Parameter estimation for computationally intensive nonlinear regression with an application to climate modeling

TL;DR

This paper introduces a surrogate-based nonlinear regression method that efficiently estimates climate model parameters, including climate sensitivity, by accounting for surrogate uncertainty in computationally intensive models.

Contribution

It develops a surrogate modeling approach for nonlinear regression that handles computationally expensive functions and incorporates surrogate uncertainty into parameter estimation.

Findings

Successfully estimated climate sensitivity using the surrogate-based method.

Reduced computational time compared to direct maximum likelihood estimation.

Validated approach on the MIT 2D climate model.

Abstract

Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by maximum likelihood is not feasible. The method presented in this paper proposes to construct a faster running surrogate for such a computationally intensive nonlinear function, and to use it in a related nonlinear statistical model that accounts for the uncertainty associated with this surrogate. A pivotal quantity in the Earth's climate system is the climate sensitivity: the change in global temperature due to doubling of atmospheric $\mathrm{CO}_2$ concentrations. This, along with other climate parameters, are estimated by applying the statistical method developed in this paper, where the computationally intensive nonlinear function is the MIT 2D climate model.