A distributed hydrological model in the Heihe River basin and its potential for estimating the required irrigation water

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 (K_c), 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.

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).

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).

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

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.

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.

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 .
1	FAO Penman–Monteith
2	Penman
3	Kimberly–Penman
4	Hargreaves–Samani
5	Priestley–Taylor
6	Makkink
7	Turc
8	Doorenboss–Pruitt

No. .	Name .	Equation .
1	FAO Penman–Monteith
2	Penman
3	Kimberly–Penman
4	Hargreaves–Samani
5	Priestley–Taylor
6	Makkink
7	Turc
8	Doorenboss–Pruitt

R_n 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 (T_mean); T_max and T_min are the daily maximum and minimum air temperatures, respectively; e_s is the vapour pressure of the air at saturation; e_a 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; R_s is the solar or shortwave radiation; and R_a is the extra-terrestrial radiation.

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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 (K_c) are divided into four stages (initial, development, mid-season and late-season stages) according to the development stages of Doorenbos & Pruitt (1977).

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).

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

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.

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.

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, Ef_a 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 K_c 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). K_c increases at the development and mid-season stages and then decreases at harvest.

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 K_c 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 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.

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.

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.

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.

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.

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.