Mowing and grazing

Biomass losses due to management $M_{t x y s}$ [kg ha⁻¹] are caused by mowing $M O W_{t x y s}$ [kg ha⁻¹] and grazing $G R Z_{t x y s}$ [kg ha⁻¹]:

M_{t x y s} = M O W_{t x y s} + G R Z_{t x y s}

Mowing

The mown biomass $M O W_{t x y s}$ [kg ha⁻¹] is decribed by:

M O W_{t x y s} = \frac{max (H_{t x y s} - C U T_{t x y}, 0)}{H_{t x y s}} \cdot B_{A, t x y s}

none

julia

mowing!(
;
    container,
    mowing_height,
    above_biomass,
    actual_height
)

Simulate the mown biomass of each plant species.

The grazed biomass $G R Z_{t x y s}$ [kg ha⁻¹] is defined as:

\begin{aligned} G R Z_{t x y s} & = \frac{κ_{G R Z} \cdot L D_{t x y} \cdot (B_{F, t x y})^{2}}{(κ_{G R Z} \cdot L D_{t x y} \cdot η_{G R Z})^{2} + (B_{F, t x y})^{2}} \cdot \frac{L N C_{G R Z, t x y s} \cdot H_{G R Z, t x y s} \cdot B_{F, t x y s}}{\sum_{i = 1}^{S} L N C_{G R Z, t x y i} \cdot H_{G R Z, t x y i} \cdot B_{F, t x y i}} \\ B_{F, t x y s} & = max (1 - \frac{η_{G R Z, H}}{H_{t x y s}}, 0) \cdot B_{A, t x y s} \\ B_{F, t x y} & = \sum_{s = 1}^{S} B_{F, t x y s} \\ L N C_{G R Z, t x y s} & = {(\frac{l n c_{s}}{L N C_{c w m, t x y}})}^{β_{G R Z, l n c}} \\ L N C_{c w m, t x y} & = \sum_{s = 1}^{S} \frac{B_{F, t x y s}}{B_{F, t x y}} \cdot l n c_{s} \\ H_{G R Z, t x y s} & = {(\frac{H_{t x y s}}{H_{c w m, t x y}})}^{β_{G R Z, H}} \\ H_{c w m, t x y} & = \sum_{s = 1}^{S} \frac{B_{F, t x y s}}{B_{F, t x y}} \cdot H_{t x y s} \end{aligned}

The equation is partly based on Moulin et al. (2021).

$κ_{G R Z}$ maximum consumption of biomass per livestock and day [kg ha⁻¹]
$η_{G R Z}$ controls when the farmer starts to supply additional fooder [-]
$η_{G R Z, H}$ plant parts below this height are not accessible to grazers. [m]
$β_{G R Z, l n c}$ scales the influence of the leaf nitrogen content on the preference of the grazers [-]
$β_{G R Z, H}$ scales the influence of the height on the preference of the grazers [-]

Livestock Density (LD)	3
Controls when the farmer starts to supply additional fooder (η_GRZ)	2
Consumption per livestock and day (κ_GRZ)	22

julia

grazing!(; container, LD, above_biomass, actual_height)

Simulates the removal of biomass by grazing for each species.