# MMF

The MMF soil erosion model requires the following land use specific model parameters (Table 11):

*Table 16: MMF\_table*

| Land use class | Plant height (PH) | Stem density (NV) | Stem diameter (D) | Canopy cover (CC) | Ground cover (GC) | No erosion | Tillage | Manning | No vege-tation |
| -------------- | ----------------- | ----------------- | ----------------- | ----------------- | ----------------- | ---------- | ------- | ------- | -------------- |
| -99            | 1                 | 2                 | 3                 | 4                 | 5                 | 6          | 7       | 8       | 9              |
| 1              | 10                | 0.5               | 0.4               | 0.8               | 0.65              | 0          | 0       | 0.2     | 0              |
| 2              | 0.5               | 4                 | 0.2               | 0.5               | 0.5               | 0          | 0       | 0.1     | 0              |
| 3              | 0.2               | 20                | 0.15              | 0.3               | 0.35              | 0          | 1       | 0       | 1              |
| …              | …                 |                   |                   |                   |                   |            |         |         | …              |

Values for the plant height, stem density, stem diameter, canopy cover and ground cover can be found in Table 3 of Morgan & Duzant (2008), however, this table is mostly focused on British crop types and natural vegetation. Still, this table gives some suggestions for different vegetation types, which may help to define the model parameters for other geographical regions. The “no erosion” column is used to indicate with 0 (erosion) or 1 (no erosion) which land use types do not experience erosion, such as water and pavement. In case of no erosion, the sediment taken into transport will be set to 0. The “tillage” column indicates which land use classes apply tillage, i.e. 0 for no tillage and 1 for tillage. In case of tillage, the Manning’s roughness coefficient for soil will be obtained with the surface roughness parameter RFR (see below). The “Manning” column can be used to provide a Manning’s coefficient for irregular-spaced vegetation, commonly used for natural cover types (e.g. forest and shrubland). This column will be ignored in case it is set to 0, then the Manning’s roughness coefficient for vegetation will be determined with the stem density and stem diameter. When another value is provided, then the stem density and stem diameter will be ignored and the provided Manning’s coefficient will be considered. Manning’s coefficient values for different vegetation conditions can be obtained from Chow (1959). The “no vegetation” column is used to ignore the Manning’s roughness coefficient for vegetation. This can be useful in case of orchards, where the stem density is very low, which may result in unrealistic Manning’s roughness values.

Stem density, stem diameter and ground cover are commonly used for model calibration. Although literature values are available, these values are difficult to obtain for large study areas and may differ from agricultural field to agricultural field or from forest to forest.

The MMF soil erosion model may consider the changes of vegetation conditions in case of a sow-harvest cycle. In that case, the harvestFLAG should be set to 1. Another land use specific table (Table 12) should be provided, which gives the values for the period between harvest and sowing (commonly a fallow period):

Table 17: MMF\_harvest

| Land use class | Sowing | Harvest | Plant height (PH) | Stem density (NV) | Stem diameter (D) | Canopy cover (CC) | Ground cover (GC) | Tillage |
| -------------- | ------ | ------- | ----------------- | ----------------- | ----------------- | ----------------- | ----------------- | ------- |
| -99            | 1      | 2       | 3                 | 4                 | 5                 | 6                 | 7                 | 8       |
| 1              | 102    | 241     | 0.05              | 500               | 0.01              | 0.3               | 0.35              | 1       |
| 2              | 278    | 51      | 0                 | 0                 | 0                 | 0                 | 0                 | 0       |
| 3              | 0      | 0       | 0                 | 0                 | 0                 | 0                 | 0                 | 0       |
| …              |        |         | …                 |                   |                   |                   |                   |         |

In the “sowing” and “harvest” column the days of the year (julian dates) should be provided of sowing and harvest, respectively. The other columns are similar to the MMF\_table, with the difference that the values provided here (MMF\_harvest) will be considered in the period between harvest and sowing and the MMF\_table between sowing and harvest. When a land use class does not consider the sowing-harvest cycle (e.g. natural vegetation or orchards/vineyards), the dates should be set to 0.

Intensity of the erosive rain can be provided with the PrecInt model parameter. (Morgan and Duzant, 2008) propose 10 mm h-1 for temperate climates, 25 mm h-1 for tropical climates and 30 mm h-1 for strongly seasonal climates (e.g. Mediterranean, tropical monsoon). The intensity of the erosive precipitation will be based on the rainfall intensity obtained from the rainfall input when the infiltration excess surface runoff is used (i.e. Infil\_excess = 1 in the INFILTRATION section of the config file).

The canopy cover values provided in the two tables, i.e. MMF\_table and MMF\_harvest, will be ignored when CanopyCoverLAIFlag is set to 1. In that case, the canopy cover will be obtained from the LAI determined by the vegetation module

The detachability of the soil by raindrop impact should be provided for each texture class. Based on laboratory experiments, (Quansah, 1982) proposed , and g J-1. Similarly, the detachability of the soil by runoff should be provided for each texture class, for which (Quansah, 1982) proposed , and g mm-1.

The particle diameter of the three textural classes should be provided, for which Morgan & Duzant (2008) proposes 2∙10-6 m for clay, 60∙10-6 m for silt and 200∙10-6 m for sand.

The Manning’s roughness coefficient for bare soil should be provided, for which a default value of 0.015 s m1/3 should be a reasonable first estimate.

The flow depth of bare soil, in-field flow depth and flow depth for transport capacity are used in the immediate deposition calculation. Values of, respectively, 0.005, 0.1 and 0.25 m are taken as default values.

The surface roughness parameter RFR is used for land use classes that apply tillage (see MMF\_table and MMF\_harvest). Morgan & Duzant (2008) provide a table (Table IV) with common values for RFR for different ploughing equipment.

The sediment and flow density are commonly set to 2650 and 1000 kg m-3, where the flow density may be slightly higher (e.g. 1100 kg m-3) for runoff on hillslopes (Abrahams et al., 2001).

The fluid viscosity is nominally set to 0.001 kg m-1 s-1, but often taken as 0.0015 to allow for the effects of the sediment in the flow ((Morgan and Duzant, 2008).

Table 18: Model parameters

| Model parameter                              | Model variable | Unit            | Range/default                   |
| -------------------------------------------- | -------------- | --------------- | ------------------------------- |
| Plant height                                 | PH             | m               | 0-50                            |
| Stem density                                 | NV             | stems m-2       | 0-10,000                        |
| Stem diameter                                | D              | m               | 0-5                             |
| Canopy cover                                 | CC             | -               | 0-1                             |
| Ground cover                                 | GC             | -               | 0-1                             |
| No erosion                                   |                | -               | 0 or 1                          |
| Tillage                                      |                | -               | 0 or 1                          |
| Manning                                      | n              | s m-1/3         | 0.01-0.5                        |
| No vegetation                                |                | -               | 0 or 1                          |
| Sowing                                       |                | day of the year | 1-365                           |
| Harvest                                      |                | day of the year | 1-365                           |
| Intensity of the erosive rain                | I              | mm h-1          | 10-50                           |
| Detachability of the soil by raindrop impact | Kc, Kz, Ks     | g J-1           | 0.1, 0.5, 0.3                   |
| Detachability of the soil by runoff          | DRc, DRz, DRs  | g mm-1          | 1.0, 1.6, 1.5                   |
| Particle diameter                            | δc, δz, δs,    | m               | 2 ∙ 10-6, 60 ∙ 10-6, 200 ∙ 10-6 |
| Bare soil Manning’s roughness coefficient    | nsoil          | s m-1/3         | 0.015                           |
| Flow depth bare soil                         | dbare          | m               | 0.005                           |
| Flow depth in field                          | dfield         | m               | 0.1                             |
| Flow depth transport capacity                | dTC            | m               | 0.25                            |
| Surface roughness parameter for tillage      | RFR            | cm m-1          | 6-48                            |
| Sediment density                             | ρs             | kg m-3          | 2650                            |
| Flow density                                 | ρ              | kg m-3          | 1100                            |
| Fluid viscosity                              | η              | kg m-1 s-1      | 0.0015                          |
