  Data-driven models, such as FourCastNet (FCN), have shown exemplary
performance in high-resolution global weather forecasting. This performance,
however, is based on supervision on mesh-gridded weather data without the
utilization of raw climate observational data, the gold standard ground truth.
In this work we develop a methodology to correct, remap, and fine-tune gridded
uniform forecasts of FCN so it can be directly compared against observational
ground truth, which is sparse and non-uniform in space and time. This is akin
to bias correction and post-processing of numerical weather prediction (NWP), a
routine operation at meteorological and weather forecasting centers across the
globe. The Adaptive Fourier Neural Operator (AFNO) architecture is used as the
backbone to learn continuous representations of the atmosphere. The spatially
and temporally non-uniform output is evaluated by the non-uniform discrete
inverse Fourier transform (NUIDFT) given the output query locations. We call
this network the Deep-Learning-Corrector-Remapper (DLCR). The improvement in
DLCR's performance against the gold standard ground truth over the baseline's
performance shows its potential to correct, remap, and fine-tune the
mesh-gridded forecasts under the supervision of observations.
