The Danish Eulerian Model



The Danish Eulerian model is a large air pollution model for studying different phenomena connected with transport of air pollutants in the atmosphere. The space domain of the model contains the whole of Europe. All important physical processes (advection, diffusion, deposition, emissions and chemical reactions) are represented in the mathematical formulation of the model. All important chemical species (sulphur pollutants, nitrogen pollutants, ammonia-ammonium, ozone, as well as many radicals and hydrocarbons) can be studied by the model. The chemical reactions are described by using the well-known condensed CBM IV scheme. The space domain is discretized by using (96x96) grid in the two-dimensional version of the model and (96x96x10) grid in the three-dimensional version. The horizontal discretization is performed by using equidistant grid-squares (50 km x 50 km), while non-equidistant grid is used in the vertical direction (finer resolution close to the surface).

The discretization leads to huge computational problems. Systems of ordinary differential equations containing many thousands or even several millions of equations are to be treated during several thousand time-steps in a typical run. Therefore modern high-speed computers (both vector machines and parallel processors) must be used in the numerical treatment of the model.

A general description of the Danish Eulerian Model is given in [1] and [5]. Many results obtained by the model are also given (and discussed in detail) in [1] and [5]. The numerical treatment of the

Danish Eulerian model is discussed in many papers (see, for example, [2] and the references given there). The three-dimensional version of the model is described in [3]. A long term simulation used in the study of relationship between emission sources and high ozone concentrations is presented in [4].

The development of the Danish Eulerian Model is continuing by adding more advanced modules to the model.



[1] Z. Zlatev:

"Computer treatment of large air pollution models".

KLUWER Academic Publishers, Dorsrecht-Boston-London, 1995.


[2] Z. Zlatev, I. Dimov and K. Georgiev:

"Studying long-range transport of air pollutants".

Computational Science and Engineering, Vol 1, No. 3 (1994), 45-52.


[3] Z. Zlatev, I. Dimov and K. Georgiev:

"Three-dimensional version of the Danish Eulerian Model".

Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 76 (1996) S4, 473-476.


[4] Z. Zlatev, J. Fenger and L. Mortensen:

"Relationships between emission sources and excess ozone concentrations".

Computers and Mathematics with Applications, Vol. 22 (1996), 101-123.


[5] Z. Zlatev and I. Dimov:

"Computational and numerical challenges in environmental modelling".

Elcevier, Amsterdam-Boston-Heudekberg-London-New York-Oxford-Paris-Sandiego-San Francisco-Singapore-Sydney-Tokyo, 2006.





The Danish Eulerian model was recently run over a long time period of nine years; from 1989 to 1997. The results of these runs were carefully studied. The following topics were of special interest:

(i) to prepare maps presenting the pollution levels in Denmark and in other parts of Europe,

(ii) to estimate the occurences of days with high ozone concentrations (higher than prescribed critical levels according to the last draft of the EU Ozone Directive),

(iii) to evaluate the damaging effects of high ozone concentrations on crops and forest trees by using the AOT40 values and

(iv) to validate the results by comparing them with measurements taken in different European countries.

Selected results of this study can be found in many of the references quoted in this home page. Other results can been found in the home pages for the different projects in which the Danish Eulerian Model is the main tool used to achieve the planned results; see the home pages on WEPTEL, EUROAIR and SARA.

3. Impact of Climate Changes on High Pollution Levels

The impact of climate changes on high pollution levels is studied in Chapter 9 of [5] (see above) as well as in the following publications:


1. I. Dimov, G. Geernaert and Z. Zlatev: “Impact of future climate changes on high pollution levels”. International Journal of Environment and Pollution, Vol. 32, No. 2 (2008), 200-230.


2. I. Dimov, G. Geernaert and Z. Zlatev: “Influence of future climate changes in Europe on exceeded ozone critical levels”. In: “Proceedings from the EUROTRAC-2 Symposium 2002” (P. M. Midgley and M. Reuther, eds.). Margraf Verlag, Weikersheim, 2002.


3. I. Dimov, G. Geernaert and Z. Zlatev: “Influence of future climate changes in Europe on exceeded ozone critical leve ”. In: “Nordic Meteorological Meeting 23, Copenhagen, 2002” (H. E. Joergensen, ed.)., 2002.


4. Z. Zlatev: “Impact of Climate Changes in Europe on European Pollution Levels”. Problems in Programming, Vol. 8 (2006), 659-663.


Home Page of Zahari Zlatev | WEPTEL | DREAM

Department of Atmospheric Environment, National Environmental Research Institute (Denmark)