Sensitivity Analysis: A Variational Approach

International audienceA sensitivity analysis is defined by some response function and the variable with respect to which the sensitivity is evaluated. In many cases the observations have errors and it is important to estimate the impact of this error, If the state of the system is retrieved through a variational data assimilation then the observation is found only in the Optimality System (O.S.). Therefore the sensitivity analysis has to be carried out on the optimality system, in that sense sensitivity analysis is a second order property and the O.S. can be considered as a generalized model because it contains all the available information. In this presentation we will see how a sensitivity analysis can be carried out. The method is applied to water pollution. The model is derived from shallow water equations and an equation of concentration of the pollutant, it is discretized using a finite volume method and the sensitivity with respect to the source term of the pollutant is studied

Sensitivity Analysis: A Variational Approach

International audienceA sensitivity analysis is defined by some response function and the variable with respect to which the sensitivity is evaluated. In many cases the observations have errors and it is important to estimate the impact of this error, If the state of the system is retrieved through a variational data assimilation then the observation is found only in the Optimality System (O.S.). Therefore the sensitivity analysis has to be carried out on the optimality system, in that sense sensitivity analysis is a second order property and the O.S. can be considered as a generalized model because it contains all the available information. In this presentation we will see how a sensitivity analysis can be carried out. The method is applied to water pollution. The model is derived from shallow water equations and an equation of concentration of the pollutant, it is discretized using a finite volume method and the sensitivity with respect to the source term of the pollutant is studied

Stochastic data assimilation of the random shallow water model loads with uncertain experimental measurements

International audienceThis paper is concerned with the estimation of a parametric probabilistic model of the random displacement source field at the origin of seaquakes in a given region. The observation of the physical effects induced by statistically independent realizations of the seaquake random process is inherent with uncertainty in the measurements and a stochastic inverse method is proposed to identify each realization of the source field. A statistical reduction is performed to drastically lower the dimension of the space in which the random field is sought and one is left with a random vector to identify. An approximation of the vector components is determined using a polynomial chaos decomposition, solution of an optimality system to identify an optimal representation. A second order gradient-based optimization technique is used to efficiently estimate this statistical representation of the unknown source while accounting for the non-linear constraints in the model parameters. This methodology allows the uncertainty associated with the estimates to be quantified and avoids the need for repeatedly solving the forward model

Stochastic data assimilation of the random shallow water model loads with uncertain experimental measurements

International audienceThis paper is concerned with the estimation of a parametric probabilistic model of the random displacement source field at the origin of seaquakes in a given region. The observation of the physical effects induced by statistically independent realizations of the seaquake random process is inherent with uncertainty in the measurements and a stochastic inverse method is proposed to identify each realization of the source field. A statistical reduction is performed to drastically lower the dimension of the space in which the random field is sought and one is left with a random vector to identify. An approximation of the vector components is determined using a polynomial chaos decomposition, solution of an optimality system to identify an optimal representation. A second order gradient-based optimization technique is used to efficiently estimate this statistical representation of the unknown source while accounting for the non-linear constraints in the model parameters. This methodology allows the uncertainty associated with the estimates to be quantified and avoids the need for repeatedly solving the forward model

Optimal Control and Stochastic Parameter Estimation

International audienceAn efficient sampling method is proposed to solve the stochastic optimal control problem in the context of data assimilation for the estimation of a random parameter. It is based on Bayesian inference and the Markov Chain Monte Carlo technique, which exploits the relation between the inverse Hessian of the cost function and the error covariance matrix to accelerate convergence of the sampling method. The efficiency and accuracy of the method is demonstrated in the case of the optimal control problem governed by the nonlinear Burgers equation with a viscosity parameter that is a random field

Error Propagation in Variational Data Assimilation

International audienceThe approach of Data Assimilation via Optimal Control Methods leads to a dynamical system: the Optimality System in which all the available information is gathered. The propagation of uncertainties must be carried out not just from the model but from the O.S. I introduced a second adjoint from where the evaluation of the dynamics of uncertainties are studied

Error Propagation in Variational Data Assimilation

International audienceThe approach of Data Assimilation via Optimal Control Methods leads to a dynamical system: the Optimality System in which all the available information is gathered. The propagation of uncertainties must be carried out not just from the model but from the O.S. I introduced a second adjoint from where the evaluation of the dynamics of uncertainties are studied