Title: ON THE POSSIBILITIES AND LIMITS OF DIRECT PHYSICAL INTERPRETATION AND SYNOPTICAL USE OF MATHEMATICAL OBJECTS RELATED TO THE ADJOINT HYDRO-THERMODYNAMICAL EQUATIONS

Authors: Tamas Prager (University of Budapest)
Éva König (University of Budapest)
Fanni Kelemen (University of Budapest)

Adjoint applications have approximately 25 years history. However the solution of the tangent linear equat ions, the adjoint equations and, also the solution of the equations with composite operators L*L and LL*, i.e. the right and left singular vectors appear in most applications only as pure mathematical tools, or intermediate step s of a complex chain of computations. This is the case with EPS forecasts, variational data assimilation, or forec asts using targeted observations, etc.

The main question which the presentation intended to be focused on, is, whether there is a possibility of direct physical or in other words synoptico-dynamical interpretation of these objects, which is simple enough for synopticians to use in their everyday work, or so to say in their conceptual models. In other words, is there a po ssibility to gain directly some additional information from these „intermediate products”, which can be straightly used in everyday forecasting. The philosophy behind all this is similar to that of Hoskins, McIntytre and others in the 1980s, when they initiated the direct use of potential vorticity, Q-vector and other mathematical objects, more or less new for the synopticians at that time, in everyday synoptic work. They also recommended a methodology for use. The main difference from our trial is that their objects had absolutely clear physical meaning, while th e physical meaning is not so clear in our case, even using the energy norm and scalar product.

We investigated the above in a number of case studies of extreme and near-to average weather situations an d received partly positive and partly negative results. We try to give a short picture of our methodology and then present some results. In summary we try to assess the power and limits of these direct applications.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: May 27 2011