Recently, members of our Physics Department's Chaos Group have teamed with meteorologists in an effort to develop novel techniques aimed at achieving greatly improved weather forecasts. Currently we are the only University-based group capable of running state-of-the-art global weather forecasting codes on our own computer facilities.

Our goal is to use this capability to conclusively demonstrate superior performance of our methods within the next year, or so. Thus we hope that our ideas will be widely used in future weather prediction.

The chaos group at the University of Maryland is working to improve weather forecasts. Colors show the improvement in a forecast (in surface pressure) compared to conventional forecasting techniques when the information about the local complexity of the atmosphere (contours) is used.

In order to introduce the crucial aspect of weather prediction that our group addresses, we note that weather prediction may be thought of as consisting of three main components: (i) measurement of atmospheric variables (e.g. measurements of temperature, pressure, humidity, and winds taken from ground stations, balloons, aircraft, and satellites); (ii) 'data assimilation', in which the measurements are used to best estimate the current state of the Earth's atmosphere; and (iii) model integration, in which a physics-based computer code modeling the Earth's atmosphere takes the atmospheric state estimate from (ii) as an initial condition and integrates it forward in time to obtain the forecast. The key step that we focus on is step (ii), the estimation of the current atmospheric state. In terms of computer time, it may be surprising for most people to learn that, in present operational weather forecasting, as much computer time is spent on step (ii) as on step (iii). That is, obtaining a best guess of the current state is computationally just as costly as integrating a full global model of the Earth's atmosphere. Furthermore, step (ii) is regarded by many as the most poorly done step in the weather prediction process, and as the step for which major improvement currently holds the greatest potential for significantly enhancing forecasting.

Why is atmospheric data assimilation hard? The measurements have errors and are incomplete: measurements may only be at discrete points; there may be geographic regions or altitudes with little data, etc. The basic problem of state estimation from limited, noisy data and a dynamical model for the evolution of the system is a classical one that arises in many contexts. The weather context, however, presents difficulties, not present in most of the classical applications of data assimilation techniques. In particular, usual data assimilation methods require matrix operations on matrices whose dimensions are equal to the number of variables describing the system state. For current Earth weather models, the number of state variables in the model is huge, on the order of millions. The matrix operations required by the classical methods are way beyond computer

capabilities likely to be available in the foreseeable future. Thus current atmospheric data assimilation adopts much faster, but very much less accurate approaches, and this inaccuracy may be the Achilles heel of present weather forecasting.

We have developed a way around these difficulties. Briefly, our idea is to geographically break the data assimilation problem up into many overlapping regions, where the size of each region is of the order of several correlation lengths. We then do the assimilations independently (in parallel) in each of these regions. (Because the regions are relatively small, the matrices involved are not large.) Following that, we piece together the assimilations from the individual regions to form our best guess of the state of the Earth's atmosphere. So far, our tests of this method indicate that it is both very accurate and fast. We are keeping our fingers crossed, hoping that things really are as good as they currently seem to be. So, if, in a few years, you notice that your TV weatherman is giving you better predictions, we hope to have been the cause.

Readers interested in more detail on our work can download relevant papers from http://www.chaos.umd.edu/paperframe.html.
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