A Simple Technique to Infer the Missing Gravity Wave Drag in the Middle Atmosphere Using a General Circulation Model: Potential Vorticity Budget

A simple technique to infer the missing momentum forcing in a general circulation model is developed and evaluated. The response of the large-scale dynamic equations to an external momentum forcing presents a nonlocal response in the zonal and meridional wind. On the other hand, the response to the external momentum forcing in the potential vorticity (PV) is a local growing geostrophic mode, so that there is a direct relationship between the external momentum forcing and the response in PV. In this work, this fact is exploited to diagnose the missing momentum forcing in the extratropics using a general circulation model. The capability of the simple technique to estimate a concentrated gravity wave forcing is evaluated. A dynamical model is evolved with prescribed sources and sinks of PV and then the technique is used to estimate these known momentum sources and sinks. PV is found to give a much better diagnostic of gravity wave drag compared to the more traditional zonal wind differences. The technique is also used in a realistic environment, in which the sources and sinks of PV in Met Office analyses are determined. The estimation of this missing forcing with this simple technique is compared with the estimation given by a more complex data assimilation technique developed by Pulido and Thuburn and, in general, a good agreement is found. The simple gravity wave drag estimation technique can be used in an online data assimilation cycle, using the increments of the analysis, and also offline, using a general circulation model and observations.