### Empirical approach for soil evaporation

The empirical approach for soil evaporation is based on the
Penman combination equation
as suggested by Monteith (1965). It uses the available energy at the soil
surface, *R*_{ns}-q_{h}, to calculate latent
heat flux from the soil surface, *L*_{v}E_{s}, from which the
soil surface evaporation, *E*_{s}, can be
derived:

(4.26)

where *R*_{ns}_{
}is the net radiation at the soil surface, *q*_{h} is the soil
surface heat flux from the previous time step, *r*_{as} is the
aerodynamic resistance, *r*_{ss} is the surface
resistance at the soil surface, *e*_{s} is the vapour pressure at
saturation in the air, *e*_{a}*
*is the actual vapour pressure in the air, and *∆* is the
slope of saturated vapour pressure versus temperature curve. The density, *ρ*_{a}, and heat capacity, *c*_{p}, of air, the latent heat of
vaporisation, *L*_{v}, as well as
the psychrometer constant, *γ,* are all
considered as physical constants.

The aerodynamic resistance between the soil surface and the
reference height, *r*_{as}, is
calculated in the same way as in the physically based approach using Eq. (4.12)- (4.15).

The surface resistance at the soil surface, *r*_{ss}, can be estimated by two different
empirical functions accounting for moisture conditions at the soil surface and
the water tension in the uppermost soil layer. The first approach (“PM-eq,
Rs(1Par)”) is based on only one governing parameter:

(4.27)

where *r*_{ψ} is an
empirical coefficient and *ψ*_{s} is the water tension
in the uppermost layer (see viewing function Surface Resistance,
Penman eq. 1 par). The *δ*_{surf} is the
mass balance at the soil surface in units mm of water (see eq. 4.9).

The second approach (“PM-eq, Rs(3Par)”) is based on three
governing parameters:

(4.28)

where *r*_{ψ1}, *r*_{ψ2} and *r*_{ψ3} are empirical coefficients
(see viewing function Surface Resistance, Penman eq. 3 par).

Optionally, (“K-function”) the soil evaporation can be
estimated as the minimum value of the flow rate that could be supplied from the
middle point of the uppermost soil layer and the potential rate according to Eq.
(4.26)
taking *r*_{ss}=0.

The soil surface temperature will also be estimated (for all
of the three approaches described above) if the switch

Surface cover

Value |
Meaning |

No |
No surface cover |

Plastic sheet |
A plastic sheet covering parts of the soil and thus
preventing soil evaporation. |

Surface Temperature

is put to “f(PM-equation)”. This is done by first solving the
heat balance equation for the sensible heat flow to the air as:

(4.29)

where the soil surface heat flux, *q*_{h}, is taken from
the preceding time steps. The soil surface temperature is finally given as:

(4.30)

Alternatively the soil
surface temperature can be set equal to the air temperature except when snow
covers the surface (option “Air temperature”).