Semi- Lagrangian Methods in Air Pollutions Models – Niels Bohr Institute - University of Copenhagen

Niels Bohr Institute > Calendar > 2009 > MSc Ayoe Buus Hansen

Semi- Lagrangian Methods in Air Pollutions Models

Ayoe Buus Hansen

Various semi-Lagrangian methods are tested for use in air pollution modeling. The aim is to find an efficient and conserving method fulfilling as many of the desirable properties by Rasch and Williamson (1990) and Machenhauer et al. (2008) as possible. The focus is to fulfill accuracy, local mass conservation and computational efficiency.

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, by Kaas (2008), and last, semi- Lagrangian cubic interpolation with a locally mass conserving monotonic
filter by Kaas (2008).

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 calculated or analytical tra jectories and with advection alone or with advection and chemistry together under both typical rural and urban conditions. The methods are compared with a current state-of-the-art scheme presently used at the National Environmental Research Institute (NERI) in Denmark.

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 currently used ASD scheme used in DEHM.

Eigil Kaas, NBI, KU, Jesper Christensen and Jørgen Brandt, NERI, AU