| The equations governing geophysical fluid flows are a complex set of partial differential equations describing a number of conservation laws of physics. Understanding their solutions is central to operational weather prediction. However, when written in their "primitive" form, these equations are difficult to use in day-to-day weather forecasting activities. These difficulties can be alleviated through the use of scale analysis and quasigeostrophic theory, which allow the derivation of several diagnostic equations from the primitive equations. These diagnostic relationships, the quasigeostrophic omega, geopotential tendency and Zwack-Okossi development equations, are directly applicable to operational weather charts and can be used to obtain a more complete understanding of the solutions to the primitive equations.; Until now, solutions to these diagnostic equations have not been available to weather forecasters. Instead, forecasters have applied over-simplified and idealized qualitative approximations to the equations in their routine forecasting procedures. In this work, a unique method is developed that can provide numerical solutions of the three aforementioned diagnostic equations to weather forecasters in real time. By using these solutions, it is shown that many of the approximations and idealizations historically used when applying these equations are of questionable value, and can lead to incorrect conclusions in many cases. Furthermore, bringing the solutions of the diagnostic equations into the weather prediction process can give forecasters the ability to better understand the physics of the ongoing weather. These solutions can also provide a means to make better use of the output from more sophisticated numerical weather prediction models. |
