Simulation of maize drought degree in Xi"an City based on cusp catastrophe model

Hi-to Chen ,Ji He ,Wen-chun Wng ,,Xio-nn Chen

a School of Water Resources,North China University of Water Resources and Electric Power,Zhengzhou 450045,China

b Construction and Administration Bureau of South-to-North Water Diversion Middle Route Project,Beijing 100038,China

Received 11 February 2020;accepted 10 June 2020 Available online 24 March 2021

Abstract Drought generally has significant impacts on crops.It is essential to quantitatively evaluate the relationship between crop production and drought degree to provide technical support for drought disaster prevention.In this study,a drought degree index that can reflect the changes in precipitation,evapotranspiration,and soil moisture was developed on the basis of crop yield reduction rate.Four drought scenarios were set up to simulate the effects of meteorological drought on drought degree of crops at different growth stages.A cusp catastrophe model was constructed to analyze the mutation characteristics of the drought degree of maize at different growth stages under different meteorological drought conditions.Xi"an City in China was selected as the study area,and summer maize was selected as the research crop.Precipitation and crop yield data from 1951 to 2010 were used as the fundamental data to investigate drought degree mutation of summer maize.The results show that,under the meteorological drought conditions at the emergence-jointing stage,drought degree may change abruptly,and soil moisture content at the sowingemergence,jointing-tasseling,and tasseling-mature stages should be kept higher than 39%.? 2021 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Cusp catastrophe;Drought degree;Crop growth period;Soil moisture content;Maize

1.Introduction

Drought is one of the most common and serious types of natural disaster.It is far more severe than other meteorological disasters(Trenberth et al.,2014).China is a large agricultural country,and drought impacts agriculture significantly.Serious and catastrophic droughts occurred in China in 24 of the years from 1951 to 2010,and 11 of these droughts occurred during the period from 1990 to 2010(Weng and Yan,2010).From 2004 to 2015,the annual direct economic loss due to droughts was 64.07 billion yuan,second only to losses caused by heavy rains and floods.China is also the most populous country with drought-hazardous areas.Nearly 100 million people are threatened by drought all year round(Zhao et al.,2021).

Drought and flood disasters have become a research hotspot in the field of catastrophology(Cui,2016).A large number of studies have been carried out.Based on meteorological factors(e.g.,air temperature and precipitation),several drought indices have been developed,including the precipitation anomaly percentage index(Mohammad et al.,2020),precipitation-temperature homogenization index(Wu et al.,2004),standardized precipitation index(McKee et al.,1993),standardized precipitation-evapotranspiration index(Vicente-Serrano et al.,2010),Z index(Wu et al.,2001),and Palmer index(Edossa et al.,2016).The thresholds and spatiotemporal distribution characteristics of agricultural drought and flood disasters have also been studied using the water profit and loss index(Wang et al.,2013)and Mann-Kendall trend analysis(Ashraf et al.,2020).A few statistical methods,such as the moving average model(Shi et al.,2008)and logistic function(Hao et al.,2007)have been adopted to simulate the trends of crop yields and quantify the impacts of droughts and floods on crop production.

Various definitions of agricultural drought have been proposed from different aspects.With regard to crop production,agricultural drought refers to the phenomenon of crop damage resulting from abnormal water content deficit under certain natural and artificial conditions.The study of agricultural drought should focus on the following issues:(1)research should be conducted for specific regions;(2)easily obtained evaluation factors should be considered;(3)agricultural drought assessment should reflect crop yield information;(4)different yields under the same drought conditions should be studied;and(5)the relationship between water supply and crop growth processes should be investigated.From these perspectives,this study mainly examined catastrophic crop yields or drought degree.A large number of phenomena show that catastrophe can be triggered by drought disasters.According to crop growth characteristics,the growth period can be divided into several stages.Crop yields can vary,and there can be a gap in yields,even when water supply is consistent at a certain growth stage over different years.The reason for this phenomenon is the mismatch between water supply and water demand during the crop growth period.Analysis of drought catastrophes in certain regions and identification of critical factors in the catastrophe may provide theoretical support for the design of local irrigation systems and help to increase crop yields and farmers’income.As a branch of nonlinear theory,the catastrophe theory was first proposed by Rene(1992).He defined the overall jump of the internal state of a system as a sudden change,and it was characterized by continuous processes and a discontinuous result.The catastrophe theory studies the phenomena and laws of transition from one stable state to another stable state.As a powerful mathematical tool for studying system evolution,it can explain sudden phenomena in nature to a certain extent,and has broad application prospects in the fields of physics,chemistry,biology,and engineering technology.At present,the catastrophe analysis method has been applied extensively.Angelis et al.(2015)used the cusp catastrophe model to study the attractiveness of banks.Sadeghfam et al.(2017)described the cusp catastrophe characteristics of forced hydraulic jumps.It is also feasible to analyze the degree of crop drought catastrophe using the catastrophe theory.

Notably,the change of soil moisture during the crop growth period directly affects crop yields,and soil moisture is the key factor controlling the water deficit for crop growth.Ways of potentially maintaining soil water content have been extensively investigated(Feng et al.,2018;Han et al.,2018;Cheng et al.,2018).The relationship between soil moisture and drought severity has been assessed as well.One general approach is to use historical conditions as a baseline to define the statistical characteristics of soil moisture at each location,and a relative indicator of drought severity has been developed(Carrao et al.,2016;Rahmani et al.,2016).However,this approach requires historical soil moisture data to define the baseline statistical conditions(Champagne et al.,2015).Another approach uses soil water constants,such as field capacity and wilting point,or the available measured field capacity to determine water storage for certain soil(Mishra et al.,2017).These studies are highly significant to the efficient utilization of water resources,crop yield augmentation,and drought mitigation.However,the quantitative relationship between soil moisture content and its corresponding drought severity cannot be obtained in a short period because of large data inputs and computational resource consumption.It is essential to construct a rational mathematical model,through which numerical simulation of soil moisture content and drought severity can be achieved.

Agricultural drought assessment is necessary for Shaanxi Province,which is a major agricultural province in China.Xi"an City,the capital city of Shaanxi,is located in the central part of the province.It is a typical region for agricultural drought studies.The main food crop in Xi"an City is maize,with an annual cultivated area of approximately 1.845×105hm2,accounting for three quarters of the total cultivated land area.Therefore,Xi"an City was selected as the study area,and maize was selected as the main crop type for agricultural drought assessment.The main objectives of this study were(1)to develop a drought index that can reflect the changes in precipitation,evapotranspiration,and soil moisture content based on the crop yield reduction rate;(2)to set up several drought scenarios to simulate the effects of meteorological droughts on agricultural drought severity at different crop growth stages;and(3)to construct the cusp catastrophe potential function between the relative water shortage rate and drought at different growth stages,and to use the cusp catastrophe model to analyze the mutation characteristics of crop drought under different meteorological drought conditions.We hope the findings of this study can provide a basis for optimizing the irrigation system for maize cultivation in Xi"an City,stabilizing crop production,and increasing the income of local farmers.

2.Materials and methods

2.1.Study area

Xi"an City is located in the Guanzhong Basin of the Weihe River Basin,with the longitude band of 107°40′E－109°49′E and a latitude band of 33°39′N－34°44′N.The administrative region of Xi"an City is approximately 204 km long from east to west and approximately 116 km wide from south to north.The total area of Xi"an City is 10 096.81 km2,and the city governs 11 districts and two counties.The planned downtown area is 865 km2,and the urban built-up area is 565.75 km2.Located in the warm temperate zone,the plains region of Xi"an City has a semi-humid continental monsoon climate and four distinct seasons.The annual average air temperature ranges from 13.0°C to 13.7°C,and the mean annual precipitation ranges from 522.4 mm to 719.5 mm,with an increasing trend from north to south.July and September are the two peak precipitation months.The annual sunlight duration ranges from 1 646.1 h to 2 114.9 h.

Winter wheat and summer maize are the two most important crop types in Xi"an City.Currently,the local maize plantation area exceeds 1 500 km2.However,due to uneven distribution and the temporal variation of precipitation,drought is the most severe disaster affecting maize yields.

2.2.Data source

The data for maize drought assessment include meteorological data,crop data,and soil data.Precipitation data were collected from the website of the National Meteorological Information Center of China(http://data.cma.cn),and included the daily precipitation records from 1951 to 2010 at six weather stations:the Pucheng,Wugong,Xingping,Fuping,Weinan,and Yangling stations(Fig.1).The areal mean precipitation of the study area was derived using the Thiessen polygon method(Xue et al.,2019).Soil type data were downloaded from the website of the Institute of Soil Science,Chinese Academy of Sciences(http://www.issas.ac.cn),and soil parameters such as soil porosity,field capacity,and wilting point were obtained.According to Li and Fan(2015),the maize growth period in Xi"an City is from June 7 to September 30.

2.3.Catastrophe theory and cusp catastrophe model

2.3.1.Catastrophe theory

As a branch of nonlinear theory,catastrophe theory arises from bifurcation theory,singularity theory,and the concept of structural stability.It uses a mathematical model to explore the universal law of skipping changes of status in dynamic systems(Ling,1984).Elementary mutations,which occur under the control of four factors in three dimensions of space and one dimension of time,can be categorized simply as seven basic types with different properties,i.e.,the fold,cusp,swallowtail,butterfly,hyperbolic,elliptic,and parabolic mutations.Of these,cusp mutation is the most widely used and has been successfully applied to many mutation-related problems.

2.3.2.Cusp catastrophe model

The standard potential function of the cusp catastrophe model(V(x))is expressed as follows:

Fig.1.Study area.

whereuandvare control variables,andxis a state variable.According to the standard potential function,V(x)is a twoparameter function controlled byuandv.

The equilibrium curve equation(catastrophe manifold)is as follows:

The minimum value of the point on the curve denotes a stable equilibrium of system energy,and the maximum value represents an unstable equilibrium.In these cases,the force that the system bears reaches a balance.The equilibrium curve is divided into upper,middle,and lower lobes(Xiao et al.,2020).The system status can be represented by coordination of any points on the upper or lower lobe of the equilibrium curve,while the middle lobe corresponds to the single point set of the unstable equation.

The bifurcation setΔis given as follows:

Being observable and located in the control space,the bifurcation set is the most important in most applications,where all jumps in the system take place.Eq.(3)is often used as the standard to judge system stability:ifΔ>0,the system has a stable status and has a sole status parameter;ifΔ<0,the system has an unstable status and has three possible status parameters;and ifΔ=0,the system has a critical stable status,and a micro-disturbance may cause system catastrophe.

2.4.Drought degree index and drought scenarios

2.4.1.Drought degree index based on crop yield reduction rate

Agricultural drought is the phenomenon leading to crop damage due to abnormal water deficit under certain natural and artificial conditions.In combination with the extensively used Jensen model,the drought degree index based on the crop yield reduction rate has been developed(Chen et al.,2009):

whereDris the crop drought degree index based on yield reduction rate;ETaiis the actual crop evapotranspiration at theith growth stage(mm);ETmiis the maximum evapotranspiration at theith growth stage(mm);λiis the sensitive coefficient at theith growth stage;Kciis the crop coefficient at theith growth stage;ET0iis the reference crop evapotranspiration at theith growth stage(mm),which can be calculated with the Penman formula;andK（θ）is the modified soil moisture coefficient,also known as the water stress coefficient,which can be calculated as follows(Li,1999):

whereθis the actual average soil moisture content in a soil layer(%),Awis the ratio of the available soil water content to the maximum available water content that can be stored,θxis the critical soil moisture content(%),andθwis the wilting point(%).

In the aforementioned equations,the crop growth period should be divided into several growth stages based on the actual conditions of the study area and theSpecifications for Irrigation Experiment(SL13－2015),which were issued by Ministry of Water Resources of China.The crop sensitivity coefficient and soil constants were estimated according to available research results in China(Chen et al.,2009).In this method,the modified soil moisture coefficient,which considers the crop root zone as one soil layer,is used to calculate actual crop evapotranspiration.However,given that the relationship between soil moisture and crop growth is dynamic,the soil layer should be generalized into at least two layers(Chen et al.,2009).

2.4.2.Actual crop evapotranspiration based on two-layer soil model

Given that the influence of soil moisture on crop growth changes dynamically,the soil is divided into two layers.The upper layer reaches from the soil surface to the depth ofZmin,whereZminis the minimum designed soil layer depth for the crop growth stage(m);and the lower layer covers the soil depth fromZmintoZi,whereZiis the depth of the planned moisture layer at theith growth stage(m).The two-layer soil model assumes that evapotranspiration consumes soil moisture in the upper soil layer at first.When the upper layer cannot meet water supply demand,evapotranspiration continues in the lower layer.Water supply first recharges the upper soil layer.After the upper layer reaches its storage capacity,the rest of the replenished water supplies the lower soil layer.Soil water content is calculated at daily intervals,as follows(Lei et al.,1988):

whereΔWtis the difference between potential evapotranspiration and water supply on dayt(mm),ETmtis the potential evapotranspiration on dayt(mm),Ptis the precipitation on dayt(mm),Xtis the irrigation volume on dayt(mm),Ktis the water recharged from the aquifer on dayt(mm),andWbtis the total water supply on dayt(mm).

When water supply is less than potential evapotranspiration(ΔWt>0),all the supplied water is consumed as evapotranspiration,and the total daily actual evapotranspiration of crops is as follows:

whereETatis the actual evapotranspiration on dayt(mm);ETastandETaxtare the evapotranspiration from the upper and lower soil layers on dayt,respectively(mm);andθstandθxtare the soil moisture contents in the upper and lower soil layers on dayt,respectively(%).When water supply exceeds potential evapotranspiration(ΔWt<0),the supplied water can meet evapotranspiration demand,and the daily actual evapotranspiration is equal to the potential evapotranspiration.In the two-layer soil model,the storage-excess runoff scheme,which assumes that runoff is produced when soil water content reaches field capacity,is used to calculate runoff,and the water balance method is used to calculate soil moisture content on the next day.

2.4.3.Drought scenarios

The growth period of maize can be divided into four stages:the sowing-emergence,emergence-jointing,jointing-tasseling,and tasseling-mature stages(Table 1).The initial soil moisture content and water supply at each growth stage affect the initial soil moisture content at the next growth stage.Therefore,soil moisture conditions at all growth stages jointly determine the drought status of maize.If irrigation does not occur at one growth stage but does occur at the other three growth stages,the impact of meteorological drought on regional crop droughts in the growth period in the region can be quantified.In this context,this study developed a simulation scheme based on drought scenarios.Four drought scenarios were set up to simulate the changes in the drought degree of summer maize when meteorological drought occurs at different growth stages.As shown in Table 1,scenarios I,II,III,and IV assume that no irrigation occurs at the sowing-emergence,emergence-jointing,jointingtasseling,and tasseling-mature stages,respectively,and that irrigation does occur at the other three stages.In each drought scenario,several groups of irrigation plans were designed by setting different irrigation volumes at different growth stages,and the drought status of crops at different growth stages was analyzed under different irrigation intensity conditions.

2.5.Drought evaluation model based on cusp catastrophe theory

In this study,the cusp catastrophe theory was used to establish the potential function of the cusp catastrophe modelof drought degree at different growth stages under various water deficit conditions:

Table 1Drought scenarios at each growth stage.

whereDriis the crop drought degree index derived from the yield reduction rate when water deficit occurs at theith growth stage;andWriis the relative water deficiency ratio at theith growth stage,which is expressed as follows:

whereWciis the water supply at theith growth stage,andWniis the water demand at theith growth stage.Based on observed precipitation data from 1951 to 2010,data sets of the relative water deficiency ratio and drought degree time series were generated,and a quartic polynomial was used to fit the potential function of the cusp catastrophe model based on these data sets:

wherea0,a1,a2,a3,anda4are the coefficients for polynomial fitting.Afterwards,the Tschirnhaus transformation,a type of polynomial transformation(Dong et al.,2017),was conducted to transform Eq.(15)into the standard potential function of the cusp catastrophe model,which is as follows:

whereris a state variable representing drought degree;andcis a constant,which does not affect catastrophe evaluation and can be neglected.

2.6.Model parameters

The growth period of summer maize in Xi"an City was divided into four growth stages:the sowing-emergence(from June 7 to June 20),emergence-jointing(from June 21 to July 20),jointing-tasseling(from July 21 to August 21)and tasseling-mature(from August 22 to September 30)stages(Li and Fan,2015).At these growth stages,the sensitivity coefficients were 0.34,0.40,0.72,and 0.50,respectively;the designed wetting soil depths were 0.3 m,0.5 m,0.5 m,and 0.6 m,respectively;and the potential evapotranspiration values were 51.87 mm,92.65 mm,118.40 mm,and 54.18 mm,respectively.Soil porosity reflects soil conditions,and it is related to soil texture,human disturbance(e.g.,plowing and fertilization),and soil animal intervention.Generally,the porosity of loam ranges from 50% to 65%.Soil texture in this region is medium loam.According to relevant data,soil porosity in the study area was set as 50%,and field capacity was considered to be 70%of soil porosity.The critical soil moisture content and wilting point were defined as 70% and 30% of field capacity,respectively.Given that the local groundwater aquifer is deep below the land surface,the recharge from the aquifer to the designed soil layers was not considered.The accumulated precipitation at each growth stage in Xi"an City from 1951 to 2010 is shown in Fig.2.

3.Results

3.1.Drought degree of maize based on yield reduction rate in different drought scenarios

In accordance with precipitation,weather,soil,and crop growth characteristics in Xi"an City,the drought indices of maize in different scenarios were calculated according to Eqs.(4)through(12).The direct control factor affecting crop evapotranspiration is soil moisture content.According to the drought model,severe droughts occur when soil moisture content is below the wilting point,and no drought occurs when soil moisture content exceeds critical soil moisture content.In this study,we maintained the soil moisture content of the studied soil layers within the range between the wilting point and the critical soil moisture content(21%－49%),and the mutation phenomena of agricultural droughts under general drought conditions were investigated.Several drought scenarios were established by changing the controlled soil moisture content before sowing and in the irrigation period.The controlled soil moisture content was the minimum soil moisture content in the irrigation period.When natural soil moisture content in the irrigation period was higher than the controlled soil moisture content,irrigation was not conducted.Given that soil moisture content before sowing affects final crop yields,this study used the soil moisture content before sowing as an additional control variable.

This study conducted numerical experiments for two cases of drought degree simulations.Case 1 assumed that soil moisture content before sowing was 21% and considered soil moisture content at irrigation stages to be 39%.Case 2 assumed that soil moisture content before sowing was 40%and considered soil moisture content at irrigation stages to be 33%.The annual series of the simulated drought degree from 1951 to 2010 in the two cases are shown in Fig.3.

Fig.2.Accumulated precipitation at each maize growth stage in Xi"an City from 1951 to 2010.

Fig.3.Calculated results of maize drought degree in Case 1 and Case 2.

The magnitude of soil moisture content before sowing significantly influences drought degree and directly affects maize growth status at the sowing-emergence stage.When soil moisture content before sowing was very low,the drought degree of maize was still high in Scenario I(Fig.3(a)).With the soil moisture content of 21% before sowing and the controlled soil moisture content of 39%at irrigation stages,the mean drought degree in Scenario I was 0.31.In the case of soil moisture contents of 40% and 33% before sowing and at irrigation stages,respectively,the mean drought degree decreased to 0.02(Fig.3(b)).

As the soil moisture content before sowing increases,the jointing-tasseling growth stage has the most significant impact on the drought degree of maize.For example,when the soil moisture contents before sowing and in the irrigation stages were maintained to be 40%and 33%,respectively,the average drought degree of maize under Scenario III was 0.17(Fig.3(b)).By contrast,the mean drought degree values in other three drought scenarios were only 0.018,0.036,and 0.017.

Soil moisture content at the tasseling-mature stage does not significantly affect drought degree.As shown in Fig.3,when the soil moisture content before sowing and the controlled soil moisture content at the first three irrigation stages were maintained at 21% and 39%,respectively,the mean drought degree in Scenario IV was 0.006.When soil moisture content values before sowing and in the irrigation stages were 40%and 33%,respectively,the mean drought degree in Scenario IV was 0.017.

3.2.Drought catastrophe in different drought scenarios

Based on the calculated drought degree,the drought catastrophe levels of maize in different drought scenarios were analyzed.Calculation results show that under local natural conditions,Scenario II leads to catastrophe.Table 2 shows the calculation results of Scenario II when the soil moisture content before sowing was 30%,and soil moisture contents at the irrigation stage were 28%,33%,and 39%,respectively.

When the soil moisture content before sowing was 30%and the soil moisture content at the irrigation stage was 28%,Δ>0,and the maize drought did not have a mutation.In other words,the maize drought degree and water deficiency ratio had a single corresponding relationship.When the soil moisture content before sowing was 30% and the soil moisture content at the irrigation stage was 33%,Δ<0,and the maize drought led to a catastrophe.Specifically,the same water deficiency ratio may have different drought degrees at this stage.When the soil moisture content before sowing was 30%and the soil moisture content at the irrigation stage was 39%,Δ>0,and the maize drought did not have a mutation.In other words,the maize drought degree and water deficiency ratio had a single corresponding relationship.

Regardless of the variation of soil moisture content at the early stage of sowing,drought mutations might exist in Scenario II.Table 3 shows that in certain intervals of soil moisture content,mutation occurs.According to the drought model adopted in this study,the soil moisture content at each growth stage is related to the soil moisture content at the end of previous stage and precipitation at this stage.In Scenario II,irrigation was not conducted at the emergence-jointing stage,and a low soil moisture content appeared at the end of this stage.When the minimum soil moisture content was controlled at the other three growth stages,the entire growth period was in a state of water deficit,likely leading to a severe and stable drought situation.In the case of a high controlled minimum soil moisture content at the other three growth stages,even if precipitation during the emergence-jointing stage was low,soil moisture content at this stage was notvery low,due to the influence of soil moisture content at the end of previous stage.Thus,the drought degree was low and stable without mutations.When the minimum soil moisture content was controlled at a middle-level interval at the other three growth stages,soil moisture content at each growth stage allowed for change triggered by the influence of precipitation.Therefore,the drought degree corresponding to the same relative water shortage rate at the emergence-jointing stage may show enormous variation,which may cause drought mutation.Notably,the crop sensitivity coefficient was highest at the jointing-tasseling stage,meaning it is the most important.If water supply is adequate at this stage,drought will not be too severe,and vice versa.

Table 2Calculation results of drought scenario II.

Table 3Drought mutation at different soil moisture levels in Scenario II.

4.Discussion

In this study,summer maize in Xi"an City was selected as the research object,and a cusp mutation-based drought degree model was established to quantify the mutation characteristics of the maize drought degree.The results show that this model reflects the relationship between the relative water shortage rate and drought degree at different growth stages of summer maize.

An important procedure in constructing the drought mutation potential function is the selection of suitable drought indices.The crop water deficit index(CWDI)comprehensively reflects water deficit and agricultural drought in the crop growing season.As one of the widely used agricultural drought indicators in China,CWDI is highly effective in agricultural drought monitoring and evaluation in different regions.Li et al.(2019)used it to investigate spring maize drought catastrophes in Northeast China.However,the index only denotes the severity of crop water deficit,with no link between crop yield and water deficit.The catastrophe theorybased evaluation method has been widely used in many fields,but there are not many cases of agricultural drought evaluation using this approach.We conducted case study on this aspect.This study developed a drought index based on the yield reduction rate along with the crop water production function,which favorably established the relationship between water deficit and crop yields.This study also constructed a catastrophe potential function with a relative water deficit rate as the state variable.The approach adopted in this study can reflect the impact of slight changes in water deficit during crop growth on crop yields.

Overall,this study can provide a scientific basis for optimizing the irrigation system of maize cultivation in Xi"an to stabilize food production and increase the income of local farmers.We hope that the proposed approach can be promoted and applied in other regions.

5.Conclusions

This study used a cusp catastrophe-based approach to simulate the drought degree of maize in the Xi"an region of China from 1951 to 2010.The main conclusions are as follows:

(1)Under local natural conditions,soil moisture content before sowing strongly affects the drought degree of maize.The low pre-sowing soil moisture content significantly influences the soil moisture content at the sowing-emergence stage,leading to a high drought degree of maize in the growth season.In the case of high pre-sowing soil moisture content and in the designed drought scenarios,the drought degree of maize is alleviated,even with no irrigation at the sowing-emergence stage.

(2)As the pre-sowing soil moisture content increases,the controlled soil moisture content at the jointing-tasseling stage significantly affects the drought degree of maize.By contrast,the variation of soil moisture content at the tasseling-mature stage has trivial effects on drought degree.

(3)In the case of meteorological drought at the emergencejointing stage,the drought degree of maize was unstable in the study area.When soil moisture content at the other three stages was maintained within a range of 28%－39%,drought mutations occurred.In order to prevent the occurrence of drought instability and maintain a low drought degree,soil moisture content at the other three stages should be kept higher than 39%.

Declaration of competing interest

The authors declare no conflicts of interest.