Variational inverse methods for transport problems

• Main Author: Yang, Zhaoqing
• Format: Others
• Language: English
• Published: W&M ScholarWorks 1996
• Subjects: Environmental Sciences; Oceanography
• Online Access: https://scholarworks.wm.edu/etd/1539616917; https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=2484&context=etd

Variational inverse data assimilation schemes are developed for three types of parameter identification problems in transport models: (1) the tracer inverse for the Lagrangian mean transport velocity in a long-term advection-diffusion transport model; (2) determination of inflow salinity open boundary condition in an intra-tidal salinity transport model; and (3) determination of settling velocity and resuspension rate for a cohesive sediment transport model. The gradient of the cost function with respect to the control variables is obtained by the adjoint model. A series of twin experiments are conducted to test the inverse models for the three types of problems. Results show that variational data assimilation can successfully retrieve poorly known parameters in transport models. The first problem is associated with the long-term advective transport, represented by the Lagrangian mean transport velocity which can be decomposed into two parts: the Eulerian transport velocity and the curl of a 3-D vector potential A. The optimal long-term advective transport field is obtained through adjusting the vector potential using a variational data assimilation method. Experiments are performed in an idealized estuary. Results show that the variational data assimilation method can successfully retrieve the effective Lagrangian mean transport velocity in a long-term transport model. Results also show that the smooth best fit model state can still be retrieved using a penalty method when observations are too sparse or contain noisy signals. A variational inverse model for optimally determining open boundary condition is developed and tested in a 3-D intra-tidal salinity transport model. The maximum inflow salinity open boundary value and its recovery time from outflow condition are treated as control variables. Effects of scaling, preconditioning, and penalty are investigated. It is shown that proper scaling and preconditioning can greatly speed up the convergence rate of the minimization process. The spatial oscillations in the recovery time of the inflow boundary condition can be effectively eliminated by an penalty technique. A variational inverse model is developed to estimate the settling velocity and resuspension constant. The settling velocity &w\sb{lcub}s{rcub}& and resuspension constant &M\sb{lcub}o{rcub}& are assumed to be constant in the whole model domain. The inverse model is tested in an idealized 3-D estuary and the James River, a tributary of the Chesapeake Bay. Experimental results demonstrate that the variational inverse model can be used to identify the poorly known parameters in cohesive sediment transport modeling.