where k3 > 1 is a constant and subscript a and h presents the anomaly and high-passed SST respectively.
Eq. (26) is based on the fact that the spatial pattern of the anomaly MSE is very similar to that of the high-passed MSE. The correlation coefficients and the ratio k3 in the whole tropical Pacific (P) and 8 sub-regions (A-H) are shown in Tab. 2 for a prescribed L=150, M=20 and T=4 weeks. Not only for the whole Pacific but also for each sub-regions, the correlation between anomaly MSE and high-passed MSE is significant. The average correlation coefficient in the sub-regions is as high as 0.91. The average ratio k3 is about 2.0.
Table 2. Correlation coefficient (r) between anomaly MSE and high-passed MSE and the ratio k3
Then the anomaly sampling error can be written as:
The second approximation is supposing:
where kσ is a constant about 1.0.
Then we obtained the sampling error formula describing the anomaly SST:
where sampling error for high-passed SST ε2h/σ2Ah is decided by Eq. (24)
One may concern with the accuracy of the formula Eq. (29). With the same sampling parameters as in the formula validation in the last section, the anomaly sampling error field is simulated by Eq. (29) with k3 = 2.0, kσ = 1.0 and γ0 = 1.75 days. The result is illustrated in Fig. Sb. Comparing with observed sampling error for anomaly SST in Fig. 8a, it is visible that the formula (29) successfully simulates the spatial pattern and quantitatively estimates the value except for the equatorial front area.
