Estimation of optimal gravity wave parameters for climate models using data assimilation

Abstract

There is a current need to constrain the parameters of gravity wave drag schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because most gravity wave drag schemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the `observed´ gravity wave drag) and the gravity wave drag calculated with a parameterisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity-wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed `true´ parameters. When real experiments using an independent estimate of the `observed´ gravity wave drag are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed gravity wave drag at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in the gravity wave drag found in the tropical lower stratosphere, which are associated with part of the QBO forcing, cannot be captured by the parameterisation with optimal parameters.