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Haidong Pan, Zheng Guo, and Xianqing Lv

Abstract

Open boundary conditions (OBCs) of the M2 tidal constituent in the Bohai and Yellow Seas (BYS) were inverted successfully through assimilation of TOPEX/Poseidon (T/P) altimeter data. An improved independent points (IPs) scheme was employed in the inversion. Under the assumption that the OBC was spatially varying, values at a set of IPs along the open boundary were inverted using the adjoint method and those at other points were calculated by the spline interpolation. The OBC inverted with the improved scheme was closer to reality in terms of smoothness than that inverted with the Cressman interpolation. The scheme was calibrated in twin experiments. Practical experiments showed that the misfits between simulated results and observations were smaller when the spline interpolation was used.

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Yafei Nie, Yuzhe Wang, and Xianqing Lv

Abstract

Snow on sea ice is a key variable in Arctic climate studies and thus plays an important role in geophysics. However, snow depths (SDs) derived from passive satellite remote sensing data are missing on multiyear ice due to the limitation of algorithm. We interpolate the SDs using the polynomial fitting (PF) method, trigonometric polynomial fitting (TPF) method, and multiquadric function interpolation method, and NASA’s Operation IceBridge (OIB) SD product is used to assess errors. Results show that TPF with the highest degree in x direction equaling 2 and the highest degree in y direction equaling 4 (TPF24) is the most satisfactory method, which has a deviation of 7.19 cm from OIB SD. Although PF with the highest degree in x and y directions being 7 and 8, respectively (PF78), also performs well in terms of error (7.22 cm), unreasonable value will be obtained at the edge due to its high degree. Results of TPF24 show a thicker SD area located in the north of Greenland, which is in good agreement with the actual situation.

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Li-Li Fan, Bin Wang, and Xian-Qing Lv

Abstract

Harmonic analysis of 10 yr of Ocean Topography Experiment (TOPEX)/Poseidon (T/P) along-track altimetry is performed to derive the semidiurnal and diurnal tides (M 2, S 2, N 2, K 2, K 1, O 1, P 1, and Q 1) near Hawaii. The T/P solutions are evaluated through intercomparison for crossover points of the ascending and descending tracks and comparison with the data of tidal stations, which show that the T/P solutions in the study area are reliable. By using a suitable order polynomial to fit the T/P solutions along every track, the harmonic constants of any point on T/P tracks are acquired. A new fitting method, which is characterized by applying the harmonics from T/P tracks to produce directly empirical cotidal charts, is developed. The harmonic constants derived by this fitting method show good agreement with the data of tidal stations, the results of National Astronomical Observatory 99b (NAO.99b), TOPEX/Poseidon 7.2 (TPXO7.2), and Finite Element Solutions 2004 (FES2004) models, which suggests that the fitting method is reasonable, and the highly accurate cotidal chart could be directly acquired from T/P altimetry data by this fitting method.

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Junyong Zheng, Xinyan Mao, Xianqing Lv, and Wensheng Jiang

Abstract

The harmonic constants extracted from tidal gauge stations and satellite altimeter observations are usually sparsely distributed in the continental marginal seas, but they are precious data for addressing the main characteristics of different constituents. In this paper, a dynamically constrained interpolation methodology (DCIM) is developed and applied to interpolate the observed harmonic constants of the M2 constituent from satellite altimeter observations in the Bohai, Yellow, and East China Seas (BYECS) with those from tidal gauge stations for validation. In the DCIM, the tide model provides dynamical constraints to interpolate the observations, and the adjoint assimilation method provides iterative optimization for the interpolated results by adjusting key model parameters. In particular, a substantial quantity of enhanced “observations” generated from the interpolated results of the domain are further interpolated with the sparse observations in the subdomain. The final interpolated results for each subdomain, naturally blending the dynamical constraints from the dynamical model with statistical information from observations, can describe the main characteristics of the M2 constituent in the BYECS, the continental shelf sea of the East China Sea, and the Zhejiang–Fujian coastal area, respectively. The results indicate that the DCIM is feasible and effective to utilize the observations to obtain high-accuracy cotidal charts for regional ocean.

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Guang-Zhen Jin, An-Zhou Cao, and Xian-Qing Lv

Abstract

To investigate the equilibration of numerical simulation (ENS) of internal tide, a three-dimensional isopycnic coordinate internal tide model is applied to simulate the M2 internal tide on idealized topography and around the Hawaiian Ridge. An idealized experiment is carried out on a Gaussian topography, and the temporal variations of the baroclinic velocity and the baroclinic energy flux are analyzed, then ENS is studied, and two criteria are presented. Moreover, the impacts of four parameters [horizontal and vertical eddy viscosity coefficients, bottom friction coefficient, and damping coefficient (to parameterize the nonhydrostatic processes in the model)] on ENS during numerical simulations, the baroclinic velocity, the baroclinic tidal energy, and the baroclinic energy flux are investigated. It appears that ENS for the M2 internal tide is more sensitive to the horizontal eddy viscosity coefficient and the damping coefficient. To further examine the criteria of ENS, a numerical experiment is carried out to simulate the M2 internal tidal constituent near the Hawaiian Ridge. The simulated surface tide shows good agreement with results from the Oregon State University tidal model and TOPEX/Poseidon (T/P) observations. The simulation results indicate that a 50 M2 tidal period (25.88 days) run is capable of ensuring ENS for the M2 internal tide in this case. In short, this paper presents a method and two criteria for examining ENS for internal tides for modelers.

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Minjie Xu, Yuzhe Wang, Shuya Wang, Xianqing Lv, and Xu Chen

Abstract

Sufficient and accurate tide data are essential for analyzing physical processes in the ocean. A method is developed to spatially fit the tidal amplitude and phase lag data along satellite altimeter tracks near Hawaii and construct reliable cotidal charts by using the Chebyshev polynomials. The method is completely dependent on satellite altimeter data. By using the cross-validation method, the optimal orders of Chebyshev polynomials are determined and the polynomial coefficients are calculated by the least squares method. The tidal amplitudes and phase lags obtained by the method are compared with those from the Finite Element Solutions 2014 (FES2014), National Astronomical Observatory 99b (NAO.99b) and TPXO9 models. Results indicate that the method yields accurate results as its fitting results are consistent with the harmonic constants of the three models. The feasibility of this method is also validated by the harmonic constants from tidal gauges near Hawaii.

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Xinyan Mao, Daosheng Wang, Jicai Zhang, Changwei Bian, and Xianqing Lv

Abstract

The observed suspended sediment concentrations (SSCs) obtained from the water sampling are usually sparsely distributed in both space and time, which are traditionally applied just to calibrate other types of observations. In this study a dynamically constrained interpolation methodology (DCIM) is developed to interpolate these sparsely observed SSCs in the Bohai Sea. In this method the suspended sediment transport model is taken as dynamical constraints to interpolate the observations. Meanwhile, the interpolated results are optimized iteratively by adjusting the key model parameters using the adjoint method.

The DCIM is first verified using the synthetic observations produced by twin model runs. The modeling results reveal that this method is effective at interpolating the sparsely observed artificial SSCs, even when the observations are heavily contaminated by data noise. Then, the sparsely observed practical SSCs obtained from a large area survey in the Bohai Sea are interpolated using the DCIM. The interpolated results are verified by randomly selected independent observations. The discrepancies between the interpolated SSCs and the observations are significantly decreased. When all the observations are interpolated, the final interpolated SSCs captured a majority (96.88%) of observations with a factor of 2 and the correlation coefficient between the observed and interpolated SSCs is 0.98. Besides, the interpolated results have presented the reasonable dynamical variations of SSCs in the space and time domains. The modeling results indicate that the DCIM is an effective tool for interpolating the sparsely observed SSCs in both space and time.

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Zheng Guo, Haidong Pan, Wei Fan, and Xianqing Lv

Abstract

A new method for the inversion of bottom friction coefficients (BFCs) in a two-dimensional tidal model is proposed in this study. In this method, the field of BFCs is constructed by interpolating values at independent points using a surface spline. The surface spline interpolation has an advantage: that the constructed surface is smoother than the surface constructed by the traditionally used linear interpolation, which has unrealistic extrema. The method is validated in twin experiments where the prescribed nonlinear distribution of BFCs are better inverted with the surface spline interpolation. In practical experiments, the BFCs are inverted and the M2 tide in the Bohai Sea is simulated by assimilating the TOPEX/Poseidon (T/P) data. The small errors between the simulation results and the observations, as well as the accurate cotidal charts, demonstrate the feasibility of the new method in practical application.

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An-Zhou Cao, Dao-Sheng Wang, and Xian-Qing Lv

Abstract

To investigate the optimum length of time series (TS) for harmonic analysis (HA) in the simulation of multiple constituents, a two-dimensional tidal model is used to simulate the M2, S2, K1, and O1 constituents in the Bohai and Yellow Seas. By analyzing the HA results of several nonoverlapping TS of the same length, which varies from 15 to 365 days, a field-average deviation of HA results is calculated. A deviation that is sufficiently small means that HA results are independent of the choice of TS, and the corresponding TS length is regarded as the optimum. Results indicate that the range of 180–195 days is the optimum length of TS for HA in the simulation of the four principal constituents. To investigate what determines the optimum length, experiments with different computed area and model settings are carried out. Results indicate that the optimum length is independent of advection, nodal corrections, and computed area, and only depends on bottom friction. Nonlinear bottom friction results in the appearance of higher harmonics and explains why the optimum length of TS for HA is 180–195 days.

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An-Zhou Cao, Bing-Tian Li, and Xian-Qing Lv

Abstract

To obtain internal tidal currents and full-depth tidal currents from limited mooring observations, a method is put forward combining harmonic analysis and modal decomposition. Harmonic analysis is used to separate tidal currents of different constituents, and modal decomposition is used to calculate full-depth tidal currents of each mode. By adding the barotropic tidal currents to all the baroclinic ones, the full-depth tidal currents of each constituent are reconstructed. The feasibility and accuracy of the proposed method is tested by twin experiments. Then, the method is used to extract tidal currents of each mode and to reconstruct full-depth tidal currents for M2 and K1 from a 3-month-long time series of acoustic Doppler current data observed at a station in the northern South China Sea. Results indicate that the total kinetic energy (KE) of M2 is 25% larger than that of K1. For M2, the first baroclinic mode is the dominant one, followed by the barotropic one, and the sum of these modes accounts for more than 90% of the total M2 KE. Tidal constituent K1 is dominated by the barotropic mode, which accounts for more than 90% of the total K1 KE.

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