When planning for ship navigation or compiling data for a bathymetry map, the navigator or mapper use many different sources of bathymetry information and navigation hazards. Sources include electronic charts at different scales, gridded bathymetry of different ages and quality, special purpose vector products, sonar data, crowdsourced data, etc. The quality of these sources, however, are inconsistent in general, making it especially challenging to provide a coherent picture for planning. An experienced navigator or mapper not only would use more than just the soundings, grids and depth areas to form a mental model of the seafloor, but also subjective assessment of information reliability and attitudinal character varying between optimistic/aggressive to pessimistic/conservative outlooks (or in between) depending on the purpose for the map. Here, we present an expert system approach for consistent planning/mapping that uses a combination of Bayesian and fuzzy logic processes. We present two examples of using these processes with sources of differing subjective reliabilities as follows: 1) navigation risk surface / or safety contour and 2) fusion of multiple bathymetry grids/sources for mapping. The major contribution of this process is the capability to record subjective weighting of source and the fusion process used. For the first application, we first interpolate each bathymetry source with control over the user\&$\#$39;s subjective risk allowed in the reconstruction. Each cell is set to 2, 1, or 0, for \"Known Unsafe\", \"Maybe Safe\" and \"Known Safe\" status, based on the ship\&$\#$39;s current draft. Weighted Bayesian categorical estimation (Dirichlet conjugate prior) computes a fused risk surface. The fuzzy logic process known as Order Weighted Averaging (OWA) provides the weights for each source. This component provides quantitative methods to generate, use and record subjective weights. The maximum a posteriori reconstruction for each cell provides a best estimate of status from all sources; analysis of the probability mass distribution in the cell provides guidance on reliability of the assignment. The second application uses this same process, but instead of pre-interpolation and categorical fusion, the OWA provides average bathymetry directly.

}, url = {https://agu.confex.com/agu/fm18/meetingapp.cgi/Paper/393098}, author = {Paul A. Elmore and Brian R Calder and Giuseppe Masetti and Ronald R Yager and Fredrick E Petry} } @article {5947, title = {Development of an Uncertainty Propagation Equation for Scalar Fields}, volume = {40, 5}, year = {2017}, month = {August 1}, pages = {341-360}, publisher = {Taylor \& Francis Group}, abstract = {The uncertainty of a scalar field is essential structuring information for any estimation problem. Establishing the uncertainty in a dense gridded product from sparse or random uncertainty-attributed input data is not, however, routine.\ This manuscript develops an equation that propagates the uncertainty of individual observations, arbitrarily distributed in R^{2}, to a common estimation location at which they can be used to determine the composite uncertainty of the output field. The equation includes the effect of the distance between the observation and estimation locations, the field and horizontal uncertainty of the observation, and user-parameters to control the expected variability in the field as a function of distance. Two computational versions of the equation, a lower cost conservative approach and a higher cost mean-distance approach, are developed and evaluated for computational cost and resulting accuracy in numerical experiments over simulated bathymetric data. The mean-distance approach is more accurate, but more costly; suitable numerical approximations are proposed to control computational costs. A benefit of the work described is flexibility and enhancement for applications of the model, such as the Combined Uncertainty and Bathymetry Estimator (CUBE) algorithm, which is used as a demonstration of the difference between the two versions of the equation.