Inside Numerical Weather Prediction Models

Catalog description

METEO 426 will provide students with a practical understanding of the structure of numerical weather prediction (NWP) models in the context of their application to real world precipitation forecasting. The course combines lecture material on the inner workings of NWP models with a forecasting module that applies the lecture material to daily precipitation forecasts. The course begins with a full description of the mathematical backbone of NWP models - the primitive, or governing, equations. The primitive equations that describe the future state of the atmosphere, given some initial state, are a set of non-linear, partial differential equations that are only solvable by numerical methods. The sophistication of numerical methods, in turn, depends on available computing capacity. A discussion of the historical development of simplified NWP models in the context of limited computing resources follows. While the advent of modern computers allowed for the explicit computation of the primitive equations, their use in operational forecast settings uncovered additional important theoretical limitations on forecast skill. In particular, the future state of the atmosphere is extremely sensitive to initial conditions yet there are insufficient observations to fully initialize an NWP model. Techniques for initializing NWP models - called data assimilation - were and continue to be a key source of model error. As a result, we cover these methods in detail. Beyond initial condition uncertainty, there are fundamental limits on the predictive skill of NWP models. These limits, a consequence of the fundamentally non-linear dynamics of the atmosphere, were first described by Edward Lorenz and usually referred to as "chaos theory." For operational weather forecasting, the implication is that single, deterministic models are necessarily limited in skill, even with near-perfect initial conditions. As a result, operational forecast centers have moved towards ensemble-based forecasting. The development and use of ensemble models are discussed in detail in this class. Next, the model must be moved forward in time. Basic numerical methods used to advance the model in time, typically using finite difference techniques, are described and the recent shift to finite volume methods are introduced and discussed in the context of the latest NWP models. We then describe parameterization schemes that NWP models use to account for phenomena not directly resolved by the model. We discuss several important schemes relevant to precipitation, including convective parameterizations and microphysics, and the planetary boundary layer. The course concludes with a review of one of the latest operational NWP models.