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

High-dimensional parametric uncertainty exists in many parts of atmospheric climatemodels. It is computationally intractable to fully understand their impact on the climatewithout a significant reduction in the number of dimensions. We employ Bayesian CompressedSensing (BCS) to perform adaptive sensitivity analysis in order to determine whichparameters affect the Quantity of Interest (QoI) the most and the least. In short, BCSfits 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 fewestterms, while still trying to retain high accuracy. This procedure is adaptive in the sensethat higher order polynomial terms can be added to the polynomial model when it is likely thatparticular 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 byCLUBB (Cloud Layers Unified By Binormals), an atmospheric cloud and turbulence model.This liquid cloud fraction QoI depends on 29 different input parameters. We compare mainSobol sensitivity indices obtained with the BCS algorithm for the liquid cloud fraction in6 cases, with a previous approach to sensitivity analysis using deviance. We show BCS canprovide almost identical sensitivity analysis results. Additionally, BCS can provide animproved, lower-dimensional, higher order model for prediction. In the secondapplication, we study the time averaged ozone concentration, at varying altitudes, as afunction of 95 photochemical parameters, in order to study the sensitivity to theseparameters. To further improve model prediction, we also explore k-fold cross validationto obtain a better model for both liquid cloud fraction in CLUBB and ozone concentrationin 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.