| 30 Apr 2026
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.
This paper presents an OSSE on assimilating phase difference in repeat pass interferometric SAR data at C- L- and P-band, and its implication in estimating dSWE and SWE compared to direct retrievals. The manuscript is well written, and I really appreciated reading this paper. In my opinion, this paper is of great relevance to the community and highlights the strengths and weaknesses of the different sensors/platforms with respect to snowpack properties on the ground. The authors are very transparent in highlighting that this is not an extensive experiment covering all the possible outcomes of what can be expected in reality, but present the impact of key components such as wavelength, snow state (wet-dry), temporal correlation, signal-to-noise ratio, and phase ambiguity.
This paper also highlights the advantage of Bayesian approaches compared to more direct retrievals described by Eq. 2. This shows that even the Bayesian approaches to retrievals could be more suitable, simply by providing an uncertainty on the retrieved value.
Very minor comments:
1. One thing that is not discussed and could support the discussion is the higher sensitivity to atmospheric phase delays with lower frequencies. This gives more certainty to estimations at C-Band, since atmospheric corrections mostly rely on modelled atmospheric conditions. Maybe adding a line on this in the discussion could help guide future work.
2. I would standardize the phase units across the text to avoid confusion between degrees and radians. I would stick with the units that is used to convert dSWE to phi.
3. This might be outside the scope of this study and could be included in future studies is combining the different frequencies. It's been shown that combining C- and L-band phase information greatly improves dSWE/SWE estimates. In this data assimilation framework, I feel it would makes things very interesting showing that this method might/would benefit from the advantages of each frequency while minimizing the down sides.
4. If I understood correctly, the conversion from dSWE to phi assumes a homogeneous snowpack. Given that FSM2 can provide up to three layers, it would be nice to have an understanding of the stratification of the snowpack for the three sites. If the snowpacks are very heterogeneous, this also has implications in how phi changes between two observations, which can be a source of uncertainty in this analysis. Maybe adding a line in the discussion about this.
5. As for temporal correlation between wet-wet pairs, this assumes there is no major snow surface roughness change between the two acquisitions. A change in surface roughness, especially during melt/refreeze events is not uncommon. This could be added in the discussion, but I don't feel it is possible to quantify this in the current OSSE.