| 12 Feb 2026
Simulating SAR altimeter echoes from cryospheric surfaces with the Snow Microwave Radiative Transfer (SMRT) model version sarm-v0
Abstract. Radar altimeters are essential tools for observing the cryosphere, especially for estimating ice-sheet elevation change and sea-ice thickness. However, retrieving these quantities remains challenging, and progress depends on physically based numerical simulations of the recorded waveforms to understand their sensitivity to the geophysical parameters of the medium. Such models can also guide the design of future satellite missions. Accurate simulations require a balanced combination of a realistic description of the medium, precise calculation of wave–medium interactions, and an accurate representation of the altimeter measurement process, including downstream processing. The Snow Microwave Radiative Transfer (SMRT) model has addressed the first two aspects for a decade and includes an altimetric Low Resolution Mode (LRM) module, but has, until now, lacked a delay-Doppler (SAR) altimetric capability used by most modern sensors. This study introduces the new SMRT SAR altimetry module, which operates in three steps. First, it calculates the backscatter of all layers and interfaces using existing SMRT modules. Next, it models the waveforms of each layer and interface using a delay-Doppler approach. Finally, these components are combined to produce the final waveform. The user selects the delay-Doppler model from one of eight formulations reviewed, implemented, and compared in the literature. The validation first assesses these models under simple conditions, confirming they produce consistent results but differ in computational efficiency and flexibility. Subsequently, the new module is compared with external models to confirm its accuracy. Finally, it is applied to Antarctic conditions, where the simulations reproduce observed Sentinel-3 waveform variability linked to surface roughness. The open-source module, equipped with the eight options, now enables a wide range of numerical experiments, from studying penetration bias to exploring the potential for snow retrieval on sea ice and lake ice thickness.
The authors present a novel snow microwave radiative transfer model for SAR altimetry signals including surface scattering and snow-volume scattering. Overall, the manuscript is well written but sometimes lacks some clarity. Especially, the volume and interface backscattering function implementation on DDMs was hard to understand from the equations and text presented. Therefore, I believe the manuscript requires major revision.
Page 2 line 31: I personally would write cm/yr instead of cmyr^{-1}
Page 3 line 59: I am not sure about the formulation “an inverse method”. I guess you mean a nonlinear optimization approach fitting a measured waveform with a modelled waveform maximizing the likelihood?
Table 1: I guess AN means analytical (okay it is probably analytical numerical based on table 2, but then I do not understand why Ray is AN and Dinardo is A)? The antenna pattern in Ray et al. (2015) was really a free function? I thought it was Ellip. Gaussian as well. Okay in the paper he did not seem to define the antenna pattern to be Gaussian, but in the SAMOSA based retrackers I am very sure that the Ellip. Gaussian approximation is used. The surface backscatter in SAMOSA should be Gaussian as well? Please check the Halimi retracker as well for the surface backscatter
Table 2: The caption should be changed to match with figure 1. Figure 1 is early models and Figure 2 is models. Maybe say something like newer or recent approaches? Or make one table for ocean and one for ice-sheets and one for sea-ice and soil (not sure to be honest)? Buchhaupt (2018) is a bit outdated but fine to use. Maybe add in the text that an update for stack retracking (10.3390/rs15174206, 10.1016/j.asr.2022.12.034 ) and an antenna pattern update of that approach ( 10.1016/j.asr.2025.02.056 ). The missing yes or no in terrain slope means that e.g. Boy and Dinardo don’t consider the terrain slope? The PTRs in Buchhaupt 2018 is btw arbitrary the paper only uses the sinc^2 PTR as an example.
Table 3: Jack Landy is a coauthor, so I guess he checked it, but wasn’t the facet based retracker allowing an arbitrary antenna pattern and PTR or do you refer to the final LARM implementation here? If yes, I think that pitch and roll only had a limited support which might be worth mentioning? Maybe check with Jack.
Page 9 line 178 needs some clarification as I do not understand why they do not account for slope variations. For open ocean and sea-ice those are considered in the backscatter function as far as I know. Or do you mean non random variations?
Page 9 line 180: The ocean PDF for SAR altimetry is actually 2D (one dimension is the elevation and one dimension the vertical velocity) and the 1D PDF is an approximation yielding SWH errors for open ocean surfaces. However, for sea-ice it is indeed 1D. Not sure if you want to discuss this here of not since your focus is sea-ice.
Line 185: The height and slope are correlated for non-Gaussian surfaces? Please provide a reference for this claim.
Section 3.1: The DDM and \sigma^0 terms need a clearer definition, preferably with equations defining each. Otherwise, it is unfortunately very hard to follow the authors intention in this section.
Eq. 3: Is \sigma^0_{interface i} a function of the incident angle? In the text below q. 3 it is not. It would also be helpful to define \sigma^0_{volume} and DDM_{volume}. In my (still unpublished) work I just assumed DDM_volume == DDM \conv \sigma^0_{volume}(\tau)
Line 517: A horizontal correlation length of 10 cm sounds very short. Are you sure that this is not a typo?
Line 557: A more detailed description of your roughness scales would be helpful if I did not overread it. Is the roughness w.r.t. the air-snow interface?
Figure 6: What extinction coefficient would that correspond to?