  Global Climate Model (GCM) tuning (calibration) is a tedious and
time-consuming process, with high-dimensional input and output fields. Experts
typically tune by iteratively running climate simulations with hand-picked
values of tuning parameters. Many, in both the statistical and climate
literature, have proposed alternative calibration methods, but most are
impractical or difficult to implement. We present a practical, robust and
rigorous calibration approach on the atmosphere-only model of the Department of
Energy's Energy Exascale Earth System Model (E3SM) version 2. Our approach can
be summarized into two main parts: (1) the training of a surrogate that
predicts E3SM output in a fraction of the time compared to running E3SM, and
(2) gradient-based parameter optimization. To train the surrogate, we generate
a set of designed ensemble runs that span our input parameter space and use
polynomial chaos expansions on a reduced output space to fit the E3SM output.
We use this surrogate in an optimization scheme to identify values of the input
parameters for which our model best matches gridded spatial fields of climate
observations. To validate our choice of parameters, we run E3SMv2 with the
optimal parameter values and compare prediction results to expertly-tuned
simulations across 45 different output fields. This flexible, robust, and
automated approach is straightforward to implement, and we demonstrate that the
resulting model output matches present day climate observations as well or
better than the corresponding output from expert tuned parameter values, while
considering high-dimensional output and operating in a fraction of the time.
