Sensitivity Analysis of the Data Assimilation-Driven Decomposition in Space and Time to Solve PDE-Constrained Optimization Problems

This paper is presented in the context of sensitivity analysis (SA) of large-scale data assimilation (DA) models. We studied consistency, convergence, stability and roundoff error propagation of the reduced-space optimization technique arising in parallel 4D Variational DA problems. The results are helpful to understand the reliability of DA, to assess what confidence one can have that the simulation results are correct and to determine its configuration in any application. The main contributions of the present work are as follows. By using forward error analysis, we derived the number of conditions of the parallel approach. We found that the parallel approach reduces the number of conditions, revealing that it is more appropriate than the standard approach usually implemented in most operative software. As the background values are used as initial conditions of local PDE models, we analyzed stability with respect to time direction. Finally, we proved consistency of the proposed approach by analyzing local truncation errors of each computational kernel.