Data-driven equation discovery of a sea ice albedo parametrisation

In the sea ice model Finite-Element Sea Ice Model (FESIM), a part of the Finite-Element Sea ice Ocean Model (FESOM), sea ice albedo is treated as a tuning parameter defined by four constant values depending on snow cover and surface temperature. This parametrisation is too simple to capture the spatiotemporal variability in sea ice albedo observed via satellites. Our work aims to improve this 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 pan-Arctic satellite and reanalyses data from 2013 to 2020, we apply sequential feature selection to identify the most informative input variables for sea ice albedo. With sequential feature selection, we develop parsimonious models that perform well with as few input variables as possible. To understand how additional model complexity reduces error, we evaluate our discovered equations against baseline models with different complexities, such as multilayer perceptron neural networks and polynomials on an error-complexity plane, identifying the models on the Pareto front. Our results indicate that parsimonious models demonstrate better generalisation to unseen data than models using the full set of input variables. Compared to the current FESIM parametrisation, our best equation reduces the mean squared error by about 51%, while excelling in balancing error and complexity. Unlike neural networks, our equation allows for further regional and seasonal analyses due to its inherent interpretability by fine-tuning the coefficients representing the weights of each term and input variable. Through the synergy of observations with machine learning, we aim to deepen the process-level understanding of the Arctic Ocean’s surface radiative budget and reduce uncertainty in climate projections.