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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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Yuzhe Wang, Haidong Pan, Daosheng Wang, and Xianqing Lv

Abstract

Snow depth is an important geophysical variable for investigating sea ice and climate change, which can be obtained from satellite data. However, there is a large number of missing data in satellite observations of snow depth. In this study, a methodology, the periodic functions fitting with varying parameter (PFF-VP), is presented to fit the time series of snow depth on Arctic sea ice obtained from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E). The time-varying parameters are obtained by the independent point (IP) scheme and cubic spline interpolation. The PPF-VP is validated by experiments in which part of the observations are artificially removed and used to compare with the fitting results. Results indicate that the PPF-VP performs better than three traditional fitting methods, with its fitting results closer to observations and with smaller errors. In the practical experiments, the optimal number of IPs can be determined by only considering the fraction of missing data, particularly the length of the longest gaps in the snow-depth time series. All the experimental results indicate that the PPF-VP is a feasible and effective method to fit the time series of snow depth and can provide continuous data of snow depth for further study.

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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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Yongzhi Liu, Jie Yu, Youli Shen, and Xianqing Lv

Abstract

A modified Cressman interpolation method (MCIM) is presented for the routine monitoring data of total nitrogen (TN) in the Bohai Sea to reduce interpolation errors by decreasing the influence radius and introducing background value. In twin experiments, two prescribed distributions are successfully estimated by MCIM with lower interpolation errors than the traditional Cressman interpolation method (TCIM) and the kriging method. In practical experiments, cross validation is applied to evaluate the interpolation results for four quarters in 2009 and 2010. Practical experimental results show that the interpolation results obtained with MCIM are greatly improved and can describe the spatial distribution characteristics of TN in the Bohai Sea with lower mean absolute error than the kriging method.

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Yuzhe Wang, Yibo Zhang, Minjie Xu, Yonggang Wang, and Xianqing Lv

Abstract

In Part I, the Chebyshev polynomial fitting (CPF) method has been proved to be effective to construct reliable cotidal charts for the eight major tidal constituents (M2, S2, K1, O1, N2, K2, P1, and Q1) near Hawaii and yields accurate results which are consistent with the Finite Element Solutions 2014 (FES2014), National Astronomical Observatory 99b (NAO.99b), and TPXO9 models. In this paper, the method is extended to estimate the harmonic constants of some minor tidal constituents. The mesoscale variation correction is applied to tidal elevations from satellite altimeters to eliminate the potential influence of background mesoscale ocean noise when estimating minor tidal constituents. This correction is necessary and makes the amplitude ratio between P1 and K1 constituents more consistent with the equilibrium tidal theory. Compared with the harmonic constants directly extracted from satellite altimeter data, FES2014 and NAO.99b yield mean root-mean-square (RMS) errors of 0.238 and 0.226 cm, respectively, while CPF method yields a mean RMS error of 0.210 cm, causing a 7%–12% decrease in the RMS error. At the crossover points between ascending and descending tracks, the decrease of RMS errors becomes 15%–18%. The accuracy of this method is also validated by comparing the estimated harmonic constants with those derived from tidal gauges and bottom-pressure recorders. These results indicate that the CPF method is also effective for estimating harmonic constants of minor tidal constituents. More importantly, the CPF method can obtain the harmonic constants of minor tidal constituents directly from satellite altimeter data, instead of being inferred via admittance theory.

Significance Statement

Ocean tides originate from the gravitational attraction of the sun and moon. Among the large number of tidal constituents, the major tidal constituents have been extensively studied. We extend the method proposed in Part I to estimate the harmonic constants of some minor tidal constituents with low amplitudes. The method relies on actual observations of water level variations from satellite altimeters without considering the hydrodynamic equations. We compared the results of this method with those of other models, using the data from satellite altimeters, tidal gauges, and bottom-pressure recorders. We find that the method performs well in estimating harmonic constants for some minor tidal constituents and causes a decrease of 7%–18% in RMS errors compared to other models.

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Daosheng Wang, Jicai Zhang, Ya Ping Wang, Xianqing Lv, Yang Yang, Daidu Fan, and Shu Gao

Abstract

The model parameters in the suspended cohesive sediment transport model are quite important for the accurate simulation of suspended sediment concentrations (SSCs). Based on a three-dimensional cohesive sediment transport model and its adjoint model, the in situ observed SSCs at four stations are assimilated to simulate the SSCs and to estimate the parameters in Hangzhou Bay in China. Numerical experimental results show that the adjoint method can efficiently improve the simulation results, which can benefit the prediction of SSCs. The time series of the modeled SSCs present a clear semidiurnal variation, in which the maximal SSCs occur during the flood tide and near the high water level due to the large current speeds. Sensitivity experiments prove that the estimated results of the settling velocity and resuspension rate, especially the temporal variations, are robust to the model settings. The temporal variations of the estimated settling velocity are negatively correlated with the tidal elevation. The main reason is that the mean size of the suspended sediments can be reduced during the flood tide, which consequently decreases the settling velocity according to Stokes’s law, and it is opposite in the ebb tide. The temporal variations of the estimated resuspension rate and the current speeds have a significantly positive correlation, which accords with the dynamics of the resuspension rate. The temporal variations of the settling velocity and resuspension rate are reasonable from the viewpoint of physics, indicating the adjoint method can be an effective tool for estimating the parameters in the sediment transport models.

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Bingtian Li, Zexun Wei, Yonggang Wang, Xinyu Guo, Tengfei Xu, and Xianqing Lv

Abstract

An enhanced harmonic analysis (S_TIDE) approach is adopted to examine the seasonal variations of internal tidal amplitudes in the northern South China Sea (SCS). Results of idealized experiments reveal that the seasonality can be captured by S_TIDE. By applying S_TIDE to mooring data, observed seasonality of internal tidal amplitudes in the northern SCS are explored. Not diurnal and semidiurnal internal tides (ITs), but overtides and long-period constituents of ITs exhibit clear seasonal cycles. However, differences between amplitudes of the eastward velocity and the northward counterpart are evident for K1, M2, and MK3, which may be caused by the intensification of background currents. Amplitudes of those ITs are stronger at intersection time between spring and summer in the eastward direction, but weaker in the northward direction. EOF analysis reveals that modes of diurnal ITs are higher than those of semidiurnal ITs, which induces relatively more complicated seasonal variations. In addition to intensification of background currents, influences of surface tides and stratification will also induce variations of internal tidal amplitudes, introducing tremendous difficulty in predicting variation trends of internal tidal amplitudes, which greatly reduces predictability of ITs.

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Daosheng Wang, Haidong Pan, Lin Mu, Xianqing Lv, Bing Yan, and Hua Yang

Abstract

The coastal ocean sea level (SL) variations result from multiscale processes and are dominated by SL changes due to meteorological forcing. In this study, a new methodology, which combines inverted barometer correction and regression analysis (IBR), is developed to estimate the coastal ocean response to meteorological forcing in shallow water. The response is taken as the combination of the static ocean response calculated using the inverted barometer formula and the dynamic ocean response estimated using the multivariable linear regression involving atmospheric pressure and the wind component in the dominant wind orientation. IBR was implemented to estimate the coastal ocean response at two stations, E1 and E2, in Bohai Bay, China. The analyzed results indicate that at both stations, the adjusted SLs are related more to the regional wind, which is the averaged value of ERA-Interim data in Bohai Bay, than to the local wind. The estimated response using IBR with the regional meteorological forcing is much closer to the observed values than other methods, including the classical inverted barometer correction, the dynamic atmospheric correction, the multivariable linear regression, and the IBR with local forcing. The deviations between the observed values and the estimated values using IBR with regional meteorological forcing can be primarily attributed to remote wind. This case study indicates that IBR is a feasible and relatively effective method to estimate the coastal ocean response to meteorological forcing in shallow water.

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Guangzhen Jin, Haidong Pan, Qilin Zhang, Xianqing Lv, Wei Zhao, and Yuan Gao

Abstract

As an effective tool to distinguish different tidal components, classical tidal current harmonic analysis has been widely used to obtain harmonic parameters of internal tidal currents. However, harmonic parameters cannot exactly reveal the motion of internal tides, as the irregular temporal variations for internal tides are significant in many regions of the world’s oceans. An enhanced harmonic analysis (EHA) algorithm based on the independent point scheme and cubic spline interpolation is presented in this paper to obtain harmonic parameters with temporal variations for different tidal constituents of internal tides. Moreover, this algorithm is applied to analyze 14 months of current data obtained from a mooring located on the continental shelf in the northeastern region of the South China Sea. The obvious irregular temporal variations for the four principal constituents—M2, K1, S2, and O1—of internal tides in this region are indicated. It is hoped that this algorithm might present a brand-new view for researchers to investigate the irregular temporal motions of internal tides.

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