A Scheme for Estimating Time-Varying Wind Stress Drag Coefficient in the Ekman Model with Adjoint Assimilation

Abstract

In this study, the time-varying wind stress drag coefficient in the Ekman model was inverted by the cubic spline interpolation scheme based on the adjoint method. Twin experiments were carried out to investigate the influences of several factors on inversion results, and the conclusions were (1) the inverted distributions with the cubic spline interpolation scheme were in good agreement with the prescribed distributions of the wind stress drag coefficients, and the cubic spline interpolation scheme was superior to direct inversion by the model scheme and Cressman interpolation scheme; (2) the cubic spline interpolation scheme was more advantageous than the Cressman interpolation scheme even if there is moderate noise in the observations. The cubic spline interpolation scheme was further validated in practical experiments where Ekman currents and wind speed derived from mooring data of ocean station Papa were assimilated. The results demonstrated that the variation of the time-varying wind stress drag coefficient with time was similar to that of wind speed with time, and a more accurate inversion result could be obtained by the cubic spline interpolation scheme employing appropriate independent points. Overall, this study provides a potential way for efficient estimation of time-varying wind stress drag coefficient.

A Study of Wind Stress Effects on the Vertical Eddy Viscosity Coefficient Using the Ekman Model with Data Assimilation

“…The Ekman model does not need to express the buoyancy-forcing and stratification effects explicitly, but rather responds to them through the values of the viscosity and boundary layer parameters, and it is easy to solve the Ekman model to explore the effects of specific parameters [21]. Wu et al [22] studied the inversion of VEVC in ideal experiments using the optimal control theory and variational principle based on the adjoint assimilation method. This paper extends Wu's [22] work to invert the depth distribution of VEVC using the measured data and to explore the effect of wind stress.…”

“…Wu et al [22] studied the inversion of VEVC in ideal experiments using the optimal control theory and variational principle based on the adjoint assimilation method. This paper extends Wu's [22] work to invert the depth distribution of VEVC using the measured data and to explore the effect of wind stress. The triangular polynomial interpolation scheme was adopted to enhance the adjoint assimilation process of the data, which has been demonstrated to be more effective in improving the accuracy of the Ekman model inversion.…”

Advancing parameter estimation with Characteristic Finite Difference Method (CFDM) for a marine ecosystem model by assimilating satellite observations: Spatial distributions

“…The adjoint method is a typical four-dimensional variational data assimilation method and has been widely used to optimize uncertain parameters in numerical models (Qian et al, 2021;Wang et al, 2021;Wu et al, 2021). Pelc et al (2012) provided a useful theoretical background for different 4D-Var approaches and showed how this adjoint method can be used to estimate ecosystem model parameters jointly with a large number of initial condition parameters.…”

Application of interpolation methodology with dynamical constraint to the suspended particulate matter in the Liaodong Bay

“…Since the adjoint assimilation method have been widely used to reverse the open boundary conditions (Pan et al, 2017 andChen et al, 2014), optimize the initial field (Peng and Xie, 2006) and optimize the control parameters of marine ecosystem dynamical models (Qi et al, 2011;Li et al, 2013 andGoldberg andHeimbach, 2013), researchers start to use interpolation method with dynamical constraint based on adjoint assimilation method in marine research. Wu et al (2021) adjusted the parameters in Ekman model based on the cubic spline interpolation method with the adjoint assimilation model, and obtained the optimized wind stress resistance coefficient. Zheng et al (2020) applied the dynamically constrained interpolation method to the Bohai, Yellow, and East China Seas.…”