Bott advection scheme

The transport of heavy metals in the atmosphere is described by means of a monotone version of Bott s advection scheme. Pressure-based s-coordinate in the vertical makes possible to take into account an effect of the underlying surface elevation. Vertical eddy... 

Baklanov A, Sprensen JH (2001) Parameterisation of radionuclide deposition in atmospheric long-range transport modelling. Phys Chem Earth (B) 26(10) 787-799 Bott A (1989a) A positive definite advection scheme obtained by non-linear renormalization of the advective fluxes. Mon Weather Rev 117 1006—1015 Bott A (1989b) Reply. Mon Weather Rev 117 2633-2636... 

Bott A (1989) A Positive Definite Advection Scheme Obtained by Nonlinear Renormalization of the Advective Eluxes. AMS 117 1006-1015... 

It would be good to find an optimal advection scheme for integrated ACT-HIRLAM, however, estimations of ACT and NWP modellers can be different, because they can use different requirements/criteria for the best scheme for NWP and ACTM. At least it is reasonable to analyze and compare different schemes used in the HIRLAM community (for NWP and ACT including the semi-Lagrangian, CISL, Bott, Easter, Chlond, Walcek, Galperin and Kaas). 

Bott, A., A positive definite advection scheme obtained by nonlinear normalization of the advective fluxes. Mon Weath Rev 117, 1006, 1989... 

The horizontal and vertical resolutions of the model depend on a resolution of the meteorological and emission data. At present the model run over a 0.2° x 0.2° horizontal grid (Fig. 16.3b), and it has a vertical resolution of 25 levels. These vertical levels cover the lowest 3 km of the troposphere. The amount of chemical compounds, which is transported from the free troposphere into the atmospheric boundary layer, is determined by the meteorological information and the concentration of the chemical compounds in the free tropospheric. These concentrations depend on the longitude, latitude, land/sea and month (Gross et al. 2005). The advection is solved using the Bott and PPM schemes (Bott 1989 Colella 1984). 

A large number of explicit numerical advection algorithms were described and evaluated for the use in atmospheric transport and chemistry models by Rood [162], and Dabdub and Seinfeld [32]. A requirement in air pollution simulations is to calculate the transport of pollutants in a strictly conservative manner. For this purpose, the flux integral method has been a popular procedure for constructing an explicit single step forward in time conservative control volume update of the unsteady multidimensional convection-diffusion equation. The second order moments (SOM) [164, 148], Bott [14, 15], and UTOPIA (Uniformly Third-Order Polynomial Interpolation Algorithm) [112] schemes are all derived based on the flux integral concept. 

All the problems encountered during application of the algorithms presented above illustrate the difficulty of solution of the advection problem in atmospheric transport models. A number of techniques have been developed to treat advection accurately, including flux-corrected transport (FCT) algorithms (Boris and Book, 1973), spectral and finite element methods [for reviews, see Oran and Boris (1987), Rood (1987), and Dabdub and Seinfeld (1994). Bott (1989, 1992), Prather (1986), Yamartino (1992), Park and Liggett (1991), and others have developed schemes specifically for atmospheric transport models. 

---