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| Titel |
A regularization of the carbon cycle data-fusion problem |
| VerfasserIn |
Sylvain Delahaies, Ian Roulstone, Nancy Nichols |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250075404
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| Zusammenfassung |
| Improving our understanding of the carbon cycle is an important component of
modelling climate and the Earth system, and a variety of data assimilation techniques
have been used to combine process models with different types of observational
data.
Here, we carry out a careful mathematical analysis on a simple, yet generic, version of the
carbon allocation inverse problem. At the heart of a Bayesian approach to data-model
fusion is the following problem: given a generalized observation operator H, and
observations y, determine the model state x that minimizes |Hx - y| in a given
norm. Such a problem is well-posed if a unique solution x = H-1y exists, and if
the inverse of H is continuous. However, in discrete models such a problem can
be ill-conditioned, and hence ill-posed, when the singular values of H decay to
zero.
Our analysis is carried out on the evergreen version of the Data Assimilation-Linked
Ecosystem model (DALEC EV). DALEC EV depicts a forest ecosystem as a set
of five carbon pools: the gross primary production (GPP) is calculated at a daily
time step as a function of the foliar carbon and meteorological drivers, following a
mass conservation principle the GPP is then entirely allocated to carbon pools and
respiration via fluxes. While this model is very simple, it represents the basic processes
simulated by more sophisticated models of the carbon cycle and the low dimension of
the state variable (five carbon pools and eleven parameters) allows direct solution
using otherwise hopeless methods. Using synthetic observations of net ecosystem
exchange (NEE), defined as the difference between GPP and respirations, we study the
conditioning of the inverse problem. We found that the generalized observation operator is
ill-conditioned and we study the impact of various regularization techniques: generalized
Tikhonov regularization, total least square etc. Finally we use the formalism of
control theory to apply model reduction techniques to the regularization problem. |
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