eTheses Repository - University of Birmingham

A force restore model is used to solve the surface energy budget equation following Tiedke
et al. (1975) and Deardroff (1978):
∂T
∂t
s
2 π k
=
υ h
−
s
s
{ µ I
T
πυ
s
s
∞
cos Z(
t)
− εσT
− T ( −hθ
)
}
h
θ
4
s
+ c ρ θ * u * + l ρ q * u *
p
0
21
0
(Equation 3.8)
where ks is the thermal diffusivity and υs is the thermal conductivity of the soil, hθ is the
depth of the daily temperature wave calculated according to Deardroff (1978) and T(-hθ)
can be selected to be either the prescribed soil temperature or is calculated according to
Deardroff (1978).
3.1.3 Model boundary conditions
The METRAS model area is limited in both in the vertical and horizontal directions. Over
land the surface height coincides with the lower model boundary, whereas all other
boundaries are artificial and therefore the boundary conditions must be formulated such
that waves can pass the boundaries without reflections. The boundary conditions used by
METRAS are described in this Section. All the boundary conditions are implemented at the
model boundary directly – this does not always correspond to a grid point depending on the
selected variable. If this is the case the value at the outer grid point is calculated assuming:
χ(boundary) = 0.5 * (χ(outer grid point) + χ(next inner grid point))
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