Tests of a NonUniform Mixing Model for Transfer of Herbicides to Surface Runoff

1
Tests of a Non-Uniform Mixing Model for Transfer
of Herbicides to Surface Runoff

• G. C. Heathman, L.R. Ahuja, and J.L. Baker.
  Trans ASAE 29(2)450-455, 1986.

2
Importance of Surface Mixing

• 8 to 80 of Nitrogen Loss occurs in solution in
  surface runoff
• 7 to 30 of Phosphorus Loss occurs in solution in
  surface runoff
• Up to 90 of Pesticide Loss occurs in solution in
  Surface Runoff

3
PARTITIONING OF CHEMICAL BETWEEN SOIL AND WATER

• GIVEN
• WA The total mass of chemical A in a liter of
  moist soil, mg/L
• ? The volumetric moisture content of the soil,
  L water/L soil
• Kd The soil-water partitioning coefficient for
  chemical A, L water/kg soil

4
PARTITIONING OF CHEMICAL BETWEEN SOIL AND WATER

• GIVEN
• Bd The soil bulk density,
• kg soil/L soil
• FIND
• Cw Concentration of chemical A in the soil
  water, mg/L

5
PARTITIONING OF CHEMICAL BETWEEN SOIL AND WATER

• SOLUTION
• Total mass of chemical A in a liter of moist
  soil
• WA Cw? KdCwBd
• Cw(? KdBd)
• Cw WA/(? KdBd)

6
Uniform Surface Mixing Model

• WA Cw(Q KdBd)
• Assume all transfer of chemical to surface runoff
  occurs in a thin surface layer lt1cm thick.
• Assume the layer is saturated
• Assume complete mixing according to the formula
  above

7
Schematic of thin mixing zone
8
Research On Surface Mixing

• Chemical transfer to Surface Runoff occurs from
  as deep as 2cm below the surface.
• The degree of mixing of runoff water with
  chemical decreases exponentially with depth.

9
Non-Uniform Surface Mixing Model

• Assumes mixing occurs to a maximum depth of 2cm.
• Divides the mixing zone into 20 layers, each 1mm
  thick.
• Assumes mixing decreases exponentially with depth.

10
Non-Uniform Surface Mixing Model Need to Know

• For each layer
• initial soil moisture, Q (liters/liter)
• layer Bulk Density, Bd (kg/liter)
• initial chemical concentration of each layer, Cw
  (mg/L)
• Partitioning Coefficient for each layer, Kd (L/kg)

11
Non-Uniform Surface Mixing Model Need to Know

• Rainfall rate for each time increment
• Time when surface runoff begins
• Runoff rate for each time increment

12
Non-Uniform Surface Mixing Model Before Runoff
Starts

• All rainfall infiltrates into the soil
• Each rainfall increment is set equal to the depth
  of water needed to saturate the next 1mm layer
• Complete mixing is assumed in each layer (B 1.0)

13
Non-Uniform Surface Mixing Model After Runoff
Starts

• The amount of water added to the mixing zone is
  RDT
• R is the rainfall intensity (cm/min)
• DT is the time increment in minutes
• The degree of mixing between the rainwater and
  soil solution, B, decreases exponentially with
  depth

14
Non-Uniform Surface Mixing Model

• Bi exp(-bzi) the mixing coefficient
• b is assumed to be a constant fitted parameter
• zi is the depth below the surface to the middle
  of the layer in mm.
• B 1.0 at the surface and for all layers prior
  to runoff

15
Non-Uniform Surface Mixing Model Need to Know

• For each layer
• initial soil moisture, Q (liters/liter)
• layer Bulk Density, Bd (kg/liter)
• initial chemical concentration of each layer,
  C1wi (mg/L)
• Partitioning Coefficient for each layer, Kd (L/kg)

16
Non-Uniform Surface Mixing Model Need to Know

• For each layer
• Mixing coefficient, B
• Added Rainfall Increment, RDT
• Chemical Concentration being leached from the
  next upper layer C1wi-1 mg/L (at the surface this
  value is assumed to equal 0)

17
Non-Uniform Surface Mixing Model

• Total Chemical in Layer i after leaching from the
  layer above includes the initial content plus the
  amount leached from above
• superscript 1 means at the beginning of the time
  increment

18
Non-Uniform Surface Mixing Model

• Total Chemical in Layer i after mixing with the
  leached water from the layer above will be the
  same mass but with a new average concentration

19
Non-Uniform Surface Mixing Model

• Equating the total chemical amount in layer i at
  the beginning and end of the time increment and
  solving for the concentration at the end of the
  time increment

20
Non-Uniform Surface Mixing Model

• After completion of calculations for each layer
  for a time step the average concentration of the
  water in the layer is calculated as

21
Non-Uniform Surface Mixing Model

• The average concentration from the model is used
  as the concentration in surface runoff and
  infiltration for this time period.
• Runoff depth is subtracted from the Rainfall
  depth to determine Infiltration depth.