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ROOT_DIST - Root distribution function
Distributes roots (or other soil parameters) using an exponential decay curve from a maximum value in the top soil to a minimum value at depth.
Inputs:
- M = Maximum value in the top PP cm of soil (units depend on variable)
- PP = depth of top soil, or pivot point of curve (cm)
- RD = maximum rooting depth (cm), or depth at which the value is 2% of the maximum value
Implicit Inputs (i.e., available in the data):
- SLLB = array of depths to bottom of soil layer (cm)
Outputs:
- F = array of soil factors which decline exponentially between PP and RD (units depend on variable, same units as M)
Procedure:
/* exponential decay rate */
k = LN(0.02)/(RD - PP)
/* loop thru soil layers */
/* midpoints of soil layers */
mid(1) = SLLB(1) / 2
mid(j) = [SLLB(j) + SLLB(j-1)] / 2
If mid(j) <= PP
then F(j) = M
else F(j) = M * EXP{k *(mid(j) - PP)}
Examples
Example 1 - Root growth factor:
FILL, SLRGF, ROOT_DIST(), 1.0, 20, 180
For M = 1.0, PP = 20 cm, RD = 180 cm, the rate constant, k is calculated to be -0.02445 and the array of factors, F, are computed as:
| sllb | mid | F |
|---|---|---|
| 5 | 2.5 | 1.000 |
| 15 | 10 | 1.000 |
| 30 | 22.5 | 0.941 |
| 60 | 45 | 0.543 |
| 90 | 75 | 0.261 |
| 120 | 105 | 0.125 |
| 150 | 135 | 0.060 |
| 180 | 165 | 0.029 |
More Samples: The following DOME spreadsheet uses this function: Machakos Overlay DOME