∫=1,..., Nr is the sequential number of the sub-regions.
In this way, a comprehensive global design problem for the whole tropical Pacific is replaced by Nr local design problems for Nr sub-regions.
4 Optimal network design with observed SST
4.1 Sub-region division
For simplicity, the whole tropical Pacific is divided into 8 sub-regions based on the spatial distribution of SST statistics (She and Nakamoto (1996) and She (1996)). The division is shown in Fig. 1. It is visible that sub-region A (far-west near-equatorial Pacific (NEP)), B (west NEP) and G (north-east tropical Pacific) are warm water dominated areas. There exists some generic features in these warm water areas, such as small spatial and temporal scales, smaller variance, high sampling error and large value of ratio of variance for semi-annual and intraseasonal part to that for unfiltered data. Sub-region C (central NEP) is controlled by ENSO signal with a large spatial and temporal scale, large variance and smaller sampling error. For anomaly SST, sub-region E (south-east NEP) has similar features to those in region C. Although sub-region D (north-east NEP) is also dominated by ENSO signal, high-frequency instability wave with small spacescales and SST front in this area leads to high mean-square-error (MSE). Then the remaining region is divided into sub-region F (north-west tropical Pacific) and H (south tropical Pacific) naturally. Due to the above intrinsic nature of statistics in each sub-region, it is reasonable to assume that local homogeneity condition is satisfied in the above 8 sub-regions. Details of above basic SST statistics can be found in
4.2 Relationship between sampling error and sampling parameters
Consider a random field of oceanic scalar field ψ(x, y, t), where x, y, t are the eastward coordinate, the northward coordinate, and the time axis. By sub-sampling the ψ at points (xi, yi, t) with sampling distances of△x degrees in longitude, △y degrees in latitude and continuously in time, we may define the MSE in a space-time box with L degrees in longitude, M degrees in latitude, and T days in time as follow: where
