Model Terrain Correction Using Variational Adjoint Method With Tikhonov-Total Variation Regularization

Numerical weather prediction models require optimal topographic data to improve the accuracy of the forecasts. A framework for bottom terrain correction of a shallow-water equations model is proposed with variational adjoint and regularization methods. The Tikhonov-total variation (TV) regularization with dual regularization parameters is introduced as a constraint for unique and stable correction. The limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method is used to minimize the cost function. Numerical results indicate that the Tikhonov-TV regularization helps improve the corrections by reducing both overall shifts and surface fluctuations. These positive impacts become much more obvious after considering dual regularization parameters. The corrections at final time of assimilation significantly improve the numerical predictions. Tests confirm the potential of the computational framework for bottom terrain correction of numerical weather prediction models to reduce model errors.