Application of Adjoint Method to the Evaluation of Temporal and Spatial Variations of the Eddy Viscosity Coefficient

Ting Zhang^*

• Fujian University of Technology, Fuzhou, China

This study investigated the temporal and spatial variations of the eddy viscosity coefficient (EVC) in an Ekman model using an adjoint method. The time-and depth-dependent EVC was represented as a Fourier series, which consisted of four summations. The effectiveness of the model was significantly influenced by the number of terms included in each summation. In the first three groups of ideal experiments, a constant drag coefficient was used at low surface wind speeds. An analysis of the inversion results indicated that more terms should be added to each summation if the EVC varied over shorter periods, whether in time or depth. Additionally, the findings indicated that the model performed better when simulating the time-and depth-dependent EVC over longer periods. Two additional groups of ideal experiments were conducted to investigate the impact of near-surface wind speeds on the inversion of the K-Profile EVC. The drag coefficient associated with wind speeds over time was utilized in these experiments. An analysis of the inversion results indicated that the model effectively captured the temporal and spatial distribution of the EVC. Finally, the EVC was simulated during a super typhoon. The evaluation of the simulated EVC and ocean currents suggested that greater values of the simulated EVC appear at depths ranging from 50 to 65 m under strong wind conditions. Variations in wind directions could further enhance the inverted EVC within the Ekman layer.