Uncertainty quantification (UQ) studies often demand prohibitively
many simulations of computationally expensive climate models.
In such situations, surrogate models are usually employed instead of
full physical models. We rely on Polynomial Chaos (PC)
spectral expansions to build surrogate relationships between output
quantities of interest and model parameters using as few forward model
simulations as possible. These surrogate models are
inexpensive and greatly accelerate both forward and
inverse UQ studies such as global sensitivity analysis and parameter
calibration, respectively.
Motivated by the Community Land Model (CLM), we develop a PC-based
surrogate construction in presence of a large number of input
parameters and non-smooth behavior of the forward model. Namely,
given a sparse set of training simulations, Bayesian compressive
sensing is implemented to obtain a PC surrogate with an optimal,
reduced basis set that best captures the model output
behavior. Furthermore, an iterative algorithm is proposed to improve
the accuracy of the surrogate while reducing the dimensionality of the
PC representation. Since purely polynomial-based surrogates are not
accurate enough for strongly nonlinear models, we generalize the
surrogate construction to a piecewise PC expansion that relies on
clustering and classification of input parameter samples according to
model output values. The resulting sparse, piecewise PC expansion is used to
perform global sensitivity analysis and dimensionality reduction for the
80-parameter CLM.