A simulation of winter wheat crop responses to irrigation management using CERES-Wheat model in the North China Plain

ZHOU Li-li , LIAO Shu-hua, WANG Zhi-min, WANG Pu, ZHANG Ying-hua, YAN Hai-jun GAO Zhen, SHEN Si, LIANG Xiao-gui, WANG Jia-hui, ZHOU Shun-li

1 College of Water Resources & Civil Engineering, China Agricultural University, Beijing 100083, P.R.China

2 College of Agronomy & Biotechnology, China Agricultural University, Beijing 100193, P.R.China

1. Introduction

Winter wheat is one of the most important food crops in the North China Plain (NCP) (Muelleret al.2012).Approximately one-third of the total arable land in the NCP is currently used for winter wheat cultivation (CAYN 2013). In the NCP, the growth and yield of winter wheat is mainly determined by water availability from precipitation and irrigation. The average precipitation during the winter wheat growing season (October–June) in this area is approximately 117 mm, which is less than the water requirements for achieving the maximum grain yield and water use efficiency (WUE) for winter wheat. Irrigation is thus critical for maintaining high wheat production (Chenet al.2015). Traditional high-yielding irrigation strategies are usually based on the full water requirements at different growth stages in winter wheat. Previous studies have reported three to five or more irrigation strategies to maintain wheat yield (Zhanget al.2005). Through studies over the course of many years, cultivation systems with water-saving,fertilizer-saving, high-yielding and simplified management have been developed for winter wheat, and the WUE has improved by 20% compared to the traditional high-yielding technology (Wanget al.2006).

Underground water is the major source of irrigation water in the NCP. Large-scale irrigation in this region began in the 1970s, and since the adoption of this practice, the extraction of groundwater increasingly exceeds depletion of groundwater table. As a result, groundwater levels are continuously decreasing (Fanget al.2010; Piaoet al.2010).Although more efficient irrigation technologies have been introduced over the past 40 years, these developments have not slowed the depletion of underground water (Maet al.2015). Studies have shown that the groundwater table in the NCP is declining at a rate of 0.8 m yr–1, and this has led to a serious underground water crisis in the area (Chenet al.2003; Hanet al.2016). On the other hand, precipitation in NCP has exhibited a long-term trend of decline (Piaoet al.2010). The groundwater resource crisis has led to an urgent need for a reduction of irrigation to maintain agricultural sustainability in the area (Fanget al.2010). In the future, irrigation strategies will emphasize maximizing the productivity per unit of water used rather than the productivity per unit of crop area (Fereres and Soriano 2007).

Reduction of the overall application of irrigation water to conserve water resources is possible through deficit irrigation (Guoet al.2014). Deficit irrigation is defined as the application of irrigation water in volumes less than the full evapotranspiration (ET) requirement of the crop(Geerts and Raes 2009). Irrigation only at certain stages of crop growth is a strategy that has been widely utilized in areas where water resources are limited (Kang 2004). In the NCP, deficit irrigation can be applied to wheat crop at specific growth stages to mitigate the adverse effects of water stress on plants (Zhanget al.2013). For example,Kang (2002) reported that irrigation below the full potential ET requirement did not necessarily reduce the winter wheat yield. Determining the critical growth stages for applying the limited water available for irrigation will be crucial for reducing the impact of water shortage on wheat grain yield while maintaining economic returns. Precipitation is also a critical factor affecting wheat production in the NCP because it directly affects irrigation requirements and water balance in wheat (Sunet al.2010).

The CERES-Wheat model is a cropping system model that is a component of the Decision Support System for Agrotechnology Transfer, popularly known as DSSAT (Joneset al.2003; Hoogenboomet al.2004). High performance has been reported for CERES-Wheat in simulating wheat growth and yield in response to environmental factors and management under a wide range of soil and climatic conditions (Aroraet al.2007; Heet al.2013; Jiet al.2014;Mavromatis 2014; Yuet al.2014; Dokoohaki 2015; Ahmedet al.2016; Attiaet al.2016). The objectives of this study were to: (1) calibrate the CERES-Wheat model to accurately predict the winter wheat grain and biomass yield, harvest index (HI), and WUE responses to different irrigation scheduling practices using long-term weather datasets available for NCP; (2) simulate the development and growth of winter wheat under different irrigation treatments using historical weather data from 33 years (1981–2014) with crop seasons that were classified into three types according to seasonal precipitation; and (3) discuss the possibility of further reducing irrigation by optimizing the irrigation strategies for sustainable groundwater management.

2. Materials and methods

2.1. Model description

In this study, we used CERES-Wheat, a component of the DSSAT Cropping System Model v4.6 (Hoogenboomet al.2015) that can simulate the growth and development of wheat using a daily time-step model. Since its initial development and evaluation (Ritchie and Otter 1985), the model has been documented extensively. It has been widely used to simulate the effects of weather, genotype,soil properties, and management factors on wheat growth and development and water and nitrogen dynamics (Aroraet al.2007; Heet al.2013; Attiaet al.2016). The crop growth model divides phasic development into nine growth stages from pre-sowing to harvest in relation to thermal time.The DSSAT-Wheat model calculates plant phenological development based on the calibration of three varietyspecific coefficients (P1V, P1D, and P5), while three other specific coefficients (G1, G2, and G3) control grain yield.The phyllochron interval is controlled by PHINT (Joneset al.2003).

Daily soil water balance is modeled based on rainfall,irrigation, transpiration, soil evaporation, in filtration,drainage, and surface run-off. Each layer has a characteristic lower limit (LL), a drained upper limit (DUL), and a saturated water content (SAT). The model utilizes the LL, DUL,and SAT to estimate water flow using a simple cascading approach. Runoff from rainfall is estimated based on the USDA Natural Resources Conservation Service curve number method by Joneset al.(2013), and the remaining water in filtrates into the soil pro file. Drainage is estimated following the slowest draining layer of the soil pro file. Plant transpiration (EP) is calculated from the distribution of roots and available water in the soil layers. Actual soil evaporation(ES) is independently estimated using the two-stage soil evaporation model (Ritchie 1972).

2.2. Experimental datasets

To calibrate and evaluate the CERES-Wheat model, data from eight field studies conducted in NCP were used.These field experiments were conducted at the Wuqiao Experimental Station of the China Agricultural University in Hebei Province, China (37°41′N, 116°37′E, elevation 20 m above sea level, groundwater table 6–9 m). The soil series at this location is Calcaric Fluvisol with sandy clay loam texture (FAO 1990). The physiochemical characterization of the soil pro file in this region is given in Table 1. The study area is characterized by a summer monsoon climate with average annual rainfall of approximately 545 mm(1981–2014). The growing season for winter wheat is from mid-October to early June of the following year, and the annual rainfall is approximately 117 mm.

Data from four studies were used for calibrating,while data from the remaining four studies were used for evaluating the model. Experiments 1 through 4 were conducted in the 2004–2008 growing seasons (Zhang 2009), and these data were used for model calibration. In these studies, the researchers investigated winter wheat growth and yield responses to three irrigation treatments(rainfed, one irrigation and two irrigations) applied at different plant developmental stages in plot areas of 56 m2. The details of the irrigation treatments for the four experiments are shown in Table 2 and more details about the cultural practices in the experiments can be found in Zhang (2009).The data included measurements of grain yield, biomass yield, grain weight, grains per spike, and HI. The data from Experiments 5 to 8 were used for model evaluation and were obtained from previous studies by Wu (2005), Liu(2010) and Zhang (2009); these studies focus on the effect of irrigation strategies ranging from rainfed to four-irrigation treatments on winter wheat grain yield, yield component,biomass yield and WUE in the 2003–2004, 2007–2008,and 2008–2009 growing seasons, respectively. The plot area in these studies ranged from 30 to 150 m2. The details of the irrigation treatments for these four experiments are shown in Table 2.

All the experiments mentioned above were conducted with randomized complete block design with three or four replicates. The wheat cultivar Shijiazhuang 8 was planted with 15.6 cm row spacing using a seed rate of 300 kg ha–1for all experiments. All treatments received 75 mm of irrigationprior to sowing to ensure uniform emergence. Irrigation was applied through gated pipes and measured with propellertype meters in all experiments. Fertilizer was applied at planting at a rate of 157.5 kg N ha–1. Weeds, diseases and pests were controlled following the local agronomic recommendations. Additional details of cultural practices and crop management are reported in Wanget al.(2006).

Table 1 Soil physical and chemical properties in the experimental area

Table 2 Details of the irrigation treatments used for calibration and evaluation of the CERES-Wheat model

2.3. Model calibration and evaluation

The CERES-Wheat model requires daily weather data,crop management data, soil pro file data, and genotype coefficients as basic input. Daily precipitation, sunshine hours, and maximum and minimum air temperatures were obtained from the Wuqiao County Bureau of Meteorology,Hebei Province, China. We used GLUE method (Heet al.2010) and trial and error for calibration. The CERESWheat model was calibrated using field experimental data obtained from the 2004 to 2008 cropping seasons (Zhang 2009). To calibrate the phenology and crop growth of the specified wheat variety, three types of coefficients were de fined: cultivar, ecotype, and species coefficients. The phenological development parameters related to anthesis and physiological maturity date (i.e., P1V, P1D, P5 and PHINT) were calibrated first. The crop growth parameters(G1, G2 and G3) were then con firmed based on field data. Meanwhile, the ecotype and species coefficient parameters were also adjusted to the precise model. After calibration, the model was used for evaluation by comparing field observations and simulated data. In this study, the observed and simulated grain yield, biomass yields, grain weight, grains per spike, and HI were compared. The calibrated genetic coefficients for the winter wheat cultivar Shijiazhuang 8 in the CERES-Wheat model are shown in Table 3.

2.4. Long-term scenario analyses using historical meteorological data

The development and growth of winter wheat under different irrigation treatments was simulated using the CERES-Wheat model over the 33 crop seasons, and the results were classified into three types according to seasonal precipitation.The three-year types include seasons with precipitation below 100 mm, between 100 and 140 mm, and above 140 mm. There were 11 seasons with precipitation ＜100 mm,12 seasons with precipitation between 100 and 140 mm, and 10 seasons with precipitation ＞140 mm during the 33 crop seasons. Long-term precipitation in the winter wheat crop season at the experimental site is shown in Fig. 1.

Climate data, including daily minimum and maximum temperature, solar radiation and daily precipitation from 1981–2014, were obtained from the Wuqiao County Bureau of Meteorology. Eight irrigation treatments, representing rainfed (T0); one irrigation of 75 mm at the jointing stage(T1); one irrigation of 75 mm at anthesis stage (T2); two irrigations of 75 mm each at the jointing stage and anthesis stage (T3); two irrigations of 75 mm each at the jointing stage and grain- filling stage (T4); three irrigations of 75 mm each at the upstanding stage, booting stage and 20 days after anthesis (T5); three irrigations of 75 mm each at the upstanding stage, booting stage and anthesis stage (T6);and four irrigations of 75 mm each at the upstanding stage,booting stage, anthesis stage and grain- filling stage (T7),were used for long-term simulations. These treatments were similar to those described in the experiments used for calibration and evaluation using CERES-Wheat model(Table 2). The scenario analyses were defined by flood irrigation, and 75 mm irrigation was applied before wheat crop planting for all irrigation treatments. Therefore, the initial soil water content pro file was considered to be near field capacity. Rates of 157 kg ha–1nitrogen and 70 kg ha–1phosphorus were applied at planting, which was set to October 17 in all years. Other cultivation practices like those described by Zhang (2009) were used in the model.

Table 3 Genetic coefficients for the winter wheat cultivar Shijiazhuang 8 in the CERES-Wheat model

Fig. 1 Long-term precipitation at the experimental site from 1981 to 2014 during the winter wheat growing season from October 10 of the current year to June 15 of the following year.There were 11 seasons with precipitation ＜100 mm, 12 seasons with precipitation between 100 and 140 mm, and 10 seasons with precipitation ＞140 mm.

2.5. Statistical analysis

The root mean square error (RMSE) and normalized RMSE(NRMSE) were calculated to evaluate the simulation error for the different parameters between the observed values from field experiments and the simulated values from the CERES-Wheat model.

The NRMSE provides a measure of the relative difference(percentage of the mean observed value,O) between the simulated (Si) versus observed (Oi) values. The simulation was identified as excellent when the NRMSE was less than 10%, good when the NRMSE was greater than 10% and less than 20%, fair when the NRMSE was greater than 20% and less than 30%, and poor when the NRMSE was greater than 30% (Bannayan and Hoogenboom 2009; Dettoriet al.2011).

The coefficient of residual mass (CRM) indicates whether the model predictions tend to over- or underestimate observed data. A negative CRM value indicates a tendency of the model toward overestimation, while a positive CRM value indicates a tendency of the model toward underestimation (Loague and Green 1991).

The D-index values range from 0 to 1. A D-index value of 1 indicates perfect agreement between the observed and simulated data. A D-index value less than 0.50 suggests greater diversity and inconsistency in the model predictions. D-index values closer to 0.0 indicate that the model predictions are equal to the average of the observed data, which indicates no agreement between the observed and simulated values (Willmott 1981, 1982).

3. Results

3.1. Model calibration and evaluation

The simulated and observed values for anthesis, maturity dates, grain and biomass yields, product number, final shoot number, thousand-grain weight (TGW), and HI after calibration based on data from Experiments 1–4 are presented in Table 4. The results indicate a very close match between the simulated and observed anthesis (mean values:204vs. 204 days after planting) and physiological maturity dates (mean values: 235vs. 236 days after planting).There was excellent agreement between the observed and simulated grain yields (mean value: 7 327vs. 7 261 kg ha–1). The calibrated model explained 80% of the variation(Fig. 2-A) with a NRMSE＜10% and a D-index value of 0.92. The simulated biomass yields also closely matched the observed values with a NRMSE＜10% and a D-index value of 0.93 (Fig. 2-B). The performance of the calibrated model regarding simulation of product number, final shoot number, and TGW was considered good according to the statistic results.

Overall, the calibrated model accurately simulated phenology (anthesis day, maturity day), grain and biomass yields, yield components, and HI as indicated by the goodness of fit statistics (Table 4).

The independent field studies (Experiments 5–8) were used for further evaluation of the performance of the calibrated model. The observed grain yield averaged 7 145 kg ha–1and ranged from 3 723 to 8 502 kg ha–1with a NRMSE of 10.37%, and 73% of yield variation could be explained by the calibrated model (Table 5; Fig. 2-C). The treatments with three irrigations in Experiments 5 and 6 and the treatment with four irrigations in Experiment 7 overestimated the yield, were considered to be the major sources of error in the model simulation accuracy. Biomass yield was predicted well by the calibrated model (Fig. 2-D),producing a mean value of 15 657 kg ha–1compared to the observed value of 15 117 kg ha–1. The NRMSE was 9.81%, withr2=0.83. The product number was adequately predicted in all treatments withr2=0.91 and NRMSE=5.77%.However, TGW was not accurately estimated by the model(r2=0.2, D-index=0.57) with a value of NRMSE=12.58%.The final shoot number was also not well predicted, with similar values (Table 5). The stability and accuracy of the calibrated model was con firmed by the above evaluation.The calibrated model can be used to simulate grain and biomass yields of winter wheat in response to irrigation management in the NCP.

3.2. Scenario analyses using long-term weather data

Grain and biomass yieldsUsing the calibrated and validated CERES-Wheat model, the effects of different yearly rainfall and irrigation amounts on grain and biomass yields were simulated for the NCP based on historical weather data from 1981 to 2014 (Table 6). Simulated grain yield from different rainfall years was more affected by irrigation when the growing season precipitation was below 100 mm (Fig. 3). Compared to rainfed, the treatments T1,T3, T4, T5, T6, and T7 significantly improved wheat grain yield. The average T0 yield was 4.06 Mg ha–1, while T6 increased grain yield to 7.87 Mg ha–1during seasons when precipitation was below 100 mm. The grain yield in T3 was almost the same as in T5, T6 and T7. We also found that T1 produced higher yield than T2, but yield was the same as T4. This result con firmed that the timing of irrigation has a strong impact on grain yield under deficit irrigation conditions. When the precipitation was between 100 and 140 mm for the winter wheat growing season, the rainfed wheat grain yield increased to 5.25 Mg ha–1(Table 6). T1, T3, T4, T5,T6, and T7 increased the wheat grain yield significantly compared to T0. These results showed that T1 attained 89% of maximum grain yield of T6 and T7 strategies, while T3 attained 96% of the highest grain yield. When precipitation in the winter wheat crop growing season was above 140 mm, grain yield varied from 5.91 Mg ha–1of T0 to 8.44 Mg ha–1of T6. Overall,the long-term scenario analyses based on 33 years of weather data demonstrated that deficit irrigation at the jointing stage and anthesis stage (T3) produced yield that was not significantly different from the three irrigations at T6, which was the treatment that produced the highest yield of all the irrigation strategies. A single irrigation at T1 significantly improved the grain yield compared to the rainfed treatment, and the yield was similar to that of the T3 treatment, especially when precipitation was higher.

Table 4 Calibration results from the CERES-Wheat model for winter wheat cultivar Shijiazhuang 8 using experimental data from the 2004–2008 crop seasons (Zhang 2009)1)

Fig. 2 Results of the model calibration for observed vs. simulated grain yield (A) and observed vs. simulated biomass yield (C),and the model evaluation results for grain yield (B) and biomass yield (D) from the CERES-Wheat model. The line represents the 1:1 relationship.

Table 5 Results of the evaluation of the CERES-Wheat model for winter wheat cultivar Shijiazhuang 8 using experimental data from the 2007–2009 (Liu 2010), 2007–2008 (Zhang 2009), and 2003–2004 (Wu 2005) crop seasons1)

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Similar to the trend for variation in grain yield, different rainfall amounts among years and irrigation treatments significantly affected the simulated biomass yield over the long-term simulation period(Table 6). Biomass increased with the increase in irrigation (Fig. 4).The rainfed treatment had the lowest biomass yield at 7.15 Mg ha–1, while the biomass yield was 17.68 Mg ha–1of T7 when the crop season precipitation was below 100 mm. In those crop seasons,T1 resulted in almost two times the biomass yield of T0. The rainfed biomass yield was significantly increased to 9.55 Mg ha–1at crop seasons with precipitation was between 100 and 140 mm, while was added to 78% on account of T1, the biomass yield improved to 18.45 Mg ha–1when the crop was irrigated four times (T7). When the crop season precipitation was above 140 mm, the biomass yield ranged from 11.23 Mg ha–1for T0 to 18.55 Mg ha–1for T7. There was an obvious difference between biomass yield and grain yield in response to irrigation treatment. The biomass of the three-irrigation(T5, T6) and four-irrigation (T7) treatments were significantly higher than for T3.

Fig. 3 Simulated grain yield using the CERES-Wheat model as affected by irrigation treatments, using long-term weather data from 1981 to 2014 in the North China Plain. T0, rainfed; T1, a single irrigation at the jointing stage; T2, a single irrigation at the flowering stage; T3, two irrigations at the jointing and anthesis stages; T4, two irrigations at the jointing and grain- filling stages;T5, three irrigations at the upstanding stage, booting stage and 20 days after anthesis; T6, three irrigations at the upstanding stage, booting stage and anthesis stage; T7, four irrigations at the upstanding stage, booting stage, anthesis stage and grain- filling stage. Crop seasons were classified into three rainfall/year categories according to the amount of precipitation:＜100 mm (11 seasons), 100–140 mm (12 seasons), and ＞140 mm(10 seasons).

Fig. 4 Simulated biomass yield using the CERES-Wheat model as affected by irrigation treatments, using long-term weather data from 1981 to 2014 in the North China Plain. T0, rainfed;T1, a single irrigation at the jointing stage; T2, a single irrigation at the flowering stage; T3, two irrigations at the jointing and anthesis stages; T4, two irrigations at the jointing and grainfilling stages; T5, three irrigations at the upstanding stage,booting stage and 20 days after anthesis; T6, three irrigations at the upstanding stage, booting stage and anthesis stage;T7, four irrigations at the upstanding stage, booting stage,anthesis stage and grain- filling stage. Crop seasons were classified into three rainfall/year categories according to the amount of precipitation: ＜100 mm (11 seasons), 100–140 mm(12 seasons), and ＞140 mm (10 seasons).

Harvest indexThe effect of irrigation strategy on HI in wheat crop in semi-arid regions has been broadly con firmed throughout the world (Eck 1988; Zhanget al.2008). This effect is more obvious in the NCP, where the water deficit is very serious. The HI of different irrigation treatments was averaged over the long-term simulation period based on the rainfall year category, and the values are presented in Table 6. When the precipitation was below 100 mm for the winter wheat growing season, HI ranged from 0.39 for T2 and T4 to 0.48 for T1 and T3. A similar trend of irrigation strategy effect was found in the other two precipitation crop seasons with precipitation between 100 and 140 mm and above 140 mm (Fig. 5). This result is consistent with previous studies of NCP irrigation systems (Zhang 2008;Dong 2011) and in the arid and semi-arid region of Northwest China (Kang 2002).

Fig. 5 Simulated harvest index using the CERES-Wheat model as affected by irrigation treatments, using long-term weather data from 1981 to 2014 in the North China Plain. T0, rainfed;T1, a single irrigation at the jointing stage; T2, a single irrigation at the flowering stage; T3, two irrigations at the jointing and anthesis stages; T4, two irrigations at the jointing and grainfilling stages; T5, three irrigations at the upstanding stage,booting stage and 20 days after anthesis; T6, three irrigations at the upstanding stage, booting stage and anthesis stage; T7, four irrigations at the upstanding stage, booting stage, anthesis stage and grain- filling stage. Crop seasons were classified into three rainfall/year categories according to the amount of precipitation:＜100 mm (11 seasons), 100–140 mm (12 seasons), and＞140 mm (10 seasons).

Water use efficiencyThe water use efficiency (WUE) was calculated as the ratio of grain yield to seasonal ET and showed significant differences in the response to irrigation treatments (Table 6). There was an obvious difference between the WUE and grain yield in response to irrigation strategy. Unlike the grain yield, the WUE did not always increase with higher irrigation. Generally, the WUE of T1 and T3 was greatly improved compared to the other irrigation treatments (Fig. 6). When the crop season precipitation was below 100 mm, the average rainfed WUE was 12.52 kg ha–1mm–1, whereas the highest WUE was 18.26 kg ha–1mm–1of T3. The WUE of T1 was near that of T3, and the WUE in these two treatments was higher than in the other irrigation treatments with 100% probability (Fig. 7-A). Compared to the rainfed treatment, the treatment T2 resulted in the lowest WUE of 11.31 kg ha–1mm–1. When the crop season precipitation was between 100 and 140 mm (Fig. 7-B), the WUE ranged from 13.09 kg ha–1mm–1of T2 to 17.88 kg ha–1mm–1of T3. With precipitation ＞140 mm, the WUE ranged from 13.92 kg ha–1mm–1for the treatment T2 to 17.70 kg ha–1mm–1for T1, and this value showed little difference from the other rainfall year categories. In addition, there was no noticeable difference between the WUE in T3 compared to T1 or of the WUE in T4 compared to T5, T6 and T7 (Figs. 6 and 7-C). The improvement in WUE compared to T0 varied from 12.52 to 15.31% among the three rainfall year categories, and the WUE was most affected by this variable.

4. Discussion

4.1. Yield and water use efficiency as winter wheat responses to irrigation strategies

Fig. 7 Cumulative probability distribution of the water use efficiency under different irrigation treatments using a historical weather dataset from 1981 to 2014 in the North China Plain. A, amount of precipitation below 100 mm (11 seasons). B, amount of precipitation between 100 and 140 mm (12 seasons). C, amount of precipitation above 140 mm (10 seasons). T0, rainfed; T1, a single irrigation at the jointing stage;T2, a single irrigation at the flowering stage; T3, two irrigations at the jointing and anthesis stages; T4, two irrigations at the jointing and grainfilling stages; T5, three irrigations at the upstanding stage, booting stage and 20 days after anthesis; T6, three irrigations at the upstanding stage, booting stage and anthesis stage; T7, four irrigations at the upstanding stage, booting stage, anthesis stage and grain- filling stage.

Irrigation is one of the most important cultivation management measures to ensure winter wheat high-yield production in regions such as the NCP and mainly depends on the water supply from underground. However, declined underground water level in this area is a major concern for producers and policy makers. For ensuring crop irrigation, deep wells below 100 m deep or more are needed in the NCP. This situation has caused the underground water table to decline rapidly. Three- and four-irrigation treatments were the traditional irrigation practices for high-yielding wheat in the NCP (Liet al.2005). In recent years, one- or two-irrigation strategies were recommended for this area, especially in Hebei Province and surrounding areas, and are being accepted by farmers and applied to winter wheat production due to a higher WUE and higher grain yield. The results of our study indicated that the average yield increase was 2.39 Mg ha–1from T0 to T1 and 0.59 Mg ha–1from T1 to T3, and the yield increase with increased irrigation was non-significant. The maximum average yield increase occurred from the rainfed treatment to the single irrigation at the jointing stage (T1).

Fig. 6 Simulated water use efficiency (WUE; kg ha–1 mm–1)using the CERES-Wheat model as affected by irrigation treatments, using long-term weather data from 1981 to 2014 in the North China Plain. T0, rainfed; T1, a single irrigation at the jointing stage; T2, a single irrigation at the flowering stage; T3, two irrigations at the jointing and anthesis stages;T4, two irrigations at the jointing and grain- filling stages; T5,three irrigations at the upstanding stage, booting stage and 20 days after anthesis; T6, three irrigations at the upstanding stage, booting stage and anthesis stage; T7, four irrigations at the upstanding stage, booting stage, anthesis stage and grainfilling stage. Crop seasons were classified into three rainfall/year categories according to the amount of precipitation: ＜100 mm (11 seasons), 100–140 mm (12 seasons), and ＞140 mm(10 seasons).

Chenet al.(2015) and Chennafiet al.(2006) indicated that the impact of water deficit on wheat yield and WUE differs among the growth stages of wheat crop, and the most sensitive stage depends on the area. Adequate water supply during sensitive stages is critical for growth and yield formation. Liet al.(2005) concluded that in the NCP,the jointing to booting stage was the growth period most sensitive to a soil water deficit with respect to wheat growth,and con firmed that irrigating at the jointing stage increased the number of ears per unit area and grain number per ear.This result is similar to those of our study. A single irrigation at the jointing stage can maintain sustainable positive wheat production in the NCP while protecting underground water resources from further depletion (Lan and Zhou 1995; Zhanget al.1998). On the other hand, although a negative effect on grain yield is usually found under water deficit, crops have complex mechanisms of response to water stress (Chaves and Oliveira 2004; Cattivelliet al.2008). Moderate water stress at certain growth stages can stimulate the redistribution of photosynthates to grain and improve the HI. Zhanget al.(2008) reported a moderate water deficit at the grain- filling stage increased the mobilization of assimilates stored in vegetative organs to grains, and this resulted in higher grain yield, HI and WUE. Hocking (1994) found that water deficit at the grain- filling stage increases the redistribution of dry matter accumulated before anthesis from vegetative organs to reproductive organs. In this region, annual precipitation is concentrated during the summer months. The higher grain yield in T1 may have been due to the moderate water deficit that occurred around the grain- filling stage, which stimulated the redistribution of photosynthates to grain and improved the HI. Furthermore, when exposed to soil drying, winter wheat crop develops a deeper root system and modi fies its canopy structure when grown in waterlimited environments. This is one of the positive effects of a moderate water deficit. The irrigation strategy of T1, which limited irrigation to before the jointing stage to maintain the soil drying environment, promoted the development of a deep root system. And the deep root system allows the plants to use water from a greater depth, which is stored from precipitation in the previous summer season (Xueet al.2003). Thus, where there is water deficit in the NCP,T3 is the best irrigation strategy for winter wheat production for higher grain yield, and T1 may be used as an alternative irrigation scheme for further water savings.

4.2. The effects of different rainfall year categories on winter wheat production

The WUE also varied among the different rainfall categories per year (i.e., growing season). Chenet al.(2014) found that seasonal precipitation obviously affected winter wheat yield and that the effect of precipitation significantly declined when the crops were well irrigated. Our results showed that grain yield varied with rainfall year category. The average yield of T3 varied from 7.85 to 8.26 Mg ha–1for the three rainfall categories and had the lowest range of yield values among those different categories. The average yield of T1 varied from 7.01 to 7.91 Mg ha–1for the three rainfall categories, and the variation in yield was lower than in the rainfed treatment. Meanwhile, the highest WUE was achieved with one irrigation at the jointing stage for most of the year. The WUE declined significantly with increased irrigation. The mean values of WUE in this study conform with those of a previous study on irrigated winter wheat crop(Zhanget al.2008) and indicated that one irrigation at the jointing stage (T1) or two irrigations at the joint and anthesis stage (T3) may be adequate for winter wheat production in the NCP. Considering the water resource crisis in this area, a substantial decrease in water consumption for winter wheat production is needed to meet the underground water challenges facing the NCP in the next few decades. A single irrigation at the jointing stage is possibly the most suitable irrigation strategy for winter wheat production.

5. Conclusion

The CERES-Wheat model was very well simulated winter wheat phenology, grain and biomass yields, and WUE responses to irrigation management in the NCP after genetic coefficients calibrated, based on the data got from field experiments. Scenario analyses indicated that simulated grain yield based on different growing season rainfall categories was more affected by irrigation when the growing season precipitation was below 100 mm. Two irrigations(75 mm each at the jointing stage and anthesis stage)resulted in the highest grain yield and WUE. Meanwhile,simulated grain yield based on two irrigations (one each at the jointing and anthesis stages) was not obviously impacted by the different rainfall levels. For the other irrigation treatments, grain yield was improved when rainfall increased. A single irrigation at the jointing stage may thus be an alternative irrigation scheme for further water savings.

Acknowledgements

This work was funded by the Special Fund for Agro-scientific Research in the Public Interest of China (201203031,201303133) and the National Natural Science Foundation of China (31071367).

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