102
in Eq. (26) yields
(27)
In Eq. (27), the first term to the r.h.s. represents water gravitational drainage and the
second term describes water diffusion. Boundary conditions for Eq. (27) assume water
net flux due to precipitation, snow melt, runoff and evaporation at z = 0 and either free
drainage, zero permeability, or exchange with a deep water table, at z = Hs. Soil ice
formation, important for the simulation of permafrost, can be included by assuming that,
when the temperature of a given soil layer goes below the freezing point, an amount of
ice is formed whose release of heat of fusion brings the temperature of the layer back to
O°C.
The particular aspect of Eq. (27) is that it is highly non linear in s. In practice, this
implies that in the numerical solution of this equation, explicit schemes become rapidly
unstable as s approaches unity. In order to be able to simulate the motion of wetting
fronts associated for example to heavy precipitation events, it is thus necessary to devise
implicit schemes which remain stable also when s is close to 1.
When using a soil layered model, the ground skin temperature is calculated by using
the temperature at the top soil layer in place of the reservoir temperature in Eq. (8)
and the (3 parameter is expressed in terms of the soil water content of the top soil layer
(e.g. Mahfouf and Noilhan 1991). The main issue in the use of soil layer models is the
number of layers necessary to simulate accurately temperature and wat.er vertical profiles.
Numerical experiments indicate that at least 6-10 layers in the top few meters of soil, with
layer width decreasing towards the surface, are generally required (Dickinson 1984).
3.2.2 Vegetation SUb-component
Most state-of-the-art ESEMs include bio-physical vegetation processes by describing
vegetation as a one layer canopy or as an upper canopy layer (trees) overlying a lower
canopy layer (grass and short shrubs). Up to 10-15 different vegetation types are accounted for in advanced schemes, with specification of the corresponding relevant vegetation characteristics. To describe vegetation models, it is useful to introduce a general
formalism for a canopy of Nv layers. The basic set of equations in a layered canopy model
is aimed at calculating foliage temperature, Tf, canopy air temperature Tc and canopy air
specific humidity, qc. These quantities are strongly coupled to each other and eventually
determine the energy and water exchange with the atmosphere and with the underlying
soil. In many models it is assumed that both foliage and air canopy have negligible heat
and water capacity. With this assumption, at each layer (i = 2, Nv - 1) a set of three
balance equations can be defined:
in Eq. (26) yields
(27)
In Eq. (27), the first term to the r.h.s. represents water gravitational drainage and the
second term describes water diffusion. Boundary conditions for Eq. (27) assume water
net flux due to precipitation, snow melt, runoff and evaporation at z = 0 and either free
drainage, zero permeability, or exchange with a deep water table, at z = Hs. Soil ice
formation, important for the simulation of permafrost, can be included by assuming that,
when the temperature of a given soil layer goes below the freezing point, an amount of
ice is formed whose release of heat of fusion brings the temperature of the layer back to
O°C.
The particular aspect of Eq. (27) is that it is highly non linear in s. In practice, this
implies that in the numerical solution of this equation, explicit schemes become rapidly
unstable as s approaches unity. In order to be able to simulate the motion of wetting
fronts associated for example to heavy precipitation events, it is thus necessary to devise
implicit schemes which remain stable also when s is close to 1.
When using a soil layered model, the ground skin temperature is calculated by using
the temperature at the top soil layer in place of the reservoir temperature in Eq. (8)
and the (3 parameter is expressed in terms of the soil water content of the top soil layer
(e.g. Mahfouf and Noilhan 1991). The main issue in the use of soil layer models is the
number of layers necessary to simulate accurately temperature and wat.er vertical profiles.
Numerical experiments indicate that at least 6-10 layers in the top few meters of soil, with
layer width decreasing towards the surface, are generally required (Dickinson 1984).
3.2.2 Vegetation SUb-component
Most state-of-the-art ESEMs include bio-physical vegetation processes by describing
vegetation as a one layer canopy or as an upper canopy layer (trees) overlying a lower
canopy layer (grass and short shrubs). Up to 10-15 different vegetation types are accounted for in advanced schemes, with specification of the corresponding relevant vegetation characteristics. To describe vegetation models, it is useful to introduce a general
formalism for a canopy of Nv layers. The basic set of equations in a layered canopy model
is aimed at calculating foliage temperature, Tf, canopy air temperature Tc and canopy air
specific humidity, qc. These quantities are strongly coupled to each other and eventually
determine the energy and water exchange with the atmosphere and with the underlying
soil. In many models it is assumed that both foliage and air canopy have negligible heat
and water capacity. With this assumption, at each layer (i = 2, Nv - 1) a set of three
balance equations can be defined: