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Parameter estimation for energy balance models with memory

Profile image of Mickael David ChekrounMickael David Chekroun

2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

https://doi.org/10.1098/RSPA.2014.0349
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20 pages

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Abstract

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 definitionD, using only temperature information in a small subdomainE⊂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 l...

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