Abstract

Abstract. 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. 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. 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) (http://modb.oce.ulg.ac.be/mediawiki/index.php/divand).

Highlights

  • Deriving a complete gridded field based on a set of observations is a common problem in oceanography

  • The data analysis problem is closely related to data assimilation where the observations are used in combination with a first guess coming from a model

  • Optimal interpolation in the local approximation can be quite efficiently applied to distributedmemory parallel computing architectures. The aim of this manuscript is to implement and test a variational analysis program that can operate in an arbitrary high dimensional space and with a cost function that can be extended with additional constraints

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Summary

Introduction

Deriving a complete gridded field based on a set of observations is a common problem in oceanography. Optimal interpolation in the local approximation can be quite efficiently applied to distributedmemory parallel computing architectures The aim of this manuscript is to implement and test a variational analysis program that can operate in an arbitrary high dimensional space and with a cost function that can be extended with additional constraints. The benefit of this method will be assessed in comparison to assembled twodimensional analyses using an advection constraint forcing the gradients of an analysis to be aligned with a given vector field.

Formulation
Kernel
Additional constraints
Minimization and algorithms
Primal formulation
Direct solver
Factorization
Conjugate gradient method
Benchmark
Implementation
Realistic test case
Findings
Conclusions
Full Text
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