Inversion Study of Vertical Eddy Viscosity Coefficient Based on an Internal Tidal Model with the Adjoint Method

Abstract

Based on an isopycnic-coordinate internal tidal model with the adjoint method, the inversion of spatially varying vertical eddy viscosity coefficient (VEVC) is studied in two groups of numerical experiments. In Group One, the influences of independent point schemes (IPSs) exerting on parameter inversion are discussed. Results demonstrate that the VEVCs can be inverted successfully with IPSs and the model has the best performance with the optimal IPSs. Using the optimal IPSs obtained in Group One, the inversions of VEVCs on two different Gaussian bottom topographies are carried out in Group Two. In addition, performances of two optimization methods of which one is the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method and the other is a simplified gradient descent method (GDM-S) are also investigated. Results of the experiments indicate that this adjoint model is capable to invert the VEVC with spatially distribution, no matter which optimization method is taken. The L-BFGS method has a better performance in terms of the convergence rate and the inversion results. In general, the L-BFGS method is a more effective and efficient optimization method than the GDM-S.