Atmospherical dispersion

Atmospheric dispersion models implemented in ESTE are LPM and PTM.

Puff trajectory model (PTM) implementation: The model is a method for calculation of dispersion in the atmosphere. Atmospheric diffusion in horizontal direction is described by Gaussian dispersion and atmospheric dispersion in vertical direction is described and solved by diffusion equation.

The lower part of the atmosphere (between the terrain and mixing boundary layer) is divided into "N" (e.g. 10) layers (boxes). The exchange of radioactive material between vertical layers is described by diffusion equation and horizontal dispersion is described by Gaussian equation. In the ESTE model we assume that the wind rate and wind direction are in each box (layer) of the atmosphere represented by weighting mean of the real wind rate and wind direction. Therefore the i-th trajectory of the puff has the same coordinates (LAT and LONG) at each layer (in each box).


Lagrange particle model (LPM) implementation: Lagrangean particle model uses large number of the particles to describe the diffusion of the pollutant in the atmosphere. Each particle is representing a small air parcel that contains an amount of the pollutant. Diffusion process is simulated by modeling the trajectories of each particle independently on the movement of other particles.

The main advantages of the LPM are:

1. As the conclusion of independent particle movement, the LPM better simulates local weather conditions.

2. LPM is independent of computational grid and has, in principle, infinitesimally small resolution.

Basic equations – Our implementation of LPM is based on the description of FLEXPART model [see: "Stohl,A., Forster,C., Frank,A.,  Seibert,P. and Wotawa, G.: Technical Note: The Lagrangian particle dispersion model FLEXPART version 6.2", Atmos. Chem. Phys. 5, 2461-2474 (2005)] – a Lagrangean particle dispersion model that simulates the long-range and mesoscale transport, diffusion, dry and wet deposition, and radioactive decay of tracers released from point, line, area or volume sources.

Numerical weather prediction data – the specific implementation of LPM uses meteorological data in GRIB format. Following meteo data are used as input for ESTE implementation of the LPM:

1. Single level parameters (from both forecast or analysis): 10 meter U-velocity (10U), 10 meter V-velocity (10V), 2 meter dewpoint temperature (2D), 2 meter temperature (2T), Surface pressure (SP), Total cloud cover (TCC), Boundary layer height (BLH), Convective precipitation (CP), Large scale precipitation (LSP), Surface sensible heat flux (SSHF), friction velocity (ZUST), Land/sea mask (LSM), Orography (Z), Variance (or standard deviation) of sub-gridscale orography (SDOR) and others.

2. Model level parameters (from both- forecast or analysis): Specific humidity (Q), Temperature (T), U-velocity (U), V-velocity (V), Vertical velocity (W) and others.

Implementation on CUDA - LPM is based on simulation of large number of particles, at least several hundred thousands, to be able to simulate atmospheric diffusion correctly. This claim is multiplied by the needs of emergency preparedness when the result of the simulation needs to be known in the reasonably short time.

In order to satisfy these requirements, our implementation uses the aid of graphics hardware (GPU) used for general computation, i.e. GPGPU – general purpose computation graphical processor unit. GPGPUs are the high-performance multi-processors units, giving the possibility for massively parallel problems when the same algorithm is performed on the large amount of data.

LPM algorithms can be very easily parallelized as each particle movement and the simulation can be solved as independent from the other particles. The implementation of LPM is based on the GPGPU with CUDA (Compute Unified Device Architecture) capability. CUDA is a parallel computing architecture which can be used to accelerate a wide range of non-graphical applications in the science area.

CUDA code runs in the kernels. Kernel is a function callable from the host system and executed on the CUDA device simultaneously by many threads. Our LPM implementation in ESTE systems is divided into several kernels for modeling particle movement, meteorological situation calculations and interpolations, and for dosimetry calculations.


Simulations are done in time steps; in each time step of the calculation, the performed actions are as follows:

1. New particles are created in the case of the pollutant release in this time step.

2. Meteorological parameters are interpolated in time for the whole area.

3. Meteorological situation is interpolated in the space for each particle.

4. The position of each particle is calculated by integrating, using the local meteorological situation to determine turbulent movement.

5. Dry and wet deposition are calculated for each particle and together with pollutant concentration mapped into the grid.

6. Time integrated concentration (TIC) and other radiological parameters are calculated from the grid cell.

These steps are repeated for the whole time and for the whole area of radiological impacts calculation.

 At the end of the simulation, the calculated radiological parameters are stored from the grid into the GIS shape and are presented to the user as the maps of radiological situation.