Solutions to the atmospheric (or oceanic) prediction equations require an understanding of the three dimensional spatial nature of the fluid, including dynamics and physics, conservation conditions, and forcing. Since the equations are exceptionally complex and highly nonlinear, it is necessary to convert those equations to some numerical form which will provide meaningful iterative solutions within the constraints of available computational capabilities. The challenge is to do so optimally. While the problem has been investigated, because of the nature of the system, horizontal and vertical representations have been considered independently in the past. It is the contention of the principal investigator that systematic truncation of the atmosphere/ocean prediction equations in all three dimensions simultaneously could improve predictive skill. Thus, the purpose of this research is to study the correlation of truncation in all dimensions in a numerical model, and to find a truncation which is systematic in all three dimensions. The principal investigator will select a truncation according to scaling arguments that are based on the results from his previous studies and define appropriate functions. To establish the optimal three dimensional truncation, the functions will be tested in the operational numerical prediction model of NOAA's National Meteorological Center (NMC). This project is part of the NSF-NMC Program Joint Program in Numerical Weather Prediction.
