Advanced Data Interpolating Variational Analysis. Application to climatological data

DIVA (Data Interpolating Variational Analysis) is a variational analysis tool designed to interpolate irregularly-spaced, noisy data onto any desired location, in most cases on regular grids. It is the combination of a particular methodology, based on the minimization of a functional, and a numerically efficient resolution method, based on a finite elements solver. The intrinsic advantages of DIVA are its natural way to take into account topographic and dynamic constraints (coasts, advection, ...) and its capacity to handle large data sets, frequently encountered in oceanography.

In the present work, we describe various improvements to the variational analysis tool. The most significant advance is the development of a full error calculation, whilst until now, only an approximate error-field estimate was available. The key issue is the numerical determination of the real covariance function in DIVA, which is not formulated explicitly. This is solved by two concurrent executions of two DIVA, one providing the covariance for the other. The new calculation of the error field is now perfectly coherent with the inherent background covariance in all cases.

The correlation length, which was previously set uniform over the computational domain, is now allowed to vary spatially. The efficiency of the tools for estimating the signal-to-noise ratio, through generalized cross-validation, has also been improved. Finally, a data quality-control method is implemented and allows one to detect possible outliers, based on statistics of the data-reconstruction misfit.

The added value of these features are illustrated in the case of a large data set of salinity measured in the Mediterranean Sea. Several analyses are performed with different parameters in order to demonstrate their influence on the interpolated fields. In particular, we examine the benefits of using the parameter optimization tools and the advection constraint. The results are validated by means of a subset of data set apart for an independent validation. The corresponding errors fields are estimated using different methods and underline the role of the data coverage.