Abstract
Abstract. Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch andWilliamson (1990) and Machenhauer et al. (2008) as possible. The focus in this study is on accuracy and local mass conservation. The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999), second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002), third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Conserving Semi-Lagrangian (LMCSL), by Kaas (2008), and last, semi-Lagrangian cubic interpolation with a locally mass conserving monotonic filter by Kaas and Nielsen (2010). Semi-Lagrangian (SL) interpolation is a classical method for atmospheric modeling, cascade interpolation is more efficient computationally, modified interpolation weights assure mass conservation and the locally mass conserving monotonic filter imposes monotonicity. All schemes are tested with advection alone or with advection and chemistry together under both typical rural and urban conditions using different temporal and spatial resolution. The methods are compared with a current state-of-the-art scheme, Accurate Space Derivatives (ASD), see Frohn et al. (2002), presently used at the National Environmental Research Institute (NERI) in Denmark. To enable a consistent comparison only non-divergent flow configurations are tested. The test cases are based either on the traditional slotted cylinder or the rotating cone, where the schemes' ability to model both steep gradients and slopes are challenged. The tests showed that the locally mass conserving monotonic filter improved the results significantly for some of the test cases, however, not for all. It was found that the semi-Lagrangian schemes, in almost every case, were not able to outperform the current ASD scheme used in DEHM with respect to accuracy.
Highlights
Semi-Lagrangian (SL) methods (Robert, 1981) do not suffer from the traditional advective CFL-condition severely limiting the maximum possible length of time step, t
This is to be compared to the top right plot showing the performance of the considered advection scheme, still without active chemistry, this corresponds to passive tracer advection
By comparing the previous three figures, the bottom right plot, it can be seen that the top of the cone is slightly rounded, like the other semiLagrangian schemes, the maximum value is higher than even the result produced by the Accurate Space Derivatives (ASD) scheme
Summary
Semi-Lagrangian (SL) methods (Robert, 1981) do not suffer from the traditional advective CFL-condition severely limiting the maximum possible length of time step, t. These methods have been used widely in the numerical weather prediction (NWP) community, since t can be defined from accuracy rather than stability considerations. Global conservation can be imposed by correcting the advected field after determining the global mass loss. In addition to chemical reactions and transport, including diffusion, in the atmosphere, it is important to consider sources and sinks, e.g., emissions into the atmosphere and dry and wet deposition of species in the atmosphere to the surface
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