Using the generalized omega equation and cruise observations in July 2012, this study analyzes the 3D vertical circulation in the upwelling region and frontal zone east of Hainan Island, China. The results show that there is a strong frontal zone in subsurface layer along the 100-m isobath, which is characterized by density gradient of O(10−4) kg m−4 and vertical eddy diffusivity of O(10−5–10−4) m2 s−1. The kinematic deformation term SDEF, ageostrophic advection term SADV, and vertical mixing forcing term SMIX are calculated from the observations. Their distribution patterns are featured by banded structure, that is, alternating positive–negative alongshore bands distributed in the cross-shelf direction. Correspondingly, alternating upwelling and downwelling bands appear from the coast to the deep waters. The maximum downward velocity reaches −5 × 10−5 m s−1 within the frontal zone, accompanied by the maximum upward velocity of 7 × 10−5 m s−1 on two sides. The dynamic diagnosis indicates that SADV contributes most to the coastal upwelling, while term SDEF, which is dominated by the ageostrophic component SDEFa, plays a dominant role in the frontal zone. The vertical mixing forcing term SMIX, which includes the momentum and buoyancy flux terms SMOM and SBUO, is comparable to SDEF and SADV in the upper ocean, but negligible below the thermocline. The effect of the vertical mixing on the vertical velocity is mainly concentrated at depths with relatively large eddy diffusivity and eddy diffusivity gradient in the frontal zone.

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.

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.