Abstract
We discuss a mathematical framework for the use of asynoptic data in determining initial states for numerical weather prediction (NWP) models. A set of measured data, synoptic and asynoptic, is termed complete if it determines the solution of an NWP model uniquely. We derive theoretical criteria for the completeness of data sets. The practical construction of the solution from a complete data set by intermittent updating is analyzed, and the rate of convergence of some updating procedures is given.
It is shown that the time history of the mass field constitutes a complete data set for the shallow-water equations. Given that the time derivatives of the mass field are small at initial time, we prove that the velocity field obtained by the diagnostic equations we derive will also have small time derivatives. Hence our diagnostic equations also solve the initialization problem for this system, namely they provide an initial state which leads to a slowly evolving solution to the system.
Finally, we review the bounded derivative principle of Kreiss. It states that in systems with a fast and a slow time scale, initial data can be chosen so that the solution starts out slowly. For such initial data, the solution will actually stay slow for a length of time comparable to the slow time scale. The application of the principle to the initialization problem of NWP is discussed.
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© 1981 Springer-Verlag New York, Inc.
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Bube, K.P., Ghil, M. (1981). Assimilation of Asynoptic Data and the Initialization Problem. In: Bengtsson, L., Ghil, M., Källén, E. (eds) Dynamic Meteorology: Data Assimilation Methods. Applied Mathematical Sciences, vol 36. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5970-1_4
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DOI: https://doi.org/10.1007/978-1-4612-5970-1_4
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