Approximate and Efficient Methods to Assess Error Fields in Spatial Gridding with Data Interpolating Variational Analysis (DIVA)

This paper presents new approximate methods to provide error fields for the spatial analysis tool Data Interpolating Variational Analysis (DIVA). The first method shows how to replace the costly analysis of a large number of covariance functions with a single analysis for quick error computations. Then another method is presented where the error is only calculated in a small number of locations, and from there the spatial error field itself is interpolated by the analysis tool. The efficiency of the methods is illustrated on simple schematic test cases and a real application in the Mediterranean Sea. These examples show that with these methods, one has the possibility for quick masking of regions void of sufficient data and the production of "exact" error fields at reasonable cost. The error-calculation methods can also be generalized for use with other analysis methods such as three-dimensional variational data assimilation (3DVAR) and are therefore potentially interesting for other implementations.