divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations
A tool for multidimensional variational analysis (divand) is presented. It allows the interpolation and analysis of observations on curvilinear orthogonal grids in an arbitrary high dimensional space by minimizing a cost function. This cost function penalizes the deviation from the observations, the...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2014-01-01
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| Series: | Geoscientific Model Development |
| Online Access: | http://www.geosci-model-dev.net/7/225/2014/gmd-7-225-2014.pdf |
| _version_ | 1818022264211243008 |
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| author | A. Barth J.-M. Beckers C. Troupin A. Alvera-Azcárate L. Vandenbulcke |
| author_facet | A. Barth J.-M. Beckers C. Troupin A. Alvera-Azcárate L. Vandenbulcke |
| author_sort | A. Barth |
| collection | DOAJ |
| description | A tool for multidimensional variational analysis (divand) is
presented. It allows the interpolation and analysis of observations on
curvilinear orthogonal grids in an arbitrary high dimensional space by
minimizing a cost function. This cost function penalizes the deviation from
the observations, the deviation from a first guess and abruptly varying
fields based on a given correlation length (potentially varying in space and
time). Additional constraints can be added to this cost function such as an
advection constraint which forces the analysed field to align with the ocean
current. The method decouples naturally disconnected areas based on
topography and topology. This is useful in oceanography where disconnected
water masses often have different physical properties. Individual elements of
the a priori and a posteriori error covariance matrix can also be computed,
in particular expected error variances of the analysis. A multidimensional
approach (as opposed to stacking two-dimensional analysis) has the benefit of
providing a smooth analysis in all dimensions, although the computational
cost is increased.
<br><br>
Primal (problem solved in the grid space) and dual formulations (problem
solved in the observational space) are implemented using either direct
solvers (based on Cholesky factorization) or iterative solvers (conjugate
gradient method). In most applications the primal formulation with the direct
solver is the fastest, especially if an a posteriori error estimate is
needed. However, for correlated observation errors the dual formulation with
an iterative solver is more efficient.
<br><br>
The method is tested by using pseudo-observations from a global model. The
distribution of the observations is based on the position of the Argo floats.
The benefit of the three-dimensional analysis (longitude, latitude and time)
compared to two-dimensional analysis (longitude and latitude) and the role of
the advection constraint are highlighted. The tool divand is free
software, and is distributed under the terms of the General Public Licence (GPL)
(<a href="http://modb.oce.ulg.ac.be/mediawiki/index.php/divand"target="_blank">http://modb.oce.ulg.ac.be/mediawiki/index.php/divand</a>). |
| first_indexed | 2024-04-14T08:29:56Z |
| format | Article |
| id | doaj.art-69abcaf9e0d949f9aaa8d5f8a17cbf9b |
| institution | Directory Open Access Journal |
| issn | 1991-959X 1991-9603 |
| language | English |
| last_indexed | 2024-04-14T08:29:56Z |
| publishDate | 2014-01-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Geoscientific Model Development |
| spelling | doaj.art-69abcaf9e0d949f9aaa8d5f8a17cbf9b2022-12-22T02:03:57ZengCopernicus PublicationsGeoscientific Model Development1991-959X1991-96032014-01-017122524110.5194/gmd-7-225-2014divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observationsA. Barth0J.-M. Beckers1C. Troupin2A. Alvera-Azcárate3L. Vandenbulcke4GHER, University of Liège, Liège, BelgiumGHER, University of Liège, Liège, BelgiumIMEDEA, Esporles, Illes Balears, SpainGHER, University of Liège, Liège, Belgiumseamod.ro/Jailoo srl, Sat Valeni, Com. Salatrucu, Jud. Arges, RomaniaA tool for multidimensional variational analysis (divand) is presented. It allows the interpolation and analysis of observations on curvilinear orthogonal grids in an arbitrary high dimensional space by minimizing a cost function. This cost function penalizes the deviation from the observations, the deviation from a first guess and abruptly varying fields based on a given correlation length (potentially varying in space and time). Additional constraints can be added to this cost function such as an advection constraint which forces the analysed field to align with the ocean current. The method decouples naturally disconnected areas based on topography and topology. This is useful in oceanography where disconnected water masses often have different physical properties. Individual elements of the a priori and a posteriori error covariance matrix can also be computed, in particular expected error variances of the analysis. A multidimensional approach (as opposed to stacking two-dimensional analysis) has the benefit of providing a smooth analysis in all dimensions, although the computational cost is increased. <br><br> Primal (problem solved in the grid space) and dual formulations (problem solved in the observational space) are implemented using either direct solvers (based on Cholesky factorization) or iterative solvers (conjugate gradient method). In most applications the primal formulation with the direct solver is the fastest, especially if an a posteriori error estimate is needed. However, for correlated observation errors the dual formulation with an iterative solver is more efficient. <br><br> The method is tested by using pseudo-observations from a global model. The distribution of the observations is based on the position of the Argo floats. The benefit of the three-dimensional analysis (longitude, latitude and time) compared to two-dimensional analysis (longitude and latitude) and the role of the advection constraint are highlighted. The tool divand is free software, and is distributed under the terms of the General Public Licence (GPL) (<a href="http://modb.oce.ulg.ac.be/mediawiki/index.php/divand"target="_blank">http://modb.oce.ulg.ac.be/mediawiki/index.php/divand</a>).http://www.geosci-model-dev.net/7/225/2014/gmd-7-225-2014.pdf |
| spellingShingle | A. Barth J.-M. Beckers C. Troupin A. Alvera-Azcárate L. Vandenbulcke divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations Geoscientific Model Development |
| title | divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations |
| title_full | divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations |
| title_fullStr | divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations |
| title_full_unstemmed | divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations |
| title_short | divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations |
| title_sort | divand 1 0 i n i dimensional variational data analysis for ocean observations |
| url | http://www.geosci-model-dev.net/7/225/2014/gmd-7-225-2014.pdf |
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