Mathematics in Atmospheric Sciences: An Overview

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Abstract

Several sectors of human activities rely on weather forecasts to plan in preparation of high impact weather events like snow storms, hurricanes or heat waves. Climate studies are needed to make decisions about the long-term development in agriculture, transport and land development. Observing and modeling the evolution of the atmosphere is needed to provide key reliable information for both weather prediction and climate scenarios. This paper gives an overview of the scientific research underlying the development and validation of numerical models of the atmosphere and the monitoring of the quality of the observations collected from several types of instruments. A particular emphasis will be given to data assimilation which establishes the bridge between numerical models and observations. The mathematical problems arising in atmospheric research are diverse as the problem is one of stochastic prediction for which errors in both the model and the observations need to be considered and estimated. Atmospheric predictability is concerned with the chaotic nature of the nonlinear equations that govern the atmosphere. Ensemble prediction is one area that has expanded significantly in the last decade. The interest stems from the necessity to evaluate more than just a forecast: it aims at giving an estimate of its accuracy as well. This brings up more questions than answers.