AgMIP open source software development and use.

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.

- 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

- SLLB = array of depths to bottom of soil layer (cm)

- F = array of soil factors which decline exponentially between PP and RD (units depend on variable, same units as M)

```
/* 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)}
```

```
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