Interferometric synthetic aperture radar (InSAR) phase data assimilation for Bayesian snow water equivalent estimation

Abstract. Active microwave measurements, including those using interferometric synthetic aperture radar (InSAR) techniques, have shown promise for characterizing seasonal snowpacks at high spatial resolution. This study demonstrates a Bayesian InSAR phase data assimilation framework for estimating snow water equivalent (SWE) changes (dSWE) and SWE accumulation from dry-snow phase delay measurements at C-, L-, and P-band wavelengths. Two idealized synthetic end-member observing system simulation experiments (OSSEs) were performed in the context of a deep snow year at sites in the Tuolumne watershed. A baseline case with 6-day temporal repeat was used to evaluate the Bayesian framework relative to a deterministic retrieval approach under the two end-member cases where: (i) phase delay data is perfectly unwrapped and (ii) phase delay data is wrapped. In the case of perfectly unwrapped phase measurements, the deterministic retrieval and Bayesian approaches both show good estimation of dSWE across all three wavelengths (< 23 mm RMSE). The Bayesian approach shows reduced RMSE in dSWE (~63-74% of deterministic retrieval RMSE) and SWE (~5-34% of the deterministic retrieval RMSE). The primary source of error in SWE for the retrieval estimates is at the site where a month-long gap in measurements, due to wet snow early in the accumulation season, leads to missing dSWE events that result in SWE underestimation. In the case of fully wrapped phase measurements, ambiguity due to wrapping leads to very large (bias) errors in deterministically retrieved dSWE. The Bayesian framework uses an appropriate likelihood function to account for phase wrapping so that, when combined with the prior information provided by the modeling framework, results show minimal degradation to the perfectly unwrapped case in most test cases (except for the C-band case with a long temporal measurement gap). Tests examining the sensitivity to measurement error standard deviation and temporal repeat highlight the ability of the Bayesian approach to add value to the retrieval of dSWE and SWE across a range of cases. Future work should test the Bayesian framework with real InSAR phase data (e.g. Sentinel-1 C-band and NISAR L-band) across the range of physiographic and snow characteristics and phase retrieval error expected in mountain snow domains.