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1. Institute of Millet Crops, Hebei Academy of Agriculture and Forestry Sciences/National Millet Improvement Center/Key Laboratory of Coarse Cereals Research in Hebei Province, Shijiazhuang 050035, China; 2. Shenze Agricultural Bureau, Shenze 052560, China; 3. Shijiazhuang Agricultural Bureau, Shijiazhuang 050021, China

1 Introduction

China is one of the largest countries lacking water in the world[1], especially in north China[2]. Deficiency of water resources often causes huge economic loss for agriculture and animal husbandry production[3]. Water resource deficiency has become restraining factor of sustainable development of agriculture and animal husbandry in arid and semi-arid regions of China[4-5]. Millet is environment-friendly grain and forage crop with low water and fertilizer consumption. In Inner Mongolia and Bashang of Hebei, more and more farmers and herdsmen spontaneously cultivate millet for fodder production[6]. In recent years, with fast development of animal husbandry, the phenomenon of animal increase and grass decrease always occurs[7-9]. The plantation of fodder millet in autumn fallow field could sufficiently use natural resources during August-October, such as sunshine, heat, air, water and soil, and increase high-quality millet straw, which has important significances for improving multiple cropping index and easing the status that winter and spring fodder is insufficient. When developing and using autumn fallow field in arid and semi-arid regions of north China, it is an urgent problem of fodder millet production to be solved to study how to improve water use efficiency. Many researches show that it is an important channel of improving water use efficiency of crops to develop water-saving agriculture and animal husbandry, select high-yield crops with low water consumption and the coupling technique of water and fertilizer[1,10-11]. The research about coupling relationship between water and fertilizer of summer millet by Wang Weilingetal.[12]showed that ideal grain yield of millet could be obtained when there was certain precipitation. The research about water use efficiency of millet hybrid by Fan Xiuwuetal.[13]showed that significant yield increase could be obtained when irrigating 30 mm of water at jointing stage of millet hybrid. Zhang Yaqietal.[14-15]studied the relationship between nitrogen fertilizer, potassium fertilizer and water use efficiency of hybrid millet, and results showed that too high or low application amounts of nitrogen and potassium fertilizers (400 kg/hm2) could cause lower water use efficiency, but reasonable utilization of nitrogen fertilizer or potassium fertilizer could coordinate the relationship between fertilizer and water and improve water use efficiency. Saseendranetal.[16]explored the impact of water on yield increase potential of fodder millet sown in summer, and determined cultivation model of triticale-millet under semi-arid environment of Canada. Liang Zhanqietal.[17]irrigated green millet for five times, and accumulative water irrigation amount was 1725 m3/hm2, and hay yield could reach 9.75-12.60 t/hm2. The above researches play huge role in scientific research and technical promotion of millet. At present, the researches about water use efficiency of millet at home and abroad are dominated by grain production[18], and there is no report on water use rate of fodder millet harvested by stages in autumn fallow field. So, taking "Jigu 18" (Setariaitlicacv., Jigu No.18) as the tested crop, and using design case of orthogonal rotation combination, the best proportion of sowing rate, water and fertilizer (N, P and K) coupling and its impact on water use efficiency of fodder millet were studied by establishing regression model and optimization analysis. The research aimed to find the best case of sowing rate, water and fertilizer of fodder millet being used efficiently, and provide theoretic basis and technical support for rational adjustment of sowing rate, water and fertilizer of fodder millet grown in autumn fallow field.

2 Materials and methods

2.1Testmaterials

2.1.1Test variety. The test fodder millet variety was "Jigu 18", which was provided by Institute of Millet Crops, Hebei Academy of Agriculture and Forestry Sciences.

2.1.2Test fertilizers. Urea containing 46% of pure N, DAP containing 46% of P2O5and potassium chloride containing 62% of K2O were all provided by Shijiazhuang Sanyuan Fertilizer Co., Ltd.

2.1.3Test soil. Test soil was light loam soil, which was collected from reserved spring blank land of test station of Institute of Millet Crops, Hebei Academy of Agriculture and Forestry Sciences(previous crop was millet), and soil of 0-20 cm tillage layer was selected. The test station is in Xima Town of Shijiazhuang Development Zone (37°58′ N, 114°36′ E), and altitude is 65 m, with 1.75% of soil organic matter, 1.11 g/kg total nitrogen, 79.4 mg/kg of alkali solution nitrogen, 19.5 mg/kg of available phosphorus, 103.9 mg/kg of available potassium and pH of 7.6.

2.2TestinstrumentsanddevicesSoil moisture meter(TZS-ⅡW)was used to measure soil moisture. Large flower pot(polytene plastic)had 40 cm of diameter, 32 cm of height and 1256.00 cm2of pot mouth area. Electric anti-rain canopy used steel frame and plastic cover, 48 m long, 13.2 m wide and 5.4 m high, and ZDY 21-4 type of generator (0.8 kW) was used for anti-rain regulation.

2.3Testmethods

2.3.1Test design. Pot experiment was conducted in electric anti-rain canopy of test station of Institute of Millet Crops, Hebei Academy of Agriculture and Forestry Sciences. During whole growth period of fodder millet, electric anti-rain canopy was used for anti-rain regulation. The canopy was covered when raining and moved away without rain, to guarantee that fodder millet was at natural status under the situation without rain. Using orthogonal rotation combination design[19-22], and selecting five major factors: water, nitrogen fertilizer, phosphate fertilizer, potassium fertilizer and sowing rate, experiment was arranged. Orthogonal table 25type of 1/2 factor test treatment’s Mc=16, and star point test treatment’s Mr=10, while center point test treatment’s M0=10, with 36 treatments in total. There were three repeats, which was arrayed randomly. Level set and encode of test factors were shown as Table 1, and encode structure matrix of test design was shown as Table 2.

Table1Factorandlevelofpotexperimentofwaterandfertilizercoupling

LevelsCodingzjFactorsxjSoilmoisturex1∥%Ncontentx2∥g/potP2O5contentx3∥g/potK2Ocontentx4∥g/potSowingratex5∥g/potUpperasteriskarmγ235.004.712.354.710.942Upperlevel128.753.531.773.530.754Zerolevel022.502.351.182.350.565Lowerlevel-116.251.180.591.180.377Lowerasteriskarm-γ-210.000000.188SpaceΔj6.251.180.591.180.188EncodingformulaZj=xj-xj0ΔjZ1=x1-2256.25Z2=x2-2.351.18Z3=x3-1.180.59Z4=x4-2.351.18Z5=x5-0.5650.188

Table2Structurematrixoftest

No.Codingzjz1z2z3z4z5No.Codingzjz1z2z3z4z5No.Codingzjz1z2z3z4z511111113-1-111125000022111-1-114-1-11-1-1260000-2311-11-115-1-1-11-12700000411-1-1116-1-1-1-11280000051-111-11720000290000061-11-1118-20000300000071-1-1111902000310000081-1-1-1-1200-200032000009-1111-12100200330000010-111-112200-200340000011-11-1112300020350000012-11-1-1-124000-203600000

To simulate environmental condition of fodder millet growth in autumn fallow field to the maximum extent, millet was sown on August 21, 2014. Before sowing, it watered to make moisture, and soil moisture was measured. When soil moisture was 20%, the obtained test soil was mixed, crushed, screened by 3 mm of sieve and put into the pot; each pot was packed by 31 kg of soil, and soil thickness reached 25 cm after compaction, and sowing area of pot mouth was 0.1256 m2. When soil was packed into pot, each layer was 5 cm, and it was vibrated slightly after packing, and was floated and compacted by board, reaching the requirement of field tillage rake and compaction. According to test design, quantitative fertilization and sowing were conducted. When strip sowing, three rows were sown in each pot, with 15 cm of row distance. After sowing, 3 cm of soil was covered and compacted. It was ditched and fertilized in middle sowing row, and phosphate fertilizer and potassium fertilizer were taken as base fertilizer according to design, and nitrogen fertilizer was mixed evenly with phosphate fertilizer and potassium fertilizer according to 50% of design amount for base fertilizer. The residual 50% of nitrogen fertilizer was taken as successive fertilizer after jointing stage. After millet sprouting, the seedlings were not removed to record seedling number. Drought stress was conducted within 33 d after sowing[23-24], and then soil moisture in test pot was measured on September 24, October 8, October 15 and October 23. According to the measured soil moisture, referring to the set soil moisture of 10%, 16.25%, 22.5%, 28.75% and 35%, it should timely supplement water. Fodder millet was harvested on November 1.

2.3.2Measurement of water use efficiency. Before and after early frost, fodder millet was harvested to measure yield. It was cut at stem base of soil surface, and then set in nylon bag for weighing fresh weight. After air drying to water contents of stem and leaves ≤13%, dry weight was weighed, and water use efficiency was calculated[25].

3 Results and analysis

3.1ComparisonofwateruseefficiencyamongdifferenttreatmentcombinationsoffoddermilletanddeterminationofitsoptimizedcombinationSeen from Table 3, in 36 treatment combinations, water use efficiency of fodder millet harvested by stages among each treatment was different. Water use efficiency of treatment 12 reached 18.33 g/kg, which was the highest, and had insignificant difference with treatment 18 that water use efficiency ranked second and extremely significant difference with other treatments. Treatment 12 was determined as the optimal combination. Water use efficiency of treatment 18 was 15.40 g/kg, which had significant difference with that of treatment 33 (10.98 g/kg), treatment 36 (10.55 g/kg), treatment 34 (10.45 g/kg), treatment 7 (10.22 g/kg), treatment 13 (9.98 g/kg), treatment 14 (9.84 g/kg) and treatment 16 (9.82 g/kg), and extremelysignificant difference with other treatments. Treatment 18 was de-

Table3Wateruseefficiency

No.Dryweight∥g/potWaterconsumptionamount∥kg/potWateruseefficiency∥g/kg1152.8bcdeBCD20.18307.5703cdefghCDE2136.4efgCDEF19.10837.1392cdefghiE3127.7fghijDEFGH15.62578.1732cdefghCDE4169.6abcdABC20.05908.4564cdefghCDE583.4nopqJKL17.28974.8250ghiE6177.1abAB21.00978.4291cdefghCDE7188.2aA18.405710.221bcdeBCD8108.2hijklmnFGHIJK19.01535.6880fghiE928.0rM9.99402.8010iE1032.4rM7.22474.4785hiE1187.5mnopqJKL9.52909.1774cdefgCD12132.8efghDEFG7.244318.333aA13105.9ijklmnFGHIJK10.60409.9865bcdefBCD1492.4lmnopqIJKL9.39479.8364bcdefBCD1580.8opqJKL8.72809.2542cdefgCD1696.2lmnopHIJK9.79779.8188bcdefBCD17171.1abcABC27.08376.3194defghiE1871.1qL4.619015.403aAB19129.3efghiDEFG13.25779.7512cdefCD20133.5efgDEFG15.13838.8193cdefghCD21101.2klmnoGHIJK14.05337.2044cdefghiDE22147.1cdefBCDE16.08909.1442cdefgCD23110.0hijklmFGHIJ13.42308.1935cdefghCDE24139.3efgCDEF15.29339.1105cdefghCD25126.9fghijDEFGH15.00408.4622cdefghCDE2675.9pqKLM13.26805.7174efghiE27124.2fghijkDEFGHI14.45638.5965cdefghCDE28104.2jklmnoFGHIJK13.58837.6680cdefghCDE29109.2hijklmFGHIJ16.32676.6857cdefghiE30125.7fghijkDEFGH16.74007.5096cdefghCDE31110.3hijklmFGHIJ14.29107.7206cdefghCDE32129.4efghiDFFG13.21639.7883cdefCD33144.8defBCDE13.185310.980bBC34126.2fghijDEFGH12.079710.452bcdBCD35115.4ghijklEFGHI12.43109.2837cdefgCD36132.3efghDEFG12.544710.548bcBC

Note: The letters in the table showed vertical comparison, and lower-case and upper-case letters respectively showed significant difference ofP<0.05 andP<0.01 among treatments.

termined as the optimized combination. Water use efficiencies of other treatments were lower and declined from 9.79 to 2.80 g/kg, and the minimum was treatment 9 (2.80 g/kg). The combination with the highest water use efficiency was 16.25% of soil moisture, 3.53 g/pot of nitrogen (N) fertilizer application amount, 0.59 g/pot of phosphorus (P2O5) fertilizer application amount, 1.18 g/pot of potassium (K2O) fertilizer application amount and 0.377 g/pot of sowing rate, and the maximum hay yield was 132.8 g/pot, which was 55.4 g/pot lower than that of treatment 7 with the highest hay yield. The combination of highest hay yield was 28.75% of soil moisture, 1.18 g/pot of nitrogen (N) fertilizer application amount, 0.59 g/pot of phosphorus (P2O5) fertilizer application amount, 3.53 g/pot of potassium (K2O) fertilizer application amount and 0.754 g/pot of sowing rate, and its hay yield was 0.1882 kg/pot. Results showed that hay yield of the combination with the maximum water use efficiency was not the highest, so it could not purely seek the highest water use efficiency, and should value the benefit balance between hay yield and water use efficiency under different conditions.

3.2EstablishmentandtestofmathematicalmodelAccording to Table 3, using calculation principle of orthogonal rotation combination design with five factors, taking water use efficiency of fodder millet as target function(dependent variabley), and soil moisture, nitrogen fertilization rate, phosphate fertilization rate, potassium fertilization rate and sowing rate as independent variables (xj), via the calculation of SPSS 18.0, full-factor normative regression model of water use efficiency (y) to independent variable (xi) was obtained:

(1)

Seen from the model (1) of Table 4, the model’s complex correlation coefficientR=0.713, and determination coefficientR2=0.508. Significance test of regression mathematical model showed thatF=4.490, and significant valueSig.=0.000 (P<0.01), with extremely significant difference, which reflected that regression relationship between water use efficiency and main tested factors was extremely significant; loss fitting test of regression model showed thatFLf=3.195, and significant valueSig.=1.757 (P>0.05), with insignificant difference, showing that unknown factors had no significant impact on test results, and regression model and actual situation were fitted well, with obvious biological significance. Via backward regression method of SPSS 18.0 orthogonal rotation combination design, after eliminating regression coefficient of insignificant item of probability ≥0.100, normative regression model of significant item factor was obtained：

y=8.834-1.471x1-1.251x3+1.006x1x3+0.870x1x4+0.990x1x5-1.356x2x3+1.471x4x5

(2)

y=44.26-1.311x1-2.298x2-3.682x3-6.401x4-34.540x5+0.273x1x3+0.118x1x4+0.843x1x5-1.948x2x3+6.631x4x5

(3)

Table4Varianceanalysisandcorrelationcoefficient

ModelQuadraticsumdfMeansquareFSig.RR2Regression725.6922036.2854.4900.0000.7130.508Residual703.143878.082(1)Lossfitting(Lf)607.9935810.4833.1951.757Error(el)95.150293.281Total1428.835107Regression592.356784.62210.1160.0000.6440.415Residual836.4791008.365(2)Lossfitting(Lf)741.3297110.4413.1821.737Error(el)95.150293.281Total1428.835107

3.3DeterminingmainfactorsaffectingwateruseefficiencyoffoddermilletSeen from test results of Table 5,ttest of regression coefficient of mathematical model showed that difference between first term coefficients b1and b3and interaction term coefficients b23and b45was extremely significant, showing that the coupling of water, phosphate fertilizer and "nitrogen fertilizer+ phosphate fertilizer and potassium fertilizer +sowing rate" all had extremely significant impact on water use efficiency. The difference among interaction term coefficients b13, b14and b15was significant, showing that the coupling of "water+ phosphate fertilizer, water+ potassium fertilizer, water +sowing rate" had obvious impact on water use efficiency. Coefficients of other items all had insignificant difference, which had no obvious effect on water use efficiency. Influence sequence of single factor on water use efficiency wasx1>x3>x4>x5>x2, showing in five factors, soil moisture had the maximum impact on water use efficiency, followed by phosphate fertilizer, and nitrogen fertilizer, potassium fertilizer and sowing rate had no obvious impact. The influence sequence of coupling effect of interaction term with significant difference wasx45>x23>x13>x15>x14, namely "potassium fertilizer +sowing rate> nitrogen fertilizer + phosphate fertilizer > water+ phosphate fertilizer > water +sowing rate > water+ potassium fertilizer". Positive and negative signs of the coefficient showed its action direction. Positive sign showed that water use efficiency increased with the related item factor or interaction increased, while negative sign showed the related item factor or interaction had antagonism to water use efficiency.

Table5Regressioncoefficientanditssignificanceanalysis(ttest)

ModelNon-standardizedcoefficientBStandarderrorStandardcoefficientbetatSig.(1)Constant9.6920.72413.3920.000x1-1.4710.335-0.330-4.3900.000x200.0340.3350.0080.1010.920x3-1.2510.335-0.281-3.7320.000x4-0.5560.335-0.125-1.6600.101x50.3090.3350.0690.9210.359x1x20.3350.4100.0610.8160.417x1x31.0060.4100.1842.4520.016x1x40.8700.4100.1592.1200.037x1x50.9900.4100.1812.4120.018x2x3-1.3560.410-0.249-3.3050.001x2x4-0.6440.410-0.118-1.5690.120x3x40.0280.4100.0050.0670.946x3x50.5430.4100.0991.3230.189x4x51.4710.4100.2703.5840.001x110.4860.2900.1261.6740.098x220.0310.2900.0080.1070.915x33-0.2400.290-0.062-0.8260.411x44-0.1300.290-0.034-0.4470.656x55-0.4740.290-0.123-1.6320.106Repeat-0.4290.335-0.096-1.2810.203(2)Constant8.8340.27831.7420.000x1-1.4710.341-0.330-4.3150.000x3-1.2510.341-0.281-3.6690.000x1x31.0060.4170.1842.4100.018x1x40.8700.4170.1592.0840.040x1x50.9900.4170.1812.3710.020x2x3-1.3560.417-0.249-3.2490.002x4x51.4710.4170.2703.5230.001

3.5ResponsecurvedsurfaceanalysisofinteractioneffectofeachfactoraffectingwateruseefficiencyIn two-factor interaction item of the test, coefficients of nitrogen fertilizer+ potassium fertilizer (b23) and sowing rate + potassium fertilizer (b45) couplings had extremely significant difference, while coefficients of water+ phosphate fertilizer, water+ potassium fertilizer, water + sowing rate couplings had significant difference. By dimension reduction of the model (2), a group of sub-models of coupling effect of interaction item factors on water use efficiency could be obtained：water+ phosphate fertilizerY13=8.834-1.471X1-1.251X3+1.006X1X3; water +potassium fertilizerY14=8.834-1.471X1+0.870X1X4; water +sowing rateY15=8.834-1.471X1+0.990X1X5; nitrogen fertilizer + phosphate fertilizerY23=8.834-1.251X3-1.356X2X3; potassium fertilizer + sowing rateY45=8.834+1.471X4X5. According to the above sub-models, response curved surface charts of two-factor coupling effect to water use efficiency of fodder millet grown in autumn fallow yield were drawn (Fig.2-Fig.6).

Fig.1Influencesofsowingrate,waterandfertilizeronwateruseefficiency

Fig.2Responsesurfaceandcontourlineofwaterandphosphatefertilizercouplingtowateruseefficiency

3.5.1Influence of water and phosphate fertilizer coupling effect on water use efficiency of fodder millet. Fig.2a showed the influence of water and phosphate fertilizer coupling effect on water use efficiency of fodder millet.XandYaxes respectively showed encoding values of soil moisture and phosphate fertilizer, andYaxis showed water use efficiency of fodder millet. Fig.2b was contour line chart corresponding with response curved surface, and each coordinate point on response curved surface represented water use efficiency of fodder millet under different levels of water and phosphate fertilizer coupling. High curved surface represented higher water use efficiency, and vice verse. Seen from Fig.2, the application of phosphate fertilizer had obvious effect of water adjustment, and watering also could regulate phosphate fertilizer. When encoding value of soil moisture was between the level of -2 and 1.25, water use efficiency declined as phosphate fertilization amount increased, which declined from 18 to 7 g/kg, with larger decline magnitude. When encoding value of soil moisture was at the level of 1.25, water use efficiency stabilized at 7 g/kg, which was not affected by phosphate fertilization amount. When encoding value of soil moisture was between the level of 1.25 and 2, water use efficiency increased with phosphate fertilization amount increased, which increased from 5 to 8.5 g/kg, with smaller increase magnitude. When encoding value of phosphate fertilization amount was between the level of -2 and 1, water use efficiency decreased with soil moisture increased, which declined from 18 to 5 g/kg, with larger decrease magnitude. When encoding value of phosphate fertilization amount was between the level of 1 and 2, water use efficiency stabilized at 7 g/kg, which was not affected by soil moisture. Results showed that although water and phosphate fertilizer coupling had increasing effect, it could not make up the negative effect of soil moisture or phosphate fertilizer increase under certain water or phosphate fertilizer.

Fig.3Responsesurfaceandcontourlineofwaterandpotassiumfertilizercouplingtowateruseefficiency

Fig.4Responsesurfaceandcontourlineofwaterandsowingratecouplingtowateruseefficiency

3.5.2Influence of water and potassium fertilizer coupling effect on water use efficiency of fodder millet. Seen from Fig.3, under certain soil moisture, soil moisture was not affected by potassium fertilizer. But under certain potassium fertilizer, water use efficiency showed decreasing trend as soil moisture increased. When soil moisture was lower(encoding value was between the level of -2 and -1), water use efficiency was higher, which stabilized between 11 and 12 g/kg. When soil moisture was higher(encoding value was between the level of -1 and 2), water use efficiency gradually declined, which declined from 11 to 6.0 g/kg, with larger decline magnitude. When encoding value of soil moisture was at the level of -2, water use efficiency was the highest. When encoding value of soil moisture was at the level of 2, water use efficiency was the lowest. Results showed that the application of potassium fertilizer had no obvious role of water adjustment under the test condition, but watering had obvious adjustment to potassium fertilizer.

3.5.3Influence of water and sowing rate interaction effect on water use efficiency of fodder millet. When water interacted with sowing rate(Fig.4), change rate of water use efficiency as soil moisture was larger than that of sowing rate. When encoding value of sowing rate was between the level of -2 and 1, water use efficiency declined with soil moisture increased, which declined from 16 to 2.5 g/kg, with obvious decline magnitude. When encoding value of sowing rate was between the level of 1 and 2, soil moisture had no obvious effect on water use efficiency, and water use efficiency basically stabilized at 8.5 g/kg. When encoding value of soil moisture was between the level of -2 and 0, water use efficiency showed declining trend with sowing rate increased, which declined from 16 to 8.5 g/kg, with obvious declining magnitude. When encoding value of soil moisture was between the level of 0 and 2, water use efficiency increased with sowing rate increased, which increased from 2.5 to 8.5 g/kg. In the coupling effect of water and sowing rate, when encoding values of soil moisture and sowing rate were both between the level of -2 and -1.5, water use efficiency was the highest (≥15 g/kg). When encoding values of soil moisture and sowing rate were both at the level of 0, or encoding value of sowing rate was between the level of 1 and 2, water use efficiency was mediated(8.5 g/kg). When encoding values of soil moisture and sowing rate were at the level of 1.5-2, and -2 - -1.5 respectively, water use efficiency was the lowest (≥2.5 g/kg). Results showed that the influences of sowing rate and phosphate fertilizer depended on not only themselves but also their coupling with soil moisture.

Fig.5Responsesurfaceandcontourlineofnitrogenfertilizerandphosphatefertilizercouplingtowateruseefficiency

Fig.6Responsesurfaceandcontourlineofpotassiumfertilizerandsowingratecouplingtowateruseefficiency

3.5.4Influence of nitrogen and phosphate fertilizers coupling effect on water use efficiency of fodder millet. Influence of nitrogen and phosphate fertilizers coupling effect on water use efficiency of fodder millet had obvious antagonistic effect(Fig.5). When encoding value of nitrogen fertilizer was between the level of -2 and -1.5, water use efficiency increased with application amount of phosphate fertilizer increased, which increased from 7.2 to 12 g/kg, with smaller increase magnitude. When encoding value of nitrogen fertilizer was between the level of 1.5 and 2, water use efficiency declined with the application amount of phosphate fertilizer increased, which declined from 15 to 1.8 g/kg, with larger declining magnitude. When phosphate fertilizer was between the level of -2 and 0, water use efficiency increased with nitrogen fertilizer increased, which increased from 7.2 to 15 g/kg. When phosphate fertilizer was between the level of 0 and 2, water use efficiency declined with nitrogen fertilizer increased, which declined from 12 to 1.8 g/kg, with larger declining magnitude. In coupling effect of nitrogen and phosphate fertilizers, when application amount of phosphate fertilizer was the least and application amount of nitrogen fertilizer was the highest, water use efficiency was the highest (15 g/kg). When encoding value of phosphate fertilizer was the level of 0, or encoding value of nitrogen fertilizer was between the level of -1.5 and -0.2, water use efficiency stabilized at 9.0 g/kg. When application amounts of nitrogen and phosphate fertilizers were both the most, they showed obvious antagonistic effect, and water use efficiency was the lowest (1.8 g/kg).

3.5.5Influence of sowing rate and potassium fertilizer coupling effect on water use efficiency of fodder millet. The coupling of sowing rate and potassium fertilizer had obvious synergistic effect on water use efficiency(Fig.6). When sowing rate was less(encoding value was between the level of -2 and -1.5), water use efficiency declined with application amount of potassium fertilizer increased, which declined from 14 to 3.9 g/kg, with larger declining magnitude. When sowing rate was more(encoding value was between the level of 1.5 and 2), water use efficiency increased with application amount of potassium fertilizer increased, which increased from 3.9 to 14 g/kg, with larger increasing magnitude. When application amount of potassium fertilizer was less(encoding value was between the level of -2 and -1.5), water use efficiency decreased with sowing rate increased, which decreased from 14 to 3.9 g/kg, with larger declining magnitude. When application amount of potassium fertilizer was more(encoding value was between the level of 1.5 and 2), water use efficiency increased with sowing rate increased, which increased from 3.9 to 14 g/kg, with larger increasing magnitude. In coupling effect of sowing rate and potassium fertilizer of the test, they had synergistic effect. When sowing rate and potassium fertilizer were moderate(encoding value was at the level of 0), water use efficiency was mediate(8.5-9.8 g/kg).

3.6Simulationoptimizationofefficientwaterusetechnologycaseoffoddermilletanddeterminationoftheoptimalcase

When simulating and finding the optimized case that water use efficiency was the maximum according to the prediction model (3) of sowing rate, water and fertilizer coupling, via planning and solution of Excel 2007 software, the maximum of water use efficiency was 26.24 g/kg. The corresponding optimized case was 10% of soil moisture, 0 g/pot of application amounts of N, P2O5and K2O, and 0.188 g/pot of sowing rate(about 15 kg/hm2), that is, soil moisture maintained 10%, and sowing rate per hectare was 15 kg, without nitrogen, phosphate and potassium fertilizers, and the maximum of hay yield in the case was 175.6 g/pot. To determine the optimal case, economic benefits of the optimized combinations with the highest water use efficiency(treatment 12), the highest hay yield(treatment 7)and optimized case were contrasted. Results showed that the optimized case had the maximum water use efficiency and investment benefit, with the highest economic benefit(Table 5), which was selected as the optimal case. Its concrete configuration was 10% of soil moisture, 15 kg/hm2of rowing rate, without nitrogen, phosphate and potassium fertilizers. The case could be viewed as the optimal case of high-yield culture technique of fodder millet in autumn fallow yield, with 13980.90 kg/hm2of hay yield and 13830.9 yuan/hm2of economic benefit, which increased by 3063.73 yuan/hm2than that of the optimized combination with the highest hay yield, with 22.15% of increase magnitude, and 6215.15 yuan/hm2than that of the optimized combination with the highest water use efficiency, with 44.94% of increase magnitude.

Table5Comparisonofeconomicbenefitsoftheoptimizedcaseandexcellentcombination

ItemEncodingoffactorcombinationx1x2x3x4x5Wateruseefficiencyg/kgMilletstrawPerunitareayield∥g/potYieldperhectarekg/hm2Outputvalueyuan/hm2Investment∥yuan/hm2SeedFertilizerWateringNetincomeyuan/hm2Efficientwaterusecombina-tion-11-1-1-118.33132.810573.2510573.25300160810507615.25Highyieldcombination1-1-11110.22188.214981.4214981.426001514210010767.17Optimizedcase-2-2-2-2-226.24175.613980.9013980.901500013830.90

Note:(1)Income and investment were calculated according to market prices of the related products on the agricultural market in 2014, in which price of millet straw was 1.0 yuan/kg, price of millet seed was 10 yuan/kg, the prices of urea, DAP and potassium chloride were 2.50, 2.50 and 2.00 yuan/kg respectively, the fees for fertilizing base fertilizer or successive fertilizer was 300 yuan/hm2, watering fee was 600 yuan/hm2, electric fee of watering was 450 yuan/hm2. Encoding values 2, 1, -1 and -2 of soil moisture respectively showed watering for 3, 2 and 1 times and not watering after sowing.(2)Investment did not contain the fees of watering and soil preparation before sowing.

4 Conclusions and discussion

4.1InfluencesoftestedfactorsonwateruseefficiencyoffoddermilletgrowninautumnfallowfieldThe research about water use of two kinds of desert plants under different precipitation conditions by Zhou Yadanetal.[28]showed that water use efficiency of plant was the highest when rainfall was the lowest. As rainfall continuously increased, soil moisture continuously increased, while water use efficiency of plant was gradually declining. Yan Changrongetal.[29]studied inter-species difference and temporal-spatial change of δ13C value in leaves of deciduous broad leaved plant of warm temperate. Results showed that plant had higher water use efficiency under arid condition. The research about water use of millet grain by Gu Shiluetal.[30]showed that when soil moisture declined from 90% to 40%, water use efficiency of millet grain was improved by 33.8%. Under the test condition, soil moisture had the maximum influence on water use efficiency of fodder millet harvested by stages, showing that water was dominant factor of water use efficiency of fodder millet in autumn fallow field[31-32], but water use efficiency of fodder millet showed negative correlation with soil moisture, and water use efficiency was the highest (14.74 g/kg) when soil moisture was 10.00% and was the lowest (8.77 g/kg) when soil moisture was 28.75%, which was basically consistent with above reports. The research about water use efficiency of hybrid millet by fertilizing nitrogen and potassium fertilizers by Zhang Yaqietal.[14-15]showed that application of nitrogen and potassium fertilizers was conducive to improving water use efficiency of millet grain, but too high or less application could decline water use efficiency of millet grain. Under the test condition, the curves of nitrogen, phosphorus and potassium showed declining trends, in which phosphorus fertilizer had important impact on water use efficiency of fodder millet, while nitrogen and potassium fertilizers had no obvious impact on water use efficiency of fodder millet, which was not consistent with research result of Zhang Yaqietal. Maybe it was because that the demands of vegetative growth stage of fodder millet harvested by stages on nitrogen and potassium fertilizers were different from that of whole growth period of millet grain production, and the reason needed further research.

4.2Influencesoftwo-factorinteractioneffectonwateruseefficiencyoffoddermilletinautumnfallowfieldUnder the test condition, the coupling of sowing rate, water and fertilizer had different effects on water use efficiency of fodder millet in autumn fallow field, and the sequence of interaction item with significant coupling effect was potassium fertilizer +sowing rate>nitrogen fertilizer+ phosphorus fertilizer >water+ phosphorus fertilizer>water +sowing rate>water+ potassium fertilizer.(1)The coupling effects of potassium fertilizer +sowing rate and nitrogen fertilizer+ phosphorus fertilizer had the largest impact on water use efficiency of fodder millet in autumn fallow yield. Among them, the coupling of potassium fertilizer and sowing rate had obvious synergistic effect on water use efficiency. The improvement of water use efficiency by potassium fertilizer depended on not only potassium fertilizer itself but also the coupling of potassium fertilizer and sowing rate. The larger the sowing rate, the larger the density of fodder millet, and the larger the demand amount of potassium fertilizer. If potassium fertilizer supply was sufficient, when sowing rate was larger, potassium fertilizer could meet the demand of plant population growth and development, thereby obtaining larger hay yield and higher water use efficiency. If potassium fertilizer supply was insufficient, when sowing rate was larger, potassium fertilizer could not meet the demand of plant population growth and development, thereby obtaining less hay yield and lower water use efficiency. The coupling of nitrogen fertilizer and phosphorus fertilizer had obvious antagonistic effect on water use efficiency. It was mainly inharmonious relationship between soil moisture and nitrogen, phosphorus, which affected the playing of fertilizer effect. It was not consistent with the research result by Yao Kemingetal.[33]that use water efficiency was the highest when N∶P was 10∶7.5, and its reason needed further research.(2)The coupling effects of water and phosphorus fertilizer, water and potassium fertilizer, and water and sowing rate had important effects on water use efficiency of fodder millet in autumn fallow yield. In the test, vegetative growth stage of fodder millet needed more water than generative growth phase, but soil moisture was controlled by watering amount and increased with watering amount. The more the watering amount, the larger the transpiration rate, and the lower the water use efficiency. When water coupled with sowing rate, water use efficiency was 8.5 g/kg under the situation that soil moisture was 28.75%, and sowing rate was 0.754 g/pot. On the contrary, water use efficiency reached more than 16 g/kg under the situation that soil moisture was 10.00%, and sowing rate was 0.188 g/pot. When water coupled with potassium fertilizer, water use efficiency was about 7.7 g/kg under 28.75% of soil moisture and more than 11 g/kg under 10.00% of soil moisture. When water coupled with phosphorus fertilizer, water use efficiency was about 8 g/kg under the situation that soil moisture was 28.75%, and application amount of phosphorus fertilizer was 1.77 g/pot. Under the situation that soil moisture was 16.25%, and application amount of phosphorus fertilizer was 0.59 g/pot, water use efficiency reached more than 15 g/kg. It was not consistent with research result of Gu Shiluetal.[30]that phosphorus fertilizer increase could make water use efficiency of millet grain improve by 37.1 %. The reason was different demands of plant vegetative growth and reproductive growth on water and fertilizer. At jointing and booting stages of millet, stem and leaves grow fast, and leaf area quickly increases, which causes that transpiration and water consumption intensity increase by 2.2 times than that at filling maturity stage, while accumulation intensity of dry matter is only 56.1% of that at filling maturity stage, with lower water use efficiency[30]. Test results showed that application of phosphorus fertilizer had obvious role of water adjustment, while application of potassium fertilizer did not have obvious water adjustment role, and watering had obvious adjustment role on phosphorus and potassium. The influence of sowing rate and phosphorus fertilizer on water use efficiency depended on not only sowing rate and phosphorus fertilizer themselves but also their coupling with soil moisture[34]. It was clear that single watering or fertilization could not improve water use efficiency of fodder millet harvested by stages, and only scientific watering and reasonable fertilization could improve hay yield and water use efficiency of fodder millet harvested by stages.

4.3InfluencesoftestfactorsoneconomicbenefitofoptimizedcaseorcombinationoffoddermilletinautumnfallowyieldUnder the test condition, the maximum water use efficiency of fodder millet grown in autumn fallow yield was 18.33 g/kg, and its optimized combination was 16.25% of soil moisture, 3.53 g/pot of nitrogen (N) fertilization amount, 0.59 g/pot of phosphorus (P2O5) fertilization amount, 1.18 g/pot of potassium (K2O) fertilization amount and 0.377 g/pot of sowing rate, and its hay yield maximum was 132.8 g/pot. The highest hay yield of fodder millet in autumn fallow yield was 188.2 g/pot, and its optimized combination was 28.75% of soil moisture, 1.18 g/pot of nitrogen (N) fertilization amount, 0.59 g/pot of phosphorus (P2O5) fertilization amount, 3.53 g/ pot of potassium (K2O) fertilization amount and 0.754 g/pot of sowing rate. The results showed that the combination with the maximum water use efficiency did not have the maximum hay yield. So, it should not purely seek the highest water use efficiency or the highest hay yield, and should value selecting the optimized case with the maximum economic benefit between hay yield and water use efficiency under different conditions[35]. By planning and solution on the established mathematical model:y= 44.26-1.311x1-2.298x2-3.682x3-6.401x4-34.540x5+0.273x1x3+0.118x1x4+0.843x1x5-1.948x2x3+6.631x4x5, the optimized case with the highest water use efficiency (26.24 g/kg) was obtained: 10% of soil moisture, 0.188 g/pot (15 kg/hm2) of sowing rate, without nitrogen, phosphorus and potassium fertilizers, and its maximum hay yield was 175.6 g/pot. The case could be viewed as the optimal case for high-yield and high-efficiency cultivation technique of fodder millet in autumn fallow field, and the yield of hay was 13980.90 kg/hm2, with 13830.9 yuan/hm2of economic benefit, which increased by 3063.73 yuan/hm2than the optimized combination with the highest hay yield, with 22.15% of increase magnitude, and increased by 6215.15 yuan/hm2than the optimized combination with the highest water use efficiency, with 44.94% of increasing magnitude. The optimal case was simulation optimized result of pot experiment, which needed further verification of field test.

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