Applying Bayesian Compressed Sensing (BCS) for sensitivity analysis ofclimate model outputs that depend on a high-dimensional input space

Abstract:

High-dimensional parametric uncertainty exists in many parts of atmospheric climate
models. It is computationally intractable to fully understand their impact on the climate
without a significant reduction in the number of dimensions. We employ Bayesian Compressed
Sensing (BCS) to perform adaptive sensitivity analysis in order to determine which
parameters affect the Quantity of Interest (QoI) the most and the least. In short, BCS
fits a polynomial to the QoI via a Bayesian framework with an L1 (Laplace) prior. Thus,
BCS tries to find the sparsest polynomial representation of the QoI, i.e., the fewest
terms, while still trying to retain high accuracy. This procedure is adaptive in the sense
that higher order polynomial terms can be added to the polynomial model when it is likely that
particular parameters have a significant effect on the QoI. This helps avoid overfitting and is much more computationally efficient.

We apply the BCS algorithm to two sets of single column CAM (Community Atmosphere Model)
simulations. In the first application, we analyze liquid cloud fraction as modeled by
CLUBB (Cloud Layers Unified By Binormals), an atmospheric cloud and turbulence model.
This liquid cloud fraction QoI depends on 29 different input parameters. We compare main
Sobol sensitivity indices obtained with the BCS algorithm for the liquid cloud fraction in
6 cases, with a previous approach to sensitivity analysis using deviance. We show BCS can
provide almost identical sensitivity analysis results. Additionally, BCS can provide an
improved, lower-dimensional, higher order model for prediction. In the second
application, we study the time averaged ozone concentration, at varying altitudes, as a
function of 95 photochemical parameters, in order to study the sensitivity to these
parameters. To further improve model prediction, we also explore k-fold cross validation
to obtain a better model for both liquid cloud fraction in CLUBB and ozone concentration
in CAM.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under the Scientific Discovery through Advanced Computing program.