  Due to the rapidly changing climate, the frequency and severity of extreme
weather is expected to increase over the coming decades. As fully-resolved
climate simulations remain computationally intractable, policy makers must rely
on coarse-models to quantify risk for extremes. However, coarse models suffer
from inherent bias due to the ignored "sub-grid" scales. We propose a framework
to non-intrusively debias coarse-resolution climate predictions using
neural-network (NN) correction operators. Previous efforts have attempted to
train such operators using loss functions that match statistics. However, this
approach falls short with events that have longer return period than that of
the training data, since the reference statistics have not converged. Here, the
scope is to formulate a learning method that allows for correction of dynamics
and quantification of extreme events with longer return period than the
training data. The key obstacle is the chaotic nature of the underlying
dynamics. To overcome this challenge, we introduce a dynamical systems approach
where the correction operator is trained using reference data and a coarse
model simulation nudged towards that reference. The method is demonstrated on
debiasing an under-resolved quasi-geostrophic model and the Energy Exascale
Earth System Model (E3SM). For the former, our method enables the
quantification of events that have return period two orders longer than the
training data. For the latter, when trained on 8 years of ERA5 data, our
approach is able to correct the coarse E3SM output to closely reflect the
36-year ERA5 statistics for all prognostic variables and significantly reduce
their spatial biases.
