XBT data is that the noise part may not be well evaluated even if the dominant signal is assumed to be well resolved by XBT dataset. The definition of the signal is another important issue which were treated as the first or second order autoregressive (AR) model in White and Bernstein (1979) and White (1995) for emphasizing the ocean waves.
In this paper, we focus on the optimal network design by using high resolution dataset. The sampling error theory developed by North and Nakamoto (1989) and Nakamoto et al. (1994) derived an analytical relation between sampling error and sampling parameters, which may make the optimal design problem be greatly simplified . This is why we want to solve a practical optimal network design problem for tropical SST measurements by developing and applying the existing sampling error theory. The design answers the following question both from observed high resolution SST dataset and sampling error formula: what are optimal sampling distances for a prescribed sampling error?
The dataset and its preprocessing are described in the section 2. Section 3 presents a formalism and the simplification of the optimal network design. Section 4 deals with optimal network design from the observed anomaly SST. In this section, the relationship between sampling error and sampling parameters is also analyzed. Section 5 solves the optimal network design problem from the sampling error formula, which includes validation and improvement of existing sampling error formula (Nakamoto et al. 1994) for estimating sampling error for high-passed SST, the derivation of a new formula for anomaly SST and the final solution of the optimal network design from the new formula. All the results of sampling error estimation and optimal solution from the new sampling error are compared with those from the observation. The conclusion and discussion are presented in section 6.
2 Dataset and preprocessing
Understanding SST variability is important in the development of seasonal to decadal prediction as well as climate variability analysis. Now the SST data are both obtained from in situ (ship and buoy) and satellite observations. The latter provides global average at high spatial and temporal resolution. However, the retrieved SST need continuous calibration by in situ data in order to achieve certain accuracy for operational use or long-term climate analysis. The ship-based observations also need the quality correction from the high quality buoy SST dataset. It is obvious that the high quality SST measurements in global ocean is still not enough, especially in the open ocean.
The topic of the best mix of the existing observing systems will not be discussed further in this paper. We focus only on estimating the optimal sampling distances based on the SST statistics and sampling error formula. The SST dataset used in this study resulted from the new NOAA operational global SST analysis (Reynolds
