Optimal coupling combinations between irrigation frequency and rate for drip-irrigated maize grown...

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Optimal coupling combinations between irrigation frequency and ratefor drip-irrigated maize grown on sandy soil

Salah E. El-Hendawy a,*, Urs Schmidhalter b

a Agronomy Department, Faculty of Agriculture, Suez Canal University, 41522 Ismailia, Egyptb Department of Plant Sciences, Technische Universitat Munchen, Am Hochanger 2, D-85350 Freising-Weihenstephan, Germany

1. Introduction

By the year 2050, it is forecast that there will be an annualglobal water shortage of 640 billion cubic meters (Spears, 2003).Given that water shortages currently plague almost every countryin North Africa and the Middle East, insufficient water supply forirrigation in these regions, even in the short term, will almostcertainly become the norm rather than the exception. Therefore,water shortage events have gained increasing importance in boththe scientific and political agendas. Because the irrigation sector isthe largest consumptive user of water, accounting for 71% of thefreshwater use across the world, it is necessary for irrigationmanagement practices to shift from emphasizing production perunit area towards maximizing the production per unit of waterconsumed (Fereres and Soriano, 2007).

Substantial progress had already been made in increasingsavings in irrigation water through the use of drip irrigation

systems, but combating the looming water crisis requires furtheroptimization of drip irrigation management. Several authors haveshown that the water use efficiency and yield of drip-irrigatedcrops could be improved under limited water applications bydecreasing the amount of water that leaches beneath the root zone(Bergez et al., 2002; El-Hendawy et al., 2008b). Under dripirrigation, the ponding zone that develops around the emitter isstrongly related to either irrigation frequency or water applicationrate (Assouline, 2002; Wang et al., 2006), which therefore play akey role in determining the soil water content around the emitter,the amount of water percolation under the root zone and the wateruptake pattern (El-Hendawy et al., 2008a,b). Thus, optimizing thecoupling or matching between irrigation frequency and waterapplication rate could help to achieve maximum yield and wateruse efficiency (WUE) by exerting positive or negative effects on theamount of water percolating under the root zone and/or availablefor uptake between two consecutive irrigation events. For instance,coupling very high irrigation frequency and rate will avoid stresssituations, but at the cost of reduced drip irrigation and WUE as aresult of the increased amount of water leaching beneath the rootzone. Coupling very low irrigation frequency and rate, by contrast,

Agricultural Water Management 97 (2010) 439–448

A R T I C L E I N F O

Article history:

Received 23 May 2009

Accepted 2 November 2009

Available online 3 December 2009

Keywords:

Deficit irrigation

Evapotranspiration

Grain yield

Sandy soil

Seasonal yield response factor (ky)

Water use efficiency

A B S T R A C T

This study was conducted over 2 years (2007 and 2008) to establish the optimal combinations between

irrigation frequency and rate for drip-irrigated maize using water production functions and water use–

yield relationships. A field experiment was conducted using a randomized complete block split plot

design with four irrigation frequencies (F1, F2, F3 and F4, irrigation events once every 1, 2, 3 or 4 days,

respectively) and three drip irrigation rates (I1: 1.00, I2: 0.80, and I3: 0.60 of the estimated

evapotranspiration, ET) as the main and split plots, respectively. Our results show that yield variables

and water use efficiencies (WUEs) increased with increasing irrigation frequency and rate, with non-

significant differences between F1 and F2 in yield variables and between I1 and I2 in WUEs. Moreover, the

combination between various irrigation frequencies and rates had an important effect on yield variables

and WUEs, with the highest values being found for F1I2 and F2 I1 and the lowest for F3I3 and F4I3. The F1I3

treatment had grain yield and yield components values similar to those obtained for the F3I2 and F4I1

treatments and WUEs values similar to those obtained for the F2I1 and F2I2 treatments. Seasonal yield

response factors (ky) were 1.81 and 1.86 in 2007 and 2008, respectively. Production functions of yield

versus seasonal crop ET were linear for all combinations of irrigation frequency and rate and for all

irrigation frequency treatments with the exception of the F1 treatment, which instead showed a second

order relationship. The relationship between WUE and grain yield was best represented by a power

equation. In conclusion, we identified the optimal coupling combinations between irrigation frequency

and water application rate to achieve the maximum yield and WUEs under either sufficient (F2I1) or

limited irrigation (F1I3) water supplies.

* Corresponding author. Tel.: +2 0103913090; fax: +20 643201793.

E-mail address: shendawy@yahoo.com (S.E. El-Hendawy).

Contents lists available at ScienceDirect

Agricultural Water Management

journa l homepage: www.e lsev ier .com/ locate /agwat

doi:10.1016/j.agwat.2009.11.002

can cause water stress between successive irrigation events(especially in sandy soils) because the amount of water appliedat each event is insufficient to meet the water requirement of theplants as time proceeds. Water deficits will usually be especiallyacute and/or crucial during the reproductive stages of the crop(tasselling, silking, or grain filling). Maize has been reported to bevery sensitive to water stress at these phenological stages. Forinstance, NeSmith and Ritchie (1992) reported that the reductionsin maize yield exceeded 90% due to water deficit during thetasselling and silking stages. Musick and Dusek (1980) also foundthat water stress during the tasselling, silking and grain fillingstages were more harmful than water stress during vegetativegrowth stages. Finally, coupling very low irrigation frequency andvery high water application rate, particularly in sandy soils, mayresult in a decreased efficiency of the drip irrigation system andfinally water use, because the amount of water applied at eachirrigation event may be higher, and possibly excessively so, thanthe soil–water storage capacity, thereby increasing the amount ofwater and nutrients that move below the root zone so as to reducetheir availability to plants as time proceeds.

The crop yield-water production function (CWPF), whichrepresents the relationship between crop yield and seasonal cropevapotranspiration, represents a practical way to assess theefficiency of the irrigation management for a given crop under agiven climatic environment and husbandry conditions (Ferreiraand Goncalves, 2007). When examined over a range of irrigationtreatments, the CWPF for maize is often linear, especially in thedeficit irrigation range, because all the applied water is used (Evettet al., 2000; Oktem, 2008; Kiziloglu et al., 2009). However, non-linear relationships have also been reported occasionally (Morianaet al., 2003; Zhang et al., 2004). Such relationships may be relatedto the increase in the amount of water that moves below theeffective rooting zone, the decrease in the amount of water that istaken up by roots and/or an increase in water stress during one ormore sensitive phenological crop stages (Al-Jamal et al., 2000;Dagdelen et al., 2006; Ferreira and Goncalves, 2007). All thesephenomena could be shown to occur when high water applicationrates are coupled to either high or low irrigation frequency or whenlow water application rate is coupled to low irrigation frequency(see above). Therefore, it is important to determine those CWPFsthat define the optimal coupling between different irrigationfrequencies and water application rates to enable maximum yieldand WUE to be determined simultaneously. Crucial here is that asuseful as a tool as CWPFs are to judge optimal couplings betweenirrigation frequency and rate, as well as to compare relative wateruse efficiencies especially when water supply is limited, they aredependent on regional variability in environment and agronomicpractices (Al-Jamal et al., 2000; Igbadun et al., 2006). For example,Sammis (1981) demonstrated that the CWPF of cotton (Gossypium

hirsutum L.), and to a lesser extent that of alfalfa, varied amonglocations. There is therefore also the need to determine the CWPFfor a site-specifically such that deficit irrigation can be effectivelymanaged by the optimal coupling between irrigation frequencyand rate.

The objectives of this study were: (1) to evaluate the impacts ofdrip irrigation frequency and rate on maize production and wateruse efficiency (WUE), and (2) to establish the optimum coupling

combinations between irrigation frequency and water applicationrate, to seek maximum yield and WUE simultaneously for drip-irrigated maize in sandy soils using water production functionsand water use–yield relationships.

2. Materials and methods

2.1. Experimental site and conditions

Field experiments on drip-irrigated maize were conducted atthe Experimental Farm of the Faculty of Agriculture, Suez CanalUniversity, Ismailia, Egypt (latitude, 308580 N; longitude, 328230

E; and elevation above sea level, 13 m) during the 2007 and2008 growing seasons. The climate in this region is arid withscarce rainfall (20 mm annually). Before the start of theexperiment, soil samples were taken with an auger from thesoil layers 0–30, 30–60 and 60–90 cm to determine selectedphysical and chemical properties of the experimental field(Table 1). The soil texture at this site is predominantly sandythroughout its profile (73.1% coarse sand, 19.6% fine sand, 5.0%silt and 2.3% clay). Soil bulk density was determined usingcylinders 100 mm in diameter and 60 mm in height inaccordance with the classical method as applied by Grossmannand Reinsch (2002). The water content at field capacity andwilting point were determined in the laboratory using apressure plate technique at �0.03 and �1.5 MPa, respectively(Cassel and Nielsen, 1986).

2.2. Experimental design, treatments and agronomic practices

A randomized complete block split plot design with threereplicates was used in each season. Different treatments ofirrigation frequency and water application rate were randomlyassigned to the main plot and subplots, respectively. A layout of theexperimental plots is shown in Fig. 1.

The drip irrigation system was divided into four main sectors,with the irrigation frequency treatments (once every 1, 2, 3 and 4days) being assigned to the four sectors. The water application ratetreatments (I1: 1.00, I2: 0.80 and I3: 0.60 of the estimated cropevapotranspiration) were randomly nested within each mainsector as a subplot, with each subplot having three replicates of thesame water application rate. Each subplot had one valve and oneflow meter to control water application and measure the irrigationquantity, respectively.

The amount of irrigation water applied, I, was determined fromthe calculated water requirement for maize (mm) as determinedfrom the crop coefficient (Kc) and the daily reference evapotran-spiration (ETo) using the following equation:

I ¼ ETo� Kc (1)

ETo was calculated by the Penman–Monteith method (Allen et al.,1998) using daily data from a meteorological station locatedwithin 500 m of the research site. The FAO Penman–Monteithequation, given by Allen et al. (1998):

ETo ¼ 0:408 DðRn � GÞ þ gð900=ðT þ 273ÞÞU2ðes � eaÞDþ gð1þ 0:34U2Þ

Table 1Physical and chemical properties of the experimental field soil (averaged over two seasons).

Soil depth

Soil bulk

density (g cm�3)

Field capacity

(m3 m�3)

Wilting point (m3 m�3) Available moisture (m3 m�3) pH Organic

matter (%)

Texture

0–30 1.58 0.072 0.015 0.057 8.00 0.60 Sandy

30–60 1.65 0.101 0.017 0.084 7.93 0.49 Sandy

60–90 1.60 0.062 0.016 0.046 7.65 0.31 Sandy

S.E. El-Hendawy, U. Schmidhalter / Agricultural Water Management 97 (2010) 439–448440

where ETo is the reference evapotranspiration (mm day�1), Rn thenet radiation at the crop surface (MJ m�2 day�1), G the soil heatflux density (MJ m�2 day�1), T the mean daily air temperature at2 m height (8C), U2 the wind speed at 2 m height (m s�1), es thesaturation vapor pressure (kPa), ea the actual vapor pressure (kPa),es � ea the saturation vapor pressure deficit (kPa), D the slope of thesaturation vapor pressure curve (kPa 8C�1), and g is the psychro-metric constant (kPa 8C�1).

The Kc is defined as the ratio of the crop evapotranspiration rateto the reference evapotranspiration rate. Since localized Kc valueswere not available for the study area, the values of Kc suggested byFAO-56 (Allen et al., 1998) were used. The values of Kc of maizeused (0.15, 1.15, and 0.15, respectively, in the initial, mid, and lateseason stages) represent the recommended values for a subhumidclimate (minimum relative humidity, RHmin � 45%) with amoderate wind speed (U2 � 2 ms�1). These recommended valuesmust be adjusted in other areas, where RHmin differs from 45% andthe wind speed is sometimes greater than 2 m s�1 or sometimesless than 2 m s�1. The Kc value (larger than 0.45) for the mid seasonstage was adjusted using the following equation:

Kc ¼ KcðtableÞ þ ½ð0:04ðU2 � 2Þ � 0:004ðRHmin

� 45Þ�ðh=3Þ0:3; (3)

where Kc (table) is the Kc recommended by FAO-56 (Allen et al.,1998), U2 the wind speed at 2 m height (m s�1), RHmin theminimum relative humidity, and h is the mean maize height duringthe mid season stage (m).

After adjustment, average Kc values for the two growingseasons in the initial, mid and late season stages were 0.30, 1.30and 0.35, respectively. The drip irrigation efficiency was assumedto be 0.9, and the root extension coefficient according to Moon andGulik (1996) was taken to be 0.8. The total amounts of waterapplied were 5960, 4768 and 3576 m3 ha�1 for I1, I2 and the ratetreatments I3, respectively. The dates of each irrigation event andthe quantities of water applied are given in Table 2. To ensure fullgermination, 65 mm of water were applied for all irrigationtreatments at sowing with an additional irrigation of 89 mm being

applied 20 days later for complete establishment of seedlings. Toavoid deep percolation losses, irrigation was carried out two andthree times during germination and seedling stage, respectively.Thereafter, irrigation treatment was started after 24 days aftersowing according to the prescribed irrigation rate and frequency.

Each 28 m2 subplot consisted of five polyethylene lateral driplines (Twin-wall IV, 16 mm in diameter, and 0.3 m emitter spacing,Chapin Watermatics, Watertown, NY) with a length of 4 m. Thelateral line was laid out along each maize row at 1.4 m. Thedrippers had a discharge rate of 3.1 l h�1 at an operating pressureof 0.13 MPa. Two seeds (cv. single cross 10) were sown around eachdripper on 21 May 2007 and 28 May 2008 to obtain a final plantpopulation of about 48,000 plants ha�1. Nitrogen fertilizer wasapplied at a rate of 285 kg ha�1 of N as ammonium sulphate(20.5%) by fertigation. Nitrogen fertilizer was added 2 weeks aftersowing in six equal weekly doses. Phosphorus fertilizer wasapplied at a level of 13.5 kg ha�1 of P as calcium super phosphate.Whole of phosphorus was applied basally before sowing in alltreatments. Potassium fertilizer was applied 5 weeks after sowingat a level of 41.5 kg ha�1 of K as potassium sulphate in two equalbiweekly doses. Weed, pest, and disease control were done in atimely manner. Hand harvesting was performed about 120 daysafter sowing.

2.3. Crop evapotranspiration measurements and irrigation water

compensation

Actual crop evapotranspiration under the different irrigationtreatments was calculated using the soil water balance equation(Heerman, 1985):

ET ¼ I þ P þ Cr� R� D�DS (4)

where ET represents seasonal crop evapotranspiration (mm), P isprecipitation (mm), Cr is the capillary rise (mm), R is the amount ofrunoff (mm), D is the amount of drainage water (mm), and DS is thedifference between soil water content values at planting and at theend of harvesting (mm).

Fig. 1. Layout of one replicate of an experimental design that includes four irrigation frequencies and three irrigation rates, showing locations of irrigation frequencies and

irrigation rates. F1, F2 F3 and F4 indicate irrigation frequency once every 1, 2, 3 and 4 days, respectively. I1, I2 and I3 indicate irrigation treatments (1.00, 0.80 and 0.60 of the

estimated crop evapotranspiration, respectively).

S.E. El-Hendawy, U. Schmidhalter / Agricultural Water Management 97 (2010) 439–448 441

In this study, both P and Cr were considered to be zero becausethere was no precipitation during either growing season and nocapillary rise from the groundwater occurred. Surface runoff wasassumed to be negligible because the amount of irrigation waterwas controlled through the drip irrigation. Whenever availablewater in the root zone (0–90 cm) and the total amount of waterapplied by irrigation were above the field capacity, it was assumedthat excess water leaked into the deeper soil zones and was calleddeep percolation (D = amount of available total water at 0–90 cmsoil depth before irrigation (mm) + irrigation water applied(mm) � soil water hold in field capacity (mm)) (Kanber andYazar, 1993). Whereas DS was estimated from the respective soilwater contents to a depth of 90 cm by using the soil water contentvalue before harvesting to subtract the soil water content valuebefore sowing.

Soil water content was monitored before irrigation every 12days for F1, F2 and F3 treatments, and every 10 days for F4 treatmentat soil depth intervals of 0–30, 30–60 and 60–90 cm. Soil sampleswere taken at positions immediately under the drippers. Soil watercontent was determined by the gravimetric method (oven drybasis). The values were converted to a percentage volumetric basisby multiplying them by the bulk density of the soil of therespective layer.

In addition, the contribution of the different treatments towardplant water consumption (Ertek et al., 2004) was determinedaccording to

Irc ¼ I

� �� 100 (5)

where Irc is the irrigation water compensation for plant waterconsumption (ET) (%).

2.4. Water use efficiencies

WUE (kg ha�1 mm�1), defined as the ratio of grain yield toseasonal water consumption per hectare, and irrigation water useefficiency (IWUE, kg ha�1 mm�1), as the ratio of grain yield to theseasonal amount of irrigation water applied per hectare, werecalculated using Eqs. (6) and (7), respectively (Howell et al., 1990).

WUE ¼ Y

� �(6)

IWUE ¼ Y

� �(7)

Table 2The dates after sowing (DAS) and quantity of water applied for each irrigation event (data averaged over two seasons).

Quantity of water applied for each irrigation event (m3 ha�1)

DAS F1 (once in 1 day) DAS F2 (once in 2 days) DAS F3 (once in 3 days) DAS F4 (once in 4 days)

1.00 ET 0.80 ET 0.60 ET 1.00 ET 0.80 ET 0.60 ET 1.00 ET 0.80 ET 0.60 ET 1.00 ET 0.80 ET 0.60 ET

24 137.1 109.7 82.3 24 147.1 117.7 88.3 24 234.0 187.2 140.4 24 291.4 233.1 174.8

26 137.1 109.7 82.3 27 147.1 117.7 88.3 28 234.0 187.2 140.4 29 317.6 254.1 190.6

28 147.1 117.7 88.3 30 177.1 141.7 106.3 32 257.1 205.7 154.3 34 343.8 275.0 206.3

30 147.1 117.7 88.3 33 177.1 141.7 106.3 36 305.9 244.7 183.5 39 370.0 296.0 222.0

32 147.1 117.7 88.3 36 177.1 141.7 106.3 40 305.9 244.7 183.5 44 370.0 296.0 222.0

34 147.1 117.7 88.3 39 200.0 160.0 120.0 44 315.9 252.7 189.5 49 383.4 306.7 230.0

36 147.1 117.7 88.3 42 200.0 160.0 120.0 48 315.9 252.7 189.5 54 393.6 314.8 236.1

38 147.1 117.7 88.3 45 216.4 173.1 129.8 52 315.9 252.7 189.5 59 422.4 337.9 253.4

40 150.0 120.0 90.0 48 223.8 179.0 134.3 56 315.9 252.7 189.5 64 422.4 337.9 253.4

42 150.0 120.0 90.0 51 275.7 220.6 165.4 60 318.9 255.1 191.3 69 422.4 337.9 253.4

44 150.0 120.0 90.0 54 275.0 220.0 165.0 64 318.9 255.1 191.3 74 422.4 337.9 253.4

46 155.0 124.0 93.0 57 275.0 220.0 165.0 68 386.1 308.9 231.7 79 383.1 306.5 229.8

48 157.6 126.1 94.6 60 275.0 220.0 165.0 72 386.1 308.9 231.7 84 383.1 306.5 229.8

50 157.6 126.1 94.6 63 275.0 220.0 165.0 76 386.1 308.9 231.7 89 356.9 285.5 214.1

52 160.0 128.0 96.0 66 275.0 220.0 165.0 80 386.1 308.9 231.7 94 291.4 233.1 174.8

54 165.0 132.0 99.0 69 275.0 220.0 165.0 84 245.7 196.6 147.4 99 239.0 191.2 143.4

56 165.0 132.0 99.0 72 275.0 220.0 165.0 88 245.7 196.6 147.4 104 147.4 117.9 88.4

58 165.0 132.0 99.0 75 275.0 220.0 165.0 92 245.7 196.6 147.4

60 170.7 136.6 102.4 78 275.0 220.0 165.0 96 160.1 128.1 96.1

62 170.7 136.6 102.4 81 249.5 199.6 149.7 100 160.1 128.1 96.1

64 170.7 136.6 102.4 84 249.5 199.6 149.7 104 120.0 96.0 72.0

66 170.7 136.6 102.4 87 175.0 140.0 105.0

68 170.7 136.6 102.4 90 175.0 140.0 105.0

70 170.7 136.6 102.4 93 175.0 140.0 105.0

72 170.7 136.6 102.4 96 138.0 110.4 82.8

74 170.7 136.6 102.4 99 135.0 108.0 81.0

76 168.1 134.5 100.9 102 135.0 108.0 81.0

78 165.5 132.4 99.3 105 111.5 89.2 66.9

80 165.5 132.4 99.3

82 162.9 130.3 97.7

84 155.0 124.0 93.0

86 145.0 116.0 87.0

88 137.1 109.7 82.3

90 135.0 108.0 81.0

92 135.0 108.0 81.0

94 111.0 88.8 66.6

96 97.9 78.3 58.7

98 97.9 78.3 58.7

100 69.0 55.2 41.4

102 63.8 51.0 38.3

104 53.3 42.7 32.0

Total 5960 4768 3576 5960 4768 3576 5960 4768 3576 5960 4768 3576

where Y is the economical yield (kg ha�1), ET the seasonal cropevapotranspiration (mm), and I is the amount of irrigation waterapplied (mm).

2.5. Water use–yield relationships and the yield response factor (ky)

for maize under semiarid condition

Regression analysis was used to evaluate the water use–yieldrelationships derived from seasonal crop evapotranspiration andgrain yield data obtained from the experiment. Seasonal values ofthe yield response factor (ky) for each year and each irrigationfrequency, which represent the relationship between relativemaize yield reduction (1 � Ya/Ym) and relative evapotranspirationdeficit (1 � ETa/ETm), were determined using the formula given byDoorenbos and Kassam (1979):

1� Ya

� �¼ ky 1� ETa

� �(8)

where ETa and ETm are the actual and maximum seasonal cropevapotranspirations (mm), respectively, and Ya and Ym are thecorresponding actual and maximum yields (kg ha�1).

2.6. Parameter assessments

After physiological maturity, 10 plants from each subplot wereharvested at random to determine the weight of ears per plant, thenumber of grains per ear and the weight of grains per plant. Plantswere cut at ground level and the ears were separated from thestover. The ears were placed in a greenhouse to air dry to a watercontent of approximately 15–16% before being weighed andshelled by hand. Total grain yield per ha was determined by handharvesting an area of two rows 4.0 m in length, each on a subplotbasis. Grain yield was adjusted to a water content of 15.5%.

2.7. Statistical analysis

All measurements in this study were analyzed using an analysisof variance (ANOVA) appropriate for a randomized complete block

split plot design with irrigation frequency as the main plot, waterapplication rate as the subplots and replicates as blocks. Meansquare of the product between the irrigation frequency and waterapplication rate was used as the error term to test the interactionbetween both factors. Mean separation of treatment effects usedFisher’s protected least significant differences (LSD) test. Prob-ability levels lower than 0.05 were categorized as significant. Allanalyses used the CoStat system for Windows, version 6.311(CoHort software, Berkeley, CA 94701). Polynomic and linearregression analyses were performed to investigate the relationshipbetween yield and evapotranspiration and the best relationshipbetween yield and WUE. Regression analyses were performedusing Microsoft Excel 2003.

3. Results

3.1. Seasonal crop evapotranspiration (ET)

Table 3 presents seasonal crop ET and irrigation watercompensation values (Irc) as estimated by Eqs. (2) and (3),respectively. In both seasons, DS values of all treatments werenegative, indicating that the soil became drier at the end of thegrowing season. However, DS values were lower for the F1I1, F4I1

and F4I2 treatments compared to the remaining treatments; theopposite held true for the Irc values.

3.2. Yield components and grain yield

All yield components (the weight of ears per plant, the number ofgrains per ear and the weight of grains per plant, and the grain yieldper hectare were significantly affected by irrigation frequency andrate (Tables 4 and 5). The maximum yield components and grainyield averaged across irrigation rate treatments were obtained at thetwo most frequent irrigation frequencies (F1 and F2). Averaged overthe two seasons, the irrigation frequency treatments F3 and F4

resulted in decreases in ear weight per plant of 27.7 and 42.3%, grainnumber per plant of 35.2 and 62.7%, grain weight per plant of 34.1and 47.8% and grain yield per hectare of 38.1 and 56.3%, respectively,when compared with the F1 treatment (Tables 4 and 5). Different

Table 3Maize evapotranspiration calculated using the water balance equation. I, P, D, DS, ET and Irc indicate amount of irrigation water applied (mm), precipitation (mm), deep

percolation (mm), change of soil water storage (mm), evapotranspiration (mm) and irrigation water compensation (%), respectively.

Year Treatments I (mm)a P (mm) D (mm) DS (mm) ET (mm) Irc (%)

2007 F1 (once in 1 day) 1.00ET 596.0 0.0 22.3 �8.9 582.6 102.2

0.80ET 476.8 0.0 0.0 �30.2 507.0 93.9

0.60ET 357.6 0.0 0.0 �32.9 390.5 91.5

F2 (once in 2 days) 1.00ET 596.0 0.0 0.0 �31.3 627.3 94.9

0.80ET 476.8 0.0 0.0 �29.8 506.6 94.0

0.60ET 357.6 0.0 0.0 �29.8 387.4 92.2

F3 (once in 3 days) 1.00ET 596.0 0.0 0.0 �29.9 625.9 95.1

0.80ET 476.8 0.0 0.0 �28.9 505.7 94.2

0.60ET 357.6 0.0 0.0 �32.0 389.6 91.7

F4 (once in 4 days) 1.00ET 596.0 0.0 36.3 �6.6 566.3 105.2

0.80ET 476.8 0.0 10.4 �18.0 484.4 98.3

0.60ET 357.6 0.0 0.0 �30.2 387.8 92.1

2008 F1 (once in 1 day) 1.00ET 596.0 0.0 26.8 �11.6 580.8 102.5

0.80ET 476.8 0.0 0.0 �32.1 508.9 93.6

0.60ET 357.6 0.0 0.0 �34.7 392.3 91.1

F2 (once in 2 days) 1.00ET 596.0 0.0 0.0 �32.9 628.9 94.7

0.80ET 476.8 0.0 0.0 �29.7 506.5 94.0

0.60ET 357.6 0.0 0.0 �33.7 391.3 91.3

F3 (once in 3 days) 1.00ET 596.0 0.0 0.0 �32.9 628.9 94.7

0.80ET 476.8 0.0 0.0 �31.1 507.9 93.8

0.60ET 357.6 0.0 0.0 �34.7 392.3 91.1

F4 (once in 4 days) 1.00ET 596.0 0.0 40.4 �8.0 563.6 105.7

0.80ET 476.8 0.0 9.5 �19.2 486.5 97.9

0.60ET 357.6 0.0 0.0 �33.2 390.8 91.4

a Amount of irrigation water applied was calculated by using Penman–Monteith equations.

yield components and grain yield were also significantly affected bythe water application rate regardless of the irrigation frequency. Inboth seasons, 0.80 (I2) and 0.60 ET (I3) consistently resulted in loweryields than 1.00 ET (I1) treatments. Averaged over the two seasons,decreases in yield components and grain yield for 0.80 and 0.60 ETrelative to 1.00 ET were 13.8 and 50.9% for ear weight per plant, 20.7and 63.8% for grain number per plant, 14.9 and 56.1% for grainweight per plant and 18.0 and 60.8% for grain yield per hectare,respectively (Tables 4 and 5).

The combination of irrigation frequency and rate had a significanteffect on both yield components and grain yield in both seasons(Tables 4 and 5). The Fisher’s protected LSD test of the various

combinations for the effect on yield components and grain yieldplaced F1I2 and F2I1 in the first position; F1I1, F2I2 and F3I1 in thesecond position; F1I3, F3I2 and F4I1 in the third position; F2I3 in thefourth position; F4I2 in the fifth position and F3I3 and F4I3 in the sixthposition, with similar results for all parameters in both seasons.

3.3. Water use efficiencies

The effects of irrigation frequency and rate on IWUE and WUEwere significant in both seasons (Table 5), with high irrigationfrequencies and rates displaying the highest values in both seasons.Averaged over two seasons, IWUE and WUE values for the F2

Table 4Effects of irrigation frequency, irrigation rate and their combination on selected yield components in 2007 and 2008.

Irrigation frequency 2007 2008

1.00 ET (I1) 0.80 ET (I2) 0.60 ET (I3) Mean 1.00 ET (I1) 0.80 ET (I2) 0.60 ET (I3) Mean

Weight of ears per plant (g)

F1 (once in 1 day) 175.5 b 197.1 a 154.7 c 175.8 A 164.5 b 182.2 ab 133.5 d 160.1 A

F2 (once in 2 days) 209.0 a 172.4 bc 115.0 d 165.5 A 194.6 a 160.4 bc 98.3 e 151.1 A

F3 (once in 3 days) 177.0 b 153.7 c 50.0 f 126.9 B 167.7 b 139.9 cd 40.0 f 115.8 B

F4 (once in 4 days) 158.7 bc 95.7 e 50.6 f 101.6 C 141.3 cd 94.7 e 40.2 f 92.1 C

Mean 180.0 A 154.7 B 92.6 C 167.0 A 144.3 B 78.0 C

LSD (0.05) F 21.3 ET 9.6 F�ET 19.2 F 17.0 ET 10.9 F�ET 21.8

Number of grains per ear

F1 (once in 1 day) 393.5 b 433.7 ab 293.9 c 373.7 A 354.2 bc 401.7 ab 270.6 e 342.2 A

F2 (once in 2 days) 460.2 a 395.4 b 203.7 d 353.1 A 420.3 a 348.0 c 203.6 f 323.9 A

F3 (once in 3 days) 397.2 b 318.7 c 27.4 f 247.8 B 335.2 cd 290.0 de 24.4 h 216.5 B

F4 (once in 4 days) 305.9 c 79.2 e 23.4 f 136.2 C 290.6 de 78.6 g 21.8 h 130.3 C

Mean 389.2 A 306.8 B 137.1 C 350.1 A 279.6 B 130.1 C

Weight of grains per plant (g)

F1 (once in 1 day) 160.8 b 182.3 a 110.8 d 151.3 A 137.6 b 150.4 a 105.7 c 131.2 A

F2 (once in 2 days) 181.8 a 145.5 c 88.3 e 138.5 A 153.4 a 130.8 b 81.3 d 121.8 A

F3 (once in 3 days) 146.0 c 115.1 d 37.4 f 99.5 B 128.3 b 109.4 c 22.3 f 86.7 B

F4 (once in 4 days) 124.2 d 75.9 e 31.7 f 77.3 C 115.9 c 67.2 e 26.6 f 69.9 B

Mean 153.2 A 129.7 B 67.1 C 133.8 A 114.5 B 59.0 C

Means followed by the same letter are not significantly different from one another based on Fisher’s protected LSD test at P�0.05.

Table 5Effects of irrigation frequency, irrigation rate and their combination on grain yield, irrigation water use efficiency and water use efficiency in 2007 and 2008.

Irrigation frequency 2007 2008

1.00 ET (I1) 0.80 ET (I2) 0.60 ET (I3) Mean 1.00 ET (I1) 0.80 ET (I2) 0.60 ET (I3) Mean

Grain yield (kg ha�1)

F1 (once in 1 day) 7620.3 b 8906.8 a 5133.7 d 7220.3 A 6917.0 b 8236.8 a 4830.4 c 6661.4 A

F2 (once in 2 days) 9145.7 a 6820.8 c 4219.6 e 6728.7 A 8411.3 a 6528.5 b 3860.7d 6266.8 A

F3 (once in 3 days) 7062.9bc 5299.3 d 1304.0 g 4555.4 B 6548.3 b 4840.4 c 734.0 f 4040.9 B

F4 (once in 4 days) 5348.4 d 2991.1 f 1290.7 g 3210.1 C 5278.4 c 2593.2 e 720.7 f 2864.1 C

Mean 7294.3 A 6004.5 B 2987.0 C 6788.7 A 5549.8 B 2536.4 C

Irrigation water use efficiency (kg ha�1 mm�1)

F1 (once in 1 day) 12.80 c 18.70 a 14.37 b 15.29 A 11.62 cd 17.30 a 13.52 b 14.14 A

F2 (once in 2 days) 15.36 b 14.32 b 11.81 cd 13.83 B 14.12 b 13.71 b 10.81def 12.88 B

F3 (once in 3 days) 11.86 cd 11.13 d 3.65 g 8.88 C 11.00 de 10.16 ef 2.05 h 7.74 C

F4 (once in 4 days) 8.98 e 6.28 f 3.61 g 6.29 D 8.86 f 5.45 g 2.02 h 5.44 D

Mean 12.25 A 12.61 A 8.36 B 11.40 A 11.66 A 7.10 B

Water use efficiency (kg ha�1 mm�1)

F1 (once in 1 day) 13.08 c 17.57 a 13.15 c 14.60 A 11.91 bc 16.19 a 12.31 b 13.47 A

F2 (once in 2 days) 14.58 b 13.46 bc 10.89 d 12.98 B 13.38 b 12.89 b 9.87 d 12.04 B

F3 (once in 3 days) 11.28 d 10.48 de 3.35 g 8.37 C 10.41 cd 9.53 d 1.87 f 7.27 C

F4 (once in 4 days) 9.44 e 6.17 f 3.33 g 6.32 D 9.37 d 5.33 e 1.84 f 5.51 D

Mean 12.10 A 11.92 A 7.68 B 11.27 A 10.98 A 6.47 B

Means followed by the same letter are not significantly different from one another based on Fisher’s protected LSD test at P�0.05.

treatment were only 9.2 and 10.9% less than those at F1 treatment,whereas the respective values for the F3 and F4 treatments showedsignificant decreases: IWUE, 43.6 and 60.2%; WUE, 44.3 and 57.9%(for F3 and F4, respectively, in both cases). Averaged over all irrigationfrequencies and seasons, 0.80 ET had comparable water useefficiencies as did 1.00 ET, but 0.60 ET had IWUE and WUE valuesthat were 34.7 and 39.6% lower than those of 1.00 ET, respectively.

The interaction effect between irrigation frequency and rate onIWUE and WUE was also significant in both seasons (Table 5). Thehighest water use efficiencies (WUEs) values were obtained underthe F1I2 treatment. By contrast, the lowest WUEs values wererecorded for the F3 and F4 treatments with I3. It is interesting tonote that the F1 treatment with I3 had WUEs values similar to thoseobtained for the corresponding F2 treatment with either I1 or I2 andwere higher to those obtained for the F3 and F4 treatments with I1.

3.4. Yield response factor (ky)

In this study, the largest grain yields (Ya) were recorded at F2I1(Table 5). The corresponding maximum ET values (ETm) were627.3 mm in 2007 and 628.9 mm in 2008. The relationship betweenthe relative yield decrease (1� Ya/Ym) and the correspondingrelative evapotranspiration deficit (1� ETa/ETm) was linear for alldata (Fig. 2), with slopes (ky values) of 1.81 and 1.86 in 2007 and2008, respectively. However, the different irrigation frequencytreatments had a significant impact on the ky values, with therespective values for the F1, F2, F3 and F4 treatments being 0.99, 1.39,2.25 and 2.52 in 2007 and 0.97, 1.37, 2.38 and 2.64 in 2008 (Table 6).

3.5. Yield–seasonal crop evapotranspiration relationship

The best fit for the relationship between grain yield and seasonalcrop ET was linear and positive for each year: 2007, Y = 21.66

ET� 5331.0 (R2 = 0.57); 2008, Y = 21.42 ET� 5711.7 (R2 = 0.56)(Fig. 3). The linear regression coefficients, which represent theincrease in grain yield for each unit increase in seasonal crop ET,were 21.66 kg mm�1 in 2007 and 21.42 kg mm�1 in 2008. Theintercepts of the two regression lines were also highly similar. Fromthe equations reported in Fig. 3, the basal seasonal crop ET necessaryto start grain yield production was determined to be 246.1 and266.7 mm in 2007 and 2008, respectively (256.4 mm on average).

When broken down according to the irrigation frequencytreatments, the graphs of grain yield versus seasonal crop ET(Fig. 4) were linear for the F2, F3 and F4 treatments. By contrast, theF1 treatment followed a second order relationship. Both the slopesof the regression lines and the values of the intercepts were almostidentical over the 2 years, with the exception of the F4 treatment.

3.6. Water use efficiency–yield relationship

Because the relationships between WUE and grain yield werenot always linear, we fitted the data according to six differentmodels: (1) linear, (2) quadratic, (3) cubic, (4) logarithmic, (5)exponential, and (6) power. However, based on R2 values, thepower model was chosen as the model that best described theWUE–yield relationship of our data (Fig. 5). This latter figure alsoshows that WUE was closely associated with grain yield.

Fig. 2. Yield response factor (ky) for 2007 and 20087 growing seasons. Linear

regression equations; **indicate significant at 0.01 P level.

Table 6Yield response factor (ky) shown as the relationship between the relative yield

decrease (1�Ya/Ym) and the corresponding relative evapotranspiration deficit

(1�ETa/ETm) for each of four irrigation frequency treatments in 2007 and 2008.

Irrigation frequency treatments 2007 2008

ky R2 ky R2

F1 (once in 1 day) 0.99 0.82* 0.97 0.81*

F2 (once in 2 days) 1.39 0.99** 1.37 0.99**

F3 (once in 3 days) 2.25 0.95** 2.38 0.95**

F4 (once in 4 days) 2.52 0.96** 2.64 0.98**

* Significant at the 0.01 level.** Significant at the 0.001 level.

Fig. 3. Relationship between seasonal crop evapotranspiration (ET) and grain yield.

Linear regression equations; **indicate significant at 0.01 P level.

Fig. 4. Relationship between seasonal crop evapotranspiration (ET) and grain yield

(GY) for each of four irrigation frequency treatments in 2007 and 2008. Regression

equations; ***indicate significant at 0.001 P level.

4. Discussion

In recent years, several researchers have addressed the conceptof ‘‘site specific management’’: applying the right amount of inputat the right place at the right time to get maximum profit per unitinput. Based on this basic definition, the profitability of irrigationcan be maximized by determining the optimal combinationbetween irrigation frequency and irrigation rate, the two variablesthat impact to the greatest extent on the soil water content and therelated soil water distribution at depth within the root zone, andconsequently, the amount of water percolation under the root zoneand the amount of water uptake by the roots (Assouline, 2002;Wang et al., 2006; Ucan et al., 2007; El-Hendawy et al., 2008a,b).

In the present study, the seasonal crop ET during the cropgrowing period (i.e., after establishment of the crop) was found to belower than the amount of irrigation water applied (I) in the F1I1 andF4I1 treatments. Furthermore, the values of DS for these twocombinations were found to be lower than those for the othertreatments and in the opposite direction for irrigation compensation(Irc) (Table 3). Two analogous explanations of these phenomenapresent themselves. First, the shorter irrigation durations for higherirrigation frequencies in combination with high irrigation rates (i.e.,F1I1) may mean that the amount of water extracted by the roots wasnot commensurate with the amount of water applied, resulting inmore water moving below the root zone. Second, in the case of lowirrigation frequencies in combination with high irrigation rates (i.e.,F4I1), the amount of water applied at each irrigation event was(excessively) higher than the water storage capacity of the sandysoil, thereby likewise increasing the amount of water that couldmove below the root zone. In both cases, the amount of water thatpercolated under the root zone was not depleted by the roots. Formaize grown in sandy loam soil, it is known that the plants extractmost of the soil water from soil depths of 0–35 cm (Panda et al.,2004). This fact may be due to approximately 85% of the total rootlength of maize when grown on sandy soil being within the upper30 cm of the soil (Laboski et al., 1998). Therefore, the soil watercontent in both these treatments was higher before harvest than forthe other treatments and, as a result, their DS values werecomparatively lower than for the other treatments (with theopposite being true for Irc).

Alternatively, standard irrigation engineering calculationsallow to estimate the application depths that should be sufficiently

small to avoid deep percolation losses for a given wetted area androoting depth. Since there is little lateral spread of irrigation waterbeneath the soil surface in a sandy soil, the allowable irrigationapplication (IA, depth) is given by

IA ¼ ðFC� PWPÞ dm

� �Z

� �(9)

where FC is water content (m3 m�3) at field capacity, PWP is soilwater content (m3 m�3) at permanent wilting point, dm is allowablemoisture depletion (percent), P is the wetted soil area (percent), Z isthe root zone depth and the units of Z and IA are the same. Lateralspreading of water from drip emitters will be minimized, probablynot exceeding the 30-cm spacing between emitters. Since the tapelaterals were 1.4 m apart, and considering that overlap betweenwetted areas along each drip lateral would provide virtually a linearwetted area along the drip laterals of 0.8 m width, making thepercentage wetted area = 100 � (1.4� 0.8)/1.4 = 43%. Irrigationdepths greater than the value of IA calculated with the aboveequation will push water to below the root zone. Using the P of 43%estimated above, and estimating that a rooting depth of 100 cm islikely and PWP and FC of 0.016 and 0.078 m3 m�3 as mean values inTable 1, respectively, and assuming an allowable moisture depletionof 100%, given the largest IA value, one can calculate IA� 26.8 mm toprevent deep percolation losses. These amounts are in the range ofthe two initial irrigations of 65 and 89 mm, that were split in two orthree applications, respectively. However due to the shallow depthof rooting particularly at germination and seedling deep percolationlosses may occur. Table 1 suggests that, whereas the risk for deeppercolation losses is reduced for the frequent irrigation treatments,the less frequent irrigation treatments such as F3I1, F4I1 may bear anenhanced risk for deep percolation losses. Data in Evett et al. (2000)indicate that the water content in the top soil dropped to0.02 m3 m�3, representing a lower limit of water extraction.Whereas the assumption of an allowable moisture depletion of100% has to be questioned, results from Evett (2000) indicate, thatwater extraction by corn roots could reach to 1.5 m depth on asimilar site at Ismailia and ETc (crop water use or evapotranspira-tion) for maize was 10 mm day�1 for well-watered plants. Underthe imposed water regime the author recommended to switchfrom irrigation every other day to much smaller irrigations severaltimes. Interestingly, results from this study suggest that theirrigation treatment F2I1 was optimal under sufficient water supply.A higher irrigation frequency may entail the risk for a more localizedroot growth, thus restricting the possible root extension to lowerdepths.

An important finding of this study was the strong response ofboth grain yield and yield components to the combination ofirrigation frequency and amount. It is interesting to note that thevalues of both grain yield and yield components obtained for F1I2

were comparable with those of F2I1, and that both were higher thanthose obtained for F1I1. Crucially, the F1I3 treatment produced grainyield and yield components values similar to those obtained for theF4I1 and F3I2 treatments (Tables 4 and 5). Taken together, theseresults indicate that the grain yield of drip-irrigated maize can beimproved either through the outright application of sufficientirrigation water or through the optimal coupling betweenirrigation frequency and amount. These results also reflect thatvariation in drip irrigation frequency is useful for determiningwhether maximum yield can be obtained under sufficient andlimited water applications. For instance, the lower grain yield andyield components of F1I1 when compared with F1I2 and F2I1, despitethe higher total amount of water for this treatment than F1I2 andequal to F2I1, could be due to the fact that the F1I1 treatmentresulted in a very humid region locally in the root zone and/orpotentially resulted in deep percolation below the effective root

Fig. 5. Relationship between grain yield (GY) and water use efficiency (WUE). Power

regression equations; ***indicate significant at 0.001 P level. Each point represents a

replicate.

zone because the amount of water extracted by roots wasproportionately less than when water was applied for a shorterduration. Past studies have shown that maize is comparativelymore susceptible to excess moisture during the early seedling totasseling stages (Rathore et al., 1998; Zaidi et al., 2004). A veryhumid region in the root zone reduces the oxygen diffusion into thesoil, which in turn both affects the activity of crop enzymes andthus weakened crop photosynthesis (Huang et al., 1994) and alsoinhibits the development of the leaf surface area (Wan and Kang,2006). Conversely then, the maximum grain yield and yieldcomponents for F1I2 and F2I1 can be attributed to the maintenanceof optimal available soil water content in the root zone withoutdeep percolation and/or poor aeration conditions.

The non-significant differences between the F4I1 and F1I3

treatments for grain yield and yield components (Tables 4 and 5),despite the amount of water applied in the former case being 31.0%higher in 2007 and 30.4% in 2008 (Table 3), may be explained bythe application of water at high volume and low frequency in theF4I1 treatment exceeding the soil–water storage capacity, leadingto excessive water percolation under the effective root zone.Therefore, a portion of the water application was not used by theplant and the remaining available water will not meet the long-term water requirements of the plants till the next irrigation event.In such case, the resulting water deficit will often coincide with thecritical growth stages of maize as time proceeds. Indeed, someauthors have found that the timing of drought influenced maizeyield components: ear numbers are mainly reduced by water stressduring the vegetative stage (Cakir, 2004) whereas the number andweight of grains proved to be more susceptible during thereproductive stage (tasselling, silking, or grain filling) (Pandeyet al., 2000; Andrade et al., 2002).

It is interesting that the F1I3 treatment in this study obtainedIWUE and WUE values that were similar to those obtained for theF2I1 and F2I2 treatments and higher than those obtained for F3I1 andF4I1 treatments (Table 5). These results indicate that althoughirrigation rate is vitally important for enhancing WUEs, irrigationfrequency is instead often crucial for maximizing net income perunit water. This fact might be attributed to drip irrigationfrequency determining the soil water content and the distributionof soil water with depth in the ponding zone that develops aroundthe emitter, and, consequently, the amount of water percolationunder the root zone and also the amount of water uptake by theroots (Assouline, 2002; Wan and Kang, 2006; Wang et al., 2006; El-Hendawy et al., 2008b). Therefore, frequent low rates of irrigation(e.g., F1I3) were more effective for increasing irrigation efficienciesthan were infrequent high irrigation rates (e.g., F4I1) (Table 5). Thisresult probably derives from the latter treatment resulting both indramatic fluctuations in soil water in the root zone bringing aboutcyclic water stress for maize root growth before the next irrigationevent and in excessive water percolation due to the amount ofwater applied at each event being (excessively) higher than thesandy soil–water storage capacity. By contrast, the F1I3 treatmentappears to provide the optimum available soil water content in theroot zone without water percolation.

Seasonal water consumption of maize was reported to be 474–605 mm in the Cukurova region of Turkey (Kanber et al., 1990),505–568 mm in semiarid region of Spain (Cavero et al., 2000),353–586 mm in the Thrace region of Turkey (Istanbulluoglu et al.,2002), 581 mm in southeast of Turkey (Yazar et al., 2002), 525–574 mm in Kirklareli, Turkey (Cakir, 2004), 488–497 mm in theAegean region of western Turky (Dagdelen et al., 2006) and 466–656 mm in North Platte, Nebraska (Payero et al., 2008). Thesevalues agree closely with the results from our study.

The response of yield to water supply is quantified through theyield response factor (ky), which quantifies the decrease in yieldcaused by decreases in water supply (Doorenbos and Kassam,

1979). In maize, the decrease in yield is generally proportionallygreater with the increase in water deficit, such that ky values formaize are higher than one in most cases studies. The values of ky

obtained in this study (1.81 in 2007 and 1.86 in 2008; Fig. 2) arehigher than those reported by Doorenbos and Kassam (1979; 1.25),Retta and Hanks (1980; 1.26 (1.12–1.39)), Gencoglan (1996; 1.35(1.08–1.61)), Howell et al. (1997; 1.47) and Popova et al. (2006;1.5). As reported by Alves et al. (1991), the values for ky can be verydifferent due to differences in any of all of climatic changes, cropvarieties, crop management, soil characteristics, and irrigationmethods and may be strongly influenced by periods of water stressoccurring at critical growth stages of the crop. For instance,according to Zhang et al. (2002), water deficits occurring at moresensitive growth stages will result in higher ky values. Igbadun etal. (2007) also noted that the ky value of the flowering stage ofmaize was higher (ranged from 3.03 to 3.50) than for the othergrowth stages, followed by the grain filling and then the vegetativestages.

Thus, treatments with the highest ky values presumably havehad water deficits occurring at critical growth stages. Evidence forthis hypothesis is evident from the wide range values of ky amongdifferent irrigation frequencies observed here, with the highestvalues occurring with medium (F3) and low (F4) irrigationfrequencies and the lowest from F1 and F2, respectively (see Table6). The inferred water deficit for F3 and F4 in combination with I2

and I3 may be because the amount of water applied at eachirrigation event does not meet the long-term water requirement ofthe plants. This is also true of the combination of F4 and I1, with thewater deficit deriving again from the (excessively) high amount ofwater applied at each irrigation event moving below the root zoneto cause water stress just before the next irrigation event due to thelonger irrigation intervals.

A linear relationship has been reported between maize grainyield and seasonal crop ET (Kirnak et al., 2003; Payero et al., 2006)and was also indicated here (Fig. 3). However, when split accordingto the different irrigation frequencies, a second order relationshipis indicated for the F1 treatment (Fig. 4), indicating that theincrease in maize grain yield was not proportional with theincrement in the amount of irrigation water. This phenomenonwas especially obvious when F1 was combined with the highirrigation rate (I1) because a portion of the water applied does notcontribute to ET and is percolated under the root zone. At the sametime, this deep drainage loss did not affect grain yield by waterstress because of the shorter durations between successiveirrigation events. By contrast, the deep drainage loss that occurredunder F4I1, for example, resulted in significant reductions in grainyield due to water stress caused by the longer irrigation intervals.Accordingly, the relationship between grain yield and ET for F4 waslinear (Fig. 4).

Finally, the relationship between WUE and grain yield is oftenused for determining the optimal irrigation strategy for arid andsemiarid regions (Musick et al., 1994; Chen et al., 2003). Based onR2 values, the power model was found to fit our data best, withcoefficient of determinations of 0.95 and 0.97 in 2007 and 2008,respectively (Fig. 5). Under this model, the elasticity of y withrespect to x is defined as the percentage change in y for eachpercentage change in x. Thus, when grain yield is increased by 10%,WUE was increased by 8.0 and 8.5% in 2007 and 2008, respectively(Eqs. in Fig. 5), indicating that high values of WUE are obtained forlarge yield values. Therefore, since grain yields from the F1I3, F3I2

and F4I1 treatments and from the F1I2 and F2I1 treatments do notdiffer significantly from one another, we recommend the F2I1

treatment when irrigation water supplies are sufficient or the F1I3

treatment when they are limited as the best combinations betweenirrigation frequency and amount rate for drip-irrigated maize insandy soils.

Acknowledgements

The authors appreciate very much helpful and constructivesuggestions made by the reviewers.

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Optimal coupling combinations between irrigation frequency and rate for drip-irrigated maize grown...

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