  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, can closely mirror the systematic bias patterns of the dynamical
model. In this study, we use convolutional neural networks (CNNs) to learn a
mapping from model state variables to analysis increments, in order to showcase
the feasibility of a data-driven model parameterization which can predict
state-dependent model errors. We undertake this problem using an ice-ocean data
assimilation system within the Seamless system for Prediction and EArth system
Research (SPEAR) model, developed at the Geophysical Fluid Dynamics Laboratory,
which assimilates satellite observations of sea ice concentration every 5 days
between 1982--2017. 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 states and tendencies of
sea ice concentration, sea-surface temperature, ice velocities, ice thickness,
net shortwave radiation, ice-surface skin temperature, sea-surface salinity, as
well as a land-sea mask. We find the CNN is able to make skillful predictions
of the increments in both the Arctic and Antarctic and across all seasons, with
skill that consistently exceeds that of a climatological increment prediction.
This suggests that the CNN could be used to reduce sea ice biases in
free-running SPEAR simulations, either as a sea ice parameterization or an
online bias correction tool for numerical sea ice forecasts.
