Soil Water Balance and Water Use Efficiency of Rain-fed Maize under a Cool Temperate Climate as Modeled by the AquaCrop

The AquaCrop model has been widely studied and examined for its feasibility and applic ability in simulating the crop growth – water relationship under tropical and warm temperate. How ever, the model is rarely tested under cool temperate climates. As the second largest agricultural ar ea of China, the Sanjiang Plain is characterized with relatively lower accumulative temperature and higher annual precipitation, showing typical features of a sub-humid and cool temperate climate. Th is study employed the AquaCrop model to compute soil water balance and water use efficiency of rain-fed maize in the Sanjiang Plain using a 5-year monitoring dataset (2011 – 2015). The results demonstrated an acceptable performance of AquaCrop in depicting soil water content, biomass accu mulation and grain yield. Soil water balance including soil water content, evapotranspiration and pr ecipitation was described throughout the growing period. The hysteresis of the daily soil water cont ent as responses to daily precipitation was revealed. Water use efficiency for the observed rain-fed maize increased with rising accumulative temperature and decreased with rising atmospheric CO2 c oncentration. This study provided a perspective for the extensive application of the AquaCrop mode l and the precise simulation in water dynamics under sub-humid and cool temperate climates.


Introduction
China has been facing increasingly severe water scar city. With insufficient water resources to meet rising water consumption, over-withdrawal of both surface water and groundwater has occurred in many areas of northern and eastern China. Meanwhile, poor wat er quality caused by pollution further exacerbates the lack of water availability in water-scarce areas. The water shortages and the poor water quality are inter acting with each other and threatening China's food security, economic development, and life quality [1].
As an important commodity grain production base in China, the water resources of Sanjiang Plain regi on have a key role in the scale of agricultural prod uction. After large-scale development about nearly 50 years, the cultivated land area of Sanjiang Plain ha s increased from 7.86×10 5 hm 2 in 1949 to 3.83×10 6 hm 2 in 2008 [2]. In early 1980s, restricted by the dev elopment of agricultural technology and economic fa ctors, there was to be beginning a widespread chang e from dry land to paddy land. In particular, since 1 990, the Sanjiang Plain has implemented the compre hensive agricultural development and management m easures of "flood control by rice planting". The rice planting area has increased from 2.17×10 5 hm 2 in 19 90 to 1.42×10 6 hm 2 in 2008 [3], and there is still a t endency of continuous expansion. Field management translated from the typical dry land farming by rainfed to paddy land farming based on groundwater irri gation, which would inevitably lead to a substantial increase for agricultural water demand. As one of th e crops with a large number of water consumption, the large-scale rice planting has increased the deman d for water resources in agriculture. Thus the water supply capacity of the region has been facing a hug e challenge. In addition, with the expansion of rice planting area, uncontrolled and unplanned over-exploi tation of groundwater, groundwater dynamic balance has been destroyed. Furthermore, a large number phe nomenon of "hanging pumps" (a pump that is suspe nded in a wellbore using a wire rope, winch and fra me) and groundwater depression occur each year [4]. As for the dry land of crop rotation between soybea n and corn without irrigation, the water resources cri sis is increasingly becoming more severe. For other aspects(including the local business, industrial produc tion, wetland ecological environment as well as resid ents) competing with agriculture for water resources, there are more demands for water resources. And th e evidence provided by the deteriorating natural vege tation in this region indicates that the available wate r resources was over-utilized. Therefore, in order to maintain the overall benefit of the local economy an d preserve the integrity of the natural environment, t he quantification of the crop water consumption and the crop grain yield in this area is an essential step toward the agricultural development of more efficient systems for reasonable allocation of the limited wat er resources in Sanjiang Plain of Northeast China [4].
With regard to the effect of water content on cro p growth, different researchers have different researc h methods for different research environments. Yingx in Xie et al has selected the experimental field in th e North China Plain and has carried out three group s of experiments (including no irrigation (rain-fed) d uring the whole growth period, once irrigation only at jointing stage as well as twice respective irrigatio n at jointing and flowering stages) to analyze the eff ects of water conditions on water consumption, dry matter accumulation and grain yield of Wheat. Resul ts showed that increasing irrigation times significantl y increased mean grain yield of wheat [1]. E.K. Liu et al has conducted a mobile rain shelter experiment using winter wheat cultivar to assess the effects of d ifferent levels of water stress on photosynthetic chara cteristics, dry matter translocation and water use effi ciency (WUE) in the Shijiazhuang 8(one drought res istant cultivars) and Yanmai 20(a drought sensitive c ultivars)at different growth stages. The establishment of water stress conditions was achieved by setting fo ur degrees of irrigation including 40-45% (severe str ess), 55-60% (moderate stress), 65-70% (mild stress) and 75-80% (full irrigation) in three different growth periods of recovering-jointing stage, jointing -flower ing stage and grain-filling stage, respectively. The re sults indicated that mild soil water stress can improv e grain yields and WUE. The way of researching th e effects of water stress on crop growth by applying different levels of water stress to different crops gr owth stages has been adopted by more researchers [5]. Yang Gao et al has researched the effect of moistu re content on wheat growth and yield in North Chin a Plain by the calculation and analysis of the respon se of evapotranspiration(ET a ), crop coefficient(K cb ) an d water use efficiency(WUE) to different irrigation p ractice in different growth stages of wheat based on the application of the SIMDualKc model. There wer e differences in the growth of wheat under different irrigation amount. For the appropriate amount of irri gation, it can promote the growth of wheat; Howeve r, the higher or lower amount of irrigation does not take advantage of wheat growth. Meanwhile, the wat er demand of wheat in different growth period has i ts own characteristics. During the grain filling period of vegetative growth and reproductive growth, there is a higher demand for irrigation amount [4]. Based on STICS 4.0 simulated crop growth as well as soil water and nitrogen balances driven by daily climatic data, Philippe D EBAEKE carried out numerical exp eriments on winter wheat in order to evaluate droug ht escape and crop rationing in three climatic enviro nments:Avignon, Meknès (Morocco) and Toulouse. R esults indicated that the contribution of soil evaporati on to total water use was reduced by rapid canopy closure (fast-growing cultivar and high plant density); meanwhile, water stress during grain filling was mo re frequent with excessive plant density; furthermore, with irrigation or under wetter conditions, yield sho uld be improved by maximizing early canopy closur e and lengthening the growing season period [6]. At present, in the quantitative study of the effect of wa ter stress on crop growth process and crop yield, a considerable number of researchers has started to use the relevant model, such as the application of WOF OST model in C.A.van Diepen's research [7], the app lication of Penma-Monteith model in A. Tegos's rese arch [6]. Most traditional models of crop water demand a nalysis are built on the basis of a certain crop or m acroscopic analysis, which neglect regional crop alloc ation and the difference of water demand in differen t crop growing periods. The AquaCrop model is a c rop water productivity simulation model developed b y the Food and Agriculture Organization (FAO) of t he United Nations [7]. The AquaCrop model [8] is fre e and practitioner oriented for the users. And there i s a certain reference for a wide range of regional re search. The aim of AquaCrop is to simulate crop yi eld response to water, and is applicable for address conditions where water is a principal limiting factor for crop growth and production. The AquaCrop uses a relatively small number of explicit and mostly intu itive parameters and input variables requiring simple methods for their derivation [9]. In the simulation pr ocess of AquaCrop, the simulations of crop growth and development are implemented with daily time st eps, using temperature, precipitation, evapotranspiratio n, carbon dioxide concentration, crop growth system, etc. The applicability of AquaCrop to simulate growt h and yields for different crops has been widely test ed by numerous experts around the world in differen t environments and all have reported positive results, e.g., barley [10], teff, maize [7], potato1 [2], wheat [13].
The Advantage of AquaCrop model lies in maintain ing a balance between accuracy, robustness, however, it has not been tested in Northern east China wher e crop yields is often limited by moisture deficit. W hether it can be used to optimize the planting/sowin g and irrigation systems scheme in Northern east chi na remains unknown.
Most of the research has focused on the dry land s, which is capable of being given different levels o f irrigation, and has analysed its changes about relat ed parameters in different growth stages, based on r elevant model, such as biomass, crop evapotranspirati on and canopy development etc. Evidence clearly sh ows this is possible. Less researches were reported s o far about study on the effect of the water conditio n characteristics in arid area itself on crop growth d uring the stage of crop growth. And at present, the application of AquaCrop model is less in China, esp ecially for the application of Sanjiang plain research.
Therefore, based on the above content, this paper h as three research aspects based on AquaCrop model:  The study area is Bawujiu Farm, located in the northeast portion of the Sanjiang Plain in Heilongjia ng Province provided for our research project, which is located at 47°18′-47°50′N, 133°50′-134°33′E. The Bawujiu Farm has an area of 1356 km 2 . This farm keeps a temperate continental monsoon climate, with a mean annual temperature of 2.94°C，an average fr ost-free period of 138 day and mean annual precipit ation of 600mm. More than 60% of the annual preci pitation is concentrated between July and September. The farm was covered with extensive wetland and f orest before its establishment in 1956; since then it has been affected by widespread land reclamation [13].
According to the local land use policy, more virgin lands, such as wetland and forest, would be reclaime d as paddy land and dry land. The transformation of the Sanjiang Plain for grain production was achieve d at considerable cost to the environment. Constructi on of immense networks of drainage channels, pump ing stations, and flood control dikes have destroyed millions of hectares of peat land, further altering the water cycle of entire watersheds and destroying wet land biodiversity [14].

Crop management
The adjustment of crop pl anting structure has been changing for more than 30 years, and agricultural production has rapidly develop ed. The main changes reflected in three aspects: the accelerated adjustment of planting structure, strengthe ning of cultivation measures and improvement of pro duction management level. Planting structure adjusted from the traditional ternary planting structure of so ybean, wheat, corn to diversification planting structur e of rice, soybean, wheat, corn and other economic crops. On the application of cultivation techniques, s cientific planting and reasonable rotation system has been effectively implemented, the new technology ha s gradually been widely used. Furthermore, the agric ultural production has achieved modernagricultural pr oduction mode of formulationof technical measures, s tandardization of production management and field o peration standardization and on the whole [14]. In 19 90s, the land use situation of Sanjiang plain had bee n changed greatly due to the profound influence of t he change of grain production demand. It is the co mprehension of the conversion on dry landandpaddy field with time changing that has important guiding significance for regional food security in the Sanjian g plain of Northeast China. Especially in recent year s, the transformation from dry land to paddy land as well as from wetland to paddy land hasgradually b ecome the main form of agricultural land use status changes, which would inevitably lead to a substantial increase foragricultural water demand [15].

AquaCrop model description
AquaCrop is a water-driven, canopy level, engineerin g type model [9]. It pays particular emphasis to simu lating yield response to water under both irrigated a nd rain-fed conditions. The calculation steps and pro cedures of Aqua Crop have been described by [9]. A quaCrop model roughly simulates the four stages of crop growth (namely, the emergence stage; vegetative stage; flowering stage; the yield formation and ripe ning stage). The model mainly simulated the soil wa ter condition in the root zone using a water balance approach. The soil water condition together with the canopy cover information was then used to partition the ET to actual crop transpiration and soil evaporati on(according to the standard of FAO). The canopy c over development was modeled using first order kine tics, albeit with facilities for accommodating stress (water, temperature, etc.) induced retardations. Then t he biomass production was estimated from the actual crop transpiration using a normalized form of the water productivity (WP) parameter. The normalization of WP for climate in AquaCrop is based on the at mospheric evaporative demand as defined by ET O an d the CO 2 concentration of the atmosphere. The goal is to make the WP value in the model specific for each crop applicable to diverse location and seasons, including future climate scenarios. [16].
Aqua Crop has four sub-model components: (i) t he soil (water balance); (ii) the crop (development, g rowth and yield); (iii) the atmosphere(temperature, ra infall, evapotranspiration (ET) and carbon dioxide (C O 2 ) concentration); and (iv) the management (major agronomic practices such as planting dates, fertiliser application and irrigation if any). Aqua Crop calculat es a daily water balance that includes all the incomi ng and outgoing water fluxes (infiltration, runoff, de ep percolation, evaporation and transpiration) and cha nges in soil water content. The advantage with Aqua Crop is that it requires only a minimum of input d ata, which are readily available or can easily be coll ected. Aqua Crop has default values for several crop parameters that it uses for simulating different crop s including wheat, however, some of these parameter s are not universal and thus have to be adjusted for local conditions, cultivars and management practice [1 7]. For a more detailed description of the AquaCrop model see [7][9][18].

Model parameters and data of inputs and outputs
The model inputs included meteorological conditions, initial values of the model parameters, soil characte ristics and management practices like irrigation sched ules and water conservation measures such as mulchi ng. Apart from the Harvest Index (HI) and the wate r productivity (WP), Aqua Crop has several paramet ers for which conservative estimates were available i n the User Manual for most commonly cultivated cr ops; those may generally be used without any furthe r calibration [19]. Crop input parameters used in the Aqua Crop model were either obtained or calculated from [20]. Crop-specific but non-location-specific par ameters for major agricultural crops including maize have been determined and validated in varying locati ons by the FAO and are provided as default values in the model. These parameters are referred to as "c onservative" because they do not change with geogra phic location, management practices and time, and th ey were determined with data from favourable and n on-limiting conditions but remain applicable for stres s conditions via their modulation by stress response functions [21]. The other parameters are cultivar speci fic or less conservative and are affected by the clim ate, field management or conditions in the soil profil e and thus have to be provided by the user (user-sp ecific). However, if not available, Aqua Crop can est imate them (e.g., seeding date, plant density, etc.). I n this study, these parameters were determined from values for the five year at this study area presented in Table 1. The simulation outputs included the evol ution of soil water depletion in the root zone, the d evelopment of the green canopy cover, and the daily transpiration; thesoil water balance in a given perio d; the accumulation of biomass and the final yield.

Model calibration and validation
Models should be carefully calibrated and validated before being used in practice [22]. During the proce ss of calibration, it is necessary to change the mode l's parameters inorder to obtain simulated results that matchup well with preexisting experimental data. In contrast, during the process of validation, simulated results generated using the model without any modifi cation of the parameters are compared to independen t experimental data [23].

2.4.1.The process of calibration
In this study, base d on the purpose of calibration, the simulated yield was compared with the observed yield. The yield wa s simulated by adjusting the initial soil water conten t, characteristics of soil horizons and evaporation rel ated parameters at the time keeping the harvest inde x (HI) parameters a fixed value. Then the harvest in dex was adjusted basing on the good simulation of yield. During the process, it is mainly to assign initi al value for reference HI, the water stress sensitivity to HI with different growth stages by comparing wi th the measured yield. Finally, there is a comparison between the observed data and simulated data in so il moisture content, by comparison of values of RR MSE and EF with the evaluation criterion for Furthe r description. The above process was repeated many times until the simulation value in line with measure d value. Some of parameter were assumed to be conservat ive according to Aqua Crop manual appendix [18]. The parameters changed little with the sowing date,fi eld management, and the experiment location. When using the data of the 2011 growth season to calibrat e the model, the main parameters were first assigned with the default values, and then were modified unt il the simulated data were more consistent to the ob served data. The values of these parameters are locat ed in proposed ranges by FAO. Table 1 lists the val ues assigned to specific parameters in order to simul ate the responses of dry land crop.

Assessment of Aqua Crop performance
To assess the performance of Aqua Crop during cali bration and validation, the relative root mean square error (RRMSE), the Nash-Sutcliffe modeling efficien cy were computed as in Eqs. (2)  The relative error (RE) in the simulated final yiel d was also evaluated using: (4) where RE is the relative error (%), Y O and Y S are th e observed and simulated final yields (t/ha), respecti vely.
The relative root mean square error (RRMSE) is used to evaluate the relative error of the model, and the smaller the value, the better the simulation. The quality of the simulation is considered to be excell ent if the RRMSE is less than 0.10, good if it is b etween 0.10 and 0.20, fair if it is between 0.20 and 0.30, and poor if it is above 0.30 [25]. The efficienc y of the model (EF) is used to describe the overall predictive ability of the model, which indicates the r obustness of the model. The value of EF ranges fro m 0 to 1 with higher values indicating a better agre ement. The simulated results is considered to be exc ellent if the RRMSE is higher than 0.95 excellent, g ood if it is between 0.80 and 0.95, fair if it is betw een 0.60 and 0.80, and poor if it is above 0.65.
The relative error (RE) of the simulated yield re flects the accuracy of the simulation, whose value ra nges from 0-100%, considered to be good if it is le ss than 5%, fair if it is between 5% and 10%, and poor if it is above 10% . The lower the value of R E, the higher the accuracy of the simulatio [26].

Crop water use efficiency (WUE)
The increase of crop water use efficiency (WUE) is an indirect response to the increase of crop yield. In recent years, with the profound study of water stres s, many researchers had developed various definition of WUE. The most popular WUE are the following two types.
The conventional equation of WUE Y/ET is used to estimate the crop water use efficiency, as follow: where Y is the crop yield (kg/hm 2 ) and ET is the c rop evapotranspiration (mm), or the crop water cons umption (mm). The WUE Y/ET of dry matter levels fo cused on evaluating the crop water use status for ult imately producing grain yield. In addition, in this pa per, we used former researchers' WUE B/Tr that was c alculated as the ratio between biomass (kg/hm 2 ) and transpiration (mm), Equation is as follows: Tr B WUE B/Tr = (6) where B is the crop biomass (kg/hm 2 ) and Tr is the crop transpiration (mm). The WUE B/ET of biocoenosis level aimed at analysing of the water use status of crops during the whole growth period. Fig.2, Aqua Crop was calibrated by comparison of the averaged soil moisture in 0-100 cm depth between the simulat ed and measured data for dry land. In general, the s imulated total soil water content values follow closel y the trend of the observed values although there ar e cases where the errors are much higher than the s tandard deviation [25] of the observed values. The si mulated values were basically in accordance with the observations, with the simulated moisture content re sponding to water input through precipitation, follow ed by a gradual decrease due to the continuous evap otranspiration. At the end of the crop growth period, the simulation results showed a downward bias rela tive to the observation, such as 2015. The reason m ay be that the model overestimates the root uptake a nd transpiration at the latter growth stages due to th e inclusion of the non-transpiring dry leaves. But in 2013 there was a upward bias relative to the observ ation; the most appropriate reason is due to the com bination of a sudden precipitation event and a signifi cantly decline of the absorption of water and the ev apotranspiration of crops in the later stage of growth.

Model calibration As shown in
In terms of soil moisture assessment, the RRMSE value ranged from 0.131 to 0.189 during 2011-2015 (except 2012), indicting a good simulation accuracy. In B.Andarzian's research, the calculated RRMSE of wheat soil moisture content were 0.035 for full irrig ation and 0.04 for water deficit irrigation, respectivel y, indicating a excellent quality of the simulation [12]. The model efficiency was all above 0.696 and som e were near 0.805, indicting a fair simulation accura cy. In Dirk Raes's research of soil water balance, th e statistical analysis resulted in an EF of 0.21 for Mornag and an EF of 0.83 for the Kou Valley [26]. The calibration results of yield for dry land crop (Ta ble 2) showed the relative errors (RE) of yield for dry land crop were average 2.14% and ranged from 0.175 to 5.26%, except for the value of RE (5.26%) slightly higher than 5% in 2011, which indicated a good quality of the simulation. In Jiang Li's study, RE of yield for seed maize in 2013 were nearly 8.7 2%, which were less than the RE fair standard, indi cating a moderate ability to simulate crop yield chan ges [16]. Therefore Aqua Crop model had a moderate ability to depict the fluctuation of soil moisture and crop yield in this region.  (Table 2) showed the RE of yiel d for dry land maize in 2012 were 3.05%, less than the RE good standard. Knowing the results from Ji ang Li and Ting Zhu's study, this is a reasonable re sult [16]. The above results indicate a moderate perf ormance of this model and capable to be used for p redicting the water consumption and yield of dry lan d crop in the study area, shown in Fig 3, Table 2.

Soil water balance
With the simulation results by Aqua Crop, we analy zed the soil water balance of the dry land maize in the study area. Fig 5 showed the evolution of the a ccumulation of evapotranspiration (ET) and water co ntent in total soil profile (WCT) as simulated by Aq ua Crop, as well as the events of precipitation for d ry land maize in different stages of 2011-2015. As shown in Figure 5, the precipitation distributi on was uneven in different growing seasons during 2011-2015; especially in2011 and 2015, the uneven distribution of precipitation is more remarkable; but most of the precipitation was still concentrated in th e critical stage of crop growth, which was in favor of crop normal growing. Andthe great mass of preci pitation was still concentrated in the whole summer, in according with P patterns of temperate monsoon c limate region.
In 2011-2013, the variation of ET during crop gr owing stages was not stable, butfrom stage 2 to stag e 4, there was shown a pattern: the variation trend of ET first gradually increased at stage 2, and reach ed the peak at stage 3, finally started to reduce unti l to the lowest value at stage 4, which was consiste nt with the discipline of crop biomass growing and crop yield produced, meanwhile could reflect the law of crop growing and changing at some extent. T he reason for the lowest ET during the stage 4 was due to the fallen leaves which became yellow and was paved on the surface and thus reduce the ET. I n addition, due to the instability of P, ET in 2014 a nd 2015 also showed a anomalous variation trend, e specially in the stage 3 of 2015, ET was at the low est value instead. Previous studies for maize have fo und that 30.49% of ET occurred during the vegetati ve stage 2, remaining more than half (51.80%) durin g flowering Stage 3, the lowest (8.0%) amount durin g the yield formation and ripening stage (Stage 4), a nd the rest (9.71%) of ET occurred during Stage 1 (Hanafi et al., 2010). There was a similarity between the two researches. The reason might be that theoc currence of meteorological conditions at low tempera tures besides accumulated low precipitation, which w as caused by the combined effects of temperate cont inental climate and temperature monsoon climate in t heSiberia region north for the study area (theSanjian g plain of Northeast China) [30]. Moreover, it could be foundthat the maximum value of ET was closely followed by that of P or showed a slight hysteresis. The reason might be that the infiltration of natural p recipitation into the soil and the absorption and utili zation of crops were a cumulative process over time [32].
As shown in Figure 5, the overall trend of WCT gently increased from stage 1 to stage 4, and relati vely reached the maximum at the stage 4, whose pa ttern also conforms to the pattern of the large water requirement during the early and middle stage of cro p growth as well as the low waterrequirement durin g the later and last stage [33]. The variation of WC T was stable on the whole, however WCT always ti mely responds to the peak of P and the valleys of ET. Previous research found that the presence of flu ctuations in ET tended to increase the variance of s oil moisture dynamics to some extent, while the stab le variation trend of ET always relatively reduced th e water losses of WCT [34]. In fact, the effect of E T and precipitation on the whole variation trend of WCT was not remarkable, which indicated that the original water content of soilin the study area was r elatively high and could generally meet the basic de mand of crop growth [35]. For the above three factors, there were two differ ent data types: the mean and the sum. Thus, we ha d carried out the multivariable linear regression anal ysis between the standardized WUE Y/T , the standardiz ed WUE B/ET and the six kinds of standardized data (Wr SD.Avg : standardized average Wr, Wr SD.Cum : stand ardized cumulative Wr, P SD.Cum : standardized cumulati ve precipitation, P SD.Avg : standardized average precipit ation, T SD.Cum : standardized cumulative temperature, T SD.Avg : standardized average temperature) in different growth stage. The results were shown in table 5. In addition, as shown in Fig 6, duo to beginning with Biomass production in stage 2, there was a data defi ciency in stage 1. Similarly, duo to beginning with yield formation in stage 3, there was a data deficien cy in stage 1 and stage 2.
As shown in Table 5, the results of analysis was satisfactory with obtaining two regression equations. In Table 5, it could be seen that the P-value of the m were both 0.03, less than 0.05, which indicated t he regression analysis was statistically significant. An d the multiple determination coefficient (R 2 ) were 0. 698 and 0.893, which meant explaining 69.8% and 8 9.3% of independent variables in the total dependent variable, thus there were a explanatory of moderate and superior level for dependent variables in regressi on equation. In addition, it could be found that both of the standardized partial regression coefficients ha d a high significance that the value of them were le ss than 0.05 or 0.01.
Firstly, it could be found that both of WUE B/ET a nd WUE Y/T had a positive correlation with Wr Avg , h owever the contribution rates of Wr Avg to WUE B/ET and WUE Y/T were different owing to the standardized partial regression coefficients of 1.06 and 0.9, respe ctively. It was thus obvious that Wr was critical to t he increase of WUE B/ET and WUE Y/T . As previous st udies had found, although mild water shortage at joi nting stage and male stage was beneficial to stimulat e physiological mechanism development and slightly improve water use efficiency, moderate water abunda nce was still the key factor to improve crop water u se efficiency throughout the whole growth stage [41].
On the contrary, they had a negative correlation with P Cum , and the contribution rates of P Cum to th em were also different due to the standardized partia l regression coefficients of -0.46 and -0.88, respectiv ely. Apparently, P Cum restrained the increase of WU E B/ET and WUE Y/T . The previous studies on maize an d sorghum had found that WUE would decrease wit h the increases of cumulative precipitation in Wester n Kenya. The reason might be that seen from the a bove studied part, the temporal distribution of precip itation was not uneven with moderate rain and heav y rain in the study area, which significantly increase d soil water content in total profile during a long ti me, thus the normal growth of crop root was inhibit ed, ultimately almost resulting in crop growth stagna ted at a certain period of time [42].
In addition, the correlation between WUE B/ET and T Avg as well as WUE Y/T and T Cum were positive, a nd the standardized partial regression coefficients wer e 0.95 and 1.05 which indicated have different contr ibution rates. Although both T Avg and T Cum had a positive impact on WUE B/ET and WUE Y/T , respectivel y, there was a difference that the emphasis of the in dependent variables affecting dependent variables was different. The possible reason were as follow: (1) i n the stage 1, at high temperature condition, the wat er absorption amount, water absorption rate and obvi ously increased [43] and the duration of seeds germin ation was substantially shortened, which accelerated t he growth of crops. Since biomass and yield were n ot produced at this stage, the impact of temperature on WUE could not be seen at this stage. (2) In the stage 2, only biomass began to be produced. The te mperature mainly affected the growth of roots, stems, leaves. If the temperature moderately went up, the duration of stage would be shortened, which to som e extent, accelerated the growth of crops and reduce the total transpiration [44]. Therefore, as seen in equ ation 6, if the growth of cumulative biomass was no rmal, the WUE B/ET was increased relative to the decr ease of Tr. (3) At the stage 3 and 4 (late summer o r autumn), because precipitation and temperature sign ificantly decreased, and the crop growth stage gradua lly got into flowering period as well as ripen stage (grain stage), meanwhile the requirement of crop gro wth for moisture content gradually decreased, and th e temperature became the key factors for grain yield formation. During the period, the biomass growth was about to go into contabescence, whose reasons were complex and diverse, yet the reduction of temp erature still occupied a considerable contribution rate. While the increase of cumulative yield and the dec rease of ET led to the increase of WUE Y/T , what's more, WUE Y/T gradually increased with the decrease of ET resulting from the temperature reduction. Table 5 The Regression analysis result between soil water content in effective root zone (Wr) , precipitation (P), temperature (T) and crop water use efficiency for yield (WUE Y/ET ), crop water use efficiency for yield (WUE B/Tr ) at coenosis level during four growth stage

Conclusion
In the current study, the AquaCrop model version 5. 0 was used to simulate maize yield and soil water c ontent under no irrigation condition of the Sanjiang Plain, Northeast China. The AquaCrop model was ca librated by soil water content and was validated by soil water content in different depths. In addition, th e agreement between modelled and observed maize yield was satisfactory with the proper value of R 2 a nd RE. Results showed that both maize yield and so il water content could be simulated with relative acc uracy using AquaCrop.
For no irrigated dry land, precipitation was the k ey factor influencing soil water supplement. Althoug h the factors about influencing ET were various and complicated and the ET response to the variation of P shown a certain hysteresis, the maximum value of ET varied with that of P. The precipitation greatly v aried, but as long as the change of ET was stable, t he soil water balance would not be broken.
In the absence of precipitation events, biomass an d grain yield increased with the increase soil moistu re content. However, when precipitation occurred, es pecially with the increase of precipitation intensity, t he growth rate of biomass gradually decreased, while the growth rate of grain yield shown the trend of f irst the ascending and then the descending, which ha d a profound significance for irrigation arrangements.