One tactic for potential improvement of Numerical Weather Forecasting (NWF) is the timely incorporation of large bodies of new observational data. These will become available from networks of Doppler radars and other automated instrumental systems that are to come on line throughout the remainder of this decade. The oppor- tunity will be enhanced with the concurrent growth of computer data-handling power. Also, and just as important, will be recent developments in applied mathematics, particularly in the theory of optimal control. By the mathematical analysis of the equations (or computational algorithms) governing the behaviour of evolving systems, it is possible to identify key values whose adjustment will minimize undesirable properties of the system. However, the analysis becomes extremely difficult as the governing equations become complex, and even if it is successfully carried out, there remains the problem of implementing its results quickly and cheaply enough to be useful in practice. In the case of NWF, the procedure can be applied to the problem of adjusting the initial meteorologi- cal fields that start a forecast so that the differences between the predictions of a numerical model and measurements coming in early in the forecast period are minimized. This is done by making repeated trial predictions for a short period, while simulteneously and repeatedly fine tuning the initial fields until the desired minimum error is found. The adjusted initial field is then used to carry out the prediction over the full forecast period. The model of concern to the PIs is the workhorse operational weather prediction model of the US National Meteorological Center (NMC). In a grant just ending under the NSF-NMC Joint Program in NWF they have successfuly constructed a set of algorithms (the "adjoint model") that complement the NMC computer program in such a way that by alternately using the adjoint and prediction models during the trial prediction period the number of iterations can be significantly reduced. This has been characterized by the Director of Development of NMC as a "most significant achievement". The proposed work is to exploit the breakthrough by further analysis of the properties of the two models in order to achieve successful operational implementation of the theoretical findings. This could enhance the accuracy of the weather forecasts to levels equal to or exceeding those achieved at the European Center for Medium Range Weather Forecasting, and increase the return on the national investment in the next-generation weather observing network.
