Performance assessment and application of the DSSAT-CERES-Maize model for simulating maize yield under water stress conditions

Summer maize is a major crop in the Northern Huaihe Plain, where is one of the most important grain producing areas in Anhui Province, while the maize yield has been seriously affected by drought stress for a long period of time. To maximize maize yield and improve water use efficiency, the rule of yield loss should be clarified which was caused by drought stress in the Northern Huaihe Plain. DSSAT-CERES-Maize model was used to simulate maize yield losses caused by water stress in Bengbu Station of the Northern Huaihe Plain, which was calibrated and validated with drought stress experiments conducted in 2013. Comparing the simulated yield with measured yield under different drought stresses at different growth stages, we found that simulated losses under mild drought were higher than that of measured in all growing stages, on the contrary, simulated data under moderate and severe drought were lower than measured ones in each stage. There were 8 years that loss percentage was higher than 20% from 1961 to 2015. Results implied that maize yield under rain-fed environment was higher than that of suitable water condition, which might benefit from overcompensation of rehydration after appropriate drought stress.


Introduction
Summer maize is a main crop in the Northern Huaihe Plain, which is known as one of the most important grain producing areas in Anhui Province. Generally, its supply water for summer maize is precipitation or/and irrigation during the growing periods and the yield has been seriously affected by drought stresses for a long time [1]. Quantitative analysis of yield loss caused by water stresses is the basis for rational allocation of water resources and it is important criterion for rational water use efficiency.
However, there are a wide variety of component factors for yield loss such as droughts, floods, plant diseases and insect pests, insufficient fertility, heat waves, therefore, there is a complex mechanism among them. In addition, synergistic effects of factors are also common which including drought and locusts. Considering the above-mentioned factors, there are a lot of difficulties in determining the effects of drought on maize yield. Field experiment is the most simple and traditional method to understand the influencing mechanism. Therefore, in order to study the effect of different drought stresses during different growth stages on the final product, it needs doing large-scale and long-term experiments. However, these require a lot of manpower, material and financial resources and it is also time-consuming [2]. Furthermore, drought effects on maize yield varies with strength and lasting time of drought stress, growing stage, as well as the compensation effect after rehydration [3][4][5][6]. Considering all these factors, there were great limitations in field experiments.
With the development and application of crop model, this problem is being solved step by step. Decision Support System for Agrotechnology Transfer (DSSAT) [7] is one of the extensive application and highly praised crop model. The CERES (Crop Estimation through Resource and Environment Synthesis) model simulates the growth and development of crops including maize and wheat et al in response to meteorological and management factors. DSSAT-CERES has been used world wise under a wide range of climatic and soil conditions and it has been proven as a useful tool for determining management practices due to its outstanding performance in simulating the growth, biomass accumulation, yield and water resource use efficiency in response to various environmental factors and management. Lots of researchers simulated winter wheat, rice and maize response to irrigation management, such as deficit irrigation, water efficient utilization, conservation agriculture practices [8][9][10][11][12][13][14]. DSSAT models have been used in many regions of China in recent years. However, they have not been used in the Northern Huaihe Plain. In addition, the soil in the Plain is mainly lime concretion black soil, which has never been simulated by DSSAT models.

DSSAT CERES-Maize model
DSSAT-CERES model could simulate water balance, crop growing process, biomass and yield of maize, wheat, soybean, rice, millet and sorghum [10]. DSSAT-CERES-Maize model is one modular of DSSAT-CERES, which could simulate the effects of soil water, fertilizer conditions, field managements (sowing date, irrigation, different cultivation way, and fertilization et al.) and external environmental factors like temperature, water stress, wind speed and solar radiation on maize growth and yield. With the comprehensive consideration of crop genetic characteristics, soil, climate, and field management, DSSAT-CERES-Maize model has obvious advantages of simulating the influence of climate change, geographical condition change and management change on maize growth and yield. It can be used in all geographical areas, soil and climate conditions due to its less restrictions in its application.
The model was constituted by data module, simulation module, analysis module and tool module. This study focused on soil water and the yield, and computing method of crop yield is introduced below.
Where t represents the time, SL, SS and SR represent aging pare of leaf, stem and root, E is energy transfer, Pg is gross photosynthesis, Rm is maintenance respiration, which is calculated by Penning de Vries-SUCROS model [15], Kp represents adaptability of soil fertility, PGMAX (PAR) means response on photosynthetic active radiation (PAR=400-700 nm), fL is the response on LAI (0-1), fO is response on water supply (0-1), fN is response on nitrogen sink of leaf (0-1), fT is response on daily temperature (0-1), LEAF, STEM, ROOT and SO represent protein activity of leaf, stem, root and storage organ, respectively. DSSAT CERES-Maize model required different kinds of data, such as genotype coefficients of maize, soil data, daily meteorological data and field management data. The general input of the model and the data sources are shown in table 1, where P1, P2 are vegetatively accumulated temperature and photoperiod sensitivity coefficient, respectively, P5 is accumulated temperature from tasseling to mature period, and G2 and G3 represent grain number per plant corn and grain filling rate. Then we calibrated DSSAT-CERES-Maize model and evaluated the performance of the model in simulating maize yield under water stresses using field experiment datasets. Based on this, we simulated yield losses caused by water stress in Bengbu Station from 1961 to 2015. Clarifying the water stress as the unique influencing factor on maize yield and identifying the risk of losses caused by drought in Bengbu, rational evaluation and planning of irrigation and water conservancy facilities construction would be provided. Field experiments were conducted at Xinmaqiao experimental station (Lat. 33°09′ N, Long. 117°22′ E, elevation 19.7 m) in Anhui institute of hydraulic research, which is located in the Northern Huaihe Plain of Anhui Province. The area located in warm temperate semi humid monsoon climate, with mean annual precipitation of 911 mm (more than 60% is concentrated in June to September) and evaporation of 916 mm, and the mean annual temperature is 14.2 ℃ . The main crops are summer maize and winter wheat. The main soil type is lime concretion black soil, a typical mid-low yield soil in the Northern Huaihe Plain, which is characterized by relatively high content of clay with poor drainage and water holding capacity. Under this climate and soil background, the area is prone to drought and flood during summer maize growth season.
The soil pH is 7.4 with middle fertility (table 2). The field water-holding capacity and saturated water content is 0.298 and 0.355, with the wilting point of 0.164 and effective water content of 0.134,  Experiments were carried out in 6.75 m 2 (2.7 m×2.5 m) test-pits under rain-proof shelter. Soil depth was 180 cm with filtering layer and water supply/drainage pipeline system at the soil bottoms. In order to monitor soil moisture at any time, moisture detectors were placed at 40 cm depth of the soil. Summer maize was planted by dry seed method on June 10, 2013. In each test-pit 6 rows of maize seeds were sowed and the space between the rows was 50 cm. 9 maize seeds were sown in each row and the space between each maize crop was 30 cm, which is equivalent to 80000 plants per hectare. The maize crop was harvested on September 15, 2013 and the growth season lasts 98 days. Nitrogen, Phosphorus and Potassium Fertilizers were applied at the rate of 180 Kg N ha-1, 90 Kg P ha-1 and 90 Kg K ha-1. During the whole growth season the rain-proof shelter was opened in sunny days and closed in rainy days. The growing season was divided into four stages-seeding stage, such as seeding, jointing, headingfilling and matured stage, which were indexed as Ⅰ, Ⅱ, Ⅲ and Ⅳ, respectively. The control factor was soil water content in different growing stages of maize. Long term water control tests indicated that lower limits of the suitable water content at each stage were 65%, 70%, 75% and 70% of soil water holding capacity in lime concretion black soil. The water was available for maize which was generally the effective water content, which was 0.134 in the tested soil. Therefore, in order to better reflect the difficulty for the crop to use water and the water stress grades, the effective water content was separated into different sections. The grade classification of available water with soil moisture percentage in field capacity was shown in table 3. According to the table 3, it can be seen that the lower limits of four stages are 22%, 33%, 44% and 33% available water. Each test-pit was irrigated up to 50% of available water on June 1 in order to keep water content in each test-pits coincident at the beginning of the experiments. According to the lower limits of suitable water content (θLi, i=Ⅰ, Ⅱ, Ⅲ, Ⅳ), three water stress scenarios were set, mild drought, 1 grade lower than the grade of θLi (5% lower than θLi); moderate drought, 3 grades lower than the grade of θLi (15% Water content at moisture-control growth stage in each treatment maintains within the water grade which corresponds to the drought scenario-when water content was less than the lower limit of the water grade (GLi, i=1, 2, 3, …...9), it would be irrigated to the upper limit (GUi, i=1, 2, 3, …...9), with sprinkling irrigation method and the water use efficiency was 0.8. While water content at the other stages maintain within the θLi and the corresponding GUi, when water content was less than the θLi, it would be irrigated to the GUi. Taking the treatment of moderate drought at jointing stage as an example, θL2 was 0.21 (70% of water capacity), with the available water of 33% and the suitable water grade 2. Due to drought classification standard, water grade of moderate drought at jointing stage was 5 and water content should be controlled at (0.164, 0.177], when water content was less than 0.164, it would be irrigated to 0.177. As θL1, θL2, and θL3, were 0.194, 0.224 and 0.209, with the water grades of 3, 1 and 2, the moister at seeding stage, heading-filling stage and mature stage should be maintain at (

Model calibration and validation
In order to improve the model simulation performance, model calibration is considered as an important process. To evaluate the model performance, the simulated values of grain yields was compared with the measured values. All samples were collected from our field experiments. In order to analyze model fitting performance, we compared the results of simulated with these of measured grain yields under different drought treatments. Based on the above-mentioned data, we choose some indices to evaluate the fitting degree of model, such as the coefficient of determination (r 2 ), normalized Root Mean Square Error (nRMSE), coefficient of residual mass (CRM) [16], index of agreement (D-index) [17], and Nash-Sutcliffe coefficient (E). All indices measures the fitting degree (the mean of measured data, M) between simulated (Ei) and measured (Mi) data. For nRMSE, the value of the nRMSE was less than 10%, the fitting degree is very good. The nRMSE was greater than 10% but less than 20% which was considered as good. When the nRMSE was greater than 20%, the fitting degree of model was general or bad [18].
The value of CRM was a minus representing that simulated value was larger than measured value, and the value of CRM was more than zero representing that simulated value was less than measured value.
The value of Nash-Sutcliffe efficiencies (E) was 1 representing s perfect fitting degree of model between measured and simulated data. When E was less than 0, the mean value of measured data was considered as a better predicator than simulated data.

Model calibration and validation
Based on experimental datasets, we applied Generalized Likelihood Uncertainty Estimation (GLUE) method to calibrate the model. The GLUE method was considered as a separate tool by R programming language embed into DSSAT model. We simulated 2000, 4000, 6000, 8000 and 10000 times to estimate the values of the five genetic coefficients by using GLUE method after determining the parameter of crop (Maize) and experiment processing (drought). Many times of experiment showed that the results were good by simulating 6000 times, and we obtained the values of the five genetic coefficients for maize as showed in table 5. The simulated model was evaluated using field experiments data of summer maize yield in response to different drought treatments. Based on experimental datasets, we compared the variable of measured and simulated grain yields to validate the calibrated DSSAT CERES-Maize model. In order to validate summer maize yield performance of the validated model, we calculated the value of above statistic operation parameters based on the grain yields as shown in table 6. For the validation, most of nRMSE were less 20%, which indicated that the simulated and measured grain yields fitted each other good. With the D-index and E close to 1, the fitting degree of the calibrated model was perfect. The regression of simulated and measured grain yield indicated a good agreement with most of r 2 higher than 0.98. In addition, the CRM test showed that there were some negative values and some positive values but all values were close to 0, results indicated slight overestimation or underestimation of grain yields.  In addition, data of simulated and measured yield were plotted for comparison as shown in figure 2 during the growing conditions of different drought treatments, respectively. Results indicated that the calibrated model simulated grain yields and measured grain yields fitted each other quite well in response to different drought scenarios. YLP in maize yield caused by drought under different drought scenarios in different growing stages were shown in figure 3. Excepting failure of emergence under severe drought at seeding stage, YLP of the other treatments ranged from 2% to 70%. YLP in seven out of twelve treatments were higher than 20%, and four of them were higher than 40%, treatment 3, 9, 6 and 8. After suffering from consistent severe drought at stage Ⅰ , YLP would reach 100% due to the failure of emergence. Besides, the biggest YLP occurred in severe drought at stage Ⅱ and Ⅲ, which was around 70% and 50%. Some studies also showed that stage Ⅲ was the critical water requirement stage for summer maize [1,[19][20][21][22][23][24], which was the period for corn storage capacity building and expanding.
Simulated losses percentages under mild drought were higher than these of measured in all the growing stages, on the contrary, simulated data under moderate drought were lower than these of measured in each stage. Under severe drought, simulate results were lower than these of measured at stage Ⅱ, stage Ⅲ and stage Ⅳ, while both simulated and measured YLP at stageⅠwas 100%. Higher simulate yield loss under mild drought might be caused by the ill-conceived of DSSAT-CERES-Maize model about the yield promotion of mild drought stress and the compensation effect after rehydration. On the other hand, lower simulate yield loss under moderate and severe drought indicated that the model might underestimate the negative effect of drought on maize yield.
Many researchers studied the reasons of yield loss caused by drought stress [4,[25][26][27][28]. Hao and Mei [6] emphasized that drought stress cut down photosynthesis rate (PR) and transpiration rate (TR) and then cause decreasing in summer maize yield. In addition, the reduction degree varied with growing stage, drought stress and rehydration timing. The PR reduced 38.8-45.7% and 11.2-36.2% at stage Ⅲ and Ⅱ , with the reduction in TR of 45.6-55.9% and 29.7-52.1%. After rewatering, PR recovered to 62.0-80.0% and 75.6-89.6% at stage Ⅲ and Ⅱ, while TR recovered to 78.1-84.2% and 82.1-92.1%. Beyond that, Geng and Yan [29] found that recovery of soil microorganism, which played an important role in maintaining soil ecosystem productivity [30], varied according to the drought stress. Briefly, the reduction of PR, TR and soil productivity caused drought stress and their insufficient recovery after rehydration resulted in the loss of maize yield, while the differences between them led to difference between yield losses. The precipitations of the first three growth stages were significantly lower than the mean value in both 1966 and 1994, with very low rainfall at the fourth stage in 1966 and a much higher rainfall in 1994. However, there was no significant difference between two years' yield loss. We came to the conclusion that compensation of rehydration at the fourth stage after long-term severe drought stress was very little, due to the excessive damage of vegetative growth and storage capacity building and expanding at the first three stages. Precipitation at stage Ⅰ, Ⅱ and Ⅳ were very little in 1964, but precipitation in stage Ⅲ was much larger than the mean value with large yield compensation effect, therefore, the loss percentage was not significant, which was consistent with the findings of many other researches. Cakir [31] indicated that compensation effects on the yield of rehydration at flowering stage after experiencing drought stress at vegetative growth stage was high, while yield compensation effects of rehydration after encountering drought stress at silking and filling stage was very low. Hao [6] found that re-watering after short period of time (mild) drought could replenish soil moisture in time and promote utilization of deep soil water, while re-hydration after long time (severe) drought could not completely restore deep soil water because of over consumption during drought, which causes a negative water balance. Precipitations at all stages in both 1978 and 1966 were much less than the mean value, while at stage Ⅲ in 1966 rainfall was four times higher than that of 1978, resulting in more than double yield loss percentage of 1978, which also indicated that stage Ⅲ was the most critical period for yield formatting.
There were 8 years out of all years that the loss percentage was negative, which means that the yield under rain-fed was higher than that of under suitable water content. In both 2005 and 1961, rainfall in stage Ⅰ was lower than the mean value, while precipitation in stage Ⅱ , Ⅲ and Ⅳ was larger than the mean. The yield increased might gained from the overcompensation of in time rehydration after appropriate drought stress in seeding stage. The conception of crop overcompensation originated from the leaves being picked and increased in grain yield [32,33], which implied increasing in the amount of biomass and yield after suffering from harsh conditions like water stress, insect pest, disease, etc.
Besides, the determination of suitable soil water content was unreasonable. Suitable water content was affected by meteorological elements such as temperature and solar radiation. The present study used the same suitable water content to simulate maize yield from 1961 to 2015, due to climate backgrounds were different, results might not be in conformity with the actual.   In view of parameters of summer maize growth and yield validated model, the performance of simulated model was considered to be perfect. Results indicated that the calibrated model simulated grain yields and measured grain yields fitted each other quite well in response to different drought scenarios.  Simulated losses percentage under mild drought were higher than these of measured in all the growing stages, on the contrary, simulated data under moderate drought were lower than these of measured in each stage. Under severe drought, simulate data were lower than these of measured in stage Ⅱ, stage Ⅲ and stage Ⅳ, while both simulated and measured YLP in stage Ⅰwere 100%.  Yield loss percentages caused by water stress from 1961 to 2015 in Bengbu Station were simulated. There were 4, 4, 1, 0, 2 and 1 years that loss percentage ranges from 10-20, 20-30, 30-40, 40-50, 50-60 and 60-70, respectively.  There were 8 years out of all years that the loss percentage was negative, which means that the yield under rain-fed condition was higher than that of suitable water content. Higher maize yield might be gained from the overcompensation of rehydration after appropriate drought stress. Under the conditions of this study, maize yield losses caused by drought of the other meteorological station in Northern Huaihe Plain could be simulated and the risk distribution of the Plain would be mapped. Based on this, rational allocation of water resources, which would assist the Northern Huaihe Plain with highest maize yield and water use efficiency, could be established.