Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)


Virginia Institute of Marine Science


Albert Y. Kuo


An inverse mathematical estuarine eutrophication model has been developed. The model provides a framework to estimate unknown parameters by assimilation of the concentration data of those state variables. The inverse model developed is a laterally integrated, two-dimensional, real-time model which consists of a hydrodynamic model, an eutrophication model and an adjoint model. The hydrodynamic model provides the dynamic fields for both the eutrophication model and the adjoint model. The eutrophication model simulates eight water quality state variables which are phytoplankton, organic nitrogen, ammonium nitrogen, nitrite-nitrate nitrogen, organic phosphorus, inorganic (ortho) phosphorus, carbonaceous biochemical oxygen demand and dissolved oxygen. The adjoint model is used during the processes of parameter estimation to provide the gradients of the cost function with respect to the unknown parameters. to increase the computational efficiency and reduce computer storage space, a decoupling scheme is implemented in the inverse model, in which the kinetic processes are decoupled from the physical transport for the purpose of numerical computation. An efficient preconditioning technique is introduced in the inverse model to speed up the rate of convergence. The experiments conducted in this study provide the information of the parameter identifiability and the field data requirement for the model calibration. The model experiments with hypothetical data sets show that the parameters can be accurately estimated for short period and long period model simulations under both constant and time-varying boundary conditions. The inverse model is convergent with different initial guess parameter values and under different environments. The inverse model was successfully applied to aid calibration of the eutrophication model of the tidal Rappahannock River, Virginia. With the use of the inverse model, the eutrophication model can be calibrated efficiently and systematically. The agreement between the model predictions and observations are very satisfactory. The studies show that the inverse model is also useful in addressing the important questions of whether the estimated parameters are unique and whether the sample data are sufficient to calibrate a model. Therefore, the inverse model may also serve as a tool in helping design a field program to collect data for model calibration.



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