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.

Date

Dec 2, 2011

Event

AGU Fall Meeting 2011

Location

San Francisco, CA