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Inversion of Tidal Open Boundary Conditions of the M2 Constituent in the Bohai and Yellow SeasAbstract
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.
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.
Acquiring the Arctic-Scale Spatial Distribution of Snow Depth Based on AMSR-E Snow Depth ProductAbstract
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.
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.
A Methodology for Fitting the Time Series of Snow Depth on the Arctic Sea IceAbstract
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.
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.
The M2 Cotidal Chart in the Bohai, Yellow, and East China Seas from Dynamically Constrained InterpolationAbstract
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.
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.
Improved Estimation of Pollutant Emission Rate in an Ocean Pollutant Diffusion Model by the Application of Spline Interpolation with the Adjoint MethodAbstract
The spline interpolation method is applied to the inversion of the time-varying pollutant emission rate based on an ocean pollutant diffusion model with the adjoint method. A series of numerical experiments are performed to compare the spline interpolation with the Cressman interpolation. Experimental results show that the spline interpolation improves the inversion results in terms of the smoothness and accuracy. Furthermore, it is the advantages of spline interpolation—better resistance to the impact of errors and demand for fewer observations—that give rise to a better performance in practice.
Abstract
The spline interpolation method is applied to the inversion of the time-varying pollutant emission rate based on an ocean pollutant diffusion model with the adjoint method. A series of numerical experiments are performed to compare the spline interpolation with the Cressman interpolation. Experimental results show that the spline interpolation improves the inversion results in terms of the smoothness and accuracy. Furthermore, it is the advantages of spline interpolation—better resistance to the impact of errors and demand for fewer observations—that give rise to a better performance in practice.
Application of Surface Spline Interpolation in Inversion of Bottom Friction CoefficientsAbstract
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.
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.
A Modified Interpolation Method for Surface Total Nitrogen in the Bohai SeaAbstract
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.
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.
Estimating Smoothly Varying Open Boundary Conditions for a 3D Internal Tidal Model with an Improved Independent Point SchemeAbstract
An 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.
Abstract
An 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.
Application of the EMD Method to River TidesAbstract
A lot of tidal phenomena, including river tides, tides in ice-covered bays, and internal tides in fjords, are nonstationary. These tidal processes present a severe challenge for the conventional tidal analysis method. The empirical mode decomposition (EMD) method is useful for nonstationary and nonlinear time series and has been used for different geophysical data. However, application of EMD to nonstationary tides is rare. This paper is meant to demonstrate a new tidal analysis tool that can help study nonstationary tides, in this case river tides. EMD is applied to a set of hourly water level records on the lower Columbia River, where the tides are greatly influenced by the fluctuating river flow. The results show that the averaged period of any EMD mode almost exactly doubles that of the previous one, suggesting that EMD is a dyadic filter. The highest and second highest frequency modes of EMD represent the semidiurnal (D2) and diurnal (D1) tides, respectively. The sum of the EMD modes except for the first two is the mean water level (MWL). The study finds that the EMD method successfully captured the nonstationary characteristics of the D1 tides, the D2 tides, and the MWL induced by river flow.
Abstract
A lot of tidal phenomena, including river tides, tides in ice-covered bays, and internal tides in fjords, are nonstationary. These tidal processes present a severe challenge for the conventional tidal analysis method. The empirical mode decomposition (EMD) method is useful for nonstationary and nonlinear time series and has been used for different geophysical data. However, application of EMD to nonstationary tides is rare. This paper is meant to demonstrate a new tidal analysis tool that can help study nonstationary tides, in this case river tides. EMD is applied to a set of hourly water level records on the lower Columbia River, where the tides are greatly influenced by the fluctuating river flow. The results show that the averaged period of any EMD mode almost exactly doubles that of the previous one, suggesting that EMD is a dyadic filter. The highest and second highest frequency modes of EMD represent the semidiurnal (D2) and diurnal (D1) tides, respectively. The sum of the EMD modes except for the first two is the mean water level (MWL). The study finds that the EMD method successfully captured the nonstationary characteristics of the D1 tides, the D2 tides, and the MWL induced by river flow.
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.
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.
