Wave-modified Ekman current solutions for the vertical eddy viscosity formulated by K-Profile Parameterization scheme

2013 ◽  
Vol 80 ◽  
pp. 58-65 ◽  
Author(s):  
Jin-Bao Song ◽  
Jun-Li Xu
Keyword(s):  
Eddy Viscosity ◽  
Parameterization Scheme ◽  
Vertical Eddy Viscosity ◽  
Ekman Current ◽  
Vertical Eddy

scholarly journals Seasonal variation of the principal tidal constituents in the Bohai Sea

Ocean Science ◽  
2020 ◽  
Vol 16 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Daosheng Wang ◽  
Haidong Pan ◽  
Guangzhen Jin ◽  
Xianqing Lv
Keyword(s):  
Seasonal Variation ◽  
Harmonic Analysis ◽  
Sea Level ◽  
Seasonal Variations ◽  
Eddy Viscosity ◽  
Bohai Sea ◽  
Phase Lag ◽  
Vertical Eddy Viscosity ◽  
Tidal Constituents ◽  
Vertical Eddy

Abstract. The seasonal variation of tides plays a significant role in water level changes in coastal regions. In this study, seasonal variations of four principal tidal constituents, M2, S2, K1, and O1, in the Bohai Sea, China, were studied by applying an enhanced harmonic analysis method to two time series: 1-year sea level observations at a mooring station (named E2) located in the western Bohai Sea and 17-year sea level observations at Dalian. At E2, the M2 amplitude and phase lag have annual frequencies, with large values in summer and small values in winter, while the frequencies of S2 and K1 amplitudes are also nearly annual. In contrast, the O1 amplitude increases constantly from winter to autumn. The maxima of phase lags appear twice in 1 year for S2, K1, and O1, taking place near winter and summer. The seasonal variation trends estimated by the enhanced harmonic analysis at Dalian are different from those at E2, except for the M2 phase lag. The M2 and S2 amplitudes show semi-annual and annual cycles, respectively, which are relatively significant at Dalian. The results of numerical experiments indicate that the seasonality of vertical eddy viscosity induces seasonal variations of the principal tidal constituents at E2. However, the tested mechanisms, including seasonally varying stratification, vertical eddy viscosity, and mean sea level, do not adequately explain the observed seasonal variations of tidal constituents at Dalian.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Guangzhen Jin ◽  
Qiang Liu ◽  
Xianqing Lv
Keyword(s):  
Eddy Viscosity ◽  
Adjoint Method ◽  
Viscosity Coefficient ◽  
Optimization Method ◽  
Gradient Descent Method ◽  
Bfgs Method ◽  
Tidal Model ◽  
Vertical Eddy Viscosity ◽  
Eddy Viscosity Coefficient ◽  
Vertical Eddy

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.

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

2019 ◽  
Vol 36 (9) ◽  
pp. 1789-1812
Author(s):  
Jicai Zhang ◽  
Guoqing Li ◽  
Jiacheng Yi ◽  
Yanqiu Gao ◽  
Anzhou Cao
Keyword(s):  
Present Method ◽  
Eddy Viscosity ◽  
Adjoint Method ◽  
Ekman Layer ◽  
Present Problem ◽  
Layer Model ◽  
Gradient Descent Algorithm ◽  
Vertical Eddy Viscosity ◽  
Vertical Eddy ◽  
Better Than

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.

scholarly journals Wave-Modified Ekman Current Solutions for the Time-Dependent Vertical Eddy Viscosity

2021 ◽  
Vol 9 (6) ◽  
pp. 664
Author(s):  
Hui Chen ◽  
Shaofeng Li ◽  
Jinbao Song ◽  
Hailun He
Keyword(s):  
Eddy Viscosity ◽  
Time Variability ◽  
Surface Shear ◽  
Near Surface ◽  
Depth Dependence ◽  
Temporal Averaging ◽  
Low Level Jet ◽  
Mean Current ◽  
Ekman Current ◽  
Vertical Eddy

This study aimed to highlight a general lack of clarity regarding the scale of the temporal averaging implicit in Ekman-type models. Under the assumption of time and depth-dependent eddy viscosity, we present an analytical Fourier series solution for a wave-modified Ekman model. The depth dependence of eddy viscosity is based on the K-Profile Parameterization (KPP) scheme. The solution reproduces major characteristics of diurnal variation in ocean velocity and shear. Results show that the time variability in eddy viscosity leads to an enhanced mean current near-surface and a decrease in the effective eddy viscosity, which finally results in an intensified near-surface shear and wakes a low-level jet flow. Rectification values are dominated by the strength of diurnal mixing, and partly due to the nonlinear depth dependence of the eddy viscosity.

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