Semi-Lagrangian methods in air pollution models

Abstract

Various semi-Lagrangian methods are tested with respect to advectionin air pollution modeling. The aim is to find a method fulfilling as many ofthe desirable properties by Rasch andWilliamson (1990) and Machenhauer et al. (2008) aspossible. The focus in this study is on accuracy and local massconservation. The methods tested are, first, classicalsemi-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), andlast, semi-Lagrangian cubic interpolation with a locally mass conservingmonotonic filter by Kaas and Nielsen (2010). Semi-Lagrangian (SL)interpolation is a classical method for atmospheric modeling, cascadeinterpolation is more efficient computationally, modified interpolationweights assure mass conservation and the locally mass conserving monotonicfilter imposes monotonicity. All schemes are tested with advectionalone or with advection and chemistry together under both typical rural andurban conditions using different temporal and spatial resolution. The methodsare compared with a current state-of-the-art scheme, Accurate SpaceDerivatives (ASD), see Frohn et al. (2002), presently used at the NationalEnvironmental Research Institute (NERI) in Denmark. To enable a consistentcomparison only non-divergent flow configurations are tested. Thetest cases are based either on the traditional slotted cylinder or therotating cone, where the schemes' ability to model both steep gradients andslopes are challenged. The tests showed that the locally mass conserving monotonic filter improvedthe 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 notable to outperform the current ASD scheme used in DEHM with respect toaccuracy. © 2011 Author(s).