from the formula is about 2 degrees smaller than that from observation in the smaller sampling areas C and H while little difference in the areas A, B, D F and G. The meridional optimal sampling distance Mopt2 has a spatial pattern where it varies from 4 degrees in far-western NEP to 8 degrees in central NEP while the observation result is rather homogeneous (5 degrees in Fig. 4b). The difference of optimal sampling area size is about 5% in the regions B, G an H and 23% in other areas.
Table 4. Sub-region averaged optimal sampling distance and size
7 Conclusion and Discussion
In this paper, the global optimal network design problem is simplified and formalized into finite number of local optimal design problems under the local homogeneous condition. The optimal sampling distances are obtained both based on observation and sampling error formula for a prescribed sampling error of tropical Pacific anomaly SST.
With the Reynolds SST anomaly, the relation between sampling error and sampling distances is investigated. It is found that the sampling error does not increase monotonously with sampling parameters. When a zonal sampling separation is given, the sampling error has a minimum value in about 3-4 degrees. Results indicate that the optimal design is of great practical importance.
The optimal network design problem is first solved by using observed anomaly SST. It is shown that the optimal meridional sampling distance is about 5-7 degrees, which is rather homogeneous. The zonal one ranges from 5-25 degrees in the whole tropical Pacific. The warm water areas and equatorial front area should have a small sampling scale which is about 5-7 degrees. The small sampling error areas (such as central and south-east tropical Pacific) may have a larger sampling distances (10-20 degrees).
To obtain a sampling error of 4% in tropical Pacific, we need totally 140 spatial sampling points, with 70 in the NEP area and 70 in the tropical area. In the present TAO buoy array area, 60 spatial sampling points is enough if they are optimally distributed.
There are two steps in solving the optimal network design by using sampling error formula. The first is to derive an analytical sampling error formula which can be used
