Evaluation of the Potential E ﬀ ects of Drought on Summer Maize Yield in the Western Guanzhong Plain, China

: Drought and uneven distribution of precipitation during stages of crop growth exert a severe reduction on crop yield. It is therefore necessary to evaluate the impact of drought on crop yields. In this study, data from a two-year (2016 and 2017) ﬁeld experiment were used to calibrate and evaluate the parameters of the Decision Support System for the Agrotechnology Transfer (DSSAT) model. The evaluation model was then employed to analyze the impact of potential drought on the yield of summer maize ( Zea mays L.) over di ﬀ erent growth stages for 46 years (1970–2015). The simulated summer maize ﬂowering and harvest date di ﬀ ered by three and one days of the observed in 2017. The d-index value and the normalized root-mean-square error ( nRMSE ) of the simulated and measured values were 0.90 and 3.72%, 0.95 and 10.21%, and 0.92 and 13.12%, for summer maize yield, soil water content, and leaf area index, respectively. This indicates that the parameters of the DSSAT model were extremely reliable and that the simulation results were better. The yield reduction of summer maize was concentrated within the range of 0–40% from 1970 to 2015, and the two-stage yield reduction was higher than the one-stage yield reduction. The highest probability of yield reduction occurs if drought occurs during jointing and heading stages. Irrigation is therefore recommended during jointing stage or heading stage. If local irrigation conditions permit, irrigation can be carried out both at the jointing and heading stages. This study provides a theoretical basis for drought resistance management and scientiﬁc irrigation of summer maize in the western Guanzhong plain.


Introduction
The impact of climate change on crop growth and yield has become a focal topic in numerous studies [1][2][3][4]. As an extreme climatic event, drought severely affects global crop growth and food production [5,6] and poses major challenges to the environment [7][8][9]. Government managers therefore need scientific information to formulate effective drought disaster risk management measures to sustain the global population and ensure food security. Various factors such as climate, crop and soil characteristics, and human activities contribute to the severity of agricultural drought. However, the impact of the drought is affected by the degree and duration of reduced precipitation, soil moisture gradient, plant variety, and developmental stages [10,11]. In most instances, crops suffer a certain degree of drought due to insufficient precipitation during the growth period, lower groundwater levels, and limited irrigation opportunities [12]. Therefore, exploring how crops maintain their growth Figure 1). The study area experiences a semi-arid and humid climate and has an altitude of 471 m, an average annual temperature of 12.4 • C, and average annual sunshine duration of 2095 h. The average annual precipitation for the summer maize growing season from June to September is 360.2 mm, and the effective precipitation is 316.5 mm. The soil texture is sandy loam, the soil bulk density of the 0-20 cm soil layer is 1.32 g cm −3 , the pH is 8.14, the organic matter content is 10.2 g kg −1 , the total nitrogen content is 0.96 g kg −1 , the available phosphorus is 10.28 g kg −1 , and the available potassium is 128.5 mg kg −1 .
Agronomy 2020, 10, x FOR PEER REVIEW 3 of 17 Figure 1). The study area experiences a semi-arid and humid climate and has an altitude of 471 m, an average annual temperature of 12.4 °C, and average annual sunshine duration of 2095 h. The average annual precipitation for the summer maize growing season from June to September is 360.2 mm, and the effective precipitation is 316.5 mm. The soil texture is sandy loam, the soil bulk density of the 0-20 cm soil layer is 1.32 g cm −3 , the pH is 8.14, the organic matter content is 10.2 g kg −1 , the total nitrogen content is 0.96 g kg −1 , the available phosphorus is 10.28 g kg −1 , and the available potassium is 128.5 mg kg −1 .

Figure 1.
Location of the study area.

Field Experiments
The summer maize was planted by machines on 15 June 2016 and 2017, and harvested on 8 October 2016 and 2017. The variety of summer maize was "Zhengdan 958", the row spacing was 0.7 m, the plant spacing was 0.3 m, and the density was 60,000 plants/hm 2 . A completely random block design was employed. Four irrigation levels were set, 45 mm, 60 mm, 75 mm, and 90 mm, and four nitrogen application levels, 120 kg hm −2 , 150 kg hm −2 , 180 kg hm −2 , 210 kg hm −2 , with a total of 16 treatments, each treatment having three replicates. The plot was 28 m long, 5.7 m wide, and occupied an area of approximately 160 m 2 . A 0.5 m isolation area was set between different plots, and a 1 m isolation area was set between different treatments. The boundary of the plot was artificially ridged at a height of 0.25 m with a ridge of 0.6 m. The used nitrogen fertilizer was urea (46%), the phosphate fertilizer used was superphosphate (P2O5 16%), and the potassium fertilizer used was potassium oxide (K2O 50%). The fertilizer was applied as a base fertilizer at the time of sowing. After sowing, we sprayed the herbicide with a machine to prevent weeds. The field experiment used pumps to supply water from channels and the irrigation date in 2016 was July 5 and in 2017 was July 25. The experiment mainly measured the leaf area, phenology, and grain yield of summer maize at different growth stages.

Description of DSSAT-Maize Model
The DSSAT model is one of the more intuitive crop models in terms of the human-computer interface. It was launched with the support of the International Agricultural Technology Transfer Benchmark Network (IBSNAT) funded by the United States Agency for International Development (USAID) from 1981 to 1992. DSSAT version 2.1 was first released in 1989. DSSAT 4.7 version can simulate more than 42 kinds of crops, which is the latest version. The DSSAT model can simulate the dynamic changes in summer maize economic yield, biomass, soil moisture, and soil nutrients under different growth scenarios based on the calculation of days. The data required to run the DSSAT model are meteorological, soil, crop variety genetic parameters, and field management measured test data (the field management experiment was introduced in Section 2.2).

Field Experiments
The summer maize was planted by machines on 15 June 2016 and 2017, and harvested on 8 October 2016 and 2017. The variety of summer maize was "Zhengdan 958", the row spacing was 0.7 m, the plant spacing was 0.3 m, and the density was 60,000 plants/hm 2 . A completely random block design was employed. Four irrigation levels were set, 45 mm, 60 mm, 75 mm, and 90 mm, and four nitrogen application levels, 120 kg hm −2 , 150 kg hm −2 , 180 kg hm −2 , 210 kg hm −2 , with a total of 16 treatments, each treatment having three replicates. The plot was 28 m long, 5.7 m wide, and occupied an area of approximately 160 m 2 . A 0.5 m isolation area was set between different plots, and a 1 m isolation area was set between different treatments. The boundary of the plot was artificially ridged at a height of 0.25 m with a ridge of 0.6 m. The used nitrogen fertilizer was urea (46%), the phosphate fertilizer used was superphosphate (P 2 O 5 16%), and the potassium fertilizer used was potassium oxide (K 2 O 50%). The fertilizer was applied as a base fertilizer at the time of sowing. After sowing, we sprayed the herbicide with a machine to prevent weeds. The field experiment used pumps to supply water from channels and the irrigation date in 2016 was July 5 and in 2017 was July 25. The experiment mainly measured the leaf area, phenology, and grain yield of summer maize at different growth stages.

Description of DSSAT-Maize Model
The DSSAT model is one of the more intuitive crop models in terms of the human-computer interface. It was launched with the support of the International Agricultural Technology Transfer Benchmark Network (IBSNAT) funded by the United States Agency for International Development (USAID) from 1981 to 1992. DSSAT version 2.1 was first released in 1989. DSSAT 4.7 version can simulate more than 42 kinds of crops, which is the latest version. The DSSAT model can simulate the dynamic changes in summer maize economic yield, biomass, soil moisture, and soil nutrients under different growth scenarios based on the calculation of days. The data required to run the DSSAT model are meteorological, soil, crop variety genetic parameters, and field management measured test data (the field management experiment was introduced in Section 2.2).

Meteorological Data
Daily climate data from 2016 and 2017 during the summer maize growing season were obtained from the Meteorological Data Center of the China Meteorological Administration (http://data.cma.cn). The meteorological data used in the DSSAT model included daily solar radiation (MJ m −2 ), daily maximum and minimum temperature ( • C), and daily precipitation (mm). The maximum and minimum daily temperatures and the daily precipitation in the summer maize growing seasons of 2016 and 2017 are presented in Figure 2. Daily solar radiation was calculated according to daily sunshine data using the solar radiation empirical formula developed by Angstron [36].
where R s denotes the total solar radiation (MJ m −2 ), R max denotes the astronomical radiation (MJ m −2 ), a s and b s denote the empirical coefficients for the region according to the United Nations Food and Agriculture Organization (FAO; a s = 0.25 and b s = 0.5), n denotes the sunshine hours (h) and is taken directly from the meteorological data, and N denotes the maximum daily sunshine hours (h).  Figure 2. Daily solar radiation was calculated according to daily sunshine data using the solar radiation empirical formula developed by Angstron [36].
where Rs denotes the total solar radiation (MJ m −2 ), Rmax denotes the astronomical radiation (MJ m −2 ), as and bs denote the empirical coefficients for the region according to the United Nations Food and Agriculture Organization (FAO; as = 0.25 and bs = 0.5), n denotes the sunshine hours (h) and is taken directly from the meteorological data, and N denotes the maximum daily sunshine hours (h).

Soil Data
The input soil data in the DSSAT model include soil particle composition, soil bulk density, soil moisture characteristic parameters, and initial soil moisture content. Each layer was 20 cm, and the measured depth was 100 cm. The soil particle composition was measured using a TopSizer laser particle size analyzer (Mastersizer-2000, Britain Mastersizer). The soil moisture characteristic parameters were measured using a centrifuge method [37][38][39]. In 2016 and 2017, precipitation occurred when planting summer maize. The initial moisture content was determined to be 70% of the field capacity, and the soil moisture content was measured using the oven drying method. The soil data used to run the DSSAT model are shown in Table 1.

Soil Data
The input soil data in the DSSAT model include soil particle composition, soil bulk density, soil moisture characteristic parameters, and initial soil moisture content. Each layer was 20 cm, and the measured depth was 100 cm. The soil particle composition was measured using a TopSizer laser particle size analyzer (Mastersizer-2000, Britain Mastersizer). The soil moisture characteristic parameters were measured using a centrifuge method [37][38][39]. In 2016 and 2017, precipitation occurred when planting summer maize. The initial moisture content was determined to be 70% of the field capacity, and the soil moisture content was measured using the oven drying method. The soil data used to run the DSSAT model are shown in Table 1.

Crop Variety Genetic Parameters
A genetic algorithm was employed to debug the genetic parameters of summer maize (Zhengdan 958) crop varieties. Genetic algorithm tuning minimizes the relative error between simulated and observed values. In our model, the number of individuals was set to 10 and the maximum genetic generation to 50. Then, the executable batch file 'DSSBatch.v46' of maize in the DSSAT model was called. Finally, the calibrated genetic parameters were used to simulate the yield of summer maize. CERES-MAIZE has 6 genetic coefficients ( Table 2): degree days (based 8 • C) from seedling emergence to the end of the juvenile phase (P1), photoperiod sensitivity coefficient (P2), degree days (based 8 • C) from silking to physiological maturity (P5), maximum possible number of kernels per plant (G2), potential kernel growth rate (G3), and degree days required for a leaf tip to emerge (PHINT). Table 2. Genetic parameter and ranges for summer maize.

Model Evaluation
Measured and simulated values of yield in 2016 were used to calibrate the crop parameters. The leaf area index, soil moisture, and phenology in 2017 were used to evaluate the parameters of the DSSAT model. Model evaluation indicators included the Pearson correlation coefficient (R 2 ), d-index value (d) [40], and normalized root-mean-square error (nRMSE).
Agronomy 2020, 10, 1095 where S i denotes the simulated data, O i denotes the observed data, O i denotes the mean value of observed data, S i denotes the mean value of simulated data, RMSE denotes the root-mean-square error, and n denotes the number of samples. A high value for the d-index and a low value for nRMSE indicate a good fit between the simulated and observed values. When the nRMSE values were <10%, 10-20%, 20-30%, and >30%, the model simulation effects were excellent, good, fair, and poor, respectively [41].

Summer Maize Drought Loss Setting
To formulate an experimental simulation strategy, first, the crop water requirements and effective precipitation were calculated for each growth period of summer maize from 1970 to 2015 ( Figure 3). The meteorological data from 1970 to 2015 came from the Meteorological Data Center of the China Meteorological Administration (http://data.cma.cn), mainly including rainfall, temperature, radiation and sunshine hours. The water deficits in the summer maize growth stage were then calculated based on the difference between the crop water requirements and the effective precipitation. The formula for calculating the water deficit was as follows: where WD denotes the water deficit (mm), ETc denotes the crop water requirement at a certain stage in mm, and Pe denotes the effective precipitation at a certain stage in mm.
where k c denotes the crop coefficient as stated in the results of Liang et al. [42], and ET 0 is the reference crop evapotranspiration, calculated using the Penman-Monteith formula recommended by the FAO [43].
Agronomy 2020, 10, x FOR PEER REVIEW 7 of 17 As shown in Figure 3, the main growth stages of summer maize occurred in a state of water deficit. The water deficits in the emergence stage, jointing stage, and heading stage were relatively large while that in the filling stage was smaller. According to the planting traditions of farmers in the Guanzhong Plain, the general seeding selection was carried out after rainfall or an adequate irrigation, so that the initial soil moisture content meets the requirements for crop emergence. Additionally, In the early stage of crop growth, the crop is allowed to withstand a certain degree of water deficit, and the limited amount of water is irrigated to a period that is more sensitive to crop growth, thereby ensuring the balance between irrigation and crop yield. Thus, no irrigation was needed at the seedling stage. Potential drought simulations were only conducted on the jointing, heading, and filling stages of summer maize.
Under conditions of consistent soil and field management measures, a simulation test plan was developed on the basis of the water deficit at various stages of the summer maize growth period and  As shown in Figure 3, the main growth stages of summer maize occurred in a state of water deficit. The water deficits in the emergence stage, jointing stage, and heading stage were relatively Agronomy 2020, 10, 1095 7 of 16 large while that in the filling stage was smaller. According to the planting traditions of farmers in the Guanzhong Plain, the general seeding selection was carried out after rainfall or an adequate irrigation, so that the initial soil moisture content meets the requirements for crop emergence. Additionally, In the early stage of crop growth, the crop is allowed to withstand a certain degree of water deficit, and the limited amount of water is irrigated to a period that is more sensitive to crop growth, thereby ensuring the balance between irrigation and crop yield. Thus, no irrigation was needed at the seedling stage. Potential drought simulations were only conducted on the jointing, heading, and filling stages of summer maize.
Under conditions of consistent soil and field management measures, a simulation test plan was developed on the basis of the water deficit at various stages of the summer maize growth period and the actual irrigation situation in the western Guanzhong plain. The simulated sowing data of summer maize was 15 June. The simulated irrigation time was 25 July, 15 August and 2 September. Simulated fertilization was carried out uniformly during sowing. The model was initialized for water and Nitrogen seasonally. In Table 3, CK indicates sufficient irrigation conditions; T1-T3 denote single stage drought at jointing, heading, and filling stages, respectively; T4-T6 denote two stages of drought at heading and filling stage, jointing and filling stage, and jointing and heading stage, respectively; T7 denotes rainfed conditions.
Note: WD1, WD2, and WD3 represent the amount of water deficit at the jointing, heading, and filling stages, respectively. 0 represent no irrigation at this stage.
The yield reduction rate was employed to express the yield reduction caused by drought in the growth stage of summer maize. The formula for this was as follows: where Y d denotes the yield reduction rate of summer maize caused by drought  in kg hm −2 , Y si denotes the yield of summer maize under different irrigation treatments in kg hm −2 , and Y CK denotes the yield of the sufficient irrigation in kg hm −2 .
In this study, the cumulative probability distribution function was used to explore the probability distribution of yield reduction caused by drought in the jointing, tasseling and filling stages. The calculation formula was: where P(x) denotes the cumulative probability that the relative change rate of yield was lower than x i , and Px i denotes the probability of the relative change rate of yield in year i. Finally, the Savitzky-Golay method [45] was used to perform a smoothed analysis of the data. This was based on the average trend of the time-series curve; a polynomial was used to achieve the least squares fit within the sliding window, which can effectively retain the original characteristics of the data.

DSSAT Model Calibration
To ensure the simulation accuracy of the DSSAT model, calibration needed to be conducted under nonstress conditions. The calibrated crop parameters by using genetic algorithm method for the DSSAT model were shown in Table 4. Figure 4 shows the relationships between simulated and observed yields of summer maize under different treatments at Wugong County. The R 2 , d, and nRMSE between the simulated and observed values of summer maize yield were 0.80, 0.90, and 3.72%, respectively. This indicates that the parameters of the DSSAT model were extremely reliable and that the simulation results were better.

DSSAT Model Calibration
To ensure the simulation accuracy of the DSSAT model, calibration needed to be conducted under nonstress conditions. The calibrated crop parameters by using genetic algorithm method for the DSSAT model were shown in Table 4. Figure 4 shows the relationships between simulated and observed yields of summer maize under different treatments at Wugong County. The R 2 , d, and nRMSE between the simulated and observed values of summer maize yield were 0.80, 0.90, and 3.72%, respectively. This indicates that the parameters of the DSSAT model were extremely reliable and that the simulation results were better.

DSSAT Model Evaluation
Model evaluation was identical to calibration, and both used nonstress conditions. Therefore, treatment (irrigation: 60 mm; nitrogen: 150 kg hm −2 ) was used for evaluation of the model. The simulated and observed values of phenology was presented in Table 5, soil moisture (20-40 cm) and leaf area index during the growth period of summer maize are presented in Figure 5. The simulated summer maize flowering and harvest date differed by three and one days of the observed. The R 2 , d, and nRMSE between the simulated and observed values of soil moisture (20-40 cm) were 0.84, 0.95, and 10.21%, respectively. The R 2 , d, and nRMSE between the simulated and observed values of leaf area index were 0.80, 0.92, and 13.12%, respectively. The results indicated that the DSSAT model after calibration and evaluation could effectively simulate the growth of summer maize.

DSSAT Model Evaluation
Model evaluation was identical to calibration, and both used nonstress conditions. Therefore, treatment (irrigation: 60 mm; nitrogen: 150 kg hm −2 ) was used for evaluation of the model. The simulated and observed values of phenology was presented in Table 5, soil moisture (20-40 cm) and leaf area index during the growth period of summer maize are presented in Figure 5. The simulated summer maize flowering and harvest date differed by three and one days of the observed. The R 2 , d, and nRMSE between the simulated and observed values of soil moisture (20-40 cm) were 0.84, 0.95, and 10.21%, respectively. The R 2 , d, and nRMSE between the simulated and observed values of leaf area index were 0.80, 0.92, and 13.12%, respectively. The results indicated that the DSSAT model after calibration and evaluation could effectively simulate the growth of summer maize.   Figure 6 illustrates the effective precipitation at different growth stages of summer maize in the western Guanzhong plain. The average effective precipitation of summer maize during the entire growth season is 328 mm, and the precipitation exhibits bimodal distribution. The effective precipitation in the jointing and heading stages is generally smaller than that in the filling stage, and the average effective precipitation is 59 mm, 58 mm, and 92 mm, respectively.  Figure 6 illustrates the effective precipitation at different growth stages of summer maize in the western Guanzhong plain. The average effective precipitation of summer maize during the entire growth season is 328 mm, and the precipitation exhibits bimodal distribution. The effective precipitation in the jointing and heading stages is generally smaller than that in the filling stage, and the average effective precipitation is 59 mm, 58 mm, and 92 mm, respectively.   Figure 7 shows the simulated grain yields under no drought stress based on which yield reductions were calculated. Figure 8 shows the temporal variability of the simulated yield reduction rate of summer maize based on climatic data between 1970 and 2015. For single-stage drought, the potential yield reduction exhibits a trend of up and down around 2000s. This rate fluctuated the most during drought in the heading stage, followed by the jointing stage, with the least fluctuation during the grain filling stage. The maximum potential yield reduction rate occurred around the 2000s. Extremely low-value areas appeared around the 2010s as a result of heavy rainfall during the summer maize growth period in 2010.  Figure 7 shows the simulated grain yields under no drought stress based on which yield reductions were calculated. Figure 8 shows the temporal variability of the simulated yield reduction rate of summer maize based on climatic data between 1970 and 2015. For single-stage drought, the potential yield reduction exhibits a trend of up and down around 2000s. This rate fluctuated the most during drought in the heading stage, followed by the jointing stage, with the least fluctuation during the grain filling stage. The maximum potential yield reduction rate occurred around the 2000s. Extremely low-value areas appeared around the 2010s as a result of heavy rainfall during the summer maize growth period in 2010.  For two-stage drought (1970-2015), the smoothed curve shows that the results are similar to the single-stage change. When drought occurs in the jointing and heading stage, the yield reduction fluctuates the most, followed by reduction rates in the heading and filling stage, with the smallest fluctuation in the jointing and filling stage. The potential yield reduction rate in the two stages of drought exhibited a maximum value around 1995 and an extremely low value around the 2010s.

Potential Yield Reduction of summer maize from 1970 to 2015
For the three-stage drought or rainfed conditions (1970-2015), the potential drought reduction  For two-stage drought , the smoothed curve shows that the results are similar to the single-stage change. When drought occurs in the jointing and heading stage, the yield reduction fluctuates the most, followed by reduction rates in the heading and filling stage, with the smallest fluctuation in the jointing and filling stage. The potential yield reduction rate in the two stages of drought exhibited a maximum value around 1995 and an extremely low value around the 2010s.
For the three-stage drought or rainfed conditions , the potential drought reduction was more volatile than in the single-stage and two-stage drought. Therefore, through a long-term series analysis (1970-2015), it became clear that the drought in the summer maize growth period in the western Guanzhong plain would result in a serious yield loss. Reasonable irrigation decisions therefore need to be made urgently to coordinate the balance between summer maize production and agricultural irrigation water. Figure 9 shows the potential yield reduction rate at the different growth stages of summer maize during drought. For single-stage drought, the maximum potential yield reduction rate in the jointing (J) stage, heading (H) stage, and filling (F) stage is 31.6%, 43.5%, and 22.6%, respectively. Thus, the potential yield reduction in the jointing and heading stages are clearly larger than that in the filling stage. This indicates that water deficit during the jointing and heading stages have a greater impact on summer maize yield than that during the grain filling stage. For two-stage drought, the maximum potential yield reduction at the heading and filling (HF) stages (drought at the heading stage and then again at the filling stage), jointing and filling (JF) stages (drought at the jointing stage and then again at the filling stage), and jointing and heading (JH) stages (drought at the jointing stage and then again at the heading stage) are 60.7%, 40.6%, and 87%, respectively. At the different growth stages of summer maize, water deficit at the jointing-heading stages has the greatest impact on the production of yield, followed by the heading and filling stages, and finally the jointing and filling stages. This indicates that water deficit at in the early stage of summer maize filling has a serious effect on grain yield, especially in the heading stage.

Potential Yield Reduction during Different Growth Stages of Summer Maize
Agronomy 2020, 10, x FOR PEER REVIEW 12 of 17 potential yield reduction at the heading and filling (HF) stages (drought at the heading stage and then again at the filling stage), jointing and filling (JF) stages (drought at the jointing stage and then again at the filling stage), and jointing and heading (JH) stages (drought at the jointing stage and then again at the heading stage) are 60.7%, 40.6%, and 87%, respectively. At the different growth stages of summer maize, water deficit at the jointing-heading stages has the greatest impact on the production of yield, followed by the heading and filling stages, and finally the jointing and filling stages. This indicates that water deficit at in the early stage of summer maize filling has a serious effect on grain yield, especially in the heading stage. The potential yield reduction in three-stage (JHF, drought during jointing, heading, and filling stages) drought is similar to that in two-stage drought, with the maximum potential yield reduction reaching 88.3%. This demonstrates the importance of irrigation in the early stage of summer maize grain filling, especially during the heading period. The analysis indicates that two-stage drought has a greater potential yield reduction than does single-stage drought. Therefore, when conditions permit, irrigation should be conducted during the jointing and heading stages of summer maize to ensure robust grain production in the western Guanzhong plain.  The potential yield reduction in three-stage (JHF, drought during jointing, heading, and filling stages) drought is similar to that in two-stage drought, with the maximum potential yield reduction reaching 88.3%. This demonstrates the importance of irrigation in the early stage of summer maize grain filling, especially during the heading period. The analysis indicates that two-stage drought has a greater potential yield reduction than does single-stage drought. Therefore, when conditions permit, irrigation should be conducted during the jointing and heading stages of summer maize to ensure robust grain production in the western Guanzhong plain.

Cumulative Probability of Potential Yield Reduction
To study the impact of drought at different stages of summer maize on yield more precisely, the cumulative probability of potential yield reduction in single-stage and two-stage drought were analyzed ( Figure 10). For single-stage drought, the probability of drought in the heading stage is greater than in the jointing stage and the filling stage. When the yield reduction is between 0 and 10%, the cumulative probability of potential yield reduction rate of the filling stage is the largest and that of the heading stage is the smallest. This shows that the potential yield reduction rate during drought in the filling stage is mainly distributed between 0 and 10% and the impact on the yield is less than that in the heading stage. When the yield reduction is 10-30%, the cumulative probability of a reduced yield rate due to drought in jointing and filling stages is close to 100%. When the yield reduction is greater than 30%, the cumulative probability of a reduced yield rate in the heading stage continues to increase. Thus, drought during the heading stage has the greatest impact on yield reduction. For the two-stage drought, the probability of drought in the jointing and heading stages are greater than in the heading and filling stages, and the jointing and filling stages. When the yield reduction is in the range of 0-20%, the cumulative probability of drought in the jointing and filling stages, heading and filling stages, and jointing and heading stages is 81%, 70%, and 58%, respectively. When the yield reduction is greater than 60%, the cumulative probability of drought in the jointing and filling stages, and heading and filling stages both reach 100%, whereas the cumulative probability of drought in the jointing and heading stages are still increasing. Thus, drought in the jointing and heading stages clearly has a greater impact on the yield of summer maize than that in the jointing and filling stages, and the heading and filling stages.
According to the cumulative probability curves for single-stage drought and two-stage drought, when the cumulative probability exceeds 80%, the yield reduction of single-stage drought is distributed between 0 and 20%, 0 and 30%, and 0 and 40%. The two-stage yield reduction is distributed between 0 and 40%, 0 and 60%, and 0 and 80%. The yield reduction in the two-stage drought is therefore much greater than that in the single-stage drought. Thus, single-stage drought has the greatest impact on summer maize yield during the heading stage, and two-stage drought has the greatest impact on yield during the jointing and heading stages. Therefore, combined with the actual irrigation situation in the western Guanzhong plain, irrigating at least once during the heading stage of summer maize is recommended. In areas with good irrigation conditions, irrigation can be conducted during the jointing and heading stages of summer maize to ensure robust production of summer maize. For the two-stage drought, the probability of drought in the jointing and heading stages are greater than in the heading and filling stages, and the jointing and filling stages. When the yield reduction is in the range of 0-20%, the cumulative probability of drought in the jointing and filling stages, heading and filling stages, and jointing and heading stages is 81%, 70%, and 58%, respectively. When the yield reduction is greater than 60%, the cumulative probability of drought in the jointing and filling stages, and heading and filling stages both reach 100%, whereas the cumulative probability of drought in the jointing and heading stages are still increasing. Thus, drought in the jointing and heading stages clearly has a greater impact on the yield of summer maize than that in the jointing and filling stages, and the heading and filling stages.

Discussion
According to the cumulative probability curves for single-stage drought and two-stage drought, when the cumulative probability exceeds 80%, the yield reduction of single-stage drought is distributed between 0 and 20%, 0 and 30%, and 0 and 40%. The two-stage yield reduction is distributed between 0 and 40%, 0 and 60%, and 0 and 80%. The yield reduction in the two-stage drought is therefore much greater than that in the single-stage drought. Thus, single-stage drought has the greatest impact on summer maize yield during the heading stage, and two-stage drought has the greatest impact on yield during the jointing and heading stages. Therefore, combined with the actual irrigation situation in the western Guanzhong plain, irrigating at least once during the heading stage of summer maize is recommended. In areas with good irrigation conditions, irrigation can be conducted during the jointing and heading stages of summer maize to ensure robust production of summer maize.

Discussion
Damage caused by drought to crops is related to the season, duration, and characteristics of the crop such as variety and growth period. Under water deficit conditions, crop growth, photosynthesis, and stomatal pore size may be restricted. This is regulated by physical and chemical signals [46]. In this study, the DSSAT model was used to simulate the yield loss of summer maize under different drought scenarios based on water deficit during the growth period in the western Guanzhong plain. We concluded that drought has the greatest potential impact on yield during the jointing and heading stages. This result is consistent with those of Akir [47] and Hirich et al. [48], who found that drought at the heading stage has the greatest impact on crop yield. However, through a four-year drought experiment on maize under shelter conditions, Ning et al. [49] showed that maize was more sensitive to water stress in the early growth stage. This may be due to sufficient irrigation during maize planting under field conditions, high soil moisture in the early stage, and low drought stress on summer maize growth. When planting under a rain shed, the soil moisture was not replenished, resulting in a lack of water in the early stage.
Even distribution of precipitation and duration of drought have an important impact on maize yield. Mokany et al. [50] and Bu et al. [51] have shown that mild drought stress can increase the root vitality of maize and improve its drought resistance. With the improvement of soil moisture, maize yield increases because of the compensation effect. As the degree of drought increases, the self-recovery capacity of maize gradually decreases or becomes irreversible after drought stress, resulting in a decline in yield. Second, the crop growth restrictions caused by drought generally depend on the drought cycle and the sensitivity of different growth stages to drought [52]. A sustained drought of 10 to 40 days at the seedling stage or jointing stage has a negative impact on maize grain filling and eventually leads to a decline in yield. A long duration of a drought prolongs the filling period, which causes serious yield reduction [53]. Liu et al. [54] found that mild drought at the seedling stage can lead to higher antioxidant enzyme activity and removal of active oxygen, rendering photosynthetic efficiency compensatory after rewatering.
Liu et al. [55] demonstrated that after maize enters the jointing stage, the plants grow vigorously and the male ears begin to differentiate and form, and this represents the most active period of growth and development. At this time, a lack of water causes poor crop growth and the plants will be short. Therefore, to compensate for the lack of natural precipitation, irrigation of maize during the jointing and heading stages is essential. According to the actual irrigation situation in the Guanzhong Plain, the recommendation is for summer maize to be irrigated at the jointing and heading stages, with an irrigation volume of 60 mm [56].
The crop model can effectively simulate and predict the crop growth and development process and its spatial and temporal response to environmental conditions under climate change. The DSSAT crop growth model is widely recommended and is extremely effective in assessing the impact of drought on crop yields. However, this study only conducted simulation studies in the western Guanzhong plain; further simulation studies should therefore be conducted on a larger regional scale. In addition, the water deficit in this study was calculated based on meteorological conditions without taking account of early precipitation during the growth stage and actual soil water consumption. In future studies, meteorology, soil, and crop growth process should be considered to provide a more accurate simulation of summer maize drought.

Conclusions
The simulated and measured values of summer maize yield, phenology, leaf area index, and soil moisture are in good agreement. This indicates that the DSSAT model can effectively simulate the growth process and yield of summer maize in the Guanzhong Plain. It can also assess the effect of different drought conditions on summer maize yield loss, indicating that drought has different effects on yield at different growth stages. For single-stage drought, highest yield reductions are seen during heading stage and greater yield reduction occurs with more extended (two-stage) droughts. For two-stage, yield reductions greatest in jointing and heading stage (three-stage drought is not really a whole lot worse than two-stage). It is therefore recommended that the summer maize in the western Guanzhong plain should be irrigated during the jointing and heading stages to ensure the stable production of summer maize.