Deep learning of systematic sea ice model errors from data assimilation increments

Data assimilation is often viewed as a framework for correcting short-term error growth in dynamical climate model forecasts. When viewed on the time scales of climate however, these short-term corrections, or analysis increments, closely mirror the systematic bias patterns of the dynamical model. In this work, we show that Convolutional Neural Networks (CNNs) can be used to learn a mapping from model state variables to analysis increments, thus promoting the feasibility of a data-driven model parameterization which predicts state-dependent model errors. We showcase this problem using an ice-ocean data assimilation system within the fully coupled Seamless system for Prediction and EArth system Research (SPEAR) model at the Geophysical Fluid Dynamics Laboratory (GFDL), which assimilates satellite observations of sea ice concentration. The CNN then takes inputs of data assimilation forecast states and tendencies, and makes predictions of the corresponding sea ice concentration increments. Specifically, the inputs are sea ice concentration, sea-surface temperature, ice velocities, ice thickness, net shortwave radiation, ice-surface skin temperature, and sea-surface salinity. We show that the CNN is able to make skilful predictions of the increments, particularly between December and February in both the Arctic and Antarctic, with average daily spatial pattern correlations of 0.72 and 0.79, respectively. Initial investigation of implementation of the CNN into the fully coupled SPEAR model shows that the CNN can reduce biases in retrospective seasonal sea ice forecasts by emulating a data assimilation system, further suggesting that systematic sea ice biases could be reduced in a free-running climate simulation.