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Anthropogenic surface warming dominates and drives a global acceleration of the upper ocean currents in a warmer climate.

Unlike greenhouse gases (GHGs), anthropogenic aerosol (AA) concentrations have increased and then decreased over the past century or so, with the timing of the peak concentration varying in different regions. To date, it has been challenging to separate the climate impact of AAs from that due to GHGs and background internal variability. We use a pattern recognition method, taking advantage of spatiotemporal covariance information, to isolate the forced patterns for the surface ocean and associated atmospheric variables from the all-but-one forcing Community Earth System Model ensembles. We find that the aerosol-forced responses are dominated by two leading modes, with one associated with the historical increase and future decrease of global mean aerosol concentrations (dominated by the Northern Hemisphere sources) and the other due to the transition of the primary sources of AA from the west to the east and also from Northern Hemisphere extratropical regions to tropical regions. In particular, the aerosol transition effect, to some extent compensating the global mean effect, exhibits a zonal asymmetry in the surface temperature and salinity responses. We also show that this transition effect dominates the total AA effect during recent decades, e.g., 1967–2007.

In this paper, we apply two fully-discrete local discontinuous Galerkin (LDG) methods to the compressible wormhole propagation. We will prove the stability and error estimates of the schemes. Traditional LDG methods use the diffusion term to control of convection term to obtain the stability for some linear equations. However, the variables in wormhole propagation are coupled together and the whole system is highly nonlinear. Therefore, it is extremely difficult to obtain the stability for fully-discrete LDG methods. To fix this gap, we introduce a new auxiliary variable including both the convection and diffusion terms. Moreover, we also construct a special time integration for the porosity, leading to physically relevant numerical approximations and controllable growth rate of the porosity. With a reasonable growth rate, it is possible to handle the time level mismatch in the first-order fully discrete scheme and obtain the stability of the scheme. For the whole system, we will prove that under weak temporal-spatial conditions, the optimal error estimates for the pressure, velocity, porosity and concentration under different norms can be obtained. Numerical experiments are also given to verify the theoretical results.