A Grid-based Integrated Surface–Groundwater Model (GISMOD) was developed to estimate the required irrigation water using a control-site method. The entire catchment is divided into multiple grid cells of equal size, and several grid cells can be chosen as the control sites by users in this model. The grid cells from the upper stream of each control site, which have a land-use type of farmland, are automatically identified as a controlled grid cell. The crop information around each controlled grid cell is set to be the same as its corresponding control site. Next, the irrigation water requirement for each controlled grid cell is calculated using a crop coefficient method that is integrated into the human water-use module of the GISMOD. After runoff is generated, the actual discharge of each control site is computed by comparing the available water sources with the irrigation water requirement based on the water-supply operation rules of the model. This paper subsequently presents a case study in the upper-middle reaches of the Heihe River to evaluate the performance of the GISMOD. The results demonstrate that the actual water consumption for irrigation in the Heihe River basin could be generally estimated by the GISMOD on a monthly basis.

INTRODUCTION

The shortage of water is one of the greatest challenges to the sustainable social and economic development in northwest China. In this area, agriculture has been specifically identified as the major consumer of water. The water use from the middle stream of the Heihe River basin, which accounts for approximately 78% of the total water consumption (approximately 32 × 108 m3/yr), has increased steadily during the past few years (Wang & Cheng 1999; Chen et al. 2005; Zang et al. 2012). With increases in both population and cultivated area, the disparity between water supply and demand has been greatly exacerbated by the high water demand from irrigated agriculture, which has been rapidly expanding (Kang et al. 2007). Therefore, an understanding of the water use in agriculture is critical both for maintaining an adequate food supply and for improving the efficiency of water use. To achieve a fair allocation of water resources, the local government has issued a series of water policies and encouraged water-efficient agriculture during the last 15 years (Wang et al. 2010). However, there is a lack of detailed data regarding irrigation and human water uses (Bormann et al. 1999), and it has been difficult to evaluate the balance in supply and demand for water in this large inland basin. Such knowledge gaps hamper our ability to resolve the regional problems of water resource utilisation.

Traditional methods to determine agricultural water use in China use the statistical data on cultivated areas from local water authorities, which is generally a rough estimation and cannot reflect the spatial and temporal variations in agricultural water use (Yang et al. 2010). The most common method, which employs the Penman–Monteith formula for the reference evapotranspiration (ET0) (Allen et al. 1998) in combination with the crop coefficient (Kc), which expresses the difference in evapotranspiration between the cropped and reference grass, is widely used to estimate the requirement for irrigation water in different regions throughout the world (Ray & Dadhwal 2001; Suyker & Verma 2009; Hanafi et al. 2010; Lei & Yang 2012). Several researchers have also integrated this method with spatial data to estimate the spatial distribution of irrigation water requirements (Knox et al. 1996; Döll & Siebert 2002). With the appearance of hydrological models that can be used to clarify hydrological processes with conceptual or physical representation (Abbott et al. 1986; Lu et al. 1989, 1995), the crop coefficient has been used to allow the models to simulate the water requirement and the entire hydrological cycle in several irrigation regions (Gosain et al. 2005; Santhi et al. 2005; Minacapilli et al. 2008; Zheng et al. 2010). For instance, Minacapilli et al. (2008) successfully assessed the actual irrigation water demand in a study in Italy using the spatially distributed agro-hydrological model SIMODIS. Zheng et al. (2010) added the crop coefficient method into the SWAT hydrological model to simulate the water balance of the Fenhe irrigation district in China. However, the spatial variability in the irrigation schedules and the crop coefficients cannot be adequately portrayed using this method. For instance, the crop type of each sub-basin is generally considered to be uniform by hydrological models (e.g., SWAT), but crop type should be identified specifically according to a land-cover map.

In this study, a Grid-based Integrated Surface–Groundwater Model (GISMOD) was developed as a physically based distributed hydrological model focused on simulating the agricultural water uses at a regional scale using a simple and efficient method. The principles of the GISMOD are presented, and subsequently provide a case study estimating the water utilisation by individuals and agricultural systems in the Heihe River basin.

MATERIALS AND METHOD

Study area description

The Heihe River is the second-largest inland river in Northwest China. The river originates at the north foot of Qilian Mountain and flows 821 km north through the Qinghai and Gansu provinces before finally reaching its terminus, Lake Juyan, in the Inner Mongolia Autonomous Region (Tang et al. 1992; Lu et al. 2003). Yingluoxia (Yingluoxia Gorge) and Zhengyixia (Zhengyixia Gorge) divide the drainage area of the Heihe River into upper, middle and lower reaches (Qin et al. 2011).

The climate in the upper reaches is damp and cold because 70% of the area is mountainous (Shan 2007). The average annual temperature and precipitation of the upper reaches are approximately 2 °C and 350 mm, respectively. Grassland farming is the major economic activity in the upper stream (Zhao et al. 2005; Zhu et al. 2008).

In the middle reaches, the annual precipitation is only 140 mm because of the dry weather, and the average annual temperature is between 14 and 18 °C. The agriculture in this region depends on irrigation. The effective irrigation area is more than 2,200 km2 (Cheng et al. 2006). Spring wheat and corn are the main crops. The population of the middle stream accounts for almost 90% of the total population in the Heihe River basin (Ji et al. 2006; Zang et al. 2012).

We selected the upper-middle reaches of the Heihe River basin as the study area to improve the understanding of the farmland water cycle and the mechanisms of agricultural water utilisation in the basin (72,200 km2) (Figure 1).

Figure 1

Location of the study area and the observation stations.

Figure 1

Location of the study area and the observation stations.

GISMOD

The GISMOD is a grid-based distributed hydrological model of the groundwater–surface water interaction that uses a simplification method as is found in the Physically Based Distributed Tank model (Xu et al. 2001).

The watershed is divided into hundreds or thousands of grid cells with equal size in the GISMOD (Figure 2). The total number of grid cells is dependent upon the resolution of the input data (e.g., digital elevation model (DEM), land cover or soil type), and the precision of the simulation is also dependent upon the quantity and quality of the input data.

Figure 2

Schematic map of the GISMOD.

Figure 2

Schematic map of the GISMOD.

There are two types of grid cell in the model. One is the ordinary grid cell that contains the surface, soil and groundwater layers. The water exchange is considered in the GISMOD by computing the infiltrate and recharge flow generated from the layers of the ordinary grid cell. The second cell type is the river grid cell with a single layer for channel routing. According to the flow direction matrix provided by the pre-processing module, the grid cells that have flow accumulation values greater than a user-specified threshold can be identified as river grid cells, and other grid cells are set as ordinary grid cells. The outflow that is generated from each layer of the ordinary grid cell would pour into its corresponding parts when the downstream grid is also an ordinary grid cell. Otherwise, all of the outflows from the ordinary grid cell will be combined as one stream and flow into the river grid cell, subsequently moving among the river grid cells and eventually draining out of the watershed. Figure 3 is a schematic drawing that illustrates the process of water transfer and exchange in the GISMOD.

Figure 3

Runoff generation module of the GISMOD.

Figure 3

Runoff generation module of the GISMOD.

The GISMOD is composed of seven components: the pre-processing module, interpolation module, evapotranspiration module, runoff simulation module, water-use module, parameter identification module and the simulation setting module (Figure 4). The instructions to use the GISMOD are as follows. (1) The pre-processing module is used to extract the drainage networks and identify the routing order of each grid cell. (2) Next, the precipitation data and meteorological data (such as air temperature, relative humidity and average wind speed) from observation stations are used for spatial interpolation. (3) A suitable method is selected to calculate the evapotranspiration of each grid cell. (4) After the parameter value is assigned by using the available input data (such as a land use map, soil map and geology map), the runoff module can be executed with or without considering the impact of human activities.

Figure 4

System structure of the GISMOD.

Figure 4

System structure of the GISMOD.

Details of each component in the GISMOD are shown as follows.

Pre-processing module

Similar to the hydrological tool in ArcGIS, the pre-processing programme is used to delineate the river basin and to extract the drainage networks automatically from the DEM data (Li et al. 2013). This module has various functions:

  • determination of flow direction;

  • calculation of flow accumulation;

  • calculation of flow length;

  • generation of drainage network;

  • identification of runoff routing order.

Interpolation module

The disaggregation of the available hydro-meteorological data from the limited observation stations to the entire catchment is essential for estimating the evapotranspiration and precipitation at each grid cell in the GISMOD. Considering the different architectures of the observation networks and climatic characteristics, the Thiessen method, Gradient Plus Inverse Distance Squared method and Inverse Distance Squared method are all given in the GISMOD for spatial interpolation.

Evapotranspiration module

The calculation methods for the potential evapotranspiration (PET) can be classified into four types: temperature-based, radiation-based, mass-transfer and combination methods. Most require many types of input data, such as air temperature, air pressure, humidity, wind speed and solar radiation. Eight methods for determining PET are integrated into GISMOD (Table 1). As it is widely used, the FAO Penman–Monteith method was selected for the case study.

Table 1

Eight methods for estimating the PET in the GISMOD

No. Name Equation 
FAO Penman–Monteith  
Penman  
Kimberly–Penman  
Hargreaves–Samani  
Priestley–Taylor  
Makkink  
Turc  
Doorenboss–Pruitt  
No. Name Equation 
FAO Penman–Monteith  
Penman  
Kimberly–Penman  
Hargreaves–Samani  
Priestley–Taylor  
Makkink  
Turc  
Doorenboss–Pruitt  

Rn is the net radiation flux; G is the sensible heat flux into the soil, which can be ignored for the daily estimation; T is the temperature, usually taken as the daily mean air temperature (Tmean); Tmax and Tmin are the daily maximum and minimum air temperatures, respectively; es is the vapour pressure of the air at saturation; ea is the actual vapour pressure; Δ is the slope of the saturation vapour pressure temperature relationship curve; γ is the psychometric constant; U2 is the wind speed at 2 m height; λ is the latent heat of vaporisation; Rs is the solar or shortwave radiation; and Ra is the extra-terrestrial radiation.

Runoff module

Surface layer
The basic equation for the surface layer is expressed as: 
formula
1
where h1 is the water level in the surface layer; t is the time step; R is the daily precipitation; Qr0 is the sum of the inflow from upstream neighbouring surface layers; Qb0 is the recharge flow from the soil layer; E is the actual evapotranspiration; Qs1 is the infiltration excess overland flow; Qs2 is the saturation excess overland flow; Qc0 is the lateral outflow (surface flow); and Qx0 is the infiltration.
Two types of overland flow (saturation excess overland flow and infiltration excess overland flow), lateral flow and the infiltration flow are calculated from: 
formula
2
 
formula
3
 
formula
4
 
formula
5
where sf2 is the height of the surface layer; i is the slope of the grid; L is the length of the grid cell; n is Manning's roughness coefficient; f0 is the percolation rate of the surface layer; A is the area of the grid; tha is the discharge coefficient; and a is the storage coefficient of the surface layer.
Soil layer
The water balance equation of the soil layer can be written as: 
formula
6
where h2 is the water level of the soil layer; t is the simulation time step; Qr1 is the inflow of the soil layer; Qb1 is the recharge flow from the groundwater layer; Qc1 is the outflow of the soil layer; and Qx1 is the infiltration flow of the soil layer.
Recharge flow is generated if the available water exceeds the limit or capacity of the soil layer, according to three situations:
  1. Less water can be supplied from the soil layer when there is a water shortage in the surface layer: 
    formula
    7
  2. The available water of the soil layer is sufficient to meet the needs of the surface layer: 
    formula
    8
  3. Additional water is unnecessary in the surface layer while there is an abundance of water in the soil layer:

 
formula
9
where sf0 is the particular water level of the surface layer, which means that the surface layer needs the water supply from the soil layer if the water level is lower than this value; s2 is the height of the soil layer; s1 is the particular water level of the soil layer, which means that the soil layer can afford water to the surface layer once the water level is higher than this value.
The equation of the interflow and the infiltration flow in the soil layer is 
formula
10
 
formula
11
where kx is the horizontal hydraulic conductivity of the soil layer, and kz is the vertical hydraulic conductivity of the soil layer.
Groundwater layer
As in a semi-closed system, only unconfined water can flow into the river grid layer in the GISMOD: 
formula
12
where h3 is the water level in the groundwater layer; t is the simulation time step; Qc2 is the unconfined groundwater flow; and Qc3 is the confined groundwater flow.
Similar to the soil layer, there are also three types of water supply from the groundwater layer:
  1. The groundwater layer cannot meet the needs of the soil layer: 
    formula
    13
  2. The amount of available water held by the groundwater layer can satisfy the requirement of the soil layer: 
    formula
    14
  3. The water level of the soil layer is greater than the particular value (s0), and the total water is simultaneously beyond the limit of the water-holding capacity in the groundwater layer:

 
formula
15
where s0 is the particular value of the water level of the soil layer, which means that the soil layer needs water from the groundwater layer if the water level is higher than this value; ss2 is the height of the groundwater layer; and ss1 is the designated water level of the groundwater layer.
Referring to Darcy's law, the two types of outflow (unconfined and confined flows) from the groundwater layer are calculated as: 
formula
16
 
formula
17
where Au is the permeability coefficient of the unconfined water; and Ag is the permeability coefficient of the confined water.
River layer
For the river layer, a basic equation from Wang & Xu (2011) is used as follows: 
formula
18
where L is the channel length; B is the channel width; Qr3 is the inflow of the river grid; and Qout3 is the discharge of the river grid.
The channel flow is simulated by coupling this with the Manning equation: 
formula
19
B is simulated as a function of the upper catchment area Aup: 
formula
20
where k and s are constants (k = 7.0, s = 0.5).

Water-use module

A control-site method was used in the GISMOD to estimate the water requirement of each component (Figure 5). By using this method, some river channel grids should be selected as control grids, which divide the river basin into several parts according to the flow direction. Then, all water requirements including industrial, domestic and irrigation of each part according to the given water-use data, are calculated and compared with the water amount of the first control grid from the upper stream first. If the water resources are available for use, then cut that water amount and turn to flow routing of the next grid. Otherwise, cut only domestic or irrigation water use and turn to the next grid by flow direction. Compare the available water sources with the water demand at each grid. Finally, the water requirement based on the different planting structure in different areas could be obtained for analysing the obvious changes of general water resources and various components in the basin under the impacts of strong human activities. The control-site method can be described in five steps:

  1. The total number of control sites is confirmed, and the location of each site should later be specified based on the actual situation. If the defined grid cell is not a river grid cell, the nearest river grid cell will be automatically selected as a control site.

  2. Next, the module defines the grid from the upper stream of each control site by flow direction. The land use type farmland is then marked as the controlled area of the corresponding control site.

  3. Statistical data (e.g., population, crop type, gross industrial production, water consumption) for the industrial production of the control site are needed for calculating the water requirement of each section (industry, domestic use and irrigation).

  4. The runoff module will be executed to estimate the available water sources of each river grid cell according to the routing order obtained by the pre-processing module.

  5. Compare the available water sources with the water demand at each control site. If the available water resources can meet all types of water uses, the total amount of water required will be withdrawn from the control site. Otherwise, domestic use is given the first priority of water supply, irrigation is second and industry last.

Figure 5

Schematic diagram of the control site method.

Figure 5

Schematic diagram of the control site method.

Domestic uses
The amount of domestic use depends significantly on the population of the study area and the habits and customs of the local residents: 
formula
21
where Td is the water volume for the domestic use per day; Sumd is the total population of the control site; U is the daily water consumption per capita; and Red is the drainage rate of living sewage.
Industrial uses
The industrial water is difficult to estimate because of the various water-use plans during different production periods. For a rough estimation of daily water consumption, the annual water use by industry is divided equally in this module: 
formula
22
where Ti is the industrial water consumption per day; GIP is the gross industrial production per year; Cper_i is the amount of water consumed per unit output of industry; and Efi is the utilisation efficiency.
Irrigation

The required irrigation for farmland includes not only the available water resources from rainfall but also the total amount of water needed by various crops. The crop water requirements are normally expressed by the rate of evapotranspiration. As different crops require different amounts of water to develop, the crop coefficient method is used to estimate the crop water requirement.

The evaporative demand can be expressed as the reference crop evapotranspiration (ET0), which can be calculated using the equation provided in the evapotranspiration module. The empirically determined crop coefficients (Kc) are divided into four stages (initial, development, mid-season and late-season stages) according to the development stages of Doorenbos & Pruitt (1977).

For a given crop at a given stage of crop development, the water requirement of each controlled grid cell (ETneed) under fully irrigated conditions is calculated with: 
formula
23
Due to infiltration through the soil and seepage through the channel, the total water loss is also considered by introducing a parameter of irrigation efficiency (Efa), the value of which varies from 0.5 to 0.9 depending on the irrigation method and the soil type. The actual amount of irrigation water (ETa) is: 
formula
24
where Pe is the effective precipitation. When the water from a control site cannot meet the actual irrigation demand, the amount of water use will be set as the actual supplying quantity of the control site.

Data preparation

The topographical, land-use, soil, geological, water-use, meteorological and hydrological data are required by the GISMOD. All of these data are provided on the DIGITAL HEIHE website (http://heihenew.westgis.ac.cn).

DEM

The size of the grid is determined by the DEM data, which has a horizontal resolution of 1 × 1 km in this study.

Land-use data

Land-use data with a spatial resolution of 1 km are obtained from the thematic mapper images from 1990, which were classified into six categories based on the Technical Rules of Land Use Survey (Figure 6). There are six parameters responsible for the surface layer simulation, the values of which are listed in Table 2.

Table 2

Parameters of the surface layer in the GISMOD

Parameters Land-use type
 
Woodland Grassland Farmland Urban Water Uncultivated land 
sf2 (m) 0.8 0.5 0.5 0.5 
sf0 (m) 0.2 0.2 0.1 0.01 0.05 0.1 
h1 (m) 0.5 0.4 0.3 0.01 0.3 0.3 
f0 (m/d) 0.004 0.002 0.001 0.0004 0.001 0.004 
tha 0.24 0.28 0.28 0.32 0.24 0.32 
n (m-1/3d-10.7 2.0 1.5 0.3 0.03 0.7 
Parameters Land-use type
 
Woodland Grassland Farmland Urban Water Uncultivated land 
sf2 (m) 0.8 0.5 0.5 0.5 
sf0 (m) 0.2 0.2 0.1 0.01 0.05 0.1 
h1 (m) 0.5 0.4 0.3 0.01 0.3 0.3 
f0 (m/d) 0.004 0.002 0.001 0.0004 0.001 0.004 
tha 0.24 0.28 0.28 0.32 0.24 0.32 
n (m-1/3d-10.7 2.0 1.5 0.3 0.03 0.7 
Figure 6

Land use map.

Figure 6

Land use map.

Soil data

The soil types are generalised into three categories by the soil infiltration capacity provided by the China Soil Database from the Institute of Soil Science, Chinese Academy of Sciences. The initial values of these parameters are given in Table 3.

Table 3

Parameters of the soil layer in the GISMOD

Parameters Soil infiltration capacity
 
Low Medium High 
s2 (m) 30 40 50 
s1 (m) 10 15 
s0 (m) 10 
h2 (m) 15 20 25 
kz (m/d) 0.0001 0.0002 0.0005 
kx (m/d) 0.0003 0.0015 0.008 
Parameters Soil infiltration capacity
 
Low Medium High 
s2 (m) 30 40 50 
s1 (m) 10 15 
s0 (m) 10 
h2 (m) 15 20 25 
kz (m/d) 0.0001 0.0002 0.0005 
kx (m/d) 0.0003 0.0015 0.008 

Geological data

Similar to the soil data (Figure 7), the geological data are also grouped into three types considering the permeability and porosity of different types of rock (Figure 8). Table 4 lists the reference values of the parameters of the groundwater layer that was used in the GISMOD.

Table 4

Parameters of the groundwater layer in the GISMOD

Parameters Rock penetrability
 
Low Medium High 
ss2 (m) 30 40 50 
ss1 (m) 10 15 
h3 (m) 15 20 25 
Au (m-1/2d-1/20.0001 0.0002 0.0003 
Ag (1/d) 0.00002 0.00004 0.00008 
Parameters Rock penetrability
 
Low Medium High 
ss2 (m) 30 40 50 
ss1 (m) 10 15 
h3 (m) 15 20 25 
Au (m-1/2d-1/20.0001 0.0002 0.0003 
Ag (1/d) 0.00002 0.00004 0.00008 
Figure 7

Reclassified soil map (the value of class is defined as 1, 2 and 3, which means low, medium and high infiltration capacity of soil, respectively).

Figure 7

Reclassified soil map (the value of class is defined as 1, 2 and 3, which means low, medium and high infiltration capacity of soil, respectively).

Figure 8

Reclassified geological map (the value of class is defined as 1, 2 and 3, which means low, medium and high percolation capacity of rock, respectively).

Figure 8

Reclassified geological map (the value of class is defined as 1, 2 and 3, which means low, medium and high percolation capacity of rock, respectively).

Observed data

Data series that were observed daily from nine meteorological stations, 18 precipitation stations and four hydrological stations located in or around the study area were selected (Figure 1) with the daily data series of atmospheric pressure, mean/maximum/minimum air temperatures, sunshine duration, relative humidity, average wind speed, precipitation and discharge over the period of 1990–1993. All of these data are provided by the Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences.

Water-use data

Four control sites were selected on the basis of such considerations as their administrative boundaries, irrigated areas and the catchments’ properties (Figure 9), information that came from the Statistical Yearbook of Gansu Province (Table 5). In addition, the industrial water requirement, which represents a small proportion of water use (less than 1%), is set as 0 in this case study.

Table 5

Detailed information of each control site in the Heihe River basin

Control site Counties Population (104U (m3/day) Red (%) Crop type* Efa (%) 
Qilian 5.02 0.18 25 0.55 
Minle, Shandan 83.71 0.2 30 0.55 
Zhangye 27.88 0.2 30 0.55 
Linze, Gaotai 42.38 0.18 25 0.55 
Control site Counties Population (104U (m3/day) Red (%) Crop type* Efa (%) 
Qilian 5.02 0.18 25 0.55 
Minle, Shandan 83.71 0.2 30 0.55 
Zhangye 27.88 0.2 30 0.55 
Linze, Gaotai 42.38 0.18 25 0.55 

*Crop types 1 and 2 mean the major crop types of wheat and maize, respectively.

Figure 9

Division of the irrigated area by the control site method (values of 1, 2, 3, 4 and 5 represent the irrigated area of Qilian, Minle & Shandan, Zhangye, Linze & Gaotai, and Jiuquan, respectively).

Figure 9

Division of the irrigated area by the control site method (values of 1, 2, 3, 4 and 5 represent the irrigated area of Qilian, Minle & Shandan, Zhangye, Linze & Gaotai, and Jiuquan, respectively).

The irrigated farmland was divided into five categories from the land-use map according to the four defined control sites, and was mainly distributed over six districts (Shandan, Minle, Zhangye, Linze, Gaotai and Jiuquan) in the Heihe River basin. As seen in Figure 6, the middle stream section is mainly agricultural fields with major crops of wheat and corn. There are few crops in the upper reaches. In this study, Efa is assumed to be a constant (0.55) at all of the control sites due to the traditional irrigation methods and the unique effects of human activity on the water resources of the Heihe River basin.

To enhance food production, wheat–maize inter-planting is widely adopted by farmers in the middle stream of the Heihe River basin (Li & Zhao 2004; Knörzer et al. 2009). Spring wheat is generally sown in the middle of March and harvested in the middle of July. Maize is normally seeded at the end of May and is harvested at the end of October (Wu et al. 2006; Wang et al. 2012). Thus, the crop is divided into two inter-planting types (wheat–maize) in the basin, one of which is mainly cultivated at the low latitudes (crop type 1) and another one which is mainly planted at the high latitudes (crop type 2). The total growing season of crop type 1 is approximately 205 days and that of crop type 2 approximately 212 days. Table 6 provides the growth days of four stages of the two wheat–maize inter-planting types. The value of Kc for different crop types at the four growth stages was adopted by referencing the results of the previous field studies (Zhao et al. 2005; Chen & Wu 2010; Zheng et al. 2010). Kc increases at the development and mid-season stages and then decreases at harvest.

Table 6

Parameters of the two crop types

Crop type Growth days (day) Seeding day (day) Initial stage (day)/Kc Development stage (day)/Kc Mid-season stage (day)/Kc Late-season stage (day)/Kc 
205 75 30 80 60 35 
0.4 1.1 0.6 0.3 
212 85 36 60 81 35 
0.5 0.7 1.2 0.4 
Crop type Growth days (day) Seeding day (day) Initial stage (day)/Kc Development stage (day)/Kc Mid-season stage (day)/Kc Late-season stage (day)/Kc 
205 75 30 80 60 35 
0.4 1.1 0.6 0.3 
212 85 36 60 81 35 
0.5 0.7 1.2 0.4 

Model application

Two objective functions are adopted to optimise the parameters, the relative error and the Nash–Sutcliffe coefficient of efficiency (NSE) (Nash & Sutcliffe 1970). The relative error (RE) represents the systematic water balance error. Positive values indicate overestimation, while the negative values indicate underestimation. The NSE measures the fraction of the variance of the observed values that is explained by the model, which can vary from minus infinity to 1 and should be as close as possible to 1. The RE and NSE are estimated as follows: 
formula
25
 
formula
26
where and are the mean values of the observed and simulated discharge, respectively; and Qiobs and Qisim are the observed and simulated discharge series, respectively.

RESULTS AND DISCUSSION

PET

The spatial distribution of annual PET (the same as ET0) in the upper-middle reaches of the Heihe River basin exhibited obvious regional trends. Annual PET decreased from northwest to southeast, with a maximum value of 1,111 mm in the southern part and a minimum value of 986 mm in the northern part. It can be seen from Figure 10 that the annual PET is less than 1,000 mm in the upper reaches and increased gradually in the middle stream.

Figure 10

Spatial distribution of annual average PET (1990–1993).

Figure 10

Spatial distribution of annual average PET (1990–1993).

The daily PET of the four control sites was selected for a detailed analysis (Figure 11). In each of the sites the pattern was the same: the daily PET usually peaked (ranging from 4 to 6 mm) in July and August and later started to decrease and reached its lowest value (close to 1 mm) in December and January. However, the annual PET was different for each site during 1990–1993. The averages were approximately 990 mm, 1,087 mm, 1,096 mm and 1,090 mm at sites 1, 2, 3 and 4, respectively. Based on the spatial data for PET, the requirement for irrigation water in the Heihe River basin could be estimated according to the land-use map and the control-site method by the GISMOD.

Figure 11

Daily PET at the four control sites.

Figure 11

Daily PET at the four control sites.

Irrigation water requirement

The spatial and temporal variation in irrigation water requirements in the Heihe River basin are shown in Figure 12. It can be observed that agriculture relies heavily on irrigation water requirement from March to November, although the degree of dependence depends heavily on the crop type and the location of the planting area.

Figure 12

Spatial distribution of the monthly irrigation water requirement.

Figure 12

Spatial distribution of the monthly irrigation water requirement.

Temporally, the minimum irrigation need (approximately 0–20 mm) occurs in March and November because only spring wheat is sown in March, and there is little water demand at the late-season stage in November. From April to May, the irrigation requirement increases steadily with the crop development. The maximum irrigation occurs in June, which is the mid-season stage of crop type 1 and the development stage of crop type 2. During this month, the maximum Kc values were adopted for these two crop types because it is the peak period of spring wheat development. From July to August, the quantity of required water varies between 100 and 200 mm and later decreases to between 20 and 50 mm in October.

Spatially, the irrigation amount increases from southeast to northwest in the first half of the year and is relatively even in the second half of the year. From April to June, the northwest region requires more irrigation than does the southeast; this finding may be the result of the increased radiation during the summer, the uneven seasonal distribution of precipitation and, especially, the crop types, which have different daily water needs at different growing stages. From July to September, the irrigation requirement in the southeast is slightly greater than that of the northwest, which is reflected in the characteristics and growth stages of the two crop types.

The simulated irrigation values were higher in the northwest than in the southeast because of the large irrigation areas in Linze, Gaotai, Jiuquan and Jinta (Figure 13). Approximately 4.51 × 106 m3/yr in Qilian, 1,309.08 × 106 m3/yr in Minle, Shandan and Ganzhou, 285.89 × 106 m3/yr in Linze and Gaotai, and 1,746.64 × 106 m3/yr in Jiuquan and Jinta are irrigated. The total amount of irrigation simulated by the GISMOD (approximately 3,346 × 106 m3/yr) was slightly smaller than the estimates (3,531 × 106 m3/yr) from Zhang et al. (2003) because we did not include water transfer and groundwater exploitation. The GISMOD has the advantage of incorporating the spatial and temporal variations in the water requirements, which can be used for water resource assessment, management and utilisation on regional and watershed scales. However, the irrigation need may be inaccurate in some parts of the study area because neither measured nor remote sensing data are available to verify the results from the GISMOD. Therefore, two types of simulated runoff (one with irrigation, one without) were compared against the observed runoff to evaluate the simulated effect of the irrigation requirement at four hydrological stations in the section below.

Figure 13

Irrigation water requirement in five regions divided by four control sites (1990–1993).

Figure 13

Irrigation water requirement in five regions divided by four control sites (1990–1993).

Water balance analysis

The simulated results were validated by measuring runoff at four hydrological stations (Zhamashenke, Yingluoxia, Gaoya and Zhengyixia) (Figure 1). The period of 1990–1993 was selected to simulate the runoff in this study. The result (Sim_1) that ignored the impact of irrigation was considered first, and the effects of human activity and runoff (Sim_2) were subsequently simulated for comparison.

Daily runoff

The simulated daily runoff series under the two scenarios were consistent for the Zhamashenke and Yingluoxia stations. As observed, GISMOD reproduces the observed runoff fairly well. The NSE is unchanged at Zhamashenke station (0.67) and slightly changed (from 0.70 to 0.71) at Yingluoxia station during the period (Table 7). Chen et al. (2003a) found a poor performance, with relatively small NSE values (less than 0.4), without validation. Xia et al. (2003) and Wang et al. (2003) provided very good results, with NSEs of 0.75 and 0.83, with only one year of data for calibration. According to the previous studies, the performance of the GISMOD is acceptable in the daily runoff estimation of the upper reaches, where there is little influence from human activities. However, due to the complexity of the water sources in this region (including glaciers and snowmelt), runoff is highly variable, especially during the rainy season. Therefore, the simulated results capture the observed peak flow but usually underestimate NSE at these two stations.

Table 7

NES and RE of two kinds of simulated runoff

Station   NSE
 
RE
 
Sim_1 Sim_2 Sim_1 Sim_2 
Zhamashenke Daily 0.67 0.67 − 19.4% − 19.6% 
Monthly 0.82 0.82 
Yingluoxia Daily 0.70 0.71 18.3% 16.4% 
Monthly 0.89 0.90 
Gaoya Daily −29.67 0.23 651% 6.5% 
Monthly −74.95 0.52 
Zhengyixia Daily −15.97 0.17 389% − 3.6% 
Monthly −34.64 0.72 
Station   NSE
 
RE
 
Sim_1 Sim_2 Sim_1 Sim_2 
Zhamashenke Daily 0.67 0.67 − 19.4% − 19.6% 
Monthly 0.82 0.82 
Yingluoxia Daily 0.70 0.71 18.3% 16.4% 
Monthly 0.89 0.90 
Gaoya Daily −29.67 0.23 651% 6.5% 
Monthly −74.95 0.52 
Zhengyixia Daily −15.97 0.17 389% − 3.6% 
Monthly −34.64 0.72 

At the Gaoya and Zhengyixia stations, the NSE differs significantly between Sim_1 and Sim_2 (from −29.67 to 0.23 at Gaoya station and from −15.97 to 0.17 at Zhengyixia station). It can be seen from Figure 8 that although runoff was overestimated by Sim_1, the observed runoff and Sim_1 are quite consistent from November to March but differ greatly from April to October. This finding overlaps with the period that water is diverted for crops in the middle reaches. Wang & Cheng (1999) and Ji et al. (2006) suggest that over-exploitation of water resources to sustain the irrigated agricultural system has already led to a decrease in stream flow in the lower reaches of the Heihe River basin. The NSE is greatly improved by considering the irrigation requirement. Although the results are still unsatisfactory and failed to capture certain peak flows during the summer, Sim_2 exhibits the same trend as the observations, and the average simulated runoff is much closer to the average of the observations than that of Sim_1 (Figure 14). The performance of the GISMOD was significantly influenced by the shortage of detailed records of water volume in the well-irrigated area. The water volume varies depending on the weather and cultivation conditions, and this variability makes it difficult for the GISMOD to simulate the runoff accurately on a daily basis.

Figure 14

Comparison between the observed discharge and two kinds of simulated discharge on a daily scale.

Figure 14

Comparison between the observed discharge and two kinds of simulated discharge on a daily scale.

Monthly runoff

The simulated results of the daily runoff are aggregated to monthly values for comparison with the measured data in this study. The performances of the GISMOD are acceptable at the Zhamashenke and Yingluoxia stations. The monthly efficiency coefficient is unchanged (0.82) at Zhamashenke station and varies slightly (from 0.89 to 0.90) at Yingluoxia station (Table 7), which is similar to the daily results. Chen et al. (2003b) employed a distributed runoff model to simulate the monthly discharge, and the NSE values were 0.86 and 0.88 for the calibration and validation periods, respectively. Jia et al. (2006) obtained good results using a new model with an NSE of 0.85 during the calibration and values of 0.89 and 0.91 in two separate validation periods. These studies indicate that several hydrological models are suitable in mountainous area of the Heihe River basin, as are those of the GISMOD.

The NSE is much better at the Gaoya and Zhengyixia stations (from −74.94 to 0.52 at Gaoya and from 34.64 to 0.72 at Zhengyixia). The GISMOD can perform well for runoff simulation in middle reaches of the Heihe River through its consideration of irrigation, which is calculated by a control-site method in the human water use module of the model. Moreover, the simulated result reflects the real variation of runoff under the influence of human activities. This result also means that the actual water consumption for irrigation can be estimated by the GISMOD on a monthly basis (Figure 15).

Figure 15

Comparison between the observed discharge and two kinds of simulated discharge on a monthly scale.

Figure 15

Comparison between the observed discharge and two kinds of simulated discharge on a monthly scale.

We added the differences between the two simulated results for each year from 1990 to 1993 at Zhengyixia station and used that difference for comparison with the average annual water consumption of the upper-middle reaches of Heihe River (Table 8). Although the overestimated quantity of water is less than the actual consumption (approximately 34.09 to 35.23 108 m3/yr), because industrial water consumption and groundwater exploitation are not included, the variation in runoff under different situations relative to overestimated volumes is significant and demonstrated that the water flow from upstream is mainly intercepted by humans for irrigation. For a more precise simulation, the parameters of each crop type (e.g., growth days, crop coefficients and irrigation efficiency) in the GISMOD should be defined based on more detailed field investigations, and the control site could be set to distinguish the different types of crops as much as possible using locations in the various irrigation districts.

Table 8

Comparison of water amount between actual consumption and model overestimation (108/yr)

  1990 1991 1992 1993 Average 
Overestimated water volume 34.02 34.12 34.09 34.15 34.09 
Actual water consumption 35.23 35.90 34.33 35.46 35.23 
  1990 1991 1992 1993 Average 
Overestimated water volume 34.02 34.12 34.09 34.15 34.09 
Actual water consumption 35.23 35.90 34.33 35.46 35.23 

CONCLUSIONS

This research presents a distributed hydrological model (GISMOD) that adapts a control-site method to estimate the requirement for irrigation water. This model has been designed to furnish an accurate description of the hydrological behaviour in a catchment influenced by human activities. A case study is performed in the upper-middle reaches of the Heihe River basin to demonstrate the applicability of the GISMOD, which was tested in two situations (with and without the human water-use module) to validate the simulated results for irrigation. In comparing these two types of results, we found that the discharges estimated by the GISMOD agree with the observed data at the monthly scale but fail to represent the flow dynamics in the middle reach accurately at the daily scale when irrigation is included. The GISMOD can quantify the required irrigation water more reliably at the monthly scale using the parameterised crop types at different phonological stages. Generally, the GISMOD can estimate the monthly irrigation using a control-site method and can model the spatial and temporal variations of the irrigation water requirement in the study area. This output can be useful for regional planning, regional management and water resource assessment.

ACKNOWLEDGEMENTS

This study is supported by the Major Research Plan of National Natural Science of China (No. 91125015). We would like to thank the anonymous reviewers for their constructive comments to improve the quality of the manuscript. Thanks are also given to Environmental and Ecological Science Data Center for West China (http://westdc.westgis.ac.cn) and Digital River Basin (http://heihe.westgis.ac.cn) for providing the necessary data.

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