In a physical sense, it can be useful to define inverse problems as those
in which the direction of mathematical inference is opposite to the direction
of real-world causality. Since many real-world processes are dissipative,
leading to loss of information, inversions that attempt to recover this
attenutated information are subject to what is termed ill-conditioning,
i.e. extreme sensitivity to errors in the models and data. Quantifying
the sensitivity to model error can be particularly difficult since there
are few ways to identify model error and inclusion of model error often
requires non-linear estimation techniques.
Mathematical studies of inverse problems often take the ill-conditioning
as the defining characteristic of inverse problems.
Inverse problems occur widely in fields such as seismology, satellite-based
remote sensing, medical imaging and oceanography.
Trace gas inversions
The trace gas inversion problem is that of using measurements of concentrations
of trace atmospheric gases such as carbon dioxide in order to deduce the
sources and sinks of these gases. My recent book, Inverse Problems in
Atmospheric Constituent Transport, by I.G. Enting (CUP, 2002) reviews
the field of global-scale trace gas inversions. A bibliography of papers
on CO2 inversions, including all references from my book, is on this site
The study of inversions of CO2 data, designed to enhance understanding
of the global carbon cycle, have been greatly assisted by the
activity. The TransCom intercomparison aims to investigate differences
between transport models in order to help quantify the model error in trace
gas inversions. (In the earth system sciences community, the term "intercomparison"
has been adopted to denote comparison between models, often at greater
detail that that for which observational data are available).
MASCOS projects on inversions
Statistical diagnostics for inversions
This project is undertaken within the TransCom
project, jointly with Anna
Michalak of U. Michigan and other members of the TransCom group.
The aim is to develop and apply statistical diagnostics for synthesis
inversion of CO2 and similar trace gases.
Complex systems linkages
Data assimilation as a framework for analysing a range of complex systems
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Ian Enting: last update 29/5/06.