6. Optimal Network Design for GOOS
Network design theory allows us to determine objectively what the optimum sampling density for the global ocean observing system (GOOS) should be in order to detect and resolve global climate signals on biennial and interannual timescales (White, 1995). The determination of optimum sampling begins by computing three-dimensional covariance matrices at each 5° latitude by 10° longitude location from approximately 30°S-60°N at depths of 0 m, 200 m, and 400 m from temperature anomalies about the mean annual cycle for the 13 years from 1979-1991. Lags are chosen to focus on seasonal-to-interannual time scales resolved on gyre-to-basin space scales. These sample covariance matrices are fit with a second-order auto-regressive (AR) model, allowing for the detection of horizontal wave propagation in the presence of dissipation. White (1995) found biennial and quadrennial signals over most of the ocean and at all depths, (i.e., with zero-crossing scales of 6-12 months) dominating the frequency range extending from biennial to interdecadal variability, with eastward propagation found at the sea surface over most of the Pacific, Indian, and Atlantic oceans, and westward propagation found over most of the Pacific ocean at 200 m and 400 m, the latter qualitatively consistent with Rossby wave propagation. The noise variance was found to be approximately equal to the signal variance at all depths, while the ratio of zero-crossing scale-to-decay scale (i.e., 1.5-2.5) finds biennial and interannual wave propagation critically dissipated most everywhere. This effectively reduced the second-order AR model to a first-order AR model, with decay scales and not zero-crossing scales defining decorrelation scales.
White (1995) analyzed these covariance statistics within the framework of optimum interpolation, allowing sampling rates to be estimated for detecting seasonal-to-interannual variability to within prescribed error limits. Utilizing a first-order AR covariance model, he found 1-2 observations per decorrelation scale in each dimension allowing the interpolation error to be 0.8-0.6 of the signal standard deviation. A uniform set of decorrelation scales (e.g., 2.5° latitude, 5° longitude, 3 months) and 1.0 for the noise-to-signal ratio were chosen for detecting minimum gyre-scale biennial variability at all depths uniformly over the global domain. Therefore, sampling the global ocean at 2500-3000 observations per month yields maximum interpolation errors for biennial signals (i.e., ±0.4℃ at the sea surface, ±0.5℃ at 200 m, and ±0.2℃ at 400 m) that are similar to those for the mean annual cycle. This sampling rate is adequate for detecting the space-time evolution of biennial signals (and, hence. ENSO and interdecadal signals) over the interior global ocean. But, it is inadequate for detecting year-to-year changes in upper ocean heat storage averaged over large portions of the global ocean as required by the WOCE Heat Budget Study.
7. Global Ocean Observing System Present and Future
The optimum global sampling density estimated for GOOS (White, 1995) is that chosen by the proposed ARGO program to sample the global ocean (Figure 5a). The proposed ARGO program is composed of 3000 floats, each of which profiles temperature and salinity in the water column down to 1000 m every 10 days, with a mean float separation of 2° latitude and longitude, with a mean lifespan of 5 years. This is an international program and is expected to be operated by an international consortium under the auspices of the Intergovernmental Oceanographic Commission (IOC) and the World Meteorological Organization (WMO). The present temperature profile sampling program produces much less sampling density than this (Figure 5b), composed of expendable bathythermographs (XBT'S) deployed from volunteer observing ships (VOS) and thermistor chains deployed from moored buoys in the TOGA TAO array. The reader can see how woefully inadequate the present global ocean observing system is, with large gaps in the South Pacific, the Indian, and Atlantic oceans, with no temperature profiles at all being collected in the Southern Ocean. The proposed ARGO program, in addition to providing optimal sampling of the upper ocean temperature over the global ocean, will also sample upper ocean salinity, which will allow the computation of density and geostrophic currents, allowing heat, salt, and vorticity budgets in the upper ocean to be examined.