Mapping runoff based on hydro-stochastic approach for ... - CiteSeerX

J. Geogr. Sci. 2011, 21(3): 441-457 DOI: 10.1007/s11442-011-0856-3 © 2011

Science Press

Springer-Verlag

Mapping runoff based on hydro-stochastic approach for the Huaihe River Basin, China YAN Ziqi1,2, *XIA Jun1, Lars GOTTSCHALK3 1. Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China; 2. Graduate University of Chinese Academy of Sciences, Beijing 100049, China; 3. Department of Geosciences, University of Oslo, N-0315 Oslo, Norway

Abstract: Theoretical difficulties for mapping and for estimating river regime characteristics in a large-scale basin remain because of the nature of the variable under study: river flows are related to a specific area, i.e. the drainage basin, and are hierarchically organized in space through the river network with upstream-downstream dependencies. Another limitation is there are not enough gauge stations in developing countries. This presentation aims at developing the hydro-stochastic approach for producing choropleth maps of average annual runoff and computing mean discharge along the main river network for a large-scale basin. The approach applied to mean annual runoff is based on geostatistical interpolation procedures coupled with water balance and data uncertainty analyses. It is proved by an application in the upstream at Bengbu in the Huaihe River Basin, a typical large-scale basin in China. Hydro-stochasitic approach in a first step interpolates to a regular grid net and in a second step the grid values are integrated along rivers. The interpolation scheme includes a constraint to be able to account for the lateral water balance along the rivers. Grid runoff map with 10 km × 10 km resolution and the discharge map along the river with the 1 km basic length unit are the main results in this study. This kind of statistic approach can be widely used because it avoids the complexity of hydrological models and does not depend on the meteorological data. Keywords: kriging method; hydro-stochastic; runoff; water balance; Huaihe River Basin

1

Introduction

A key issue in applied hydrology is to be able to map runoff parameters in a large-scale basin. The problem is especially accentuated in “Flow Regimes from International Experimental and Network Data” (FRIEND) program, which is a cross-cutting programme that interacts with all five core IHP-VI themes. Since the 1990s, it has been an international collaborative study intended to develop, through the mutual exchange of data, knowledge and

Received: 2010-07-21 Accepted: 2010-09-20 Foundation: National Basic Research Program of China, No.2010CB428406; Key Project of the National Natural Science Foundation of China, No.40730632 Author: Yan Ziqi (1983–), Ph.D Candidate, specialized in hydrology. E-mail: [email protected] * Corresponding author: Xia Jun, Professor, E-mail: [email protected]

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Journal of Geographical Sciences

techniques at a regional level and a better understanding of hydrological variability and similarity across time and space. In modern times, GWSP also contains a project called “GWSP Digital Water Atlas*”. The purpose and intent of this project is to describe the basic elements of the Global Water System, the interlinkages of the elements and changes in the state of the Global Water System by creating a consistent set of annotated maps. At present, many tasks in climate change, hydro-ecology and water quality require information about the temporal variation of runoff at many points on the river network. This necessitates the development of interpolation procedures to estimate flows between measurements at gauging sites. Mapping large-scale regional variations in hydrological behavior has a long tradition in hydrology as well as in other geosciences like meteorology, climatology and geography. The main hydrometerological processes (rainfall, evapotranspiration, temperature etc.) observed at the land surface develop in a three-dimensional space – the two geographical coordinates (x, y) and time t. The variation of these variables across space is described as contour maps in classical works, i.e. they are space-filling phenomena and allow straightforward interpolation. River discharge (surface runoff), on the other hand, is formed in a two- dimensional space – the distance along a river lA (related to the point with area A in a basin) and time t. This relationship to the area (and not the (x, y) coordinates) explains why the variation of runoff characteristics across space, determined from discharge measurements, cannot be plotted as simply as hydrometerological variables. Neither is it a space-filling phenomenon. These are the key issues in mapping runoff parameters. Various methods have been developed for mapping hydrological elements. Until recently, when automatic interpolation procedures offered attractive alternatives, the isopleth maps have played a dominant role. The most common isopleths used are the contour lines on topographic maps (isohypses). This kind of maps produced manually (Gannett, 1912) were published first since calculating capacities were limited at the time they were created but they are still in use in the 1990s (Krug et al., 1990). This method is a widely used to plot the runoff depth across the space. But it is based on the human experience, and can not be coupled with the climate models and distributed hydrological models. By the second half of the 20th century, new technologies, e.g. geographical information systems, emerged. Empirical relationships between streamflow and land use, geomorphology and climate have received wide attention for several decades (Solomon et al., 1968; Liebscher, 1972; Dingman, 1981; Hawley and Mac Cuen, 1982; Gustard et al., 1989; Gottschalk and Krasovskaia, 1992a; Herschy and Fairbridge, 1998; Vogel et al., 1999). Such formulas have been usually established by multivariate regional regression. Drainage area and precipitation are by far the most significant explanatory variables and consequently are found in numerous published works. Other basin characteristics (annual maximum temperature, basin perimeter, slope and length of the main channel, mean basin elevation, gauging station co-ordinates, area controlled by lakes, etc.) may be incorporated but their relevance in relationships is usually not warranted when a new region is examined. The empirical formulas are only valid within the region where fitting was achieved. Besides, rather than estimating one single characteristic, hydrologists may simulate the whole hydrological behavior over the domain applying lumped rainfall-runoff models (Jut*

GWSP Digital Water Atlas: http://atlas.gwsp.org

YAN Ziqi et al.: Mapping runoff based on hydro-stochastic approach for the Huaihe River Basin, China

443

man, 1995) or more physically based models (Bishop et al., 1998). Several difficulties may restrict the application of this approach:  a large set of basins is required to calibrate the models against records;  the spatial coverage of rainfall conditions the inputs of the models and their efficiency in simulating discharge time series;  the model parameters vary spatially but are not suited to regionalisation since their link to the physical parameters of the basin is not well known.  complexity of the model results in the uncertainty of parameters, it is difficult to quantify errors of the input variables;  scale issue exists when people couple hydrological models with the climate models. In order to avoid the uncertainty caused by hydrological models, hydrologists start to pay attention to interpolating runoff in special random field with geo-statistical method, which has already been used for interpolating precipitation and evaporation (Villeneuve et al., 1979; Gottschalk, 1993a, b; Huang and Yang, 1998; Gottschalk and Krasovskaia, 1998; Merz and Blöschl, 2005). Three key points need to be taken into account: First, consideration of the fact that runoff data refer to the area of drainage basins (the support); second, definition of distances between basins; third, water balance between the upstream and downstream. Thus, Gottschalk (1993a, b) introduced a so-called hydro-stochastic approach that takes into consideration these aspects. This approach differs from other mapping and regionalization techniques in that simple physical and statistical laws are inherent in the methods used for mapping. In this approach, the distance and the covariance between points are replaced by specific distance and covariance for drainage basins. The most advantage of this approach is that it is consistent with the water balance along the river network in its interpolation process. Compared with the development of the research on mapping runoff in the world, the current studies on spatial distribution of runoff in China are mainly divided in three ways: (1) The most widely used method for mapping runoff is contour map. People used to get the characteristics of the spatial distribution of runoff by drawing the runoff depth contour (Li et al., 2008; Guo, 1958; Sun et al., 2009). The atlas of hydrological and meteorological in the Yellow River Basin, in which 1956-2000 average annual runoff was described with the traditional contour method, was produced by Liu Changming et al. (2004). (2) Relationship between rainfall and runoff has been added to the distributed hydrological models. The observed precipitation is the input parameter and the runoff is the output of distributed hydrological models (Ye, 2007; Pang, 2005; Wu et al., 2002). This method can only get the streamflow at outlet, while simulations of runoff on high resolution grids are still confined to the experiment in small basins (Du et al., 2006), and are subjected to the limitation of data. (3) Spatial distribution of runoff has also been simulated in large scale with climate models and land surface models (Zhang et al., 2003; Xie et al., 2004; Lin et al., 2008; Xie et al., 2008). However, compared with the spatial scale used in water resource management, the resolution of this method is still not high enough. Thus, the key issue is that, on the one hand, here have been mature theories such as hydro-stochastic approach to describe the spatial variability of runoff. But these methods (hydro-stochastic approach) are mainly applied in small basins in Europe. On the other hand, in

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China, this kind of research is still in initial stage. The approaches used now can not guarantee the physical and statistical laws that are associated with a certain statistical runoff variable are satisfied. And the accuracy and spatial resolution also need to be improved. The main objective here is to apply the hydro-stochastic approach in a Chinese river basin under intensive human activities. This work is motivated by an application on a large scale basin to explain the problems of Chinese water sources. This paper is divided into three sections. “The interpolation system: a hydro-stochastic approach” section focuses on methodological aspects. First, the basic equations of kriging are presented. The developed approach, called “hydro-stochastic” is then introduced to account for the fact that gauging-station data represent flows contributed by drainage areas with varying sizes and characteristics rather than point values. The section focuses on data and distance to be considered. “Application” section illustrates the application to a dataset in the Huaihe River Basin, China, including 20 gauging stations. Runoff estimates were computed for more than 7322 elements along the river network. We quantified the performance of the proposed framework by analyzing the standard errors of the runoff interpolation and the water balance constraint. Last, conclusions are given in “Conclusions” section.

2

Hydro-stochastic approach

Hydro-stochastic approach is used to mapping average annual runoff herein, with a consideration of the specific topics discussed above. The point of departure is the stochastic interpolation procedure developed by Gottschalk (1993a, b). Runoff is interpolated across the whole study region with block kriging. Then estimations are provided by aggregation along the river network. The interpolation procedure guarantees that the water balance equation is satisfied so that the sum of runoff from all upstream grid cells is equal to the discharge from downstream outlet. A data processing called “denesting runoff” should be the first step of interpolating program. It is also necessary to redefine the distance between the sub-basins. Finally, to calculate the runoff along the river, river network with hierarchical structure is required. 2.1

Theory of block kriging

The method of estimation embodied in regionalized variable theory is known in earth sciences as kriging, after Krige (1966), who first devised it empirically for use in the South African goldfields. It is essentially a means of weighted local averaging in which the weights are chosen so as to give unbiased estimates while at the same time minimizing the estimation variance. Kriging is this sense optimal (Webster, 1985). In earth sciences, such as meteorology and hydrology, this geo-statistics method is widely used to predict unknown values from data observed in gauge station. The block kriging interpolation method is developed from kriging, and is used to make estimation for regions and grids. In its interpolation system, a value for an area or block with its center at X0 is estimated, and the influence of the areas of regions and grids can be estimated. The kriged value of property Z for any block V is a weighted average of the observed values Xi in the neighborhood of the block, i.e.,

YAN Ziqi et al.: Mapping runoff based on hydro-stochastic approach for the Huaihe River Basin, China n

Z * (V )   i Z ( xi )

445

(1)

i 1

where n is the number of neighboring samples Z ( xi ) and i is the weight applied to each

observed value Z(xi). The weights are chosen so that the estimated Z*(V) of the true value Z(V) is unbiased: E  Z * (V )  Z (V )   0 . And the estimated variance n

n

 V2

for block V is:

 V2  Var  Z * (V )  Z (V )  

n

2 i  (V , xi )   (V ,V )   i  j  ( xi , x j ) , the minimized  V2 can be obtained when: i 1

i 1 j 1

n   j  ( xi , x j )     ( xi ,V ) i  1, 2, , n  j 1 n   i  1  i 1

where  is a Lagrange multiplier,

n

 i  1

(2)

is the unbias condition and (xi,V) is the

i 1

semivariogram. Furthermore, equation (2) can be written in covariance format as follows: n   j C ( xi , x j )    C ( xi ,V ) i  1, 2, , n  j 1 n   i  1  i 1

(3)

where

C (V ,V ) 

1 V2

 Cov( x  t )dxdt

VV

C (V , xi )  V1  C ( x  xi )dx V

V is block, x is point. C (V ,V ) and C (V , xi ) are the covariances function for block-block and block-point separately. Equation (3) is the foundation of interpolation algorithm in this study. 2.2

Water balance

In case of runoff, the formulas are altered to account for the drainage basin area A (the local support) upstream the runoff gauging site: n

q* (ai )    ij q ( A j )

i=1, …, M

(4)

j 1

where q*(ai) is the runoff in a grid,  is the weight, q(Aj) is the average annual discharge of basin Aj, M is the number of grids contained in a sub-basin and N is the number of sub-basins. Then, the streamflow at a downstream point for a drainage basin, say A1, is calculated from:

446


M1 M1 a   a  N1 qˆ  A1     i q* (ai )    i    ij q A j (5) i 1  A1  i 1  A1  j 1 where M1 is the number of grid cells that approximate the drainage basin area A1. This sum of interpolated runoff for grids, calculated from equation (5), does not necessarily add up to the observed runoff in the downstream point. A further step is to include a constraint so that the interpolated runoff for grids is balanced with observed runoff in the river system: qˆ  A1   Q( A1 ) (6)

 

where Q(A1) is the observed discharge of the outlet. Then the new interpolation equations are: Q  ΛTM Q (7) where Q  [q* (a1 ),...q* (aM )]T

(8)

T

ΛTM





Q  [q ( A1 ),...q ( AN )]

11 ,



, N1 ,

12 ,



, N2 ,



, 1M

(9)

, 

, NM

, 1 ,  , M



Λ M  CM 1 C0M

(10) (11)

CT0M  (Cov  A1 , a1  ,, Cov  AN , a1  , Cov  A1 , a2  ,, Cov  AN , a2  , , Cov  A1 , aM  ,, Cov  AN , aM  ,1,0,,0)

(12)

CM   Var  A1      Cov  AN , A1   0     0      0     0  a1   A1      0  

 Cov  A1 , AN    

Var  An  0 



0  0

 





0



 a1 A1

0  0 Var  A1  





0 



0 

 0   Cov  A1 , AN   

0 0 

 

0 0 

0  Var  A1 



Cov  AN , A1    0   0 a2 A1

Var  AN   0

 



 0

  Cov  AN , A1 



0



 0

0 



 a2 A1

aM A1

0   Cov  A1 , AN   Var  AN  

 

0



0  aM A1

1  0    0  1  1  0    0  1    1  0    0  1  0  0      0  0  

(13)

where Cov is the covariance function between two elements, ai (i = 1, …, M) is the area of each grid in the specific sub-basin, Aj (j=1, …, M) is the area of each sub-basin, q*(a1) is the estimate runoff in gird aj, q(Aj) is the observed outlet discharge of sub-basin Aj. 2.3

Distance measure

The kriging approach is of wide use for interpolation of meteorological fields (Creutin and Obled, 1982; Dingman et al., 1988; Goovaerts, 2000) but needs to be modified for runoff features since the runoff observations are related to specific areas rather than to points. In particular, a relevant distance between pairs of basins has to be defined. Huang and Yang


447

(1998) and Merz and Blöschl (2005) allocate the representative value of the runoff depth to the centre of gravity of the basin and thus chose the distance between centres of gravity. Unfortunately this distance may bring together basins with significantly different river flow regimes, particularly when basins are nested. Gottschalk (1993a) suggested a measure of distance, named Ghosh distance (Ghosh, 1951; Matérn, 1960), taking both the river network and the drainage basins into account. This distance h between two geographical sectors S1 and S2, of areas, respectively, equal to A1 and A2, is defined by the average distance between all the couples of points within the two sectors: 1 h( S1 , S2 )  u1  u2 du1du2 (14) A1 A2 u1S1 u2 S2 These sectors A1 and A2 could be basins or sub-basins to accomplish the spatial analysis of runoff data. This distance allows better identification of the spatial structure of runoff (Gottschalk, 1993a). Adopting an assumption of local second-order stationarity of the runoff process, a kriging system may be established and resolved (Gottschalk, 1993b). The Ghosh distance is used in all steps of the interpolation framework in the hydro-stochastic approach, which means this distance replaces the classical Euclidian distance. Some links exist between these two distance measures. The following inequality between these two distance measures is verified: h( S1 , S2 ) ≥ uG1  uG2

(15)

where h(S1, S2) is Ghosh distance between basin S1 and basin S2, |uG1 – uG2| is classical Euclidian distance, uGi denotes the coordinates of the centre of gravity of basin Si. |uG1 – uG2| converges towards h(S1, S2) when S1 and S2 are not over-lapping and have small size or when S1 and S2 are distant. 2.4

Variables under study

Traditionally when mapping river discharge, the variable under study introduced in the interpolation procedure is runoff observed at the outlet of gauged basins. Handling this variable has one major drawback. Because interpolation of runoff is more complicated than interpolation of other components of the water balance. Runoff observations might be nested, i.e. the drainage basin of one gauging station is part of a larger basin contributing to another gauging station. When runoff from nested gauged basins is directly used in the interpolation scheme, information on the headwaters is introduced several times in the dataset due to the over-lapping drainage area. This redundancy may bias the spatial analysis. To remedy such a problem, it is therefore worthwhile to make a “denesting” of observed runoff within a larger basin first. It is common that a larger drainage basin with a gauging station at its outlet contains one or several other gauging stations upstream. Runoff production for the area of the basin area between the outlet station and an upstream one should be possible to obtain, in principle, by a simple subtraction of the discharge values at the upstream gauging station from those at the downstream one. For a simple case with only one upstream station the denesting thus involves two values only q(A1) and q(A2), where A2 is the upstream area and A1 is the intermediate area calculated from A1=A–A2, where A is the area at the outlet. q(A1) is estimated from:

448


q  A1    Aq  A   A2 q  A2   A1

(16)

There is a resemblance between this approach and the Thiessen method as the variable takes constant values over areas, which, of course, are defined from quite different principles. There is also a drawback in the denesting when equation (16) represents a difference between too large numbers, which compromises the accuracy. On the other hand, this data processing can be considered as a first good control of the quality of data, and is the first step of the area weighted average gridded mapping method (Arnell, 1995). 2.5

Estimating discharge along the river network

The kriging procedure suited to runoff characteristics enables one to estimate runoff for any delineated element. Estimations are provided by aggregation along the river network (Gottschalk and Krasovskaia, 1992b; Estrela et al., 1997). The annual discharges qa generated by the area upstream to the location u are the sums of the runoffs qa generated in all fundamental units Ai flowing into that location u: qa (u )   qa (Ai )Ai

(17)

Ai  A

where A is the drainage area at location u and discharge is expressed in mm/year. This process can be considered as flow concentration. The yield runoff from each grid cell flows into the river channel according to the direction defined in the river network. The highest accuracy of the flow concentration is determined by the accuracy of the river network. And the fundamental units of the partition can also define the finest level of detail that can be achieved for describing runoff variability.

3

Application

The study area is located upstream of Bengbu Sluice in the downstream part of the Huaihe River Basin, and has an area of 121,000 km2. The climate in this area is in general characterized by monsoonal weather conditions with significant seasonal changes of precipitation, which is mainly concentrated in the summer (60%–70% of the annual precipitation). There is a gradient in average annual precipitation across the basin from about 1000 mm in the southeast to less than 600 mm in the northwest, while the maximum precipitation is observed in the inner mountain areas. Temperature variation in the basin is big due to the continental climatic conditions, with high summer temperature of 30℃ (July) and low winter temperature of 0℃ (January). Water problems are significant in this region. Both spatial and temporal distribution of water resources is uneven and human impact on water resources is very big. In this area, water resources per capita and per unit area is less than one-fifth of the national average. Moreover, more than 50% of the water resources are overexploited, much higher than the recommended rate for international inland rivers (30%). Along with the intensive human activity and the excessive dam and floodgate constructions, hydrological regimes in the basin have changed dramatically. Thus attempts to adequately describe runoff in the region represent a challenge and face complex problems. Manually derived contour maps are still often used in this region to de-


449

scribe distribution of runoff in space. That is why objective quantitative estimation of runoff characteristics has become the priority issue for water resources management in this river basin. There is a substantial water use in this area but no quantitative information is available concerning water exploitation. Here, an attempt is made to use the basic hydro-stochastic concepts to describe the special characteristics of annual runoff (Figure 1). 3.1

Data collection

In this application, commonly used characteristic or classification system derived from physical properties including soil type, hydrogeology and climate characteristics were not available. The only information we used is given by the stream flows observed at gauging stations, topography depicted by the DEM and derived drainage network. (1) Runoff data In this study, the basic data used are average monthly runoff series at 20 hydrological stations located in the study area. These time series covering the period from 1956 to 2008 Figure 1 Flowchart were used to estimate the long-term annual average runoff at each station. (2) Spatial data The hydro-stochastic approach used requires a unique numeric description of the hierarchical structure of the river network as a background for runoff interpolation. DEM with a resolution of 1 km×1 km was used to extract river network. Flow direction from each grid cell was obtained by standard methods assuming that there is only one outflow from each grid cell. The standard method can be described step by step as follows: 1) to calculate the outflow direction of each unit grid cell; 2) to calculate the flow accumulation matrix with this direction; 3) to select the threshold value and link the grid cells whose flow accumulations are greater than the threshold to get the river network. In this case, the threshold value is 300. Most of the study area is situated in flatland and the accuracy in extracting the river network directly from the DEM in these parts might be relatively poor. Corrections were needed using a previously digitized stream network. Since the accuracy of the extracted river net can directly affect the integration process along the river network, there are two requirements that the identified river network should meet: - the river network should pass through the 20 hydrometric stations in Table 1; - the drainage basin areas extracted for the 20 hydrometric stations should be as close as possible to the “official” value (from the archives). In order to meet these two requirements, it is essential to repeatedly extract and correct

450

Journal of Geographical Sciences Average annual runoff from 1956 to 2008 (104 m3)

Table 1

Station

Runoff

Station

Runoff

Baiguishan

77252

Mengcheng

137249

Bantai

293033

Xuanwu

23620

Bengbu

3061417

Zhaopingtai

54812

Changtaiguan

121489

Shenqiu

47560

Fuyang

523274

Wangjiaba

1036144

Hengpaitou

333249

Xianghongdian

108263

Huaibin

635667

Xincai

95170

Jiangjiaji

298053

Xixian

430929

Lutaizi

2530761

Zhoukou

366821

Meishan

136276

Zhuanqiao

21412

the digital river network until the extraction achieved the required accuracy. The extracted river network structure and the location of hydrological stations in Table 1 are shown in Figure 2. In this study, information about official basin area from the governmental database* was used to check the derived area. Figure 3 compares the final sub-basin areas extracted from DEM and the “true” sub-basin areas, which reveals that some uncertainties remain in the delineation of the 20 drainage basins in relation to the official figures. 3.2

Denesting runoff

The principle for denesting was described earlier in section 2.4. The background for the denesting is the structure of the identified river network illustrated in Figure 2 and the information concerning gauging stations shown in Table 1. The discharge(s) [m3/s] measured at

Figure 2 *

River network deduced from DEM

China Ministry of Water Resources, Water Yearbook of the Huaihe River Basin, 2006, volumes 1-6


Figure 3

451

Comparison of estimated areas with actual topographic areas

the neighboring upstream gauging station(s) are subtracted from the value observed at a downstream gauging station successively from headwaters towards the outlet. From the gauged discharge in 20 basins new discharge values are determined for 20 denested basins according to the following steps. 1) Extract 20 sub-basins with the stream network and the gauging stations’ information in Figure 2. The outlet of each sub-basin is the stations in Table 1. The area of each sub-basin is Ai, i=1, …, 20; 2) Subtract the discharge(s) measured at neighborhood upstream gauging stations from the value observed at downstream gauging stations. Every station gets a new value dQi, i=1, …, 20; 3) Calculate the denesting value q(Ai) for each specific sub-basin: q(Ai) = dQi/Ai, i=1, …, 20. To eliminate scale effect within the dataset due to the size of the basin, runoff q(Ai) generated for denested sub-basin is expressed in mm/year. Figure 4 shows the average runoff in each denested sub-basin after the normalization of data to mm/year. The runoff q(Ai) for the denested basins is the background data for the construction of a covariance function and for the interpolation exercises developed in the following. The denested runoff map is very informative concerning the spatial signal in our data, i.e., the pattern of variability of runoff across space that the available gauging network is able to reveal. There are, for example, two small basins in the southwestern part that show high runoff values that probably are representative for this part of the Huaihe River Basin. The downstream basins, in which these two small ones are nested, cover a large area that also borders the much drier northwestern part. As a result, the runoff for this larger basin average out the dry north and the wet south and we are not able to detect any details. In the present study we will accept the available runoff data as a base for the runoff mapping exercise. In an applied situation it would, of course, be necessary to look for supplementary information. 3.3

Result

The interpolation schemes, in the first step the runoff was interpolated to a grid cell network.

452

Figure 4


Denested runoff estimated by the disaggregation procedure

And the result is consistent with its expected spatial pattern (Figure 5). The grid size is 10 km × 10 km. The value q(a) for a grid cell can be interpreted as the average surface runoff from this cell that may flow towards the river channels. The runoff map mirrors the main features already revealed by the denested map (Figure 4). And this kind of grid map can be coupled with the land-surface models, GCM and RCM, which are also based on grids, to help people analyze the spatial variation of hydrological elements in any given region.

Figure 5

Runoff interpolation map

In the second step, the integrated values along rivers (Figure 6) were computed based on Figure 5. In this result, the river network is divided into 7322 segments, the length of each segment is 1km, denoted as a channel unit. Thus, the attribute value for each channel unit is the average annual discharge from 1956 to 2008.


Figure 6

3.4

453

Discharge map along the river network (105 m3/year)

Accuracy analysis

To verify the performance of hydro-stochastic method in this study, accuracy analysis of the results is essential. We took two aspects into account to analyze the predictive performance of this approach: firstly derived the interpolation error for each grid; secondly verified the lateral water balance along the river. (1) The accuracy of grid interpolation Interpolation process in hydro-stochastic approach can give the standard error for each grid cell (Figure 7) with the Geostatistical Analyst tool in ArcGIS 9.2. This estimation error

Figure 7

Standard error map

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of the interpolation mainly reflects the location of the observation sites. As the drainage basin and grid cell support are taken into account in the interpolation scheme, the errors are not reduced to zero at these locations. Furthermore, the smallest errors are, as a rule, found upstream the gauging station because of the smaller Ghosh distance. At the edge of the study region and the central parts of the large sub-basins, the interpolation errors are bigger due to the larger Ghosh distances from the cells to sub-basins. The error map is a quantitative test for the result in Figure 5. And it can be used, as a production of hydro-stochastic approach, to help people analyze the credibility of the interpolation. In this study, the standard error map was drawn under a limited data condition. If there are more observational site data available, and accordingly, the error will be reduced. (2) Verify the water balance Water balance is the main control objective of hydro-stochastic. Based on Figure 6, we are able to introduce the observed values at different gauged sites. To verify the water balance on each site, a comparison between the estimated outflow and the observed outflow on each sub-basin is required. This task should be done after aggregating mean annual flow along the river network. Figure 8 show the correlation between the estimated discharges and the observed values of the 20 observation stations. The linear regression equation between the estimated value and observed one is y=0.9602x – 1.0389, and regression coFigure 8 Comparison of estimated discharge with obefficient is 0.99. (the one-to-one line (dashed) is repreThe agreement for all sites is very served discharge sented) (108 m3/year) good as the water balance constraint is built into this approach. With this result, we can say that although we do not have the high quality data, the constraint (Equation 7) will give us good results when we look into the runoff along the rivers. It can also be indicated that the aggregation process in hydro-stochastic method is highly consistent with the natural process, the water balance along the river system can be satisfied well.

4

Conclusions

One technique for mapping long term mean runoff describing water resource at large scale is presented. It is based on objective methods specially developed to account for the related drainage basin supporting areas and the hierarchy in the discharge data imposed by the structure of the river network. The proposed procedure ensures consistency in space: the continuity equation is fulfilled by aggregation along the water path to derive discharge. Thus, inconsistencies are avoided when two main rivers flow together. The uncertainty analysis


455

demonstrate that hydro-stochastic approaches for interpolation give acceptable results by introducing hydrological properties of the variable under study in the mapping procedure. In this study, hydro-stochastic approach was applied in the Huaihe River Basin above Bengbu in southeastern China. The main conclusions of the study are: (1) With the ability of obtaining the spatial distribution characteristics of runoff in a continuous space with the discontinuous observed data, the hydro-stochastic approach is useful to analyze the characteristics of hydrological and meteorological elements in ungauged areas. Nevertheless, in China, due to the limited observation, the number of datasets in a large scale basin may be only equivalent to that of a small or medium scale basin in Europe. Thus, considering the limitations of data, it is suggested that, in China, directly interpolating in a large basin is more feasible while the application of hydro-stochastic approach in small basin will be more restricted. (2) Compared with the resolution of DEM, the geometry and density of the observation sites in space have more impact on the performance of hydro-stochastic approach. The output resolution should be decided by the smallest catchment area of all stations, and the higher resolution is not necessary. For instance, the DEM grid size in this study is with 1 km × 1 km. But, considering the smallest catchment area, the resolution of output grids was here subjectively chosen to 10 km × 10 km. (3) Without enough observation dataset, by controlling the accuracy of the input space information, such as DEM, site locations, digital river network, the interpolation results of hydro-stochastic approach for large-scale river basin can still be consistent with the water balance to an acceptable extent, and describe estimate errors across the study area. (4) There are intense human activities in the Huaihe River Basin. The observations include not only the natural runoff but also the impact of human activities. However, in this study, the spatial variability of runoff estimated by hydro-stochastic approach can still show a good satisfaction of the water balance. Which indicated that, to a certain extent, the special random field can reflect the changes of the underlying surface. Thus, the method presented here can guarantee the reliability of the runoff interpolation results. Compared with the contour method, runoff maps produced by hydro-stochastic approach (Figures 5–7) include more information. By simulating the distribution of runoff in the spatial random field, the result maps can give exhibitions of yield runoff for each grid as well as the discharge along the river channel. At the same time, the standard errors of interpolation can also be precisely quantified. Coupled with large-scale distributed hydrological models and climate models, the results can become more systematic theoretical tools for studying the impact of climate change and human activities. And they are also important references for river basin water resources management. Compared with hydrological models, spatial interpolation of runoff in a large-scale basin with hydro-stochastic approach can avoid the complexity in model structural and the uncertainty of parameters, describe runoff process without meteorological data. The only data used here are observations in gauging stations and the DEM. Compared with the land surface models, the hydro-stochastic approach can significantly improve the spatial resolution. Hydro-stochastic approach can be regarded as a hydrological model based on the geographic correlation. It can output hydrology elements’ distribution information with high spatial resolution. This kind of information, associated with output of other models or the-

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matic information, can be used to help people analyze the river process with more details. For example, the Huaihe River Basin suffers from serious water quality problems. Combining output of water quality models with Figure 6, people will be able to look into the water quality condition in each river unit, and this can become a support for decision-making in river management. Finally, the condition of river basins in China is more complicated. Human activities and climate change have significant impacts on water resources. How to analyze the responses of runoff under different driving factors with more knowledge and rules is an urgent issue. At the same time, compared with the hydrological models, hydro-stochastic approach is independent of the physical process, and is more like a method based on the statistical laws of physical geography. The combination of these two concepts will also be a further research content.

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