Rapid population growth is increasing pressure on the world water resources. Agriculture will require crops to be grown with less water. This is especially the case for the closed Yellow River basin, necessitating a better understanding of the fate of irrigation water in the soil. In this paper, we report on a field experiment and develop a physically based model for the shallow groundwater in the Hetao irrigation district in Inner Mongolia, in the arid middle reaches of the Yellow River. Unlike other approaches, this model recognizes that field capacity is reached when the matric potential is equal to the height above the groundwater table and not by a limiting soil conductivity. The field experiment was carried out in 2016 and 2017. Daily moisture contents at five depths in the top 90 cm and groundwater table depths were measured in two fields with a corn crop. The data collected were used for model calibration and validation. The calibration and validation results show that the model-simulated soil moisture and groundwater depth fitted well. The model can be used in areas with shallow groundwater to optimize irrigation water use and minimize tailwater losses.
With global climate change and increasing human population, much of the
world is facing substantial water shortage (Alcamo et al., 2007). The water
crisis has caused widespread concern among public governmental officials and
scientists (Guo and Shen, 2016; Oki and Kanae, 2006). Years of rapid
population growth have squeezed the world water resources. The available
fresh water per capita decreased from 13 400 m
Water supply in China is especially stressed. When averaged over the whole
country, available water per capita is at the water stress threshold of 1700 m
In the Yellow River basin, crop irrigation accounts for 96 % of the total
water use (Li et al., 2004). Due to the increased demand for irrigation,
the river has stopped flowing downstream for an average of 70 d yr
Central to modeling irrigation management practices under shallow groundwater conditions (such as in the Yellow River basin) is simulating the soil moisture content accurately (Batalha et al., 2018, Gleeson et al., 2016; Jasechko and Taylor, 2015; Venkatesh et al., 2011a) because the moisture content plays a critical role in the growth of crops (Rodriguez-Iturbe, 2000), groundwater recharge (Hodnett and Bell, 1986) and upward movement of water to the root zone in areas (Gleeson et al., 2016; Jasechko and Taylor, 2015; Venkatesh et al., 2011a; Batalha et al., 2018). The last effect is unique to shallow groundwater areas where the moisture content and thus the unsaturated conductivity are high and where the drying of the surface soil sets up the hydraulic gradient that causes the upward capillary movement from the shallow groundwater (Kahlown et al., 2005; Liu et al., 2016; Luo and Sophocleous, 2010; Yeh and Famiglietti, 2009). The upward-moving water contains salt that is deposit in the root zone and at the surface.
There is tendency with the ever-increasing computer power to include all processes and the highly heterogeneous field conditions in hydrological models (Asher et al., 2015). In the case of simulating moisture contents, these models become complex and often fully distributed in three dimensions (Cui et al., 2017). Examples of these fully developed models are HYDRUS (Šimůnek et al., 1998), SWAP (Dam et al., 1997) and MODFLOW (Mcdonald and Harbaugh, 2003; Langevin et al., 2017). These models have long run times when applied to scenario simulations for real-world problems. In addition, calibration effort increases exponentially with the number of model parameters (Rosa et al., 2012; Flint et al., 2002). This makes the use of the complex models for real-time management and decision support cumbersome where many model runs are needed (Cui et al., 2017).
To overcome the disadvantages of the full and more complete models, computationally efficient surrogate models have been developed to speed up the modeling process without sacrificing accuracy or detail. Surrogate models are known under several names, such as metamodels, reduced models, model emulators, proxy models and response surfaces (e.g., Razavi et al., 2012a; Asher et al., 2015). We call the complex models “full” or comprehensive models.
Computational efficiency is the main reason for applying surrogate models in place of full models. Other advantages of surrogate models are shortening the time needed for calibration and identifying insensitive and irrelevant parameters in the full models (Young and Ratto, 2011). Most importantly, surrogate models allow investigating structural model uncertainty (Matott and Rabideau, 2008). Finally, surrogate models might be able to deal better with the self-organization of complex systems prevalent in hydrology than the full models (Hoang et al., 2017). For example, full models based on small-scale physics (Kirchner, 2006) cannot necessarily model the repetitive wetting patterns observed in humid watersheds, and for that reason, simple surrogate models often outperform their complex counterparts in predicting runoff when a perched water table is present in sloping terrains (Moges et al., 2017; Hoang et al., 2017).
Surrogate models can be classified in two categories (Todini, 2007; Asher et al., 2015): data-driven and physically derived models. Data-driven surrogates analyze relationships between the data available and physically derived surrogates simplifying the underlying physics or reduce numerical resolution. In recent years, most emphasis in the research literature has been on data-driven surrogate approaches (Razavi et al., 2012a). Relatively little research has been published on physically derived approaches. Despite its popularity, data-driven surrogates can be an inefficient and unreliable approach for optimizing complex field situations, especially when data are scarce, such as in groundwater systems (Razavi et al., 2012b). The physically derived surrogates overcome many of the limitations of data-driven approaches and are therefore superior over data-driven methods (Asher et al., 2015).
In the Yellow River basin various water-accounting models have been
developed to simulate the soil water content and water fluxes (Xu et al.,
2012; Chen et al., 2014; Xue and Ren, 2017; Yang et al., 2017; Ren et al.,
2019). Numerical implementations are the finite-element model HYDRUS-1D by
Ren et al. (2016) and Luo and Sophocleous (2010) and a finite-difference
model by Moiwo et al. (2010). Surrogate models for the North China Plain,
where the groundwater is more than 20 m deep, were published by Wang et al. (2001), Kendy et al. (2003), Chen et al. (2010), Ma et al. (2013), Yang et al. (2015, 2017a, b) and Li et al. (2017). In these models, the
matric potential is ignored, and the hydraulic potential is equal to the
gravity potential; thus the gradient of the hydraulic potential is unity
(at least when it is expressed in head units). Under these conditions the
water flux becomes negligible when the soil reaches field capacity at
For the irrigation perimeters with shallow groundwater in the Yellow River basin, we could find only two surrogate models developed by Xue et al. (2018) and Gao et al. (2017a, b). These two models do not consider the dynamics of groundwater depth and matric potential. By including these dynamics, more realistic predictions of moisture contents and upward flow can be obtained and would give better results when extended outside the area they are developed for (Wang and Smith, 2004). The reason is that for areas with shallow groundwater, evapotranspiration sets up a hydraulic gradient that causes the upward capillary water movement to sustain the evapotranspiration demands and crop water use (Kahlown et al., 2005; Liu et al., 2016; Luo and Sophocleous, 2010; Yeh and Famiglietti, 2009).
Advantages of physically driven surrogates are particularly relevant to groundwater studies where water tables are simulated over entire large areas, as shown by Brooks et al. (2007). Despite this, Asher et al. (2015) poses that physically driven methods have not been applied widely to groundwater problems, and even fewer have been applied with the interaction of moisture contents in the vadose zone, which is key in salinization and plant growth of the many cropped irrigated field in arid and semi-arid regions. In these water short areas it is extremely important to develop models that give directions on how to save water. The main objective of this study is, therefore, to develop a novel surrogate model and to validate this approach using experimental data collected in a field with shallow groundwater, where the ultimate goal is to save water in irrigation districts. In addition, sensitive and insensitive model parameters were identified for simulating moisture content in the shallow groundwater area to optimize future data collection efforts. The experimental fields are located in the Hetao irrigation district, Inner Mongolia, China, where in two maize fields, the moisture content and the groundwater table depth were measured over a 2-year period.
The surrogate model developed is a one-dimensional model simulating the moisture content in the root zone using the groundwater depth and information of the soil moisture characteristic curve. It can be easily adapted to the field scale by including the lateral movement of the regional groundwater. However, over short times, lateral movement can be neglected in nearly level areas outside a strip of 5–100 m from the river (Saleh et al., 1989), such as in deltas and lakes (Dam et al., 1997; Kendy et al., 2003).
The Hetao irrigation district (HID) is the third-largest irrigation district
of China. It covers an area of
Location of the field experiment in Hetao irrigation district. The blue line is the Yellow River.
Crop growth stage in 2016 and 2017 for corn growth on the Fenzidi experimental fields in the Hetao district.
The experiment was carried out in Fenzidi, Bayannur (41
Daily reference evapotranspiration, ET
Irrigation scheduling carried out at Fenzidi experimental fields in 2016 and 2017.
Precipitation, air temperature, relative humidity, sunshine duration and
wind speed were collected from the weather station at the experimental
station. The reference evapotranspiration (ET
Soil samples were collected in rings from the same five layers where
moisture contents were measured and used for determining soil physical
properties including soil moisture at field capacity (
Soil physical properties of the Fenzidi experimental fields.
Note:
In developing the shallow-aquifer–vadose zone surrogate model for modeling moisture contents in the vadose zone, we followed the standards of good modeling practice by Jakeman et al. (2006). We made the model as simple as possible, provided justification for our surrogate technique, tested the surrogate model performance and finally provided detail on the method to encourage discussion on the technique that was followed.
For shallow groundwater (less than 3.3 m deep), the matric potential is a function of depth under equilibrium conditions. Since the soil moisture characteristic curve for each soil is the relationship of moisture content and matric potential, the moisture content is also a function of the depth of the water table under equilibrium conditions.
There are several formulations describing the soil moisture characteristic curve (Bauters et al., 2000; Brooks and Corey, 1964; Gupta and Larson, 1979; Haverkamp and Parlange, 1986; van Genuchten, 1980); the van Genuchten and Brooks–Corey models are widely used in hydrological and soil sciences. Here, we selected the Brooks–Corey model for its simplicity.
The Brooks–Corey model can be expressed as (Gardner et al., 1970a, b; Mccuen et al., 1981; Williams et al., 1983)
The soil of the crop root zone is divided into several soil layers, and each soil layer has its specific soil moisture characteristic curve. After a sufficiently large irrigation and rainfall event, the moisture content is at equilibrium after the drainage stops. After such an event, the soil moisture of the vadose zone stays at the equilibrium moisture content as long as the evapotranspiration is less than upward flux from the groundwater.
The equilibrium soil moisture content,
The drainable porosity, or specific yield, is defined as the amount of water drained from the soil for a unit decrease in the groundwater table when the soil moisture is at equilibrium. It is a crucial parameter in modeling the moisture content in our case or the amount of runoff for a shallow perched water table when there is rain (Brooks et al., 2007).
Illustration of drainable porosity for a soil moisture characteristic curve with a bubbling pressure of 40 cm. The yellow and the blue lines are the equilibrium moisture contents for the groundwater depth at 130 and 150 cm, respectively. The area between the two lines represents the amount of water for the decrease in groundwater table drained from the profile when the groundwater decreases from 130 to 150 cm.
By subtracting the total moisture content at equilibrium in the profile at the initial water table depth and at the new position one unit lower, we obtain the drainable porosity. For example, the area between the yellow and blue curve is the amount of water drained for a decrease in the water table from 130 to 150 cm (Fig. 3).
The total water content amount of the soil over a prescribed depth with a
water table at depth
The model accounts for the downward flux due to the irrigation and rainfall, evapotranspiration by plants and soil, and upward flux from the groundwater to satisfy some or all the evapotranspiration demand by the crop and soil. There are sets of rules implemented in an Excel spreadsheet to calculate the fluxes.
The plant evapotranspiration was calculated in two steps. First the daily
reference evapotranspiration (ET
On days without rain or irrigation, the evapotranspiration lowers the water table, and the moisture content in the soil decreases due to upward movement of water to the plant roots and soil surface. On days with rain or irrigation, the potential evapotranspiration is subtracted from the irrigation and/or rainfall, and water moves downward.
The upward flux from the groundwater,
The rules for downward flux on days with the effective rain and/or
irrigation are relatively simple. If the net flux at the surface (irrigation
plus rainfall minus actual evapotranspiration) is greater than that needed to
bring the soil up to equilibrium moisture content, the groundwater will be
recharged, the distance to soil surface decreases and the moisture
content will be equal to the equilibrium moisture content at the new depth.
When the groundwater is not recharged, the following water balance is
calculated: the rainfall and the irrigation are added to first layer. This
layer will be brought up to the equilibrium moisture content, the
remaining water fills up the next layer to the equilibrium moisture content
and so on. The calculations can be expressed as follows:
Soil texture of Field A and B.
The groundwater in Hetao irrigation district has a small hydraulic gradient
of 0.10 ‰–0.25 ‰ (Ren et al., 2016). In addition, the soil
varies from silt loam to clay loam (Table 4) that has saturated
hydraulic conductivity of less than 2 m d
The soil moisture contents were measured from 30 May to 25 September in 2016 and 2017. Groundwater depth was observed from 13 June to 26 September in 2016 and 2017. For the convenience of simulation, the period of 13 June to 25 September was set as the simulation period. The model parameters were calibrated with the 2016 data and the validation with data collected in 2017 growing seasons. Soil moisture content of the top 90 cm (0–10, 10–30, 30–50, 50–70 and 70–90 cm) and the groundwater depth were simulated for model calibration and validation.
Relatively few parameters can be calibrated in the shallow-aquifer–vadose
zone model. These are the crop coefficient, the
For better understanding the model fitting performance, statistical
indicators were used to evaluate the hydrological model goodness of fit
(Ritter and Muñoz-Carpena, 2013). The statistical indicators including
the mean relative error (MRE; Dawson et al., 2006), the root-mean-square
error (RMSE; Abrahart and See, 2000; Bowden et al., 2002), the
Nash–Sutcliffe efficiency coefficient (NSE; Nash and Suscliff, 1970), the
regression coefficient (
In this section, we present first the 2016 and 2017 experimental observations of the Fenzidi experimental fields in the Hetao irrigation district (Fig. 1). This is followed by the calibration and validation of the shallow-aquifer–vadose zone model of moisture content in each of the five layers and the groundwater table depth.
Simulated and observed groundwater depth during the growing period
for the Fenzidi experimental fields in the Hetao irrigation district:
The total precipitation at the experimental during growing season was 62 mm
in 2016 and 67 mm in 2017. The maximum daily rainfall was 23 mm in July 2017
(Fig. 2). The reference evapotranspiration varied between 1 to 5.5 mm d
Simulated and observed soil moisture content for five soil depths
during the growing period for the Fenzidi experimental fields in the Hetao
irrigation district:
In 2016, the groundwater depth was generally more than 100 cm, except during the last two irrigation events in Field B, when it reached a depth of 72 cm for 1 or 2 d (Fig. 4). In 2017, groundwater tables were slightly closer to the surface than in 2016, especially in Field B2. The minimum groundwater depth was 61 cm on 21 June 2017 in Field B2 after an irrigation event.
In general, groundwater rose during an irrigation event and then decreased slowly due to upward movement of water to the plant roots to meet the transpiration demand. However, in the beginning of the growing season, we can see that the water table increased without an irrigation event. This occurred in Field A on 24 June 2016 and in Field B1 and B2 on 20 June 2017 (Fig. 4). This is curious and could be due to water originating from irrigation in a nearby field.
The water table at the end of the period of observation on 24 September 2016 is approximately 2 m deep, whereas on 15 June 2017, the depth decreased to around 125 cm. This is due to an irrigation application after the crops were harvested to leach the salt from the surface to deeper in the profile, bringing the water table up to near the surface. Evapotranspiration during the winter is small but sufficient for bringing the water table down. There was also a rainfall event on 5 June 2017 of 13 mm (Fig. 2) before the water table was measured, increasing the water level.
Moisture contents are shown for the five layers and the two fields for 2016
and 2017 in Fig. 5. The moisture contents were near saturation when
irrigation water was added and subsequently decreased (Fig. 5). For example,
the soil moisture content changed in the 0–10 cm layer from 0.26 cm
Fitted Brooks–Corey parameters for the soil moisture characteristic curve.
It is interesting that while the soil profile was saturated (Fig. 4), the
groundwater table was between 75–100 cm (Fig. 5). Before equilibrium
moisture content was reached the water table was likely near the surface
during the irrigation event. Because the drainable porosity was extremely
small, even a minimum amount of evapotranspiration or drainage would cause
the water table to decrease to roughly the height of the capillary fringe
equal to the bubbling pressure,
Soil moisture characteristic curve of the four experiment fields for the Fenzidi experimental fields. The red line is the fit with the Brooks–Corey equation.
In 2016 and 2017, the observed reduced moisture contents were plotted versus the height above the water table for the five soil layers of the two field sites in Fig. 6. These plots were used to define the soil moisture characteristic curves, which were of critical importance in simulating the moisture contents.
To define the soil moisture characteristic curve, the Brooks–Corey equation (Eq. 1) was fitted through the points closest to saturation at each matric potential representing the equilibrium conditions after an irrigation event. The fitted parameter values are shown in Table 5. Points to the left of the soil moisture characteristic curve are a result of evapotranspiration drying out the soil when the upward movement of water was insufficient for replenishing the moisture content in these layers, and thus matric potential and groundwater depth were not in equilibrium. In addition, the few points to the right indicate that the soil moisture was greater than the equilibrium moisture content. Many of the outlier soil moisture contents occurred in the layer from 0–10 cm, indicating that the soil was still draining after a rainfall event shortly before the measurements. Thus, the soil was not at the equilibrium moisture content.
The saturated moisture contents in Table 5 agree in general with those measured in Table 3 but are not exact. This is not a surprise, as the alluvial soil deposited by the rivers with layers varies over short distances. The variation within the field was also obvious from the soil's physical measurements. Field B1 and B2 are within Field B. The soil's physical properties of the various layers (Table 4) were not the same for the three sites, clearly showing the variability within the field.
Generally, large values of a pore size index coefficient
The four parameters that can be calibrated in the shallow-aquifer–vadose
zone model are the crop coefficient
Calibrated parameter values of the shallow-aquifer–vadose zone model.
The first step in the calibration was to fit the
Model statistics for calibration of the shallow aquifer model in 2016. The mean relative error (MRE), root-mean-square error (RMSE), regression slope, coefficient of determination (
The second step was calibrating the moisture content by adapting the root
function indicating the layers from which the water was taken up. Calibration was
done manually by trial and error. We found that we could use the same root
function for Field A, B, B1 and B2 (Table 6). The calibrated soil moisture
contents of the five soil layers for the two fields in general are in
agreement with the measured values in 2016 (Fig. 5a, b), with the coefficient
of determination
The moisture contents predicted by the shallow-aquifer–vadose
zone model
were validated with the 2017 data in Field B1 and B2. Although the
validation statistics of the five layers were slightly worse than for
calibration in Table 7, the overall fit was still good, as shown in Fig. 5c and
d. The coefficient of determination varied between 0.39 and 0.90. The MRE
varied between
The final step was to calibrate the groundwater table coefficients with the
2016 data for both fields. We found that for fields not in the same location
(e.g., A, B), the subsurface was sufficiently different; thus the same set
of parameters could not be used (Table 6). The difference between the
calibrated parameters for the two fields was small (Table 6). The measured
and simulated groundwater depths were in good agreement with the chosen set
of parameters (Fig. 4a, b), with the coefficient of determination
Since Field B1 and B2 are in the same location as Field B, we used the same
set of groundwater parameters for the three fields (Table 6). The resulting
fit between observed and predicted daily groundwater depths for Field B1
and B2 in 2017 was better than for the calibration in 2016 (Fig. 4c, d),
with
In this paper, a novel surrogate model was developed for irrigation
systems where the groundwater is close to the surface. The model uses the
soil moisture characteristic curve to derive the drainable porosity and to
predict the moisture contents in the soil. It is based on a
definition of field capacity that is used less often (or equilibrium moisture content, as it is
called in this paper) based on the observation that the flow becomes
negligible when the hydraulic gradient is zero. In other words, the system
is in equilibrium when the sum of the matric potential and the gravity
potential is constant. Thus, when we chose the groundwater level as the
reference point for the gravity potential, the matric potential is equal to
the height above the groundwater. This is different from other applications
of Darcy's law, where the groundwater is below 3.3 m. In these cases,
groundwater movement stops when the conductivity becomes negligible at
In general, this surrogate model simulated the soil moisture content in each
soil layer well, especially when compared to other models that attempted the
soil moisture contents in the Yellow River basin such as the North China Plain
(Kendy et al., 2003) and the Hetao irrigation district in Gao et al. (2017b) during the crop growth period. Our simulation results suggest that
the reduction factor of the potential evaporation for soil saline
The simulations, together with the observed data, indicated that information about the soil is very important to obtain the exact moisture content in the soil. However, generalized soil moisture characteristic curves for each soil type can be used in the simulation and will not result in great differences in water use by plants, since percolation to deeper layers was negligible, and thus the only loss of water was by evapotranspiration independent of the soil moisture content.
Finally, in the simulations we did not consider the influence of crop type and the influence of crop growth on soil moisture and groundwater depth. It would be of interest to investigate in future work whether the simulations would be improved by considering the dynamic crop characteristics during the growing season (Singh et al., 2018; Talebizadeh et al., 2018). A mature crop model, such as the EPIC model (Williams et al., 1989), which needs relatively few parameters, will certainly help to predict the crop yield but might not change the water use predictions. Actually, the EPIC model was already applied to the Hetao irrigation district by many researchers to analyze the crop growth during the crop growth period (Jia et al., 2012; Xu et al., 2015).
A novel surrogate vadose zone model for an irrigated area with a shallow aquifer was developed to simulate the fluctuation of groundwater depth and soil moisture during the crop growth stage in the shallow groundwater district. To validate and calibrate the surrogate model we carried out a 2-year field experiment in the Hetao irrigation district in upper Mongolia with groundwater close to the surface. Using meteorological data and the soil moisture characteristic curve and upward capillary movement, the surrogate model predicted the soil water content with depth and groundwater height on a daily time step with acceptable accuracy during validation and was an improvement of two previous models applied in the Hetao district that could predict the overall water content in the root zone but not the distribution with depth.
The surrogate modeling results show that after an irrigation event, as long as the upward flux from the groundwater to the root zone was greater than the plant evapotranspiration rate, the moisture contents in the vadose zone could be found directly from the soil moisture characteristic curve by equating the depth to the groundwater with the absolute value of the matric potential. When the plant evapotranspiration rate exceeded the upward movement, moisture contents would be indicated by groundwater depth and were predicted by a root zone function. Another finding was that the daily moisture contents were simulated without using the unsaturated hydraulic conductivity function in the surrogate model. For a daily time step, equilibrium (defined as the hydraulic potential being constant) in moisture contents in the profile was attained; thus precise unsaturated conductivity was not needed. Of course, for shorter time steps, for predicting the transient fluxes and groundwater, the conductivity function is needed. For management purposes a daily time step is acceptable.
Future improvement to this model will focus on coupling the EPIC model and applying it to simulate other crops and other locations with a shallow groundwater table. The surrogate model should also be compared with a “full” model to test the conditions under which the surrogate model will fall short.
The observed data used in this study are not publicly accessible. These data have been collected by personnel the College of Water Resources and Civil Engineering, China Agricultural University, with funds from various cooperative sources. Anyone who would like to use these data should contact Zhongyi Liu, Xingwang Wang and Zailin Huo to obtain permission.
XW collected the data. ZL, ZH and TS contributed to the development of the model. The simulations with the novel model were done by ZL and TS. Preparation and revision of the paper were done by ZL, under the supervision of TS and ZH.
The authors declare that they have no conflict of interest.
Peggy Stevens helped greatly with polishing the English. We thank Xingwang Wang, who helped in collecting data.
This research has been supported by the National Key Research and Development Program of China (grant no. 2017YFC0403301) and the National Natural Science Foundation of China (grant nos. 51639009 and 51679236).
This paper was edited by Nunzio Romano and reviewed by Jan Boll, Tiago Ramos and one anonymous referee.