and the ratio of high-passed variance to anomaly variance at a spatial point, the sampling error of anomaly SST only depends on the zonal and meridional sampling separations analytically in the formula. The formula is quantitatively consistent with the observation except in equatorial front area.
The size of optimal sampling box derived from the formula for anomaly SST quantitatively agrees with that from observation. The former is about 4-23 % smaller than the latter except for central Pacific with a 30% larger than the latter. The zonal optimal sampling distance of the former has the similar spatial pattern with that of the latter while the meridional one of the former is less uniform than that of the latter.
1 Introduction
After the successful development of the mid-range forecasting, one of the most challenging problems in atmospheric and oceanic sciences may be to forecast climate variation. The ocean plays a key role in heating atmosphere, storing climate signals and regulate CO2 in atmosphere. This is why ocean science becomes one of the central topics in the recent and future climate research programs such as the Climate Variability and Predictability program (CLIVAR) etc. Our knowledge on the ocean observing systems, their functions and features, though much less than that on atmospheric observing systems, have been studied by many researchers. This includes sampling error study (Bell, 1987; North and Nakamoto, 1989; Shen et al., 1994), impaction study (Bengtson, 1979), observing system simulation experiment (OSSE, Daley and Mayer, 1986) , predictability study (Leith, 1978) and optimal network design (Bretherton et al. 1976). Although the existing knowledge has not yet been widely applied on solving comprehensive optimal observing system design problems, some continuous and fruitful efforts has been made in this field, such as network design for global upper layer temperature measurement by using Expendable Bathythermograph (XBT).
XBT network design was investigated earlier in the 1970s, (Bretherton et al., 1976; White and Bernstein, 1979). The purpose of their works was to make oceanographic sampling networks more efficient detectors of the dominant signal of interest. The XBT dataset and optimal interpolation (01) method (Gandin, 1963) are used to determine optimal sampling rates, which were defined to be the sampling number in one length scales for temperature anomaly. Since then, this issue was extensively studied by Sprintall and Mayers (1991), Mayers et al. (1991) and White (1995). The question which was answered in XBT network designs is what are the optimal sampling rates for a prescribed optimal interpolation error. As long as the noise-signal ratio and the signal correlation are known, the optimal interpolation error depends only on the sampling rates. Then the sampling rate can be estimated for a prescribed interpolation error. Although the qualitative feature of the sampling rate-interpolation error relation depends only on the definition of signal, a practical design needs the exact information of noise-signal ratio. One difficulty in estimating noise-signal ratio from low-resolution
