We address challenges that sensitivity analysis and uncertainty
quantification methods face when dealing with complex computational
models. In particular, climate models are computationally expensive and
typically depend on a large number of input parameters. We
consider the Community Land Model (CLM), which consists of a nested
computational grid hierarchy designed to represent the spatial
heterogeneity of the land surface. Each computational cell can be
composed of multiple land types, and each land type can incorporate
one or more sub-models describing the spatial and depth
variability. Even for simulations at a regional scale, the
computational cost of a single run is quite high and the
number of parameters that control the model behavior is very
large. Therefore, the parameter sensitivity analysis and uncertainty
propagation face significant difficulties for climate models. This
work employs several algorithmic avenues to address
some of the challenges encountered by classical uncertainty
quantification methodologies when dealing with expensive computational
models, specifically focusing on the CLM as a primary application.
First of all, since the available climate model predictions
are extremely sparse due to the high computational cost of model runs,
we adopt a Bayesian framework that effectively incorporates
this lack-of-knowledge as a source of uncertainty, and
produces robust predictions with quantified uncertainty
even if the model runs are extremely sparse. In
particular, we infer Polynomial Chaos spectral expansions that
effectively encode the uncertain input-output relationship and allow efficient
propagation of all sources of input uncertainties to outputs of
interest.
Secondly, the predictability analysis of climate models strongly suffers
from the curse of dimensionality, i.e. the large number of
input parameters. While single-parameter perturbation studies can
be efficiently performed in a parallel fashion, the multivariate
uncertainty analysis requires a large number of training runs, as well as
an output parameterization with respect to a fast-growing spectral basis set.
To alleviate this issue, we adopt the Bayesian view of compressive
sensing, well-known in the image recognition community. The
technique efficiently finds a sparse representation of the model
output with respect to a large number of input variables, effectively
obtaining a reduced order surrogate model for the input-output
relationship. The methodology is preceded by a sampling strategy that takes into account input parameter constraints by an initial mapping of the
constrained domain to a hypercube via the Rosenblatt transformation,
which preserves probabilities. Furthermore, a sparse quadrature sampling,
specifically tailored for the reduced basis, is employed in
the unconstrained domain to obtain accurate representations.