An ideal DDDAS will optimally coordinate state estimation and the observation process. This is indispensable for environmental applications, where models are imperfect and measurements are limited and uncertain. A key part of environmental DDDAS is data assimilation, broadly defined as the process of estimating the state of a system using all relevant information. This project will develop a new approach to data assimilation that makes better use of observations to deal with model imperfections. This new approachwill be developed in the context of mesoscale weather, such as thunderstorms, squall-lines, hurricanes, precipitation, and fronts. In these situations, forecast errors occur in both position ("the storm is in the wrong place") and amplitude ("forecast winds are off"). Position errors are particularly important since they degrade our ability to predict storm tracks, issue warnings, and properly target observation platforms such as aircraft. Current assimilation methods have problems dealing with position errors. Instead of correcting these errors directly, they tend to compensate for them by distorting amplitudes. Distorted amplitude estimates can produce poor forecasts. Poor forecasts are a problem in their own right but, in the case of an environmental DDDAS, they can easily make strategies for gathering new observations ineffective. In this new formulation for data assimilation accounts for errors in both position and amplitude. This leads to a minimization algorithm that can be expressed in two steps: a regularized variational alignment problem and an amplitude adjustment problem. Alignment can be formulated with or without feature detection, it maintains dynamical consistency, and it permits the smoothness of the solution to be systematically controlled. Field alignment should significantly advance the state of DDDAS for environmental problems.
This work will lead to better analysis of mesoscale weather, especially hurricanes and severe storms. It turns out that expressing errors in terms of position and amplitude is quite general. Thus, from the perspective of DDDAS, this work will provide new ways to deal with model error in applications as diverse as hydrology, ecology, and oceanography. Field alignment also nicely complements existing amplitude-oriented assimilation methods used in operational weather forecasting centers. Finally, the regularization aspects of this work will also advance the state of the art in alignment methods, which will benefit biomedical imaging and object recognition research.
