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Dry deposition and spray drift of pesticides to nearby water bodies

Appendix G. Documentation of PESTDEP

In this appendix the different processes of the PESTDEP model are described as well as the way they are integrated. For each process the input parameters are given as well as the output parameters. Moreover, it is indicated which equations from this report are used in the calculations. It should be noted here, that the version of the model discussed here is the version that is integrated in the model-based tool for evaluation of exposure and effects of pesticides in surface water being developed by DHI Water & Environment. As this model has to be used by people that are not familiar with atmospheric sciences in the approval procedure for pesticides to describe generalised situations, the number of parameters that can be chosen freely is limited.

In the model the wind direction (x direction) is always perpendicular to the water body (y direction). The deposition is assumed to be the same everywhere in the y direction along the river (in the model the river and the emission field are indefinitely long in this direction). The z direction is the vertical. The wind is always blowing from the emission area to the water body. Although this sounds unrealistic, it is in fact not so unrealistic because there are usually fields on both sides of the water body. Part of the time the wind will be blowing along the water body. This situation is not taken into account. In this way a maximum dry deposition to the water body is calculated.

The model version described here is made for streams and small ponds, not for large water bodies, such as seas.

Emission

In the input file the indicator indicvol indicates the type of volatilisation calculation that has to be made:

• If indicvol = 1, the accumulated emission after application to crops during 7 days is calculated. In that case the parameters necessary for the calculation of the accumulated emission after application to normal moist fallow soil are read, but not used.
• If indicvol = 2, the accumulated emission after application to normal moist fallow soil during 21 days is calculated. In that case the parameters necessary for the calculation of the accumulated emission after application to crops are read, but not used. If the fraction of the pesticide in the gas phase in the soil is outside the range for which the accumulated emission can be calculated a value of 0 is given (otherwise e.g. negative emissions will be generated).

The length of the emission zone in the x direction (downwind direction, perpendicular to the water body) is needed to calculate the absolute emission for the whole emission zone.

Emission from crops

Input data:

• Dose (kg active ingredient ha^-1).
• Vapour pressure at a reference temperature (Pa).
• Reference temperature vapour pressure (K).
• Actual temperature of the crop (K). It is set to the actual air temperature that is read in the input file.

Output data:

• Accumulated emission during 7 days (% of the dose).

The accumulated emission of pesticides during 7 days after application to crops is calculated with equation (1) in the main report. The vapour pressure is calculated for the actual temperature using equation (A-16) in Appendix A and assuming a heat of evaporation of 95000 J mol^-1. For some pesticides the parameterisation of the accumulated emission from crops will lead to an emission of more than 100% of the dose. This is of course not correct. In that case the emission is set to 100%. This is not necessarily correct either, but should be used as a first guess and an indication that the accumulated emission is rather large.

Emission from normal moist fallow soil

Input data:

• Dose (kg active ingredient ha^-1).
• Henry’s law coefficient (cgas/cwater) at a reference temperature (dimensionless).
• Reference temperature Henry’s law coefficient (K).
• Soil temperature (K).
• Dry bulk density soil (kg solid/m³ soil).
• Content of organic matter of the soil (%).
• Volumetric moisture content of the soil (%).
• Soil-liquid partitioning coefficient Kd (kg kg^-1 solid/kg m^-3 liquid).

Output data:

• Accumulated emission during 21 days (% of the dose).

The accumulated emission of pesticides during 21 days after application to normal moist fallow soil is calculated with equation (2) in the main report. The fraction of the pesticide in the gas phase in the soil needed in this equation is calculated with equations A-1 to A-10 in Appendix A. The Henry’s law coefficient at the actual temperature is calculated with equation (A-20) in Appendix A, assuming a heat of dissolution at constant temperature and pressure of –68000 J mol^-1. It should be noted that the organic matter content is not used here to calculated the adsorption to the soil, but to find the density of the soil needed to calculate the volume fraction of air in the soil (see Appendix A). The parameterisation of the accumulated emission from normal to moist soil has a maximum of 95.1%.

Dry deposition

In the model there are 3 zones (see Figure 1):

• Emission zone.
• Non-spray zone.
• Water body.

In an emission zone no dry deposition occurs. In the model the dry deposition velocity in the non-spray zone is set to zero. This is done for two reasons. The first reason is that no information is available on the dry deposition of pesticides to vegetation. The second reason is that in this way the maximum dry deposition to the water body will be estimated.

The flux to the water body is calculated assuming that the concentration of the pesticide in the water body is zero. This is done, because normally the concentration in the water body will be highly variable in time and often been unknown during the emission periods (water bodies are not often sampled). In that way a maximum dry deposition is obtained. The following input and output data are used for the dry deposition velocity:

Input data:

• Friction velocity (m s^-1).
• Henry’s law coefficient (cgas/cwater) at a reference temperature (dimensionless).
• Reference temperature Henry’s law coefficient (K).
• Actual temperature of the water body (K).
• Molecular weight pesticide (g mol^-1).
• Average depth water body (m).
• Width of the non-spray zone in the x direction (downwind direction).
• Width of the water body in the x direction (downwind direction).
• Length of the water body (y direction, perpendicular to the wind direction) (m)
• Average aeration coefficient (day^-1). This coefficient is calculated by DHI Water & Environment using the hydraulic MIKE 11 model that uses the Thyssen and Erlandsen parameterization (equation 25 in the main report).

The laminar boundary layer resistance (for rivers and lakes) is found from equation (11) in the main report.

The surface resistance for rivers is found from equation (14), (21) and (25) in the main report (for rivers) and from equation (14), (27) and (28) in the main report (for lakes). The calculation of K_2d with equation (25) in the main report is made by DHI using stream parameters derived with one of their models. In equation (21) and 28 in the main report the diffusivity of the pesticide in water is used, which is calculated from the molecular mass and corrected for the actual water temperature using equations (B-6) and (B-7) in Appendix B.

At last the dry deposition velocity is found from these resistances and equations (5), (6) and (7) in the main report.

Two combinations of surface roughness length (z_0m) and friction velocity (u*) are used:

• For emission from crops: z_0m = 0.1 m and u* = 0.386 m s^-1.
• For emission from fallow soil: z_0m = 0.01 m and u* = 0.284 m s^-1.

These combinations are chosen in such a way that they give the average wind speed at 60 m height in Denmark. This average wind speed is calculated from the measured average wind speed at Kastrup Airport (near Copenhagen) for the period 1974-1983 at 10 m of 5.4 m s^-1 using the local surface roughness length of 0.03 m.

The combinations of z_0m and u* mentioned above are also used describe atmospheric diffusion.

Output data (not visible for the user; used as input to calculate the dry deposition):

• Dry deposition velocity (m s^-1):
  
• For streams kw in equation (21) is derived from the aeration coefficient provided by DHI Water & Environment and equation (30).
• For stagnant water bodies kw in equation (17) is derived from equations (37) using equations (35) and (36).
  

Atmospheric diffusion

Input data:

• Surface roughness length (m)
• Friction velocity (m s^-1).

Output data (not visible for the user):

• Wind speed as a function of height (m s^-1) calculated with equation (3) in the main report.
• Vertical exchange (eddy diffusivity) (m² s^-1) calculated with equation (4) in the main report.

For a choice of values for the surface roughness length and the friction velocity see the previous section of this appendix.

Integration of processes in the PESTDEP model

The PESTDEP model is a two-dimensional steady state K-model, which integrates all above mentioned processes and is based on the following equation (Asman, 1998):

where:
x = downwind distance (m).
z = height (m).
u(z) = wind speed at height z (m s^-1).
c_g(x,z) = concentration of the pesticide in the gas phase (kg m^-3).
K_Heat(x,z) = eddy diffusivity (m² s^-1).
Q(x,z) = flux into the atmosphere (kg m^-1 s^-1). This is equal to the emission rate.
S(x,z) = flux out of the atmosphere (kg m^-1 s^-1). This is equal to the dry deposition rate given by equation (13).

Example of an input file.

References

Asman, W.A.H. (1998) Factors influencing dry deposition of gases with special reference to ammonia. Atmospheric Environment 12, 415-421.

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