Objective array design for three-dimensional temperature and salinity observation: Application to the South China Sea
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Abstract: In this study, a moored array optimization tool (MAOT) was developed and applied to the South China Sea (SCS) with a focus on three-dimensional temperature and salinity observations. Application of the MAOT involves two steps: (1) deriving a set of optimal arrays that are independent of each other for different variables at different depths based on an empirical orthogonal function method, and (2) consolidating these arrays using a K-center clustering algorithm. Compared with the assumed initial array consisting of 17 mooring sites located on a 3°×3° horizontal grid, the consolidated array improved the observing ability for three-dimensional temperature and salinity in the SCS with optimization efficiencies of 19.03% and 21.38%, respectively. Experiments with an increased number of moored sites showed that the most cost-effective option is a total of 20 moorings, improving the observing ability with optimization efficiencies up to 26.54% for temperature and 27.25% for salinity. The design of an objective array relies on the ocean phenomenon of interest and its spatial and temporal scales. In this study, we focus on basin-scale variations in temperature and salinity in the SCS, and thus our consolidated array may not well resolve mesoscale processes. The MAOT can be extended to include other variables and multi-scale variability and can be applied to other regions.
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Figure 1. Topography of the South China Sea. White squares represent the locations of the assumed initial array.
Figure 2. Standard deviation of sea surface temperature (a) and salinity anomalies (b).
Figure 3. Spatial patterns of the first (a), second (b), and third (c) empirical orthogonal function (EOF) modes for sea surface tem-perature anomalies (SSTA) in the South China Sea; d–f are the same as a–c but for sea surface salinity anomalies (SSSA).
Figure 4. Cumulative contribution of different numbers of empirical orthogonal function leading modes to the total variance for temperature (a) and salinity (b) anomalies at different depths.
Figure 5. RMSEs of reconstructed temperature (a–h) and salinity (i–p) derived from the initial array at different depths. The black squares are the locations of the initial array. D and E in the sub-panels represent the depth (unit: m) and the corresponding area averaged RMSE, respectively.
Figure 6. RMSEs of reconstructed temperature (a–h) and salinity (i–p) derived from the optimal arrays at different depths. The black squares are the locations of the optimal arrays for each depth. D and E in the sub-panels represent the depth (unit: m) and the corresponding area averaged RMSE, respectively.
Figure 7. Consolidated array based on the K-center clustering algorithm. The solid stars indicate the clustered sites. The colored dots indicate locations for the optimal arrays at all depths, and different colors represent different categories in the K-center cluster.
Figure 8. RMSEs of reconstructed temperature (a–h) and salinity (i–p) derived from the consolidated array at different depths. The black squares are the locations of the consolidated array. D and E in the sub-panels represent the depth (unit: m) and the corresponding area averaged RMSE, respectively.
Figure 9. Area averaged RMSEs divided by corresponding ranges (normalized RMSEs, NRMSEs) at different depths in the South China Sea. a. Temperature; b. salinity. Vertical bars indicate the standard deviation of the NRMSEs.
Figure 10. Optimization efficiency for temperature (a) and salinity (b) of the consolidated array in comparison with the initial array; c and d are the same as a and b but in comparison with the optimal arrays. The hollow squares and solid stars in a and b are the locations of initial and consolidated arrays, respectively. The colored dots in c and d indicate locations for the optimal arrays at all depths, and different colors represent different categories in the K-center cluster.
Figure 11. Averaged NRMSEs of temperature and salinity of the consolidated arrays with different site numbers (a), and NRMSEs of temperature (b) and salinity (c) at different depths in the South China Sea with consolidated arrays consist of 17, 20, 23, and 26 stations. Vertical bars in b and c indicate the standard deviation of the NRMSEs.
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