Statistical Interpolation of Tidal Datums and Computation of Its Associated Spatially Varying Uncertainty

Tidal datums are key components in NOAA’s Vertical Datum transformation project (VDatum). In this paper, we propose a statistical interpolation method, derived from the variational principle, to calculate tidal datums by blending the modeled and the observed tidal datums. Through the implementation of this statistical interpolation method in the Chesapeake and Delaware Bays, we conclude that the statistical interpolation method for tidal datums has great advantages over the currently used deterministic interpolation method. The foremost, and inherent, advantage of the statistical interpolation is its capability to integrate data from different sources and with different accuracies without concern for their relative spatial locations. The second advantage is that it provides a spatially varying uncertainty for the entire domain in which data is being integrated. The latter is especially helpful for the decision-making process of where new instruments would be most effectively placed. Lastly, the test case results show that the statistical interpolation reduced the bias, maximum absolute error, mean absolute error, and root mean square error in comparison to the current deterministic approach.