Toward a weak constraint operational 4D-Var system: application to the Burgers' equation

Abstract

Strong constraint (perfect model assumption) 4D-Var algorithms are increasingly used for synoptic and global scale atmospheric data assimilation at operational numerical weather prediction centers around the world. The data assimilation windows currently range from 6 hours to 12 hours at different centers. It is preferable to have as many independent observations as possible in each data assimilation window under the variational framework. Longer data assimilation windows generally increase the information content from the observations, but also make the perfect model assumption more improper. It is clear that weak constraint (imperfect model assumption) 4D-Var algorithms will be required to properly combine the background forecast with high resolution observations in longer data assimilation windows in the not too distant future. A weak constraint observation space atmospheric 4D-Var system, NAVDAS-AR (NRL Atmospheric Variational Data Assimilation System - Accelerated Representer), is currently under development at the Naval Research Laboratory (NRL) in Monterey. The impact of the model errors is presented in a residual term resulting from a four-dimensional matrix/vector multiplication of the model error covariance with the adjoint field in the right hand side of the tangent linear model. The calculation of the residual term is generally very computationally intensive. However, it can be obtained accurately and efficiently when some special choices are made for the model error covariances. In this short contribution we present an approach to include the impact of the model errors in the NAVDAS-AR. The steps involved in this approach are demonstrated through an application to the Burgers' equation.