to estimate sampling error of anomaly SST with enough accuracy. The second step is to find out the optimal solution from all the possible sampling parameters with the sampling error formula.
In the first step, the sampling error formula by Nakamoto et al. (1994) was validated for high-passed SST. It is found that the formula describes qualitatively the correct relations between sampling error and sampling parameters L, M and averaging time T and simulates the similar spatial pattern with that of observation. However, the formula also shows some unresolved questions. In order to quantitatively agree with observed sampling error, the characteristic time scale γ0 has to be selected as 15 times larger than the e-folding correlation time scale. Even so, the sampling error in the areas with big sampling error is still greatly overestimated. One reason is the undue simplification in the integration to getting areal averaged variance. Then the variance of the areal average was obtained by integration without any simplification in this paper. The new sampling error formula shows an obvious improvement. The γ0 is selected as about 1.75 days or 1/3 of the e-folding time scale. The simulation difference is about 15% of the real sampling error for the averaging over sub-regions in NEP.
However, this new sampling error formula can not be applied to simulate the sampling error of anomaly SST. Some approximations have been made according to basic SST statistics and the formula is modified to describe the sampling error of anomaly SST. The validation indicates that, in most parts of the tropical Pacific ocean, the modified formula (Eq. (29)) simulates the sampling error of anomaly SST with the similar accuracy to that in estimating the high-passed sampling error by Eq. (24). For given high-passed length scales and the ratio of high-passed variance to anomaly variance at local points, the sampling error is analytically decided only by sampling parameters.
In the second step, optimal sampling distances derived from the sampling error formula are consistent with those from the observation quantitatively. For 8 sub-regions, the relative simulation difference of optimal sampling box size between the formula and observation results is only 5% in regions of warm water areas (B and G) and south tropical Pacific (H) and about 23% in .other areas. Considering that a wide range of sampling parameters are experienced in order to obtain the solution of the optimal sampling, this suggests that the modified sampling error formula should have a good performance to simulate the sampling error of anomaly SST.
It should be noted that this is just a preliminary study of SST sampling problem based on sampling error study. Practically, the SST sampling strategy should be a best mix of satellite and in. situ observation system. Then the most important question becomes: how many in situ sampling points are needed to produce an accepted error (including sampling and measurement error) for the mixed observation systems? Another issue should be pointed out that the sampling error criterion (4%) used here is mean sampling error but not optimal sampling error. This suggests that the optimal
