degrees, rather larger than that of the existing TAO buoy array (20 - 30 latitude). The optimal zonal sampling distance ranges from 5 to 25 degrees. It is shown that warm water areas, equatorial front area and north tropical Pacific need short zonal sampling separations (5-7 degrees) in order to arrive a mean sampling error of 4% while south tropical Pacific, central NEP and cold tongue area may have larger sampling separations (11-25 degrees).
From the optimal sampling distances, we may calculate how many spatial points we need to obtain a SST sampling error of 4% . It is found that about 140 spatial sampling points are needed in the whole tropical Pacific in which 70 for NEP and 70 for tropical area. In the present TAO buoy array area (NEP areas except for area A), only 60 spatial points are enough for a SST sampling error of 4%.
5 Optimal network design with sampling error formula
5.1 Validation of existing sampling error formula
To solve the optimal network design (I") with sampling error formula, we must obtain an analytical sampling error formula which can simulate sampling error of anomaly SST with enough accuracy. To this end, we start with the validation of existing sampling error by Nakamoto et al. (1994). The details of this validation can be found in She and Nakamoto (1996). The main conclusion can be made as follows:
Sampling error formula derived by Nakamoto et al. (1994) presents the correct relations between sampling error and length scales and averaged time T. The formula can simulate the spatial distribution of observed sampling error for the high-frequency part. For interior ocean and for the averaging time T between 1 week and 3 mons, the comparison shows agreement between theory and observation.
However, there are some unsolved issues to be improved. The first is the characteristic timescale γ0, which is selected as 90 days while no explanations can support so large difference ofγ0 from e-folding timescale for high-passed SST (about 1 week, She, 1996). The second is that the sampling error estimated from the formula is unreasonably large in the equatorial front area with a zonal scale less than 8 degrees. The last one is that the formula can not simulate the sampling error for anomaly SST. To find where the problem is, we must start with the beginning of North-Nakamoto sampling error theory.
5.2 Summary of North-Nakamoto formalism
Supposing that the space-time box averaged element Ψ in Eq. (5) is zero centered, the variance of II, can be written as:
