Spatial and temporal characteristics of
actual evapotranspiration over Haihe River
basin in China
Ge Gao, Chong-Yu Xu, Deliang Chen &
V. P. Singh
Stochastic Environmental Research
and Risk Assessment
ISSN 1436-3240
Volume 26
Number 5
Stoch Environ Res Risk Assess (2012)
26:655-669
DOI 10.1007/s00477-011-0525-1
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Stoch Environ Res Risk Assess (2012) 26:655–669
DOI 10.1007/s00477-011-0525-1
ORIGINAL PAPER
Spatial and temporal characteristics of actual evapotranspiration
over Haihe River basin in China
Ge Gao • Chong-Yu Xu • Deliang Chen
V. P. Singh
•
Published online: 7 October 2011
Springer-Verlag 2011
Abstract Spatial and temporal characteristics of actual
evapotranspiration over the Haihe River basin in China
during 1960–2002 are estimated using the complementary
relationship and the Thornthwaite water balance (WB)
approaches. Firstly, the long-term water balance equation is
used to validate and select the most suitable long-term
average annual actual evapotranspiration equations for nine
subbasins. Then, the most suitable method, the Pike equation, is used to calibrate parameters of the complementary
relationship models and the WB model at each station. The
results show that the advection aridity (AA) model more
closely estimates actual evapotranspiration than does the
Granger and Gray (GG) model especially considering the
annual and summer evapotranspiration when compared with
the WB model estimates. The results from the AA model and
the WB model are then used to analyze spatial and temporal
changing characteristics of the actual evapotranspiration
over the basin. The analysis shows that the annual actual
evapotranspirations during 1960–2002 exhibit similar
decreasing trends in most parts of the Haihe River basin for
the AA and WB models. Decreasing trends in annual precipitation and potential evapotranspiration, which directly
affect water supply and the energy available for actual
evapotranspiration respectively, jointly lead to the decrease
in actual evapotranspiration in the basin. A weakening of the
water cycle seems to have appeared, and as a consequence,
the water supply capacity has been on the decrease, aggravating water shortage and restricting sustainable social and
economic development in the region.
G. Gao (&)
Laboratory for Climate Studies, National Climate Center, China
Meteorological Administration, No. 46 Zhongguancun Nandajie,
Haidian, Beijing 100081, China
e-mail: gaoge@cma.gov.cn
Keywords Complementary relationship Thornthwaite
water balance model Actual evapotranspiration Trend Haihe River basin China
G. Gao D. Chen
Department of Earth Sciences, University of Gothenburg,
PO Box 460, 405 30 Gothenburg, Sweden
1 Introduction
C.-Y. Xu
Department of Geosciences, University of Oslo, Norway, Oslo
C.-Y. Xu
School of Geographic and Oceanographic Sciences,
Nanjing University, Nanjing 210093, China
V. P. Singh
Department of Biological and Agricultural Engineering,
Texas A & M University, College Station, TX, USA
V. P. Singh
Department of Civil & Environmental Engineering,
Texas A & M University, College Station, TX, USA
The Haihe River is one of the major rivers in China. Over
the past few decades shortage of water was a serious
problem, partly due to the rapid social and economic
development, and the problem was further aggravated by
climate change (Cui et al. 2009). In the recent 50 years,
annual precipitation in the Haihe River basin is found to be
decreasing (Ren et al. 2005; Wang et al. 2011a) as a result
of weakening summer monsoon (Wang et al. 2004). Runoff
in the basin also exhibits a steadily declining trend, which
was attributed to increased human activity and possibly
climate change (Ren et al. 2002; Liu et al. 2004; Yang and
Tian 2009; Zhang et al. 2011b). A significant decline in
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runoff is found in five of the eight sub-basins and abrupt
changes in runoff occurred in 1978–1985 for most of the
sub-basins (Yang and Tian 2009; Zhang et al. 2011b).
Because of the decreasing rainfall and persistent groundwater overexploitation, the water level declined in both
shallow and deep aquifers, and generally with the greatest
decrease in cities and intensively groundwater-irrigation
areas (Liu and Yu 2001). Groundwater depletion has
severely impacted the environment of the region (Liu and
Yu 2001; Xia et al. 2007).
Water management in river basins, based on evapotranspiration, has become a developing trend in arid and
semi-arid areas (e.g., Qin et al. 2009). Compared with
traditional management based on water supply and
demand, the main difference is that the utility of water
resource can be managed more efficiently through the
reduction of evapotranspiration for achieving the goal of
reducing overall regional water consumption. Evapotranspiration is a major consumer of water in the water cycle,
particularly in semi-arid regions like the Haihe River basin.
Reducing and controlling evapotranspiration will augment
water saving given the same amount of precipitation. For
management of evapotranspiration, accurate and reliable
estimation of actual evapotranspiration is crucial.
In hydrology and meteorology, direct observations of
actual evapotranspiration are rare, for they are difficult to
carry out on a large scale. Therefore, actual evapotranspiration is usually estimated using different methods. The Penman–Monteith method (Allen et al. 1998), considering
aerodynamic resistance and surface resistance, has been
successfully used to calculate actual evapotranspiration from
different land covers. However, the aerodynamic resistance
and surface resistance data are not readily available in practice. The method, where the water consumption of vegetation
is estimated as a fraction of a reference evapotranspiration,
depends on the accuracy of the reference chosen, reference
evapotranspiration estimation and crop coefficient (Rana and
Katerji 2000; Xu et al. 2006). Hydrological models estimate
actual evapotranspiration on a basin scale. However, lumped
models cannot provide detailed spatial variation patterns and
distributed models require the observation data for validating
the result may not be readily available. In recent years, remote
sensing data has been gradually used to estimate actual
evapotranspiration (Kustas and Norman 1996; Courault et al.
2003; El Haj El Tahir et al. 2011). The significant advantages
of the remote sensing based methods are high spatial and
temporal resolution and easy extrapolation to other sites
without measurements compared to the traditional methods
based on the ground measurements (Tsouni et al. 2008). But
the relatively long turn-around time for image delivery and
the cost involved with the acquisition of high-resolution
imagery are often unattractive for operational application
(Courault et al. 2003).
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Complementary relationship based evapotranspiration
calculation methods, proposed by Bouchet (1963), are
usually preferred, because they require only observations on
climate variables and bypass complex and poorly understood soil–plant processes (Hobbins et al. 2001; Xu and
Chen 2005). Different models have been developed in terms
of the complementary relationship concept, including the
advection-aridity (AA) model (Brutsaert and Stricker
1979), the GG model based on the relative evapotranspiration concept (Granger and Gray 1989), and the complementary relationship areal evapotranspiration (CRAE)
model proposed by Morton (1978, 1983). All of these
methods have been tested in different climate regions (e.g.,
Yang et al. 2009; Xu and Singh 2005; Qiu et al. 2004;Zhang
et al. 2011a; Wang et al. 2011b). One of the weaknesses of
the CRAE model is that it cannot be conceptually used for
short-time intervals because of the subsurface heat storage
changes and the lag time associated with the change in the
storage of heat and water vapour in the atmospheric
boundary layer (Doyle 1990; Xu and Li 2003). In this study,
the AA and GG methods will be compared and the one
which performs better will be used, together with the
Thornthwaite water balance approach (Gao et al. 2007), to
analyze trends in actual evapotranspiration.
Long-term trend in actual evapotranspiration is a useful
indicator of the changes in the water cycle and climate. The
change in the water cycle in the Haihe River basin plays an
important role for water resource management and planning, and has attracted much attention. However, so far
only a very few studies have been devoted to the role
played by actual evapotranspiration in the change of water
cycle in the Haihe River basin. Gao et al. (2007) used a
modified Thornthwaite water balance model to estimate
monthly actual evapotranspiration over China and investigated the trend in actual evapotranspiration during
1960–2002. Based on the Budyko method, Ni et al. (2007)
also found a significant decreasing trend in actual evapotranspiration in eastern China during 1951–2003. Van
Heerwaarden et al. (2010) showed the trend in actual
evpotranspiration can be inferred from data sets containing
pan evaporation, vapor pressure deficit and wind speed
which are interrelated due to land surface-atmosphere
feedbacks. One of their main conclusions is that an
increase in soil moisture leads to more actual evapotranspiration and less pan evaporation under all conditions.
These studies suggested that more detailed studies focusing
on a particular region would be needed using different
methods. Teuling et al. (2009) identified that the trends in
actual evapotranspiration can only be understood regionally (and temporally), by considering regional (and temporal) variations in the main drivers of evapotranspiration.
The objectives of this study are (1) to compare the
performance of different models (two complementary
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Stoch Environ Res Risk Assess (2012) 26:655–669
relationship approaches and the Thornthwaite water balance approach) for calculating regional evapotranspiration
for the Haihe River basin, which, to our knowledge, has not
been done before; (2) to evaluate temporal and spatial
variability of actual evapotranspiration in the basin; and (3)
to discuss implications of the estimated actual evapotranspiration changes for the water cycle in the region.
2 Study area and data
Located in the northern China, the Haihe River basin is
surrounded by Bohai Sea in the east, Taihang Mountain in
the west, Mongolia Plateau in the north and lower reaches
of Yellow River in the South (Fig. 1). The topography
decreases gradually from the plateau and mountainous
regions in northern and western parts to the plain region in
the eastern part (Fig. 1). In plateau and mountainous
regions, lands are mainly covered by shrubs, partly by
grasslands, meadow and one crop per year. In plain area,
two crops per year and three crops per 2 years are major
vegetations. The basin area is 31.8 9 104 Km2 and occupies 3.3% of the total area of China. Mountains and plateau
make up 60%, plain comprises 40% of the area (Zhu et al.
2010). There are three major rivers in this area, i.e., Haihe
River, Luanhe River and Tuhaimajia River.
657
Lying in a transition region between humid climate and
arid climate, the Haihe River basin belongs to the Temperate East Asia monsoon climate zone. The annual precipitation is not very abundant with uneven spatial and
temporal pattern. The annual precipitation varies from
371 mm in west to 771 mm in northeast mountains.
Affected by monsoon, precipitation is mainly concentrated
in summer in the form of rainstorms. In spring, drought
occurs frequently as a result of low precipitation, rapid
increase of temperature, more windy days and large
evapotranspiration. Spring drought constituents a great
threat to the production of winter wheat in this region (Yao
1969; Song et al. 2006).
The area covered by the basin is not only a political,
economic and cultural center with a high density of population, but also a key area for food and economic crop
production in China. It contains Beijing, Tianjin, parts of
Hebei, Shanxi, Shandong, Henan, and Liaoning provinces
as well as a small part of Inner Mongolia. Since the 1970s,
the conflict between water demand and supply has been
gradually increasing, along with the social and economical
development and climate change in the region.
The climate data used to the water balance estimation
were obtained from the National Meteorological Information Center of China Meteorological Administration. These
data included observed daily and monthly mean air
Fig. 1 The location and
topography of Haihe River
basin in China, and the
distribution of meteorological
stations and selected nine
subbasins in Haihe River basin.
The symbols ‘‘9’’ denote
stations at nine selected
subbasins which are listed in
Table 1 and ‘‘4’’ denote the
other meteorological stations
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temperature, maximum and minimum air temperature,
wind speed, sunshine duration, relative humidity and precipitation at 29 stations over the Haihe River basin during
1960–2002 (Fig. 1). During the study period the percentages of missing daily data for different elements varied
from 0.01% to 0.02%, except for the sunshine duration
which was 0.3%. The data were checked for two kinds of
potential errors, i.e., outliers and inconsistency. The outliers were identified by using the threshold value method,
and the consistency was checked by using the double mass
curve method (Dingman 2002). These tests show that the
data are homogenous and reliable at 5% significance level.
Long-term averaged annual runoff and basin average
precipitation data during 1956–1984 for nine subbasins of
the Haihe River basin were collected from the report of
Water Resource Assessment of North China by the Ministry of Water Resources. The nine subbasins are distributed evenly from south to north and meteorological stations
in these subbasins are shown in Fig. 1. General information
of these nine subbasins is shown in Table 1.
(3)
(4)
(5)
3 Methods
(6)
Evaluation methods consist of the following steps which
are described in the following sections:
(1)
(2)
The long-term average annual evapotranspiration for
the nine sub-basins is calculated using the long-term
water balance equation, which is used as ‘measured’
values and a reference to select the most suitable
equations used in step 2.
Long-term average annual values of actual evapotranspiration for each station are calculated using three
different methods (i.e., Schreiber 1904; Ol’dekop
1911; Pike 1964). The most suitable method, the one
having the minimum bias as compared with the values
calculated in step 1, is then used as a reference to
calibrate parameters of the complementary relationship models and the Thornthwaite water balance
model at each station. Among the two complementary
relationship evapotranspiration models, the one which
correctly estimates the annual total and summer
evapotranspiration is selected as the most suitable
complementary relationship model for the basin.
Daily actual evapotranspiration for each station is
calculated by the selected complementary relationship model, and monthly and annual values are
obtained by summing up the daily values.
The Thornthwaite water balance method is used to
calculate actual evapotranspiration for each station as
an alternative method to the complementary relationship model and the results are compared with that of
the selected complementary method in step 2.
The linear regression method and the Mann–Kendall
method (e.g., Fu et al. 2008) are used to calculate the
temporal trend of the actual evapotranspiration
calculated in steps (3) and (4).
The annual and seasonal actual evapotranspiration
values and the temporal trend in actual evapotranspiration are regionally mapped using the Cressman
(1959) interpolation method. There are many spatial
interpolation methods available in the literature and
each method has its own advantages and disadvantages depending on the variables to be interpolated
and on the regions, among others.
The selection of the Cressman method in the study is
twofolds, firstly, previous studies (e.g., Xia et al. 1999)
have shown that this method is one of the choices in
Table 1 Basic information of selected nine subbasins in Haihe River Basin
Name of nine subbasins
Stations
1. Plain between Zhanghe and Weihe Rivers
2
Area (km2)
9300
Elevation
range (m)
40–100
Land use
Crop
2. West plain of Fuyanghe River
1
7180
30–200
Crop
3. Plain between Hutuohe and Fuyanghe Rivers
2
8205
20–200
Crop
4. Plain located west to Baiyang Lake and south
to Daqinghe River
1
9504
10–200
Crop
5. Plain located east to Baiyang Lake and south
to Daqinghe River
2
11089
0–20
Crop
6. Plain of North branch of Haihe River
1
16232
0–100
Crop
7. Plain of Luanhe River and coast area in Hebei Province
3
7410
0–30
Crop
8. Mountain area of Yongdinghe River
3
45179
300–2000
Crop, shrubs
and grassland
9. Mountain area of Luanhe River
4
44070
100–2000
Shrubs and crop
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659
interpolating evaporation related parameters, and secondly,
the authors are experienced with this method which makes
it easier to check the correctness of the results.
3.1 Basin-wide long-term average annual actual
evapotranspiration
Actual evapotranspiration data are usually unavailable
because of the limited observations. However, long-term
average annual actual evapotranspiration over a basin can
be reliably estimated by the residual of observed basinwide long-term average annual precipitation and streamflow (see Eq. 1, Xu and Singh 2004; Özhan et al. 2010),
which are considered as ‘measured’ values to validate the
estimates of other methods:
AE ¼ P þ Q
ð1Þ
where P, AE and Q are the long-term average annual
precipitation, actual evapotranspiration and streamflow,
respectively. In this study, nine subbasins in the Haihe
River basin were selected to estimate long-term average
annual actual evapotranspiration.
3.2 Long-term average annual actual
evapotranspiration at stations
Three commonly used methods based on the relationships
between AE/PE and P/PE were used to estimate long-term
average annual actual evapotranspiration for each station,
namely Schreiber (1904), Ol’dekop (1911) and Pike
(1964), which are expressed, respectively, as
AE
P
PE
¼
1 exp ð2Þ
PE PE
P
AE
P
¼ tanh
ð3Þ
PE
PE
,sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ffi
AE
P
P
¼
1þ
ð4Þ
PE PE
PE
where AE and P are the same as in Eq. 1, PE is the longterm average annual potential evapotranspiration calculated by the Penman–Monteith equation (Chen et al.
2005).
In order to evaluate the accuracy of the three methods
and select the most suitable method for the study area, the
long-term average values calculated by the three methods
are compared with values calculated by the water balance
Eq. 1 in Sect. 3.1, the most suitable equation from Eqs. 2 to
4 is selected. The selected method is used to calibrate the
parameters of the complementary relationship methods and
WB model described in the following section.
3.3 Daily actual evapotranspiration estimations based
on complementary methods
The concept of complementary relationship, proposed by
Bouchet (1963) on the basis of empirical observations, states
that the actual evapotranspiration would reduce when a
region changed from a saturated condition to dry and
simultaneously an equal, but opposite, change in potential
evapotranspiration driven by a certain amount of the energy
release. The complementary relationship corrected the misconception that a larger potential evapotranspiration necessarily signifies a larger actual evapotranspiration (Granger
1989). The complementary relationship is described as
ETa þ ETP ¼ 2ETw
ð5Þ
where ETa, ETp and ETw are actual, potential and wet
environment evapotranspiration, respectively. ETa is usually calculated as a residual such as 2ETw ETp . Two of
the most widely used models AA and GG are applied to the
estimation of actual evapotranspiration in this study.
For AA model, ETwAA is calculated by the partial equilibrium evapotranspiration equation of Priestley and Taylor
(1972) and regulated to the following form introduced by
Xu and Singh (2005):
ETwAA ¼ a1 þ b1
D ðRn Gs Þ
Dþc
k
ð6Þ
where a1 represents the minimum energy available for
ETwAA ; b1 indicates the capacity of available energy
ðRn Gs Þ to transform latent heat (Eagleson 2002). Original parameters a1 ¼ 0; b1 ¼ 1:26 are not suitable for
many places in China (e.g., Yang et al. 2009; Xu and Singh
2005) and an underestimation of ETwAA is reported in the
seasons with low or negative net radiation. Rn is the net
radiation near the surface, Gs is soil heat flux, Gs/Rn usually
ranges from 0.05 to 0.3 depending on the time, soil moisture and thermal properties, vegetation amount and height
(Kustas et al. 1993), here Gs ¼ 0:2Rn ; k is the latent heat, D
is the slope of the saturation vapor pressure curve at the air
temperature, c is the psychometric constant, respectively.
Potential evapotranspiration ETpAA is calculated using the
equation introduced by Brutsaert and Stricker (1979).
Then the actual evapotranspiration was calculated as
ETaAA ¼ 2a1 þ ð2b1 1Þ
D ðRn Gs Þ
c
f ðUz Þðes
Dþc
k
Dþc
ea Þ
ð7Þ
where es and ea are the saturation vapor pressure and the
actual vapor pressure, f ðUz Þ is a function of the mean
wind speed at a reference level z above the ground,
i.e., f ðUz Þ f ðU2 Þ ¼ 0:26ð1 þ 0:54U2 Þ, where f ðU2 Þ is
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the same as f ðUz Þ but at 2 m elevation. The calculation
procedures of the above mentioned parameters are provided by Allen et al. (1998).
For GG model, Granger and Gray (GG) (1989) derived a
modified form of Penman’s equation for estimating the
actual evapotranspiration from different unsaturated land
covers:
ETaGG ¼
DG ðRn Gs Þ
cG
þ
Ea
DG þ c
k
DG þ c
ð8Þ
where G is a dimensionless relative evapotranspiration parameter, G ¼ ETa =ETp ; Ea ¼ f ðUz Þðes ea Þ. The
relationship between G and relative drying power D is
proposed by Xu and Singh (2005) which is modified from
Granger (1998):
G¼
1
þ 0:006D
a2 þ b2 e4:902D
D¼
Ea
Ea þ ðRn Gs Þ=k
ð9Þ
where a2 and b2 are considered as parameters to be calibrated in the study.
3.4 Monthly actual evapotranspiration estimated
by the Thornthwaite water balance model
The water balance model (WB) introduced by Thornthwaite and Mather (1955) is used to estimate monthly
actual evapotranspiration. Details on the procedure can be
seen in Gao et al. (2007). As compared with the complementary relationship models, the influence of soil water
content in addition to climatic factors can be reflected
dynamically, which is important in arid and semi-arid
regions and during the dry season in other climatic regions
for actual evapotranspiration.
3.5 Trend analysis and associated significance test
The slope of linear regression equation with actual
evapotranspiration as dependent variable and time as
independent variable was calculated and the rate of change,
mm/10a was determined. The Mann–Kendall trend test
(Mann 1945; Kendall and Gibbons 1990; Ziegler et al.
2003) was used to test the significance of the trend for
actual evapotranspiration. The rank-based Mann–Kendall
method is a nonparametric and commonly used to assess
the significance of monotonic trends in hydro-meteorological time series (Zhang et al. 2009). The procedure of
the test starts by simply comparing the most recent data
with earlier values. A score of ?1 is awarded if the most
recent value is larger, or a score of -1 is awarded if it is
smaller. The total score for the time-series data is the
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Mann–Kendall statistic, Z, which is then compared to a
critical value, Z1-a/2 (where a is significance level, and
Z1-a/2 is the Z value found in the standard normal distribution table), to test whether the trend in the data is significant by comparison the computed Z values with the
critical value of Z1-a/2. The advantages of the method are
not assuming any distribution form for the data and less
sensitive to outliers (Mann 1945). The significance level of
the test is 0.05.
4 Results
4.1 Calibration of parameters of the AA, GG and WB
models and verification
4.1.1 Selection of long-term actual evapotranspiration
equations
Figure 2 compares the estimated long-term averaged
annual actual evapotranspiration for the nine subbasins by
the three methods mentioned in Sect. 3.2 with the ‘measured’ value on basin scale by long-term average annual
water balance (mentioned in Sect. 3.1) during 1956 to
1984. For easy comparison, the point estimations of actual
evapotranspiration from the three methods and WB model
are averaged to get areal mean values for each subbasin.
The estimated long-term average annual actual evapotranspiration by the Pike method was between the results
by Schreiber and Ol’dekop methods, and was very close to
the ‘measured’ values with only 2.8% mean absolute relative errors for the nine subbasins. The Pike method was
chosen to estimate long-term average annual evapotranspiration for all stations in the Haihe River basin during
1956–1984 which was then used as the reference value to
calibrate the parameters of the AA, GG and WB methods.
The regional actual evapotranspiration estimated by WB
model with original parameters are about 10% greater than
‘measured’ values, which means that WB model also needs
to be calibrated in the region.
4.1.2 Calibration of parameters and verification
The original parameters of the AA, GG and WB models
were first used to calculate the actual evapotranspiration
and the results were compared with the Pike method. The
mean relative bias and absolute relative errors estimated
under original parameters are listed in the upper part of
Table 2. It is seen that using the original parameter values
the estimated long-term average annual evapotranspiration
by the AA, GG and WB models are 34.2%, 36.1% and
9.8% larger than the values by Pike method, respectively,
which shows that the original parameters are not suitable
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Long-term average annual actual
evapotranspiration during 1956-1984(mm)
Fig. 2 Comparison of
estimated regional long-term
averaged annual actual
evapotranspiration by Schreiber,
Ol’dekop, and Pike methods, by
monthly WB models with
original parameters and by longterm averaged annual
precipitation minus runoff at
nine subbains during 1956–1984
661
600
550
500
450
Schreiber
Ol'dekop
Pike
Precipitation-runoff
WB with original parameters
400
350
1
2
3
4
5
6
7
8
9
Subbasins
Table 2 Mean relative bias and absolute relative errors (%) of the
long-term averaged annual actual evapotranspiration estimated under
original parameters, calibrated parameters and verification conditions
of the AA, GG and WB models as compared with values calculated
by Pike model in the Haihe River basin
Periods
Models
Mean relative
bias (%)
Mean absolute
relative errors (%)
Original parameters
(1956–1984)
AA
34.2
34.2
GG
36.1
36.1
WB
9.8
9.8
AA
0.2
0.7
GG
0.1
0.4
WB
0.0
0.0
AA
3.6
7.4
GG
0.6
4.6
WB
1.9
2.6
Calibration
(1956–1984)
Verification
(1985–2000)
The calibration period is from 1956 to 1984. The verification period is
from 1985 to 2000
for the Haihe River basin, especially for the AA and GG
models.
Using the long-term mean annual actual evapotranspiration calculated by the Pike method as the reference data
the parameters in the three models are calibrated with trial
and error method and the parameters values gave smallest
errors are selected. For the AA model, the b1 value of 1.26
was replaced by a smaller value varying from 1 to 1.23 for
different stations and the value decreased with the increase
in the distance from the sea due to the impact of advection.
Similar findings have been reported by Yang et al. (2008).
A constant value of 0.15 mm/day was found for parameter
a1, which accounts for large scale advection during seasons
of low or negative net radiation and represents the minimum energy available for ETAA
w (Xu and Singh 2005). For
the GG model, the constant value 0.793 (Granger 1998)
was replaced by 0.8 and 0.20 was found varying from 0.23
to 0.58 for different stations and to have a positive relationship with the distance from coast to inland. In WB
model, two parameters are regulated, which are the soil
moisture content at field capacity and wilting point. As
mentioned above the main reason that we used Pike
method as the reference data for calibrating the parameters
of WB model, AA and GG models instead of directly using
the runoff data is because runoff is an areal averaged value,
while WB model, AA and GG models work on meteorological stations.
The calibration and verification results are also shown
in Table 2. Based on the modified parameter values, the
mean relative bias and absolute relative errors decrease to
0.2% and 0.7% for AA, to 0.1% and 0.4% for GG, and
to 0 for WB, respectively. The meteorological data from
the period of 1985–2000 was used for verification purposes. The mean relative bias and absolute relative errors
for the verification period were 3.6% and 7.4% for AA,
0.6% and 4.6% for GG, 1.9% and 2.6% for WB,
respectively. Generally, WB model are better than AA
and GG for the long-term annual actual evapotranspiration estimation.
4.2 Monthly variation of actual evapotranspiration
calculated by AA, GG and WB models
Figure 3 shows monthly variation of actual evapotranspiration averaged over 1960 to 2002 estimated by the AA,
GG and the WB models. For comparison purposes, mean
monthly values of precipitation are also shown in the figure. Long-term average actual evapotranspirations estimated by the three methods have a similar monthly
variation feature with maximum in summer and minimum
in winter. Comparing to WB, the mean absolute errors of
monthly long-term average actual evapotranspiration are
7.0 mm and 12.7 mm by the AA and GG models, respectively. From July to September, the actual evapotranspiration is about 16–25 mm underestimated by the GG model
as compared with WB. From February to May, about
10–23 mm overestimated. For AA model, 14–20 mm
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4.3 Seasonal and annual actual evapotranspiration
averaged over 1960–2002 estimated by the WB
and AA model
overestimated in May and June but 13 mm underestimated
in October. For the other months, the absolute errors are
less than 10 mm.
From Fig. 3 we can also see that, in spring the estimated
actual evapotranspiration is greater than precipitation. The
additional water used for evapotranspiration mainly comes
from soil water content. In this region, spring is the key
period when a large amount of water is required for crop
growth, drying soil would affect the growth of crops as a
result of large actual evapotranspiration. In July and
August, precipitation is obviously more than actual
evapotranspiration, the surplus of water is partly stored in
the soil. And this leads to more water supply and more
actual evapotranspiration in autumn than that in spring
from WB model. Generally speaking, the monthly variation of actual evapotranspiration is reasonable. For the
estimations of AA and GG, actual evapotranspiration are
more in spring than in autumn. It is because that monthly
change of water supply from soil are not directly considered by the AA model and GG model and the change of
actual evapotranspiration mainly depends on the change of
climate factors.
Based on the above analysis of Fig. 3, we can see that
when mean monthly actual evapotranspiration is concerned, the AA model produced more closely seasonal
variations as compared with that of WB model, and the
differences between GG and other two models are larger.
Therefore, in the rest of the paper only the actual evapotranspiration calculated by the AA model is selected as a
representative result of the complementary relationship
models. The similarity and differences of AA model with
WB estimations will be discussed in details.
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Actual evapotranspiration and precipitation(mm)
Fig. 3 Comparison of regional
mean monthly actual
evapotranspiration averaged
1960–2002 estimated by AA
(AA_ETa), GG (GG_ETa) and
WB (WB_ETa) as well as
precipitation (P)
Seasonal and annual actual evapotranspiration distributions
over the Haihe River basin are shown in Fig. 4 for the WB
model. The differences between the WB and AA estimations are shown in Fig. 5.
It is seen from Fig. 4e that for the annual actual
evapotranspiration estimated by the WB model, a high
center exceeding 540 mm is located in northeastern part of
the Haihe River basin and the maximum value is
572.7 mm. In east and south parts of the Haihe River basin
the actual evapotranspiration is between 460 and 540 mm.
Towards western and northern mountainous regions of the
Haihe River basin, the values decrease gradually, reaching
a minimum of 345.7 mm. A similar pattern is found for the
AA model estimation as can be seen from Fig. 5e that in
most regions the difference of the annual total actual
evapotranspiration is generally smaller than 20 mm except
in the south edge of the basin.
The spatial distribution of annual actual evapotranspiration is consistent with that of annual precipitation (Figure
is omitted). More actual evapotranspiration corresponds to
more precipitation which is a typical feature of semi-arid
climate. The correlation coefficient between long-term
mean annual actual evapotranspiration estimated by the
WB and AA models and precipitation are about 0.98 and
0.95, respectively.
The seasonal actual evapotranspirations estimated by
the WB model (Fig. 4a–d) exhibit different distribution
patterns in different seasons. Actual evapotranspiration in
160
WB_ETa
140
AA_ETa
GG_ETa
120
P
100
80
60
40
20
0
1
2
3
4
5
6
Month
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7
8
9
10
11
12
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Fig. 4 Distributions of seasonal
(Spring, Summer, Autumn,
Winter, a–d) and annual
(e) actual evapotranspiration
(mm) in the Haihe River basin
estimated by the WB model
averaged on 1960–2002
663
a
b
c
d
e
summer varies from 212.3 mm to 300.8 mm and occupies
57% of the yearly totals for the WB model. In spring, the
actual evapotranspiration varies from 52.2 mm to
122.8 mm and occupies 18% of the yearly totals. In autumn,
the actual evapotranspiration is greater than that in spring
and occupies 24% of yearly totals. This is because the soil
moisture are obviously wetter after wet summer than that in
spring and provide more water for evapotranspiration when
using the WB model. The highest value is found in the
northeast part and the value is about 140–150 mm, which is
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Fig. 5 Same as in Fig. 4 but for
differences (mm) between AA
and WB
Stoch Environ Res Risk Assess (2012) 26:655–669
a
b
c
d
e
gradually decreasing towards the north part and the minimum value is about 62.4 mm. In winter, the actual evapotranspiration in the region is very small, the maximum is
20.4 mm which is located in the south part. The distributions of autumn and spring have more similarities to annual
123
evapotranspiration than the other seasons with 0.95 and
0.91 correlation coefficient respectively.
The spatial distributions of seasonal actual evapotranspiration estimated by the AA model (Figures are omitted)
show similar patterns in general as compared with the WB
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665
model. But in spring, the actual evapotranspiration are
generally greater than that in autumn which are different to
WB model. As for the difference between the AA model
and the WB model, negative biases are dominant in autumn
(Fig. 5c) and positive biases are dominant in winter, spring
and summer (Fig. 5a, b, d).
4.4 Trends of actual evapotranspiration
during 1960–2002
The relation between annual actual evapotranspiration and
potential evapotranspiration along with change of annual
precipitation is a manifestation of the complementary relationship in Haihe River basin from the estimation by WB and
AA models (Figure that reveals the complementary relationship between potential and actual evapotranspiration is
omitted).
4.0
a
AA_ETa
WB_ETa
P
WB_SM
3.0
Standardized values
Fig. 6 Time series of
standardized annual actual
evapotranspiration by the AA
(AA_ETa) and WB (WB_ETa)
models as well as the annual
precipitation (P), annual mean
soil moisture (WB_SM) during
1960–2002 at Haihe River basin
(a) and their linear trends (b).
The significance level of 5% is
used
The standardized annual time series for actual evapotranspiration calculated by the AA and WB models, precipitation and the soil moisture averaged over the Haihe
River basin are shown in Fig. 6. Figure 6a shows that all
the four series correspond well with each other. Figure 6b
shows that although with different changing rates, all the
four series are decreasing simultaneously, meaning that in
this semi-arid region, both actual evapotranspiration and
soil moisture are dominated by precipitation. Among these
four series, declining trends of soil moisture is significant.
The sign and the changing rates of actual evapotranspiration, potential evapotranspiration, precipitation and soil
moisture are different in different seasons (Table 3). In
Haihe River Basin, climatic factors and water supply are two
controlling factors for the changes of seasonal and annual
actual evapotranspiration. The potential evapotranspiration
reflects energy available for evapotranspiration and is used
2.0
1.0
0.0
-1.0
-2.0
-3.0
1960
1965
1970
1975
1980
1985
1990
1995
2000
Year
1.0
b
AA_ETa
WB_ETa
P
WB_SM (Significant)
Linear trends
0.6
0.2
-0.2
-0.6
-1.0
1960
1965
1970
1975
1980
1985
1990
1995
2000
Year
Table 3 The change rates of seasonal and annual actual evapotranspiration (ETa ) estimated by the AA model and the WB model, potential
evapotranspiration (ETp ) estimated by AA, precipitation (P) and soil moisture (SM) estimated by WB at Haihe River Basin during 1960–2002
ETaAA
Spring
ETp
ETaWB
P
SM
2.6
-6.0*
-0.8
Summer
-6.6*
-8.2*
-6.0
-20.7*
1.4
-2.8
-1.2*
Autumn
-2.3*
-0.5
-5.5
-4.7
-3.3
Winter
0.1
-1.1
0.5
-0.3
-2.5*
Annual
-6.0
-11.7
-23.9
-2.4*
-16.4*
Unit is mm/10a. * The change rate is at 5% significant level
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to represent the combined effect of climatic factors including solar radiation, wind speed, humidity, and temperature.
The water supply is reflected directly by soil moisture content or indirectly by precipitation. It is seen in Table 3 that
Fig. 7 Distributions of
changing rates of seasonal
(Spring, Summer, Autumn,
Winter, a–d) and annual
(e) actual evapotranspiration
(mm/10a) in Haihe River basin
during 1960–2002 estimated by
AA. Triangles indicate stations
with significant trend at the 5%
significance level tested by
Mann–Kendall method
a
c
e
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both annual precipitation and potential evapotranspiration
show decreasing trends which will directly affect the water
supply and available energy for annual actual evapotranspiration. The two factors jointly lead to the decreasing actual
b
d
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evapotranspiration. Decreasing potential evapotranspiration
has explained by significant declining trends of wind speed
and solar radiation from Gao et al. (2006). From the changes
of precipitation and actual evapotranspiration, a weakening
feature of the water cycle is expected in the Haihe River
basin during 1960–2002, which further supports the viewpoint of Gao et al. (2007).
For illustrative purposes, spatial distributions of the
changing rates of seasonal and annual actual evapotranspiration calculated by the AA model in the Haihe River
basin are shown in Fig. 7a–e. In most areas of the Haihe
River basin, the annual actual evapotranspiration showed a
decreasing trend and the changing rate varied from
-5 mm/10a to -30 mm/10a (Fig. 7e), which has a trend
similar to those of previous studies (Gao et al. 2007; Ni
et al. 2007). In some areas at the northeast, southeast and
northwest parts, increasing trends are found with rates
being greater than 5 mm/10a. In spring (Fig. 7a), a slightly
increasing trend mainly occur in the northern and southeastern parts of the Haihe River basin as a result of the
increasing spring precipitation. Areas with negative trend
mainly located in the southwest part of the basin. In
summer and autumn, patterns in trends of actual evapotranspiration are similar to that in annual values with the
same decreasing characteristic (Fig. 7b–c). Over 2/3 stations have decreasing trends. In winter, the actual evapotranspiration increases mainly in the northeastern part and
some local stations (Fig. 7d). In the southwest and middle
areas decreasing trends are found. The trend distributions
of summer and spring have more similarities to the annual
evapotranspiration than the other seasons with 0.95 and
0.90 correlation coefficient respectively.
The index of annual precipitation minus actual evapotranspiration means the net water supply to land surface.
The long-term averaged annual net water supply during
two periods 1960–1979 and 1980–2002 are compared, and
the annual net water supply decreased about 61% and 41%
by AA and WB respectively during the second period. This
decreasing feature is consistent with the changes of runoff
in the area with decrements about 40–80% (Zhang et al.
2008).
5 Conclusions
In this study, two reference data, ‘measured’ long–term
averaged actual evapotranspiration based on water balance
model on a regional scale and climatological estimation
based on the relationship between AE/PE and P/PE by
three classical methods at stations, are used for parameter
calibration and verification of the two complementary
relationship models and WB model. Temporal and spatial
variations of the actual evapotranspirations estimated by
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the AA, GG and WB models are analyzed in the Haihe
River basin. The following conclusions can be drawn:
•
•
•
•
In the Haihe River basin, the results by the AA model
are better than those by the GG model considering
annual and summer months estimations as compared to
the WB model.
Annual actual evapotranspirations averaged over
1960–2002 in western and northern mountainous
regions are smaller than those in northeastern part of
the Haihe River basin. Seasonal values are maximum in
summer and minimum in winter. In spring, the values
are higher than that in autumn for AA but opposite for
WB. This is because the AA model based on the concept
of complementary relationship between actual and
potential evapotranspiration does not consider the effect
of the soil moisture which is wetter autumn than that in
spring and provides more water for evapotranspiration
when using the WB model.The estimation of seasonal
actual evapotranspiration by the AA model is higher in
summer, spring and winter, and smaller in autumn
comparing to those of the WB model estimations.
Annual actual evapotranspiration from the AA model
based on complementary relationship and WB of water
balance approach exhibits similar decreasing trends in
most parts of the Haihe River basin during 1960–2002.
Decreasing trends in annual precipitation and potential
evapotranspiration directly affect the water supply and
available energy, respectively. These decreasing trends
jointly lead to a decreasing trend in actual evapotranspiration in the region.
Similar decreasing trends found in precipitation and soil
moisture, potential and actual evapotranspiration affect
the water cycle in the Haihe River basin during 1960 to
2002. Water resources also exhibit decreasing trend.
Under the condition of increasing water demand as the
result of social economic development, which will further
aggregate the problem of water shortage in the region.
Acknowledgments This research is supported by 973 National
Project in China—Mechanism research to water cycle evolution and
high effective utilization of water resources in Haihe River Basin
(2006CB403404), the Ministry of Water Resources’ special funds for
scientific research on public causes, (No. 200901042), the Key Project
of the Natural Science Foundation of China (No. 40730632), and the
Program of Introducing Talents of Discipline to Universities—the 111
Project of Hohai University. We also would like to thank Dr. Shuiqing Yin, Mr.Tinghai Ou and Ms. Yumei Hu, for their helps on
geographic information to make the figures.
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