and the absolute average of relative difference:

and the average of relative difference:

where N is the total umber of available points, E1 the sampling error derived from formula and F0 from observed data. It is worth of noticing that the unit of F1 is the percentage (%) of the variance of areal average while that of F2 and F3 is the percentage (%) of the observed sampling error for high-passed SST.

The simulation difference is calculated at each point and then averaged for the NEP area (120E-90W, 10N-10S), tropical area (TP, 120E-90W, 10N-23N and 10S-23S) and the whole area (NETP, 120E-90W, 23N-23S) in Tabs. 1a and 1b. Considering that the formula by Nakamoto et al. (1994) is sensitive to the smaller length scales, the cases of a > 1 and a < 1 are treated separately. a < 1 means zonal e-folding scale is smaller than sampling distance L, which often happens in warm water areas and north-east NEP with a larger sampling error.

Table 1a. Averaged simulation difference E1(%)

Table 1b. Absolute averaged relative simulation difference E2(%)

In the first row of Tab. 1a-b, N means the results in corresponding column is derived from the sampling error formula by Nakamoto et al. (1994) while S from the new one in this report. It is shown that the average simulation difference (TAb. 1a) in the small sampling error area (a > 1) is about -2% from formula N (with γ0 = 90 days) and formula S. γ0 = 60 days causes a better result than γ0 = 90 days in the

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