A grid-based integrated surface–groundwater model (GISMOD)

The dynamic processes of surface water and groundwater interaction are mainly affected by geological/meteorological characteristics and represent the natural features and hierarchical structure of the watershed (Imagawa et al. 2011). These two kinds of process are not isolated components of the hydrological system in the environment, and the interactions between them are complex and usually difficult to estimate due to the problems of heterogeneity and scale (Halford & Mayer 2000; Kalbus et al. 2006). Therefore, a better understanding of the basic principles of interactions between groundwater and surface water is important for efficient management of water resources (Gardner 1999; Sophocleous 2002). The hydrological model is an important scientific tool, which has focused on the simulation of rainfall-runoff relationships according to a conceptual or physical representation method. Models can be used to reflect groundwater and surface water interaction as well as runoff generation for water resources evaluation, management and utilization on regional or watershed scales (Krause et al. 2009; Khakbaz et al. 2011).

A number of hydrological models have been utilized to quantify stream–aquifer flow in recent years. For instance, Kim et al. (2008) developed the SWAT-MODFLOW model and applied it to estimate groundwater and streamflow reduction by pumping groundwater out. A coupled surface water and groundwater flow model (MODBRANCH) was developed by Swain & Wexler (1996), and it integrated MODFLOW and BRANCH to simulate unsteady flow dynamics in an open channel network. MIKE-SHE and MOD-HMS have been developed to describe the overall exchange and interaction by coupling surface water and groundwater flows (Abbott et al. 1986; Refsgaard & Storm 1995; Graham 2001; Panday & Huyakorn 2004; Graham & Butts 2005). Some of these models were developed to investigate the variations of groundwater level and surface water level for special purposes. For example, Yuan et al. (2011) adopted a coupled model that simulates the interaction between surface water and groundwater flow, and solute transport processes in the coastal wetland. Zhang & Ross (2007) developed a two-layer vadose zone model for surface and groundwater interactions. Imagawa et al. (2011) improved the hydro-environmental watershed model in a water exchange process through surface water-groundwater interaction, and applied it to an agricultural watershed.

However, all of these models have different strengths and limitations. As a matter of fact, hydrological processes are far from simple: watershed is highly heterogeneous in terms of land use, soil characteristics and topography (Pilgrim et al. 1988; Thornes et al. 1996; Kosmas et al. 1997). Conceptually, complex models should perform well by numerical simulation with high quality input data. However, several studies show that simple models can perform as well as complex ones (Michaud & Sorooshian 1994; Refsgaard & Knudsen 1996). Therefore, it is always difficult to select between a simple model and a complex one for hydrological simulation.

In order to describe the interaction between surface water and groundwater in a simple and efficient way, a new kind of hydrological model (a Grid-based Integrated Surface water–groundwater interaction MODel, simplified GISMOD) was developed to estimate the exchange water amount based on a three-layer tank method. The principles of GISMOD are presented first and then a case study in the Heihe River basin is presented to evaluate the performance of this model.

GISMOD is a physically based distributed hydrological model that was developed to simulate hydrologically relevant processes in river basins, such as water movement, infiltration, interaction and evapotranspiration, by a simplified tank method (Xu et al. 2001).

Similar to the hydrological tool in ArcGIS, the preprocessing program is used to delineate the river basin and to extract the drainage networks automatically from the DEM data (Li et al. 2013). This program has various functions such as flow direction definition, flow accumulation calculation, and drainage network generation, and the order of runoff simulation can be analyzed conveniently by using a special approach (Xu 2009).

The accuracy of the simulation result depends primarily on how well the variability of the hydro-meteorological information can be specified in a certain area. Thus, the disaggregation of the available hydro-meteorological data from the limited observation station to the entire catchment is essential to estimate 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 developed in the model for spatial interpolation (Nalder & Wein 1998; Teegavarapu & Chandramouli 2005).

In order to measure the ability of water to move from the surface to the atmosphere, and to measure and the processes of evaporation and transpiration without control of water supply, potential evapotranspiration (PET), as an important component of the hydrological cycle and the key variable of the hydrological models, should be estimated as accurately as possible. Calculation methods of PET can be classified into four types (temperature-based, radiation-based, mass-transfer and combination). Most of them need many kinds of input data such as air temperature, air pressure, humidity, wind speed, solar radiation, etc. In order to satisfy the needs of the different available data, GISMOD has integrated eight methods (Turc 1961; Monteith 1965; Priestley & Taylor 1972; Hargreaves & Samani 1985; Allen et al. 1998) to estimate PET (Table 1) and also enable users to import their own PET data.

Table 1

Eight methods for estimating PET in GISMOD

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

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

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When ET₀ is the potential evapotranspiration, R_n is net radiation flux, G is sensible heat flux into the soil, which can be ignored for daily estimation; T is the temperature, usually taken as the daily mean air temperature (T_mean), T_max and T_min is the daily maximum and minimum air temperatures, respectively; e_s is the vapor pressure of the air at saturation, e_a is the actual vapor pressure, Δ is the slope of the saturation vapor pressure temperature relationship curve and γ is the psychometric constant, U₂ is the wind speed at 2 m height, λ is the latent heat of vaporization, R_s is the solar or shortwave radiation, and R_a is the extraterrestrial radiation.

The surface layer is a thin top soil layer covered by vegetation and regarded as a kind of reservoir with an opening bottom in GISMOD. Rainwater, the discharge from upstream grids and the water supplied by the soil layer are regarded as the inflow to the surface layer. Apart from evapotranspiration and infiltration, water in the surface layer is generated by two kinds of overland flow (saturation excess overland flow and infiltration excess overland flow), and by the lateral and infiltration flow.

Checking for water balance in each layer is carried out independently in GISMOD. First of all, the amount of available water in the surface layer should be estimated, including outflow from upstream, rain water and existing water in the layer. Then, available outflow from the surface layer will be calculated by considering different situations. When the available water is not enough to meet the demand for release, all of the water from the surface layer should be pouring out on the basis of proportional distribution. Afterwards, the water level in the surface layer will be decreased to 0. Otherwise, each part of the outflow should be estimated by using Equations (6)–(9), and the water level in the surface layer will be re-computed according to the continuity equation of water balance. In order to take account of the recharge flow from the soil layer, the water level in the surface layer will be finally adjusted.

Recharge flow will be generated if the available water exceeds the capacity of the soil layer. Another possibility is that the moisture content of the surface layer falls to fill the needs of evapotranspiration and infiltration. Meanwhile, free water from the soil layer could be provided for the requirements of the surface layer. There are three possible scenarios that can be described by the following equations.

1. Less water can be supplied from the soil layer during the periods when there is a water shortage in the surface layer:

   

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• 2. The available water of the soil layer is sufficient to meet the needs of surface layer:

  

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• 3. Additional water is unnecessary in the surface layer, while there is an abundance of water in the soil layer:

  

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A designated water level is used to distinguish unconfined flow and confined flow in this model, below which only confined water can be generated from the groundwater layer. Specifically, it is worth noting that the flow pattern of this layer is not only controlled by the configuration of the water table but also by the distribution of hydraulic conductivity of the rocks.

Similar to the soil layer, three kinds of water supply from the groundwater layer are shown as follows.

1. The water level of the soil layer is below the particular value (s0) and the water level of the groundwater layer is above the designated value (ss1):

   

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A number of parameters are used in GISMOD, which should be categorized into three groups according to the grid structure and relevance with the properties of the soil, the geology and the type of land cover.

There are six parameters responsible for surface layer simulation (Table 2), the values of which are evaluated according to the land use map. In order to utilize the land use data effectively, land use type is classified into six categories on the basis of the Technical Rules of Land Use Survey (TCADC 1984). Initial values of the parameters in different land use type are listed in Table 2.

The parameters responsible for the soil layer are adjusted according to the land use map and generalized into three sorts by the soil infiltration capacity (Table 3). Initial values of parameters of the three soil types are given in Table 3.

As with the soil layer, the parameters of the groundwater layer are also classified into three categories depending on the different rock permeabilities in the model. Although there is no classification standard for rock permeability, the rock porosity can be assumed instead. In general, greater grain size and smaller porosity tend to decrease the penetrability, while a decrease in range of particle size and greater porosity tends to increase penetrability. Table 4 shows the reference value of parameters of the groundwater layer used in GISMOD.

While the output grid is determined, calibration and validation can be conducted on a daily or monthly time step according to the spatially interpolating hydro-meteorological data. The simulation result can be compared on the basis of model performance with regards to objective criteria representing the water balance.

The Heihe River is the second largest inland river in Northwest China. The river originates from the north foot of Qilian Mountain and passes nearly 821 km north through Qinghai and Gansu provinces, and finally reaches 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; 70% of the area is mountainous. The average annual temperature and precipitation in the upper reaches are about 2 °C and 350 mm, respectively. In the middle reaches, annual precipitation is only 140 mm because of the dry weather, and the average annual temperature is between 14 and 18 °C.

For parameterization, topography data, land use data, soil data, geological data, and observed metrological and hydrological data are required in GISMOD provided by the DIGITAL HEIHE website (http://heihenew.westgis.ac.cn).

The size of the grid is determined by DEM data with a horizontal resolution of 1 × 1 km in this study. DEM data should be converted from other formats to ASCII to satisfy the input requirement of GISMOD, and other related data such as soil type and land use should be transformed using the same method.

Observed daily data series from nine meteorological stations located in or around the study area were selected (Figure 4), which include daily atmospheric pressure, mean, maximum and minimum air temperature, sunshine duration, relative humidity and average wind speed data over the period 1961–2006. All these data were provided by NCC (National Climatic Centre of China). In addition, 18 precipitation stations and three hydrological stations were selected with the daily data series of precipitation and discharge provided by CAREER (Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences). Unfortunately, some of the daily precipitation data were only available for several non-consecutive series, which included daily series for 1964, 1971, 1976–1979, 1981, 1983–1984, 1990–1993 and 2001–2002, and therefore the period of 1990–1993 is selected in this study.

In order to present the model performance in the upper-middle reaches of Heihe River basin, which is divided by the Yingluoxia and Zhengyixia hydrological station, grid A (100.18, 38.81) near the Yingluoxia hydrologic station in the upper reaches and grid B (100.41, 39.13) and C (99.46, 39.81) around Zhangye City in the middle reaches were selected in this study. Simulated results of the three ordinary grids (see Figure 4) were exported for better understanding the water exchange characteristics of Heihe River basin. In addition, the simulated runoff of a river gird near Yingluoxia hydrological station was used to compare with the measured data for model validation.

In the soil layer, the water content varied more gently, the peak value of which had a half-month delay with the surface layer during the whole period. In general, the soil water content showed an increasing tendency at grid A and C and decreased at grid B, the average of which was about 40%, 33% and 32%, respectively.

Groundwater increased rapidly in 1990 and then remained stable from 1991 to 1993 at grid A. However, groundwater descended linearly at grid B and C, which demonstrates that the groundwater resources increased in the upper streams and is then exhausting in the middle reaches. Field monitoring data by former studies have also found that the groundwater level of the middle reach is decreasing in recent decades. For instance, Hu et al. (2007) has shown the groundwater level from four observation wells around Zhangye City, which has fallen rapidly from 1987 to 2000. Zhu et al. (2004) also found that the water-table had dropped the most in the alluvial-diluvial fan zone in the middle reaches of the Heihe River basin.

From grids A–C, the water infiltrated from the surface layer is about half of the total amount of infiltrated water, which increased from 54.27 to 65.46%, with the soil infiltration decreasing from 45.73 to 34.54%. Recharged water from the soil layer occupied the main part of recharge water, the ratio of which ranged from 65.19 to 93.8%. According to grid A, the ratio of groundwater recharge increased at grids B and C (from 6.20 to 34.81%). These results show that the groundwater layer is mainly supplied by the soil layer in the upper streams and then recharging recharged water to the soil layer in the middle streams.

For a more detailed understanding of the water exchange process, the water infiltrated from the surface layer and soil layer were summed up as the infiltrated water to compare with the recharged water, which was considered the total volume of water supplied from the groundwater layer and the soil layer. The statistical results from these three sites are shown in Table 7.

GISMOD is a grid-based distributed hydrological model which has been designed to furnish a description of hydrological processes with the emphasis on surface-groundwater exchange in a catchment. A specific method based on a water balance equation is used to simulate the hydrological processes of different soil layers by taking into account precipitation, evapotranspiration and infiltration in GISMOD. The advantage of this model is that water interaction between different soil layers can be simply described by a generalized physical process under various situations.

A case study was performed in the upper-middle reaches of the Heihe River basin to demonstrate the applicability of the GISMOD. Compared with the observed runoff data, we found that both calibration and validation of GISMOD were performed with reasonable accuracy at the daily and monthly scales. The hydrological processes in the different soil layers are generally reflected by GISMOD, which also gives the seasonally changing laws of water exchange in the Heihe River basin. Generally, the GISMOD can estimate hydrological processes and model the spatial and temporal variations of the infiltrated water and recharged water in the study area.

GISMOD is a modular modeling system developed independently and primarily for a program task, and it needs to be improved in future studies to add the module of human water use, automatic parameter calibration, snowmelt simulation and so on.

This study was supported by the Major Research Plan of the National Natural Science of China (No. 91125015). Thanks are given to the Environmental and Ecological Science Data Center for West China (http://westdc.westgis.ac.cn) and the Digital River Basin (http://heihe.westgis.ac.cn) for providing the necessary data.