Abstract.We consider the application of the Ensemble Kalman Filter (EnKF) to a coupled ocean ecosystem model (HYCOM-NORWECOM). Such models, especially the ecosystem models, are characterized by strongly nonlinear interactions active in ocean blooms and present important difficulties for the use of data assimilation methods based on linear statistical analysis. Besides the non-linearity of the model, one is confronted with the model constraints, the analysis state having to be consistent with the model, especially with respect to the constraints that some of the variables have to be positive. Furthermore the non-Gaussian distributions of the biogeochemical variables break an important assumption of the linear analysis, leading to a loss of optimality of the filter. We present an extension of the EnKF dealing with these difficulties by introducing a nonlinear change of variables (anamorphosis function) in order to execute the analysis step in a Gaussian space, namely a space where the distributions of the transformed variables are Gaussian. We present also the initial results of the application of this non-Gaussian extension of the EnKF to the assimilation of simulated chlorophyll surface concentration data in a North Atlantic configuration of the HYCOM-NORWECOM coupled model.

This paper introduces an efficient algorithm for computing the Reeb graph of a scalar function f defined on a volumetric mesh M in R3. We introduce a procedure called "loop surgery" that transforms M into a mesh M' by a sequence of cuts and guarantees the Reeb graph of f(M') to be loop free. Therefore, loop surgery reduces Reeb graph computation to the simpler problem of computing a contour tree, for which well-known algorithms exist that are theoretically efficient (O(n log n)) and fast in practice. Inverse cuts reconstruct the loops removed at the beginning. The time complexity of our algorithm is that of a contour tree computation plus a loop surgery overhead, which depends on the number of handles of the mesh. Our systematic experiments confirm that for real-life data, this overhead is comparable to the computation of the contour tree, demonstrating virtually linear scalability on meshes ranging from 70 thousand to 3.5 million tetrahedra. Performance numbers show that our algorithm, although restricted to volumetric data, has an average speedup factor of 6,500 over the previous fastest techniques, handling larger and more complex data-sets.We demonstrate the versatility of our approach by extending fast topologically clean iso surface extraction to non simply-connected domains. We apply this technique in the context of pressure analysis for mechanical design. In this case, our technique produces results in matter of seconds even for the largest meshes. For the same models, previous Reeb graph techniques do not produce a result.

International audienceBuilding the capacity for monitoring and forecasting marine biogeochemistry and ecosystem dynamics is a scientific challenge of strategic importance in the context of rapid environmental change and growing public awareness of its potential impacts on marine ecosystems and resources. National Operational Oceanography centres have started to take up this challenge by integrating biogeochemistry in operational systems. Ongoing activities are illustrated in this paper by presenting examples of (pre-)operational biogeochemical systems active in Europe and North America for global to regional applications. First-order principles underlying biogeochemical modelling are briefly introduced along with the description of biogeochemical components implemented in these systems. Applications are illustrated with examples from the fields of hindcasting and monitoring ocean primary production, the assessment of the ocean carbon cycle and the management of living resources. Despite significant progress over the past 5 years in integrating biogeochemistry into (pre-)operational data-assimilation systems, a sustained research effort is still needed to assess these systems and their products with respect to their usefulness to the management of marine systems

This paper discusses convergence issues for the saddle variational formulation of the weakly constrained 4D‐Var method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationally coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.

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An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most O(| log(ǫ)| ǫ −2 ) evaluations of the problem's functions and their derivatives for finding an ǫ-approximate first-order stationary point. This complexity bound therefore generalizes that provided by [Bellavia, Gurioli, Morini and Toint, 2018] for inexact methods for smooth nonconvex problems, and is within a factor | log(ǫ)| of the optimal bound known for smooth and nonsmooth nonconvex minimization with exact evaluations. A practically more restrictive variant of the algorithm with worst-case complexity O(| log(ǫ)| + ǫ −2 ) is also presented.