Improved Estimation of Pollutant Emission Rate in an Ocean Pollutant Diffusion Model by the Application of Spline Interpolation with the Adjoint Method

Zong, Xiaolong; Pan, Haidong; Liu, Yongzhi; Lv, Xianqing

doi:10.1175/jtech-d-17-0208.1

Cited by 8 publications

(5 citation statements)

References 51 publications

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“…Values of a c 0 and b c 0 at other points can be obtained by interpolation between the IPs. Equations ( 6) and ( 7) represent the independent point scheme, which has been examined successfully in many previous works [27,31,32]. Equations ( 2) and ( 3) are modified as:…”

Section: Methodsmentioning

confidence: 99%

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

Zong

Zhang

et al. 2021

JMSE

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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.

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Section: Methodsmentioning

confidence: 99%

“…To guarantee stabilization, convergence, and smoothness in the interpolation process, the cubic spline interpolation is implemented in this work [30,31]. The calculation method of the weighted coefficient refers to Equations ( 20) and ( 21) in Zong et al [32].…”

Section: Methodsmentioning

confidence: 99%

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

Zong

Zhang

et al. 2021

JMSE

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“…Considering the convection and diffusion processes, the governing equation of marine pollutant transport model is presented as follows [17,26,27] ∂C∂t+u∂C∂x+v∂C∂y+w∂C∂z=∂∂xfalse(AH∂C∂xfalse)+∂∂yfalse(AH∂C∂yfalse)+∂∂zfalse(KH∂C∂zfalse)−rC where C denotes the concentration of pollutants; t and x , y , z are the symbols of time and space, respectively; u and v represent the horizontal velocities (in x and y directions, respectively) and w represents the vertical velocity (in z direction); A H and K H denote the horizontal and vertical diffusion coefficients ( A H = 100 m 2 /s, K H = 0.00001 m 2 /s), respectively; r is the pollutant attenuation coefficient, and r = 0, which means that the pollutant is treated as conservative substance [17]. For the finite difference scheme readers can be referred to the Appendix A.…”

Section: Methodsmentioning

confidence: 99%

Application of Dynamically Constrained Interpolation Methodology to the Surface Nitrogen Concentration in the Bohai Sea

Zheng

2019

IJERPH

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Observations of ocean pollutants are usually spatiotemporally dispersive, while it is of great importance to obtain continuous distribution of ocean pollutants in a certain area. In this paper, a dynamically constrained interpolated methodology (DCIM) is proposed to interpolate surface nitrogen concentration (SNC) in the Bohai Sea. The DCIM takes the pollutant transport advection diffusion equation as a dynamic constraint to interpolate SNCs and optimizes the interpolation results with adjoint method. Feasibility and validity of the DCIM are testified by ideal twin experiments. In ideal experiments, mean absolute gross errors between interpolated observations and final interpolated SNCs are all no more than 0.03 mg/L, demonstrating that the DCIM can provide convincing results. In practical experiment, SNCs are interpolated and the final interpolated surface nitrogen distribution is acquired. Correlation coefficient between interpolated and observed SNCs is 0.77. In addition, distribution of the final interpolated SNCs shows a good agreement with the observed ones.

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“…The reason why the cubic spline interpolation is applied in the method is that it retains the advantages of the piecewise low-order interpolation polynomial and improves the smoothness of the interpolation function. At present, because of stability and smoothness, the cubic spline interpolation is a useful technique, which has become an extremely important branch of numerical approximation and has been increasingly used in many fields (Jiang et al 2018;Zong et al 2018).…”

Section: A Pff-vpmentioning

confidence: 99%

A Methodology for Fitting the Time Series of Snow Depth on the Arctic Sea Ice

Wang

Pan

Wang

et al. 2019

Journal of Atmospheric and Oceanic Technology

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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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Improved Estimation of Pollutant Emission Rate in an Ocean Pollutant Diffusion Model by the Application of Spline Interpolation with the Adjoint Method

Cited by 8 publications

References 51 publications

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

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

Application of Dynamically Constrained Interpolation Methodology to the Surface Nitrogen Concentration in the Bohai Sea

A Methodology for Fitting the Time Series of Snow Depth on the Arctic Sea Ice

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