Implicit treatment of model error using inflated observation-error covariance

International audience; Data assimilation involving imperfect dynamical models is an important topic in meteorology, oceanography and other geophysical applications. In filtering methods, the model error is compensated for by inflation. In variational data assimilation, authors usually try to estimate it, which means that all uncertainty-loaded model inputs are included into the control vector. However, this approach suffers from implementation difficulties. In this paper we suggest an alternative method, motivated by the 'nuisance parameter' concept known in statistics. This method allows the model error to be treated implicitly by inflating the observation-error covariance. The equivalency theorem substantiating the method has here been proved. We also consider a case with a biased model error. In the corresponding mixed formulation, the spatially distributed mean error is included into the control vector, whereas the time-dependent fluctuations around the mean are subjected to the proposed implicit treatment. Numerical experiments for the 1D generalized Burgers' equation illustrate the presented theory. In these experiments the model error related to uncertainty in the advection coefficient has been considered.