divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations

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 threedimensional 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)

ECCO version 4: an integrated framework for non-linear inverse modeling and global ocean state estimation

“…The (re)implementation of Eq. 12within MITgcm provides a versatile environment for such projects, and for variational estimation purposes most generally (and is complementary to, e.g., Moore et al, 2011;Barth et al, 2014;Wilson et al, 2014;Hoppe et al, 2014).…”

“…Looking to the future, the need for associating formal error estimates with the full, evolving ocean state remains of utmost importance. Aside from this aspect, extensions of the state estimation framework to include other climate components (atmosphere, land, cryosphere) and different variables (biology, chemistry) would be desirable (see, e.g., Blessing et al, 2014;Prinn et al, 2011). By providing ECCO v4 as a fully integrated framework along with a useful baseline solution that any interested investigator should be able to reproduce for the foreseeable future, the authors aim to stimulate independent research along those lines.…”

Surface ocean pH and buffer capacity: past, present and future

“…Spatial mapping was conducted using a MATLAB version (Divand Software) of the Data-Interpolating Variational Analysis (DIVA) 42 . Correlation lengths of 42° Longitude × 21° Latitude and a Signal to Noise ratio (SN) of 3.0 were chosen to minimize disagreements between pH gridded based on SOCATv6 calculations and that based on GLODAPv2 calculations.…”

Variational interpolation of high-frequency radar surface currents using DIVAnd

“…The DIVA method, as any method related to optimal interpolation, naturally allows extrapolation of the measurements. Such plots are useful because they visually represent the underlying background error covariance matrix (e.g., Keppenne et al 2008;Barth et al 2014). The final analysis is in fact a linear combination of these functions represented in Fig.…”

“…The DIVAnd method (Barth et al 2014) is an extension of DIVA (Data Interpolating Variational Analysis, Brasseur and Haus 1991;Troupin et al 2012;Beckers et al 2014) for more than 2 dimensions. In this work, DIVAnd is first applied to radial current measurements using various dynamical constraints in Section 2.…”