Simulation of the Microwave Emission of Multi-layered Snowpacks Using the Dense Media Radiative Transfer Theory: the DMRT-ML Model

DMRT-ML is a physically based numerical model designed to compute the thermal microwave emission of a given snowpack. Its main application is the simulation of brightness temperatures at frequencies in the range 1-200 GHz similar to those acquired routinely by spacebased microwave radiometers. The model is based on the Dense Media Radiative Transfer (DMRT) theory for the computation of the snow scattering and extinction coefficients and on the Discrete Ordinate Method (DISORT) to numerically solve the radiative transfer equation. The snowpack is modeled as a stack of multiple horizontal snow layers and an optional underlying interface representing the soil or the bottom ice. The model handles both dry and wet snow conditions. Such a general design allows the model to account for a wide range of snow conditions. Hitherto, the model has been used to simulate the thermal emission of the deep firn on ice sheets, shallow snowpacks overlying soil in Arctic and Alpine regions, and overlying ice on the large icesheet margins and glaciers. DMRT-ML has thus been validated in three very different conditions: Antarctica, Barnes Ice Cap (Canada) and Canadian tundra. It has been recently used in conjunction with inverse methods to retrieve snow grain size from remote sensing data. The model is written in Fortran90 and available to the snow remote sensing community as an open-source software. A convenient user interface is provided in Python

Review Article: Global Monitoring of Snow Water Equivalent Using High-Frequency Radar Remote Sensing

Seasonal snow cover is the largest single component of the cryosphere in areal extent, covering an average of 46 × 106 km2 of Earth\u27s surface (31 % of the land area) each year, and is thus an important expression and driver of the Earth\u27s climate. In recent years, Northern Hemisphere spring snow cover has been declining at about the same rate (∼ −13 % per decade) as Arctic summer sea ice. More than one-sixth of the world\u27s population relies on seasonal snowpack and glaciers for a water supply that is likely to decrease this century. Snow is also a critical component of Earth\u27s cold regions\u27 ecosystems, in which wildlife, vegetation, and snow are strongly interconnected. Snow water equivalent (SWE) describes the quantity of water stored as snow on the land surface and is of fundamental importance to water, energy, and geochemical cycles. Quality global SWE estimates are lacking. Given the vast seasonal extent combined with the spatially variable nature of snow distribution at regional and local scales, surface observations are not able to provide sufficient SWE information. Satellite observations presently cannot provide SWE information at the spatial and temporal resolutions required to address science and high-socio-economic-value applications such as water resource management and streamflow forecasting. In this paper, we review the potential contribution of X- and Ku-band synthetic aperture radar (SAR) for global monitoring of SWE. SAR can image the surface during both day and night regardless of cloud cover, allowing high-frequency revisit at high spatial resolution as demonstrated by missions such as Sentinel-1. The physical basis for estimating SWE from X- and Ku-band radar measurements at local scales is volume scattering by millimeter-scale snow grains. Inference of global snow properties from SAR requires an interdisciplinary approach based on field observations of snow microstructure, physical snow modeling, electromagnetic theory, and retrieval strategies over a range of scales. New field measurement capabilities have enabled significant advances in understanding snow microstructure such as grain size, density, and layering. We describe radar interactions with snow-covered landscapes, the small but rapidly growing number of field datasets used to evaluate retrieval algorithms, the characterization of snowpack properties using radar measurements, and the refinement of retrieval algorithms via synergy with other microwave remote sensing approaches. This review serves to inform the broader snow research, monitoring, and application communities on progress made in recent decades and sets the stage for a new era in SWE remote sensing from SAR measurements

Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135885/1/srtan_1.pd

SMRT: an active–passive microwave radiative transfer model for snow with multiple microstructure and scattering formulations (v1.0)

The Snow Microwave Radiative Transfer (SMRT) thermal emission and backscatter model was developed to determine uncertainties in forward modeling through intercomparison of different model ingredients. The model differs from established models by the high degree of flexibility in switching between different electromagnetic theories, representations of snow microstructure, and other modules involved in various calculation steps. SMRT v1.0 includes the dense media radiative transfer theory (DMRT), the improved Born approximation (IBA), and independent Rayleigh scatterers to compute the intrinsic electromagnetic properties of a snow layer. In the case of IBA, five different formulations of the autocorrelation function to describe the snow microstructure characteristics are available, including the sticky hard sphere model, for which close equivalence between the IBA and DMRT theories has been shown here. Validation is demonstrated against established theories and models. SMRT was used to identify that several former studies conducting simulations with in situ measured snow properties are now comparable and moreover appear to be quantitatively nearly equivalent. This study also proves that a third parameter is needed in addition to density and specific surface area to characterize the microstructure. The paper provides a comprehensive description of the mathematical basis of SMRT and its numerical implementation in Python. Modularity supports model extensions foreseen in future versions comprising other media (e.g., sea ice, frozen lakes), different scattering theories, rough surface models, or new microstructure models.</p

Microwave scattering coefficient of snow in MEMLS and DMRT-ML revisited: the relevance of sticky hard spheres and tomography-based estimates of stickiness

International audienceThe description of snow microstructure in microwave models is often simplified to facilitate electromagnetic calculations. Within dense media radiative transfer (DMRT), the microstructure is commonly described by sticky hard spheres (SHS). An objective mapping of real snow onto SHS is however missing which prevents measured input parameters from being used for DMRT. In contrast, the microwave emission model of layered snowpacks (MEMLS) employs a conceptually different approach, based on the two-point correlation function which is accessible by tomogra-phy. Here we show the equivalence of both electromagnetic approaches by reformulating their microstructural models in a common framework. Using analytical results for the two-point correlation function of hard spheres, we show that the scattering coefficient in both models only differs by a factor which is close to unity, weakly dependent on ice volume fraction and independent of other microstructural details. Additionally , our analysis provides an objective retrieval method for the SHS parameters (diameter and stickiness) from to-mography images. For a comprehensive data set we demonstrate the variability of stickiness and compare the SHS diameter to the optical equivalent diameter. Our results confirm the necessity of a large grain-size scaling when relating both diameters in the non-sticky case, as previously suggested by several authors

Development and evaluation of an advanced microwave radiance data assimilation system for estimating snow water storage at the continental scale

Snow cover modulates the Earth's surface energy and water fluxes, and snowmelt runoff is the principal source of water for humans and ecosystems in many of the middle to high latitudes in the Northern Hemisphere. Understanding spatial and temporal variation in snowpack is crucial for climate studies and water resource management and thus the climate and hydrological research communities have invested in improving large-scale snow estimates. This dissertation aims to develop an advanced snow radiance assimilation (RA) system to improve continental-scale snow water storage estimates. The RA system is comprised of the Community Land Model version 4 (CLM4) (for snow energy and mass balance modeling), radiative transfer models (RTMs) (for brightness temperature estimates), and the Data Assimilation Research Testbed (DART) (for ensemble-based data assimilation). Two snowpack RTMs, the Microwave Emission Model for Layered Snowpacks (MEMLS) and the Dense Media Radiative Transfer--Multi Layers model (DMRT-ML), are used to simulate T[subscript B] of a multi-layered snowpack. Through an error characterization study, this dissertation presents that the correlations between snow water equivalent (SWE) error and brightness temperature (T[subscript B]) error and subsequent RA performance in estimating snow are significantly affected by all physical properties of soil and snow involved in estimating T[subscript B]. Based on the error characterization results, it is hypothesized that the continental-scale RA performance in estimating snow water storage can be improved by simultaneously updating all model physical states and parameters determining T[subscript B] based on a rule, in which prior estimates are updated depending on their correlations with a prior T[subscript B]. The results of a series of RA experiments show that the improved continental-scale snow estimates are obtained by applying the hypothesis. This dissertation also shows that further improvement of the performance of the RA system can be achieved, especially for vegetated areas, by assimilating the best-performing frequency channels (i.e., 18.7 and 23.8 GHz) and by considering the vegetation single scattering albedo to represent the vegetation effect on T[subscript B] at the top of the atmosphere.Geological Science

Estimation of Snow Parameters Based on Passive Microwave Remote Sensing and Meteorological Information

A method to incorporate passive microwave remote sensing measurements within a spatially distributed snow hydrology model to provide estimates of the spatial distribution of Snow Water Equivalent (SWE) as a function of time is implemented. The passive microwave remote sensing measurements are at 25 km resolution. However, in mountain regions the spatial variability of SWE over a 25 km footprint is large due to topographic influences. On the other hand, the snow hydrology model has built-in topographic information and the capability to estimate SWE at a 1 km resolution. In our work, the snow hydrology SWE estimates are updated and corrected using SSM/I passive microwave remote sensing measurements. The method is applied to the Upper Rio Grande River Basin in the mountains of Colorado. The change in prediction of SWE from hydrology modeling with and without updating is compared with measurements from two SNOTEL sites in and near the basin. The results indicate that the method incorporating the remote sensing measurements into the hydrology model is able to more closely estimate the temporal evolution of the measured values of SWE as a function of time

Snow Properties Retrieval Using Passive Microwave Observations

Seasonal snow cover, the second-largest component of the cryosphere, is crucial in controlling the climate system, through its important role in modifying Earth’s albedo. The temporal variability of snow extent and its physical properties in the seasonal cycle also make up a significant element to the cryospheric energy balance. Thus, seasonal snowcover should be monitored not only for its climatological impacts but also for its rolein the surface-water supply, ground-water recharge, and its insolation properties at local scales. Snowpack physical properties strongly influence the emissions from the substratum, making feasible snow property retrieval by means of the surface brightness temperature observed by passive microwave sensors. Depending on the observing spatial resolution, the time series records of daily snow coverage and a snowpacks most-critical properties such as the snow depth and snow water equivalent (SWE) could be helpful in applications ranging from modeling snow variations in a small catchment to global climatologic studies. However, the challenge of including spaceborne snow water equivalent (SWE) products in operational hydrological and hydroclimate modeling applications is very demanding with limited uptake by these systems. Various causes have been attributed to this lack of up-take but most stem from insufficient SWE accuracy. The root causes of this challenge includes the coarse spatial resolution of passive microwave (PM) observations that observe highly aggregated snowpack properties at the spaceborne scale, and inadequacies during the retrieval process that are caused by uncertainties with the forward emission modeling of snow and challenges to find robust parameterizations of the models. While the spatial resolution problem is largely in the realm of engineering design and constrained by physical restrictions, a better understanding of the whole range of retrieval methodologies can provide the clarity needed to move the thinking forward in this important field. Following a review on snow depth and SWE retrieval methods using passive microwave remote sensing observations, this research employs a forward emission model to simulate snowpacks emission and compare the results to the PM airborne observations. Airborne radiometer observations coordinated with ground-based in-situ snow measurements were acquired in the Canadian high Arctic near Eureka, NT, in April 2011. The observed brightness temperatures (Tb) at 37 GHz from typical moderate density dry snow in mid-latitudes decreases with increasing snow water equivalent (SWE) due to the volume scattering of the ground emissions by the overlying snow. At a certain point, however, as SWE increases, the emission from the snowpack offsets the scattering of the sub-nivean emission. In tundra snow, the Tb slope reversal occurs at shallower snow thicknesses. While it has been postulated that the inflection point in the seasonal time series of observed Tb V 37 GHz of tundra snow is controlled by the formation of a thick wind slab layer, the simulation of this effect has yet to be confirmed. Therefore, the Dense Media Radiative Transfer Theory forMulti Layered (DMRT-ML) snowpack is used to predict the passive microwave response from airborne observations over shallow, dense, slab-layered tundra snow. The DMRT-ML was parameterized with the in-situ snow measurements using a two-layer snowpack and run in two configurations: a depth hoar and a wind slab dominated pack. Snow depth retrieval from passive microwave observations without a-priori information is a highly underdetermined system. An accurate estimate of snow depth necessitates a-priori information of snowpack properties, such as grain size, density, physical temperature and stratigraphy, and, very importantly, a minimization of this a prior information requirement. In previous studies, a Bayesian Algorithm for Snow Water Equivalent (SWE) Estimation (BASE) have been developed, which uses the Monte Carlo Markov Chain (MCMC) method to estimate SWE for taiga and alpine snow from 4-frequency ground-based radiometer Tb. In our study, BASE is used in tundra snow for datasets of 464 footprints inthe Eureka region coupled with airborne passive microwave observations—the same fieldstudy that forward modelling was evaluated. The algorithm searches optimum posterior probability distribution of snow properties using a cost function between physically based emission simulations and Tb observations. A two-layer snowpack based on local snow cover knowledge is assumed to simulate emission using the Dense Media Radiative Transfer-Multi Layered (DMRT-ML) model. Overall, the results of this thesis reinforce the applicability of a physics-based emission model in SWE retrievals. This research highlights the necessity to consider the two-part emission characteristics of a slab-dominated tundra snowpack and suggests performing inversion in a Bayesian framework

Exploiting the ANN Potential in Estimating Snow Depth and Snow Water Equivalent From the Airborne SnowSAR Data at X- and Ku-Bands

Within the framework of European Space Agency (ESA) activities, several campaigns were carried out in the last decade with the purpose of exploiting the capabilities of multifrequency synthetic aperture radar (SAR) data to retrieve snow information. This article presents the results obtained from the ESA SnowSAR airborne campaigns, carried out between 2011 and 2013 on boreal forest, tundra and alpine environments, selected as representative of different snow regimes. The aim of this study was to assess the capability of X- and Ku-bands SAR in retrieving the snow parameters, namely snow depth (SD) and snow water equivalent (SWE). The retrieval was based on machine learning (ML) techniques and, in particular, of artificial neural networks (ANNs). ANNs have been selected among other ML approaches since they are capable to offer a good compromise between retrieval accuracy and computational cost. Two approaches were evaluated, the first based on the experimental data (data driven) and the second based on data simulated by the dense medium radiative transfer (DMRT). The data driven algorithm was trained on half of the SnowSAR dataset and validated on the remaining half. The validation resulted in a correlation coefficient R ≃ 0.77 between estimated and target SD, a root-mean-square error (RMSE) ≃ 13 cm, and bias = 0.03 cm. ANN algorithms specific for each test site were also implemented, obtaining more accurate results, and the robustness of the data driven approach was evaluated over time and space. The algorithm trained with DMRT simulations and tested on the experimental dataset was able to estimate the target parameter (SWE in this case) with R = 0.74, RMSE = 34.8 mm, and bias = 1.8 mm. The model driven approach had the twofold advantage of reducing the amount of in situ data required for training the algorithm and of extending the algorithm exportability to other test sites

Derivation and evaluation of a new extinction coefficient for use with the n-HUT snow emission model

In this study, snow slab data collected from the Arctic Snow Microstructure Experiment were used in conjunction with a six-directional flux coefficient model to calculate individual slab absorption and scattering coefficients. These coefficients formed the basis for a new semiempirical extinction coefficient model, using both frequency and optical diameter as input parameters, along with the complex dielectric constant of snow. Radiometric observations, at 18.7, 21.0, and 36.5 GHz at both horizontal polarization (H-Pol) and vertical polarization (V-Pol), and snowpit data collected as part of the Sodankylä Radiometer Experiment were used to compare and contrast the simulated brightness temperatures produced by the multi-layer Helsinki University of Technology snow emission model, utilizing both the original empirical model and the new semiempirical extinction coefficient model described here. The results show that the V-Pol RMSE and bias values decreased when using the semiempirical extinction coefficient; however, the H-Pol RMSE and bias values increased on two of the lower microwave bands tested. The unbiased RMSE was shown to decrease across all frequencies and polarizations when using the semiempirical extinction coefficient