Data-driven equation discovery of a sea ice albedo parametrisation

Abstract. In many sea ice models, a single-category, zero layer thermodynamic scheme is employed, in which sea ice albedo is prescribed based on surface types depending on snow cover, surface temperature, or sea ice thickness. The Parkinson and Washington parametrisation (PW79) is a commonly used one, which assigns four constant albedo values corresponding to distinct surface types. This parametrisation is too simple to capture the spatiotemporal variability of observed sea ice albedo. Here, we aim for an improved parametrisation by discovering an interpretable, physically consistent equation for sea ice albedo using symbolic regression, an interpretable machine learning technique, combined with physical constraints. Leveraging daily pan-Arctic satellite and reanalyses data from 2013–2020 – dominated by conditions representative of the Central Arctic – we apply sequential feature selection which identifies snow depth, surface temperature, sea ice thickness and 2 m air temperature as the most informative features for sea ice albedo. As a function of these features, our data-driven equation identifies two critical mechanisms for determining sea ice albedo: the high sensitivity of sea ice albedo to small changes in thin snow and a weighted difference of the sea ice surface and 2 m air temperature, serving as a seasonal proxy that indicates the transition between melting and freezing conditions. To understand how additional model complexity reduces errors, we evaluate our discovered equation against baseline models with different complexities, such as multilayer perceptron neural networks (NNs) and polynomials on an error-complexity plane, showing that the equation excels in balancing error and complexity and reduces the mean squared error by about 51 % compared to PW79. Unlike NNs, our discovered equation allows for further regional and seasonal analyses due to its inherent interpretability. When fine-tuning its coefficients offline on regional or seasonal subsets, we uncover differences in physical conditions that drive sea ice albedo. As a use case, we further assess the Barents Sea as a contrasting sea ice regime compared to the Central Arctic, showing that the functional form of the equation remains transferable across different sea ice regimes. This study demonstrates that learning an equation from observational data can deepen the process-level understanding of the Arctic Ocean’s surface radiative budget and improve climate projections.