Geoscience Reference
In-Depth Information
B6.1.4 Moisture Accounting: Unsaturated Zone Fluxes
The basic soil structure illustrated in Figure B6.1.1 may be used to accommodate a variety
of unsaturated zone process descriptions as defined by the modeller. One formulation that
has been adopted in past TOPMODEL applications assumes that the root zone store for each
topographic index value is depleted only by evapotranspiration and that water is added to the
unsaturated zone drainage store only once the root zone reaches field capacity. The drainage
is assumed to be essentially vertical and a drainage flux
q
v
[LT
−1
] is calculated for each topo-
graphic index class.
Expressed in terms of storage deficit, Beven and Wood (1983) suggested that a suitable
functional form for the vertical flux
q
v
at any point
i
is:
S
uz
D
i
t
d
q
v
=
(B6.1.10)
where
S
uz
[L] is storage in the unsaturated (gravity drainage) zone;
D
i
is the local saturated
zone deficit due to gravity drainage and dependent on the depth of the local water table [L];
t
d
is a time constant, expressed as a mean residence time for vertical flow per unit of deficit
[TL
−1
]. Equation (B6.1.10) is the equation of a linear store but with a time constant
that
increases with increasing depth to the water table. Note that there is no physical justification
for this functional form, but it has the advantages that it allows for longer residence times and
slower drainage rates for lower values of the index where the water table is predicted as being
deeper below the surface and yet it only introduces one parameter value. It has generally been
found that modelling results are not very sensitive to this parameter.
Accounting for evapotranspiration with a minimal number of parameters poses a problem
of similar complexity to that of the unsaturated zone drainage. TOPMODEL follows the widely
adopted practice of calculating actual evapotranspiration,
E
a
, as a function of potential evap-
oration,
E
p
, and root zone moisture storage for cases where
E
a
cannot be specified directly. In
the TOPMODEL description of Beven (1991a), evaporation is allowed at the full potential rate
for water draining freely in the unsaturated zone and for predicted areas of surface saturation.
When the gravity drainage zone is exhausted, evapotranspiration may continue to deplete the
root zone store at the rate
E
a
, given by:
{
D
i
t
d
}
S
rz
S
r
max
E
a
=
E
p
(B6.1.11)
where the variables
S
rz
and
S
r
max
are, respectively, root zone storage [L] andmaximum available
root zone storage [L]. If some effective root zone depth
z
rz
[L] can be assumed,
S
r
max
can be
estimated approximately from:
S
r
max
=
z
rz
fc
−
wp
(B6.1.12)
where
fc
[-] is moisture content at
field capacity
and
wp
[-] is moisture content at wilting point.
For calibration it is only necessary to specify a value for the single parameter
S
r
max
. An effective
value for
S
r
max
might be greater than that suggested by Equation (B6.1.12) due to capillary rise
of water into the root zone under dry conditions.
The flux of water entering the water table locally at any time is
q
v
. This drainage is also a
component of the overall recharge of the lumped saturated zone. To account for the catchment
average water balance, all the local recharges must be summed. If
Q
v
is the total recharge to
the water table in any time step, then:
Q
v
=
q
v,i
A
i
(B6.1.13)
i
where
A
i
is the fractional area associated with topographic index class
i
as a fraction of total
catchment area.
