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NASA's Potential Contributions to Avalanche Forecasting Using Active and Passive Microwave Measurements

This Candidate Solution is based on using active and passive microwave measurements acquired from NASA satellites to improve USDA (U.S. Department of Agriculture) Forest Service forecasting of avalanche danger. Regional Avalanche Centers prepare avalanche forecasts using ground measurements of snowpack and mountain weather conditions. In this Solution, range of the in situ observations is extended by adding remote sensing measurements of snow depth, snow water equivalent, and snowfall rate acquired by satellite missions that include Aqua, CloudSat, future GPM (Global Precipitation Measurement), and the proposed SCLP (Snow and Cold Land Processes). Measurements of snowpack conditions and time evolution are improved by combining the in situ and satellite observations with a snow model. Recurring snow observations from NASA satellites increase accuracy of avalanche forecasting, which helps the public and the managers of public facilities make better avalanche safety decisions.

Blonski, Slawomir↗

Differences Between the HUT Snow Emission Model and MEMLS and Their Effects on Brightness Temperature Simulation

Microwave emission models are a critical component of snow water equivalent retrieval algorithms applied to passive microwave measurements. Several such emission models exist, but their differences need to be systematically compared. This paper compares the basic theories of two models: the multiple-layer HUT (Helsinki University of Technology) model and MEMLS (Microwave Emission Model of Layered Snowpacks). By comparing the mathematical formulation side-by-side, three major differences were identified: (1) by assuming the scattered intensity is mostly (96) in the forward direction, the HUT model simplifies the radiative transfer (RT) equation into 1-flux; whereas MEMLS uses a 2-flux theory; (2) the HUT scattering coefficient is much larger than MEMLS; (3 ) MEMLS considers the trapped radiation inside snow due to internal reflection by a 6-flux model, which is not included in HUT. Simulation experiments indicate that, the large scattering coefficient of the HUT model compensates for its large forward scattering ratio to some extent, but the effects of 1-flux simplification and the trapped radiation still result in different T(sub B) simulations between the HUT model and MEMLS. The models were compared with observations of natural snow cover at Sodankyl, Finland; Churchill, Canada; and Colorado, USA. No optimization of the snow grain size was performed. It shows that HUT model tends to under estimate T(sub B) for deep snow. MEMLS with the physically-based improved Born approximation performed best among the models, with a bias of -1.4 K, and an RMSE of 11.0 K.

Pan, Jinmei↗

Comparison of Commonly-Used Microwave Radiative Transfer Models for Snow Remote Sensing

This paper reviews four commonly-used microwave radiative transfer models that take different electromagnetic approaches to simulate snow brightness temperature (T(sub B)): the Dense Media Radiative Transfer - Multi-Layer model (DMRT-ML), the Dense Media Radiative Transfer - Quasi-Crystalline Approximation Mie scattering of Sticky spheres (DMRT-QMS), the Helsinki University of Technology n-Layers model (HUT-nlayers) and the Microwave Emission Model of Layered Snowpacks (MEMLS). Using the same extensively measured physical snowpack properties, we compared the simulated T(sub B) at 11, 19 and 37 GHz from these four models. The analysis focuses on the impact of using different types of measured snow microstructure metrics in the simulations. In addition to density, snow microstructure is defined for each snow layer by grain optical diameter (Do) and stickiness for DMRT-ML and DMRT-QMS, mean grain geometrical maximum extent (D(sub max)) for HUT n-layers and the exponential correlation length for MEMLS. These metrics were derived from either in-situ measurements of snow specific surface area (SSA) or macrophotos of grain sizes (D(sub max)), assuming non-sticky spheres for the DMRT models. Simulated T(sub B) sensitivity analysis using the same inputs shows relatively consistent T(sub B) behavior as a function of Do and density variations for the vertical polarization (maximum deviation of 18 K and 27 K, respectively), while some divergences appear in simulated variations for the polarization ratio (PR). Comparisons with ground based radiometric measurements show that the simulations based on snow SSA measurements have to be scaled with a model-specific factor of Do in order to minimize the root mean square error (RMSE) between measured and simulated T(sub B). Results using in-situ grain size measurements (SSA or D(sub max), depending on the model) give a mean T(sub B) RMSE (19 and 37 GHz) of the order of 16-26 K, which is similar for all models when the snow microstructure metrics are scaled. However, the MEMLS model converges to better results when driven by the correlation length estimated from in-situ SSA measurements rather than D(sub max) measurements. On a practical level, this paper shows that the SSA parameter, a snow property that is easy to retrieve in-situ, appears to be the most relevant parameter for characterizing snow microstructure, despite the need for a scaling factor.

Snow↗

Study of Martian Polar Caps with GISS ROCKE-3D GCM

Martian polar caps consist of both H 2 O and CO 2 ice. While H 2 O ice is mainly passive on modern Mars, it may have not been the case in recent Martian history, when its obliquity was higher, or when it was changing rapidly. The distribution of ice species in the snowpack affects its physical and thermodynamic properties. In the upper layers, it determines its albedo and thermal emissivity. Thus understanding the mutual effect between these ices and their interaction with the atmosphere is crucial for understanding the evolution of Martian polar regions. In this study, we employ a newly-developed Exotic Ices snow model coupled to the NASA Goddard Institute for Space Studies (GISS) ROCKE-3D planetary General Circulation Model (GCM) [1] to study the behavior of Martian polar caps. ROCKE-3D is a planetary GCM developed at NASA GISS as an extension of its Earth climate model, modelE [2]. It has been extensively used to simulate climate of various planets, including Mars (e.g. [3,4]). The Exotic Ices snow model was specially developed for planetary applications which involve more than one condensable in the atmosphere, in which case snow can contain multiple species of ice (CO2 and H 2 O in the Mars case). For each species of ice, the model uses their proper physical properties and phase diagram, but otherwise it treats all species of ice on an equal footing. The combined effects on albedo, thermal inertia and mutual insulation are treated accordingly. The snowpack interacts with the atmospheric dust cycle, and can accumulate a prognostic amount of dust, though the effect of dust on snow properties is not currently treated explicitly, and is prescribed. In this study, we first validate our model against the modern Martial climate, for which we use mission results from Mars Climate Sounder (atmospheric temperature and dust optical depth), SPICAM on Mars Express (atmospheric water), and Viking 2 (surface pressure). We investigate the effect of snow radiative properties on CO 2 and water cycles and the ability of our model to accurately reproduce those with minimal model tuning. We then perform simulations for several obliquities from a recent Martian past, and investigate the behavior of the Martian polar caps in such conditions.

Mars↗

The Impact of Detailed Snow Physics on the Simulation of Snow Cover and Subsurface Thermodynamics at Continental Scales

The three-layer snow model is coupled to the global catchment-based Land Surface Model (LSM) of the NASA Seasonal to Interannual Prediction Project (NSIPP) project, and the combined models are used to simulate the growth and ablation of snow cover over the North American continent for the period 1987-1988. The various snow processes included in the three-layer model, such as snow melting and re-freezing, dynamic changes in snow density, and snow insulating properties, are shown (through a comparison with the corresponding simulation using a much simpler snow model) to lead to an improved simulation of ground thermodynamics on the continental scale.

Stieglitz, Marc↗

Snow hydrology in a general circulation model

A snow hydrology has been implemented in an atmospheric general circulation model (GCM). The snow hydrology consists of parameterizations of snowfall and snow cover fraction, a prognostic calculation of snow temperature, and a model of the snow mass and hydrologic budgets. Previously, only snow albedo had been included by a specified snow line. A 3-year GCM simulation with this now more complete surface hydrology is compared to a previous GCM control run with the specified snow line, as well as with observations. In particular, the authors discuss comparisons of the atmospheric and surface hydrologic budgets and the surface energy budget for U.S. and Canadian areas. The new snow hydrology changes the annual cycle of the surface moisture and energy budgets in the model. There is a noticeable shift in the runoff maximum from winter in the control run to spring in the snow hydrology run. A substantial amount of GCM winter precipitation is now stored in the seasonal snowpack. Snow cover also acts as an important insulating layer between the atmosphere and the ground. Wintertime soil temperatures are much higher in the snow hydrology experiment than in the control experiment. Seasonal snow cover is important for dampening large fluctuations in GCM continental skin temperature during the Northern Hemisphere winter. Snow depths and snow extent show good agreement with observations over North America. The geographic distribution of maximum depths is not as well simulated by the model due, in part, to the coarse resolution of the model. The patterns of runoff are qualitatively and quantitatively similar to observed patterns of streamflow averaged over the continental United States. The seasonal cycles of precipitation and evaporation are also reasonably well simulated by the model, although their magnitudes are larger than is observed. This is due, in part, to a cold bias in this model, which results in a dry model atmosphere and enhances the hydrologic cycle everywhere.

Marshall, Susan↗

Quantifying the Observational Requirements of a Space-borne LiDAR Snow Mission

This study quantifies the level of observational accuracy required from a spaceborne light detection and ranging (LiDAR) snow depth retrieval mission for enabling beneficial impacts for snow estimation. The study is conducted over a region in Western Colorado using a suite of observing system simulation experiments(OSSEs).The Joint UK Land Environment Simulator, version 5.0 (JULES v5.0) is employed to simulate a suite of idealized LiDAR observations, considering a range of LiDAR snow depth retrieval errors, different hypothetical sensor swath widths, and the impact of cloud cover on observability. These simulated observations are then assimilated into the Noah land surface modelwith multi-parameterization options, version 3.6 (Noah-MP v3.6) model. This data assimilation setup is used to systematically evaluate the potential utility of LiDAR observations for improving modeled snow water equivalent (SWE)estimates and water budget variables such as runoff. Results from the OSSE runsshow that, in general, assimilation of synthetic LiDAR observations provide beneficial impacts when theLiDAR snow depth retrieval error standard deviation (σerror) is below 60 cm.Based on comparisons between the realistic (i.e., swath-limited and cloud-attenuated) case and the idealized (i.e., infinite swath width in the absence of cloud cover) case,this study concludes that observations with a conservative error standard deviation threshold of 40 cm (i.e., upper limit of the snow depth retrieval error that adds value to the SWE estimates viaassimilation) are needed for improving modeled snow estimates. More than a 33% reduction in SWEroot mean square errors and more than a 15% increase in correlation coefficientsare achieved when σ error ≤ 40 cmusing a 170-km sensor swath width in the presence of cloud attenuation effects. Further, the integrated hydrologic response, as represented by total (surface and subsurface) runoff estimates during the snow ablation season, are also enhanced when assimilating synthetic LiDAR snow depth retrievals with errors below this level.

Yonghwan Kwon↗

Assessment of climate variability of the Greenland ice sheet: Integration of in situ and satellite data

The proposed research involves the application of multispectral satellite data in combination with ground truth measurements to monitor surface properties of the Greenland ice sheet which are essential for describing the energy and mass of the ice sheet. Several key components of the energy balance are parameterized using satellite data and in situ measurements. The analysis will be done for a ten year time period in order to get statistics on the seasonal and interannual variations of the surface processes and the climatology. Our goal is to investigate to what accuracy and over what geographic areas large scale snow properties and radiative fluxes can be derived based upon a combination of available remote sensing and meterological data sets. Data analysis showed the following results: (1)cloud classification based on longwave sky radiation revealed that overcast sky occurred for 25% of the time in winter, and for 15% in spring and summer respectively (winter and summer both show the same occurrence of clear sky of approximately 26%); (2) comparison of aerodynamic profile method with eddy correlation method to derive sensible and latent heat flux showed good agreement in the diurnal cycle and the turbulent fluxes were underestimated with the aerodynamic method by 10 - 30% as compared to the in situ eddy flux method; (3) the katabatic wind shows a distinct diurnal cycle with a maximum in the morning (7-9 h solar time) and a minimum in the later afternoon (18 h solar time); (4) snow grain size was modeled with a surface energy balance model (SNTHERM) and compared with in situ measurements. Sharp decreases in the modeled snow grain size, caused by accumulation events such as precipitation and deposition, could be verified with observational data; (4) radiative transfer modeling of firn supports our beliefs that the observed trends in 18 and 19 GHz passive microwave brightness temperatures are attributable to accumulation rate changes (modeling also indicates the above relationship is detectable because of the presence of depth hoar; (5) snow melt can be detected by a distinct signal in the passive microwave cross-polarized gradient ratio (19h-37v)/(19h+37v) and has been used for wet/dry snow classification; (6) top of the atmosphere (TOA) broadband albedos were derived from AVHRR visible and near infrared reflectances for the entire ice sheet from May 1990 - June 1991, and the highest albedo values are found along the southeast coast of the ice sheet which is consistent with the summer peak of precipitation due to onshore flow loaded with high water vapor content (TOA albedo values dropped to around 40% along the south-western coast during July and August due to bare ice surfaces); and (7) the net all-wave radiation balance at the top of the atmosphere is negative over the entire ice sheet except for the summer months - June-July-August (in June, the net radiation balance is slightly positive over the dry snow areas--15 W/m2).

Steffen, K.↗

Cartographic modeling of snow avalanche path location within Glacier National Park, Montana

Geographic information system (GIS) techniques were applied to the study of snow-avalanche path location within Glacier National Park, Montana. Aerial photointerpretation and field surveys confirmed the location of 121 avalanche paths within the selected study area. Spatial and nonspatial information on each path were integrated using the ARC/INFO GIS. Lithologic, structural, hydrographic, topographic, and land-cover impacts on path location were analyzed. All path frequencies within variable classes were normalized by the area of class occurrence relative to the total area of the study area and were added to the morphometric information contained within INFO tables. The normalized values for each GIS coverage were used to cartographically model, by means of composite factor weightings, avalanche path locations.

Walsh, Stephen J.↗

Monitoring global snow cover

A snow model that supports the daily, operational analysis of global snow depth and age has been developed. It provides improved spatial interpolation of surface reports by incorporating digital elevation data, and by the application of regionalized variables (kriging) through the use of a global snow depth climatology. Where surface observations are inadequate, the model applies satellite remote sensing. Techniques for extrapolation into data-void mountain areas and a procedure to compute snow melt are also contained in the model.

Armstrong, Richard↗

GEOS-5 Seasonal Forecast System: ENSO Prediction Skill and Bias

The GEOS-5 AOGCM known as S2S-1.0 has been in service from June 2012 through January 2018 (Borovikov et al. 2017). The atmospheric component of S2S-1.0 is Fortuna-2.5, the same that was used for the Modern-Era Retrospective Analysis for Research and Applications (MERRA), but with adjusted parameterization of moist processes and turbulence. The ocean component is the Modular Ocean Model version 4 (MOM4). The sea ice component is the Community Ice CodE, version 4 (CICE). The land surface model is a catchment-based hydrological model coupled to the multi-layer snow model. The AGCM uses a Cartesian grid with a 1 deg × 1.25 deg horizontal resolution and 72 hybrid vertical levels with the upper most level at 0.01 hPa. OGCM nominal resolution of the tripolar grid is 1/2 deg, with a meridional equatorial refinement to 1/4 deg. In the coupled model initialization, selected atmospheric variables are constrained with MERRA. The Goddard Earth Observing System integrated Ocean Data Assimilation System (GEOS-iODAS) is used for both ocean state and sea ice initialization. SST, T and S profiles and sea ice concentration were assimilated.

GEOS-↗

Assimilation of Sea Ice Thickness Derived from Cryosat-2 Along-Track Freeboard Measurements into the Met Office's Forecast Ocean Assimilation Model (FOAM)

The feasibility of assimilating sea ice thickness (SIT) observations derived from CryoSat-2 along-track measurements of sea ice freeboard is successfully demonstrated using a 3D-Var assimilation scheme, NEMOVAR, within the Met Office's global, coupled ocean–sea-ice model, Forecast Ocean Assimilation Model (FOAM). The CryoSat-2 Arctic freeboard measurements are produced by the Centre for Polar Observation and Modelling (CPOM) and are converted to SIT within FOAM using modelled snow depth. This is the first time along-track observations of SIT have been used in this way, with other centres assimilating gridded and temporally averaged observations. The assimilation leads to improvements in the SIT analysis and forecast fields generated by FOAM, particularly in the Canadian Arctic. Arctic-wide observation-minus-background assimilation statistics for 2015–2017 show improvements of 0.75 m mean difference and 0.41 m root-mean-square difference (RMSD) in the freeze-up period and 0.46 m mean difference and 0.33 m RMSD in the ice break-up period. Validation of the SIT analysis against independent springtime in situ SIT observations from NASA Operation IceBridge (OIB) shows improvement in the SIT analysis of 0.61 m mean difference (0.42 m RMSD) compared to a control without SIT assimilation. Similar improvements are seen in the FOAM 5 d SIT forecast. Validation of the SIT assimilation with independent Beaufort Gyre Exploration Project (BGEP) sea ice draft observations does not show an improvement, since the assimilated CryoSat-2 observations compare similarly to the model without assimilation in this region. Comparison with airborne electromagnetic induction (Air-EM) combined measurements of SIT and snow depth shows poorer results for the assimilation compared to the control, despite covering similar locations to the OIB and BGEP datasets. This may be evidence of sampling uncertainty in the matchups with the Air-EM validation dataset, owing to the limited number of observations available over the time period of interest. This may also be evidence of noise in the SIT analysis or uncertainties in the modelled snow depth, in the assimilated SIT observations, or in the data used for validation. The SIT analysis could be improved by upgrading the observation uncertainties used in the assimilation. Despite the lack of CryoSat-2 SIT observations available for assimilation over the summer due to the detrimental effect of melt ponds on retrievals, it is shown that the model is able to retain improvements to the SIT field throughout the summer months due to prior, wintertime SIT assimilation. This also results in regional improvements to the July modelled sea ice concentration (SIC) of 5 % RMSD in the European sector, due to slower melt of the thicker sea ice.

Emma K. Fiedler↗

Enabling Advanced Snow Physics within Land Surface Models Through an Interoperable Model-Physics Coupling Framework

Accurate estimation of snow accumulation and melt is a critical part of decision-making in snow-dominated watersheds. In this study, we demonstrate a flexible methodology to couple a detailed snow model, Crocus, separately to two different land surface models (LSMs), Noah-MP and Noah. The original LSMs and the coupled models (Noah-MP-Crocus and Noah-Crocus) are used to simulate snow depth, snow water equivalent, and other water and energy states and fluxes. The results of simulations are compared against a wide range of independent gridded and point scale reference datasets. Our results show that coupling the detailed snow model, Crocus, with the LSMs improves the snow depth and snow water equivalent relative to independent observations. Overall, larger improvements are obtained with coupling Crocus to the Noah LSM, with the coupled Noah-Crocus configuration reducing the RMSE and bias of snow depth from 2-12% and 57-75%, respectively, relative to Snow Data Assimilation System (SNODAS) and snow product from the University of Arizona. On the other hand, smaller improvements are obtained by coupling Crocus with Noah-MP. The Coupled Noah-MP-Crocus reduces the snow depth bias but slightly degrades the RMSE of snow depth and snow water equivalent. The corresponding impacts in other water budget terms such as evapotranspiration, soil moisture, and streamflow, however, are mixed, pointing to the significant need to improve the coupling assumptions of these processes within land models. Overall, the interoperable coupling framework demonstrated here offers the opportunity to include more detailed snow physics and processes, and to advance data assimilation systems through improved exploitation of information from snow remote sensing instruments.

Snow model↗

Multilayered models for electromagnetic reflection amplitudes

The remote sensing of snowpack characteristics with surface installations or with an airborne system could have important applications in water resource management and flood prediction. To derive some insight into such applications, the electromagnetic response of multilayer snow models is analyzed. Normally incident plane waves are assumed at frequencies ranging from 10 to the 6th power to 10 to the 10th power Hz, and amplitude reflection coefficients are calculated for models having various snow-layer combinations, including ice sheets. Layers are defined by a thickness, permittivity, and conductivity; the electrical parameters are constant or prescribed functions of frequency. To illustrate the effect of various layering combinations, results are given in the form of curves of amplitude reflection coefficients, versus frequency for a variety of models. Under simplifying assumptions, the snow thickness and effective dielectric constant can be estimated from the reflection coefficient variations as a function of frequency.

Linlor, W. I.↗

Exploring the Spatiotemporal Coverage of Terrestrial Snow Mass Using a Suite of Satellite Constellation Configurations

Terrestrial snow is a vital freshwater resource for more than 1 billion people. Remotely-sensed snow observations can be used to retrieve snow mass or integrated into a snow model estimate; however, optimally leveraging remote sensing observations of snow is challenging. One reason is that no single sensor can accurately measure all types of snow because each type of sensor has its own unique limitations. Another reason is that remote sensing data is inherently discontinuous across time and space, and that the revisit cycle of remote sensing observations may not meet the requirements of a given snow applications. In order to quantify the feasible availability of remotely-sensed observations across space and time, this study simulates the sensor coverage for a suite of hypothetical snow sensors as a function of different orbital configurations and sensor properties. The information gleaned from this analysis coupled with a dynamic snow binary map is used to evaluate the efficiency of a single sensor (or constellation) to observe terrestrial snow on a global scale. The results show the efficacy achievable by different sensors over different snow types. The combination of different orbital and sensor configurations is explored to requirements of remote sensing missions that have 1-day, 3-day, or 30-day repeat intervals. The simulation results suggest that 1100 km, 550 km, and 200 km are the minimum required swath width for a polar-orbiting sensor to meet snow-related applications demanding a 1-day, 3-day, and 30-day repeat cycles, respectively. The results of this paper provide valuable input for the planning of a future global snow mission.

Lizhao Wang↗

Evaluation of long-term Northern Hemisphere snow water equivalent products

Nine gridded Northern Hemisphere snow water equivalent (SWE) products were evaluated as part of the European Space Agency (ESA) Satellite Snow Product Intercomparison and Evaluation Exercise (SnowPEx). Three categories of datasets were assessed: (1) those utilizing some form of reanalysis (the NASA Global Land Data Assimilation System version 2 – GLDAS-2; the European Centre for Medium-Range Weather Forecasts (ECMWF) interim land surface reanalysis – ERA-Interim/Land and ERA5; the NASA Modern-Era Retrospective Analysis for Research and Applications version 1 (MERRA) and version 2 (MERRA-2); the Crocus snow model driven by ERA-Interim meteorology – Crocus); (2) passive microwave remote sensing combined with daily surface snow depth observations (ESA GlobSnow v2.0); and (3) stand-alone passive microwave retrievals (NASA AMSR-E SWE versions 1.0 and 2.0) which do not utilize surface snow observations. Evaluation included validation against independent snow course measurements from Russia, Finland, and Canada and product intercomparison through the calculation of spatial and temporal correlations in SWE anomalies. The stand-alone passive microwave SWE products (AMSR-E v1.0 and v2.0 SWE) exhibit low spatial and temporal correlations to other products and RMSE nearly double the best performing product. Constraining passive microwave retrievals with surface observations (GlobSnow) provides performance comparable to the reanalysis-based products; RMSE over Finland and Russia for all but the AMSR-E products is ∼50 mm or less, with the exception of ERA-Interim/Land over Russia. Using a seven-dataset ensemble that excluded the stand-alone passive microwave products reduced the RMSE by 10 mm (20 %) and increased the correlation from 0.67 to 0.78 compared to any individual product. The overall performance of the best multiproduct combinations is still at the margins of acceptable uncertainty for scientific and operational requirements; only through combined and integrated improvements in remote sensing, modeling, and observations will real progress in SWE product development be achieved.

Northern Hemisphere snow water equivalent (SWE) pr↗

Microwave Signatures of Melting/Refreezing Snow: Observations and Modeling Using Dense Medium Radiative Transfer Theory

Microwave brightness temperatures of snow covered terrains can be modeled by means of the Dense Radiative Transfer Medium Theory (DMRT). In a dense medium, such as snow, the assumption of independent scattering is no longer valid and the scattering of correlated scatterers must be considered. In the DMRT, this is done considering a pair distribution function of the particles position. In the electromagnetic model, the snowpack is simulated as a homogeneous layer having effective permittivity and albedo calculated through the DMRT. In order to account for clustering of snow crystals, a model of cohesive particles can be applied, where the cohesion between the particles is described by means of a dimensionless parameters called stickiness (z), representing a measure of the inversion of the attraction of the particles. The lower the z the higher the stickiness. In this study, microwave signatures of melting and refreezing cycles of seasonal snowpacks at high altitudes are studied by means of both experimental and modeling tools. Radiometric data were collected 24 hours per day by the University of Michigan Tower Mounted Radiometer System (TMRS). The brightness temperatures collected by means of the TMRS are simulated by means of a multi-layer electromagnetic model based on the dense medium theory with the inputs to the model derived from the data collected at the snow pits and from the meteorological station. The paper is structured as follows: in the first Section the temperature profiles recorded by the meteorological station and the snow pit data are presented and analyzed; in the second Section, the characteristics of the radiometric system used to collect the brightness temperatures are reported together with the temporal behavior of the recorded brightness temperatures; in the successive Section the multi-layer DMRT-based electromagnetic model is described; in the fourth Section the comparison between modeled and measured brightness temperatures is discussed. We dedicate the last Section to the conclusions and future works.

Tedesco, Marco↗