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, . . . ) 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.

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[1] An innovative multi-model fusion technique is proposed to improve short-term ocean temperature forecasts: the threedimensional super-ensemble. In this method, a Kalman Filter is used to adjust three-dimensional model weights over a past learning period, allowing to give more importance to recent observations, and take into account spatially varying model skills. The predictive performance is evaluated against SST analyses, CTD casts and gliders tracks collected during the Ligurian Sea Cal/Val 2008 experiment. Statistical results not only show a very significant bias reduction of this multimodel forecast in comparison with the individual models, their ensemble mean and a single-weight-per-model version of the super-ensemble, but also the improvement of other pattern-related skills. In a 48-h forecast experiment, and with respect to the ensemble mean, surface and subsurface rootmean-square differences with observations are reduced by 57% and 35% respectively, making this new technique a suitable non-intrusive post-processing method for multimodel operational forecasting systems.