This article was downloaded by: [Jintao Liu]
On: 24 February 2012, At: 05:12
Publisher: Taylor & Francis
Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,
37-41 Mortimer Street, London W1T 3JH, UK
Hydrological Sciences Journal
Publication details, including instructions for authors and subscription information:
http://www.tandfonline.com/loi/thsj20
Grid parameterization of a conceptual distributed
hydrological model through integration of a sub-grid
topographic index: necessity and practicability
Jintao Liu
a b c
, Xi Chen
a c
b
c
c
, Jichun Wu , Xingnan Zhang , Dezeng Feng & Chong-Yu Xu
e
a
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai
University, Nanjing, 210098, China
b
Department of Hydrosciences, Nanjing University, Nanjing, 210093, China
c
Department of College of Hydrology and Water Resources, Hohai University, Nanjing,
210098, China
d
Department of Geosciences, University of Oslo, PO Box 1047, Blindern, NO-0316, Oslo,
Norway
e
Department of Earth Sciences, Uppsala University, Uppsala, Sweden
Available online: 24 Feb 2012
To cite this article: Jintao Liu, Xi Chen, Jichun Wu, Xingnan Zhang, Dezeng Feng & Chong-Yu Xu (2012): Grid
parameterization of a conceptual distributed hydrological model through integration of a sub-grid topographic index:
necessity and practicability, Hydrological Sciences Journal, 57:2, 282-297
To link to this article: http://dx.doi.org/10.1080/02626667.2011.645823
PLEASE SCROLL DOWN FOR ARTICLE
Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions
This article may be used for research, teaching, and private study purposes. Any substantial or systematic
reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to
anyone is expressly forbidden.
The publisher does not give any warranty express or implied or make any representation that the contents
will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should
be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims,
proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in
connection with or arising out of the use of this material.
d
282
Hydrological Sciences Journal – Journal des Sciences Hydrologiques, 57(2) 2012
Grid parameterization of a conceptual distributed hydrological model
through integration of a sub-grid topographic index: necessity and
practicability
Jintao Liu1,2,3 , Xi Chen1,3 , Jichun Wu2 , Xingnan Zhang3 , Dezeng Feng3 and Chong-Yu Xu4,5
Downloaded by [Jintao Liu] at 05:12 24 February 2012
1
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China
jtliu@hhu.edu.cn
2
Department of Hydrosciences, Nanjing University, Nanjing 210093, China
3
Department of College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China
4
Department of Geosciences, University of Oslo, PO Box 1047 Blindern, NO-0316 Oslo, Norway
5
Department of Earth Sciences, Uppsala University, Uppsala, Sweden
Received 7 June 2010; accepted 22 June 2011; open for discussion until 1 August 2012
Editor D. Koutsoyiannis
Citation Liu, J.T., Chen, X., Wu, J.C., Zhang, X.N., Feng, D.Z. and Xu, C.-Y., 2012. Grid parameterization of a conceptual, distributed
hydrological model through integration of a sub-grid topographic index: necessity and practicability. Hydrological Sciences Journal,
57 (2), 282–297.
Abstract Grid-based distributed models have become popular for describing spatial hydrological processes.
However, the influence of non-homogeneity within a grid on streamflow simulation was not adequately addressed
in the literature. In this study, we investigated how the statistical characteristics of soil moisture storage within
a grid impacts on streamflow simulations. The spatial variation of the topographic index, TI, within a grid was
used to determine parameter B of the statistical curve of soil moisture storage in the Xinanjiang model. For
comparison of influences of the non-homogeneity within a grid on streamflow simulation, two parameterization
schemes of soil moisture storage capacity were developed: a grid-parameterization scheme for a distributed model
and a catchment-averaged scheme for a semi-distributed model. The practicability and usefulness of the gridparameterization method were evaluated through model comparisons. The two models were applied in Jiangwan
experimental catchment Zhejiang Province, China. Streamflow discharge data at the catchment outlet from 1971 to
1986 at different temporal resolutions, e.g. 15 min and daily time step, were used for model calibration and validation. Statistical results for different grid scales demonstrated that the mean and variation of TI and B decline
significantly as the grid scale increases. The simulated streamflow discharges of the two models were similar and
the semi-distributed model outperformed the distributed model slightly when the streamflow at the outlet of the
catchment was used as the only basis for comparison. In addition, a relatively larger bias in the predicted discharges between these two models was observed along with an abrupt increase of soil moisture saturation ratio.
A further analysis of the simulated soil moisture content distribution revealed that the distributed model can provide a reasonable representation of the variable source area concept, which was justified to some extent by the field
experiment data.
Key words Xinanjiang model; conceptual parameters; grid-based model; parameterization
Paramétrage de grille d’un modèle hydrologique distribué conceptuel par l’intégration d’un indice
topographique sous grille : nécessité et faisabilité
Résumé Les modèles distribués basés sur des grilles sont devenus populaires pour décrire des processus
hydrologiques spatialisés. Cependant, l’influence des hétérogénéités au sein d’une grille sur la simulation des
débits n’a pas été suffisamment abordée dans la littérature. Dans cette étude, nous avons étudié comment les
caractéristiques statistiques des stocks d’humidité du sol au sein d’une grille influencent les simulations de
débit. La variation spatiale de l’indice topographique, TI, au sein d’une grille a été utilisée pour déterminer
le paramètre B de la courbe statistique des stocks d’humidité du sol dans le modèle Xinanjiang. Pour comparer les influences de l’hétérogénéité au sein d’une grille sur la simulation des débits, deux schémas de
paramétrage de la capacité des stocks de l’humidité du sol ont été développés : un schéma de paramétrage de
grille pour un modèle distribué et un schéma moyenné à l’échelle du bassin pour un modèle semi-distribué.
ISSN 0262-6667 print/ISSN 2150-3435 online
© 2012 IAHS Press
http://dx.doi.org/10.1080/02626667.2011.645823
http://www.tandfonline.com
Grid parameterization of the Xinanjiang model using a sub-grid topographic index
283
La faisabilité et l’utilité de la méthode de paramétrage de grille ont été évaluées par comparaison des modèles.
Les deux modèles ont été appliqués au bassin versant expérimental de Jiangwan, dans la province du Zhejiang, en
Chine. Les données de débit à l’exutoire du bassin versant de 1971 à 1986 à différentes résolutions temporelles,
par exemple à pas de temps de 15 min et journalier, ont été utilisées pour le calage et la validation du modèle.
Les résultats statistiques pour différentes échelles de grille ont démontré que la moyenne et la variation de TI et
B diminuent de façon significative avec l’augmentation de l’échelle de la grille. Les débits simulés par les deux
modèles sont similaires et le modèle semi-distribué surclasse légèrement le modèle distribué lorsque le débit à
l’exutoire du bassin versant a été utilisé comme seule base de comparaison. En outre, un biais relativement plus
important dans les débits prévus entre ces deux modèles a été observé, avec une augmentation brutale du taux de
saturation en eau du sol. Une analyse plus approfondie de la distribution de l’humidité du sol simulée a révélé que
le modèle distribué peut fournir une représentation raisonnable du concept d’aire source variable, qui a été justifié
dans une certaine mesure par les données expérimentales de terrain.
Mots clefs modèle Xinanjiang; paramètres conceptuels; modèle basé sur grille; paramétrage
Downloaded by [Jintao Liu] at 05:12 24 February 2012
1
INTRODUCTION
Because of their simple structure, fewer parameters
and easier application, conceptual hydrological models are of great importance for practical utilization
such as flood forecasting, water resources planning
and water resources management. The Xinanjiang
model (Zhao et al. 1980), for example, is one of the
most popularly used conceptual hydrological models
in China. The model outperforms some other lumped
models in that it inherently represents the spatial distribution of the soil storage capacity over the basin by
using a parabolic curve, i.e. the soil moisture storage
capacity curve (SMSCC) (Gan et al. 1997), and this
was later widely adopted by other hydrological models, e.g. the VIC model (Liang et al. 1996) and the
ARNO model (Todini 1996).
However, a large amount of spatio-temporal
information (e.g. digital maps, digital terrain models and land-use data) combined with many powerful tools (geographic information systems, GIS and
remote sensing, RS) has challenged the traditional
lumped structure and parameter determination of the
conceptual models.
For instance, in order to make good use of the
distributed information, GIS was used to regionalize
lumped catchment characteristics and the conceptual
parameters by Schumann et al. (2000). Information of
land use and land cover was applied to parameterize
two lumped storage capacity curves in a conceptual
model by Wooldridge et al. (2001). For better representation of the spatial distribution of hydrological
processes, many efforts have been made to upgrade
the conceptual lumped models to distributed models.
For example, the lumped HBV model was modified
into a distributed and semi-distributed structure by
dividing a catchment into lots of grid cells or a number of homogenous zones in order to account for
detailed catchment characteristics (e.g. soil and land
use) (Das et al. 2008).
The Xinanjiang model was recently improved to
be a semi-distributed model that was run on a resolu-
tion of 1 × 1 km2 to utilize higher-resolution rainfall
data (Li et al. 2004, Lu et al. 2008) and was coupled with a grid-based kinematic flow method by
Liu et al. (2009). However, in the above studies, the
effect of landscape heterogeneity on runoff generation within each 1 × 1 km2 grid was not evaluated.
That is to say, the Xinanjiang model was applied in
each grid, using the same soil moisture storage capacity curve and only a unique set of parameters was to be
estimated.
In order to develop a physically-based structure
for the Xinanjiang model, Guo et al. (2000) found that
the soil storage curve can be substituted by a curve
of normalized cumulative frequency of area fraction versus TOPMODEL’s topographic index (Beven
et al. 1984). Chen et al. (2007) developed a new
approach that incorporates the TOPMODEL topographic index into the mechanism of runoff generation of the Xinanjiang model. The runoff generation
can be computed at a sub-catchment scale, thus making the model a distributed structure with small data
requirements and high applicability.
The existing studies tend to apply the physicallybased method for conceptual model parameterization
in a catchment or sub-catchment toward different
aims. The question arises as to whether it is necessary to resolve the non-homogeneity within the scale
of a grid with a cell size of 1 km × 1 km, or even
smaller, such as 200 m × 200 m. That is to say, one
needs to evaluate the heterogeneity of storage capacity for each grid and to assess whether it is necessary
and practicable to run the simulation on a grid-based
conceptual model.
The main objective of this study is to evaluate and
develop a grid-based model for simulating streamflow
at different temporal resolutions and to investigate
how the statistical characteristics of soil moisture
storage within a grid will impact on the streamflow
simulation. Here, parameterization of a grid-based
conceptual model is first evaluated for different sizes
of grids and a suitable grid size is then defined. A conceptual rainfall–runoff model, the Xinanjiang model,
Downloaded by [Jintao Liu] at 05:12 24 February 2012
284
Jintao Liu et al.
was selected and modified to incorporate different
parameterization strategies for a computational grid
network.
The study includes: (a) exploration of the question as to “whether it is more important for runoff
generation to reproduce the spatial variability of soil
moisture content within a grid or the spatial variability from the grid scale to the catchment, as the
Xinanjiang model attempted to do by using the soil
moisture storage capacity curve”; (2) investigation of
the spatial variability of the soil moisture curve for
different grid scales, on the one hand, and how this
spatial variability affects the model simulation at different time resolutions (daily, quarter-hourly) on the
other hand; and (3) proof that the distributed model
is able to describe the variable source area concept,
which was examined by the relationship between soil
moisture content and the distance to the river channel,
on the basis of field data.
Fig. 1 Location of Jiangwan catchment and its DEM.
2 MATERIALS AND METHODS
2.1 Study catchment
The selected catchment in this study is the Jiangwan
catchment, located in the Mogan Mountains, Zhejiang
province, China (Fig. 1). The catchment has an area
of 20.9 km2 and is characterized by mountains and
steep forest slopes of 25–45◦ . The surface elevation
is 500–600 m a.s.l. in the northwestern region and
decreases to 78 m a.s.l. at the outlet of the Jiangwan
hydrological station (119◦ 50 E, 30◦ 35 N).
Hydro-meteorological data were provided by
Zhejiang Provincial Hydrology Bureau; the data quality was checked according to the National Standard
of People’s Republic of China for Water Resources
(2000) before the data were released. Hydrometeorological data are available for the period
1957–1986. Precipitation records in a quarter-hourly
(15-min) time step are available at 10 raingauge
Downloaded by [Jintao Liu] at 05:12 24 February 2012
Grid parameterization of the Xinanjiang model using a sub-grid topographic index
stations. The average annual precipitation is about
1580 mm according to 30 years’ data. Daily pan evaporation and temperature were monitored at Hemuqiao
station (119◦ 48 E, 30◦ 35 N) and the average annual
evaporation and temperature are 805 mm and 14.6◦ C,
respectively. Streamflow discharges at 15-min time
step were monitored at Jiangwan station. The average
daily discharge at Jiangwan station is about 0.56 m3 /s
and the largest flood flow discharge of 464 m3 /s was
observed on 13 September 1961.
Contour lines were digitized using the TOPOGRID function in ArcInfo (ESRI Inc.) from topography maps (scale 1:10 000) with 5-m vertical intervals.
A DEM of 10-m resolution was generated first. The
DEM was resampled on 50 m × 50 m, 60 m × 60 m,
70 m × 70 m, 80 m × 80 m, 90 m × 90 m, 100 m ×
100 m, 150 m × 150 m, 200 m × 200 m and 250 m ×
250 m spatial resolutions for TI (TOPMODEL
topographic index) aggregation and hydrological
modelling.
In this study, TI was computed according to a
grid-based DEM with a cell size of 10 m× 10 m. A triangular multiple flow-direction algorithm (MD∞)
(Seibert and McGlynn 2007), which combines the
algorithms of Quinn et al. (1995) and Tarboton
(1997), was used to calculate upslope accumulated
area for each cell. All the algorithms and computations were implemented on the digital drainage
network extraction software package, DigitalHydro
(Liu 2009).
Soil moisture content was sampled at 72 sites in
the Hemuqiao sub-catchment in the Jiangwan basin
(Fig. 1) over four days. In the sub-catchment, 18 hillslopes were derived by the DigitalHydro software.
The distance to channel (DC) in each hillslope was
also derived and contour lines with 30-m intervals are
depicted in Fig. 1.
The soil texture within the catchment is sand and
sandy loam with a large porosity due to worms or
decayed tree roots in the A horizon (about 30 cm
deep) on top of a thinner clay B horizon underlain
by non-permeable bed rock. Therefore, infiltrationexcess runoff is rare and saturation-excess runoff is
the main source of runoff on hillslopes. Vegetation
distribution is dominated by bamboo forest, covering
about 95% of the whole area. The remaining area is
rural and crop land.
2.2 The Xinanjiang model and two
grid-parameterization schemes
2.2.1 The basic concept of the Xinanjiang
model The Xinanjiang model (Zhao et al. 1980) has
285
been successfully used to simulate catchment discharge in humid and semi-humid regions in China.
In the original version of the Xinanjiang model, the
basin to be modelled is divided into a set of subbasins. In each sub-basin, a three-layer evapotranspiration sub-model is used to account for soil water
balance, and runoff generation is described by a single parabolic curve, i.e. soil moisture storage capacity
curve (SMSCC) to represent the spatial distribution
of the soil moisture storage capacity over the whole
basin or sub-basin (Zhao et al. 1980):
Wm B
f
=1− 1−
F
Wmm
(1)
where Wm is the storage capacity at a point in the
basin, which varies from zero to the maximum of the
whole watershed Wmm ; B is the exponent of the spatial
distribution curve of tension water storage capacity
that represents the non-uniformity of the spatial
distribution of the soil moisture storage capacity
over the catchment; f denotes the partial area whose
storage capacity is equal to or smaller than a certain
value of W m ; and F is the total area. The catchment
average storage capacity, Wm , can be obtained by:
Wm =
Wmm
1+B
(2)
Then, runoff in each sub-basin is separated into overland flow, interflow and groundwater flow in terms
of a similar non-uniform distribution curve. At the
sub-basin scale, different flow components are routed
through the linear reservoir method and channel flow
routing is carried out by the Muskingum method.
More detailed descriptions of the Xinanjiang model
are available in Zhao et al. (1995), Cheng et al.
(2006), Chen et al. (2007), Li et al. (2009) and Liu
et al. (2009).
The Xinanjiang model parameters needed to be
calibrated in this study are defined in Table 1. The
parameter Wm has a strong influence on catchment
runoff generation. Zhao et al. (1980) suggested that
the values of Wm are about 80–100 mm in south China
and 140–170 mm north of the Yanshan Mountains and
in northeastern China. For thin soils, SM is around
10 mm and ex is between 1.0 and 1.5 (Zhao and Liu
1995). As Ki and Kg are the outflow coefficients of
the free water storage to interflow and groundwater,
it is suggested that the sum Ki + Kg may be taken
as 0.7–0.8 and the ratio of the three runoff components will be changed by altering the ratio of Kg /Ki
(Zhao and Liu 1995). In the Xinanjiang model, K is
286
Table 1 Main parameters in the Xinanjiang model.
IRDGi =
Parameters
Description
K
Ratio of potential evapotranspiration to pan
evaporation
Average tension water capacity
Areal mean free water capacity
Exponent of the spatial distribution curve of
free water storage capacity influencing the
development of the saturated area
Outflow coefficient of free water storage to the
interflow
Outflow coefficient of free water storage to the
groundwater
max(TI1 , TI2 , . . . , TIl ) − TIi
max(TI1 , TI2 , . . . , TIl ) − min(TI1 , TI2 , . . . , TIl )
Wm (mm)
SM (mm)
ex
Ki
Kg
Downloaded by [Jintao Liu] at 05:12 24 February 2012
Jintao Liu et al.
the ratio of potential evapotranspiration to pan evaporation (Table 1), which is influenced by elevation and
size of the pan; the value of K always varies from
0.5 to 1.1 (Zhao 1984).
Based on the concept of the Xinanjiang model,
two different model structures, namely distributed
and semi-distributed, were developed and adopted for
this study; both the models use a grid network to
represent spatial distribution of rainfall input, vegetation, land use and topography of the basin. In these
two models, the key discrepancy lies in the different
parameterization schemes, i.e. the sub-grid parameterization scheme for the distributed model and the
catchment-averaged scheme for the semi-distributed
model. Furthermore, it is worth noting that the flow
routing model used in both models is the same kinematic wave model for raster systems described by
Liu et al. (2009). The two different parameterization
schemes (models) are described below.
2.2.2 Grid-based representation of SMSCC
and the distributed model Traditionally, the
SMSCC and its parameters are determined in an
empirical way and one set of curves was used at the
basin scale. By comparing the spatial distribution of
the Xinanjiang model SMSCC with TOPMODEL’s
topographic index, both Guo et al. (2000) and Chen
et al. (2007) suggested that distribution of SMSCC
in the Xinanjiang model can be replaced by using the
TOPMODEL topographic index, TI (= ln(a/tanβ))
(Beven et al. 1984), in which a is the upstream
contributing area per unit contour line width and tanβ
is the local topographic slope gradient. Then, f /F
versus W m /Wmm in equation (1) can be substituted
by a curve of f /F versus IRDG (defined as an index
of relative difficulty of runoff generation) (Guo et al.
2000, Chen et al. 2007):
(3)
where max(TI1 , TI2 , . . ., TIl ), min(TI1 , TI2 , . . ., TIl )
are the maximum and minimum TI, respectively, i is
the ith sub-grid within the grid, and l is the number of
sub-grids (Fig. 2).
In order to explore the spatial heterogeneity of
sub-grid and inter-grid and derive the IRDG versus
f /F curves for each grid, the 10 m × 10 m DEM was
further sampled to generate more coarse grids, such
as 50 m × 50 m, 60 m × 60 m, 70 m × 70 m, 80 m ×
80 m, 90 m × 90 m, 100 m × 100 m, 150 m × 150 m,
200 m × 200 m, 250 m × 250 m. The idea is to study
whether and how the soil moisture storage distributes
and varies within a larger-scale grid. We suggest a
procedure to assess the variability quantitatively, as
shown in Fig. 2. An arbitrarily selected dark grid at
200 m × 200 m scale is shown in Fig. 2(a), while
Fig. 2(b) shows the schematic of sub-dividing a
computational grid (e.g. scale 200 m × 200 m) into
a sub-grid network of 10 m × 10 m. The values of
the bar for each sub-grid represent the TI for the
10 m × 10 m grid. Then the 400 TI values are sorted
to estimate the cumulative frequency curve of TI.
Figure 2(c) shows the curve of IRDG versus f /F.
Thus, the soil moisture storage curve in the
Xinanjiang model can be calculated from DEM data.
Two parameters need to be defined in equations (1)
and (2): the exponent of the spatial distribution curve,
B, and the average tension water storage capacity,
Wm . Parameter B for each computational grid can be
determined by using curve-fitting procedures based
on least square theory, as follows:
B=
l
i=1
ui v i
l
u2i
(4)
i=1
where ui = ln(1–IRDGi ), vi = ln(1–fi /F) and l is
the number of sub-grids within the grid (e.g. 400 in
Fig. 2(b)). So, in the SMSCC only one parameter, Wm
needs to be calibrated using hydrological data from
the catchment.
In the distributed model, the above proposed
method was used to define the SMSCC (Fig. 2) and
to evaluate the sub-grid variations of topographic
characteristics in each computational grid. That is
to say, the Xinanjiang model parameters describing
Grid parameterization of the Xinanjiang model using a sub-grid topographic index
(b)
(a)
(c)
IRDG
Downloaded by [Jintao Liu] at 05:12 24 February 2012
287
Tabular data of f/F vs
IRDG
Fitted curve
Cumulative frequency (f/F)
Fig. 2 Schematic diagram for the parameterization of a grid: (a) the 200 m × 200 m grid network for Jiangwan catchment;
(b) the distribution of topographic index within a 200 m × 200 m grid of (a); and (c) the fitted cumulative frequency curve
for IRDG defined by Chen et al. (2007) as an index of relative difficulty of runoff generation.
runoff generation processes can be adjusted differently for each individual grid in the distributed model
structure. Thus, the Xinanjiang model is applied for
computation of runoff within each grid.
For the flow routing in a grid-based model, the
catchment is divided into numerous hillslopes and
consists of a raster grid of flow vectors that define the
water flow directions. Here, the kinematic wave flow
routing model for a grid network developed by Liu
et al. (2009) was used. In this flow routing model, discharge leaving the downstream boundary of a raster
enters the upstream boundary of a higher-level raster
and serves to establish the boundary conditions of
depth and discharge required by the kinematic wave
method. Flows are routed from the most upstream
cells to the outlet cell.
2.2.3 Catchment-averaged
scheme
and
the semi-distributed model Compared with
the distributed model structure, in which the
parameterization method of SMSCC (see equations
(3) and (4)) is used on the grid scale, the semidistributed model structure uses a unique SMSCC on
the entire catchment to represent catchment-averaged
spatial variation of soil moisture storage capacity.
The semi-distributed model is different from the
traditional Xinanjiang model in two aspects. First,
the parameter B of SMSCC in equation (1) was
determined in terms of TI in equations (3) and
(4) instead of model calibration. Second, for flow
routing, the same kinematic wave method as that of
the distributed model was used.
2.3 Model calibration method and evaluation
criteria
The model parameters were calibrated by a trialand-error method. The following procedures for
the Xinanjiang model calibration were proposed
by Zhao and Liu (1995): (a) setting initial values
of the parameters; (b) calibrating the parameters
of runoff generation processes, e.g. K and Wm in
288
Jintao Liu et al.
Table 1, by comparing the simulated and observed
daily streamflow discharges; and (c) calibrating other
parameters in Table 1 by comparing the simulated and
observed 15-min streamflow discharges.
Model performance is usually evaluated by a
series of statistical criteria. Each of them has its
own strengths and weaknesses. No universal criteria
are available for evaluation of different models with
different application purposes. Multi-criteria performance evaluation is adopted in this study since we are
evaluating different combinations of spatial parameterization, flow routing and time steps. The evaluation
criteria adopted in the study include:
Downloaded by [Jintao Liu] at 05:12 24 February 2012
2.3.1 Efficiency coefficient
R2ec
=1− (Qobs − Qsim )2
(Qobs − Qobs )2
(5)
where Qobs and Qsim are observed and simulated discharges (m3 /s), respectively and Qobs is the average
value of observed discharge.
2.3.2 Relative bias of the simulated total
runoff
(Qobs − Qsim )
RBv =
(6)
Qobs
2.3.3 Relative bias of simulated peak flow
RBp =
Qobs,max − Qsim,max
Qobs,max
(7)
where Qobs,max and Qsim,max are the observed and
simulated peak discharge (m3 /s), respectively.
2.3.4 Peak time error For the quarter-hourly
model, another statistical criterion, peak time error
(PTe )—the time difference in the appearance of simulated and observed peak flow—is used. This is crucial
for assessing model performance in flood-event simulation, and is defined as:
PTe = PTsim − PTobs
(8)
where PTsim and PTobs are the simulated peak time
and the observed peak time, respectively.
2.3.5 Linear regression and determination
coefficient In addition, the model results include
runoff volume and peak flow, which were evaluated,
respectively, by a linear regression equation, and the
determination coefficient, R2 cc :
y=a·x+b
(9)
R2cc
=
(X − X )(Y − Y )
2 2
(X − X ) · (Y − Y )
(10)
where x, y are variables in X , Y which are observed
and simulated runoff volume or peak flow for different events; while X , Y are their average values,
respectively; and a and b are coefficients for the linear
regression equation. A good simulation can be justified by these equations with a and R2 cc close to 1 and
b close to zero.
2.3.6 Relative peak bias and predicted
discharge bias The above criteria were used to
evaluate model performance compared with the
observation. Two additional criteria were used for
evaluating the differences (bias) between the two
modelling approaches, i.e. distributed and semidistributed models, at two different time resolutions.
For 15-min time step simulations, we first calculated
the relative peak bias, PBr as:
D
Qsim,max − QLsim,max × 100%
(11)
PBr =
Qobs,max
L
where QD
sim,max and Qsim,max are the simulated peak
discharges of the distributed and the semi-distributed
models, respectively.
For daily time step simulations, we adopted the
predicted discharge bias, PDb as:
L
PDb = QD
sim − Qsim
(12)
L
3
where QD
sim and Qsim are simulated discharge (m /s)
of distributed and semi-distributed models, respectively.
3 RESULTS AND DISCUSSION
3.1 Spatial variations of SMSCC
As Quinn et al. (1995) suggested that large grids
(e.g. 50 m × 50 m or larger) are unrepresentative
of detailed catchment characteristics, DEMs with
fine resolution should be used to test internal state
Downloaded by [Jintao Liu] at 05:12 24 February 2012
Grid parameterization of the Xinanjiang model using a sub-grid topographic index
Fig. 3 Spatial distribution of the topographic index (TI)
calculated by the MD∞ method for a 10 m × 10 m grid.
processes and avoid bias caused by a large grid
resolution. Based on the 10 m × 10 m DEM, the
spatial distribution of TI shown in Fig. 3 was calculated by the MD∞ method (Seibert and McGlynn
2007). In this catchment, TI values of between
2.00 and 8.40 account for nearly 90% of the total
area. The mean and median values are 5.65 and 6.18,
respectively.
The statistical variables of TI within a grid were
averaged over the whole catchment and are listed in
Table 2. As the grid scale increases from 50 m to
250 m, the standard deviation increases from 1.42 to
2.01, the average value of maximum TI increases
from 8.76 to 13.38, the minimum value decreases
from 3.26 to 2.24, and the mean and median do
not show remarkable changes. These results indicate that variation of soil moisture capacity becomes
large as the grid scale increases. Additionally, the
probability density function (pdf) of TI within each
grid appears to be a skewed distribution, because
all the median values are larger than the mean
values.
289
Figure 4 shows the cumulative frequency curves
of IRDG for the grids at different scales. As the grid
scales increase from 50 m to 250 m, the domain
interval with grey colour decreases. Thus, the calibrated parameter B in terms of IRDG curves is less
varied as the grid scale increases (Fig. 5). The B
value ranges between 0.30 and 6.98 for the 50-m
grid scale—much larger than that of the 250 m grid
scale (0.40–1.56). The domain interval for parameter B decreases markedly as the grid scale increases
from 50 m to 100 m, i.e. from 6.68 to 2.31. The
decrease becomes smaller as the grid scale is larger
than 100 m: from 1.61 to 1.15 for 150- and 250-m
grid scales, respectively (Fig. 5). The mean value of B
has the same trend; it decreases from 3.64 to 0.98 as
the grid scale increases from 50 m to 250 m (Fig. 5).
The calibrated mean value of B is 0.84 for the whole
catchment scale.
The results above indicate that spatial variation among the larger grids becomes less significant
because large grids include more topographic conditions and tend to have similar statistical characteristics. It may be seen from Fig. 5 that the value of B
reaches a relatively stable state when the grid scale
is larger than 100 m. This more stable grid scale
can be used as a representative unit for catchment
computation, because the statistical characteristics of
topographic conditions for different grids behave similarly. In this study, we selected the scale, 200 m ×
200 m as the representative unit, because both the
mean and variation of B values become relatively
stable at this scale.
3.2 Model calibration and validation
The model parameters for Jiangwan catchment were
calibrated and validated against the observed discharge at the outlet of Jiangwan station. Two models
were executed at a 15-min time step to study flood
events and at a daily time step to study long-term
water balance.
Table 2 Catchment average results for statistical values of topographic index (TI) within a grid at different DEM scales.
DEM
Maximum value
Minimum value
Mean value
Median value.
Standard deviation
50 m
60 m
70 m
80 m
90 m
100 m
150 m
200 m
250 m
8.76
9.15
9.52
9.84
10.15
10.44
11.75
12.64
13.38
3.26
3.12
3.02
2.92
2.83
2.76
2.53
2.34
2.24
5.40
5.43
5.37
5.38
5.34
5.32
5.27
5.25
5.17
5.60
5.60
5.61
5.60
5.60
5.58
5.60
5.60
5.57
1.42
1.48
1.54
1.60
1.64
1.68
1.84
1.93
2.01
Jintao Liu et al.
Fig. 4 Cumulative frequency curves of relative topographic index, IRDG, for different grid scales.
Value of parameter B
Downloaded by [Jintao Liu] at 05:12 24 February 2012
290
8
7
6
5
4
3
2
1
0
40
80
120
160
200
240
280
DEM resolution (m)
Fig. 5 Value of parameter B in the Xinanjiang model, as a
function of DEM resolution.
Before the calibration, initial values for all the
parameters were given. As parameters K and Wm
are related to the average climate and surface conditions of the study region, the initial values were
taken as K = 0.8 and Wm = 100 mm, according to
Zhao (1984). Due to the unevenness of rainfall over
a long period, SM for the daily time step was less
than for a shorter time step. Therefore, it was initially
given as 5 mm and 15 mm for daily and 15-min time
step models, respectively. The initial values of ex , Ki
and Kg were set to 1.0, 0.35 and 0.35, respectively.
The Manning’s roughness coefficients for all of the
grids within the catchment were defined according to
the land-use information: The value for forest land
varies from to 0.100 to 0.230 (Liu et al. 2009). In this
catchment, a fixed initial value of 0.100 was chosen,
as the catchment is covered by bamboo forest.
The statistical results of the model performance
for the calibration period of 1971–1979 and the
validation period of 1980–1986 are presented in
Tables 3 and 4 for the daily and 15-min time step,
respectively. The calibrated values of K and Wm are
0.85 and 90 mm, respectively; SM is 6 mm for the
daily time step and 14 mm for the 15-min time step;
ex , Ki , Kg and Manning’s n are 1.2, 0.44, 0.36 and
0.126, respectively.
3.3 Discussion of the model performance
The distributed and semi-distributed models followed
the same performance pattern during the calibration
and validation periods at the daily time step and
quarter-hourly time step. For the daily time step,
the efficiency coefficient, R2ec , simulated by the distributed model ranges from 0.57 to 0.91 with a mean
value 0.74 for the calibration period and ranges from
0.51 to 0.82 with a mean value of 0.72 for the validation period. The minimum, maximum and mean values for the semi-distributed model are 0.56, 0.91 and
0.76 for the calibration period and 0.51, 0.82 and
0.73 for the validation period. Overall, the simulated
Grid parameterization of the Xinanjiang model using a sub-grid topographic index
291
Table 3 Model performance statistics for the calibration period (1971–1979) and validation period (1980–1986) at the daily
time step using distributed and semi-distributed Xinanjiang model structure.
Downloaded by [Jintao Liu] at 05:12 24 February 2012
Period
Statistical criterion
Distributed model
Semi-distributed model
Min.
Max.
Ave.
Min.
Max.
Ave.
Calibration
R2 cc
RBv
RBp
0.57
–0.07
–0.27
0.91
0.15
0.17
0.74
0.04
0.03
0.56
–0.05
–0.26
0.91
0.16
0.17
0.76
0.05
0.03
Validation
R2 cc
RBv
RBp
0.51
–0.25
–0.58
0.82
0.14
0.21
0.72
–0.06
–0.08
0.51
–0.24
–0.55
0.82
0.15
0.22
0.73
–0.04
–0.08
Period
Statistical criterion
Distributed model
Semi-distributed model
Runoff volume
Peak flow
Runoff volume
Peak flow
Cali bration
a
b
R2 cc
1.009
167.4
0.870
1.1683
−0.098
0.725
1.013
153.5
0.871
1.168
−0.128
0.727
Validation
a
b
R2 cc
0.859
257.9
0.948
0.640
4.088
0.605
0.864
242.3
0.949
0.648
3.894
0.613
Note: Max., Min. and Ave. refer to maximum, minimum and average values of statistical criteria, respectively. The definitions of the
statistical criteria are found in Section 2.3.
Table 4 Model performance statistics for the calibration period (1971–1979) and validation period (1980–1986) at the
15-min time step using distributed and semi-distributed Xinanjiang model structure.
Period
Statistical criterion
Distributed model
Semi-distributed model
Min.
Max.
Ave.
Min.
Max.
Ave.
Calibration
R2 cc
RBv
RBp
PTe (h)
0.49
–0.17
–0.35
–2
0.96
0.23
0.18
2.25
0.77
0.12
–0.04
0.34
0.50
–0.17
–0.36
–2
0.96
0.22
0.17
2.25
0.77
0.12
–0.04
0.34
Validation
R2 cc
RBv
RBp
PTe (h)
0.52
–0.19
–0.46
–0.50
0.91
0.32
0.38
3.50
0.74
0.04
–0.15
0.87
0.52
–0.19
–0.47
–0.50
0.92
0.31
0.38
3.50
0.74
0.04
–0.15
0.87
Period
Statistical criterion
Distributed model
Semi-distributed model
Runoff volume
Peak flow
Runoff volume
Peak flow
Calibration
a
b
R2 cc
0.883
–0.303
0.918
0.512
15.65
0.900
0.882
–0.274
0.919
0.516
15.55
0.902
Validation
a
b
R2 cc
0.898
6.706
0.892
1.324
−3.052
0.941
0.898
6.827
0.893
1.325
−3.133
0.940
Note: Max., Min. and Ave. refer to maximum, minimum and average values of statistical criteria, respectively. The definitions of the
statistical criteria are found in Section 2.3.
runoff volumes in the validation period are larger than
those of the calibration period for the two models.
The average relative bias for runoff volume, RBv ,
ranges from 0.04 to 0.06 for the distributed model
and from 0.04 to 0.05 for the semi-distributed model.
The relative bias for peak flow, RBp , has a similar
pattern to RBv in Table 3. The linear regression analysis also indicates that the two models’ results are
closely matched. The accuracy of the simulated runoff
volume is somewhat higher than that of the simulated peak flow for a daily time step. This is because,
at a longer time step, simulation aims to assess the
Jintao Liu et al.
long-term water balance. Daily averaged data are not
useful for predicting the peak discharge especially in
small basins which are characterized by flash flood
events. Simulation results at quarter-hourly time steps
are similar to those of daily time step (Table 4).
Generally, the semi-distributed model outperformed
the distributed model when only the streamflow at the
outlet of the catchment was used for evaluation.
The results are somewhat surprising as one would
expect a larger difference in the simulated results
between these two models. The reason for this can
be partly explained by the fact that the models adopt
the same structure in flow routing, except for the
parameterization scheme within each grid for parameter B. Moreover, though the predicted peak discharge
and runoff volume at the outlet are very close, it
is considered unreasonable to select discharge at the
outlet as the sole criterion without considering the
spatial heterogeneity of internal fluxes and state variables for model assessment.
The aim of the distributed model is to generate a detailed description of the spatial heterogeneity
of internal fluxes and state variables. This spatial
heterogeneity has a more significant influence on
streamflow during the initial onset of drought than
during wet conditions. This is seen in differences of
simulated results of these two models in terms of initial soil moisture saturation ratio, ISMSr (=W 0 /Wm ).
As shown in Fig. 6, most flood events have a high
ISMSr value. The events with ISMSr values larger
than 0.80 (0.95) are about 84% (40%) and the number of events with ISMSr value less than 0.7 is only
four. As the initial soil moisture content among most
of the flood events is close to saturation and rainfall
volume is mostly centred in several time steps after
the flood event begins, the average soil moisture storage will quickly achieve its maximum capacity Wm
in the model and a large part of rainfall is converted
to runoff. Different runoff yielding modules in the
PBr (%)
Downloaded by [Jintao Liu] at 05:12 24 February 2012
292
7
6
5
4
3
2
1
0
0.6
0.65
0.7
0.75
0.8
ISMSr
0.85
0.9
0.95
1
Fig. 6 Relative peak discharge bias, PBr as a function of
initial soil moisture saturation ratio, ISMSr .
two models will play a relatively minor role compared
with the flow routing model and thus the two models
behave similarly. When the ISMSr is larger than or
equals to 0.90, the mean value of the simulated bias
(PBr ) is less than 1%.
However, differences of simulated streamflow
from initial drought conditions for the distributed
and semi-distributed models become relatively
significant. Figure 6 shows that the lower ISMSr is
always accompanied by a larger peak bias between
the two models. In the four events (start times:
08:00 h on 18 September 1964; 0:00 h on 5 August
1972; 0:00 h on 19 August 1974; and 12:00 h on
4 October 1983) the ISMSr values are 0.66, 0.63,
0.62 and 0.68, respectively; the RBp is 4.5, –11.4,
–3.3 and –15.2% for the distributed model, and 8.3,
–12.8, –3.3 and –13.4% for the semi-distributed
model. The R2 ec values for the distributed model are
0.89, 0.84, 0.94 and 0.66, respectively, and for the
semi-distributed model, 0.86, 0.83, 0.94 and 0.67,
respectively. The distributed model behaves a little
better than the semi-distributed model.
Spatial variation of the simulated soil moisture
content further demonstrates the influences of differences in the model structure. Figure 7 shows the
rainfall and soil moisture saturation ratio hydrograph
from 08:00 h on 18 September 1964 to 01:45 h on
20 September. Soil moisture saturation ratio maps
at six time steps (12:15, 17:15, 20:00 and 22:00 h
on 18 September 1964; 01:45 and 08:15 h on
19 September 1964: marked by dashed lines) were
selected to show the discrepancy in simulated spatial variables between these two models (Fig. 8). It is
shown that the soil moisture near the riparian area
was saturated faster in the distributed model simulation. The soil moisture maps simulated by the
semi-distributed model do not show this trend and
the soil moisture appears to be strongly influenced
by the rainfall distribution instead of runoff variation.
Therefore, the distributed model has demonstrated
greater ability in reasonably predicting the spatial
distribution of hydrological variables.
The differences in description of soil moisture contents by the two models would influence
streamflow discharges. As shown in Fig. 9, the overall PDb is generally greater than zero, indicating
that simulated discharge of the distributed model is
larger than that of the semi-distributed models. The
extreme positive value of PDb is closely correlated
with an abrupt variation of soil moisture saturation
ratio, SMSr (W/Wm ). A further analysis in Fig.10
demonstrates that PDb greater than 0.01 has some
2.50
3.00
3.50
4.00
0.75
0.70
0.65
0.60
Time
1964-9-18 1964-9-18 1964-9-18 1964-9-18 1964-9-18 1964-9-18 1964-9-18 1964-9-18 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-19 1964-9-20
8:00:00
10:00:00 12:00:00 14:00:00 16:00:00 18:00:00 20:00:00 22:00:00
0:00:00
2:00:00
4:00:00
6:00:00
8:00:00
10:00:00 12:00:00 14:00:00 16:00:00 18:00:00 20:00:00 22:00:00
0:00:00
2.00
1.50
0.80
Soil Moisture Saturation Ratio
1.00
0.90
Rainfall
0.50
0.95
0.85
0.00
Fig. 7 Rainfall and soil moisture saturation ratio hydrograph for a flood event that started at 08:00 h on 18 September 1964.
SMSr
1.00
Downloaded by [Jintao Liu] at 05:12 24 February 2012
Grid parameterization of the Xinanjiang model using a sub-grid topographic index
293
Rainfall (mm)
1964/9/18 22:00
Distributed Model
1964/9/19 8:15
Semi-distributed Model
1964/9/19 1:45
Distributed Model
1964/9/19 1:45
1964/9/19 8:15
Semi-distributed Model
1964/9/18 22:00
Semi-distributed Model
1964/9/18 17:15
Semi-distributed Model
Fig. 8 Simulated soil moisture saturation ratio, SMSr of the distributed and semi-distributed models for the flood event that started at 08:00 h on 18 September 1964 to
01:45 h on 20 September 1964.
Distributed Model
Semi-distributed Model
1964/9/18 20:00
1964/9/18 20:00
1964/9/18 17:15
1964/9/18 12:15
1964/9/18 12:15
Distributed Model
Distributed Model
Semi-distributed Model
Distributed Model
Downloaded by [Jintao Liu] at 05:12 24 February 2012
294
Jintao Liu et al.
-0.2
1971-1-1
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
1972-1-1
1973-1-1
1974-1-1
1975-1-1
1976-1-1
1977-1-1
1978-1-1
1979-1-1
Time
1980-1-1
1981-1-1
1982-1-1
1983-1-1
Fig. 9 Simulated daily discharge bias, PDb and soil moisture saturation ratio, SMSr from 1 July 1971 to 31 December 1986.
PDb (m3/s)
0.7
Downloaded by [Jintao Liu] at 05:12 24 February 2012
1984-1-1
1985-1-1
1986-1-1
Soil moisture Saturation Ratio,SMSr
Simulated Daily Discharge Bias,PDb
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Grid parameterization of the Xinanjiang model using a sub-grid topographic index
295
SMSr
296
Jintao Liu et al.
0.65
300
250
0.45
0.35
0.25
0.15
0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Increment of SMSr
Fig. 10 Simulated daily discharge bias, PDb (≥0.01) as a
function of soil moisture saturation ratio increments for two
adjacent days.
Downloaded by [Jintao Liu] at 05:12 24 February 2012
#23
#63
#22 L.R.L.
#43 L.R.L.
#71 L.R.L.
200
DC (m)
PDb (m3/s)
0.55
#22
#43
#71
#23 L.R.L.
#63 L.R.L.
relationship with the increments of the soil moisture
saturation ratio between the initial and peak time of a
flood hydrograph (mostly one day for the daily computation). The greater the increment of SMSr , the
greater the value of the predicted discharge bias, PDb .
The distributed model was developed according to the
variable source area concept by TOPMODEL. The
model is capable of showing that saturated excess
runoff starts from the area with higher value of TI, i.e.
riparian zone. Our field experiment on five hillslopes
in the study catchment also demonstrates that the
soil moisture content is inversely proportional to the
distance from the sample sites to channel segments
(Fig. 11). During a heavy rainfall, the distributed
model can catch the large discharge primarily produced in the area of the large SMSr while the
semi-distributed model flattens the flood discharge
because of averaged SMSr . Thus the predicted discharges of the distributed model shown in Figs 9
and 10 are larger than those of the semi-distributed
model.
The above comparison indicates that if the models are evaluated only by the discharge at the outlet
and without considering spatial variability of state
variables and process parameters, e.g. soil moisture or flow fluxes, the distributed model will not
outperform the semi-distributed model. That is to say,
a further investigation would be meaningful to study
the parameterization and verification of grid-based
conceptual distributed models with detailed spatial
information.
4 SUMMARY AND CONCLUSIONS
In this study, we developed a grid-based distributed
model for simulation of streamflow at different temporal resolutions based on the Xinanjiang model. The
distributed model includes the soil moisture storage
150
100
50
0
5
10
15
20
25
Volume water content (%)
30
35
Fig. 11 Relationship between soil moisture content and
distance to channel (DC) and linear regression lines (LRL)
for five selected hillslopes (#22, #23, #43, #63 and #71).
capacity curve within a grid, which is derived by integrating the TOPMODEL’s topographic index with the
soil moisture storage. Through comparative study of
the semi-distributed model with the distributed model
at different spatial resolutions, we investigated how
the statistical characteristics of soil moisture storage impact the streamflow simulation in the Jianwan
catchment in China’s Zhejiang province.
The study results demonstrate that variations of
topographic wetness index, TI and the Xinanjiang
model’s parameter, B, for different grid scales reflect
the spatial heterogeneity within a grid. However, the
domain interval and mean of the parameter B decrease
as the grid scale increases. The results indicate that
spatial variation among the larger grids becomes less
significant because the large grids include more topographic conditions and tend to behave with similar
statistical characteristics.
After the two models were calibrated and validated against observed discharge data, the performances of the models was assessed using different
statistical criteria. It was somewhat surprising that the
overall results were very close for these two models and that the semi-distributed model performed as
well as the distributed model for the study catchment
when discharge at the outlet of the catchment was
used as a sole criterion. The possible explanation is
that the two models have a similar structure except for
the model parameterization scheme. The differences
of simulated streamflow under initial drought conditions for the distributed and semi-distributed models
become more significant than that in wet conditions
because the distributed model describes the spatial
heterogeneity of internal fluxes and state variables in
more detail.
Downloaded by [Jintao Liu] at 05:12 24 February 2012
Grid parameterization of the Xinanjiang model using a sub-grid topographic index
Another finding of comparing these two models’
results for quarter-hourly and daily time step simulations is that the predicted peak discharge discrepancy
would likely occur during a heavy storm rainfall when
the soil moisture is abruptly changed. The possible
explanation is that the averaged and spatially distributed parameterization schemes result in different
runoff yielding mechanisms during rainfall events.
The distributed model is able to simulate spatial distribution of soil moisture content and thus reflects
the runoff generation mechanism more correctly. The
simulated spatial distribution pattern of soil moisture
content in the distributed model was justified to some
extent by a field observation experiment. We found
that soils near the channel segments tend to have a
higher value of water content. This finding demonstrates, in part, the distributed model’s superiority in
model structure. The distributed model still needs to
be verified with detailed spatial information, if available. This also was the main limitation of this study,
that is, we did not have detailed spatially distributed
data to calibrate and validate the distributed model
structure, a recommended topic for future study.
Acknowledgements This work was supported
by the National Natural Science Foundation of
China (41030636, 40801013, 40930635, 51190090
and 51079038), the Key Research Grant from
Chinese Ministry of Education (308012), the
National Natural Science Foundation of Jiangsu
Province (BK2010516), the China Postdoctoral
Science Foundation funded project (201003572),
the Special Fund of State Key Laboratory of
Hydrology, Water Resources and Hydraulic
Engineering (2009585312 and 2010585612) and
the Fundamental Research Funds for the Central
Universities (2009B06414). The manuscript was
edited by Kyle D. Hoagland and Rachael Hoagland.
Thanks to the editor and two anonymous reviewers for
their constructive comments on the earlier manuscript
that led to a great improvement of the article.
REFERENCES
Beven, K., Kirkby, M.J., Schofield, N. and Togg, A.F., 1984. Testing
a physically-based flood forecasting model (TOPMODEL)
for three U.K. catchments. Journal of Hydrology, 69,
119–143.
Chen, X., Chen, Y.D. and Xu, C.Y., 2007. A distributed monthly
hydrological model for integrating spatial variations of
basin topography and rainfall. Hydrological Processes, 21,
242–252.
297
Cheng C.T., Zhao, M.Y., Chau, K.W. and Wu X.Y., 2006. Using
genetic algorithm and TOPSIS for Xinanjiang model calibration
with a single procedure. Journal of Hydrology, 316, 129–140.
Das, T., Bárdossy, A., Zehe, E. and He, E., 2008. Comparison of conceptual model performance using different representations of
spatial variability. Journal of Hydrology, 356, 106–118.
Gan, T.Y., Dlamini, E.M. and Biftu, G.F., 1997. Effects of model complexity and structure, data quality and objective functions on
hydrologic modeling. Journal of Hydrology, 192, 81–103.
Guo, F., Liu, X.R. and Ren, L.L., 2000. Topography based watershed hydrological model—TOPOMODEL and its application.
Advances in Water Science, 11, 296–301 (in Chinese).
Li, H.X., Zhang, Y.Q., Chiew, F. and Xu, S.G., 2009. Predicting
runoff in ungauged catchments by using Xinanjiang model with
MODIS leaf area index. Journal of Hydrology, 370, 155–162.
Li, Z.J., Ge, W.Z., Liu, J.T. and Zhao, K., 2004. Coupling between
weather radar rainfall data and a distributed hydrological model
for real-time flood forecasting. Hydrological Sciences Journal,
49 (6), 945–958.
Liang, X., Lettenmaier, D.P. and Wood, E.F., 1996. One-dimensional
statistical dynamic representation of subgrid spatial variability
of precipitation in the two-layer variable infiltration capacity model. Journal of Geophysical Research, 101 (D16), 21,
403–21, 422.
Liu, J.T., 2009. Digital drainage network automatic extraction software. DigitalHydro V1.0, China: 2009SR033528.
Liu, J.T., Chen, X., Zhang, J.B. and Markus, F., 2009. Coupling
the Xinanjiang model to a kinematic flow model based on
digital drainage networks for flood forecasting. Hydrological
Processes, 23, 1337–1348.
Lu, G.H. et al., 2008. Real-time flood forecast and flood alert map
over the Huaihe River Basin in China using a coupled hydrometeorological modeling system. Science China Series E –
Technol. Sciences 51, 1049–1063.
National Standard of People’s Republic of China for Water Resources, 2000. Code for hydrologic data compilation (SL247-1999)
Hydrological Bureau of China (in Chinese).
Quinn, P.F., Beven, K.J. and Lamb, R., 1995. The ln(a/tan beta) index:
How to calculate it and how to use it within the TOPMODEL
framework. Hydrological Processes, 9, 161–182.
Schumann, A.H., Funke, R. and Schultz, G.A., 2000. Application of
a geographic information system for conceptual rainfall–runoff
modeling. Journal of Hydrology, 240, 45–61.
Seibert, J. and McGlynn, B.L., 2007. A new triangular multiple flow
direction algorithm for computing upslope areas from gridded digital elevation models. Water Resources Research, 43,
W04501, doi:10.1029/2006WR005128.
Tarboton, D.G., 1997. A new method for the determination of flow
directions and upslope areas in grid digital elevation models.
Water Resources Research, 33, 309–319.
Todini, E., 1996. The ARNO rainfall–runoff model. Journal of
Hydrology, 175, 339–382.
Wooldridge, S., Kalma, J. and Kuczera, G., 2001. Parameterisation
of a simple semi-distributed model for assessing the impact of
land-use on hydrologic response. Journal of Hydrology, 254,
16–32.
Zhao, R.J. et al., 1980. The Xinanjiang model. Hydrological forecasting, Proceedings of the Oxford Symposium. Wallingford, UK:
IAHS Press, IAHS Publ. 129, 351–356.
Zhao, R.J., 1984. Water hydrological modelling—the Xinanjiang
model and Shanbei model. Beijing: China Water Resources and
Hydropower Publishing House (in Chinese).
Zhao, R.J and Liu, X.R., 1995. The Xinanjiang model. Chapter 7 in:
V.P. Singh, ed., Computer models of watershed hydrology.
Highlands Ranch, CO: Water Resources Publications, 215–232.