Physically Informed Bayesian Retrieval of SWE and Snow Depth in Forested Areas from Airborne X And Ku-Band SAR Measurements

📝 Abstract

This study presents a coupled physical statistical framework for retrieving snow water equivalent (SWE) in forested areas using dual frequency X and Ku band SAR observations. The method combines a multilayer snow hydrology model (MSHM) with microwave propagation and backscatter models, and includes a canopy parameterization based on a modified Water Cloud Model that accounts for canopy closure. The framework is applied to airborne SnowSAR measurements over Grand Mesa, Colorado, and evaluated against snow pit SWE and LiDAR snow depth from the SnowEx'17 campaign. Prior distributions of snowpack properties are generated with MSHM forced by numerical weather prediction, and vegetation and soil parameters are initialized from Ku HH observations under frozen conditions and interpolated from open to nearby forested areas using kriging. Successful SWE and snow depth retrievals in forested pixels are obtained where relative backscatter residuals are below 30% for incidence angles between 30 and 50 degrees, capturing both the mean and variance of snowpack distributions. For 90 m forested pixels, the snow depth RMSE is 0.033 m (less than 8% of maximum pit SWE), with improved spatial patterns relative to hydrology only simulations. Performance degrades in highly heterogeneous land cover such as mixed forest and wetlands and along canopy and water boundaries due to uncertainty in canopy closure, although absolute snow depth differences remain below 10% and 20% for about 62% and 82% of pixels, respectively. Retrievals at 30 m resolution for one flight further reduce spatial errors and increase the fraction of low error pixels by about 78% at a 10% absolute error threshold, demonstrating the feasibility of dual frequency Bayesian SWE retrievals in forested landscapes by combining physical modeling with SAR observations.

💡 Analysis

This study presents a coupled physical statistical framework for retrieving snow water equivalent (SWE) in forested areas using dual frequency X and Ku band SAR observations. The method combines a multilayer snow hydrology model (MSHM) with microwave propagation and backscatter models, and includes a canopy parameterization based on a modified Water Cloud Model that accounts for canopy closure. The framework is applied to airborne SnowSAR measurements over Grand Mesa, Colorado, and evaluated against snow pit SWE and LiDAR snow depth from the SnowEx'17 campaign. Prior distributions of snowpack properties are generated with MSHM forced by numerical weather prediction, and vegetation and soil parameters are initialized from Ku HH observations under frozen conditions and interpolated from open to nearby forested areas using kriging. Successful SWE and snow depth retrievals in forested pixels are obtained where relative backscatter residuals are below 30% for incidence angles between 30 and 50 degrees, capturing both the mean and variance of snowpack distributions. For 90 m forested pixels, the snow depth RMSE is 0.033 m (less than 8% of maximum pit SWE), with improved spatial patterns relative to hydrology only simulations. Performance degrades in highly heterogeneous land cover such as mixed forest and wetlands and along canopy and water boundaries due to uncertainty in canopy closure, although absolute snow depth differences remain below 10% and 20% for about 62% and 82% of pixels, respectively. Retrievals at 30 m resolution for one flight further reduce spatial errors and increase the fraction of low error pixels by about 78% at a 10% absolute error threshold, demonstrating the feasibility of dual frequency Bayesian SWE retrievals in forested landscapes by combining physical modeling with SAR observations.

📄 Content

Snow accumulation changes in cold regions such as the Arctic are monitored with great interest as they reflect concerted changes in precipitation patterns as well as regional weather (Lee et al., 2021;Curk et al., 2020;Shi and Liu, 2021;Switanek et al., 2024;Kacimi and Kwok, 2022;Pongracz et al., 2024;Gottlieb and Mankin, 2024). Snow cover and snowpack microphysical properties govern terrestrial albedo over large regions of the world and thus play a key role in regulating the planet’s energy budget (Fassnacht et al., 2016;Xu and Dirmeyer, 2013;Jennings and Molotch, 2020). Snowpacks represent an important form of transient water storage in the cold season (Rodell and Houser, 2004;Lim et al., 2021;Mazzotti et al., 2024) followed by melt and runoff in the warm season. Monitoring and predicting snowpack properties is essential for a myriad of applications from water resources management to agriculture production to flood response and mitigation (Gardner et al., 2013;Semádeni-Davies, 2004;Falk and Lin, 2019;Nicolaus et al., 2021;Sthapit et al., 2022;Horrigan and Bates, 1995;Li et al., 2025).

Remote sensing of snowpack properties relies on Mie scattering theory, which describes the interaction between electromagnetic waves (EMW) and particles based on their relative sizes (Aoki et al., 2000;Hall et al., 2004;Tsang et al., 2007). Thus, the EM wavelength and the diameter of the particle (D) determine the type of information gathered. When the EM wavelength (λ) is much smaller than the particle diameter D (λ« D), surface reflectance is the dominant scattering process. Conversely, when the wavelength is equal to or larger than the particle diameter (λ ≥ D), volumetric scattering is dominant, revealing information about the internal structure of the snowpack. The trade-off between surface and volume scattering is crucial in selecting and combining appropriate wavelengths for remote sensing applications. Previous research has demonstrated value in the combination of X and Ku-band backscatter measurements to quantify snow mass properties from volume backscatter (Singh et al., 2024 (a), Boyd et al., 2022, Tsang et al., 2021) Snow water equivalent (SWE), obtained as the product of snow depth and snow density, represents the amount of water stored in a snowpack if melted completely. Thus, to estimate SWE is to estimate snow water resources. Statistical models that integrate SWE estimates from microwave backscatter observations with ground-based measurements, often through cost minimization or data assimilation approaches, have been widely employed to estimate SWE at high spatial resolution (Mote et al. 2005;Li et al. 2017;Zhu et al., 2021). However, purely statistical or machine-learning approaches frequently show reduced accuracy when extrapolated to higherresolution or more heterogeneous datasets, where scale and physical complexity differ from the training domain (Bonavita 2024;Hernanz et al., 2024;Slater et al., 2025). This issue will become more important with the increasing availability of high-resolution remote sensing data (Wrzesien et al., 2017;Sabetghadam et al., 2025;Boueshagh et al., 2025). Data assimilation into snow hydrology models provides a general path for SWE estimation constrained by physical principles (Sturm et al., 2010;Shrestha and Barros 2025). Cao and Barros (2020) integrated the Multilayered Snow Hydrology Model (MSHM) earlier developed by Kang and Barros (2011 a and b) and simulates the temporal evolution of snowpacks and captures detailed changes in snow stratigraphy and internal structure with the Microwave Emission Model of Multilayered Snowpacks (MEMLS, Proksch et al., 2015) for forward simulations of snowpack microstructure. Pan et al. (2023) implemented MEMLS in a Bayesian framework, referred to as BASE-AM, to estimate SWE from active microwave backscatter measurements. Building on these, Singh et al. (2024) modified the BASE-AM algorithm to derive snowpack priors from MSHM simulations driven by weather forecasts and to improve ground backscatter estimates for frozen soils. They applied the modified algorithm to retrieve SWE from Ku-and X-band SnowSAR observations from the NASA SnowEx'17 campaign in Grand Mesa, Colorado achieving an RMSE of less than 7% when compared with snow pit observations in open snow-covered grasslands.

The scattering behavior of active microwaves in forested snowpacks is very complex including interactions among vegetation, snowpack, submerged vegetation, and ground (Figure 1; Mahat and Tarboton, 2012;Essery et al., 2024) resulting in strong attenuation of backscatter and challenging separation of scattering and attenuation sources (Cho et al., 2022;Lemmetyinen et al. 2022). The goal of this study is to extend the physical-statistical retrieval framework from Singh et al. (2024) to forested environments. Retrieving SWE in forested landscapes remains a major challenge for snow remote sensing, yet it is essential because forests account for roughly one-third of Ear

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