HYDRUS-1D was combined with lysimeter experiments to study extinction depth and steady water storage in root zone (Ws) of groundwater evaporation (ETgw) under winter wheat and silt soil. The measured soil water contents and daily ETgw with various groundwater depths were used to calibrate and validate the parameters in HYDRUS-1D. In total, 13 groundwater depths ranging from 0.5 to 5.0 m were set up for scenario simulation to determine the extinction depth and Ws. The results showed that HYDRUS-1D had an acceptable performance in simulating the soil water storage in the 0–60 cm layer and the daily ETgw. Moreover, the ETgw decreased linearly with increasing groundwater depth from 0.5 to 2.5 m and decreased as a power function with increasing groundwater depth from 2.5 to 5.0 m. Under the condition of winter wheat and silt soil, the extinction depth of ETgw was about 5.0 m. Ws decreased linearly with increasing groundwater depth from 0.7 to 2.0 m, but was not influenced further by the groundwater at depths beyond 2.0 m.

INTRODUCTION

In areas where the water table is within or slightly below the root zone, crops uptake water from both a thin unsaturated vadose zone and saturated ground water (Shah et al. 2007). Groundwater contribution to crop water use by groundwater evaporation (ETgw) is one important term of soil water balance in the presence of shallow water tables (Liu et al. 2006; Bourgault et al. 2014). Therefore, groundwater should be used efficiently (Boyraz & Kazezyilmaz-Alhan 2014). The volume of drainage and irrigation water can be reduced by using shallow groundwater to meet a portion of the crop water requirement (Ayars et al. 1999). However, the groundwater contribution is influenced by many factors, and among them, groundwater depth and the soil water storage in root zone are two important influencing factors of ETgw (Raes & Deproost 2003; Doble et al. 2006; Luo & He 2008).

Table 1

Bulk density and soil texture of the silt soil in the lysimeters

  Soil texture
 
Soil depth (m) Bulk density (g cm−3Sand (%) Silt (%) Clay (%) 
0–0.2 1.25 15.0 80.3 4.7 
0.2–1.5 1.42 13.4 81.7 4.9 
  Soil texture
 
Soil depth (m) Bulk density (g cm−3Sand (%) Silt (%) Clay (%) 
0–0.2 1.25 15.0 80.3 4.7 
0.2–1.5 1.42 13.4 81.7 4.9 

ETgw was often assumed to have a linear or piecewise linear relationship with groundwater table depth (McDonald & Harbaugh 1988; Banta 2000; Schmid et al. 2006) and vanished at the depth which is termed extinction depth, which depends on the types of soil or vegetative cover. Vegetation types may have significant influences on soil water flux (Moiwo & Tao 2014). Based on HYDRUS simulation, Shah et al. (2007) gave the extinction depths for three land covers: bared soil, shallow-rooted (grass) and deep-rooted vegetation (forest). However, for the same type of land covers, large differences in the maximum root depth and extinction depth may occur for different vegetation. The values recommended by Shah et al. (2007) are approximate, but may not be exact in application.

Doorenbos & Pruitt (1977) assumed that ETgw was dependent upon the soil water storage in the root zone. The equation is given as 
formula
1
where W is the soil water storage in the root zone (mm); Wwp is the soil water storage in the root zone at the wilting point (mm); Wp is the root zone soil water storage corresponding to the depletion fraction for no stress (mm), p (Askri et al. 2010); ETgw-max is the maximal ETgw (mm d−1).

Liu & Luo (2012) proposed an improved approach determining ETgw-max based on the approaches of Food and Agriculture Organization of the United Nations Paper No. 24 (FAO-24) (Doorenbos & Pruitt 1977) and FMP1 (Farm Process) (Schmid 2006). Askri et al. (2010) replaced Wp with the storage at capacity (Wfc) because ETgw became negligible when the actual storage was above Wfc. Liu et al. (2006) assumed that a steady-state occurred in the soil profile and ETgw occurred at the potential rate (ETgw-max) when the actual soil water storage was lower than a steady storage (Ws), and replaced lower storage (Wwp) in Equation (1) with Ws. Liu & Luo (2012) found that the water storage in the 0–60 cm soil layer under winter wheat and silt soil trended to be a relatively steady value by the measured data through lysimeter experiments.

Many researchers have studied ETgw under crop planting with lysimeters (Hutmacher et al. 1996; Kahlown et al. 2005; Ayars et al. 2009; Huo et al. 2012). However, little experimental study has been conducted to investigate intensively the impact of soil water storage on ETgw. Moreover, because the application of a lysimeter is limited by the cost in construction, operation and maintenance (Babajimopoulos et al. 2007), it is difficult to have enough experiment treatments to determine the extinction depth and Ws of a wide range of groundwater depths. The combination of lysimeter and numerical model provides an efficient method to determine these values.

HYDRUS-1D was developed to solve the Richards equation and widely used to simulate one-dimensional water movement in variably saturated media (Simunek et al. 2008) and was applied widely to study soil water movement and root-water uptake (Ma et al. 2010; Shouse et al. 2011; Leterme et al. 2012; Cheng et al. 2013; Zhu et al. 2013). The objective of this study was to determine the extinction depth and Ws for a wide range of groundwater depths by the combination of lysimeter experiments and HYDRUS-1D simulation under winter wheat (Triticum aestivum L.) and silt soil.

MATERIALS AND METHODS

Site description

Field experiment was conducted at the Yucheng Comprehensive Experimental Station of the Chinese Academy of Sciences (116°36′E and 36°57′N) at Yucheng City, Shandong Province, China. It is under a semi-humid and semi-arid climate, and the annual mean temperature and precipitation are 13.1 °C and 600 mm, respectively. The precipitation during the growth period of winter wheat is about 150 mm, which is far less than its water requirement. However, the water table depth mainly fluctuates between 0.5 and 3.0 m due to the recharge of precipitation and irrigation (Luo & He 2008). The contribution of shallow groundwater to the crop water requirement may help to save irrigation water.

Lysimeters

A set of lysimeters were used to measure ETgw. A lysimeter comprises two parts: outside soil container and inner water supply and drainage systems (Figure 1). The soil container was made of steel board with a surface area of 1.0 m2, depth of 1.9 m below ground and height of 0.1 m above ground (Liu & Luo 2011). The middle part was backfilled with homogenous silt soil. A neutron probe tube was installed vertically in the center of each soil container to measure soil moisture. A Mariotte bottle was used to provide a constant water table within the soil container, and the water reduction in the water supplement bottle could be measured to determine ETgw. The electrical conductivity of the water supplied to the soil container from the supplement bottle was 2.0 dS m−1.

Figure 1

Schematic diagram of lysimeter. 1 – filling soil, 2 – neutron probe, 3 – filter bed, 4 – water supplement bottle, 5 – Mariotte bottle, 6 – drainage tank, 7 – valve, 8 – air inlet pipe, 9 – soil container.

Figure 1

Schematic diagram of lysimeter. 1 – filling soil, 2 – neutron probe, 3 – filter bed, 4 – water supplement bottle, 5 – Mariotte bottle, 6 – drainage tank, 7 – valve, 8 – air inlet pipe, 9 – soil container.

The wilting point and field capacity of the original silt soil in the soil container were 0.07 and 0.32 cm3 cm−3. The bulk density and mechanical composition of the soil are shown in Table 1.

Treatments

The experiments were conducted in 2004–2005 and 2007–2008, and the treatments in the two growth seasons were denoted as ‘T1’ and ‘T2’, respectively. The planting crop was winter wheat (T. aestivum L.). The field management and the development of the growth stage of winter wheat are shown in Tables 2 and 3. Three constant groundwater depths were 0.7, 1.1 and 1.5 m in the period from 23 March to 8 June 2005 during which the treatments received precipitation (Table 4). There was only one constant groundwater depth, 1.5 m, in the period from 20 March to 5 June 2008 during which the treatment did not receive precipitation. To quantify the ETgw under the condition without irrigation, no irrigation was applied for all experiment treatments in both growth seasons.

Table 2

Field management in experiment period

Experiment period Variety Planting date Seed rate (kg ha−1Nitrogen application (kg ha−1
2004–2005 13 line 14 October 2004 180 626 
2007–2008 Kenong 199 21 October 2007 240 300 
Experiment period Variety Planting date Seed rate (kg ha−1Nitrogen application (kg ha−1
2004–2005 13 line 14 October 2004 180 626 
2007–2008 Kenong 199 21 October 2007 240 300 
Table 3

Growth stages of winter wheat

Experiment period Emergence Regreen Jointing Earing Flowering Filling Harvest 
2004–2005 19 October 2004 17 March 2005 5 April 2005 28 April 2005 3 May 2005 7 May 2005 8 June 2005 
2007–2008 26 October 2007 3 March 2008 5 April 2008 18 April 2008 25 April 2008 29 April 2008 5 June 2008 
Experiment period Emergence Regreen Jointing Earing Flowering Filling Harvest 
2004–2005 19 October 2004 17 March 2005 5 April 2005 28 April 2005 3 May 2005 7 May 2005 8 June 2005 
2007–2008 26 October 2007 3 March 2008 5 April 2008 18 April 2008 25 April 2008 29 April 2008 5 June 2008 
Table 4

Experiment treatments in the two growth seasons

Experiment period Treatment Groundwater depth (m) Precipitation (mm) Irrigation (mm) 
23 March 2005, ∼6.8 T1 (70) 0.7 75.1 – 
T1 (110) 1.1 75.1 – 
T1 (150) 1.5 75.1 – 
20 March 2008, ∼6.5 T2 (150) 1.5 – – 
Experiment period Treatment Groundwater depth (m) Precipitation (mm) Irrigation (mm) 
23 March 2005, ∼6.8 T1 (70) 0.7 75.1 – 
T1 (110) 1.1 75.1 – 
T1 (150) 1.5 75.1 – 
20 March 2008, ∼6.5 T2 (150) 1.5 – – 

Measurements

Daily ETgw was measured through lysimeters. Soil volumetric water content was measured with neutron probes (CNC503B, China) at five to seven intervals and in 0.1 m increments from 0.1 to 1.3 m deep into the soil profile. Meteorological data such as precipitation and wind speed were measured in a standard weather station 50 m away from the lysimeters.

Mathematical model

One-dimensional movement of water in variably saturated media is described by a modified form of the Richards equation 
formula
2
where θ is the volumetric water content (cm3 cm−3), h is the water pressure head (cm), t is time (d), x is the spatial coordinate (positive upward), K is the unsaturated hydraulic conductivity function (cm d−1), α is the angle between the flow direction and the vertical axis, and S is the sink term (1 d−1).
An ‘atmospheric BC with surface layer’ boundary condition was used to describe the upper boundary. The lower boundary was set at the groundwater table and was assigned to be a constant soil water content boundary. The initial and boundary conditions were described using the following equations: 
formula
3
 
formula
4
 
formula
5
where q0 (t) is the net infiltration rate (cm d−1), L is the distance from groundwater depth to ground surface (cm), and θs is the saturated volumetric water content (cm3 cm−3).

Input parameters

The unsaturated soil profile was divided into two layers from 0 to 0.2 m depth and from 0.2 m depth to the constant groundwater depth. The initial soil water content was determined via measured data. The sink term, S, was estimated with the Feddes model (Feddes et al. 1976). The parameters in root-water uptake water stress response function were from the values recommended in the HYDRUS-1D database (Wesseling et al. 1991). The plant height of winter wheat was determined by observation. The daily potential transpiration (Tc-pot) and evaporation (Ec-pot) were calculated using dual crop coefficient approaches in FAO-56 (Allen et al. 1998). According to FAO-56, the recommended basal crop coefficients in initial, middle and late season stages (Kcbini, Kcbmid and Kcbend) were, respectively, 0.15, 1.1 and 0.3, and the effective root depth on day i was estimated as follows: 
formula
6
 
formula
7
where Jmid is the number of the days of the year at the beginning of the midseason period; TRZmin is the initial effective depth of the root zone (m); TRZmax is the maximum effective depth of the root zone during the middle season (m); and Kcbini, Kcbmid and Kcbi are the basal crop coefficients in initial and middle season stages and on day i. Jmid is 174 and 167 for the growth periods in 2004–2005 and 2007–2008, respectively. In this paper, the recommended values in FAO-56 were used. TRZmin and TRZmax are 0.2 and 1.5 m, respectively.

Based on the mechanical composition and bulk density of the soil, the soil hydraulic parameters such as θr, θs, α, n and Ks were determined first by using the neural network prediction function in HYDRUS-1D. The measured data including the soil water storage in the 0–60 cm layer (the main distribution zone of the root system for winter wheat) and daily ETgw in 2005 were used to manually calibrate the parameters, and the measured data in 2008 were used for validation. The calibrated parameters are shown in Table 5.

Table 5

Calibration result of soil hydraulic parameters

Soil layer (m) θr (cm3 cm−3θs (cm3 cm−3Α (1 cm−1n Ks (cm d−1l 
0–0.2 0.051 0.449 0.032 1.55 50 0.5 
0.2–1.5 0.044 0.399 0.010 1.20 25 0.5 
Soil layer (m) θr (cm3 cm−3θs (cm3 cm−3Α (1 cm−1n Ks (cm d−1l 
0–0.2 0.051 0.449 0.032 1.55 50 0.5 
0.2–1.5 0.044 0.399 0.010 1.20 25 0.5 

Evaluation of simulation results

The goodness of the fit between measured and simulated soil water storage in the 0–60 cm layer and daily ETgw were statistically calculated by the relative error (RE) and the root mean square error (RMSE) 
formula
8
 
formula
9
where Sij is simulated soil water storage in the 0–60 cm layer or daily ETgw (mm), Obj is measured soil water storage in the 0–60 cm layer or daily ETgw (mm), is mean of measured soil water storage in the 0–60 cm layer or daily ETgw (mm), and n is the number of the observations.

Numerical scheme

To determine Ws and the extinction depth for a wide range of groundwater depths, 13 groundwater depths from 0.5 to 5.0 m were set up for scenario simulation. The increment was 0.2 m from 0.5 to 1.5 m (i.e. 0.5, 0.7, 0.9, 1.1, 1.3 and 1.5 m), and 0.5 m from 2.0 to 5.0 m (i.e. 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 and 5.0 m). The simulation period was from 26 March to 8 June 2005, and the measured meteorological data in the corresponding period were used but no precipitation was considered for obtaining and keeping steady soil water distribution.

The steady soil water content was obtained by the following steps. (1) The initial soil water content above the water table was assumed to be the field capacity (0.32 cm3 cm−3), and the soil water profile was simulated for each day from 26 March to 8 June 2005. (2) The soil water profile in the last day of the first simulation period (8 June 2005) was adopted to be the initial profile of the second round of simulation (26 March 2005). (3) This process would not stop until the soil water content distribution differences in the last days of two adjacent simulation periods was negligible. The soil water storage from 0 to 60 cm depth of the last simulation was assumed to be the steady storage in the root zone for each scenario.

RESULTS AND DISCUSSION

Calibration and validation

For the calibration period, the comparison between the measured and simulated soil water storages in the 0–60 cm layer is shown in Figure 2(a). There was a general good agreement between the measured and simulated values. The RE values in the calibration period were, respectively, 0.5, −4.5 and −1.9% for T1(70), T1(110) and T1(150), and RMSE varied from 6.32 to 9.20 mm (Table 6). Figure 3 indicates that the simulated daily ETgw agreed well with the measured values. Moreover, the influences of precipitations on daily ETgw were reflected well by model simulation. Owing to the three precipitations more than 10.0 mm (29.5, 18.6 and 10.9 mm on 19 April, 5 May and 17 May, respectively), the measured ETgw of T1 (70) was influenced temporarily but significantly (Figure 3(a)), while that of T1 (110) and T1 (150) declined slightly because of the thicker unsaturated zone (Figure 3(b) and 3(c)). The daily ETgw values were overestimated for the three treatments in the calibration period. Similarly with soil water storage, T1 (70) also had the smallest RE and T1 (110) had the largest one for daily ETgw. With increasing groundwater depth, RMSE decreased from 1.54 to 0.67 mm d−1.

Table 6

Statistics of the measured and simulated soil water storages in the 0–60 cm layer and ETgw in 2005 and 2008

    Soil water storage
 
ETgw
 
Year Treatment RE (%) RMSE (mm) RE (%) RMSE (mm d−1
2005 (Calibration) T1 (70) 0.5 9.20 0.1 1.54 
T1 (110) − 4.5 8.68 10.1 0.83 
T1 (150) − 1.9 6.32 9.9 0.67 
2008 (Validation) T2 (150) − 2.6 6.91 6.0 0.67 
    Soil water storage
 
ETgw
 
Year Treatment RE (%) RMSE (mm) RE (%) RMSE (mm d−1
2005 (Calibration) T1 (70) 0.5 9.20 0.1 1.54 
T1 (110) − 4.5 8.68 10.1 0.83 
T1 (150) − 1.9 6.32 9.9 0.67 
2008 (Validation) T2 (150) − 2.6 6.91 6.0 0.67 
Figure 2

Comparison between the measured and simulated soil water storages in the 0–60 cm layer for calibration (2005) and validation (2008) periods.

Figure 2

Comparison between the measured and simulated soil water storages in the 0–60 cm layer for calibration (2005) and validation (2008) periods.

Figure 3

Comparison between the measured and simulated process of daily ETgw for calibration (2005) and validation (2008) periods.

Figure 3

Comparison between the measured and simulated process of daily ETgw for calibration (2005) and validation (2008) periods.

There was also a good agreement between the measured and simulated soil water storages in the 0–60 cm layer for the validation period (Figure 2(b) and Table 6). The RE and RMSE were −2.6% and 6.91 mm, respectively. As shown in Figure 3(d), the ETgw was overestimated around 20 April 2008 due to the influence of precipitation. The precipitation amount was 34.2 mm on 20 April 2008, and the treatments received precipitation due to operation delay at night. However, the general trends between the measured and simulated ETgw were similar, and the RE and RMSE were only 6.0% and 0.67 mm d−1, respectively. Therefore, it can be concluded that the simulation of ETgw using HYDRUS-1D is reliable.

It should be noted that the daily ETgw values were overestimated for the late season stages (30 May to 8 June 2005 and 1–5 June 2008). In the late season stage, the crop was harvested and dried out (Allen et al. 1998), and the consumption of groundwater water by winter wheat also declined. However, the model did not reflect this change well. The recommended basal crop coefficient (that was 0.3 in this study) in the late season stage (Kcbend) (Allen et al. 1998) might be large and hence result in the overestimation of ETgw.

Extinction depth

Numerical simulations were performed using the calibrated and validated parameters with the steady soil water content distribution as the initial condition during the period from 23 March to 8 June 2005. Figure 4 shows the relationship between the average daily ETgw and groundwater depth. ETgw decreased linearly with increasing groundwater depth from 0.5 to 2.5 m and decreased as a power function with increasing groundwater depth from 2.5 to 5.0 m.

Figure 4

Relationship between average daily ETgw and groundwater depths.

Figure 4

Relationship between average daily ETgw and groundwater depths.

Figure 4 shows that the average daily ETgw was higher than 1.49 mm d−1 when groundwater depth was in the range from 0.5 to 2.5 m and decreased rapidly with increasing groundwater depth. When groundwater depth was in the range from 2.5 to 5.0 m, the average daily ETgw was lower than 1.49 mm d−1 and decreased slowly with increasing groundwater depth. ETgw was lower than 0.20 mm d−1 when groundwater depth was at 5.0 m (0.19 mm d−1). Under the condition of silt soil and winter wheat, the extinction depth may be determined to be 5.0 m. Shah et al. (2007) found a similar result that the extinction depth was 5.3 m under the condition of silt soil and grass.

Steady soil water storage

The root system of winter wheat was distributed mainly in the 0–60 cm layer, and the changes of the soil moisture below 60 cm depth could be ignored (Liu & Luo 2011). Therefore, the 0–60 cm layer was regarded as the root zone and the steady water storage in the 0–60 cm layer was determined to be Ws. Ws is mainly dependent on groundwater depth (Liu et al. 2006). In this study, the relationship between Ws and groundwater depth is shown in Figure 5. Ws decreased from 190 to 94 mm when groundwater depth increased from 0.7 to 2.0 m and changed little with groundwater depth when it was larger than 2.0 m. The simulation results showed that groundwater depth had no apparent influence on Ws when groundwater depth was more than 2.0 m.

Figure 5

Relationship between Ws and groundwater depths.

Figure 5

Relationship between Ws and groundwater depths.

Under the condition of silt soil and winter wheat planted, the relationship between Ws and groundwater depth can be expressed as 
formula
10
 
formula
11
where H is groundwater depth (m).

CONCLUSIONS

HYDRUS-1D simulation was combined with lysimeter experiments to determine the extinction depth and Ws for a wide range of groundwater depths under winter wheat and silt soil. The measured soil water storage in the 0–60 cm layer and daily ETgw were used to calibrate and validate the parameters of the HYDRUS model. It showed that HYDRUS-1D simulation gave reliable results. The results showed that ETgw decreased linearly with increasing groundwater depth from 0.5 to 2.5 m and decreased as a power function with increasing groundwater depth from 2.5 to 5.0 m. Under the condition of silt soil and winter wheat, the extinction depth of ETgw was about 5.0 m. In addition, the results also showed that Ws decreased linearly with increasing groundwater depth ranging from 0.7 to 2.0 m and was not influenced by ground water depth larger than 2.0 m.

ACKNOWLEDGEMENTS

This research was partially financed by the Natural Sciences Foundation of China (No. 41301021) and the Project of Chinese Academy of Sciences (No. CXJQ120109).

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