Resolving frontal structures: On the payoff using a less diffusive but computationally more expensive advection scheme

Abstract

This article presents some advantages using a shape-preserving total variation diminishing (TVD) advection scheme in an ecosystem model. The superbee flux-limiter has been used to the second-order Lax-Wendroff advection scheme to make it TVD. We performed simulations for three shelf sea regions with different characteristic time scales, namely, the North Sea, the Barents Sea, and the Baltic Sea. To explore the advantages, we also performed reference runs with the much simpler and computationally cheaper upwind advection scheme. Frontal structures are much better resolved with the TVD scheme. The bottom salinity in the Baltic Sea stays at realistic values throughout the 10-year simulation with the TVD scheme, while with the upwind scheme, it drifts towards lower values and the permanent haline stratification in the Baltic is almost completely eroded within one seasonal cycle. Only when applying TVD for both the vertical and horizontal advections the model succeeded to preserve haline stratification in the decadal simulation. Lower trophic level patterns are far better reproduced with the TVD scheme, and for the estimated cod larval survival, the advantages seem to be even stronger. Simulations using the TVD-derived prey fields identified distinct regions such as Dogger Bank to favor potential larvae survival (PLS), which did not appear as particularly favorable in the upstream simulations. The TVD scheme needs about 25% more time on the central processing unit (CPU) in case of a pure hydrodynamic setup with only two scalar state variables (Barents Sea application). The additional CPU time cost increases for a coupled physical-biological model application with a large number of state variables. However, this is more than compensated by all the advantages found, and, hence, we conclude that it is worthwhile to use the TVD scheme in our ecosystem model. © 2012 Springer-Verlag.