and Smith, 1994, hereafter referred as Reynolds SST). The Reynolds SST is a dataset blended from NOAA Advanced Very High Resolution Radiometer (AVHRR) and the in situ data including ship and buoy data through 01 analysis. The resolution is 10 zonally by 10 meridionally by 1 week temporally. The dataset used is for the tropical Pacific from January 1984 to January 1994.
In this study, the Reynolds SST is preprocessed into several datasets for different usages. To be precise, we define the names of these preprocessed datasets. The original Reynolds SST is also called unfiltered dataset. Then monthly mean climatology is removed from the unfiltered data and the "anomaly SST" is obtained. In order to get the stationary SST time series, we divided the anomaly data into two parts, i.e., low-frequency part with a timescale longer than 1 yr and the high-frequency part with a timescale shorter than 1 yr by using a local trend removing method. The linear trends over each six mons for the 10 yr anomaly SST dataset are removed. The result shows that the time series at local points satisfy the stationarity condition. By removing this stationary high-frequency part from the anomaly data, we obtain the low-frequency dataset which includes only interannual variation.
As our local trend moving method is a nonlinear filter, the transfer function of the filter is not easily derived. However, it is possible to use a simple index to examine the filtering effect of this filter. At each spatial point, the index is defined as the ratio of the area of the spectrum of the low-frequency part for high-passed data to that for unfiltered data, where low-frequency includes frequency lower than one cycle per year. Results show that less than 1% of interannual variance remained in our high-passed data in the open ocean domain (the figure is omitted here).
3 Optimal network design theory and its simplification
3.1 How to define the optimal network design?
The optimal observing system design (OOSD) means the design is optimal in the cost- efficient sense. Obviously, it is a goal-dependent concept. The cost of the observing system is generally related with the numbers and types of instruments of the observing system while the efficiency (i.e., benefit made from the system) is related with the quality of the datasets. For different purposes, the quality of the datasets may be defined as a function of noise (instrumental error, sampling error and the variance of noisy with scale smaller than lowest boundary of dominant scales of interest) or as that of signal (the variance of variation with interested scales) or as that of the ratio of noise to signal. In the first and third cases, the noise part is involved and usually high resolution datasets are needed since the noise generally relates to small scale variation. The designed systems in both cases can provide datasets for climate analysis and/or operational modeling. However, the design in the second case can only be applied to climate analysis since only signal is dealt with. In this paper, we focus only on
