Stably numerical solving inverse boundary value problem for data assimilation

In remote sensing data assimilation, inverse methods are often used to retrieve the boundary conditions from some of the observations in the interior scanning region. Needless to say, the inverse boundary value problem (IBVP) is ill-conditioned in general. Ultimately, the data assimilation must incl...

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Bibliographic Details
Published in:Applied Mathematical Modelling Vol. 82; p. 825
Main Authors: Mu, Xiyu, Cheng, Hao, Xu, Qi, Liu, Guoqing
Format: Journal Article
Language:English
Published: New York Elsevier BV 01.06.2020
Subjects:
Boundary conditions
Boundary value problems
Data assimilation
Ill-conditioned problems (mathematics)
Remote sensing
ISSN:1088-8691, 0307-904X
Online Access:Get full text
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Summary:In remote sensing data assimilation, inverse methods are often used to retrieve the boundary conditions from some of the observations in the interior scanning region. Needless to say, the inverse boundary value problem (IBVP) is ill-conditioned in general. Ultimately, the data assimilation must include mechanisms that enable them to overcome the numerical instability for solving IBVP. In this paper, we begin by studying the behavior of ill-conditioned IBVP, and find that the condition number varies with the number of the observations and distribution locations of the observations. Next, we define the number of equivalent independent equations as a novel measurement of ill-conditioning of a problem, which can measure the degree of bad conditions. Furthermore, the novel measure can answer how many additional observations are needed to stabilize the retrieving problem, and where additional observations are fixed up. Finally, we illustrate the proposed methodology by applying it to the study of precipitation data assimilation, with a particular emphasis on the analysis of the effect of the number of observations and their distribution locations. The new methodology appears to be particularly efficient in tackling the instability of the retrieving problem in data assimilation.
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ISSN:1088-8691
0307-904X
DOI:10.1016/j.apm.2020.01.071