Geoscience Reference
In-Depth Information
Q
b
Q
o
t
1/Q
b
1
m
1/Q
o
t
ln(Q)
b
_
D
o
D
Figure B6.1.2
Derivation of an estimate for the TOPMODEL
m
parameter using recession curve analysis
under the assumption of an exponential transmissivity profile and negligible recharge.
The catchment average storage deficit before each time step is updated by subtracting the
unsaturated zone recharge and adding the baseflow calculated for the previous time step, thus:
D
t
=
D
t
−1
+
Q
b
t
−1
−
Q
v
t
−1
(B6.1.20)
Equation (B6.1.18) can be used to initialise the saturated zone of the model at the start of a
run. If an initial discharge,
Q
t
=0
,
is known and assumed to be only the res
ult
of drainage from
the saturated zone, Equation (B6.1.18) can be inverted to give a value for
D
at time
t
=
0 as:
D
=−
m
ln
Q
t
=
0
Q
o
(B6.1.21)
