By Eugenia Kalnay
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With this approximation, it is convenient to use atmospheric pressure, instead of height, as a vertical coordinate. The continuous equations of motions are solved by discretization in space and in time using, for example, ﬁnite differences (Chapter 3). It has been found that the accuracy of a model is very strongly inﬂuenced by the spatial resolution: in general, the higher the resolution, the more accurate the model. Increasing resolution, however, is extremely costly. For example, doubling the resolution in the three space dimensions also requires halving the time step in order to satisfy conditions for computational 5 Anders Persson (1999 personal communication) kindly provided the notes on the historical development of NWP in the USA and Sweden reproduced in Appendix A.
7 Weather predictability 25 waves). 3). The hydrostatic approximation is very accurate if the horizontal scales are much larger than the vertical scales. For atmospheric models with horizontal grid sizes of the order of 100 km, the hydrostatic equation is very accurate and convenient. , the hydrostatic approximation can be used even in mesoscale models with grid sizes of the order of 10 km or larger without introducing large errors. However, in order to represent smaller-scale phenomena such as storms or convective clouds which have vertical accelerations that are not negligible compared to buoyancy forces, it is necessary to use the equations of motion without the hydrostatic approximation.
1), with regions like North America and Eurasia which are relatively datarich, while others much more poorly observed. For this reason, it became obvious rather early that it was necessary to use additional information (denoted background, ﬁrst guess or prior information) to prepare initial conditions for the forecasts (Bergthorsson and D¨oo¨ s, 1955). , Gandin, 1963), but as the forecasts became better, a short-range forecast was chosen as the ﬁrst guess in the operational data assimilation systems or “analysis cycles”.
Atmospheric Modeling, Data Assimilation and Predictability by Eugenia Kalnay