Methods of Sequential Estimation for Determining Initial Data in Numerical Weather Prediction

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Excerpt from Methods of Sequential Estimation for Determining Initial Data in Numerical Weather Prediction: June 1982 Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear partial differential equations, in which Initial values are known Incompletely and inaccurately. Observational data available at the Initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so-called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic-dynamic systems provides a natural approach to such problems. For linear stochastic-dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method. We show that, for linear models, the optimal combined data assimilation-initialization method is a modified version of the Kb filter. This modified Kb filter combines the standard Kb filter with a projection onto the slow solution subspace. The shallow-water equations are a simple system whose solutions exhibit many features of large-scale atmospheric flow important in NWP. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.