Uncertainty estimation of historical bathymetric data from Bayesian networks

We have developed a Bayesian network to aid estimation of uncertainty for gridded bathymetry data sets in the Digital Bathymetric Data Base - Variable Resolution, maintained at the Naval Oceanographic Office. These estimates did not previously exist and are now needed so that these data can be stored in the Bathymetric Attributed Grid files, which require both bathymetry and uncertainty. Monte Carlo simulations have been used in the literature to calculate how navigation error, sensor error, and bottom gradient propagates into bathymetric uncertainty. This procedure, however, requires the use of original soundings data. Attempting this approach for all soundings used to make the data base is not pragmatic due to the vast quantity of data used. Bayesian networks can be a pragmatic alternative, however, as this approach propagates probability densities of the inputs to calculate probabilities of the end result, resulting in computations that are simpler and more rapid than direct simulations. Valid application of the technique relies on the assumption that measurement errors and bottom slope propagate into bathymetric uncertainty independent of actual measurement location. We discuss how we used the published Monte Carlo techniques on representative sets of soundings data to train the network and implemented the network to estimate the propagation of navigation error and bottom slope to bathymetric uncertainty in historic data. We also test the validity of applying this approach to estimate bathymetric uncertainty through comparisons of these estimates from the Bayesian net and Monte Carlo techniques.