Grantee: ** University of Maryland**, College Park, MD, USA

Researcher: Brian R. Hunt, Ph.D.with Istvan Szunyogh

Grant Title: Weather Forecasting, Complexity, and Chaos

https://doi.org/10.37717/21002044

Program Area: Studying Complex Systems

Grant Type: Research Award

Amount: $450,000

Year Awarded: 2001

Duration: 4 years

**Weather Forecasting, Complexity, and Chaos**

Some results from chaos theory have already been applied to medium range forecasts. For example, until recently, a single numerical forecast was obtained by solving the atmospheric partial differential equations, providing forecasters with a deterministic solution. However, due to the effect discovered by Lorenz, the reliability of the forecast deteriorates exponentially fast in time, and this occurs at different rates in different places.

This makes it difficult to tell when and for how long the forecasts are reliable. One simple method to gain insights to this problem is to use ensembles of forecasts. That is, several forecasts are performed every day, replacing the classical single "deterministic" forecast. The different forecasts are started from carefully chosen perturbed initial conditions and then remain similar for some time before they begin to give different results. This gives an indication of how long the forecast is reliable. For example if we create an ensemble of forecasts for 10 days, but we find that they separate within 3 days, then we can say that we have confidence in our forecasts only for up to 3 days. This also gives a measure of the complexity in the forecast. Such techniques have been used in the past on fairly simple systems where applications of chaos theory are now well developed. However, weather forecasting involves many more variables which leads to important theoretical and practical problems. We believe that addressing these problems will yield substantially improved forecasts.

What can complexity and chaos do for weather prediction now? C. Leith, one of the pioneers in ensemble weather prediction illustrated the predictability problem in an American Geophysical Union lecture (Nov. 1999): "It is not just butterflies; even talking about the weather will change the weather outcome", but he added, "Fortunately, talking about climate will not produce climate change". In fact, there is increasing evidence that the atmosphere is not as chaotic as it was initially believed to be.

A numerical forecast involves solving for several million variables that change with time (e.g., temperature, pressure, velocity, humidity at a large number of grid points). In contrast, ensemble forecasts of perhaps 20 solutions are computed by taking small perturbations of a "primary" solution and following these new perturbed solutions in time. Whenever they deviate too far from the primary solution, they are renormalized and reinitialized by being brought closer to the primary solution. These solutions result in what are called the "local bred vectors" or "LBVs". The LBVs represent the naturally occuring perturbations that are most unstable. For example, when modeling the Northern Hemisphere, we find that 20 ensemble solutions typically yield about 10 geographically isolated LBVs. Thus we can say that the space spanned by the unstable perturbations is of dimension 10 (not thousands, or millions, as the number of variables in the models). If the system was extremely chaotic, as previously believed, then we would expect to find many more unstable directions.

Of course, these numbers have been obtained using only 20 ensemble solutions while in theory there are an infinite possibility of acceptable perturbations. If we used all possible perturbations to find the total number of LBVs then we would completely describe what we will loosely call "the local surface". This is the set of solutions that have diverged most rapidly from the primary solution and yet are still close to the primary solution.

We propose to develop new techniques to isolate and study the time evolution of this space (the local surface) which we believe is responsible for the breakdown of forecasts. Our preliminary work indicates that it is, in fact, possible to isolate the LBVs in space and in time. Together all of the LBVs determine the local surface which is crucial for increasing the length of forecasts. By understanding properties of the local space, we believe that major improvements can be made to forecasting at all scales. For example, if we know characteristics of the LBVs, it should be possible to "target" only a few key high quality observations (i.e., flying a plane out to a location to make observations) in such regions to remove major errors in the forecasts.

The time is now at hand for a multidisciplinary project like the one we have proposed, and given our dependence on advance knowledge of the weather, it is essential to improve our understanding of the mechanisms through which forecasts breakdown. We believe that the research we propose has the potential to dramatically improve the quality of forecasts.