Generation of analysis and consistent error fields using the Data Interpolating Variational Analysis (DIVA)

The Data Interpolating Variational Analysis (DIVA) is a method 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 minimisation of a cost function, and a numerically efficient method, based on a finite-element solver. The cost function penalises the misfit between the observations and the reconstructed field, as well as the regularity or smoothness of the field. The method bears similarities to the smoothing splines, where the second derivatives of the field are also penalised.The intrinsic advantages of the method are its natural way to take into account topographic and dynamic constraints (coasts, advection, etc.) and its capacity to handle large data sets, frequently encountered in oceanography. The method provides gridded fields in two dimensions, usually in horizontal layers. Three-dimension fields are obtained by stacking horizontal layers.In the present work, we summarize the background of the method and describe the possible methods to compute the error field associated to the analysis. In particular, we present new developments leading to a more consistent error estimation, by determining numerically the real covariance function in DIVA, which is never formulated explicitly, contrarily to Optimal Interpolation. The real covariance function is obtained by two concurrent executions of DIVA, the first providing the covariance for the second. With this improvement, the error field is now perfectly consistent with the inherent background covariance in all cases.A two-dimension application using salinity measurements in the Mediterranean Sea is presented. Applied on these measurements, Optimal Interpolation and DIVA provided very similar gridded fields (correlation: 98.6%, RMS of the difference: 0.02). The method using the real covariance produces an error field similar to the one of OI, except in the coastal areas.

► The covariance function in DIVA is influenced by the physical boundaries (coastline, bottom) and by dynamics (current, diffusion).
► The analysis performed using DIVA and OI in an infinite domain are equivalent.
► The real data covariance can be accessed using two concurrent executions of DIVA.
► The error fields provided by OI and DIVA are similar.