Comparison of different tracer advection schemes and estimation of their numerical mixing properties

The advection of tracer quantities through ocean currents is an important process in ocean dynamics. To simulate the tracer transport processes, numerical models can use different types of advection schemes. Using the numerical ocean model ROMS, three different tracer advection schemes – a multidimensional positive definite advection transport algorithm (MPDATA), a third-order Upstream-biased horizontal scheme (U3H) and a third high-order spatial interpolation at the middle temporal level coupled with a total variation diminishing limiter (HSIMT-TVD) have been tested. The HSIMT-TVD scheme has been implemented in the ROMS model for this work in addition to the existing MPDATA and U3H schemes. The resolution of the three schemes is compared for three cases: (1.) a one-dimensional linear advection equation with periodic boundary conditions (2.) a two-dimensional Estuary test case that represents mixing process typical of estuarine conditions, and (3.) a realistic application of the Hudson River estuary system. To evaluate the performance of the three schemes, numerical mixing caused by discretization errors is estimated by calculating the variance of the tracer concentration. Preliminary results indicate that the U3H advection scheme shows a smaller variance indicating lower numerical mixing compared to MPDATA and HSIMT-TVD advection schemes. Although the MPDATA and HSIMT-TVD schemes show similar levels of variance, the MPDATA scheme shows an increased variance at the bed of the estuary.