Watershed Model Uncertainty Analysis Based On Information Entropy And Mutual Information

With the growing knowledge of hydrological processes and finer hydrologicalsimulation, the issue of hydrological model uncertainty attracts more and more attention.Currently the hydrological model uncertainty is classified into three sources: input,parameter and structure uncertainty. However, not all “model uncertainty” depends on“model”. Current uncertainty qualification methods depend on one (or multiple) specificmodel, which are lack of the ability to distinguish the two categories thatindependent/depend on model. The concepts of information entropy and mutualinformation is introduced in order to qualify the information content of hydrologicalvariables and distinguish aleatory uncertainty that independent to model and epistemicuncertainty that dependent on model. A framework of uncertainty analysis based oninformation theory is proposed and primary case studies are carried out in order to showthe applicability of the new framework.First, the proposed framework uses the most up to date methods to explicitlycompute three kinds of information: the information required by streamflow simulation,the information offered by currently available hydrological observation data, and theinformation expressed by a specific model. For a specific catchment and model, theinformation entropy of observed streamflow is the information required by streamflowsimulation; the mutual information that meteorological data, previous streamflow andsoil moisture data contributes to streamflow observation data is the availableinformation for streamflow simulation offered by currently available data; the mutualinformation between simulated and observed streamflow is the amount of informationused by a model. The difference between the first two is aleatory uncertainty, which theinformation is required by simulation but not offered by data; the difference between thelast two is epistemic uncertainty, which the information has been offered by data but notproperly utilized by the model.To mitigate the influence of curse of dimensionality on computing mutualinformation of high-dimensional hydrological variables, Leonenko’s method that cancompute information content without estimating joint probability density function isintroduced and applied for the first time in the context of hydrology. The result shows that Leonenko’s method performs well in low-dimension and high-dimensionlow-correlation case, but not applicable to the high-dimensional high-correlation case.Further tests are carried out and another two methods: ISOMAP and SVM are able toqualify information content of hydrological variables. ISOMAP can identify the relativeinformation content of hydrological datasets, while SVM is good at regressing to theinformation while eliminating the random error so that one can compute the informationcontent from the regression result. The result of numerical experiment based onhydrological model demonstrated that both of the two methods are capable ofidentifying the information content of hydrological observation data.The framework is applied in multiple catchments that have different data qualityand multiple models that have different model structure complexity. The result ofapplication shows that the framework is able to distinguish aleatory and epistemicuncertainty, identify how much of the uncertainty comes from model structureinadequacy, and potentially guide model structure improvement in the future.The novel contribution of this thesis is1) proposing a hydrological modeluncertainty qualification framework based on information entropy and mutualinformation;2) improving current methods of entropy and mutual informationestimation by proposing new method that applicable to high-dimensionalhigh-correlated cases;3) applying the framework to various catchments and models andproposed a model selection and improvements strategy in hydrological prediction.