Environmental Engineering Reference
In-Depth Information
where
N
is in days and
A
is surface drainage area
in km
2
. The variable 2
N
*, defined by Pettyjohn
and Henning (
1979
) as the odd integer between 3
and 11 nearest to 2
N
, determines the time inter-
val used by HYSEP for hydrograph separation.
For the fixed-interval method, the period of
record is broken down into a contiguous series
of time intervals of length 2
N
*. Within each
time interval, base flow for all days is set equal
to the lowest daily discharge rate within the
interval (
Figure 4.9a
). With the sliding-interval
method, base flow for each day of the period,
I
, is
defined as the lowest daily discharge that occurs
within the interval extending from 0.5(2
N
* - 1)
days before day
I
to 0.5(2
N
* - 1) days after day
I
(
Figure 4.9b
). The local-minimum method uses
the same time intervals, centered on each day,
as the sliding-interval method. Local minima
occur on days for which daily discharge is less
than that of every other day within the inter-
val. Daily base flow values are determined by
linearly interpolating in time between adjacent
local minima (
Figure 4.9c
). Risser
et al
. (
2005b
)
applied the methods to three sites underlain by
fractured bedrock in eastern Pennsylvania. The
local-minimum method produced the lowest
estimate of base flow (229 mm), followed by the
sliding-interval method (292 mm) and the fixed-
interval method (295 mm).
Another approach to hydrograph separa-
tion uses digital filtering, a technique origi-
nally used in signal processing (Nathan and
McMahon,
1990
; Chapman,
1999
; Arnold
et al
.,
1995
; Eckhardt,
2005
). Although digital filtering
is a purely empirical approach, it removes much
of the subjectivity from manual separation, pro-
viding consistent, reproducible results. A single
parameter filtering equation is given by:
(
1999
) compared results from Equation (
4.7
)
with independent estimates of base flow for
six watersheds with historic data; R
2
values for
comparisons of monthly values ranged between
0.62 and 0.98. Many variations of Equation (
4.7
)
exist (Chapman,
1999
). Eckhardt (
2005
) pro-
posed a two-parameter model for determining
base flow:
Q
bf
=−
[(1
BFI
)
α
+ +
Q
bf
Q
i
max
i
−
1
i
(4.8)
(1
−
α
)
BFI
] /(1
−
α
BFI
)
max
max
where
Q
bf
i
is the filtered base flow at time step
i and
BFI
max
is the maximum value of base-flow
index. Eckhardt (
2005
) suggested values for
BFI
max
of 0.8 for perennial streams, 0.5 for ephemeral
streams, and 0.25 for perennial streams con-
nected with hard-rock aquifers. Lim
et al
. (
2005
)
described a web-based automatic streamflow
hydrograph analysis tool (WHAT; http://cobweb.
ecn.purdue.edu/~what/; accessed November 10,
2008) capable of using Equations (
4.7
) and (
4.8
) as
well as the local-minimum approach of HYSEP.
Lim
et al
. (
2005
) analyzed hydrographs for 50
watersheds in Indiana and found good agree-
ment in results from Equations (
4.7
) and (
4.8
).
Eckhardt (
2008
) compared results for Equations
(
4.7
) and (
4.8
) and the three HYSEP methods and
the PART (Rutledge,
1998
) and UKIH (Piggott
et al
.,
2005
) models for 65 watersheds in North
America (Neff
et al
.,
2005
). Although there were
no measured base flow values to assess the
accuracy of the methods, pair-wise correlation
coefficients ranged from 0.85 to 1.00, indicating
similarity among all methods.
4.5.2 Recession-curve displacement
analysis
The recession-curve displacement method
(Rorabaugh,
1964
) is based on the assump-
tion that an aquifer can be described by one-
dimensional flow from a distant no-flow
boundary at the edge of the aquifer to a stream
(
Fig ure 4.10
). The groundwater flow equation
under those conditions takes the form:
Q
fil
=
α
Q
fil
++ −
(1
α
)(
QQ
) / 2
(4.7)
i
i1
−
i
i1
−
where
Q
il
i
is filtered direct runoff at time step i,
α
is the filter parameter, and
Q
i
is total stream-
flow at time step i. Base flow at time step i (
Q
bf
i
)
is equal to
Q
i
-
Q
il
i
. Nathan and McMahon (
1990
)
and Arnold
et al
. (
1995
) found that a value of
α
= 0.925 produced reasonable results relative to
those of manual separation methods. Eckhardt
(
2008
) proposed a recession curve analysis
technique for estimating
α
. Arnold and Allen
THx S Ht
∂ ∂=∂∂
2
/
2
/
(4.9)
y
where
T
is transmissivity,
H
is hydraulic head,
S
y
is specific yield, and
t
is time. Groundwater is
assumed to move in a direction,
x
, perpendicular
