Bayesian inversion of satellite altimetry for Arctic sea ice and snow thickness

Abstract. Inverse methods have been widely used in the field of Earth Sciences, particularly in seismology. Here, we introduce a new application of inversion theory to retrieve Arctic sea ice thickness (SIT) and its overlying snow depth (SD) using freeboard data from Ku-band/Ka-band radar and laser altimeters. We do this using the TransTessellate2D algorithm, a Bayesian trans-dimensional approach that allows us to invert for an unknown number of model parameters. This new inversion method is probabilistic in nature, and can offer a novel understanding of covariances between fields of interest as well as their uncertainties. We use this approach to jointly retrieve SIT and SD in one step, without using a climatology for SD. The inversion results are statistically encouraging when compared to snow and ice evaluation products: for April 2019, we obtain a higher linear correlation coefficient and a slope closer to the one-to-one line than the AWI CryoSat-2 SIT product compared to the Operation Ice Bridge (OIB) SIT product. For the inverted SD, our results exhibit similar statistical properties to the UiT and AMSR2 SD products when regressed against the OIB SD product. The SD is similar in terms of spatial patterns to the AMSR2 product in the 2018–2021 winter periods. We evaluate the inversion against data from MOSAiC and IceBird missions. These evaluations are also promising, especially for IceBird. Using this approach, we can choose the number of physical variables (SIT, SD and penetration factors) to be inverted for. Thus, we can also invert for the penetration factor, either from one or both satellites (in addition to inverting for SIT and SD at the same time). This paves the way for further research in understanding these penetration factors and their link to SIT and SD retrievals. We obtain values for the penetration factors between 0.5 and 1.2 for CryoSat-2 and around 0 for ICESat-2. Lastly, we investigate the multi-frequency inversion using data from the Ka- and Ku-band radar altimeters, thus preparing for the European Space Agency's planned dual-frequency altimetry mission, CRISTAL.