The Representation of Atmospheric Motion in Models of Regional-Scale Air Pollution

Abstract

A method is developed for generating ensembles of wind fields for use in regional scale (1000 km) models of transport and diffusion. The underlying objective is a methodology for representing atmospheric motion in applied air pollution models that permits explicit treatment of the uncertainty inherent in the specification of atmospheric states. The nature of this uncertainty is illustrated by showing that a set of discrete meteorological observations made at a given moment in time, together with the diagnostic equations of fluid motion, defines a manifold in function space, each point of which is a possible description of the state of the atmosphere at the moment the observations were made. It is argued that hypotheses can be adduced regarding the likelihood that individual points on the manifold describe the atmospheric state at the time of the observations, but that contrary to common practice, adequate information does not exist to allow one to state with certainty that a specific function is the correct description. We advance the hypothesis that the most likely descriptions of the wind field are those points on the manifold of possible states whose velocity descriptions are compatible with given kinetic energy spectra. Using methods of operations research, we develop a technique for selecting such points from the manifold and creating finite ensembles of wind field descriptions for each of N hours that meteorological data are available. By selecting one member from each of the N ensembles, we form a sequence of functions that is a possible description of the evolution of the flow field in time. We advance the hypothesis that among the set of all such sequences that one can construct those that provide the most likely descriptions of the flow evolution are those that best satisfy the principle of momentum conservation. We show that dynamic programming is ideally suited to finding these sequences, which constitute the desired ensemble of wind specifications in space and time.