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Quantifying the relative contribution of the climate and direct
human impacts on mean annual streamflow in the contiguous
United States
Dingbao Wang
1
and Mohamad Hejazi
2
Received 28 November 2010; revised 10 July 2011; accepted 26 July 2011; published 24 September 2011.
[1] Both climate change and human activities are known to have induced changes to
hydrology. Consequently, quantifying the net impact of human contribution to the
streamflow change is a challenge. In this paper, a decomposition method based on the
Budyko hypothesis is used to quantify the climate (i.e., precipitation and potential
evaporation change) and direct human impact on mean annual streamflow (MAS) for 413
watersheds in the contiguous United States. The data for annual precipitation, runoff, and
potential evaporation are obtained from the international Model Parameter Estimation
Experiment (MOPEX), which is often assumed to only include gauges unaffected by human
interferences. The data are split into two periods (1948–1970 and 1971–2003) to quantify the
change over time. Although climate is found to affect MAS more than direct human impact,
the results show that assuming the MOPEX data set to be unaffected by human activities is
far from realistic. Climate change causes increasing MAS in most watersheds, while the
direct human-induced change is spatially heterogeneous in the contiguous United States,
with strong regional patterns, e.g., human activities causing increased MAS in the Midwest
and significantly decreased MAS in the High Plains. The climate- and human-induced
changes are found to be more severe in arid regions, where water is limited. Comparing the
results to a collection of independent data sets indicates that the estimated direct human
impacts on MAS in this largely nonurban set of watersheds might be attributed to several
human activities, such as cropland expansion, irrigation, and the construction of reservoirs.
Citation: Wang, D., and M. Hejazi (2011), Quantifying the relative contribution of the climate and direct human impacts on mean
annual streamflow in the contiguous United States, Water Resour. Res., 47, W00J12, doi:10.1029/2010WR010283.
1. Introduction
[2] Climate change and human activities have altered the
hydrologic cycle and have exerted global-scale impacts on
our environment with significant implications for water
resources [Barnett et al., 2008; Milly et al., 2008; Wagener
et al., 2010; Vogel, 2011]. Climate change includes the
redistribution of precipitation and temperature change,
which together affect streamflow discharge [Karl et al.,
1996; Vörösmarty et al., 2000]. Human activities can alter
the streamflow directly by affecting the hydrological proc-
esses or indirectly by disturbing the climate variables. The
direct human impacts on streamflow include land use
change [Schilling et al., 2010; Arrigoni et al., 2010], dam
construction and reservoir operation [Rossi et al., 2009],
and surface water and groundwater withdrawal and return
flow [Weiskel et al., 2007; Wang and Cai, 2010]. Human
impacts on climate can operate at various spatial scales.
For example, at the global scale, human-induced elevated
CO
2
emissions contribute to global warming, while at the
regional scale, irrigation in the U.S. High Plains increases
the rainfall and streamflow during the summer season in
the Midwest [Kustu et al., 2011]. An example of local-scale
impact is the urban heat island effect related to human de-
velopment and urbanization.
[
3] Precipitation and streamflow trends in the contiguous
United States have been investigated in several recent stud-
ies. Increases in precipitation across the United States dur-
ing the twentieth century have been reported by Karl and
Knight [1998] and Groisman et al. [2004]. Streamflow has
been increasing in the United States since at least 1940
[Lins and Slack, 1999; McCabe and Wolock, 2002]. On the
basis of 400 sites in the conterminous United States meas-
ured during 1941–1999, McCabe and Wolock [2002] identi-
fied noticeable increases in annual minimum and median
daily streamflow around 1970, especially in the eastern
United States. They attributed streamflow increases to a
step change that coincided with an increase in precipitation
[McCabe and Wolock, 2002]. By developing maps of an-
nual streamflow anomalies over the contiguous United
States using streamflow records selected to reflect mini-
mum direct impacts from human land disturbances and
water diversion, Krakauer and Fung [2008] found a similar
trend, i.e., increased streamflow around 1970 in concert
with an increase in precipitation. Annual average flow and
1
Department of Civil, Environmental, and Construction Engineering,
University of Central Florida, Orlando, Florida, USA.
2
Joint Global Change Research Institute, Pacific Northwest National
Laboratory, College Park, Maryland, USA.
Copyright 2011 by the American Geophysical Union.
0043-1397/11/2010WR010283
W00J12 1of16
WATER RESOURCES RESEARCH, VOL. 47, W00J12, doi:10.1029/2010WR010283, 2011
annual total precipitation have increased during the period
of 1948–1997 across the eastern United States, and the
trends appear to arise primarily from the increase in autumn
precipitation [Small et al., 2006]. More recently, Luce and
Holden [2009] examined changes to the distribution of an-
nual streamflow from 43 gauges in the Pacific Northwest of
the United States between 1948 and 2006, and they found
that the mean annual flow exhibited a decreasing trend in 25
gauges and no significant trend in the remaining 18 gauges.
[
4] In all of these studies, streamflow was assumed to be
unaffected by human activities; detected trends of stream-
flow discharge were attributed to climate change alone.
However, the flow of water in most rivers in the United
States reflects some level of human activities [National
Research Council, 2002]. Dams and diversions for irriga-
tion may be the most cited activities, but groundwater
pumping and land use change are also important factors.
Recently, Arrigoni et al. [2010] found that direct anthropo-
genic modifications (i.e., irrigation, damming, and urban-
ization) of the river basins across the northern Rocky
Mountains have altered the flow regimes to a much greater
extent than climate change over the past 59 years. To
secure a complete picture of future water resources, it is
necessary to consider climate change, human systems, and
hydrology in an integrated framework [Vörösmarty et al.,
2000]. The separation and quantification of climate change
and human impacts on streamflow is a challenge because of
the complexity and interaction of climate, human, and
hydrologic processes. Several recent studies have estimated
the contributions of climate and human impacts on mean
annual streamflow (MAS) for specific watersheds using dis-
tributed hydrologic models [Wang et al., 2009; Ma et al.,
2010] and climate sensitivity or elasticity methods [Li et
al., 2007; Zhang et al., 2008; Ma et al., 2008; Zhao et al.,
2009]. Tomer and Schilling [2009] studied the relative
effects of climate change and land use change on hydrology
in the Midwest on the basis of ecohydrologic plots of water
versus energy use efficiency indices. Particularly, in the
Upper Mississippi River Basin, Schilling et al. [2010]
found that the runoff coefficient increased 32% because of
land use change, i.e., increasing soybean acreage.
[
5] In this paper an attempt is made to categorize stream-
flow change into climate-induced and direct human-induced
streamflow change. The climate-induced streamflow change
is caused by the alterations of precipitation and potential
evaporation, which can be due to natural climate variability,
global climate change, and the regional and local climate
effects of human activities. The human impact on the cli-
mate includes the interdependence between evaporation (E)
and potential evaporation (E
p
) and the contribution from E
to the recycle of precipitation (P)[Brutsaert and Parlange,
1998; Roderick and Farquhar,2002;Szilagyi, 2007]. The
direct human-induced streamflow change is the alteration of
precipitation portioning into evaporation and runoff. On the
basis of historical data during the period of 1948–2003 for
413 gauge stations across the contiguous United States, the
climate-induced and direct human-induced changes of MAS
are quantified, and the quantification is based on a proposed
decomposition method in the Budyko framework. An order
of magnitude estimate of model uncertainty is obtained
through sensitivity analysis. The estimation of the direct
human impact is compared with independent data such as
population density, percent of urban, crop, and irrigated
lands, and storage of reservoirs. The spatial patterns of cli-
mate- and direct human-induced changes to streamflow are
analyzed and discussed. The results provide a comprehen-
sive view on the climate- and direct human-induced MAS
changes over the contiguous United States in the past
60 years.
2. Methodology
2.1. Budyko Curves
[
6] To quantify the relative contributions of climate and
direct human impacts on MAS, a hydrologic model is
needed to link both climatic forcing and human impact on
hydrological response. In this study, instead of applying a
detailed hydrologic model to over 400 watersheds, which
can be a very tedious exercise, a simple conceptual model
based on the Budyko hypothesis [Budyko, 1974] is used to
quantify the impact of climate and humans on MAS. Thus,
this study is focused on the long-term MAS change.
[
7] The water-energy balance at the watershed scale over
a long-term temporal scale describes the partitioning of pre-
cipitation into evaporation and runoff. Budyko [1958] postu-
lated that mean annual evaporation from a watershed could
be determined, to first order, from rainfall and net radiation.
On the basis of worldwide data on a large number of water-
sheds, Budyko [1974] demonstrated that the ratio of mean
annual evaporation to mean annual precipitation (E/P, evap-
oration ratio) is primarily controlled by the ratio of mean
annual potential evaporation to mean annual precipitation
(E
p
/P, climatic dryness index), as shown in Figure 1. For
watersheds with E
p
/P less than 1, the energy supply is the
limiting factor for evaporation, while for watersheds with
E
p
/P larger than 1, the water supply is the limiting factor.
Watersheds in different climatic regions fall at different
points along the Budyko curve depending on the values of
E
p
/P. Observations from real watersheds are scattered
around the Budyko curve because in addition to the dryness
index other factors can also affect the partitioning of mean
annual precipitation, such as soil water storage [Milly,
Figure 1. Budyko curve and diagram to show the direct
human and climate impacts on runoff coefficient (R ¼ Q/P).
W00J12 WANG AND HEJAZI: CLIMATE AND DIRECT HUMAN IMPACTS ON STREAMFLOW W00J12
2of16
1994], vegetation [Zhang et al., 2001; Donohue et al., 2007,
2010; Yang et al., 2009], infiltration capacity and slope
[Yang et al., 2007], and rainfall seasonality and characteristics
[Gerrits et al., 2009; Jothityangkoon and Sivapalan, 2009].
[
8] Many researchers have studied the mean annual
water balance and proposed different functional forms to
represent the Budyko hypothesis [Schreiber, 1904; Ol’de-
kop, 1911; Turc, 1954; Pike, 1964; Fu, 1981; Milly;
1993; Zhang et al., 2001; Sankarasubramanian and Vogel,
2002; Porporato et al., 2004; Yang et al., 2008]. The sensi-
tivity of various Budyko-type curves has been assessed by
other studies [e.g., Potter and Zhang, 2009]. In this paper,
the Fu [Fu, 1981] and Turc-Pike [Turc, 1954; Pike, 1964]
equations are used, and both of them are single-parameter
Budyko-type curves, as shown in Table 1.
2.2. Decomposition Method for Separating the
Climate and Direct Human Impacts on MAS Change
[
9] In this paper, the direct human impact represents the
change of precipitation partitioning given climate condi-
tions, and it does not include indirect human-induced cli-
mate change. The climate change represents the contribution
of mean annual potential evaporation and precipitation to
the streamflow change. As a result, in Figure 1 the move-
ment of a watershed along the horizontal direction (i.e., the
change of E
p
/P) is only driven by climate change or variabil-
ity. The movement of a watershed along the vertical direc-
tion can be driven by both climate change and direct human
impacts since human activities can affect runoff generation
and evaporation, and climate change can affect actual evap-
oration and precipitation. The challenge becomes how to
separate the effects of climate change and direct human
impact on the vertical movement.
[
10] The proposed decomposition method assumes that
for a watershed without direct human impact, if the climate
(E
p
/P) moves to a drier or wetter region because of climate
change, the evaporation ratio (E/P) will also change to a
new region but will still follow the same Budyko-type curve
as the prechange period. The rationale for this assumption is
based on the concept of geographic zonality; that is, at less
than the geological time scales, the soil and vegetation prop-
erties are dependent only on the long-term P and E
p
[Dooge,
1992]. The original Budyko hypothesis is that natural water-
sheds follow the Budyko curve [Budyko, 1974]. The catch-
ment properties, especially vegetation, will respond to
climate variability and change through evaporation [Jones,
2011]. Therefore, with the change of climate (i.e., E
p
/P), a
watershed will evolve to a new state (i.e., change of evapo-
ration ratio) but is still on the Budyko curve. Moreover, a
watershed can move along the Budyko-type curve because
of climate change only, and direct human interferences can
push the watershed to move on the vertical direction, i.e.,
change of E/P due to change of E. On the basis of this
assumption, vertical movement of the watershed from the
Budyko-type curve can be divided into climate- and direct
human-induced changes. As shown in Figure 1, there are
four possible movement directions for a watershed. If the
watershed moves to the top right corner, the climate and
direct human interferences affect the streamflow in the
same direction by decreasing the runoff coefficient (R ¼
Q/P); if the watershed moves to the bottom left corner, cli-
mate and humans cause increased and decreased runoff
coefficients, respectively.
[
11] The proposed decomposition method is described in
Figure 2. Suppose a watershed has shifted over time from
point A (prechange period) to point B (postchange period)
because of both climate change and direct human interfer-
ences (Figure 2). The dryness index and the evaporation ra-
tio in the prechange period are denoted as E
p1
/P
1
and E
1
/P
1
,
respectively. These two ratios are changed to E
p2
/P
2
and E
2
/
P
2
in the postchange period (point B). Under climate change
only, the watershed will evolve from (E
p1
/P
1
,E
1
/P
1
)to(E
p2
/
P
2
,E
2
=P
2
) along the Budyko-type curve (point C). Since the
climate at points B and C is same, the precipitation at point
CisP
2
. Thus, climate change causes both horizontal and
vertical shifts, i.e., from E
p1
/P
1
to E
p2
/P
2
on the horizontal
direction and from E
1
/P
1
to E
0
2
=P
2
on the vertical direction;
direct human interferences cause a vertical change from
E
0
2
=P
2
to E
2
/P
2
. For the case shown in Figure 2, the contri-
bution of the direct human impact counteracts the vertical
component attributed to the climate change impact, and the
overall vertical change caused by both climate and direct
human impacts is from E
1
/P
1
to E
2
/P
2
.
[
12] The climate change impact can induce both horizon-
tal and vertical components, and both components can affect
streamflow, but direct human interferences only can induce
a vertical component. Thus, the contribution of direct human
interferences to streamflow change is computed first. For
long-term annual average, the soil water storage change can
be ignored, and the streamflow is a function precipitation
and evaporation ratio:
Q ¼ Pð1 E=PÞ: ð1Þ
Table 1. Functional Forms of Two Budyko-Type Curves
Name of Model Functional Forms of Budyko-Type Curves
Fu
E
P
¼ 1 þ
E
p
P
1 þ
E
p
P
w
hi
1
=
w
Turc-Pike
E
P
¼ 1 þ
E
p
P
v
hi
1
=
v
Figure 2. Decomposition method to quantify the direct
human and climate contributions to the mean annual
streamflow change.
W00J12 WANG AND HEJAZI: CLIMATE AND DIRECT HUMAN IMPACTS ON STREAMFLOW W00J12
3of16
Similarly, the direct human contribution to streamflow
change can be computed by
Q
h
¼ P
2
ðE
0
2
=P
2
E
2
=P
2
Þ; ð2Þ
where Q
h
is the magnitude of the direct human-induced
change of streamflow. The climate change contribution to
streamflow change can be obtained by subtracting the
human-induced change from the total streamflow change:
Q
c
¼ Q Q
h
; ð3Þ
where Q
c
is the climate-induced change of streamflow.
Both Q
h
and Q
c
can be positive or negative. Q is the
total streamflow change and is computed by
Q ¼ Q
2
Q
1
: ð4Þ
[13] Given annual precipitation, streamflow, and poten-
tial evaporation data, the procedures for computing the con-
tribution of climate change and direct human interferences
to the MAS change are as follows.
[
14] 1. The mean annual evaporation is calculated by
assuming zero storage change, i.e., E
1
¼ P
1
– Q
1
and E
2
¼
P
2
– Q
2
. The mean annual values of E
1
/P
1
and E
p1
/P
1
for
the prechange period and E
2
/P
2
and E
p2
/P
2
for the post-
change period are computed.
[
15] 2. This study is focused on the change between the
two periods. The watersheds in the prechange period are
not natural. Thus, the prechange watersheds are not on the
same Budyko-type curve. Recall that the shapes of
Budyko-type curves depend on the physical properties of
watersheds, such as soil properties, vegetation type and
coverage, and topography [e.g., Milly, 1994; Zhang et al.,
2001; Yang et al., 2007; Yokoo et al., 2008]. Therefore, a
single-parameter Budyko-type curve is used, and the pa-
rameter is calibrated to the prechange period; that is, sepa-
rate Budyko curves are fitted for each watershed.
[
16] 3. The evaporation ratio due to climate change only
(E
0
2
=P
2
) is computed on the basis of the calibrated Budyko-
type curve in step 2 corresponding to the observed dryness
index under the postchange condition (E
p2
/P
2
). For the
Budyko curve that is fixed, E
1
/P
1
may not be on the curve
exactly, but E
0
2
=P
2
is assumed to be on the Budyko curve
corresponding to E
p2
/P
2
in the decomposition method.
[17] 4. The streamflow change due to direct human inter-
ferences is computed by equation (2).
[
18] 5. The climate-induced change of streamflow (Q
c
)
can be computed by equation (3). It can also be computed
directly from the postchange condition without direct
human interferences, i.e., Q
c
¼ Q
0
2
Q
1
. Given negligi-
ble storage change for mean annual water balance, Q
0
2
¼
P
2
E
0
2
¼ P
2
1
E
0
2
P
2
. Therefore, one obtains
Q
c
¼ P
2
ð1 E
0
2
=P
2
ÞQ
1
: ð5Þ
[19] Recently, several related studies have quantified the
climate and direct human contributions to the streamflow
change on the basis of the Budyko framework [Li et al.,
2007; Zhang et al.,2008;Ma et al.,2008;Zhao et al.,
2009]. In these studies, the climate contribution to the
streamflow change is computed by the sensitivity or elastic-
ity method, which is based on the perturbations in precipita-
tion and potential evaporation. The climate-induced change
on MAS is determined by
Q
c
¼ P þ E
p
; ð6Þ
where and are the sensitivity coefficients of streamflow
to precipitation and potential evaporation, respectively, i.e.,
¼ @Q
=@
P and ¼ @Q
@E
p
. The two sensitivity coeffi-
cients can be obtained by the partial derivatives on the ba-
sis of the functional form of Budyko curve. For example, if
Fu’s equation is used, ¼ P
w1
1
ðE
p1
w
þ P
w
1
Þ
ð1=wÞ1
and
¼ E
p1
w1
ðE
p1
w
þ P
w
1
Þ
ð1=wÞ1
1[Ma et al., 2008]; then
Q
c
¼ P
w1
1
ðE
w
p1
þ P
w
1
Þ
1
w
1
ðP
2
P
1
Þ
þ E
p1
w1
ðE
p1
w
þ P
w
1
Þ
1
w
1
1
hi
ðE
p2
E
p1
Þ:
ð7Þ
After computing Q
c
, the direct human impact is the dif-
ference between the total observed change in streamflow
and streamflow change attributed to climate change, i.e.,
Q
h
¼ Q Q
c
.
[
20] For the decomposition method, if Fu’s equation is
used, substituting Fu’s equation into equation (5), one obtains
Q
c
¼ðP
w
2
þ E
p2
w
Þ
1
w
E
p2
Q
1
: ð8Þ
The decomposition method treats the climate dryness index
as one component in equation (5), while in the sensitivity
method the individual sensitivities of precipitation and
potential evaporation to streamflow are computed separately.
Comparing equations (7) and (8) for the case of Fu’s equa-
tion, for the sensitivity method, Q
c
is a function of precipi-
tation and potential evaporation during prechange and
postchange periods, while for the decomposition method,
Q
c
is a function of streamflow during the prechange period
and the precipitation and potential evaporation during the
postchange period. It also should be noted that both direct
human and climate contributions to streamflow change can
be estimated independently in the decomposition method,
i.e., equations (2) and (5), respectively, while for the sensi-
tivity method, the direct human impact results from the re-
sidual after subtracting the climate impact.
2.3. Comparing the Results from the Decomposition
Method With Published Data
[
21] The climate- and direct human-induced percentage
changes of annual streamflow have been estimated for spe-
cific watersheds in several studies [Zhao et al., 2009; Wang
et al., 2009; Zhang et al., 2008; Ma et al., 2008; Li et al.,
2007] using the climate sensitivity method:
C ¼ 100ðQ
c
=QÞ;
H ¼ 100ðQ
h
=QÞ:
ð9Þ
The watersheds and their estimated climate (C) and direct
human (H) impacts on mean annual streamflows from these
studies are shown in Table 2. Both climate and direct
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