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.
[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.
An overview of the technique called DINEOF (Data Interpolating Empirical Orthogonal Functions) is presented. DINEOF reconstructs missing information in geophysical data sets, such as satellite imagery or time series. A summary of the technique is given, with its main characteristics, recent developments and future research directions. DINEOF has been applied to a large variety of oceanographic variables in various domains of different sizes. This technique can be applied to a single variable (monovariate approach), or to several variables together (multivariate approach), with no complexity increase in the application of the technique. Error fields can be computed to establish the accuracy of the reconstruction. Examples are given to illustrate the capabilities of the technique. DINEOF is freely offered to download, and help is provided to users in the form of a wiki and through a discussion email list.
Abstract. A method is presented to create an ensemble of perturbations that satisfies linear dynamical constraints. A cost function is formulated defining the probability of each perturbation. It is shown that the perturbations created with this approach take the land-sea mask into account in a similar way as variational analysis techniques. The impact of the land-sea mask is illustrated with an idealized configuration of a barrier island. Perturbations with a spatially variable correlation length can be also created by this approach. The method is applied to a realistic configuration of the West Florida Shelf to create perturbations of the M2 tidal parameters for elevation and depth-averaged currents. The perturbations are weakly constrained to satisfy the linear shallow-water equations. Despite that the constraint is derived from an idealized assumption, it is shown that this approach is applicable to a non-linear and baroclinic model. The amplitude of spurious transient motions created by constrained perturbations of initial and boundary conditions is significantly lower compared to perturbing the variables independently or to using only the momentum equation to compute the velocity perturbations from the elevation.
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