Environmental Engineering Reference
In-Depth Information
(
Figure 3.3
). Transfer functions have proved use-
ful in several areas in hydrology including sur-
face-water flow (Dooge,
1959
), stream/aquifer
interaction (Hall and Moench,
1972
), and solute
transport through the unsaturated zone (Jury,
1982
). Morel-Seytoux (
1984
), Bierkens (
1998
),
O'Reilly (
2004
), and Berendrecht
et al
. (
2006
)
used transfer-function models to simulate the
movement of drainage from the root zone to
the water table. Transfer models can be cali-
brated with measured groundwater levels and
independent recharge estimates (such as from
the water-table fluctuation method,
Section 6.2
).
Model coefficients are adjusted, either manu-
ally or automatically, so that model output is
in agreement with the independent estimates
(Berendrecht
et al
.,
2006
).
Effective
infiltration
Time
Bottom of
root zone
TRANSFER FUNCTION
Water
table
Recharge
Time
Example: Orange County, Florida
A water-budget transfer-function (WBTF) model
was developed and applied at a site in west
Orange County, Florida (O'Reilly,
2004
). The site
contained herbaceous vegetation with rooting
depth generally less than 0.3 m. Runoff from
the site was negligible because of the high per-
meability of the sandy soils. Water-table depths
(2-3.5 m) were deemed too great for plants to
draw water from the aquifer. Evapotranspiration
at the site was determined for a 1-year period in
1993 and 1994 by the eddy-correlation method
(Sumner,
1996
). Daily precipitation and water-
table depth were also measured. The WBTF
model calculates the water budget (as described
in Equation (
3.2
)) for the soil zone with input
data consisting of daily precipitation and evapo-
transpiration, initial and maximum root-zone
and vegetation storage, and three parameters
of the transfer-function model. (In areas where
runoff is nonnegligible, the difference between
daily precipitation and runoff is entered in place
of precipitation.) The model delays and attenu-
ates the drainage signal, but the transfer func-
tion model is conservative in that all drainage
calculated in the water budget is ultimately
delivered to the water table.
Optimum values for the three model parame-
te r s we r e d e te r m i ne d w it h t he p a r a me te r e s t i m a -
tion program, UCODE (Poeter and Hill,
1998
), by
minimizing the differences between simulated
Figure 3.3
Schematic plot showing how a transfer
function attenuates effective infiltration as it moves through
the unsaturated zone (after O'Reilly,
2004
).
The HELP3 model (Schroeder
et al
.,
1994
), which
allows the user to select the number of layers,
has been used to estimate recharge in a number
of studies (Jyrkama
et al
.,
2002
; Risser,
2008
;
and Risser
et al
.,
2009
). Bucket models are easy
to apply, but they provide little information on
the physics of water movement.
Besbes and de Marsily (
1984
) proposed use of
a transfer function for transporting drainage
from the bottom of the root zone to the water
table. Recharge is determined according to the
following equation:
∫
t
Rt
( )
=
I
(
t
−
τ ττ
)
Φ
'( )
d
(3.3)
net
0
where
R(t
) is cumulative recharge arriving at
the water table between times 0 and
t
;
I
net
is net
infiltration or drainage from the base of the
root zone;
Φ
' is a linear transfer function; and
τ
is the variable of integration that represents the
time lag of the transfer function measured back-
wards in time from
t
. Transfer-function models
can be viewed as black boxes relative to the
physics of water movement; drainage is delayed
and smoothed before arriving at the water table