Independent Point Scheme Research Articles

An Analysis of the 8.85- and 4.42-Year Cycles in the Gulf of Maine

In the background of global warming and climate change, nuisance flooding is only caused by astronomical tides, which could be modulated by the nodal cycle. Therefore, much attention should be paid to the variation in the amplitude of the nodal cycle. In this paper, we utilize the enhanced harmonic analysis method and the independent point scheme to obtain the time-dependent amplitudes of the 8.85-year cycle of N2 tide and the 4.42-year cycle of 2N2 tide based on water level records of four tide gauges in the Gulf of Maine. Results indicate that the long-term trends of N2 and 2N2 tides vary spatially, which may be affected by the sea-level rise, coastal defenses, and other possible climate-related mechanisms. The comparison between Halifax and Eastport reveals that the topography greatly influences the amplitudes of those cycles. Moreover, a quasi 20-year oscillation is obvious in the 8.85-year cycle of N2 tide. This oscillation probably relates to a 20-year mode in the North Atlantic Ocean.

The Piecewise Parabolic Method for the Parameters Estimation in an Ocean Pollutant Transport Adjoint Model

In this paper, a higher-order and conservative Piecewise Parabolic interpolation is proposed to estimate key parameters of an ocean pollutant transport model. The Piecewise Parabolic interpolation quality is verified by groups of experiments. The results show that the Piecewise Parabolic Method (PPM) in independent point scheme (IPS) can realize better parameter estimation with fewer independent points.

Exploration of Tidal‐Fluvial Interaction in the Columbia River Estuary Using S_TIDE

AbstractNumerous tidal phenomena, including river tides, internal tides, and tides in ice‐covered bay, are nonstationary, which pose a great challenge for traditional tidal analysis methods. Based on the independent point scheme and cubic spline interpolation, a new approach, namely the enhanced harmonic analysis, is developed to deal with nonstationary tides. A MATLAB toolbox, S_TIDE, developed from the widely used T_TIDE, is used to realize the approach. The efficiency of S_TIDE is validated by analyzing a set of hourly water level observations from stations on the lower Columbia River. In all stations, the hindcast of S_TIDE is more accurate than NS_TIDE that is a powerful nonstationary tidal analysis tool adapted to river tides. The changing mean water level and tidal constituent properties obtained by S_TIDE are similar to those obtained by NS_TIDE, continuous wavelet transform, and empirical mode decomposition and highly consistent with theory on river tides. Moreover, different from NS_TIDE that only can be applied to river tides, enhanced harmonic analysis is free of dynamic content, assuming only known tidal frequencies. Therefore, S_TIDE can be applied to all kinds of nonstationary tides theoretically. Though powerful, S_TIDE also has some limitations: S_TIDE cannot be used for prediction and too many independent points in S_TIDE may induce computational memory overflow and unrealistic results.

Determination of Harmonic Parameters with Temporal Variations: An Enhanced Harmonic Analysis Algorithm and Application to Internal Tidal Currents in the South China Sea

AbstractAs 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.

Estimating Smoothly Varying Open Boundary Conditions for a 3D Internal Tidal Model with an Improved Independent Point Scheme

AbstractAn improved independent point (IP) scheme was proposed to estimate the open boundary conditions (OBCs) for a 3D internal tidal model through assimilating the TOPEX/Poseidon (T/P) altimeter data. Under the assumption that the OBCs were spatially and smoothly varying, values at a set of independent points along the open boundary were inverted using the adjoint method and values at other points were interpolated by the spline method. The scheme was calibrated through idealized experiments where the M2 tidal constituent in the northern South China Sea was simulated. The OBCs can be successfully inverted with the improved scheme and were better in spatial smoothness than the results obtained with the Cressman interpolation when embedded in the IP scheme. Simulations in realistic domains showed that the errors between simulations and observations were smaller when the spline interpolation was employed instead of the Cressman interpolation. Three boundary conditions of spline interpolation were used in simulations in realistic domains, and the result of the periodic boundary condition had the smallest error compared with the first and second boundary conditions.

Improvement of the ocean pollutant transport model by using the surface spline interpolation

The independent point scheme (IPS) is applied to inverting initial condition with the adjoint method for the ocean pollutant transport model in this work. As an improvement, the linear Cressman interpolation is removed and the surface spline interpolation is implemented in the IPS. A series of numerical experiments are carried out to test and compare the improved IPS. And experiment results show that through applying the improved IPS, what is further reduced is mean absolute errors between simulation results and observations. Moreover, the inverted distributions are more smooth, accurate and reasonable. In addition, the application of improved IPS also reduces the variables that need to be inverted and promotes the computational efficiency. By these numerical experiment results, it is demonstrated that the combination of improved IPS and adjoint method can be used for the inversion of initial conditions and parameters estimation more effectively and reliably.

Estimation of spatially varying parameters in three-dimensional cohesive sediment transport models by assimilating remote sensing data

Based on a three-dimensional cohesive sediment transport model with the adjoint data assimilation, the spatially varying parameters are estimated by assimilating satellite-retrieved suspended sediment concentrations (SSCs) in the Hangzhou Bay, China. To reduce the ill-posedness of the inverse problem, an independent point scheme is developed and a combined independent point and Tikhonov regularization scheme (CIPTRS) is presented. The CIPTRS is calibrated in ideal twin experiments and the results reveal that the CIPTRS can restrict the influence of ill-posedness and improve the accuracy of parameter estimation. In practical experiments, the spatially varying settling velocity is estimated by assimilating the satellite-retrieved SSCs using different strategies, and the best modeling results are obtained when the CIPTRS is used. To further improve the modeling results, the spatially varying settling velocity and initial conditions are estimated simultaneously using the CIPTRS. The data misfit between observed and simulated SSCs is largely decreased and the simulated SSCs can reproduce the spatial and temporal features of observed SSCs. The experimental results indicate that the adjoint method is a useful method to estimate the poorly known parameters in practical applications and the CIPTRS can effectively improve the results of data assimilation and parameter estimation.

The Parameters Estimation for a PM2.5Transport Model with the Adjoint Method

Based on the theory of inverse problem and data assimilation, the adjoint method is applied for the estimation of parameters including the initial condition (IC), the source and sink (SS) in a PM2.5transport model. To reduce the ill-posedness of the inverse problem, an independent point scheme (IPS) is implemented during the estimation process. In twin experiments, both the prescribed IC and SS can be inverted successfully and better inversion results are obtained when the IPS is used than not, suggesting the feasibility and validity of the PM2.5transport model as well as the IPS. In practical experiments, several inversion strategies are compared based on the simulation results of PM2.5concentrations over China. It is found that IC and SS are better estimated with smaller difference between simulated results and observations, when IC and SS are inverted simultaneously than separately. And the simulated results can reproduce the temporal and spatial variation feature of the observed PM2.5concentrations. On the basis of the numerical results, it is shown that the adjoint method and the IPS are the powerful way to improve the precision of the simulation of the PM2.5concentrations.

Inversion study on pollutant discharges in the Bohai Sea with the adjoint method

The adjoint method is presented which could be used to estimate the time-varying contamination concentration (CC) from pollution source (PS). Then the pollutant flux is calculated. In order to guarantee the continuity of pollutant distribution and make the calculated results more accurate, the independent point (IP) scheme is proposed. The contamination concentrations (CCs) at some time steps are selected as the independent points (IPs), and only CCs at these IPs are optimized while CCs at other points are calculated through linear interpolation of the independent CCs. In twin numerical experiments, all the given distributions are successfully inverted with the adjoint method. The cost functions and the mean absolute errors (MAEs) in concentrations and pollutant fluxes decrease greatly after assimilation, and the cost functions are reduced by about 5 orders of magnitude compared with their initial values. The results indicate that the adjoint method is computationally efficient to recover CCs from PS. It is easier to invert the given distribution which is less complex. The inversion efficiency with IP scheme is raised compared to that without this scheme. The IP scheme is significant for the inversion result, in which appropriate IP number could yield better inversion results. More work will be done to apply this method to real experiment.

Estimation of spatially varying open boundary conditions for a numerical internal tidal model with adjoint method

The adjoint data assimilation technique is applied to the estimation of the spatially varying open boundary conditions (OBCs) for a numerical internal tidal model. The spatial variation of the OBCs is realized by the so-called ‘independent point scheme’ (IPS): a subset is chosen as the independent points from the full set of open boundary points and the OBCs are obtained through linear interpolation of the values at the independent points. A series of ideal experiments are carried out on a real topography to further test this assimilation model, and to numerically investigate some properties of the IPS. On the basis of the numerical results, it is shown that, in most cases, the use of the IPS can indeed effectively improve the precision of the estimation of the OBCs. Furthermore, if the independent points can be arranged reasonably the improvement may be remarkable. The IPS shows us a way to improve the estimation of the OBCs for this model.

Estimation of Bottom Friction Coefficients Based on an Isopycnic-Coordinate Internal Tidal Model with Adjoint Method

Based on an isopycnic-coordinate internal tidal model with the adjoint method, three groups of ideal experiments are carried out in order to investigate the estimation of spatially varying bottom friction coefficients (BFCs). In group 1, five values of distance between independent points (DIP) are used to invert the BFCs with the distribution of conical surface. Results show that the BFCs can be inverted successfully with independent point scheme and the strategy with a DIP of 50′ can yield the best results. In group 2, five values of interpolation radius (IR) are used to invert the BFCs with the distribution of conical surface. Results show that the strategy with an IR of 1.9 times of DIP can yield the best results. Based on the results of the first two groups, group 3 adopts the optimal DIP and IR to estimate 4 kinds of spatially varying BFCs. The results indicate that the isopycnic-coordinate internal tidal model with the adjoint method has a good ability to estimate the spatially varying BFCs; the inversion results of the BFCs with the distribution of revolution paraboloid are better than those with the distribution of conical surface.