A Method on Estimating Time-Varying Vertical Eddy Viscosity for an Ekman Layer Model with Data Assimilation

Author:

Zhang Jicai1,Li Guoqing2,Yi Jiacheng2,Gao Yanqiu3,Cao Anzhou2

Affiliation:

1. Institute of Physical Oceanography, Ocean College, Zhejiang University, Zhoushan, China, and Applied Ocean Physics and Engineering Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

2. Institute of Physical Oceanography, Ocean College, Zhejiang University, Zhoushan, China

3. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou, China

Abstract

Temporal vertical eddy viscosity coefficient (VEVC) in an Ekman layer model is estimated using an adjoint method. Twin experiments are carried out to investigate the influences of several factors on inversion results, and the conclusions of twin experiments are 1) the adjoint method is a capable method to estimate different kinds of temporal distributions of VEVCs; 2) the gradient descent algorithm is better than CONMIN and L-BFGS for the present problem, although the posterior two algorithms perform better on convergence efficiency; 3) inversion results are sensitive to initial guesses; 4) the model is applicable to different wind conditions; 5) the inversion result with thick boundary layer depth (BLD) is slightly better than thin BLD; 6) inversion results are more sensitive to observations in upper layers than those in lower layers; 7) inversion results are still acceptable when data noise exists, indicating the method can sustain noise to a certain degree; 8) a regularization method is proved to be useful to improve the results for present problem; and 9) the present method can tolerate the existence of balance errors due to the imperfection of governing equations. The methodology is further validated in practical experiments where Ekman currents are derived from Bermuda Testbed Mooring data and assimilated. Modeled Ekman currents coincide well with observed ones, especially for upper layers. The results demonstrate that the assumptions of depth dependence and time dependence are equally important for VEVCs. The feasibility of the typical Ekman model, the imperfection of Ekman balance equations, and the deficiencies of the present method are discussed. This method provides a potential way to realize the time variations of VEVCs in ocean models.

Funder

Ministry of Science and Technology of the People's Republic of China

Major Research Plan

Ministry of Education of the People's Republic of China

Publisher

American Meteorological Society

Subject

Atmospheric Science,Ocean Engineering

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