It is these coefficients {djk} which contain a great of useful information which can be used to, say, select grids for efficient numerical calculation, or to detect errors in numerical models in order to know how to weight data for efficient assimilation, or, finally, for signal analysis for the detection of various features in a data set such as ENSO. Let us now explore the application of wavelet analysis for adaptive nurnerical methods.
2 A Wavelet Based Adaptive Numerical Method: Jameson and Miyama
Ocean dynamics includes many processes which occur over a wide range of spatial scales. While the scale of the general circulation is〜104km , synoptic mesoscale variability is on the order of less than 10km to several tens of kilometers. To understand the interaction of such wide range scale phenomena, numerical models which include all scales have been sought.
One way to achieve this is a very high resolution grid model. Usually the smallest grid size is determined primarily by computer limitations, rather than by the flow physics. Although this is beginning to become better with rapid progress in computer technology (Beckmann et al., 1994; Kagimoto and Yamagata, 1997; McClean et al., 1997), it is not sufficient at this point. In addition, the interesting mesoscale eddies are often seen in a limited area (e. g. western boundary regions). In that case, an evenly-spaced fine resolution is a luxury.
An alternative to overcome some of these difficulties is a nested grid model. By including a nested structure, a selected region can be examined at higher resolution while the large scale flow can be simulated with a lower resolution. This technique is widely used in meteorology (Zhang et al., 1986). There are also some applications in oceanography (Fox and Maskell 1995; Spall and Holland, 1991; Oey and Chen, 1992; Ginis et, al., 1998). However, nested grid models have difficulties in that propagating waves may produce false reflection or aliasing at the interface where the two grids meet.
