Abstract
An adjoint method of data assimilation with the characteristic finite difference (CFD) scheme is applied to marine pollutant transport problems and the temporal and spatial distribution of marine pollutants are simulated. Numerical tests of two-dimensional problems of pollutant transport with two different schemes indicate that the error of CFD is smaller than that of central difference scheme (CDS). Then the inversion experiments of the initial field and the source and sink terms of pollutants are carried out. Applying CFD in the adjoint method of data assimilation cannot only reduce simulation error to get a good inversion but can also enable larger time step size to decrease computation time and improve the calculation efficiency.
Highlights
With the rapid development of the coastal economy, offshore waters have suffered severe pollution damage and the ecological environment is gradually deteriorated, which is an important topic that attracted the attention all over the world, especially countries with long coastlines.Many scholars have used mathematical models and methods to make numerical analysis in various areas
Gupta et al [1] applied a two-dimensional model considering organized wastewater discharges to determine the waste water assimilative capacity of Tane creek; Harms et al [2] applied a threedimensional coupled ice-ocean-models of different horizontal resolution to simulate the dispersion of water from these rivers; Grell et al [3] built the WRF/Chem model to simulate the distribution of atmospheric pollutants in the northeastern United States; Guo et al [4] used the surface spline interpolation in the inversion of bottom friction coefficients in a two-dimensional tidal model to get a smoother surface; Liu et al [5] presented a modified Cressman interpolation method for the simulation of routine monitoring data of total nitrogen in the Bohai Sea, which reduces interpolation errors by decreasing the influence radius and introducing background value
In the study of Fan and Lv [11], SeaWiFS chlorophyll-a data were assimilated into a NPZD (Nutrient-PhytoplanktonZooplankton-Detritus) model by the adjoint method; Pan et Advances in Mathematical Physics al. [12] studied the open boundary condition of the M2 tidal constituent using the adjoint method of data assimilation with spline interpolation; Zhang et al [13] applied this method to study the similarities and the differences between the Ekman and the Quadratic bottom friction parameters of a two-dimensional tidal model; and many other researches (Yu and O’Brien [14], Lawson et al [15], Zhao et al [16], Zhao and Lu [17], and Qi et al [18]) have proven the validity and rationality of the adjoint method
Summary
With the rapid development of the coastal economy, offshore waters have suffered severe pollution damage and the ecological environment is gradually deteriorated, which is an important topic that attracted the attention all over the world, especially countries with long coastlines. Method of characteristics and the schemes it derives have been used to solve problems in several areas for its high accuracy and ability to use large time step size. We construct an adjoint data assimilation model using the characteristic finite difference (CFD) scheme which has high accuracy and enables large time steps. Applying CFD in the adjoint data assimilation model, simulation errors are reduced and time step sizes can be increased, which improves the calculation efficiency a lot.
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