies on differential backscatter in MODIS near-infrared channels can be biased toward the ice phase. The MODIS retrieval algorithms for cloud phase discrimination generally use both near-and mid-infrared bands, and further investigation is 620 needed specific to clouds over West Antarctica to identify possible errors. Additionally, the CERES-MODIS approach can retrieve unrealistically high IWP values over ice sheets, mainly over the Antarctic interior. An issue with this approach is that over these areas, where the contrast between the surface and cloud albedo is small, a large correction of cloud water path is necessary to match the TOA fluxes since they are insensitive to small changes. Furthermore, since LWP has limited observational constraints over Antarctica, the algorithm likely has to resort to increasing the IWP dramatically to compensate 625 for any lack of brightness owing to missing liquid (e.g., Lenaerts et al., 2017).
A second limitation involves quantifying the effect of föhn winds. In the RIS example the AWS data indicate more persistent föhn winds than are simulated by ERA5. This is most likely related to the coarse spatial resolution in the reanalysis model. While ERA5 can identify the likely presence of a föhn wind effect based on its generally accurate lower troposphere wind 630 direction relative to varying high terrain, a more quantitative analysis might need to incorporate detailed knowledge of the actual terrain elevation (Dreschel and Mayer, 2008;Elvidge et al., 2015;King et al., 2017).
Over the modern satellite record spanning nearly four decades, it should be possible to make projections regarding future atmospheric stress on the West Antarctic ice shelves by identifying the specific mechanisms, their frequency of occurrence 635 singly or concurrently, their relationships with large-scale meteorological drivers (Nicolas and Bromwich, 2011;Scott et al., 2019) and transport and abundance of atmospheric precipitable water (e.g., Suzuki et al., 2013;Wille et al., 2019). The analysis methods presented here, in which the energetics of individual melt events are diagnosed from satellite observations and reanalysis data, can supplement recent large-scale analysis using regional modelling (e.g., Deb et al., 2018). Our individual cases and their meteorological drivers are qualitatively consistent with the large-scale modelling analysis of Deb 640 et al. (2018). In conjunction with increasing understanding of shelf basal melting and its time variability (Adusumilli et al., 2020) and understanding the disposition of surface meltwater either within the structure of Antarctic ice shelves or as runoff (e.g., Bell et al. 2017), one can also envision a quantitative assessment of ice shelf resilience in a warming climate based on analysis of the surface energy balance.  Figure   A1, to estimate how errors in ERA5 cloud microphysics might impact a time series of the ME before and during a melt event. The AWARE flux measurements were made using the ARM user facility pyranometers and pyrgeometers (Mather & 650 Voyles 2013;Lubin et al. 2020). Figure A1a shows that ERA5 consistently underestimates skin temperature except on occasions when the Sun is at its lowest elevation, but that the temperature discrepancy varies from day to day. The instantaneous discrepancies between ERA5 and the measured downwelling SW flux ( Figure A1b) can sometimes be on the order of 100 W m -2 , but the similarity in amplitudes of the diurnal cycles suggest that ERA5 is reliably simulating the presence of clouds on a daily basis. Much more striking discrepancies appear between ERA5 and measured downwelling 655 LW flux ( Figure A1c). Here there are many periods, sometimes a day long, where ERA5 underestimates the LW flux by ~50 W m -2 , which would be expected if modelled LWP is too low (see Figure 14 in Lubin et al. 2020). There are, however, other periods when the ERA5 and measured LW fluxes are consistent. This episodic nature of the LW flux discrepancies, in which errors can persist throughout a day, suggest that we should find alternative estimates of the cloud LWP and ice water path (IWP) to evaluate the realism of LW flux calculations in the ME based on ERA5 data. 660 Our goal is to be able to evaluate the energetics of surface melt events anywhere in Antarctica, rather than be tied to the few instances such as AWARE where corroborating surface measurements are available. We therefore examine the contrasts between ERA5 and CERES SYN1deg cloud properties and radiative fluxes during the AWARE January 2016 melt event but at Siple Dome instead of WAIS Divide. From Nicolas et al. (2017) we know that clouds should be optically thick and that 665 the ME should be positive over several diurnal cycles after 10 January 2016. Over Siple Dome during the melt event, both ERA5 and CERES indicate LWP > 50 g m -2 ( Figure A2). However, ERA5 cloud IWP is sometimes twice as large as the 675 CERES retrieval. If cloud microphysics are more realistic in the CERES data product, one might be tempted to calculate the ME by replacing ERA5 net radiative fluxes with their CERES counterparts, while retaining the ERA5 turbulent fluxes. We tried this approach for January 2016 over Siple Dome ( Figure A3) and the result is unsatisfactory. The diurnal amplitude of the CERES net SW 685 flux is up to twice as large as that modelled by ERA5, and is also qualitatively less consistent with the AWARE measurements from WAIS Divide. There are substantial differences of order 50 W m -2 between ERA5 and CERES net LW fluxes, with CERES appearing to be an improvement compared with ERA5's known tendency to underpredict the net LW flux over Antarctica . However, the ME calculation using ERA5 for all flux terms is basically realistic in that ME > 0 over three diurnal cycles after 10 January, and almost always drops below zero at lowest Sun elevation for the 690 Figure A3. Radiative flux components and alternative estimates of the ME over Siple Dome during January 2016: (a) Individual net SW fluxes from ERA5 (red) and CERES SYN1deg data (yellow) and net LW fluxes from ERA5 (green) and CERES SYN1deg data (blue); (b) total net radiative flux from ERA5 (black) and CERES SYN1deg data (red); (c) ME computed entirely from ERA5 (black) and using ERA5 turbulent fluxes but substituting the CERES 695 SYN1deg radiative fluxes (red).
rest of the month. When we substitute the CERES radiative fluxes, both the net (SW + LW) radiative flux and ME are positive over several diurnal cycles for about half the month, including before 10 January when we know that meteorological conditions were not conducive to surface melt (Nicolas et al., 2017). We therefore conclude that a "mix and match" approach 700 to evaluating the ME is unsuitable, and this is not surprising given that ERA5 and CERES use different radiative transfer algorithms. Instead, we proceed by calculating the ME with ERA5 radiative and turbulent fluxes, and then examine the CERES SYN1deg cloud LWP and IWP as a separate check on the realism of cloud properties simulated by ERA5.

Appendix B: Examples of Satellite Passive Microwave Brightness Temperature Spatial Variability
To illustrate the spatial variability in the surface melt signature, we provide examples of the SSMIS horizontally polarized 705 19.35 GHz (K-band) brightness temperature T b measured on the days during each of the case studies when surface melt reached maximum frequency within the bounding region. At Siple Dome on 6 January 2015 ( Figure B1) the extensive surface melting also appears over the eastern edge of the RIS and throughout most of the ASE. On 6 January 2012, there is considerable spatial variability in T b over Pine Island Glacier and more uniformity over Thwaites Glacier ( Figure B2), in response to the synoptic situation that normally doesn't favour surface melt. Similarly, during the late summer melt event of 710 February 2013, there is noticeable spatial variability in T b over both Pine Island and Thwaites Glaciers ( Figure B3), even though this melt event is driven by pronounced thermal blanketing. During the December 2011 synoptic conditions that strongly favour melt, spatial variability in T b over Pine Island Glacier is still apparent ( Figure B4). Over Siple Dome during late December 2011 ( Figure B5) the measured T b exhibits spatial uniformity and values ~50 K smaller than over Thwaites Glacier ( Figure B5). At the RIS location on 23 December 2011, spatial variability in Tb is consistent with a föhn effect, as T b 715 is above the melt detection threshold close to the Transantarctic mountains and decreases throughout the bounding region moving away from the mountains.   ERA5 data were obtained as provided by ECMWF, using the Copernicus Climate Change Service (C3S) Climate Data Store (https://cds.climate.copernicus.eu). NASA CERES SYN1deg data were obtained from NASA Langley Research Center Atmospheric Science Data Center (https://asdc.larc.nasa.gov/project/CERES). MEaSUREs EASE-Grid 2.0 data were obtained from NSIDC (https://nsidc.org/data/NSIDC-0630/versions/1). AWS and Field Camp Observations are archived at the University of Wisconsin Antarctic Meteorological Research Center (https://amrc.ssec.wisc.edu/data). 745

Author Contribution
MG performed the data analysis and interpretation as part of her Master of Science thesis at the Scripps Institution of Oceanography. RS provided synoptic and local scale meteorological analysis. AV provided the AWARE surface energy balance data analysis and contributed to manuscript preparation. JL provided interpretation of the surface energy balance in the case studies and contributed to manuscript preparation. ML provided the AWS and field camp data and their 750 interpretation for this work. DL served as thesis advisor for MG and contributed to manuscript preparation.