Environmental Software and Modelling Group
Computer Science School
Technical University of Madrid

Mesoscale Meteorological Modelling

The Laboratory is using an improved and adapted version of MEMO 5.0 (EUMAC Zooming Model). This adapted version has been developed in the last 3 years in the Laboratory in order to include many different species and the chemistry. The final version is also taken some of the capabilities of MM5 (NCAR, USA) model. The combined version is called REMEST. In order to that we have developed different software tools to adapt the model to the Air Quality System so-called ANA. Meteorological and transport sections are working together. The meteorological part provides wind components, temperature and humidity 3D fields for the driver system which is the transport module.

These variables are predicted by using a non-hydrostatic numerical model with terrain-influenced co-ordinates. The efficiency of the model has been proved in recent years during several applications (Flassak, Moussiopoulos). The model equations are based on the Navier-Stokes system of equations, which for momentum, temperature and any passive pollutant are the following:

   Cartesian co-ordinates

The usual procedure for mesoscale models states that variables should be split into base-state parts and mesoscale perturbations. We assume here that base-state parts of the wind velocity are taken as zero. For the thermodynamic variables the separation yields

The mesoscale pressure perturbations are split into three components:

The first term corresponds to the large-scale horizontal pressure gradient, the second is the hydrostatic part, obtained by:

By solution of the elliptic equation, Ph  can be computed.

Terrain inhomogeneity boundary conditions at ground cannot be properly formulated in cartesian co-ordinates. Therefore, a transformation of the vertical co-ordinate to a terrain-influence one is performed by:

where H and Zs(x',y') are the height of the upper and the lower boundaries, respectively. The cells of the vertical grid are non-equidistant and they are modelled by a monotonic function:

where HHk  is the height of the upper boundary of cell k and   is a parameter to be adjusted.

For the simulation of the dispersion of all pollutants, a system of non-linear equations has to be solved. Following K-Theory to describe turbulent diffusion, the system takes the form:

where  c = (c1, c2, ..., cj, ....) is the pollutant concentration vector, v the wind velocity vector, Kc, the eddy diffusitivity, R the chemical production (or destruction) vector, and S the source or sink vectorial terms.

As in the meteorological model, we have transformed to terrain-influence co-ordinates. Resulting equations are solved numerically for the specified initial and boundary conditions. The temporal discretization adopted makes use of the 2nd Order Adam-Baschford scheme.

Adjective and horizontal diffusive transport can be shown to be rather slow compared to vertical diffusive transport and chemistry. We split off the advection and horizontal diffusion terms from vertical diffusion and chemical kinetics.

The vertical diffusion is implemented with the Crank-Nicholson method. For   a modification of the original total variation method for the three dimensional case was introduced by Harten. This method achieves a great reduction in undesirable numerical diffusion, but this spurious diffusion is not completely removed.

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