Quaternary International 208 (2009) 129–137
Contents lists available at ScienceDirect
Quaternary International
journal homepage: www.elsevier.com/locate/quaint
Regionalization study of a conceptual hydrological model in Dongjiang basin,
south China
Xiaoli Jin a, b, *, Chong-yu Xu c, Qi Zhang a, Yongqin David Chen d
a
State Key Laboratory of Lake Science and Environment, Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, No. 73, East Beijing Road,
Nanjing, Jiangsu 210008, China
b
Graduate School of the Chinese Academy of Sciences, Beijing, China
c
Department of Geosciences, University of Oslo, Norway
d
Department of Geography and Resource Management, Chinese University of Hong Kong, Hong Kong, China
a r t i c l e i n f o
a b s t r a c t
Article history:
Available online 25 September 2008
Predicting hydrological variables in ungauged catchments has been singled out as one of the major issues
in the hydrological sciences. In this study, the conceptual rainfall-runoff model, HBV, was applied to
Dongjiang basin and its 13 sub-basins for the purposes of examining the applicability of this well-known
model in south China and exploring the possibility of transferring the calibrated parameter values to
ungauged basins. For testing the applicability of the model in gauged basins, the model was calibrated for
a period of 1978–1983 and validated for a period of 1984–1988. For testing the transferability of
parameter values to ungauged basins, two parameter regionalization methods – proxy-basins and global
mean – were investigated. The results showed that: 1) the HBV model worked well in the Dongjiang
basin with the average indexes of agreement (D) and coefficient of efficiency (ME), respectively, equal to
0.79 and 0.82 in the calibration period, and 0.76 and 0.78 in the validation period; 2) transferring the
parameter values from basins that passed the cross-basin test with higher ME values to the hypothetical
ungauged catchments produced acceptable results with an average ME value equals to 0.72; 3) compared
with the proxy-basin method of parameter estimation, the model produced equally good results for the
global mean method with an average ME value equals to 0.74 when using simple arithmetic mean values.
Neither the area weighted mean method nor the Thiessen polygon method produced regional parameter
values could markedly improve the accuracy of modeling results. It was concluded that both regionalization methods could effectively estimate parameters for ungauged catchments in the Dongjiang basin,
and similar model performances were obtained.
Ó 2008 Elsevier Ltd and INQUA. All rights reserved.
1. Introduction
During the past decades, the study of hydrologic responses to
global climate change and the assessment of water resources at
large scales have placed much more emphasis on macro-scale
hydrological modeling (MHM). Following Arnell (1993, 1999), there
are at least four reasons why hydrologists have become interested
in modeling at such scales. First, for operational and planning
purposes, water resource managers need to estimate the spatial
variability of water resources over the regions for which they are
responsible, at a spatial resolution finer than can be provided by
observations alone. Second, hydrologists and water managers are
concerned about the effects of land-use changes and climate
* Corresponding author. State Key Laboratory of Lake Science and Environment,
Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, No.
73, East Beijing Road, Nanjing, Jiangsu 210008, China. Tel.: þ86 025 86882096.
E-mail address: yezi1612@hotmail.com (X. Jin).
1040-6182/$ – see front matter Ó 2008 Elsevier Ltd and INQUA. All rights reserved.
doi:10.1016/j.quaint.2008.08.006
variability over large geographic domains. Third, hydrological
models are useful in estimating point and non-point sources of
pollutant loading to streams. Fourth, hydrologists and atmospheric
modelers are aware of weaknesses in the representation of
hydrological processes in regional and global climate models.
Regional data for direct estimation of the hydrologic parameters of
MHM schemes are, however, virtually nonexistent. On the other
hand, predicting hydrological variables in ungauged catchments
has been singled out as one of the major issues in the hydrological
sciences (Sivapalan et al., 2003). Application of hydrological models
for prediction in ungauged basins is fraught with difficulties due to
the lack of data needed for model calibration and verification.
Parameter estimation for either large scale models or modeling of
ungauged basins, therefore, involves partly or totally transferring
parameters from small basins or gauged basins, or inferring from
physical characteristics of the area of interest.
Regionalization can be defined as the transfer of information
from one catchment to another (Bloschl and Sivapalan, 1995). This
transfer is typically from gauged to ungauged catchments (e.g.
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X. Jin et al. / Quaternary International 208 (2009) 129–137
Riggs, 1972; Mosley, 1981). Its aim is to estimate parameter values
of hydrological models for any/every grid cell, sub-catchment or
large geographic region without a need for calibration or ‘‘tune’’ the
model to get the best fit (Xu, 2003).
‘‘Regionalization of the parameters of rainfall-runoff models is
not an easy task’’ as was pointed by Abdulla and Lettenmaier
(1997). Parameterisation of conceptual models has received
increasing attention from the hydrology and land-surfacemodeling communities. Prediction in Ungauged Basins (PUB) was
identified as a key issue in hydrological studies by IAHS (http://
serv2.cee.yamanashi.ac.jp/iahs/2000/200310.month/116_3.doc).
Many attempts have been made, including: 1) proxy-basin
method (Klemes, 1986; Xu, 1999a), 2) spatial interpolation
method, for instance, linear interpolation by Guo et al. (2001),
kriging interpolation by Vandewiele and Elias (1995), etc., 3)
clustering approach (Burn and Boorman, 1993; Huang et al.,
2003), 4) bi- and multivariate regression method (Abdulla and
Lettenmaier, 1997; Seibert, 1999; Xu, 1999b; Muller-Wohlfeil
et al., 2003), 5) one step regression – regional calibration
(Fernandez et al., 2000). Among those, the regression method is
one of the earliest and most often tried methods, in which
parameters for ungauged basins are determined by regression
equations developed between the optimized parameters and
catchment attributes in a set of gauged basins. However, two
major limitations are presented. First, parameters may be poorly
determined and strongly interrelated, hence unstable (e.g.
Kuczera, 1983). Second, some parameters may not be well
estimated by regional relationships due to the poor correlation
between parameter values and physically measurable quantities
(Abdulla and Lettenmaier, 1997). Though Hundecha and
Bardossy (2004) and Gotzinger and Bardossy (2006) initially
defined a prior for regression functions and then calibrated
parameters of the regression functions instead of model
parameters themselves in order to avoid the first limitation, the
prior regression function couldn’t be justified and the second
limitation was far from being solved. Braun and Renner (1992)
applied the HBV model to five catchments in different parts of
Switzerland and concluded that there were no relationships
between catchments characteristics and model parameters.
Similarly, Johansson (1994) studied relationships between
parameter values and 12 catchments characteristics in 11
catchments in southern Sweden, but found only one parameter
had a clear relationship with physical data.
Recently, some studies applied two or more regionalization
methods which did enable comparisons among them. Vandewiele
and Elias (1995) and Merz and Bloschl (2004) found that kriging led
to an improvement over multivariate regression for estimation of
parameters of monthly water balance models at ungauged sites.
Kokkonen et al. (2003) concluded that: ‘‘when there is a reason to
believe that, in the sense of hydrological behaviour, a gauged
catchment resembles the ungauged catchment, then it may be
worthwhile to adopt the entire set of calibrated parameters from
the gauged catchment instead of deriving quantitative relationships between catchment descriptors and model parameters’’. One
important finding by Merz and Bloschl (2004) was that the
methods based on spatial proximity alone performed significantly
better than any of the regression methods based on catchment
attributes. A similar conclusion was drawn by Parajka et al. (2005)
after the examination of 7 regionalization methods. The above
literature review reveals that there is no universal method existing
at this time that performs best in all the cases studied. It is therefore
appropriate to continue the research in different regions.
In this study, the conceptual rainfall-runoff model, HBV (Bergström, 1995), was applied to Dongjiang basin and its 13 sub-basins
with the following objectives: (1) examining the applicability of
this well-known model in south China, and (2) exploring the
possibility of transferring the calibrated parameter values to
ungauged basins. While a regionalization study is increasingly done
for PUB or macro-scale hydrological models, this research has not
attracted enough attention among Chinese researchers and no such
study has been reported in the Pearl River basin in south China. This
study will not only contribute to filling such a knowledge gap in this
aspect, but also produce valuable results for water resources
assessment in the region. From the point view of water resource
management, the water exported from Dongjiang to Hong Kong
accounted for 8.3% of Hong Kong’s annual water supply in 1960,
and this figure has increased to 70% or over 80% in recent years. This
study will certainly bring many benefits to accurate predictions of
regional water resources amount, which is crucial for the optimization of water allocation and planning in this region.
This paper is organized as follows: after this brief introduction,
the study area and data are described in Section 2. The subsequent
section presents the HBV model structure and model calibration and
validation results. The regionalization methodologies and results are
discussed in Sections 4 and 5, and finally, the conclusions and
proposal for further investigations are presented in Section 6.
2. Study area and data
The study area is the Dongjiang (East River) basin (see Fig. 1),
a tributary of the Pearl River (Zhujiang) in southern China. The
Dongjiang basin is located in the Guangdong and Jiangxi provinces.
Originating in the Xunwu county of Jiangxi province, the river flows
from north-east to south-west and discharges into the Zhujiang
(the Pearl River) estuary with a drainage area of 25,555 km2
(upstream area of Boluo gauge station) and an average gradient of
0.39%. The landscape is characterized by hills and plains,
accounting for 78.1% and 14.4% of the basin area, respectively.
Forest covers upper elevations and intensive cultivation dominates
hills and plains.
The Dongjiang basin has a sub-tropical climate with a mean
annual temperature of about 21 C, with only occasional incidents of
winter daily air temperature dropping below 0 C in the mountainous areas of the upper stream region. The average annual rainfall
for the period of 1960–1988 is 1747 mm, and the average annual
runoff is 935 mm, roughly 54% of the annual rainfall. Precipitation is
generated mainly from two types of storms: frontal type and
typhoon-type rainfalls. There are large seasonal changes in rainfall
and runoff in the catchment: about 80% of the annual rainfall and
runoff occurs in the wet season from April to September, and about
20% occurs during the dry period of October to March.
This study not only covers the whole Dongijang basin, but also
includes 13 natural sub-basins with discharge observations. Independent or nested, these sub-basins, with areas ranging from less
than a hundred to more than 1000 km2, are almost evenly
distributed over the whole basin. Precipitation data from 51
stations, air temperature and evaporation data from 8 and 5
stations, respectively, have been used. Furthermore, the model was
calibrated against observed discharge at 14 gauges. All the data
were used for the period of 1978–1988, excepting for Dongkeng
and Honghuata sub-basins (1978–1980) due to the deficiency of
discharge records. Therefore, these two sub-basins were not used in
calculating regional parameters values; instead, they were used as
independent basins to verify the regionalization methods.
3. Model structure and model calibration and validation
A Windows-version (Seibert, 1998) of the lumped conceptual
rainfall-runoff model, originally developed by the Swedish Meteorological and Hydrological Institute, the HBV model (Bergström,
1976) was used. The basic equations are in accordance with the
SMHI-version HBV-6 (Bergström, 1995) with two minor changes.
X. Jin et al. / Quaternary International 208 (2009) 129–137
131
Fig. 1. Dongjiang basin and its sub-basins.
The model runs on a daily time step and consist of a snow routine,
a soil moisture routine, a response routine and a routing routine.
The snow routine represents snow accumulation and melt by
a simple degree-day concept (Eqs. (1) and (2)).
melt ¼ CFMAXðTðtÞ TTÞ
(1)
refreezing ¼ CFR CFMAXðTT TðtÞÞ
(2)
where melt is the amount of melt water, CFMAX is the degree-day
factor, T(t) is the mean daily air temperature, and TT is the
temperature threshold value. Refreezing again of melt water within
the snowpack is corrected by CFR.
The soil moisture routine represents runoff generation and
changes in the soil moisture state of the catchment. The contribution DR of rain and snowmelt to runoff is calculated as a function of
soil moisture using a non-linear relationship with two free
parameters, FC and BETA (Eq. (3)). Actual evaporation, Eact, is
calculated from potential evaporation, Epot, by a piecewise linear
function of soil moisture, SM(t) (Eq. (4)).
SMðtÞ BETA
¼
PðtÞ
FC
DR
Eact ¼ Epot min
SMðtÞ
;1
FC$LP
(3)
(4)
where P(t) is the sum of daily rainfall and snowmelt, SM(t) and FC
are actual and maximum soil moisture storage, respectively, BETA
controls the characteristics of runoff generation and is a non-linearity parameter, and LP is a parameter termed the limit for potential
evaporation.
In the response routine, three runoff components are computed
from two reservoirs, denoting two soil zones (Eq. (5)). The storage
states of the upper and lower zones are SUZ and SLZ, respectively.
DR enters the upper zone reservoir and leaves this reservoir
through three paths, outflow from the reservoir with a fast storage
coefficient of K1, percolation to the lower zone with a constant
percolation rate, and if a threshold UZL of the storage state is
exceeded, an additional outlet with a storage coefficient of K0 is
calculated. Water leaves the lower zone with a slow storage coefficient of K2. In the routing routine, the outflow from both reservoirs, QGM(t) is then routed by a triangular weighting transfer
function with free parameter MAXBAS, which calculates runoff
routing in the streams, Qsim(t).
QGW ðtÞ ¼ K2 SLZ þ K1 SUZ þ K0 maxðSUZ UZL; 0Þ
Q sim ðtÞ ¼
¼
MAXBAS
X
cðiÞQGW ðt i þ 1Þ;
where cðiÞ
i¼1
2
MAXBAS
4
u MAXBAS2 du
2
i1 MAXBAS
Z
(5)
i
(6)
More details about HBV model can be found in Bergström (1995),
Seibert (1998) and Hundecha (2005).
The HBV model was developed based on North European
hydrological environment and has been widely used in many
countries other than China, especially in southern tropical zone of
it. Therefore, the model’s applicability in the study area has to be
examined before regionalization. As mentioned before, the Dongjiang basin has a sub-tropical climate with a mean annual
temperature of about 21 C and only occasional incidents of winter
daily air temperature dropping below 0 C in the mountainous
areas of the upper basin. As a consequence, the snow routine has
been excluded from the model structure in this study, i.e. with all
precipitation being considered as rainfall.
Before model calibration was performed, parameter sensitivity
analysis was done for the whole Dongjiang basin (see Fig. 2). The
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X. Jin et al. / Quaternary International 208 (2009) 129–137
termed here the modified index of agreement D (Legates and
McCabe, 1999), given by Eq. (8), was also adopted.
0.81 ME
0.815
MAXBAS
P
jQobs Qsim j
D ¼ 1 P
Q sim Q 0 þ Q Q 0 obs
obs
obs
0.82
LP
BETA
0.825
PERC
0.83
K1
0.835
FC
0.84
K2
0.845
0.85
UZL
0.855
K0
0.86
-5
0
-30 -25 -20 -15 -10
5
10
15
20
25
30
a – ãi
(%)
ãi
Fig. 2. Parameters sensitivity analysis. The x-axis shows the percentage of relative
deviation of the parameter values from their optimized values and the y-axis shows
~i ¼ optimized parameter value,
the change of the criterion function (ME) value (a
ai ¼ any parameter value; in the legend, parameter names are arranged from high to
low sensitivity).
results show that the most sensitive parameter is MAXBAS, which
determines the hydrogragh’s smoothness and physically depends
on the basin size; the most non-sensitive parameter is K0, which is
pertinent to peaks’ recession slope and is controlled by basins’ land
covering characteristics.
For the whole basin and 13 sub-basins, we optimized 9 model
parameters by the procedure imbedded in the model program
starting with the most sensitive ones. The time step involved is in
days. The model was calibrated for the period of 1978–1983, and
validated for the period of 1984–1988. It is a common practice to
employ some criteria to evaluate model performance. Among many
goodness-of-fit indicators for model evaluation, the coefficient of
efficiency ME has been widely used. Nash and Sutcliffe (1970)
defined the coefficient of efficiency (Eq. (7)) which ranges from
minus infinity to 1.0, with higher values indicating better agreement as
P
ðQ Q sim Þ2
ME ¼ 1 P obs
2
Qobs Qobs
(7)
where Qobs and Q sim represent observed and simulated discharges,
and Q obs is observed mean value. Physically, ME is the ratio of the
mean square error to the variance in the observed discharges,
subtracted from unity. Thus the value of ME represents the extent to
which the simulated is a better predictor than the observed mean.
This measure is sensitive to differences in the observed and model
simulated means and variance, however, because of the squared
differences, it is overly sensitive to extreme values. More importantly, the equation ignores seasonal variation which is particularly
strong in the basins selected. Consequently, another measure,
(8)
0 is the baseline value of the time series against which the
where Qobs
model is to be compared. The baseline values used in this paper
were mean discharges of wet season (from April to September) and
dry season (the remaining months). This index varies from 0.0 to
1.0, with higher values indicating better agreement, and describes
the proportion of the seasonal variability in the observed data that
can be explained by the model.
Statistical comparisons and visual comparisons of observed and
simulated values were conducted to evaluate the performance of
the HBV model. Table 1 gives the D and ME values for both Dongjiang basin and its sub-basins in calibration and validation. It is seen
that all the D and ME values are above 0.6. There is no strong
relationship between catchment area and D or ME, that is, larger
catchments don’t necessarily obtain higher values of D or ME than
smaller catchments do. The D and ME values for sub-basins are
averaged at 0.79 and 0.82, respectively, in the calibration period,
and for the validation period they are 0.76 and 0.78, respectively.
The index of agreement (D) of 0.76 means that the model explains
76% of the seasonal variability in the observations, and the value of
0.78 for ME indicates that the mean square error is 22% of the
variance in the observed data. For visual comparison, daily and
monthly values of both simulated and observed runoff, as well as
areal precipitation for both calibration and validation, were plotted
in Figs. 3 and 4 (Only one example of Boluo station representing the
whole basin was shown for illustrative purpose.). There is a good
agreement between calculated and measured runoff, and variations
of the simulation are consistent with those of precipitation,
whatever for the whole basin or sub-basins. It is indicated that HBV
model, ignoring snow routine, can be applicable for modeling of
daily stream-flow process in Dongjiang basin characterized by
a sub-tropical climate.
4. Regionalization methodologies
To provide an easily applicable methodology for use in the
region, two simple regionalization methods have been investigated
in this study, namely proxy-basin method and global mean method.
The calibration before regionalization involved all the data series
used.
4.1. Proxy-basins method
The proxy-basin method, perhaps one of the oldest and most
widely used methods, involves firstly cross-checking parameters’
transferability over two gauged basins in the interested region and
then directly applying them to ungauged basins in the same region.
Table 1
Simulation results of HBV model in Dongjiang basin and its sub-basins.
Name
Area (km2)
Dongkeng
Honghuat
Jiuzhou
Lantang
Lianping
Lizhangf
Pingshan
849
455
385
1080
37.2
1400
2091
Calibration
Validation
D
ME
D
ME
0.80
0.76
0.77
0.79
0.82
0.81
0.85
0.80
0.77
0.90
0.86
0.86
0.82
0.90
0.85
0.71
0.75
0.79
0.79
0.79
0.73
0.97
0.62
0.80
0.84
0.84
0.75
0.77
Name
Area (km2)
Calibration
D
ME
D
ME
Shengqian
Shuibei
Shuntian
Taoxi
Xingfeng
Yuecheng
Dongjiang
684
987
1357
1306
42.6
531
25,555
0.79
0.80
0.83
0.79
0.73
0.79
0.79
0.75
0.77
0.88
0.76
0.76
0.82
0.87
0.74
0.79
0.81
0.76
0.65
0.76
0.74
0.60
0.80
0.89
0.77
0.60
0.79
0.83
Validation
X. Jin et al. / Quaternary International 208 (2009) 129–137
133
31
10
30
26
70
precipitation
simulation
observation
16
90
110
11
precipitation (mm)
Discharge (mm)
50
21
130
6
150
1
/78
01
01/
/79
01
01/
/80
01
01/
/80
31
12/
/81
31
12/
/82
31
12/
/83
31
12/
/84
30
12/
/85
30
12/
/86
30
12/
/87
30
12/
170
/88
29
12/
Date (Day/Month/Year)
Calibration
Validation
Fig. 3. Simulated and observed daily runoff and daily precipitation at Boluo station.
4.2. Global mean method
In the global mean method, three different sets of regional mean
parameter values were constructed. First, we calculated arithmetic
mean value of each parameter from all the calibrated values in subbasins and applied this parameter set to all the sub-basins and the
whole Dongjiang basin. In doing the test, we used the parameter
values from all the sub-basins and did not leave out some basins for
‘‘independent test basins’’, and the reason is the number of basins is
not large. The rationale behind this method is that in conceptual
hydrological models catchment’s physical attributes are represented by parameters and so the average attributes by mean
parameters. Merz and Bloschl (2004) found that using global
average values of parameters for all catchments led to the poorest
regionalization results for their analysis of 308 catchments in
Austria. One of the reasons for the poor performance of the method,
500
50
440
150
380
250
350
320
Precipitation
Simulation
Observation
260
200
450
550
650
140
750
80
850
19
78
19 /01
78
19 /07
79
19 /01
79
19 /07
80
19 /01
80
19 /07
81
19 /01
81
19 /07
82
19 /01
82
19 /07
83
19 /01
83
19 /07
84
19 /01
84
19 /07
85
19 /01
85
19 /07
86
19 /01
86
19 /07
87
19 /01
87
19 /07
88
19 /01
88
/0
7
20
Time (Year/Month)
Calibration
Validation
Fig. 4. Simulated and observed monthly runoff and monthly precipitation at Boluo station.
Precipitation (mm)
Discharge (mm)
The rationale behind this method is that in a hydrologically and
climatically homogeneous regime based on spatial proximity, as
climate and catchments conditions only vary smoothly over space,
one would expect the parameters of basins in the region to be
similar. To examine the transferability, cross-basin test (also
referred to as proxy-basin test), i.e. the parameter set calibrated on
one basin should be validated on another and vice versa, was performed. Only if both proxy-basin tests provide acceptable results
should one consider the model as geographically transferable
(Klemes, 1986).
Cross-basin tests between upstream sub-basins and downstream sub-basins have been done in order that the selected
parameter sets were transferable across the whole Dongjiang basin.
Subsequently, the parameter sets gaining best performance were
directly used as parameter estimation for hypothetical ungauged
sub-basins in the region.
134
X. Jin et al. / Quaternary International 208 (2009) 129–137
as Merz and Bloschl (2004) reported, is that the research was done
in a hydrologically heterogeneous region. In this study we
concentrated on a relatively small, geographically fairly homogeneous region and averaged parameters slightly deviated from
calibrated parameters; therefore, global mean method was
considered as worthwhile to investigate. As arithmetic mean
method took no account of the area and position of sub-basins, two
alternative methods were also included in this paper.
In the second method, the size of the basins was taken into
account in calculating the mean parameter values. Sub-basins with
large area contain more basin attribute information than small ones
and hence should be highlighted in averaging parameters. Based on
this, a set of weighted average parameters, termed ‘‘area weighted
mean values’’, was constructed, where weights of calibrated subbasins parameters were determined according to their area
respectively.
Similarly, a third set of mean values was formed by interpolation
with regard to sub-basins’ position and density. The Thiessen
interpolation method was selected to determine the weight of each
sub-basin, and then parameters were averaged over the whole
region, in which parameters of sub-basins distributed in a regional
center or in a sparse area had stronger effects on mean values than
those of sub-basins distributed in a regional margin or in a dense
area. We called this set of values as ‘‘Thiessen interpolated mean
values’’ for short.
4.3. Quality measures of regionalization performance
The two aforementioned measures have their own advantages
and disadvantages. When several models are compared, it is
appropriate to take a comprehensive measure to both assess the
goodness-of-fit and reflect the seasonal variation. Therefore, in
cross-basins tests, a combined measure, which allows for the
combination of two different objective functions, has been defined
as below. The combined measure (Eq. (9)) is the product of D and
ME, and value 1 means a perfect fit.
F ¼ D*ME
(9)
When a pair of sub-basins’ calibrated parameter sets is chosen
to transfer into several other ‘‘ungauged’’ sub-basins, usually
a minimum error will be used to assess the regionalization
performance. However, for ‘‘ungauged’’ sub-basins, observation
error and model structure error, etc. can also lead to poor fit in
calibration and subsequently affect the results of parameter
regionalization. For eliminating these effects, efficiency losses (EL)
which are the differences between calibration criteria and parameter transfer criteria, have been proposed. Efficiency losses are
always positive, and consist of D-loss and ME-loss. Large losses in
the criteria suggest poor transfer performances.
5. Results
5.1. Proxy-basin method
The results of cross-basin tests between upstream and downstream sub-basins are shown in Tables 2 and 3. In Table 2, parameters were calibrated in the downstream sub-basins and validated
in the upstream sub-basins. The F-values from transferring the
parameter sets of Jiuzhou and Lantang sub-basins are higher than
those from Pingshan sub-basin. When the upstream sub-basin
calibrated parameters were validated in the downstream subbasins (Table 3), smaller differences in the F-values are found and
the parameter set from Shuibei basin was selected to represent
upstream basins due to its slightly better performance. Finally the
calibrated parameter sets from Jiuzhou and Shuibei sub-basins
Table 2
Cross-basins tests between upstream and downstream sub-basins (calibration in
downstream and validation in upstream).
Upstream
Downstream
Jiuzhou
Lizhangf
Shengqian
Shuibei
Taoxi
Lantang
Pingshan
D
ME
F
D
ME
F
D
ME
F
0.75
0.72
0.75
0.73
0.76
0.60
0.73
0.70
0.57
0.43
0.55
0.51
0.77
0.75
0.76
0.75
0.75
0.67
0.68
0.65
0.58
0.50
0.52
0.49
0.75
0.72
0.74
0.73
0.72
0.57
0.70
0.70
0.54
0.41
0.52
0.51
were selected to represent the downstream and upstream subbasins, respectively, and then for the subsequent parameter
transfer.
We directly applied the Jiuzhou and Shuibei calibrated parameter sets to the other sub-basins and compared the computed and
observed discharges (Table 4). It is seen that the mean D and ME
values resulting from using the Jiuzhou and Shuibei calibrated
parameters to all the sub-basins are 0.74 and 0.72, and 0.76 and
0.72, respectively. The poorest D and ME values resulting from
Jiuzhou calibrated parameter set are 0.69 and 0.60, respectively,
and the values are 0.67 and 0.55, respectively, as resulting from the
Shuibei calibrated parameters. In other words, if we use parameter
sets of Jiuzhou and Shuibei to simulate daily discharge in ungauged
sub-basins in Dongjiang basin, D won’t be less than 0.67, and ME
won’t be less than 0.55. This regionalization method can be
considered as a candidate for parameter estimation for ungauged
basins in the region.
As for efficiency losses, the biggest D-loss and ME-loss from
Jiuzhou parameter set are 0.12 and 0.24, and from the Shuibei
parameter set these are 0.08 and 0.26, respectively, and related to
Shuntian, Pingshan sub-basins and the whole basin, which all have
good results in calibration. In the Shengqian sub-basin with the
poorest calibration results, the D-loss and ME-loss from Jiuzhou
parameter set are 0.06 and 0.11, and from the Shuibei parameter set
they are 0.03 and 0.07, respectively. For practical prediction for
ungauged basins in Dongjiang, the computed D and ME values on
the basis of the proxy-basin method are considered to be
acceptable.
It is interesting to note that in the cross-basin test between
Jiuzhou and Shuibei, the validation results based on the Shuibei
parameter set obtain remarkably higher D and ME and consequently higher F-values than those based on the Jiuzhou parameter
set (Tables 2 and 3), but when transferring their parameter sets to
the whole region, the Shuibei parameter set doesn’t perform
remarkably better than Jiuzhou parameter set does, both in terms
of minimum D and ME values and maximum ME-loss. This suggests
that better performance of parameter set in cross-basin test does
not ensure higher D and ME values in a parameter transfer study,
which is inconsistent with what one would expect. It is perhaps
because that Jiuzhou sub-basin is more representative in basin
attributes than Shuibei, and another reason can be that the number
of the studied sub-basins is not large enough to draw a general
conclusion.
Table 3
Cross-basins tests between upstream and downstream sub-basins (calibration in
upstream and validation in downstream).
Upstream
Downstream
Jiuzhou
Lizhangf
Shengqian
Shuibei
Taoxi
Lantang
Pingshan
D
ME
F
D
ME
F
D
ME
F
0.74
0.71
0.75
0.75
0.81
0.78
0.82
0.78
0.60
0.56
0.62
0.59
0.79
0.78
0.79
0.79
0.81
0.83
0.80
0.80
0.64
0.65
0.63
0.63
0.74
0.72
0.74
0.76
0.54
0.54
0.61
0.78
0.40
0.39
0.45
0.59
X. Jin et al. / Quaternary International 208 (2009) 129–137
135
Table 4
Transfer results of calibrated parameters in Jiuzhou and Shuibei sub-basins.
Name
Calibration
Calibrated Jiuzhou sub-basin parameter set
Calibrated Shuibei sub-basin parameter set
D
ME
D
ME
EL(D)
EL(ME)
D
ME
EL(D)
EL(ME)
Jiuzhou
Lantang
Lianping
Lizhangf
Pingshan
Shengq
Shuibei
Shuntian
Taoxi
Xingfeng
Yuecheng
Dongjiang
0.76
0.79
0.81
0.80
0.80
0.78
0.80
0.83
0.79
0.70
0.78
0.77
0.87
0.85
0.86
0.80
0.87
0.71
0.78
0.88
0.77
0.72
0.81
0.86
0.76
0.77
0.77
0.75
0.74
0.72
0.75
0.72
0.73
0.69
0.78
0.70
0.87
0.79
0.78
0.76
0.63
0.60
0.73
0.69
0.70
0.64
0.77
0.67
0.00
0.02
0.04
0.05
0.06
0.06
0.05
0.12
0.05
0.01
0.01
0.07
0.00
0.07
0.07
0.05
0.24
0.11
0.05
0.19
0.07
0.08
0.04
0.19
0.75
0.79
0.79
0.80
0.74
0.75
0.80
0.78
0.77
0.67
0.75
0.69
0.82
0.80
0.79
0.79
0.61
0.64
0.78
0.75
0.74
0.55
0.72
0.61
0.01
0.00
0.02
0.00
0.06
0.03
0.00
0.06
0.01
0.03
0.04
0.08
0.05
0.05
0.06
0.01
0.26
0.07
0.00
0.13
0.03
0.17
0.09
0.25
Average
0.79
0.82
0.74
0.72
0.05
0.09
0.76
0.72
0.03
0.08
5.2. Global mean method
sub-basin and are above 0.70 in Honghuata sub-basin. Using
regionalized parameter values, D and ME are still higher than 0.80
and 0.60 in the two test sub-basins, respectively. Comparison of
Table 6 with Table 5 we see that the results of these two independent testing catchments represent a best case (Dongkeng) and
a worst case (Honghuata) among the 14 sub-basins. For illustrative
purposes, the regionalization performance of Jiuzhou parameter set
in the proxy-basin method and arithmetic mean parameter set in
the global mean method is plotted against the mean monthly water
balance components of testing sub-basins in Fig. 5. It is seen that
two regionalized parameter sets result in discharges that agree
reasonably well with the observed and calibrated values. Thus, both
regionalization methods are considered to be applicable in the
prediction for ungauged basins in the study region.
The results of global mean method are shown in Table 5. It is
seen that 1) all three sets of mean parameter values give equal
performance, with average D and ME values of 0.76 and 0.74,
respectively. All the D and ME values are higher than 0.6, except for
ME in Xingfeng (0.55); 2) the average performance of the global
mean method is the same as for the proxy-basin test method. The
differences are only found for a few individual sub-basins. This
method can also be considered as a candidate for prediction for
ungauged basins in the region.
From efficiency losses, nearly all ME-losses are higher than
D-losses. This is also the case of the proxy-basins method. It is
indicated that the extremum values on hydrograph are more
difficult to catch in the prediction than seasonal variations when
using regionalized parameter values. Maximum D-loss and ME-loss
for three mean parameter sets are 0.09 and 0.26, and also are
related to the whole basin and Pingshan sub-basin which has
a good fit in calibration. In Xingfeng sub-basin, with bad fit in
calibration, three mean parameter sets provide similar D-loss and
ME-loss. This suggests that neither area weighted mean values nor
Thiessen interpolated mean values markedly improve the performance of arithmetic mean values.
6. Conclusions
The conceptual rainfall-runoff model, HBV, was applied to
Dongjiang basin and its 13 sub-basins, and two parameter regionalization methods – proxy-basin method and global mean method
were selected to estimate parameter values of ‘‘ungauged’’ subbasins in Dongjiang basin. Several useful conclusions are drawn: 1)
HBV model, ignoring snow routine, with performance of averaged
D and ME values higher than 0.75 both in calibration and validation
period, can be applicable for modeling of daily stream-flow in
Dongjiang basin characterized by a sub-tropical climate; 2) simple
proxy-basin method provide acceptable results for practical use in
the simulation of daily discharge in the basin; 3) global mean
method has the same performance as the proxy-basin method and
5.3. Verification of regionalized parameter values
Finally, independent tests of proxy-basins method and global
mean method were done in Dongkeng and Honghuata sub-basins
(Table 6). In calibration, D and ME are above 0.80 in Dongkeng
Table 5
Application of three average values in 11 sub-basins and Dongjiang basin.
Name
Calibration
Arithmetic mean values
Area weighted mean values
Thiessen interpolated mean values
D
ME
D
ME
D
ME
EL
D
ME
EL
D
ME
D
ME
D
ME
Jiuzhou
Lantang
Lianping
Lizhangf
Pingshan
Shengq
Shuibei
Shuntian
Taoxi
Xingfeng
Yuecheng
Dongjiang
0.76
0.79
0.81
0.80
0.80
0.78
0.80
0.83
0.79
0.70
0.78
0.77
0.87
0.85
0.86
0.80
0.87
0.71
0.78
0.88
0.77
0.72
0.81
0.86
0.75
0.79
0.80
0.79
0.76
0.75
0.78
0.76
0.77
0.67
0.77
0.69
0.85
0.83
0.83
0.79
0.64
0.66
0.75
0.74
0.74
0.57
0.74
0.58
0.02
0.00
0.01
0.02
0.04
0.03
0.02
0.07
0.02
0.03
0.01
0.08
0.02
0.02
0.03
0.01
0.23
0.05
0.03
0.14
0.03
0.15
0.07
0.27
0.75
0.79
0.81
0.79
0.76
0.76
0.78
0.77
0.77
0.66
0.77
0.68
0.85
0.83
0.83
0.79
0.61
0.66
0.75
0.76
0.73
0.55
0.72
0.54
0.02
0.00
0.00
0.01
0.04
0.02
0.01
0.06
0.01
0.04
0.02
0.09
0.02
0.03
0.03
0.01
0.26
0.05
0.03
0.13
0.04
0.18
0.09
0.31
0.74
0.79
0.80
0.78
0.76
0.75
0.77
0.76
0.77
0.67
0.77
0.69
0.84
0.83
0.83
0.79
0.64
0.66
0.74
0.75
0.73
0.55
0.73
0.55
0.02
0.00
0.01
0.02
0.04
0.02
0.02
0.07
0.02
0.04
0.01
0.09
0.03
0.02
0.02
0.02
0.23
0.05
0.04
0.13
0.04
0.17
0.08
0.31
Average
0.79
0.82
0.76
0.73
0.02
0.09
0.76
0.72
0.02
0.09
0.76
0.72
0.02
0.09
EL
136
X. Jin et al. / Quaternary International 208 (2009) 129–137
Table 6
Independent test in Dongkeng and Honghuata sub-basins.
Dongkeng sub-basin
Honghuata sub-basin
Calibration
D
ME
0.84
0.96
Calibration
D
ME
0.73
0.71
Proxy-basin method
Jiuzhou sub-basin
parameter set
Shuibei sub-basin
parameter set
D
ME
D
ME
0.82
0.89
0.80
0.91
Proxy-basin method
Jiuzhou sub-basin
parameter set
Shuibei sub-basin
parameter set
D
ME
D
ME
0.71
0.63
0.72
0.68
Global mean method
Arithmetic mean
values
Area weighted mean
values
Thiessen interpolated
mean values
D
ME
D
ME
D
ME
0.83
0.90
0.83
0.92
0.84
0.91
Global mean method
Arithmetic mean
values
Area weighted
mean values
Thiessen interpolated
mean values
D
ME
D
ME
D
ME
0.72
0.62
0.72
0.62
0.72
0.63
neither area weighted mean nor Thiessen interpolated mean value
of regional parameter set can markedly improve the performance
of the arithmetic mean value; 4) both proxy-basin method and
global mean method can be used for parameter regionalization in
the Dongjiang basin.
It is noted that the regionalization approaches described in this
study might be useful for testing other conceptual models that are
intended to be used in ungauged basins. However, the conclusion
derived in this study, i.e., the transferability of parameter values
obtained from the proxy-basin method and the global mean
method to sub-basins and to the large basin cannot be applied
directly to other models and regions without a similar testing
approach. Moreover, model parameter uncertainty resulting from
both calibration and regionalization also should be carefully
investigated for further study.
Acknowledgements
The authors would like to thank the 100 Talents Program of the
Chinese Academy of Sciences, the Outstanding Overseas Chinese
0
450
Calibrated Actual Evaporation
100
350
200
300
Observed
250
Precipitation
Calibrated
300
Proxy basins
200
Global mean
400
150
Discharges
100
500
Precipitation & Evaporation
(mm/month)
Discharge (mm/month)
400
50
0
1
2
3
4
5
6
7
8
9
10
11
12
600
Month
210
0
50
Calibrated Actual Evaporation
100
150
Precipitation
150
Observed
120
Calibrated
200
Proxy basins
90
Global mean
250
Discharges
60
300
30
0
Precipitation & Evaporation
(mm/month)
Discharge (mm/month)
180
350
1
2
3
4
5
6
7
8
9
10
11
12
400
Month
Fig. 5. The mean monthly water balance of the Dongkeng sub-basin, the best case (up) and the mean monthly water balance of the Honghuata sub-basin, the worst case (down).
X. Jin et al. / Quaternary International 208 (2009) 129–137
Scholars Fund from CAS (The Chinese Academy of Sciences), the 111
Program of Introducing Talents of Hydrology and Water Resources
Discipline to Hohai University, and the Project no. CUHK4627/05H
of the Research Grants Council of the Hong Kong Special Administrative Region, China for financial support. Special thanks are due
to Tao Yang in Hohai University and Hongwei Yang in Nanjing
Institute of Geography & Limnology CAS, for helping in data
collection and processing. Great thanks are due to Prof. Jan Seibert
of Stockholm University for kindly providing the HBV Light
program.
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