*2.2. Design of the Experiment*

The spring wheat variety tested was Yongliang No. 4. The spring wheat in 2015 was sowed and harvested on 19 March and 19 July, respectively, with the precipitation during the growth period being 61 mm. The spring wheat in 2016 was sowed and harvested on 14 March and 18 July, respectively, with the precipitation during the growth period being 55 mm. According to the water distribution of the irrigation region in previous years, a total of four rounds of irrigation are made throughout the spring wheat growth period. However, at the time of the fourth irrigation, the spring wheat had already been at the ripening stage, and therefore this irrigation contributed little to wheat yield. For this reason, local farmers rarely make the fourth irrigation. To improve the water productivity of spring wheat, the experiment included the first three rounds of irrigation only.

Five treatments were provided, as shown in Table 2, with three replications. Each experiment plot area was 20 m<sup>2</sup> . In order to preclude lateral permeability between the plots, each plot was fringed with a 1 m-wide protection row. According to the soil moisture of each experiment treatment at the time of water distribution, the irrigation quota was estimated such that the irrigation upper limit should not exceed the field capacity. Each experiment plot area was irrigated by pumping from the canal. The irrigation volume of the experiment plots was measured by water meters. The field management practice, such as sowing, fertilizing, and farming, for each experiment plot was the same as that of the local farmers. *Water* **2020**, *12*, x FOR PEER REVIEW 4 of 21


**Table 2.** Experiment treatments. . In order to preclude lateral permeability between the plots, each plot was

Five treatments were provided, as shown in Table 2, with three replications. Each experiment

Note: "<sup>√</sup> " means irrigation at this growing stage. T1 - -

T2 √ 100 100

**2015 2016**

#### *2.3. Data Observation* T3 √ √ 160 160 T4 √ √ 160 135

plot area was 20 m<sup>2</sup>

The relevant meteorological data include solar radiation, wind speed, temperature, atmospheric humidity, and rainfall, all taken from the Hangjinhouqi National Meteorological Station, close to the study area about 1 km. The Penman–Monteith formula, recommended by FAO, was utilized to estimate the reference crop evapotranspiration (ET0) based on the longitude, latitude, and altitude of the weather station [27]. From the Shahaoqu Experimental Station in this irrigation area, the study area groundwater table data of 57 observation wells from 1990–2016 were collected. A groundwater table distribution map was generated using the inverse distance weighting interpolation. At the same time, the groundwater table monitoring wells were also installed in the experimental site, which were read once every 2 or 3 days during the study period. The soil moisture content was determined by the oven drying method. Samples were taken from each plot at an interval of 5 days, and extra measurements were taken before and after rainfall and irrigation. Sampling depths were at 0~20 cm, 20~40 cm, 40~60 cm, 60~80 cm, and 80~100 cm. Upon the harvest, the yield of spring wheat was evaluated. For this purpose, a representative 1 m<sup>2</sup> quadrat was chosen from each experiment plot to determine the grain yield after natural air drying. The temperature, precipitation, reference crop evapotranspiration, and groundwater table change in the experiment plots throughout the experiment period are as shown in Figure 1. The interannual variation of the groundwater table in this irrigation area is shown in Figure 2. T5 √ √ √ 260 235 Note: "√" means irrigation at this growing stage. *2.3. Data Observation* The relevant meteorological data include solar radiation, wind speed, temperature, atmospheric humidity, and rainfall, all taken from the Hangjinhouqi National Meteorological Station, close to the study area about 1 km. The Penman–Monteith formula, recommended by FAO, was utilized to estimate the reference crop evapotranspiration (ET0) based on the longitude, latitude, and altitude of the weather station [27]. From the Shahaoqu Experimental Station in this irrigation area, the study area groundwater table data of 57 observation wells from 1990–2016 were collected. A groundwater table distribution map was generated using the inverse distance weighting interpolation. At the same time, the groundwater table monitoring wells were also installed in the experimental site, which were read once every 2 or 3 days during the study period. The soil moisture content was determined by the oven drying method. Samples were taken from each plot at an interval of 5 days, and extra measurements were taken before and after rainfall and irrigation. Sampling depths were at 0~20 cm, 20~40 cm, 40~60 cm, 60~80 cm, and 80~100 cm. Upon the harvest, the yield of spring wheat was evaluated. For this purpose, a representative 1 m<sup>2</sup> quadrat was chosen from each experiment plot to determine the grain yield after natural air drying. The temperature, precipitation, reference crop evapotranspiration, and groundwater table change in the experiment plots throughout the experiment period are as shown in Figure 1. The interannual variation of the groundwater table in this irrigation area is shown in Figure 2.

**Figure 1.** *Cont*.

Temperature (℃)

Groundwater depth

 (m)

*Water* **2020**, *12*, x FOR PEER REVIEW 5 of 21

**Figure 1.** Meteorological data and groundwater table of the study area during the growth period of spring wheat. **Figure 1.** Meteorological data and groundwater table of the study area during the growth period of spring wheat. (**b**) 2016 **Figure 1.** Meteorological data and groundwater table of the study area during the growth period of spring wheat.

Year

The evapotranspiration is divided into two parts by the model [28–31]: Evaporation and **Figure 2.** Interannual variation of groundwater table in Jiefangzha Region. **Figure 2.** Interannual variation of groundwater table in Jiefangzha Region.

#### transpiration. In order to separate the evaporation, the transpiration was estimated based on the variation of the crop canopy ground cover instead of leaf area index in the whole growth period. *2.4. The Aquacrop Model 2.4. The Aquacrop Model*

*2.4. The Aquacrop Model*

Crop yield is calculated based on the biomass on the ground and the harvest index. Based on the difference in the influence mechanism of environment on biomass and on harvest index, the effects of environmental stresses on biomass and harvest index were distinguished. By limiting canopy stretching, accelerating canopy senescence, controlling stomatal closure, and regulating harvest index after the start of reproductive growth, the soil water stresses on crop growth were further refined. From this basis, the crop yields under different irrigation schedules were simulated. The input data of the crop's water-yield response mechanism simulation included crop species, meteorology, soil, groundwater, and irrigation schedule, field management, and initial conditions. *2.5. Model Verification* The input database for crop model consists of crop growth data, meteorological data, soil properties, irrigation schedules, and field management data. For the study area, the soil properties and field management data have remained unchanged during the 2-year experiment. The measured data such as crop growth data, meteorological data and irrigation schedules and so on from the 2015 The evapotranspiration is divided into two parts by the model [28–31]: Evaporation and transpiration. In order to separate the evaporation, the transpiration was estimated based on the variation of the crop canopy ground cover instead of leaf area index in the whole growth period. Crop yield is calculated based on the biomass on the ground and the harvest index. Based on the difference in the influence mechanism of environment on biomass and on harvest index, the effects of environmental stresses on biomass and harvest index were distinguished. By limiting canopy stretching, accelerating canopy senescence, controlling stomatal closure, and regulating harvest index after the start of reproductive growth, the soil water stresses on crop growth were further refined. From this basis, the crop yields under different irrigation schedules were simulated. The input data of the crop's water-yield response mechanism simulation included crop species, meteorology, soil, groundwater, and irrigation schedule, field management, and initial conditions. The evapotranspiration is divided into two parts by the model [28–31]: Evaporation and transpiration. In order to separate the evaporation, the transpiration was estimated based on the variation of the crop canopy ground cover instead of leaf area index in the whole growth period. Crop yield is calculated based on the biomass on the ground and the harvest index. Based on the difference in the influence mechanism of environment on biomass and on harvest index, the effects of environmental stresses on biomass and harvest index were distinguished. By limiting canopy stretching, accelerating canopy senescence, controlling stomatal closure, and regulating harvest index after the start of reproductive growth, the soil water stresses on crop growth were further refined. From this basis, the crop yields under different irrigation schedules were simulated. The input data of the crop's water-yield response mechanism simulation included crop species, meteorology, soil, groundwater, and irrigation schedule, field management, and initial conditions.

#### spring wheat were used to calibrate the model, and those from the 2016 spring wheat were used to verify the model. Soil moisture and yield were used to verify the model parameters. The major The input database for crop model consists of crop growth data, meteorological data, soil *2.5. Model Verification*

*2.5. Model Verification*

properties, irrigation schedules, and field management data. For the study area, the soil properties and field management data have remained unchanged during the 2-year experiment. The measured data such as crop growth data, meteorological data and irrigation schedules and so on from the 2015 spring wheat were used to calibrate the model, and those from the 2016 spring wheat were used to verify the model. Soil moisture and yield were used to verify the model parameters. The major The input database for crop model consists of crop growth data, meteorological data, soil properties, irrigation schedules, and field management data. For the study area, the soil properties and field management data have remained unchanged during the 2-year experiment. The measured data such as crop growth data, meteorological data and irrigation schedules and so on from the 2015 spring wheat were used to calibrate the model, and those from the 2016 spring wheat were used to verify the model. Soil moisture and yield were used to verify the model parameters. The major parameters of the Aquacrop model for simulating the growth of spring wheat in the Hetao Irrigation District are as shown in Table 3.


**Table 3.** Some parameters of spring wheat for the crop growth simulation model.

In the verification process, the degree of agreement between the simulated and the observed value was evaluated by root mean square error (RMSE), mean absolute error (MAE), mean relative error (MBE), and the Nash efficiency coefficient (EF). RMSE and MAE is used to test the unbiasedness of the model, resulting in that the lower their values, the less biased the model, and thus the more accurate the simulation. The EF is a kind of relative error index, also a dimensionless model evaluation index. When taking a value close to 1, the model was believed to have high credibility. A value close to zero suggests that, though the simulation result is generally credible, the simulation process involves larger errors. When the MBE is greater than 0, the simulation result is believed to be on the greater side; otherwise, on the smaller side. The model evaluation indices are determined by [32–34]:

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (M\_i - Q\_i)^2} \tag{1}$$

$$MAE = \frac{1}{n} \sum\_{i=1}^{n} |\mathcal{M}\_i - \mathcal{O}\_i| \tag{2}$$

$$MBE \;= \frac{1}{n} \sum\_{i=1}^{n} (M\_i - Q\_i) \tag{3}$$

$$EF = 1.0 - \frac{\sum\_{i=1}^{n} \left(O\_i - M\_i\right)^2}{\sum\_{i=1}^{n} \left(O\_i - \overline{O}\right)^2} \tag{4}$$

where, *O<sup>i</sup>* , *M<sup>i</sup>* , and *O* stand for the measured value, simulated value, measured mean value; *n* is the times of measurement

#### *2.6. Scenarios*

#### 2.6.1. Determination of the Typical Year

The precipitation data in the study area from 1961 to 2014 were analyzed, finding that the average annual precipitation during the spring wheat growth period was 61 mm; the year closest to the typical annual precipitation was 2013, with a precipitation of 58 mm.

*2.6. Scenarios*

## 2.6.2. Determination of Groundwater Depth

the typical annual precipitation was 2013, with a precipitation of 58 mm.

2.6.1. Determination of the Typical Year

In light of the gentle terrain in the Jiefangzha Region, the year-by-year groundwater depth data of the 57 monitoring wells from 1990 to 2015 were interpolated using the inverse distance weighting method, which indicated the mean annual groundwater depth in this area was 1.6–2.3 m and the depth exceeded 2.2 m, in 2010, 2011, and 2014. 2.6.2. Determination of Groundwater DepthIn light of the gentle terrain in the Jiefangzha Region, the year-by-year groundwater depth data of the 57 monitoring wells from 1990 to 2015 were interpolated using the inverse distance weighting method, which indicated the mean annual groundwater depth in this area was 1.6–2.3 m and the depth exceeded 2.2 m, in 2010, 2011, and 2014.

*Water* **2020**, *12*, x FOR PEER REVIEW 7 of 21

The precipitation data in the study area from 1961 to 2014 were analyzed, finding that the

According to the phreatic evaporation data of the Shahaoqu Experimental Station, once the groundwater depth exceeded 2.5 m, the phreatic evaporation was significantly reduced. Groundwater depth was closely related to grain yield, for which the shallower the depth, the more serious the soil salinization was and the lower the grain yield was [35]. Still, relevant studies showed that when groundwater depth exceeded 2.5 m, the ecological environment in an arid irrigation district might be adversely affected [36]. According to the phreatic evaporation data of the Shahaoqu Experimental Station, once the groundwater depth exceeded 2.5 m, the phreatic evaporation was significantly reduced. Groundwater depth was closely related to grain yield, for which the shallower the depth, the more serious the soil salinization was and the lower the grain yield was [35]. Still, relevant studies showedthat when groundwater depth exceeded 2.5 m, the ecological environment in an arid irrigation district might be adversely affected [36].

Without compromising the ecological safety, and for the sake of preventing soil salinization and minimizing water diversion from the Yellow River, the average annual groundwater depth was taken to be 2.5 m for the future scenario. The interannual spatial variation and the intraanual difference of groundwater table were based on the mean value of 2010, 2011, and 2014. For the future scenario, the spatial distribution of groundwater depth and the zoning of the irrigation schedule are shown in Figure 3. With a groundwater depth of 2.5 m as the divide, the area was divided into zones with significant influence of phreatic evaporation and zones with insignificant influence of phreatic evaporation, which has solved the problem of spatial variability of groundwater depth. As for the future scenario simulation, Figure 4 shows the annual temperature, precipitation, reference crop evapotranspiration, and groundwater depth variation during spring wheat growth period in the typical year. When the annual mean groundwater depth is less than 2.5 m, the groundwater depth during the spring wheat growth period is 1.29–2.61 m. However, when the annual mean groundwater depth is more than 2.5 m, the groundwater depth during the growth period is between 2.59 and 3.63 m. In practical application, the groundwater depth of 2.5 m in the previous year can be used to provide dynamic division so as to ensure that the irrigation schedule optimization can be better applied to shallow groundwater areas. Without compromising the ecological safety, and for the sake of preventing soil salinization andminimizing water diversion from the Yellow River, the average annual groundwater depth was taken to be 2.5 m for the future scenario. The interannual spatial variation and the intraanual difference of groundwater table were based on the mean value of 2010, 2011, and 2014. For the future scenario, the spatial distribution of groundwater depth and the zoning of the irrigation schedule are shown in Figure 3. With a groundwater depth of 2.5 m as the divide, the area was divided into zones with significant influence of phreatic evaporation and zones with insignificant influence of phreatic evaporation, which has solved the problem of spatial variability of groundwater depth. As for the future scenario simulation, Figure 4 shows the annual temperature, precipitation, reference crop evapotranspiration, and groundwater depth variation during spring wheat growth period in the typical year. When the annual mean groundwater depth is less than 2.5 m, the groundwater depth during the spring wheat growth period is 1.29–2.61 m. However, when the annual mean groundwater depth is more than 2.5 m, the groundwater depth during the growth period is between 2.59 and 3.63 m. In practical application, the groundwater depth of 2.5 m in the previous year can be used to provide dynamic division so as to ensure that the irrigation schedule optimization can be better applied to shallow groundwater areas.

**Figure 3.** Spatial variation pattern of groundwater depth and irrigation schedule zoning in Jiefangzha region for the future scenario.

**Figure 4.** Annual temperature, precipitation, ET0, and groundwater depth variation of the typical year for the future scenario. **Figure 4.** Annual temperature, precipitation, ET<sup>0</sup> , and groundwater depth variation of the typical year for the future scenario.

#### 2.6.3. Irrigation Schedule Scenarios 2.6.3. Irrigation Schedule Scenarios

shown in Table 4.

Because the study area is a canal irrigation area, there are only four times of irrigation in the growth period of spring wheat. According to the actual water distribution in the irrigation area, a total of irrigation scenarios was considered as rain-fed, one round of irrigation, two rounds of irrigation, three rounds of irrigation, and four rounds of irrigation for the four growth stages of spring wheat. When the total irrigation times of the whole growth period were determined, all possibilities for irrigation growth period were considered. There were 16 irrigation schedules, as Because the study area is a canal irrigation area, there are only four times of irrigation in the growth period of spring wheat. According to the actual water distribution in the irrigation area, a total of irrigation scenarios was considered as rain-fed, one round of irrigation, two rounds of irrigation, three rounds of irrigation, and four rounds of irrigation for the four growth stages of spring wheat. When the total irrigation times of the whole growth period were determined, all possibilities for irrigation growth period were considered. There were 16 irrigation schedules, as shown in Table 4.



T31 √ √ √ 260 Note: "<sup>√</sup> " means irrigation at this growing stage.

T32 √ √ √ 260

#### T33 √ √ √ 260 T34 √ √ √ 300 **3. Results**

#### T44 √ √ √ √ 360 *3.1. Model Verification*

Note: "√" means irrigation at this growing stage. It can be seen from Figure 5 and Table 5 that in calibration of the model, except for the T2–T4 treatments with slightly larger simulation values for the ripening stage, the simulated values for other growth stages are in good agreement with the measured soil moisture contents. The RMSE and the MAE between the simulated and measured soil moisture contents were less than 1.740% and 1.526%, **3. Results**

respectively, and the R<sup>2</sup> was greater than 0.764, and the EF was greater than 0.722. For all irrigation treatments, in calibration of the model, the RMSE, MAE, R<sup>2</sup> , and EF were 1.203%, 0.780%, 0.860, and 0.849, respectively. In model verification, the model simulation values satisfactorily reflected the change process of the measured soil moisture contents. As shown in Figure 6 and Table 5, the RMSE and MAE between simulated and measured values of soil moisture contents were below 1.802% and 1.429%, respectively, and the corresponding R<sup>2</sup> exceeded 0.651 and the EF was greater than 0.349. In model verification of all water treatments, the RMSE, MAE, R<sup>2</sup> , and EF were 1.612%, 1.333%, 0.761, and 0.538, respectively. It can be seen that the fitting degree and accuracy of the soil moisture after model verification were both high, quite able to meet the simulation accuracy requirements of spring wheat soil water balance. treatments with slightly larger simulation values for the ripening stage, the simulated values for other growth stages are in good agreement with the measured soil moisture contents. The RMSE and the MAE between the simulated and measured soil moisture contents were less than 1.740% and 1.526%, respectively, and the R<sup>2</sup> was greater than 0.764, and the EF was greater than 0.722. For all irrigation treatments, in calibration of the model, the RMSE, MAE, R<sup>2</sup> , and EF were 1.203%, 0.780%, 0.860, and 0.849, respectively. In model verification, the model simulation values satisfactorily reflected the change process of the measured soil moisture contents. As shown in Figure 6 and Table 5, the RMSE and MAE between simulated and measured values of soil moisture contents were below 1.802% and 1.429%, respectively, and the corresponding R<sup>2</sup> exceeded 0.651 and the EF was greater than 0.349. In model verification of all water treatments, the RMSE, MAE, R<sup>2</sup> , and EF were 1.612%, 1.333%, 0.761, and 0.538, respectively. It can be seen that the fitting degree and accuracy of the soil moisture after model verification were both high, quite able to meet the simulation accuracy requirements of spring wheat soil water balance.

*Water* **2020**, *12*, x FOR PEER REVIEW 9 of 21

It can be seen from Figure 5 and Table 5 that in calibration of the model, except for the T2–T4

**Figure 5.** Simulated vs. measured values of spring wheat soil moisture content in model calibration. **Figure 5.** Simulated vs. measured values of spring wheat soil moisture content in model calibration.

Number of day after sowing (d)

Number of day after sowing (d)

**Table 5.** Evaluation indices of spring wheat soil moisture content simulation. RMSA: root mean square error.


*Water* **2020**, *12*, x FOR PEER REVIEW 10 of 21

**Figure 6.** Simulated vs. measured values of spring wheat soil moisture content in model verification. **Figure 6.** Simulated vs. measured values of spring wheat soil moisture content in model verification.

**Table 5.** Evaluation indices of spring wheat soil moisture content simulation. RMSA: root mean square error. **R<sup>2</sup> RMSE (%) MAE (%) MBE (%) EF** Model calibration T1 0.927 1.481 1.290 −1.045 0.747 T2 0.887 1.417 1.083 0.495 0.869 T3 0.887 1.740 1.526 0.735 0.862 T4 0.825 1.522 1.343 0.473 0.784 T5 0.764 1.635 1.383 0.066 0.722 All treatments 0.860 1.203 0.780 0.037 0.849 As can be seen from Figures 7 and 8, and Table 6, the simulated yields agreed well with the measured values. In model calibration, the RMSE, MAE, and MBE between the simulated and the observed values were 275.883 kg/hm<sup>2</sup> , 246.190 kg/hm<sup>2</sup> , <sup>−</sup>159.370 kg/hm<sup>2</sup> respectively, and the R<sup>2</sup> and EF were 0.985 and 0.976 respectively. In model verification, the RMSE, MAE, and MBE between the simulated and observed yields were 375.097 kg/hm<sup>2</sup> , 242.402 kg/hm<sup>2</sup> , and 145.004 kg/hm<sup>2</sup> respectively, and the R<sup>2</sup> and EF are 0.970 and 0.618 respectively. It can be seen that the RMSE and MAE between the simulated and observed values were less than 376 kg/hm<sup>2</sup> and 247 kg/hm<sup>2</sup> , respectively, and the R <sup>2</sup> and EF were greater than 0.96 and 0.61 respectively. Hence, the model after verification is able to simulate satisfactorily spring wheat yield. *Water* **2020**, *12*, x FOR PEER REVIEW 11 of 21 groundwater zones under different irrigation schedules. The model is useful in studying the relation between soil moisture contents and yield of spring wheat in shallow groundwater areas.

T1 0.710 1.578 1.278 −0.136 0.464

,

**Figure 7.** Simulated vs. measured values of spring wheat yield in model calibration. **Figure 7.** Simulated vs. measured values of spring wheat yield in model calibration.

Simulated value

T1 T2 T3 T4 T5

**) MAE (kg/hm<sup>2</sup>**

**) MBE (kg/hm<sup>2</sup>**

**) EF**

**Figure 8.** Simulated vs. measured values of spring wheat yield in model verification.

**Table 6.** Evaluation indices of spring wheat yield simulation.

Model calibration 0.985 275.883 246.190 −159.370 0.976 Model verification 0.970 357.097 242.402 145.004 0.618

Water consumption by spring wheat in different zones under different irrigation schedules is shown in Figure 9. As can be seen, where the groundwater depth was within 2.5 m, water consumption by rain-fed was 260 mm, and that by one round of irrigation was in the range of 284–387 mm. Water consumption by two rounds of irrigation was in the range of 326–424 mm. For three rounds and four rounds, the figures were 398–436 mm and 449 mm respectively. Where the

*3.2. Water Consumption by Spring Wheat in Different Zones under Different Irrigation Schedules*

0

**R<sup>2</sup> RMSE (kg/hm<sup>2</sup>**

1500

3000

4500

Yield (kg/hm2

)

6000

7500

9000

0

1500

3000

4500

Yield (kg/hm2)

6000

7500

9000

T1 T2 T3 T4 T5

groundwater zones under different irrigation schedules. The model is useful in studying the relation

between soil moisture contents and yield of spring wheat in shallow groundwater areas.

Simulated value Measured value

**Figure 8.** Simulated vs. measured values of spring wheat yield in model verification.

**Figure 8.** Simulated vs. measured values of spring wheat yield in model verification. **Table 6.** Evaluation indices of spring wheat yield simulation.


Water consumption by spring wheat in different zones under different irrigation schedules is shown in Figure 9. As can be seen, where the groundwater depth was within 2.5 m, water consumption by rain-fed was 260 mm, and that by one round of irrigation was in the range of 284–387 mm. Water consumption by two rounds of irrigation was in the range of 326–424 mm. For In summary, the verified Aquacrop model is able to simulate the dynamic process of the soil moisture contents during the spring wheat growth period as well as the yield in shallow groundwater zones under different irrigation schedules. The model is useful in studying the relation between soil moisture contents and yield of spring wheat in shallow groundwater areas.

#### three rounds and four rounds, the figures were 398–436 mm and 449 mm respectively. Where the *3.2. Water Consumption by Spring Wheat in Di*ff*erent Zones under Di*ff*erent Irrigation Schedules*

*3.2. Water Consumption by Spring Wheat in Different Zones under Different Irrigation Schedules*

Water consumption by spring wheat in different zones under different irrigation schedules is shown in Figure 9. As can be seen, where the groundwater depth was within 2.5 m, water consumption by rain-fed was 260 mm, and that by one round of irrigation was in the range of 284–387 mm. Water consumption by two rounds of irrigation was in the range of 326–424 mm. For three rounds and four rounds, the figures were 398–436 mm and 449 mm respectively. Where the groundwater depth was over 2.5 m, the water consumption by rain-fed was 210 mm. Water consumption by one round of irrigation was in the range of 234–326 mm. For two rounds and three rounds, the figures were in the range of 256–389 mm and 338–432 mm respectively. Water consumption by four rounds was 445 mm. It can be seen that within the irrigation quota of 360 mm, the water consumption of spring wheat increased with the irrigation quota. For a given irrigation number and a given irrigation quota, the water consumption varied greatly with the irrigation date. For the same irrigation schedule, less water was consumed when the groundwater depth exceeded 2.5 m than when the groundwater depth was less than 2.5 m, but the difference dwindled with the increase of irrigation quota.

groundwater depth was over 2.5 m, the water consumption by rain-fed was 210 mm. Water consumption by one round of irrigation was in the range of 234–326 mm. For two rounds and three rounds, the figures were in the range of 256–389 mm and 338–432 mm respectively. Water consumption by four rounds was 445 mm. It can be seen that within the irrigation quota of 360 mm, the water consumption of spring wheat increased with the irrigation quota. For a given irrigation number and a given irrigation quota, the water consumption varied greatly with the irrigation date. For the same irrigation schedule, less water was consumed when the groundwater depth exceeded

**Figure 9.** Water consumption by spring wheat in different zones under different irrigation **Figure 9.** Water consumption by spring wheat in different zones under different irrigation schedules.

schedules. Where the groundwater depth was less than 2.5 m, the transpiration of rain-fed spring wheat was 196 mm, this figure was in the range of 196–333 mm for one round of irrigation or 232–370 mm for two rounds of irrigation, and for three rounds and four rounds of irrigation the transpiration was 332–394 mm and 396 mm respectively. Where the groundwater depth was greater than 2.5 m, the transpiration of rain-fed spring wheat was 140 mm, and for one round, two rounds, and three Where the groundwater depth was less than 2.5 m, the transpiration of rain-fed spring wheat was 196 mm, this figure was in the range of 196–333 mm for one round of irrigation or 232–370 mm for two rounds of irrigation, and for three rounds and four rounds of irrigation the transpiration was 332–394 mm and 396 mm respectively. Where the groundwater depth was greater than 2.5 m, the transpiration of rain-fed spring wheat was 140 mm, and for one round, two rounds, and three rounds of irrigation the figure was in the range of 140–263 mm, 140–339 mm, and 244–389 mm respectively. The transpiration was 391 mm for four rounds of irrigation. It can be seen that the way the transpiration of spring wheat varied with the groundwater depth parallels the relation between water consumption and the groundwater depth. It therefore follows that the change of transpiration is one of the most critical factors affecting the change of water consumption.

Where the groundwater depth was less than 2.5 m, the phreatic evaporation of rain-fed spring wheat was 109 mm, this figure was in the range of 81–109 mm for one round of irrigation or 77–109 mm for two rounds of irrigation, and for three rounds and four rounds of irrigation the phreatic evaporation was 67–91 mm and 67 mm respectively. Where the groundwater depth was greater than 2.5 m, the phreatic evaporation of rain-fed spring wheat was 12 mm, and for one round, two rounds, and three rounds of irrigation the figure was in the range of 8–12 mm, 5–12 mm, and 5–12 mm respectively. The phreatic evaporation was 10 mm for four rounds of irrigation. It could be seen that when the groundwater depth was more than 2.5 m, the phreatic evaporation of spring wheat was less than 12 mm, and it did not change much with the irrigation quota. When the groundwater depth was less than 2.5 m, the groundwater utilization decreased with the increase of irrigation quota.

Where the groundwater depth was less than 2.5 m, the seepage, in the case of rain-fed spring wheat, was 43 mm, this figure was in the range of 43–49 mm for one round of irrigation or 43–73 mm for two rounds of irrigation, and for three rounds and four rounds of irrigation the seepage was 43–74 mm and 94 mm respectively. Where the groundwater depth was greater than 2.5 m, the seepage, in the case of rain-fed spring wheat, was 17 mm, and for one round, two rounds, and three rounds of irrigation this figure was 17 mm, 17–42 mm, and 17–33 mm respectively. The seepage was 53 mm for four rounds of irrigation. It could be seen that, within the net irrigation quota of 360 mm, the amount of seepage increased with the irrigation quota; with the same irrigation schedule, when the groundwater depth was more than 2.5 m, the seepage was smaller than when the depth was less than 2.5 m.

#### *3.3. Yield of Spring Wheat in Di*ff*erent Zones under Di*ff*erent Irrigation Schedules*

The yields of spring wheat in different zones under different irrigation schedules are shown in Figure 10. Where the groundwater depth was less than 2.5 m, the yield of rain-fed spring wheat was 2505 kg/hm<sup>2</sup> , and this figure was in the range of 2505–6283 kg/hm<sup>2</sup> , for one round of irrigation, 4384–7091 kg/hm<sup>2</sup> for two rounds of irrigation, or 6272–7640 kg/hm<sup>2</sup> for three rounds of irrigation. For four rounds of irrigation, the yield was 7672 kg/hm<sup>2</sup> . Where the groundwater depth was greater than 2.5 m, there was zero yield of the rain-fed spring wheat. The yield of spring wheat for one round of irrigation was in the range of 0–4844 kg/hm<sup>2</sup> , and this figure was in the range of 0–6498 kg/hm<sup>2</sup> for two rounds of irrigation or 4548–7600 kg/hm<sup>2</sup> for three rounds of irrigation. For four rounds of irrigation, the yield of spring wheat was 7650 kg/hm<sup>2</sup> . Where the groundwater depth was less than 2.5 m, the yield of T12 for one round of irrigation was up to 6283 kg/hm<sup>2</sup> , the yield of T24 for two rounds of irrigation was up to 7091 kg/hm<sup>2</sup> , and the yield of T31 for three rounds of irrigation was up to 7640 kg/hm<sup>2</sup> . Where the groundwater depth was more than 2.5 m, the yield of T12 for one round of irrigation was up to 4844 kg/hm<sup>2</sup> , the yield of T21 for two rounds of irrigation was up to 6498 kg/hm<sup>2</sup> , and the yield of T3 for three rounds of irrigation was up to 7600 kg/hm<sup>2</sup> . It could be seen that with the increase of irrigation quota, the yield of spring wheat generally increased. The timing of irrigation was especially important if the total times of irrigation remained constant. As shallow groundwater replenished available water to the crop, the yield in shallow groundwater depth zones was higher than that in deeper groundwater depth zones under the same irrigation schedule. In light of this, in the case of one round of irrigation, it is important to meet the wheat water demand at shooting–heading stage. Where the groundwater depth is less than 2.5 m, in order to take greater advantage of groundwater, the key is to satisfy water demand at the shooting–heading and heading–filling stages in the case of two rounds of irrigation, and where the groundwater depth is more than 2.5 m, it is important to satisfy the wheat water demand at the tillering–shooting and shooting–heading stages. In the case of three rounds of irrigation, the key is to satisfy the water demand at the tillering–shooting, shooting–heading, and heading–filling stages.

**Figure 10.** Yields of spring wheat in different zones under different irrigation schedules. **Figure 10.** Yields of spring wheat in different zones under different irrigation schedules.

#### *3.4. Optimization of Spring Wheat Irrigation Schedule Considering Groundwater Spatial Variability*

*3.4. Optimization of Spring Wheat Irrigation Schedule Considering Groundwater Spatial Variability* The sensitivity indices and test parameters of the spring wheat water production function model are shown in Table 7. When the groundwater depth was greater than 2.5 m, the absolute values of the sensitivity indices, evaluated by Jensen and Minhas models, at some growth stages were greater than 1, in conflict with the theoretical value. Therefore, the two models are not suitable for simulating the relationship between the yield and water consumption at the growth stages when the groundwater depth is greater than 2.5 m. In the three models of Blank, Stewart, and Singh, the Stewart model gave the largest R<sup>2</sup> , which was up to 0.98, and the lowest RMSE, which was only 410.58 kg·hm−<sup>2</sup> . Therefore, it is advisable to take Stewart model as the water production function of spring wheat at the growth stages when the groundwater depth is greater than 2.5 m. From the results given by the Stewart model, the sensitivity coefficient for the tillering–shooting stage was up to 0.7614 when the groundwater depth was greater than 2.5 m, suggesting that it is most sensitive to water shortage at this stage. The sensitivity coefficient was 0.6691 for the shooting–heading stage or 0.5060 for the heading–filling stage. The minimum sensitivity coefficient was −0.0109, which was for the filling–ripening stage, indicating that it is not sensitive to water shortage at this growth stage. When the groundwater depth was less than 2.5 m, the values of the sensitivity indices, evaluated by Minhas and Steward models, at some growth stages were greater than 1, in conflict with the theoretical value. Therefore, the two models are not suitable for simulating the relationship between the yield and the water consumption at the growth stages when the groundwater depth is less than 2.5 m. In the three models of Jensen, Blank, and Singh, the Jensen model gave the largest R<sup>2</sup> , which was up to 0.99, and the lowest RMSE, which was only 165.32 kg·hm−<sup>2</sup> . Therefore, it is advisable to take the Jensen model as the water production function of spring wheat at the growth stages when the groundwater depth is less than 2.5 m. From the results of the Jensen model, when the groundwater depth was less than 2.5 m the sensitivity index was up to 0.9930 for the tillering–shooting stage, was 0.6202 for the heading–filling stage, but was only 0.3591 for the shooting–heading stage. The sensitivity index for the filling–ripening stage was negative, indicating that this stage, too, is not sensitive to water shortage. By comparing the sensitivity for different spring wheat growth stages under different zones, we can see a big difference between the two zones at the shooting–heading stage. When the groundwater depth is greater than 2.5 m, spring wheat is more sensitive to water shortage, while when the depth is less than 2.5 m, the sensitivity to The sensitivity indices and test parameters of the spring wheat water production function model are shown in Table 7. When the groundwater depth was greater than 2.5 m, the absolute values of the sensitivity indices, evaluated by Jensen and Minhas models, at some growth stages were greater than 1, in conflict with the theoretical value. Therefore, the two models are not suitable for simulating the relationship between the yield and water consumption at the growth stages when the groundwater depth is greater than 2.5 m. In the three models of Blank, Stewart, and Singh, the Stewart model gave the largest R<sup>2</sup> , which was up to 0.98, and the lowest RMSE, which was only 410.58 kg·hm−<sup>2</sup> . Therefore, it is advisable to take Stewart model as the water production function of spring wheat at the growth stages when the groundwater depth is greater than 2.5 m. From the results given by the Stewart model, the sensitivity coefficient for the tillering–shooting stage was up to 0.7614 when the groundwater depth was greater than 2.5 m, suggesting that it is most sensitive to water shortage at this stage. The sensitivity coefficient was 0.6691 for the shooting–heading stage or 0.5060 for the heading–filling stage. The minimum sensitivity coefficient was −0.0109, which was for the filling–ripening stage, indicating that it is not sensitive to water shortage at this growth stage. When the groundwater depth was less than 2.5 m, the values of the sensitivity indices, evaluated by Minhas and Steward models, at some growth stages were greater than 1, in conflict with the theoretical value. Therefore, the two models are not suitable for simulating the relationship between the yield and the water consumption at the growth stages when the groundwater depth is less than 2.5 m. In the three models of Jensen, Blank, and Singh, the Jensen model gave the largest R<sup>2</sup> , which was up to 0.99, and the lowest RMSE, which was only 165.32 kg·hm−<sup>2</sup> . Therefore, it is advisable to take the Jensen model as the water production function of spring wheat at the growth stages when the groundwater depth is less than 2.5 m. From the results of the Jensen model, when the groundwater depth was less than 2.5 m the sensitivity index was up to 0.9930 for the tillering–shooting stage, was 0.6202 for the heading–filling stage, but was only 0.3591 for the shooting–heading stage. The sensitivity index for the filling–ripening stage was negative, indicating that this stage, too, is not sensitive to water shortage. By comparing the sensitivity for different spring wheat growth stages under different zones, we can see a big difference between the two zones at the shooting–heading stage. When the groundwater depth is greater than 2.5 m, spring wheat is more sensitive to water shortage, while when the depth is less than 2.5 m, the sensitivity to water shortage at this stage is lower because the groundwater supplies

water shortage at this stage is lower because the groundwater supplies the crops with available water. Therefore, the challenge of greater spatial variation of groundwater can be practically taken the crops with available water. Therefore, the challenge of greater spatial variation of groundwater can be practically taken care of by zoning method. Spring wheat is most sensitive to water deficiency at the tillering–shooting stage, is less sensitive to water deficiency at the heading–filling stage, and is least sensitive to water deficiency at the filling–ripening stage, irrespective of the zone. It can be seen that the water-sensitive results at different growth stages under different zones suggest an agreement with the above-described order of importance of satisfying water demand at different growth stages.


**Table 7.** Sensitivity indices and test parameters of water production function model of spring wheat at different growth stages.

With the verified Aquacrop as the technical support and the soil moisture content of the root layer as the control index, lower irrigation limits were set in light of the sensitivity variation across the growth stages under different groundwater depths conditions. Where the groundwater depth was greater than 2.5 m, no irrigation was given at the sowing–tillering and filling–ripening stags, but irrigation started when the soil moisture of root layer dropped below the lower irrigation limit at the tillering–shooting stage or when the content dropped below 10% of this lower irrigation limit at the shooting-filling. Where the groundwater depth was less than 2.5 m, no irrigation was given at the sowing–tillering stage and the filling–ripening stage, but irrigation started once the soil moisture of root layer dropped below the lower irrigation limit at the tillering–shooting stage or when it dropped below 20% of this lower irrigation limit at the shooting-filling stage. With per irrigation quota of 60–120 mm, the optimized irrigation schedules under different groundwater depth conditions were developed. Where the groundwater depth was greater than 2.5 m, there were two rounds of irrigation both at the tillering–shooting stage and the shooting–heading stage, with the irrigation quota being 300 mm, the water consumption being 486 mm, the yield being 8236 kg/hm<sup>2</sup> , and the water productivity being 1.694 kg/m<sup>3</sup> . Where the groundwater depth was less than 2.5 m, there were two rounds of irrigation at the tillering–shooting stage and one round of irrigation at the shooting–heading stage, with the irrigation quota of 240 mm, the water consumption of 474 mm, the yield of 8014 kg/hm<sup>2</sup> , and the water productivity of 1.690 kg/m<sup>3</sup> . Still, throughout the growth stages of spring wheat, full irrigation schedules were developed for spring wheat under different groundwater depth conditions such that irrigation started once the soil moisture content of the root layer dropped below the lower irrigation limit with the per irrigation quota being 60–120 mm. Where the groundwater depth was greater than 2.5 m, the irrigation quota was 360 mm and the water consumption was 492 mm, with the yield of 8343 kg/hm<sup>2</sup> and the water productivity of 1.697 kg/m<sup>3</sup> . Where the groundwater depth was less than 2.5 m, the irrigation quota was 320 mm and the water consumption was 493 mm, with the yield of 8384 kg/hm<sup>2</sup> and the water productivity of 1.701 kg/m<sup>3</sup> .
