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| Titel |
Kalman filters for assimilating near-surface observations into the Richards equation – Part 1: Retrieving state profiles with linear and nonlinear numerical schemes |
| VerfasserIn |
G. B. Chirico, H. Medina, N. Romano |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1027-5606
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| Digitales Dokument |
URL |
| Erschienen |
In: Hydrology and Earth System Sciences ; 18, no. 7 ; Nr. 18, no. 7 (2014-07-04), S.2503-2520 |
| Datensatznummer |
250120404
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| Publikation (Nr.) |
 copernicus.org/hess-18-2503-2014.pdf |
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| Zusammenfassung |
| This paper examines the potential of different algorithms, based on the
Kalman filtering approach, for assimilating near-surface observations into a
one-dimensional Richards equation governing soil water flow in soil. Our
specific objectives are: (i) to compare the efficiency of different Kalman
filter algorithms in retrieving matric pressure head profiles when they are
implemented with different numerical schemes of the Richards equation;
(ii) to evaluate the performance of these algorithms when nonlinearities arise
from the nonlinearity of the observation equation, i.e. when surface soil
water content observations are assimilated to retrieve matric pressure head
values. The study is based on a synthetic simulation of an evaporation
process from a homogeneous soil column. Our first objective is achieved by
implementing a Standard Kalman Filter (SKF) algorithm with both an explicit
finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite
difference scheme of the Richards equation. The Unscented (UKF) and Ensemble
Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward
Euler finite difference scheme. To accomplish the second objective, an
analogous framework is applied, with the exception of replacing SKF with the
Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so
as to handle the nonlinearity of the observation equation. While the EX
scheme is computationally too inefficient to be implemented in an
operational assimilation scheme, the retrieval algorithm implemented with a
CN scheme is found to be computationally more feasible and accurate than
those implemented with the backward Euler scheme, at least for the examined
one-dimensional problem. The UKF appears to be as feasible as the EnKF when
one has to handle nonlinear numerical schemes or additional nonlinearities
arising from the observation equation, at least for systems of small
dimensionality as the one examined in this study. |
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