Journal of Hydrology 505 (2013) 1–12
Contents lists available at ScienceDirect
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j h y d r o l
a
,
b
a , c
,
a
,
c
a , d
a
a
Department of Geosciences, University of Oslo, PO Box 1047 Blindern, N-0316 Oslo, Norway b
Department of Land Resources and Tourism, Nanjing University, 22 Hankou Road Nanjing, Jiangsu 210093, China c
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 430072, China d
Jiangsu Key Laboratory of Forestry Ecological Engineering, Nanjing Forestry University, Nanjing, China a r t i c l e i n f o
Article history:
Received 22 September 2012
Received in revised form 17 June 2013
Accepted 3 September 2013
Available online 11 September 2013
This manuscript was handled by Andras
Bardossy, Editor-in-Chief, with the assistance of Luis E. Samaniego, Associate
Editor
Keywords:
Xinanjiang Model
Xiangjiang River basin
Precipitation gauges network
Precipitation
Runoff s u m m a r y
Hydrological models are important tools for flood forecasting and for the assessment of water resources under current and changing climate. However, the accuracy of hydrological models is limited by many factors, the most important of which, is perhaps the errors in the input data. The influence of the precipitation gauge density and network distribution on the modelling results is still a challenging topic in hydrology studies. One of the reasons for the limited study of this important issue is that it needs a catchment with sufficient size, wide diversity of topography and climate, and dense rain gauges with long and good quality data. In this study, a famous and widely used hydrological model, the Xinanjiang Model, was applied in Xiangjiang River basin to examine the influence of rain gauge density and distribution on the performance of the model in simulating the stream flow. The Xiangjiang River basin, one of the most important economic belts in Hunan Province, China and the primary inflow basin of Dongting Lake – China’s second largest freshwater lake, has dense rain gauge network with long and high quality data. To perform the study, firstly, the mean areal rainfall estimated by different rain gauge densities using various statistical indices as evaluation criteria was analysed. Secondly, the influence of different rain gauge density and distribution on the model performance was rigorously evaluated. The results show that the error range of the indices in analysing mean areal rainfall and simulated runoff narrowed gradually with increasing number of rain gauges up to some threshold, and beyond which the model performance did not show considerable improvements. The methodology and results of this study will provide useful guidelines and valuable reference for studying rainfall influence in hydrological modelling.
Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction
Precipitation is one of the most important inputs in hydrological model simulations and forecasting. In a precipitation–runoff model, precise estimation of areal precipitation is essential for more accurate runoff simulations, as the representative precipita-
tion is used in determining surface hydrological processes ( Zehe et al., 2005; Xu et al., 2006; Sun et al., 2013 ). As hydrological mod-
els are abstract and simplified representations of natural hydrological processes, even those models well founded in physical theory or empirically justified by past performance will not be able to produce accurate hydrograph predictions if the inputs to the model do
not characterise the precipitation inputs ( Beven, 2001
).
Bárdossy and Plate (1992)
indicated that precipitation was a natural phenomenon governed by complicated physical processes which are
⇑
Corresponding author. Address: Department of Geosciences, University of
Oslo, PO Box 1047 Blindern, N-0316 Oslo, Norway. Tel.: +47 22855825; fax: +47 22854215.
E-mail address: c.y.xu@geo.uio.no
(C.-Y. Xu).
0022-1694/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jhydrol.2013.09.004
inherently nonlinear and extremely sensitive. Precipitation also often exhibits significant spatial and temporal variations within a catchment or a region (
Krajewski et al., 2003; Bengtsson, 2012;
Adeloye and Rustun, 2012; Li et al., in press; Parkes et al., 2013
).
Xu and Vandewiele (1994), Oudin et al. (2006)
and
Xu et al.
(2006)
stated that random errors in rainfall input considerably affect model performance and parameter values, although, model results were nearly insensitive to random errors in potential evapotranspiration input.
Oudin et al. (2006)
further found that the sensitivity of a rainfall–runoff model to input errors might depend partially on the model structure itself. Many studies have therefore focused on the impacts of precipitation input to hydrological model outputs.
Singh (1997)
reviewed hydrological literature on the effect of spatial and temporal variability in hydrological factors on the stream flow hydrograph in detail.
Wilson et al. (1979)
showed that the spatial distribution and the accuracy of the rainfall input to a rainfall–runoff model influenced considerably the volume of storm runoff, peak runoff and timeto-peak.
Jiang et al. (2012)
showed that the range of runoff

2 application.
2. Study area and data description
H. Xu et al. / Journal of Hydrology 505 (2013) 1–12 percentage change was much larger than that of precipitation in northern China.
Sun et al. (2002)
demonstrated that errors in storm-runoff estimation were directly related to spatial data distribution and the representation of spatial conditions across a catchment. They found that the accuracy of storm-runoff prediction depended very much on the extent of spatial rainfall variability.
St-Hilaire et al. (2003)
assessed the impact of the quality of flow simulations under different density of meteorological network.
Bárdossy and Das (2008)
investigated the influence of the spatial resolution of the rainfall input on model calibration and
Precipitation gauges provide the basic means of estimating precipitation at a point, over a region or catchment through spatial interpolation methods (for example, Kriging method, Thiessen polygons method, Shepard’s Method, Trend surface analysis etc.).
It is commonly believed that the calculation of areal precipitation
is more accurate with more gauges distributed in a basin ( Chen et al., 2010a
). However, geographical or economic situations often limit the ideal gauge density and location.
Michaud and Sorooshian
(1994)
observed that inadequate precipitation gauge densities, in the case of the sparse network, produced significant errors in the simulated flood peaks in a midsized semi-arid catchment.
Anctil et al. (2006)
showed that model performance reduced rapidly when the mean areal rainfall was computed using a number of precipitation gauges less than a certain threshold. It also showed that some precipitation gauge network combinations provided better forecasts than those derived from using all available precipitation gauges to compute areal rainfall. Detailed knowledge of the spatial resolution of model input data is very important as this affects the accuracy of flow simulations. The spatial and temporal resolutions of precipitation data are mutually influenced and both have a significant impact on runoff simulation results (
Dong et al., 2005
).
Precipitation gauge network structure is not only dependent on the station density, station location also plays an important role in determining whether information is gained properly. The main aim of this paper is, therefore, to investigate the influence of different rain gauge density, network distribution and location of the stations on model calibration and application. This is achieved by:
(i) randomly selecting different percentages and combinations of rain gauges from a total of 181 rain gauges and comparing their mean areal rainfall estimates using statistical indices, and (ii) investigating the sensitivity of the simulation results of the conceptual rainfall–runoff model – Xinanjiang Model when driven by different number of rain gauges and their location configurations. This study is believed to provide useful reference information for hydrologists and engineers doing research and application of hydrological models for various purposes.
ative humidity is about 75% in summer and about 80% in winter, and the mean annual evapotranspiration is 847 mm. There is a remarkable difference in runoff among different seasons with about 68% of the total runoff volume occurring during the wet season (April–September) whereas 50% of the flooding events occurring in June and July (
Fig. 2
).
Fifteen years of daily meteorological and hydrological data
(from 1991 to 2005) including air temperature, precipitation, runoff and potential evapotranspiration are used in this study. The choice of this study period is to maintain maximum number of stations and highest quality of the data. All the meteorological and hydrological data used in this paper have been quality controlled by the China Meteorological Data Sharing Service System (http:// cdc.cma.gov.cn) and the Hydrology and Water Resources Bureau of Hunan Province, China. Earlier studies (
Li et al., 1997; Hu et al., 2011; Chen et al., 2012a
) have also shown the quality of the data is adequate for water balance studies.
3. Methodology
Statistical analysis and hydrological modelling are two widely adopted methods to identify the appropriate spatial sampling of rainfall and for flow simulation. For the sake of completeness, the methods, scenarios and evaluation criteria used in the study are briefly introduced in this section.
3.1. External Drift Kriging method
The spatial distribution of rainfall in the basin was investigated by spatial interpolation using the External Drift Kriging (EDK) method (
Ahmed and Marsily, 1987
). Other studies (e.g.
Goovaerts,
1999, 2000 ) have found that the EDK method to be more accurate
in predicting the spatial distribution of rainfall than both Ordinary
Kriging and the Inverse Distance Weight Scheme methods.
The EDK method is a non-stationary geostatistical method which focuses on the use of secondary information (in this paper secondary information is ‘‘elevation’’) from a model to obtain better prediction. In the method, the rainfall data { z ( u a
) , a = 1, . . .
, n }, where z is the rainfall at the unsampled location u , are supplemented by elevation data available at all estimation grid nodes and denoted y ( u ). The usefulness of elevation data can be evaluated by using the relationship between mean annual rainfall and elevation (in this study the following relationship was established: z ( u ) = 0.5441
y ( u ) + 1371.2, R 2 = 0.53). The EDK method uses the secondary information y to derive the local mean of the primary attribute z , and then to perform simple Kriging on the corresponding residuals. More details about the EDK method can be seen in
Goovaerts (1997, 2000), Wackernagel (1998)
and
Hengl et al.
(2003) .
The Xiangjiang River basin (
Fig. 1 ) is located between 24
° –29 ° N and 110 ° 30 0 –114 ° E in the central-south China with a total area of
94,660 km 2 and a total length of 856 km. The average slope is
0.0134%. The basin is embosomed with mountains in the east, south and west. Mountains (the mean elevation >200 m) and hills
(the mean elevation between 100 m and 200 m) are mainly located in the upstream and the plains (the mean elevation <100 m) are located in the downstream. The basin shows evident characteristics of mountain streams in the upstream branches and the acres of rolling terrain accelerate the rainfall convergence and the variation of water level and runoff (
Fig. 1
). It is heavily influenced by monsoon climate, which brings heavy rainfall from the south in summer. The mean annual precipitation reaches 1584 mm, of which
68% occurs in the main rainy season from April to September.
The mean annual temperature is about 17 ° C, the annual mean rel-
3.2. Stochastically based rain gauge network design
To investigate the error range in mean areal rainfall and runoff simulated from the different rain gauge configurations, various scenarios of different rain gauge densities are built. Six broad scenarios comprising of 5% (one rainfall gauge controls 9466 km 2 drainage area), 10% (one rainfall gauge controls 4982 km 2 area), 20% (one rainfall gauge controls 2491 km 2 drainage drainage area),
30% (one rainfall gauge controls 1661 km 2 drainage area), 50%
(one rainfall gauge controls 1018 km 2
(one rainfall gauge controls 740 km 2 drainage area) and 70% drainage area) of total 181 rain gauges (one rainfall gauge controls 523 km 2 drainage area) are obtained for analysis (
Table 1 ). For each scenario, 100 different
network configurations composing of randomly selected rain gauges from the 181 gauges are derived. This results in a total of

H. Xu et al. / Journal of Hydrology 505 (2013) 1–12 3
Fig. 1.
Drainage basin delineation and location of meteorological stations in the study area.
Fig. 2.
The average monthly rainfall calculated by 181 rain gauges and observed runoff from 1992 to 2005 in Xiangtan gauge.
601 (i.e., 6 100 plus the original set of 181 gauges) different combinations of rain gauges for interpolating mean areal rainfall.
3.3. Hydrological model
It is generally recognised that a simultaneous use of both statistical and deterministic methods of analysis of hydrological processes is necessary to produce the best scientific and practical information for hydrology (
Yevjevich et al., 1972 ). In recent years,
several hydrological models have been applied in China, i.e. SWAT model (
Ji et al., 2008 ), HBV model ( Jin et al., 2009; Chen et al.,
2012b
), TOPMODEL (
Chen et al., 2010a,b; Xu et al., 2012
), VIC model (
Yuan et al., 2004; Zhou et al., 2004; Jiang et al., 2012
), LSX-HMS model (
Yang et al., 2012 ), WASMOD (
Jin et al., 2010; Li et al., 2011
), and Xinanjiang Model (
Jayawardena and Zhou, 2000; Yuan et al.,
2012; Zhang et al., 2012 ). In this study, the Xinanjiang Model is se-
lected to exemplify the proposed study approach and verify the results from the statistical analysis. It is by far the most widely used model in China (
Zhao et al., 1995 ). The Xinanjiang Model was
developed in 1973 and the English version was first published in
1980 ( Zhao et al., 1980 ). Its main feature is the concept of ‘‘runoff
formation on repletion of storage, which means that runoff ( R ) is not produced until the soil moisture content ( W ( h )) of the aeration zone reaches field capacity (WM), thereafter runoff equals the rainfall ( P ) excess ( P KE E m
) without further loss. The parameter KE is used to transfer pan evaporation measurements ( E m
) into potential evapotranspiration rate. Evapotranspiration ( E ) is calculated by a three layer conceptual model, of which WM is further divided into three layers, areal mean tension water of upper layer
(WUM), areal mean tension water of middle layer (WLM) and areal

4 H. Xu et al. / Journal of Hydrology 505 (2013) 1–12
Table 1
The number of rain gauges in different percentage of selection.
Percentage of rain gauges
Number of rain gauges
Rain gauge density
(number of rain gauges per
1000 km 2 )
0.1
5%
Rain gauges
10
10%
Rain gauges
19
20%
Rain gauges
30%
Rain gauges
38 57
50%
Rain gauges
93
70%
Rain gauges
100%
Rain gauges
128 181
0.2
0.4
0.6
1 1.4
1.9
mean tension water of deep layer (WDM). The parameter C is used to calculate evapotranspiration from deep layer. The runoff, which is further divided into surface flow (RS) and ground water (RG) by infiltration capacity (FC), is routed to the outlet of the catchment according to linear reservoir and groundwater recession (KG) respectively. Parameter IMP defines the proportion of impermeable area to the total catchment area. The parameter B is used to
describe the non-uniformity of the surface condition ( Liu et al.,
2001
). The inputs to the model are daily areal precipitation, the measured daily pan evaporation and discharge. The outputs are the outlet discharge from the whole basin, the actual evapotranspiration from the whole basin, which is the sum of the evapotranspiration from the upper soil layer, the lower soil layer, and the
deepest layer ( Zhao, 1992
).
The model has been applied successfully since it was published over very large areas including the agricultural, pastoral and forested lands of China except the loess. The model is mainly used
for hydrological forecasting ( Li et al., 2009; Liu et al., 2009; Yao et al., 2009 ). Use of the model has also spread to other fields of
application such as water resources estimation, design flood and field drainage, water project programming, hydrological station
planning, and water quality accounting ( Hu et al., 2005; Ren et al., 2006; Bao et al., 2011 ). The US National Weather Service Riv-
er Forecast System also reported its good performance in the arid
Bird Creek watershed in the United States ( Singh, 1995 ).
In this study, the model is calibrated and validated during
1992–2002 and 2003–3005, respectively, with 1991 reserved as a model warm-up period. Six broad scenarios comprising of 5%,
10%, 20%, 30%, 50% and 70% of total rain gauges (see
Table 1
) and the original set of 181 rain gauges are used to estimate mean areal rainfall for model calibration and validation.
3.4. Model evaluation criteria
To evaluate model performance, the results obtained from model simulations using different rain gauge configurations were compared using the following statistical criteria: Nash–Sutcliffe coefficient E ns
(
Nash and Sutcliffe, 1970 ), relative error (
R d
), and
Root Mean Squared Error (RMSE), which are expressed as follows:
Fig. 3.
Interpolated mean annual rainfall (mm/year) distribution during 1992–2005 over Xiangjiang River basin by using 181 rain gauges and External Drift Kriging method.

H. Xu et al. / Journal of Hydrology 505 (2013) 1–12
R d
¼
P
N t ¼ 1
ð Q
P s
N
ð t ¼ 1 t Þ
Q o
ð t
Q
Þ o
ð t ÞÞ
RMSE ¼ s
P
N t ¼ 1
ð Q o
ð t Þ Q
N s
ð t ÞÞ
2
Fig. 4.
Box plot of annual areal mean rainfall estimated by different rain gauges’ density of: (a) 100 samplings for each number of stations, (b) 10 samplings for each number of stations respectively in Xiangjiang River Basin from 1992 to 2005. 50% of all values are within the box and 90% within the whiskers, and the same meaning holds in
Figs. 5 and 7 ).
5
ð 2 Þ
ð 3 Þ where Q s
( t ) and Q o
( t ) are simulated and observed daily runoff respectively, and number of days.
Q o is mean observed daily runoff and N is the total
The E ns determines the relative magnitude of the residual variance (‘‘noise’’) compared to the measured data variance (‘‘information’’).
E ns
= 1 means a perfect model fit. The R d and RMSE examine the model’s performance with regard to its ability to maintain the water balance.
R d
= 0 means a perfect model fit and the same is true for RMSE.To understand the impact of the different rain gauge density and network on the discharge simulation accuracy, it is necessary to study how the different density of rain gauges affects the correlation between the mean areal rainfall estimated by all
181 rain gauges (MAR_181, assumed as benchmark areal rainfall value in the area) and the mean areal rainfall estimated by different rain gauges’ network (MAR_Drg), and how the MAR_Drg affects the discharge simulation results. The relationship between the
MAR_181 and the MAR_Drg is therefore studied and further tested by the hydrological model – Xinanjiang Model. Ideally, an increasing number of rain gauges should correspond to an increase in correlation between MAR_Drg and MAR_181. In addition to the three criteria mentioned above, the cross-correlation coefficient ( q ) is selected as an indicator of the relationship between the MAR_181 and the MAR_Drg and between the simulated and observed runoff.
The expected cross-correlation between two variables defined as: x i and y i is q ¼ cov ð x i
; y i
Þ
ð var x i var y i
Þ
1 = 2
ð 4 Þ where cov( x i
, y i
) is the covariance between are the variance of series x i and y i x i and y i
, var x i respectively.
and var y i
Table 2
Comparison of mean monthly rainfall (mm) with different rain gauge networks in wet and dry seasons.
Number of rain gauges
Wet season Dry season
10
19
38
57
93
128
181
Maximum
193.6
186.1
179.8
178.6
/
173.8
173.5
Minimum Maximum
158
158.3
163.7
164.7
175 /
166.8
167.7
/
96.5
94.9
92.8
93.2
91.7
91.6
Minimum
84.9
86.3
87.8
88.9
89.1
/
89.5
89.8
E ns
¼ 1
P
N t ¼ 1
ð Q s
P
N t ¼ 1
ð Q
ð t Þ Q o
ð t Þ o
Q
ð t ÞÞ
2 o
Þ
2
ð 1 Þ
4. Results and discussion
4.1. Mean areal rainfall obtained using different rain gauge densities
The rain gauges’ density affected the interpolated values by modifying the distribution and quantity of estimated mean areal rainfall in the study catchment. The relationship between the MAR_181 and the MAR_Drg is compared by several statistical indices.
As an input of the Xinanjiang Model, mean areal rainfall is an important and useful index to reflect the precision of rainfall amount.
Fig. 3
shows the interpolated mean annual rainfall from
1992 to 2005 over each 1 km 2 grid in the Xiangjiang River basin by using 181 rain gauges with the EDK method. It is seen that rainfall is larger in the south and east region than that in the north and
Table 3
Comparison of statistical indexes between MAR_181 and MAR_Drg.
Number of rain gauges
STD (mm/day) RMSE (mm/day)
10
19
38
57
93
128
181
Minimum
7.37
7.49
7.48
7.54
/
7.55
7.64
Maximum Minimum
8.83
8.41
8.08
8.03
7.72
/
7.91
7.84
/
1.87
1.43
0.85
0.66
0.45
0.29
Relative error of mean daily rainfall
Maximum Minimum (%)
2.82
2.31
1.53
1.08
/
0.72
0.49
/
5
5
4
2
2
1
0
Maximum (%)
/
1
1
9
8
4
3
/
Averaged Relative error of maximum daily rainfall
Minimum (%)
42
35
23
17
13
8
Maximum (%)
51
39
24
18
/
11
8

6 H. Xu et al. / Journal of Hydrology 505 (2013) 1–12
Table 4
Distribution of daily mean areal rainfall estimated by 181 rain gauges in different rainfall classes and their relative contributions to the total rainfall during 1992–2005 in
Xiangjiang River Basin.
Rainfall class
Percentage of days
Percentage of rainfall
0 mm (%)
3.6
0.0
0–3 mm (%)
43.4
9.0
3–10 mm (%)
18.9
25.6
10–25 mm (%)
10.9
39.5
25–50 mm (%)
3.1
23.6
>50 mm (%)
0.2
2.3
west. This is because 66% rainfall occurs in the wet season, during which this area is mainly influenced by two climate systems: the subtropical anticyclone in the western Pacific Ocean and the monsoon from the South China Sea. If the former climate system dominates the area, rainfall events will move from east to west, bringing heavy convective and stratiform rain to the east of the basin. If the latter climate system dominates the area, rainfall events will move from south to north, bringing heavy rain to the south of the basin. Moreover, there are many mountains located in the south and west border of the basin, i.e. the Nanling Mountain stretching 1400 km east–west with mean elevation about 1000 m above sea level. It easily induces heavy orographic rainfall and partly blocks the moisture transport from south and west to the inner land of the basin which causes the rainfall distribution as shown in
Fig. 3
. The spatial variability of precipitation is nonhomogeneous, which may influence the quality of interpolation and hydrological modelling. The effect of different rain gauges’ density on the mean annual areal rainfall from 1992 to 2005 with
100 different combinations is shown in
Fig. 4 a. It can be observed
that the median values of the mean annual areal rainfall from dif-
Table 5
A summary of climatology indices of Xiangjiang River basin in the calibration (1992–
2002) and validation (2003–2005) periods.
Mean annual temperature
( ° C)
Mean annual rainfall
(mm)
1641
Relative humidity
(%)
Mean annual actual evapotranspiration
(mm)
Mean annual depth of runoff
(Xiangtan
Gauge)
(mm)
80 689 831 Calibration period
Validation period
18
18.4
1374 76 775 640 ferent rain gauge configurations approximately equal to the value of 1584.2 mm of MAR_181, and the error range decreases as the number of rain gauges increases. For example, when 10 rain gauges are randomly selected to calculate the mean areal rainfall, the largest value achieved is 1733.7 mm while the smallest value is only
Fig. 5.
Box plot of the (a) daily rainfall in different rainfall classes and (b) their relative contributions to the total rainfall during 1992–2005 in Xiangjiang River Basin (here only the classes with significant variant are shown in the figure).

H. Xu et al. / Journal of Hydrology 505 (2013) 1–12
Table 6
A summary of selected parameters in calibrating the Xinanjiang Model.
Parameter name
Explanation Min.
value
Max.
value
KI
KG
N
NK
WM (mm) Areal tension water capacity
KE Evaporation coefficient
B
SM (mm)
Tension water distribution index
Areal free water capacity
EX
CI
CG
IMP
C
Free water distribution index
Fraction of free water to interflow
Interflow recession coefficient
Groundwater recession coefficient
Parameter n of Nash model
Number of time step
100
0.8
0.3
30
1
0.3
Fraction of free water to groundwater 0.3
Impermeable coefficient
Deep layer evaporation coefficient
0.0005
0.1
0.7
0.01
0.3
0.8
0.9
2
2
180
1.2
0.7
60
2
0.7
0.9
0.99
4
3
Fitted value
120
0.98
0.35
35
1.5
0.35
0.35
0.002
0.15
0.866
0.91
3.1
2.44
1497.9 mm. Comparing these with the observed mean areal rainfall from MAR_181, the relative errors are 9.4% and 5.4% respectively. On the other hand, the mean areal rainfall derived from 128 rain gauges ranged from 1604.6 mm to 1561.9 mm, resulting in the relative errors of 1.3% to 1.4%. This result demonstrates that the
100-time random selection of rain gauges for each gauge number is enough to represent different variation cases of areal rainfall.
The reduction in error range is a good indicator of improved accu-
7 racy in the derivation of mean areal rainfall as more rain gauges are included. If 10-time random selection of rain gauges is performed, the mean annual rainfall and the error ranges show a random image as can be seen in
Fig. 4 b, which means that not only the num-
ber of rain gauges but also the sampling size plays a role.
Considering the variation of areal mean monthly rainfall estimated by different rain gauge networks in wet and dry seasons,
Table 2
shows that the areal mean monthly rainfall varies from
158 193.6 mm to 167.7
173.5 mm in wet season as the number of rain gauges increased from 10 to 128, while it varies from
84.9
96.5 mm to 89.8
91.6 mm in dry season. The fact that the error range of mean monthly rainfall in wet season is larger than that in dry season demonstrates that the rainfall is unevenly distributed in the basin, especially in wet season. The result shows that a smaller number of gauges can give a larger range of rainfall amount.
The standard deviation (STD) of mean areal rainfall, the RMSE between MAR_181 and MAR_Drg, the relative error between
MAR_181 and MAR_Drg and the averaged relative error of each year’s maximum daily rainfall are shown in
Table 3 . The error
range of the STD is gradually narrowing as more rain gauges are selected. Changes in the RMSE of mean areal rainfall, the Relative error of mean areal rainfall and the Relative error of maximum daily rainfall are quite similar to that of STD. For the relative error between MAR_181 and MAR_Drg, the value for mean daily rainfall is quite low, to less than 4% when the number of rain gauges ex-
Fig. 6.
Comparison of the observed and simulated runoff, the absolute error between observed and simulated runoff from different combinations of rain gauges in Xiangjiang
River basin from 01/01/2000 to 31/12/2000 (a) 10 rain gauges; (b) 38 rain gauges; (c) 93 rain gauges; (d) 128 rain gauges).

8 a b
.
.
.
.
.
.
.
.
H. Xu et al. / Journal of Hydrology 505 (2013) 1–12 the total days and contributes 2.3% of the total rainfall. Such information is also valuable because extremely high rainfall events are responsible for hazards such as landslides and flash floods, in the
process threatening the economy and human life ( Varikoden et al., 2010
).
Fig. 5
shows that the percentage of the total rainfall for the high rainfall class increases with decreasing number of rain gauges as extremely high rainfall events are in many cases more localised with a lower probability of occurrence. Consequently, in the calculation of mean areal rainfall the total error range and the 50% uncertainty band are increasing rapidly for the high rainfall class as the number of rain gauges decreases (
Fig. 5
b right panel). The results therefore suggest that when the number of rain gauges is limited, great uncertainty exists in estimating areal average values of high rainfall class. In summary,
Table 4
and
Fig. 5
demonstrate that the rainfall in the catchment is unevenly distributed. The rainstorm centres may exist and change their locations in the basin. It is hard to detect the heavy rain correctly when less rain gauges are selected, which leads to considerable large variations of rainfall in high rainfall classes, especially in the class of rainfall >50 mm.
Fig. 7.
Box plot of Nash–Sutcliffe coefficients of Xinanjiang modelling calculated from different rain gauges’ densities for (a) the calibration period (from 01/01/1992 to 31/12/2002) and (b) the validation period (from 01/01/2003 to 31/12/2005) in
Xiangjiang river basin.
ceeds 38. There is however evident variation of the relative error of maximum daily rainfall. The error range of the relative error of maximum daily rainfall considerably decreases from to 8%
42% 51%
8% as number of rain gauges increased from 10 to 128.
This indicates that there is a high probability of having large errors, especially for rainfall extremes, when the number of rain gauges in the catchment is low.
Table 4
and
Fig. 5
show the intensity distribution of daily rainfall in different classes and their contributions to the total rainfall during the period 1992–2005 (only classes with significant variation are shown in
Fig. 5
). It can be seen from
Table 4
that the class of 0–3 mm has the largest occurrence, occurring almost half of the total days followed by the class 3–10 mm which occurs nearly 20% of the total days. With increasing number of rain gauges, the percentage of the days of the non rainy-day class and of the 0–
3 mm class is evidently decreasing and increasing, respectively.
The percentage of relative contribution to the total rainfall of the class >50 mm is on the other hand decreasing as the number of rain gauges increases. For other classes, there are no evident changes in both the percentage of the days and the percentage of the relative contribution to the total rainfall. This indicates that rainfall in the basin is not homogeneous such that not all the rain gauges can record rainfall events for a given day. When more rain gauges are selected to calculate the mean areal rainfall, the number of non-rainy day decreased. While for the other classes of the rainfall, the percentage of the days in the 0–3 mm class increases inversely. It is important to note that the high rainfall ranges play a very considerable role in contributing rainfall amounts to the total rainfall (
Li et al., 2012
). The high rainfall class (>50 mm) occurs only 0.2% of
4.2. Influence of the rain gauge network on hydrological modelling
The Xinanjiang Model is calibrated from 1st January 1992 to
31st December 2002 and validated from 1st January 2003 to 31st
December 2005.
Table 5
shows a summary of the climatology indices in order to compare the general climatic factors over the calibration and validation period. Comparing with the calibration period, it can be seen that the mean annual rainfall and mean annual runoff in validation period reduced by 267 mm and 191 mm respectively, while mean annual actual evapotranspiration increased by 86 mm. It demonstrates that the validation period is drier than the calibration period. The values of the calibrated parameters are shown in
Table 6
. For illustrative purpose,
Fig. 6
compares the observed and simulated daily runoff hydrographs and the absolute errors (=simulated runoff observed runoff) from
1st January 2000 to 31st December 2000 based on mean areal rainfall estimated from randomly selected 10, 38, 93, and 128 rain gauges. It can be observed that: (i) the ranges of the simulated hydrographs and absolute errors derived from the different rain gauge configurations narrow gradually with increasing number of rain gauges. (ii) There is a higher probability to overestimate or underestimate the peak flows when the number of rain gauges included in the simulations is less than 38. The similar change trend and characteristics can be found in validation period as well, which are not shown here considering the length of the paper.
Fig. 7
shows the Nash–Sutcliffe coefficients for the daily flow simulations during the calibration and validation periods for different number of rain gauges and their combinations. It can be seen that the Nash–Sutcliffe coefficient increases, and the total error range and 50% uncertainty band narrow rapidly during both calibration and validation periods with increasing of the number of rain gauges. When the number of rain gauges falls below 38, the E ns decreases considerably from 0.915
0.953 (38 rain gauges) to
0.817
0.931 (10 rain gauges) in the calibration period and from
0.91
0.946 (38 rain gauges) to 0.835
0.923 (10 rain gauges) in the validation period. At the same time the total error range and the 50% uncertainty band of the E ns values increase rapidly.
When the number of rain gauges is above 57, the increase in median E ns values and the decrease in the error range become relatively small. A summary of the model performances in the period 1992–
2005 for different rain gauge densities is shown in
Table 7
. With the increasing of the number of rain gauges, it can be seen that the error range of the indexes computed by the different combinations of rain gauges narrows gradually, and the model performance improves considerably. The rain gauges’ networks consisting of 10

H. Xu et al. / Journal of Hydrology 505 (2013) 1–12
Table 7
Model performance using mean areal rainfall from different numbers of rain gauges from 1992 to 2005.
Number of rain gauges
10
19
38
57
93
128
181
RMSE (m
3
/s)
Minimum
601.78
551.31
505.29
489.31
476.55
/
476.63
506.7
Maximum
948.25
792.86
667.08
608.49
564.5
/
541.7
/
Relative error
Minimum (%)
2.8
2.8
2.2
2.3
2
1.9
1.3%
Maximum (%)
/
7.5
4.6
0.5
0.7
1
1.2
Averaged relative error of maximum daily runoff
Minimum (%) Maximum (%)
/
42.9
31.7
21.6
16.6
11
20.3
6% /
32.4
25.7
17.7
15.9
8.9
7.2
9 rain gauges yield the lowest model performance, whereas the highest model performance can be obtained using the 128 rain gauges network. Moreover, when the number of rain gauges is larger than
93, there is no obvious improvement in the model performance.
Dong et al. (2005)
also discovered the similar results by using variance reduction analysis method and lumped HBV model. They used 26 rain gauges to find out the appropriate quantity and location of rain gauges in Qingjiang River basin of China, which demonstrated that both cross correlation coefficient and modelling performance increase hyperbolically and level off after more than five rain gauges are used in flow simulation for the study area.
Considering the variation of simulated mean monthly streamflow with different rain gauge networks in wet and dry seasons,
Table 8
shows that the mean monthly depth of runoff varies from
86.8
97.7 mm to 89.4
90.7 mm in wet season with the number of rain gauge increasing from 10 to 128, while it varies from
39.1
46.9 mm to 39.1
40.2 mm in dry season. The large (small) error range of mean monthly depth of runoff in wet (dry) season is in accordance with the large (small) error range of mean
monthly rainfall in wet (dry) season ( Table 2 ). It demonstrates that
there is higher uncertainty in streamflow simulation with fewer rain gauges.
4.3. Relationship between the different rain gauge networks and the simulated runoff
Fig. 8
shows the cross-correlation coefficient ( q r–r
) between the rainfall of MAR_181 and the MAR_Drg and the cross-correlation coefficient ( q f–f
) between the observed runoff and the simulated runoff with the input of MAR_Drg. It is seen that when more rain gauges are included in the computation, the cross-correlation coefficient increases, but achieved values of q r–r and q f–f q r–r q r–r is always higher than q f – f
. The highest and q f–f are respectively 0.93 and 0.91. Both increase hyperbolically in the same step with the increasing of the number of rain gauges, and the error ranges of the cross-correlation coefficients narrow gradually as number of rain gauges increases. When the number of rain gauges is above
93, both q r–r and q f–f do not show considerable changes.
Fig. 9
shows an example of rain gauge configurations in the basin with the interpolated average annual rainfall in the period
1992–2005 using the EDK method and average E ns calculated as:
A v gE ns
¼
1
2
ð E ns ; calibration
þ E ns ; v alidation
Þ ð 5 Þ where E ns , calibration and E ns , validation are the E ns in the calibration and validation periods respectively. Geographic locations of the rain gauges have a strong influence on the E ns values as can be seen from the randomly selected 10, 19, 38 rain gauge configurations which yield a minimum AvgE ns equals to 0.84, 0.88 and 0.91 respectively
(
Fig. 9
a–c). These configurations have all rain gauges unevenly located in the left and right side of the river.
Fig. 9 a also shows poor
model performance when most of the gauges are concentrated near the basin border. On the other hand, it is possible to achieve better model performance with randomly selected 10 and 19 rain gauges as shown in
Fig. 9
d and e when the rain gauges are more evenly distributed over the basin and the AvgE ns equals to 0.93 and 0.94
respectively.
Fig. 9
f shows that the maximum AvgE ns
= 0.95 is obtained with 93 rain gauges evenly distributed in the basin.
Fig. 9
also reveals that when fewer rain gauges are available, the location of the stations plays an important role. For example, when
19 stations are used in the calculation, an AvgE ns value of 0.94 can be achieved if they are evenly distributed and produce spatial distribution of areal rainfall comparable with all stations are used
(Figs.
9 e and
3
). Although 10 stations cannot reproduce the spatial distribution of areal rainfall comparable with Figs.
3
and
9
d still produces much higher AvgE ns value than
Fig. 9 a does when the sta-
tions are more evenly distributed. When
Fig. 9 d and e (both pro-
duce good AvgE ns values) are superimposed on the DEM map of the basin shown in
Fig. 1 , it can be seen that more rain gauges
are located in the mountains areas of the basin. Heavy orographic
Table 8
Comparison of mean monthly simulated depth of runoff (mm) with different rain gauge networks in wet and dry seasons.
Number of rain gauges
Wet season Dry season
10
19
38
57
93
128
181
Observed
Maximum
97.7
94
91.3
91.1
90.7
/
/
90.7
Minimum Maximum
86.8
87.9
88.6
88.8
89.3
87.3
/
89.4
89.2
/
/
/
46.9
43.6
42
42.3
40.2
40.2
Minimum
39.1
38.8
39
38.9
39
40.4
/
39.1
42.5
/
.
.
.
.
Fig. 8.
The cross-correlation coefficient of q r–r
(the cross-correlation coefficient between the areal rainfall of MAR_181 and the MAR-Drg) and q f–f
(the crosscorrelation coefficient between the observed runoff and the simulated runoff with the input of MAR-Drg) computed during the period 1992–2005.

10 H. Xu et al. / Journal of Hydrology 505 (2013) 1–12
Fig. 9.
Geographical locations of the rain gauges and space distribution of annual areal mean rainfall interpolated by different numbers of rain gauges by using External Drift
Kriging method.
rainfall frequently happens around the uphill slopes of the area.
This significantly contributes to the mean annual discharge in the basin. Although
Fig. 9 a–f only show one stochastically gener-
ated rain gauge network, they could well qualitatively demonstrate how the rain gauges’ geographic locations impact the model simulation results.
5. Conclusions
This paper investigated the characteristics of the mean areal rainfall estimated by different rain gauge densities and their influence on the performance of the Xinanjiang Model in Xiangjiang
River basin, China. The conclusions of the study are as follows:

(i) The slight change of median value of mean areal rainfall from different rain gauge networks demonstrates that the
100-time random selection for each number of rain gauges is enough to represent different variation cases of areal rainfall. Smaller sampling rate (i.e., 10-time random selection) results in unstable mean annual rainfall and inconsistent error ranges.
(ii) As compared to the observed mean areal rainfall from all available rain gauges (MAR_181), relative errors of the mean areal rainfall estimated from fewer rain gauges (MAR_Drg) increased as the number of selected rain gauges decreased.
(iii) The percentage of days in the non-rainy and 0 3 mm classes have an inverse trend with the increasing of the number of rain gauges. The error range of rainfall in the >50 mm class increases rapidly as the rain gauge density decreases while the other classes only show slight increases.
(iv) Acceptable model performance is achieved when the number of rain gauges ranged between 93 and 128 irrespective of the gauge configurations. However, the probability of getting poor model performance is very much increased when the number of rain gauges falls below 38.
(v) The correlation coefficient between the areal mean rainfall calculated by 181 stations and by fewer rain gauges ( q r–r
), and the correlation coefficient between the observed runoff and the simulated runoff with the input of different rain gauge densities ( q f–f
) increase hyperbolically in the same step with the increase of the number of rain gauges. However, after the threshold of 93 rain gauges, both q r–r and q f–f show no change.
(vi) Better model performance can be achieved with fewer rain gauges if an optimum spatial configuration is provided and is determined by considering the mountain areas where heavy orographic rainfall is the dominant pattern of the local precipitation.
It is worth noting that although the results are obtained from a specific catchment, it is anticipated that the general conclusions hold generally true in other catchments. Of course, the threshold values and magnitudes of the changes may vary with catchments.
Further studies in other regions using different models are needed so that the quantitative findings can be generalised confidently.
Acknowledgements
H. Xu et al. / Journal of Hydrology 505 (2013) 1–12
This paper is financially supported by the State Key Program of
National Natural Science of China (Grant Nos. 40930635,
51279138). The second author was also supported by the Program of Introducing Talents of Discipline to Universities – the 111 Project of Hohai University. We would like to thank the National Climate Centre in Beijing for providing valuable climate datasets.
We are grateful to the reviewers and the editor that contributed to the great improvement of the original version of this paper with their valuable comments and suggestions.
References
Adeloye, A.J., Rustun, R., 2012. Self-organising map rainfall–runoff multivariate modelling for runoff reconstruction in inadequately gauged basins. Hydrology
Research 43 (5), 603–617 .
Ahmed, S., Marsily, G., 1987. Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity. Water
Resources Research 23, 1717–1737 .
Anctil, F., Lauzon, N., Andréassian, V., Oudin, L., Perrin, C., 2006. Improvement of rainfall–runoff forecasts through mean areal rainfall optimization. Journal of
Hydrology 328, 717–725 .
Bao, H., Zhao, L., He, Y., Li, Z., Wetterhall, F., Cloke, H., Pappenberger, F., Manful, D.,
2011. Coupling ensemble weather predictions based on TIGGE database with
Grid-Xinanjiang Model for flood forecast. Advances in Geosciences 29 (6), 61–
67 .
11
Bárdossy, A., Das, T., 2008. Influence of rainfall observation network on model calibration and application. Hydrology and Earth System Sciences 12, 77–89 .
Bárdossy, A., Plate, E.J., 1992. Space-time model for daily rainfall using atmospheric circulation patterns. Water Resources Research 28, 1247–1259 .
Bengtsson, L., 2012. Daily and hourly rainfall distribution in space and time – conditions in southern Sweden. Hydrology Research 42 (2–3), 86–94 .
Beven, K.J., 2001. Rainfall–Runoff Modelling. Wiley Online Library .
Chen, D., Ou, T.H., Gong, L.B., Xu, C.-Y., Li, W.J., Ho, C.-H., Qian, W.H., 2010a. Spatial interpolation of daily precipitation in China: 1951–2005. Advances in
Atmospheric Sciences 27 (6), 1221–1232 .
Chen, X., Cheng, Q., Chen, Y.D., Smettem, K., Xu, C.Y., 2010b. Simulating the integrated effects of topography and soil properties on runoff generation in hilly forested catchments, South China. Hydrological Processes 24 (6), 714–725 .
Chen, H., Xu, H., Zhang, Z., Wang, J., Guo, J., Xu, C.Y., 2012a. Temporal and spatial variation of extreme precipitation indices in the Xiangjiang Basin, China and their possible causes during 1961–2005. Geophysical Research Abstracts. EGU
General, Assembly 2012. Vol. 14, p. 1894.
Chen, H., Xu, C.Y., Guo, S.L., 2012b. Comparison and evaluation of multiple GCMs, statistical downscaling and hydrological models in the study of climate change impacts on runoff. Journal of Hydrology 434, 36–45 .
Dong, X., Dohmen-Janssen, C.M., Booij, M.J., 2005. Appropriate spatial sampling of rainfall or flow simulation. Hydrological Sciences Journal 50, 279–298 .
Goovaerts, P., 1997. Geostatistics for Natural Resources Evaluation. Oxford
University Press, New York .
Goovaerts, P., 1999. Using elevation to aid the geostatistical mapping of rainfall erosivity. Catena 34 (3–4), 227–242 .
Goovaerts, P., 2000. Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. Journal of Hydrology 228 (1), 113–129 .
Hengl, T., Heuvelink, G.B.M., Stein, A., 2003. Comparison of kriging with external drift and regression-kriging. Technical note, ITC. < http://www.itc.nl/library/
Academic_output/ >.
Hu, C., Guo, S., Xiong, L., Peng, D., 2005. A modified Xinanjiang Model and its application in northern China. Nordic Hydrology 36, 175–192 .
Hu, L., Peng, D., Tang, S., Xiao, Y., Chen, H., 2011. Impact of climate change on hydroclimatic variables in Xiangjiang River basin, China. In: International Symposium on Water Resource and Environmental Protection – ISWREP, 2011. Vol. 4, pp.
2559–2562 (IEEE).
Jayawardena, A., Zhou, M., 2000. A modified spatial soil moisture storage capacity distribution curve for the Xinanjiang Model. Journal of Hydrology 227 (1), 93–113 .
Ji, C., Wu, Y., Chen, X., Chen, Y., Xia, J., Zhang, H., 2008. Exploring hydrological process features of the East River (Dongjiang) basin in south China using VIC and SWAT. IAHS Press (pp. 116–123).
Jiang, S.H., Ren, L.L., Yong, B., Fu, C.B., Yang, X.L., 2012. Analyzing the effects of climate variability and human activities on runoff from the Laohahe basin in northern China. Hydrology Research 43 (1–2), 3–13 .
Jin, X., Xu, C.-Y., Zhang, Q., Chen, Y.D., 2009. Regionalization study of a conceptual hydrological model in Dongjiang basin, south China. Quaternary International
208 (1–2), 129–137 .
Jin, X., Xu, C.-Y., Zhang, Q., Singh, V., 2010. Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model. Journal of Hydrology 383 (3–4), 147–155 .
Krajewski, W.F., Ciach, G.J., Habib, E., 2003. An analysis of small-scale rainfall variability in different climatic regimes. Hydrological Sciences Journal 48 (2),
151–162 .
Li, J., Wu, G., Liu, X., 1997. The Laws of hydrologic variation in the Xiangjiang River valley. Tropical, Geography. 03.
Li, H., Zhang, Y., Chiew, F.H.S., Xu, S., 2009. Predicting runoff in ungauged catchments by using Xinanjiang Model with MODIS leaf area index. Journal of
Hydrology 370, 155–162 .
Li, L., Xu, C.-Y., Xia, J., Engeland, K., Reggiani, P., 2011. Uncertainty estimates by
Bayesian method with likelihood of AR (1) &Normal model and AR (1) &Multinormal model in different time-scales hydrological models. Journal of
Hydrology 406, 54–65 .
Li, X.H., Zhang, Q., Xu, C.-Y., 2012. Suitability of the TRMM satellite rainfalls in driving a distributed hydrological model for water balance computations in
Xinjiang catchment, Poyang lake basin. Journal of Hydrology 426, 28–38 .
Li, L., Ngongondo, C.-S., Xu, C.-Y, Gong, L.B., 2013. Comparison of the global TRMM and WFD precipitation datasets in driving a large-scale hydrological model in
Southern Africa. Hydrology Research, in press. doi: 10.2166/nh.2012.175.
Liu, S., Mo, X., Leslie, LM., Speer, M., Bunker, R., Zhao, W., 2001. Another Look at the
Xinanjiang Model: From Theory to Practice. Paper presented at the Proc.
MODSIM2001 Congress.
Liu, J., Chen, X., Zhang, J., Flury, M., 2009. Coupling the Xinanjiang Model to a kinematic flow model based on digital drainage networks for flood forecasting.
Hydrological Processes 23, 1337–1348 .
Michaud, J.D., Sorooshian, S., 1994. Effect of rainfall-sampling errors on simulations of desert flash floods. Water Resources Research 30, 2765–2775 .
Nash, J.E., Sutcliffe, J., 1970. River flow forecasting through conceptual models part
I-A discussion of principles. Journal of Hydrology 10, 282–290 .
Oudin, L., Perrin, C., Mathevet, T., Andréassian, V., Michel, C., 2006. Impact of biased and randomly corrupted inputs on the efficiency and the parameters of watershed models. Journal of Hydrology 320, 62–83 .
Parkes, B.L., Wetterhall, F., Pappenberger, F., He, Y., Malamud, B.D., Cloke, H.L., 2013.
Assessment of a 1-hour gridded precipitation dataset to drive a hydrological model: a case study of the summer 2007 floods in the Upper Severn, UK.
Hydrology Research 44 (1), 89–105 .

12 H. Xu et al. / Journal of Hydrology 505 (2013) 1–12
Ren, L.L., Huang, Q., Yuan, F., Wang, J., Xu, J., Yu, Z., Liu, X., 2006. Evaluation of the
Xinanjiang Model structure by observed discharge and gauged soil moisture data in the HUBEX/GAME Project. IAHS PUBLICATION 303, 153.
Singh, V.P., 1995. Computer Models of Watershed Hydrology. Water Resources
Publications. ISBN 0-918334-91-8.
Singh, V.P., 1997. Effect of spatial and temporal variability in rainfall and watershed characteristics on stream flow hydrograph. Hydrological Processes 11, 1649–
1669 .
St-Hilaire, A., Ouarda, T.B.M.J., Lachance, M., Bobée, B., Gaudet, J., Gignac, C., 2003.
Assessment of the impact of meteorological network density on the estimation of basin precipitation and runoff: a case study. Hydrological Processes 17,
3561–3580 .
Sun, H., Cornish, P., Daniell, T.M., 2002. Spatial variability in hydrologic modeling using rainfall–runoff model and digital elevation model. Journal of Hydrologic
Engineering 7, 404 .
Sun, S., Khu, S.-T., Djordjevic, S., 2013. Sampling rainfall events: a novel approach togenerate large correlated samples. Hydrology Research 44, 351–361 .
Varikoden, H., Samah, A., Babu, C., 2010. Spatial and temporal characteristics of rain intensity in the peninsular Malaysia using TRMM rain rate. Journal of Hydrology
387, 312–319 .
Wackernagel, H., 1998. (completely revised). Multivariate Geostatistics, second ed.,
Springer, Berlin.
Wilson, C.B., Valdes, J.B., Rodriguez-Iturbe, I., 1979. On the influence of the spatial distribution of rainfall on storm runoff. Water Resources Research 15, 321–328 .
Xu, C.-Y., Vandewiele, G.L., 1994. Sensitivity of monthly rainfall–runoff models to input errors and data length. Hydrological Science Journal 39 (2), 157–176 .
Xu, C.-Y., Tunemar, L., Chen, Y.D., Singh, V.P., 2006. Evaluation of seasonal and spatial variations of conceptual hydrological model sensitivity to precipitation data errors. Journal of Hydrology 324, 80–93 .
Xu, J., Ren, L.L., Yuan, F., Liu, X.F., 2012. The solution to DEM resolution effects and parameter inconsistency by using scale-invariant TOPMODEL. Hydrology
Research 43 (1–2), 146–155 .
Yang, C.G., Yu, Z.B., Hao, Z.C., Zhang, J.Y., Zhu, J.T., 2012. Impact of climate change on flood and drought events in Huaihe River Basin, China. Hydrology Research 43
(1–2), 14–22 .
Yao, C., Li, Z., Bao, H., Yu, Z., 2009. Application of a developed Grid-Xinanjiang Model to Chinese watersheds for flood forecasting purpose. Journal of Hydrologic
Engineering 14, 923 .
Yevjevich, V., Engineer, Y., Ingenieur, J., Ingénieur, Y., 1972. Probability and Statistics in Hydrology. Water Resources Publications Fort Collins, Colorado, USA .
Yuan, F., Xie, Z., Liu, Q., Yang, H., Su, F., Liang, X., Ren, L., 2004. An application of the
VIC-3L land surface model and remote sensing data in simulating streamflow for the Hanjiang River basin. Canadian Journal of Remote Sensing 30 (5), 680–
690 .
Yuan, F., Ren, L.L., Yu, Z.B., Zhu, Y.H., Xu, J., Fang, X.Q., 2012. Potential natural vegetation dynamics driven by future long-term climate change and its hydrological impacts in the Hanjiang River basin, China. Hydrology Research
43 (1–2), 73–90 .
Zehe, E., Becker, R., Bárdossy, A., Plate, E., 2005. Uncertainty of simulated catchment runoff response in the presence of threshold processes: Role of initial soil moisture and precipitation. Journal of Hydrology 315, 183–202 .
Zhang, D.R., Zhang, L.R., Guan, Y.Q., Chen, X., Chen, X.F., 2012. Sensitivity analysis of
Xinanjiang rainfall–runoff model parameters: a case study in Lianghui, Zhejiang province, China. Hydrology Research 43 (1–2), 123–134 .
Zhao, R.J., 1992. The Xinanjiang Model applied in China. Journal of Hydrology 135,
371–381 .
Zhao, R.J., Zhuang, Y.L., Fang, L.R., Liu, X.R., Zhang, Q.S., 1980. The Xinanjiang Model.
In: Hydrological Forecasting, IAHS Publication No. 129. IAHS Press: Wallingford; pp. 351–356.
Zhao, R.J., Liu, X., Singh, V.P., 1995. The Xinanjiang Model. Computer Models of
Watershed Hydrology, 215–232 .
Zhou, S., Liang, X., Chen, J., Gong, P., 2004. An assessment of the VIC-3L hydrological model for the Yangtze River basin based on remote sensing: a case study of the
Baohe River basin. Canadian Journal of Remote Sensing. CD ROM 30(5), 840.