%0 Journal Article
%T Parameter estimation for energy balance models with memory
%+ Biostatistique et Processus Spatiaux (BioSP)
%+ Department of Atmospheric and Oceanic Sciences [Los Angeles] (AOS)
%+ Institut de Mathématiques de Marseille (I2M)
%+ Aix Marseille Université (AMU)
%+ Centre National de la Recherche Scientifique (CNRS)
%+ École Centrale de Marseille (ECM)
%+ Laboratoire de Météorologie Dynamique (UMR 8539) (LMD)
%+ Institute of Geophysics and Planetary Physics [Los Angeles] (IGPP)
%A Roques, Lionel
%A Chekroun, Mickaël D.
%A Cristofol, Michel
%A Soubeyrand, Samuel
%A Ghil, Michael
%Z This study was supported by the US National Science Foundation grant DMS-1049253 and the French 'Agence Nationale de la Recherche' within the projects PREFERED and URTICLIM
%< avec comité de lecture
%@ 0080-4630
%J Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
%I Royal Society, The
%V 470
%N 2169
%8 2014
%D 2014
%R 10.1098/rspa.2014.0349
%K age dating
%K energy balance model
%K mechanistic-statistical model
%K Bayesian inference
%K inverse problem
%K memory effects
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%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 (PDEs) 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, which 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.
%G English
%2 https://hal.science/hal-01264057/document
%2 https://hal.science/hal-01264057/file/RCCSG-PTRSA.pdf
%L hal-01264057
%U https://hal.science/hal-01264057
%~ INSU
%~ X
%~ ENS-PARIS
%~ ENPC
%~ UPMC
%~ CNRS
%~ UNIV-AMU
%~ INRA
%~ EC-MARSEILLE
%~ X-LMD
%~ X-DEP
%~ X-DEP-MECA
%~ PARISTECH
%~ LMD
%~ ENPC-LMD
%~ I2M
%~ I2M-2014-
%~ TDS-MACS
%~ PSL
%~ AGREENIUM
%~ UPMC_POLE_3
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ INRAE
%~ ENS-PSL
%~ SU-TI
%~ ALLIANCE-SU
%~ BIOSP
%~ MATHNUM
%~ INRAEPACA
%~ TEST-MATHNUM
%~ JSE2024