Gravity wave drag estimation from global analyses using variational data assimilation principles. I: Theory and implementation

Abstract

A novel technique to estimate gravity wave drag from global-scale analyses is presented. It is based on the principles of four-dimensional variational data assimilation, using a dynamical model of the middle atmosphere and its adjoint. The global analyses are treated as observations. A cost function that measures the mismatch between the model state and observations is defined. The control variables are the components of the three-dimensional gravity wave drag field, so that minimization of the cost function gives the optimal gravity wave drag field. The minimization is performed using a conjugate gradient method, with the adjoint model used to calculate the gradient of the cost function. In this work, we present the theory behind the new technique and evaluate extensively the ability of the technique to estimate the gravity wave drag using so-called twin experiments, in which the ‘observations’ are given by the evolution of the dynamical model with a prescribed gravity wave drag. The results show that the technique can estimate accurately the prescribed gravity wave drag. When the cost function is suitably defined, there is good convergence of the minimization scheme under realistic atmospheric conditions. We also show that the cost function gradient is well approximated taking into account only adiabatic processes. We note some limitations of the technique for estimating gravity wave drag in tropical regions if satellite temperature measurements are the only observational information available.