From many researches, the atmospheric parameters such as turbulence, wind velocity and direction play a very important role in determining the dispersal of a pollen grain. Since the wind is the vector by which the pollen is transported, one would think the most influential parameter would be the horizontal wind velocity (Di Giovanni & Kevan, 1991). However, there have been a very limited number of studies done to try and quantify the correlation between distance traveled and horizontal wind velocity, and those who have focused on this topic have come up with varying results.

#### Pollen Dispersal from tilted Gaussian plume models

Gaussian plume models are most commonly used in air-pollution studies, to predict particle concentrations in terms of distance from a ground-level point source. Many research and study use this model to apply for pollen grain as well.

This approach deals with light particles with a terminal velocity of zero, and ground level emission. Adding release height and gravitational effects (for “heavy” particles) brought about the next generation of Gaussian plume models, known as the tilted Gaussian plume (Okubo & Levin, 1989):

where p(x_{1}) is the probability density function of locating a seed or pollen grain at a distance, x_{1}, on the ground with respect to a point source at a given height, x_{r}. V_{t} is the terminal velocity of the grain, is the time and depth averaged horizontal wind velocity, σ is the mean eddy diffusivity (for boundary rather than canopy layer flow) and is described as 2Ax_{1}/ , where A is the diffusion coefficient given by k(u*)(x*)/2 . Where u* is the frictional velocity, x_{r }is the release height, and k is the von Kármán constant, regularly used for describing the logarithmic velocity profile of a turbulent fluid flow near a boundary layer. (Gail MacInnis, 2012)

To determine the Gaussian plume models in our study area city of Frankfurt, we use average wind speed of 4.725 mph of historical wind data. It is used to calculate pollen dispersal distance of high density pollen area.

With the Frankfurt wind data, the result of Gaussian plume models is shown in the figure below. The calculation is made by Air Resources Laboratory (ARL) through the online service showing the result as in the following figure.

#### Pollen Dispersal Conclusion

From related study about pollen dispersal (Gail MacInnis, 2012) and the Gaussian plume models calculation in city area of Frankfurt, it can be approximated that the high pollen concentration area is around 500-1000 meters from the point source location or location of the tree. Then, this number is used as a based parameter together with the pollen blooming seasonal information of the tree to calculate the ellipse parameters which used to display the pollen dispersal.