%0 Journal Article
%J Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences
%D 2014
%T Parameter estimation for energy balance models with memory
%A Roques, Lionel
%A Chekroun, Mickaël D.
%A Cristofol, Michel
%A Soubeyrand, Samuel
%A Ghil, Michael
%X We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations with integral memory terms. First, we show that a space-dependent parameter can be determined uniquely everywhere in the PDE’s domain of definition D, using only temperature information in a small subdomain E⊂D. This result is valid only when the data correspond to exact measurements of the temperature. We propose a method for estimating a model parameter of the EBMM using more realistic, error-contaminated temperature data derived, for example, from ice cores or marine-sediment cores. Our approach is based on a so-called mechanistic-statistical model that combines a deterministic EBMM with a statistical model of the observation process. Estimating a parameter in this setting is especially challenging, because the observation process induces a strong loss of information. Aside from the noise contained in past temperature measurements, an additional error is induced by the age-dating method, whose accuracy tends to decrease with a sample’s remoteness in time. Using a Bayesian approach, we show that obtaining an accurate parameter estimate is still possible in certain cases.
%B Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences
%I The Royal Society
%V 470
%G eng
%U http://rspa.royalsocietypublishing.org/content/470/2169/20140349
%N 2169
%R 10.1098/rspa.2014.0349