Study On Applying Bayesian Maximum Entropy In A Physical Oceanography Context

Bayesian Maximum Entropy(BME)is a theory first developed by Professor George Christakos in the late 1980s-early 1990s,and subsequently implemented in many scientific and engineering fields worldwide(Geology,Atmosphere,Space Epidemiology,Remote Sensing and other fields).The BME theory can be used to model the composite space-time variation of natural attributes in a mathematically rigorous and physical meaningful manner,and to generate accurate predictions of the value of these attributes at unsampled points in the space-time domain of interest under conditions of multi-sourced in-situ uncertainty.During the last 10 years,BME has been applied with increasing frequency by many researchers and scientists in China,but mostly handled the knowledge from Geostatistics.The first part of the thesis collated the relevant information and then reviewed the core theory of BME.The basic part of the theory is derived from the thought of Bayesian School,and combines the maximum entropy principle with Bayesian theorem,which explains the BME name.Underlying BME theory is the concept of spatiotemporal random field(S/TRF)also advanced by Professor Christakos.BME theory has led to the development of Modern Geostatistics,which was a major development and move forward of the field of traditional Geostatistics.The implementation of BME in real world applications basically involves four major stages:prior stage,meta-prior stage,posterior stage and mapping stage.After these four stages,BME can absorb information from general knowledge bases(G-KBs)and specific knowledge bases(S-KBs)to obtain the complete posterior probability distribution of unknown spatial points and the estimated values derived from the posterior probability distribution.In the second part of the thesis,by assuming that the general knowledge involves the semi-variance models,the BME theory was properly realized according to its four major stages,and certain important new formulas and valuable conclusions were obtained at each stage.These results were compared with the classical Geostatistics techniques,and it was shown that the popular Kriging techniques are just special cases of the BME theory under the limited conditions mentioned earlier.It also reflected that Modern Geostatistics based on BME theory is the inheritance and development of classical Geostatistics.In the third part,introduced the prediction method of physical oceanography law as part of the G-KBs in BME and applied BME in a Physical Oceanography context.This study was conducted which included advection-reaction law of ocean pollution in the form of a partial differential equation across space-time.Based on the research of second part,a novel BME formulation was developed.The novel BME connected maximum entropy and physical oceanography law by the values of first and second moments and get the G-based PDF in study area.This new method can directly involves various kinds of site-specific information in the solution of the physical oceanography law to provide a complete PDF,which make the application of BME in physical oceanography feasible.In the fourth part,a numerical simulation study was conducted,which has same first-order partial differential equation as priori knowledge and hard data,four groups of realistic soft data types(uniform,Gaussian,triangular data probability shapes and smaller dispersion triangular data probability shapes),and in order to predict the ocean pollution at 101×101 space-time nodes in 10km×10h study area.Based on the mean space-time distribution involving four groups,it was shown that BME can be successfully applied in Physical Oceanography problems being capable to rigorously integrate marine and ocean laws with many kinds of case-specific data under conditions of real world uncertainty and provide complete PDF.In fact,the prediction uncertainty obtained by the proposed BME setup is significantly lower than that obtained by directly solving the space-time ocean pollution law using a standard partial differential equation technique(which reduced 1.690ppm,1.585 ppm,1.767ppm and 1.923 ppm respectively).Moreover,it was shown that by using more accurate soft data BME can generate less uncertain predictions of the ocean pollutant in the domain of interest.In sum,the significance of this thesis for the researchers in the fields of Geostatistic,is that it can provide supports to better understand and use BME in application and provide physical law BME method in space-time prediction.And the significance for the researchers in the fields of Marine Sciences,is that it can provide new and powerful ideas and techniques to combine physical law and site-specific data to get a complete stochastic characterization of phenomenon in assessment.In the future,one very promising research avenue will be the incorporation of current Big Data developments within the framework of BME theory,and to improve the existing BME software in terms of calculation speed and time cost in the light of big data.