Ocean pollution assessment by integrating physical law and site‐specific data

This work introduces the Bayesian maximum entropy (BME) perspective in the space–time characterization and prediction of ocean pollution. The proposed approach can outperform the standard numerical techniques that can also solve the partial differential equation representing the ocean pollution law but either cannot integrate in the solution any case‐specific information (provided by the hard or soft data available) or they do not provide a complete stochastic characterization of the ocean pollution phenomenon. This happens because the BME‐based solution of the ocean pollution law can both take advantage of any case‐specific data available and derive the complete probability density function throughout the space–time domain of interest, which can be then used to derive more than one kind of ocean pollution predictors (including the mean, the median, and the mode) at every point of this domain. Valuable insight into the proposed approach is gained by means of a simulation (synthetic) experiment that considers the advection–reaction law in the light of hard data and three different types of soft information in a controlled environment so a useful sensitivity analysis of the results can be performed (which is not usually possible in a real‐world case study). The uncertainty assessment of this experiment demonstrated that BME leads to improved ocean pollution predictions compared with the standard numerical technique. In principle, the higher the quality and informativeness of the site‐specific data, the more realistic should be the BME solution of the ocean pollution law under conditions of in situ uncertainty (this result also points out the importance of collecting data as informative as possible to maximize prediction accuracy). Moreover, the uncertainty assessment of the pollutant concentration predictions demonstrated that the BME approach makes good use of the soft data leading to improved ocean pollution predictions compared with predictions that do not involve soft data.