Team:KU Leuven/Project/Ecological/Modelling

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tree ladybugcartoon

Ultimately our project aims to reduce crop loss because of aphid infestation. Given the time span of the competition, it is impossible to conduct a field experiment for this. Therefore we attempt to predict the effect of our pheromones on the ecology through a series of modeling steps.


The first step is to calculate the concentration of the pheromones released in the environment. When a colony of E. coligy in what form so ever is placed in a field, the produced substances will be transported in the air by diffusion and convection. Diffusion is always present, whereas the source of the convection term is the wind. In order to establish a realistic model, certain parameters are needed. Therefore approximate diffusion coefficients and air velocity were searched. Production of the pheromones by the colony was coupled with the other modeling approach <link to Sander’s text>.

Convection-diffusion equation


Diffusion coefficients

Because we found no measured diffusion coefficients of the pheromones in literature, estimations were made with a calculator based on methods described in i. Using the average supplied by the calculator, the results are 4.62 x 10-6 m2/s for E-beta-farnesene and 6.33 x 10-6 m2/s for methyl salicylate. The conditions supplied were a pressure of 1 atm and a temperature of 15 °C.



Plot of the wind profile

Figure 1 ǀ Wind profile for a crop height of 2 m and a wind speed of 3.39 m/s at a height of 10 m.

Wind speed

Because of friction and obstacles on the earth’s surface, wind speed varies with altitude. Generally, the velocity decreases with increasing altitude. For the part above the crops we can use the logarithmic wind profile is appropriate. The formula for this profile is

Wind profile

with u representing the velocity. Here d accounts for an upward shift above a vegetative cover. The relation d=0.63 x zc is suggested, where zc is the height of the crops. The length z0 is called the roughness length and is often supposed to be about one tenth of zc.

For the part inside the canopy, the profile is exponential.

Wind profile inside canopy

As can be noticed, the wind speed decreases exponentially with extinction factor a when approaching ground level and thus going deeper into the canopy. uc is the speed at height zc and can easily be calculated by the formula of the logarithmic wind profile.

Evidently, the wind direction changes in time. Most regions however tend to have a dominant wind , at least during a certain time period. This is the reason our model only incorporates convection in one direction, which greatly simplifies calculation. Furthermore we can also find average wind speeds, measured by KMI in Belgium. These are measured at 10 m above the ground, making it possible to calculate u*/k used in the log law. Now, all parameters for convection are known when the crop height is given. The wind profile was entered in the software using a piecewise function and self-defined parameters, making it easy to change wind speed and crop height. An example of the profile is plotted in Figure 1.