Simplification operator and its inverse for multi-incremental assimilation

This document describes the implementation of the Simplification Operator and its generalized inverse within the NEMOVAR framework

Implementation of the weak constraint 4D-Var in NEMOVAR

4D-Var is designed to handle observations that are distributed in time over a given period and to compare them with the model state at the appropriate time. Usually 4D-Var seeks the initial condition of the assimilation period such that the model trajectory best fits the observations within this interval. In most of the current 4D-Var implementations, while errors in observations and background state are accounted for, the numerical model representing the evolution of the atmospheric flow is assumed perfect, or at least the model errors are assumed small enough to be neglected compared to other errors in the system. This assumption is often called strong constraint 4D-Var. When going toward high resolution, However, in weak-constraint 4D-Var a sequence of model states are estimated (rather than just the initial state), with the consequence that the tangent linear assumption is relied upon only for the shorter time segment between successive state estimates, and not for propagation of information throughout the assimilation window. The weak-constraint 4D-Var system is truly four-dimensional in the sense that the model state vector is determined at a succession of times within the assimilation window. The present report study the implementation of weak constaint 4D-Var in NEMOVA

Toward variational data assimilation for coupled models: first experiments on a diffusion problem

International audienceNowadays, coupled models are increasingly used in a wide variety of fields including weather forecasting. We consider the problem of adapting existing variational data assimilation methods to this type of application while imposing physical constraints at the interface between the models to be coupled. We propose three data assimilation algorithms to address this problem. The proposed algorithms are distinguished by their choice of cost function and control vector as well as their need to reach convergence of the iterative coupling method (the Schwarz domain decomposition method is used here). The performance of the methods in terms of computational cost and accuracy are compared using a linear 1D diffusion problem.De nos jours, les modèles couplés sont de plus en plus utilisés dans de nombreux domaines, dont les prévisions météorologiques. Nous essayons ici d'adapter les méthodes courantes d'assimilation de données variationnelles à ce type d'applications tout en imposant des contraintes physiques entre les deux modèles couplés. Nous proposons trois méthodes d'assimilation de données pour ce problème. Les différents algorithmes se distinguent par le choix de leur fonction coût, de leur vecteur de contrôle et du nombre d'itérations de couplage nécessaires (nous utilisons les méthodes de Schwarz pour coupler nos modèles). Ces méthodes sont comparées dans le cadre d'un problème linéaire de diffusion 1D en analysant leur coût de calcul et la qualité de leur analyse

Historical reconstruction of the Atlantic Meridional Overturning Circulation from the ECMWF operational ocean reanalysis

A reconstruction of the Atlantic Meridional Overturning Circulation (MOC) for the period 1959–2006 has been derived from the ECMWF operational ocean reanalysis. The reconstruction shows a wide range of time-variability, including a downward trend. At 26N, both the MOC intensity and changes in its vertical structure are in good agreement with previous estimates based on trans-Atlantic surveys. At 50N, the MOC and strength of the subpolar gyre are correlated at interannual time scales, but show opposite secular trends. Heat transport variability is highly correlated with the MOC but shows a smaller trend due to the warming of the upper ocean, which partially compensates for the weakening of the circulation. Results from sensitivity experiments show that although the time-varying upper boundary forcing provides useful MOC information, the sequential assimilation of ocean data further improves the MOC estimation by increasing both the mean and the time variability

Contributions to the calibration of integrated land use and transportation models

International audienceThe need for land use and transport integrated modelling (LUTI modelling) as a decision aid tool in urban planning, has become apparent. Instantiating such models on cities, requires a substantial data collection, model structur-ing and parameter estimation effort. This work is a partial effort towards the integrated calibration of LUTI models. It considers one of the most widely used LUTI models and softwares, Tranus. The usual calibration approach for Tranus is briefly reviewed, then the calibration of Tranus' land use module is reformulated as an optimisation problem, proposing a clear basis for future fully integrated calibration. We analyse the case of transportable and non-transportable economic sectors. We also discuss how to validate calibration results and propose to use synthetic data generated from real world problems in order to assess convergence properties and accuracy of calibration methods. Finally, results of this methodology are presented for real world scenarios

Robust calibration of numerical models based on relative regret

Classical methods of parameter estimation usually imply the minimisation of an objective function, that measures the error between some observations and the results obtained by a numerical model. In the presence of random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced. In this paper, we are going to present how to take into account those uncertainties by defining a family of calibration objectives based on the notion of relative-regret with respect to the best attainable performance given the uncertainties and compare it with the minimum in the mean sense, and the minimum of variance

Formulating LUTI Calibration As an Optimisation Problem: Estimation of Tranus Shadow Price and Substitution Parameters

International audienceCities and their employment catchment areas are focus points of economic activity, transportation, and social interactions. The need for land use and transport integrated modelling (LUTI modelling) as a decision aid tool in urban planning, has become apparent. Instantiating such models on cities, requires a substantial data collection, model structuring and parameter estimation effort; for conciseness, the latter is referred to here as calibration. This work is a partial effort towards the integrated calibration of LUTI models. It considers one of the most widely used LUTI models and softwares, Tranus. The usual calibration approach for Tranus is briefly reviewed. It is then reformulated as an optimisa-tion problem, in order to make it amenable to the systematic incorporation of constraints on parameters and additional data and to form a clear basis for future fully integrated calibration. The problem at hand concerns a dynamic system; an approach is shown how to " eliminate " parts of the dynamics in order to ease the parameter optimisation. We also discuss how to validate calibration results and propose to use synthetic data generated from real world problems in order to assess convergence properties and accuracy of calibration methods

Accounting for correlated observation errors in image data assimilation

International audienceSatellites images can provide a lot of information on the earth system evolution. Although those sequences are frequently used, the importance of spatial error correlation are rarely taken into account in practice. This results in discarding a huge part of the information content of satellite image sequences. In this paper, we investigate a method based on wavelet or curvelet transforms to represent (at an affordable cost) some of the observation error correlation in a data assimilation context. We address the topic of monitoring the initial state of a system through the variational assimilation of images corrupted by a spatially correlated noise. The feasibility and the reliability of the approach is demonstrated in an academic context.Les images satellites sont une source importante d'information sur l'évolution du système terre. Bien que ces séquences d'images soient de plus en plus utilisées, l'importance des corrélations spatiales entre les erreurs présentes en leur sein est rarement prise en compte en pratique. Cela conduit à une sous utilisation de l'information contenue dans ces données. Dans cet article, une nouvelle manière (peu coûteuse) d'intégrer cette information dans le cadre de l'assimilation de données est proposée. Le problème de l'utilisation d'images corrompues par un bruit fortement corrélé en espace afin de contrôler l'état initial du système est abordé. La faisabilité et la pertinence de l'approche proposée est démontrée dans le cadre d'une configuration académique

Simplification operator and its inverse for multi-incremental assimilation

This document describes the implementation of the Simplification Operator and its generalized inverse within the NEMOVAR framework

Report on the use of 3D or 4D-Var for the ocean component in the coupled data assimilation context

This report describes the Inria contribution to WP2 regarding the use of 4D-Var in the ocean component of the reanalysis system. This task was twofold: 1. To study the relevance of the use of 4D-Var respect to 3D-Var. 2. To propose ways to reduce the computing cost, without altering the results. For the first part it turns out that 4D-Var is not really relevant for the ocean of the CERA reanalysis. Indeed at coarse resolution and with the use of observations of subsurface temperature and salinity only, the 3D-Var approximation is efficient enough. Getting a noticeable impact would require a data assimilation longer than 5 days, which is not feasible in coupled mode. For the CERA-SAT reanalysis however, mostly due to its use of SSH observations, 4D-Var does become a better option. The second part of the study shows that multi-incremental implementation of 4D-Var, even though challenging in the ocean, is a promising solution to significantly reduce the cost of 4D-Var, and could be used in future coupled reanalysis In addition to the scientific study of the above-mentioned points, it has required some significant technical developments. The first one was to include the ocean 4D-Var capabilities in the CERA system and was performed successfully in collaboration with P. Laloyaux at an early stage of the ERACLIM2 project. The second one was to develop the alternatives to full 4D-Var proposed in section 3. This was done in the framework of the NEMOVAR collaborative environment and is therefore available to the partners through, for instance, the ECMWF git repository more details about software transfer are given in appendix