ORIGINAL PAPER

Dean D. Steele á Earl C. Stegman á Raymond E. Knighton

Irrigation management for corn in the northern Great Plains, USA

Received: 3 February 1999

Abstract Irrigation management in¯uences productioncosts and a�ects leaching of nutrients to groundwater.This study was conducted to compare irrigation sched-uling techniques on a ®eld-scale site and to determinewhether signi®cant irrigation water savings and equiva-lent yields could be achieved compared with the prac-tices of other commercial growers in the local area. Thee�ects of four irrigation scheduling techniques on sea-sonal irrigation water requirements and corn grain yieldswere studied for the 1990±1995 seasons at a ®eld-scale(53.4 ha) site within the Oakes Test Area (OTA) of theGarrison Diversion Unit in southeastern North Dakota,USA. The four scheduling techniques, applied with ®eldquadrants and seasons as dimensions of a modi®edLatin square statistical design, included irrigating basedon tensiometer and infrared canopy temperature mea-surements, two water balance methods, and irrigatingbased on CERES±Maize estimates of plant-extractablesoil water. No statistically signi®cant di�erences in sea-sonal irrigation totals were found between irrigationscheduling methods or irrigation quadrants, while sta-tistically signi®cant di�erences were found for season.Corn grain yield was signi®cantly a�ected by seasons,quadrants, and irrigation scheduling methods for boththe current and previous seasons. Compared to othercommercial growers in the OTA, this study maintained5% higher yields and saved approximately 30% in irri-gation inputs. Careful irrigation scheduling, based onany of the four techniques, o�ers the potential to reduceinput costs for irrigated corn production in the area.

Introduction

Much irrigation scheduling research for corn in thenorthern Great Plains, USA has been conducted on aplot scale. For example, Stegman (1982) studied the ef-fects of low, moderate, and severe levels of water stresson corn grain yields at Oakes and Carrington, NorthDakota (ND). Water stresses, de®ned by depletion ofsoil moisture and leaf water potentials, were appliedduring three stages: planting to 12-leaf, 12-leaf to blisterkernel, and blister kernel to maturity. Yields werecompared to maximums obtained in well irrigated plotsin which depletions of plant-available soil moisture wereallowed to reach only 30±40% before irrigation. Steg-man (1982) summarized the study as follows: ``Yieldreduction of less than 5% from potential levels appearslikely in the climatic setting of this study when root zoneavailable water depletions are limited to 60±70% in theearly vegetative period (assumes near ®eld capacitymoisture at planting), 30±40% in the 12 leaf to blisterkernel period, and 50±60% in the later grain ®ll period.''

Stegman (1986), Prunty and Montgomery (1991), andSteele et al. (1994) also studied irrigation schedulingtechniques for corn in ND using lysimeters and small®eld plots. In addition to water balance computations,these studies employed crop water stress index compu-tations based on infrared canopy temperature sensing,tensiometer measurements of soil water potential, andCERES±Maize (Jones and Kiniry 1986) estimates ofplant-extractable soil moisture. All these ND studiesindicated that with careful irrigation management, sig-ni®cant seasonal irrigation water savings can beachieved relative to ``well-watered'' or reference irriga-tion scheduling regimes, without signi®cant corn grainyield reductions.

Compared to plot-scale research, ®eld-scale researchhas advantages because it includes commercial produc-tion constraints (time, labor, cost, energy, etc.), inte-grates across ®eld-scale soil variability, and may appealmore to producers as an educational tool due to its

Irrig Sci (2000) 19: 107±114 Ó Springer-Verlag 2000

D.D. Steele (&) á E.C. StegmanAgricultural and Biosystems Engineering Department,North Dakota State University,Fargo, ND 58105-5626, USAe-mail: steele@plains.nodak.edu

R.E. KnightonUSDA/CSREES-NRE, 808 Aerospace Center,901 D St. S.W., Washington, DC 20250, USA

production-sized nature. The objective of this study wasto compare irrigation scheduling techniques on a ®eld-scale site and determine whether signi®cant irrigationwater savings and equivalent yields could be achievedcompared to the practices of other commercial growersin the local area.

Materials and methods

A 6-year, ®eld-scale (53.4 ha) study was conducted within the OTAof the Garrison Diversion Unit in southeastern ND, USA. The siteis the northwest quarter of Section 29, Township 130 North, Range59 West, Dickey County, ND. Meteorological data were measuredat an automated weather station within 2.4 km of the site. Theweather station was located at 46°04¢ N, 98°06¢ W, and 401 melevation (Enz et al. 1995). Rainfall was measured at the site.Predominant soils at the site are a Hecla ®ne sandy loam (sandy,mixed, Udic Haploboroll) and a Wyndmere ®ne sandy loam(coarse-loamy, frigid, Aeric Calciaquoll).

The irrigation scheduling study reported here was part of alarger project containing other concurrent experiments at the site,including water quality investigations using disturbed- and undis-turbed-pro®le lysimetry (Derby et al. 1998), groundwater wells,and monitoring sites along subsurface drains; fertilizer nitrogenmanagement trials within each irrigated quadrant (Albus andKnighton 1998); and collection of data sets for crop and environ-mental modeling (Steele et al. 1998).

The ®eld was irrigated with a center pivot system and wasnot irrigated prior to 1989. The irrigation system capacity isapproximately 59 l s)1 (940 gal min)1) and can apply approxi-mately 30 mm of irrigation water in 72 h for a 360° revolution.This assumes an application e�ciency of 100% for a 50.9 ha irri-gated area (standard quarter section pivot size), excluding the areacovered by the end gun. Irrigation in 1989 did not impose anyirrigation treatments for di�erent areas of the ®eld. In 1990 thequarter section was divided into four quadrants for irrigationscheduling purposes. The quadrants are denoted by northwest(NW, 13.8 ha), northeast (NE, 12.2 ha), southeast (SE, 16.9 ha),and southwest (SW, 10.5 ha) and include areas covered by the ir-rigation system's end gun. The quadrants were intentionally madeunequal in area to study the e�ects of four irrigation schedulingtreatments on groundwater quality as measured at two locationsalong each of two subsurface plastic drains at the site. That is, thesite was selected from those available within the OTA partly be-cause of the location and con®guration of the subsurface drainageat the site. The drains at the site are ``headwater'' drains, i.e., un-a�ected by upstream agricultural practices. The drains were notperpendicular to the ®eld borders, hence the unequal quadrantsizes. The corn hybrid used each year was Pioneer 3737.

The following four irrigation scheduling techniques were used:

Method A

Irrigations were managed based on real-time sensor feedback. Soilmatric potential measurements from three tensiometers placed at0.30-m depth in the crop row were read hourly by a CR10 datalogger (Campbell Scienti®c, Logan, UT) and averaged daily. Onetensiometer was placed in soil over a nonweighing lysimeter in eachquadrant and two tensiometers were placed adjacent to the lysi-meters. The lysimeters were used for groundwater quality studies(Derby et al. 1998) and are not discussed here. When the averagetensiometer reading at 11 p.m. reached 40 � 10 cbar (kPa), irri-gations were initiated the next day. After canopy developmentpermitted canopy temperature measurements, crop water stressindex (CWSI) values were computed using methods described bySteele et al. (1994). Irrigations were scheduled when CWSI valuesreached 0.25 � 0.05. The tolerances of �10 cbar and �0.05CWSI were used to accommodate the logistics of scheduling the

center pivot irrigation system across four quadrants ± i.e., irriga-tions were started within �1 d of the time indicated by thescheduling methods.

Method B

The water balance algorithm of Stegman and Coe (1984) was usedwith in-season soil moisture corrections to schedule irrigations. The®rst irrigation was delayed until root zone available soil moisturewas estimated to be 60±70% depleted for a root zone managementdepth of 1.22 m, the latter held constant for the whole season.From the ®rst irrigation until the blister kernel (R2) stage (Ritchieet al. 1992), irrigations were timed to fully replace evapotranspi-ration (ET) while maintaining estimated root zone de®cits under50%. From R2 until maturity, estimates of depletions of soilmoisture in the root zone were again allowed to reach 60±70%before irrigations were started. Corrections to soil moisture esti-mates were made when possible by approximately weekly or bi-weekly soil moisture measurements. Soil moisture contents weremeasured by the neutron attenuation method at depths of 0.15,0.30, 0.46, 0.61, 0.91, 1.22, and 1.52 m in ten access tubes perquadrant. Plant-available soil moisture data for each quadrant aresummarized in Table 1. These values represent the average valuesfor each quadrant when the soil is at ®eld capacity.

Method C

Irrigation amounts and timing were designed to replace 80% of ET.The same timing criteria were used as in Method B. However, thegoal of this method was to apply smaller irrigations more fre-quently than in Method B to take better advantage of precipitation.Hence, irrigations were applied using 20% smaller amounts foreach irrigation event.

Method D

Irrigations were applied when CERES±Maize estimates of soilmoisture indicated 60±70% depletion of plant-extractable soil wa-ter (PESW) for a 1.22-m root zone depth. As with Methods B andC, the CERES±Maize model uses a water balance approach tomodeling soil moisture in the root zone. However, CERES±Maizeprovides no direct means to make corrections or updates to itsestimates of PESW. A way to overcome this limitation is to addarti®cial irrigations to the model ± not the ®eld ± to raise themodel's PESW estimates when the model overestimates ET (e.g.,Steele et al. 1997a). This adjustment technique was not used in thisstudy, for the sake of simplicity. Soil physical properties used in themodel were based on texture and 15-bar moisture contents mea-sured on samples from a 101-m grid at the site and averaged foreach quadrant. The version of the CERES±Maize model employedin this study uses the Priestley-Taylor method for ET calculation

Table 1 Plant-available soil moisture for each irrigated ®eldquadrant

Quadrant Plant-available soil moisturea (mm)

Soil Depth

0±0.3 m 0±0.6 m 0±1.2 m

Northeast 38 74 142Northwest 43 84 160Southwest 33 66 117Southeast 33 66 119

aValues represent the average available soil moisture when the soilpro®le is at ®eld capacity.

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(Hoogenboom et al. 1994) and this research simply tested thesuitability of that Et algorithm. That is, no other aspects of themodel, such as plant growth, yield estimations, etc., were used toschedule irrigations.

All application depths were targeted at 32 mm per irrigationduring periods of peak crop water use for Methods A, B, and D,and 25 mm per irrigation for Method C. These application depthsare typical for irrigated corn in the area. The targeted irrigationamounts were ``as measured'' amounts in rain gauges unobstructedby the plant canopy. In each quadrant, four rain gauges were lo-cated along a transect and next to each of four undisturbed-pro®lelysimeters per quadrant. Readings for each quadrant were averagedfor irrigation scheduling purposes. Rain gauges were read eachweekday morning if rain occurred or irrigation water was applied.Each rain gauge had a 101.6 mm (4.0 in) funnel opening on top, afunnel constriction of 8 mm (5/16 in) to minimize evaporation, anoverall cylindrical body 305 mm (12 in) in length, and a measure-ment precision of 2.54 mm (0.01 in).

Corn grain yields were determined by machine harvesting twostrips, each 12 rows wide, across each quadrant. In 1990 through1993, gross harvested weights were determined using a weighwagon, while in 1994 and 1995, yields were determined using acalibrated, on-the-go yield monitoring system on a combine. Yieldswere in all cases determined for each quadrant.

The ®eld-scale experiment (i.e., testing the impact of irrigationscheduling methods on seasonal irrigation requirements and corngrain yields), was conducted according to the method outlined byCochran and Cox (1957, pp. 133±143). Cochran and Cox describeda modi®ed Latin square statistical design for which seasons andquadrants were used as dimensions. To obtain a balanced designfor residual e�ects (in time, i.e., subsequent season), it was neces-sary to have any treatment preceded equally often by every treat-ment, including itself. In 1990, the initial season, all quadrants inthe test ®eld were uniformly managed with Method A. In 1995, thetreatments repeated those in 1994 to balance the design to ``giveindependent estimates of direct and residual e�ects, of approxi-mately equal precision'' (Cochran and Cox 1957). The statisticaldesign is summarized in Table 2.

The null hypothesis of the experiment was that means for sea-sonal irrigation amounts and corn grain yields would not be dif-ferent due to: (1) the e�ects of years (climatological e�ects), (2)irrigation management methods, (3) position or quadrant within

the ®eld, or (4) residual or carry-over e�ects of irrigation man-agement from the previous season. A limitation of the statisticaldesign is that it lacks replication and therefore interaction e�ectscannot be tested directly. That is, it cannot be directly determinedwhether irrigation methods interact with years or quadrants orwhether quadrants interact with years. The physical interpretationis that, as measured by seasonal irrigation amount or crop yield,this experimental design cannot be used to determine responsessuch as the following: (1) whether one irrigation scheduling methodperforms better in one quadrant than another, (2) whether a par-ticular irrigation scheduling method works best in a relatively dryyear or a relatively wet year, and (3) whether one quadrant doesbetter in a particular year compared with another. For this ex-periment, replication would have involved a 12-year cycle of re-search, rather than a 6-year experimental plan. A 12-yearexperiment was impossible because of time and cost constraints.

Seasonal irrigation amounts and corn grain yields were ana-lyzed using linear model techniques (e.g., Rao 1973; Searle 1971).The response yij in the jth quadrant for the ith year is given by

yij � l� ai � bj � ck � dl � eij �1�where l is the general e�ect; a1, a2, ¼, a6 represent the e�ect of theyears 1990±1995, respectively; b1, b2, b3, and b4 represent the e�ectsof the quadrants SW, SE, NE, and NW, respectively; c1, c2, c3, andc4 represent the e�ects of irrigation Methods A, B, C, and D, re-spectively; d1, d2, d3, and d4 represent residual e�ects, i.e., the e�ectsof the methods A, B, C, and D, respectively, in the quadrants in theimmediately following years; and eij represents random error. Twoexamples illustrate the model with and without residual e�ects: (1)Method C was applied to the NE quadrant in 1991 and Method Awas applied to the NE quadrant in 1990 (Table 2), soy23 � l + a2 + b3 + c3 + dl + e23; and (2) Method A was ap-plied to the SE quadrant in 1990 and there was no treatment ap-plied in 1989, so y12 � l + a1 + b2 + c1 + 0 + e12. TheInteractive Matrix Language procedure in SAS was used to com-pute analysis of variance (ANOVA) tables.

The irrigation management method for any quadrant was madeindependent of the methods for the remaining quadrants by occa-sional dry movement of the single center pivot irrigation system tosatisfy four irrigation schedules, i.e., one for each quadrant. Notethat amounts of applied fertilizer N were constant across quadrantsfor a given year and that the statistical plan was not a Graeco-Latin

Table 2 Irrigation schedulingmethods, seasonal irrigationwater inputs, and correspond-ing Oakes Test Area (OTA)averages

Year Irrigation scheduling methoda and seasonal irrigationtotals (mm)

Average irrigationamounts (mm)

Quadrant Fieldb OTAc

Southwest Southeast Northeast Northwest

1990 A 193 A 192 A 197 A 179 190 2541991 A 199 D 134 C 117 B 104 139 2081992 B 138 A 80 D 51 C 98 92 1631993 D 91 C 52 B 40 A 43 57 861994 C 108 B 209 A 152 D 131 150 2411995 C 155 B 132 A 207 D 205 175 201

Averages 147 133 127 127 134 192

a Irrigation scheduling methods:A, Irrigated when tensiometer at 0.30-m depth reached 40 � 10 kPa and/or CWSI = 0.25 � 0.05.B, Water balance: allowed 60±70% estimated depletion of plant-extractable water before ®rst irriga-tion, full ET replacement through blister kernel (R2) stage, then allowed estimated depletions up to 60±70% until maturity.C, Replaced 80% ET, i.e., same criteria as Method B, but each irrigation was 20% smaller.D, Irrigated when CERES±Maize predictions of PESW reached 60±70% depletion.b Field average irrigations are simple averages of quadrant totals and are not area-weighted. Irrigationamounts for each quadrant are the averages of rain gauge readings in each quadrant.c Irrigation averages for the OTA include OTA-delivered water, groundwater (not delivered by theOTA pumping plant), and farmer-reported application depths. Irrigation e�ciencies were not mea-sured or estimated and are not included in the calculations.

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square designed to test for interactions between irrigation man-agement and N fertilizer management.

Results and discussion

Irrigation water management Method A required anaverage of 160 mm, B required 125 mm, C required106 mm, and D required 122 mm. For comparison, ir-rigation amounts applied to each quadrant are summ-arized in Table 2. Irrigation amounts applied by othercommercial corn growers in the OTA (D. Esser, Agri-cultural Practices Inventory, Garrison Diversion Con-servancy District, Oakes, ND; personal communication1996) are also shown in Table 2. The weather for the siteis summarized in Table 3 and yield data are summarizedin Table 4. Yields in 1992 were depressed due to a cool

growing season. Yields in 1993 were low due to coolweather and frost in September before the crop matured.Compared to simple averages for other commercial corngrowers in the OTA for 1990±1995, this study demon-strated an average irrigation water savings of approxi-mately 30% while surpassing their yields by 5%.

Irrigation scheduling went as expected, with the ex-ception of plant canopy temperature sensing for sched-uling Method A. Reliable values of CWSI were di�cultto obtain in some years due to high relative humidity,intermittent cloudiness, and low potential ET. The resultwas that the tensiometer measurements were used pre-dominantly to schedule irrigations for this method. Notethat infrared canopy temperature sensing has a relativelyhigh equipment cost compared to the other methodsused here. However, it may compare favorably with theother methods when the cost of soil characterization isconsidered.

The ANOVA for seasonal irrigation amounts(Table 5) shows that direct and residual e�ects of irri-gation scheduling methods did not a�ect seasonal irri-gation amount, nor did ®eld quadrants. The factor of``Year'' produced a signi®cant e�ect on seasonal irriga-tion amount at the 0.05 level. The reader is remindedthat ``Year'' was a blocking factor and not an experi-mental treatment, such as in a factorial design. That is,the results indicate that blocking against the e�ects ofdi�erent years was important and strengthened the ex-perimental design.

The lack of direct irrigation scheduling e�ects onseasonal irrigation amounts indicates that the fourmethods of irrigation scheduling are essentially equiva-lent for the northern Great Plains, in terms of irrigationwater expenses. Methods B and C are recommended ®rstbecause of their similarity to the commonly usedCheckbook water balance method for irrigation sched-uling (Lundstrom and Stegman 1988) and becauseMethods B and C did not produce yield reductions,discussed below.

The labor, energy, equipment, input data (e.g.,weather), and soil characterization requirements of themethods must be considered when selecting a method.

Table 3 Weather summary for the site near Oakes, ND

Year Precipitation (mm) Growing degree

1 May to30 Sept

Prioro�-Seasonb

units (°C)a

1990 267 N/A 12991991 335 27 13891992 315 113 11511993 443 121 11151994 340 27 13201995 314 149 1299

Averages 336 87 1262

Long-termaverages

329c 172 1253

aGrowing degree unit (GDU) calculation: GDU (°C) = [(Tmax +Tmin)/2]±10, with these daily constraints: if Tmin < 10, Tmin = 10;if Tmax > 30, Tmax = 30; and if GDU < 0, GDU = 0. Totalshere computed for 3 May±26 September (Albus et al. 1990).b Indicates precipitation received at the Oakes weather station forthe period 1 October through 30 April prior to the speci®ed 1 May±30 September growing season. Data for 18 December 1990 to 30April 1991 were not available.c Long-term precipitation average was based on 1951±1980 data(US Department Commerce 1982).

Table 4 Corn grain yields (kg/ha) and corresponding OakesTest Area (OTA) averages

Year Corn Grain Yieldsa (kg/ha) Average Corn GrainYields (kg/ha)

QuadrantFieldb OTA

Southwest Southeast Northeast Northwest

1990 A 9350 A 9290 A 8350 A 8160 8790 85401991 A 9040 D 9040 C 8350 B 7970 8600 85401992 B 5840 A 5780 D 5020 C 4580 5310 57101993 D 5080 C 4210 B 3640 A 3450 4100 42701994 C 11500 B 11900 A 9600 D 9600 10700 87301995 C 9540 B 9920 A 7530 D 8100 8770 8410

Averages 8390 8360 7080 6980 7710 7370

a Letters A±D denote irrigation scheduling method, de®ned in Table 2.b Field average yields are simple averages of quadrant totals and are not area-weighted.

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For example, the smaller, more frequent, irrigations re-quired by Method C produced a smaller seasonal aver-age irrigation requirement and smaller seasonalpumping cost than the other methods. Although smaller,more frequent irrigations more e�ciently accommodatein-season rainfall when rain is relatively frequent thando larger irrigations, center-pivot movement and wearmay be reduced during periods of hot and dry weatherby applying larger irrigation water amounts with eachirrigation.

Irrigation system capacity and soil water holdingcapacity must also be considered when selecting amethod. For the water balance methods, Method Bwould be preferred for larger-capacity systems and soilswith larger water-holding capacities, while Method Cwould be preferred for smaller-capacity systems andsoils with smaller water-holding capacities. However, adrawback associated with Method C is that a mechani-cal breakdown of the irrigation system under thismethod would pose a higher risk of yield-reducing soilmoisture de®cits compared to Method B. This is becauseMethod B has larger application depths at each irriga-tion event and would therefore provide a larger reserveof soil moisture than Method C.

From a management perspective, the irrigationscheduling methods varied in the amount of ®eld ob-servation required. Daily CWSI or tensiometer readingswere used to schedule irrigations for Method A. Soilmoisture was measured and water balance algorithmsadjusted or updated approximately weekly or biweeklywith Methods B and C. The typical magnitude of in-season adjustments or corrections to this type of waterbalance algorithm is discussed by Steele et al. (1997b).No adjustments to CERES±Maize were made with in-season soil moisture measurements with Method D.

The ANOVA of irrigation amounts showed no sta-tistically signi®cant di�erences due to ®eld quadrant.This indicates that the methods were equally e�ective forall the ®eld quadrants. Since the predominant soils at thesite represent soils in the OTA with the highest (Hecla)and lowest (Wyndmere) yield potentials, our irrigation

scheduling methods appear adaptable to a wide range ofsoils in the OTA.

The lack of residual irrigation scheduling e�ects onseasonal irrigation water requirements was attributed too�-season precipitation (Table 3). The long-term (1951±1980) average of 172 mm of precipitation for 1 Octoberto 30 April is su�cient to re®ll the soil pro®le to ®eldcapacity. These data support previous recommendationsthat moisture ``banking'' for the next season is not nec-essary in this climatic setting. Moreover, excess irrigationwater applications late in the season increase the prob-ability of o�-season leaching of nitrogen from the top-soil, making it unavailable for the next growing season.In this setting, we advise an irrigation scheduling regimethat produces soil moisture de®cits of 50±60% by cropmaturity, but caution against severe late-season waterstresses as a means to reduce input costs or improveharvest-time tra�ckability. For example, in Stegman's(1982) study discussed earlier, yield reductions were 31%from potential levels when soil moisture de®cits wereallowed to reach 80±100% during the growth periodranging from blister kernel to physiologic maturity.

The amount of in-season rain and the variability ingrowing degree units, i.e., potential ET, from one seasonto another (Table 3) directly a�ect the seasonal irriga-tion water requirements. The total of May throughSeptember rainfall plus ®eld-average irrigation amountwas 457 mm for 1990, 473 mm for 1991, 407 mm for1992, 500 mm for 1993, 490 mm for 1994, and 489 mmfor 1995.

More importantly, the timing of rainfall events in thisclimatic setting requires an active and ongoing regime ofirrigation scheduling, rather than a passive or ``prepro-grammed'' approach to irrigation scheduling. For ex-ample, Fig. 1 shows the cumulative rainfall andreference crop ET values for the period 1 June to 10 Julyfor 1991 and for the same period in 1995. Referenceevapotranspiration (ETr) values were computed by theJensen±Haise method (Jensen and Haise 1963). In 1991,cumulative rain was 38 mm and cumulative ETr was41 mm for 1±9 June, then rain lagged ETr until 20 Junewhen cumulative rain nearly caught up (109 mm for rainvs 113 mm for ETr). From 10 June to 2 July 1995, therewere 23 days with no rain greater than 2 mm. The ETr

during the same period was higher than that for 1991and produced a de®cit, ETr minus rain, of 138 mm by 2July 1995. From 2 July to 5 July 1995, 67 mm rain wasrecorded at the weather station. In this case, a ®xed ir-rigation schedule developed from the 1991 data wouldhave caused underirrigation of the crop in 1995, aschedule developed from the 1995 data would havecaused overirrigation of the crop in 1991; and an ``av-erage'' schedule would ®t neither year.

The ANOVA for corn grain yields (Table 6) showsthat years and quadrants were statistically signi®cantfactors at the 0.01 level and that direct and residual ef-fects of irrigation scheduling methods were signi®cantfactors at the 0.05 level. It is important to remember thatthe same quadrants were used each year and this is a

Table 5 Analysis of variance for seasonal irrigation water amounts

Source of variation df Sum ofsquares

Meansquare

F

Years 5 41570 8310 5.02a

Quadrants 3 2480 827 <1Scheduling method:direct e�ectsb

3 3120 1040 <1

Scheduling method:residual e�ects

3 1190 397 <1

Error 9 14900 1660

Total 23 63260

a Signi®cant at the 0.05 level.b ``Direct e�ects'' refers to the e�ects of the current season's irri-gation water management on the current season's total irrigationrequirement. ``Residual e�ects'' refers to the e�ects of the previousseason's irrigation water management on the current season's totalirrigation requirement.

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Latin square experiment, not a nested design; thereforewe are not reporting results for quadrants ``within'' or``across'' years. Irrigation water management Method Aproduced an average yield of 8220 kg/ha, B produced7850 kg/ha, C produced 7660 kg/ha, and D produced7340 kg/ha.

Estimators for the terms in Eq. 1 are presented inTable 7. For both irrigation amount and crop yield, theestimators ai for years average approximately twice or

more the magnitude of the estimators for quadrants,irrigation water management methods, and residual ef-fects. This indicates that seasonal irrigation require-ments and yield potentials are highly variable from year

Table 6 Analysis of variance for corn grain yields

Source of variation df Sum ofsquares

Meansquare

F

Years 5 1.23383 ´ 108 2.46766 ´ 107 425.80a

Quadrants 3 9.97048 ´ 106 3.32349 ´ 106 57.35a

Scheduling method:direct e�ectsb

3 7.17743 ´ 105 2.39248 ´ 105 4.13c

Scheduling method:residual e�ects

3 1.03517 ´ 106 3.45057 ´ 105 5.95c

Error 9 5.21662 ´ 105 5.79624 ´ 104

Total 23 1.35628 ´ 108

a Signi®cant at the 0.01 level.b ``Direct e�ects'' refers to the e�ects of the current season's irri-gation water management on corn grain yields. ``Residual e�ects''refers to the e�ects of the previous season's irrigation water man-agement on the current season's corn grain yield.c Signi®cant at the 0.05 level.

Fig. 1 Cumulative rain and reference evapotranspiration at the sitefor 1 June±10 July for 1991 and for 1995

Table 7 Estimators for the linear statistical model yij =l + ai + bj + ck + dl + eij

Estimator Description Response variable yij

Irrigation (mm) Yield (kg/ha)

l General e�ect 129 7823a1 1990 45.5 1258a2 1991 )3.8 1192a3 1992 )36.8 )2519a4 1993 )72.1 )3727a5 1994 21.3 2848a6 1995 46.0 948b1 SW quadrant 17.0 692b2 SE quadrant )0.8 613b3 NE quadrant )9.1 )574b4 NW quadrant )7.1 )731c1 Method A 15.8 )293c2 Method B 2.5 247c3 Method C )19.8 18c4 Method D 1.5 28d1 Residual e�ect of A

the next year13.7 )416

d2 Residual e�ect of Bthe next year

0.0 86

d3 Residual e�ect of Cthe next year

)3.6 275

d4 Residual e�ect of Dthe next year

)10.2 55

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to year. As discussed previously, a near real-timemethod of irrigation scheduling is needed to account forunexpected rainfall and the weather variability in thisclimatic setting.

The estimators bj for yield are positive in the SW andSE quadrants and negative in the NE and NW quad-rants. That is, the south half of the ®eld produced largeraverage yields than the north half of the ®eld (see alsoTable 4). The di�erence in yield potential between thenorth and south halves of the ®eld was attributed to soilfactors, rather than to management factors. The northhalf of the ®eld, especially the NW quadrant, hadgroundwater seepage and attendant salinity problemsprior to installation of subsurface drainage. The readeris reminded that this a priori knowledge of the ®eld sitewas part of the decision to use a Latin square design andblocking against quadrant e�ects on yield.

The di�erences in estimators bj for irrigationamounts between the north and south halves of the ®eldre¯ect the smaller water-holding capacities of the soils inthe south half of the ®eld (Table 1). That is, the southhalf of the ®eld generally required more irrigation thanthe north half (Table 3).

Although Method A produced the highest averageyield, its estimator c1 is the largest in magnitude of the``Method'' e�ect estimators and is negative. The e�ect ofc1 � ÿ293 kg/ha is overshadowed by the e�ect ofa1 � 1258 kg/ha for the 1990 season, in which MethodA appeared four times. The physical interpretation isthat yield is a�ected more strongly by year-to-yearvariation in climate than by the choice of one of the fourirrigation scheduling methods used in this study.

Note that the residual e�ects di of irrigation schedul-ing methods on yields appear inversely proportional tothe average seasonal irrigation amounts for each method.For example, Method A produced the highest average ofseasonal irrigation amounts, 160 mm, and the strongestnegative e�ect on yield the following year, )416 kg/ha.On the other hand, Method C had the smallest seasonalirrigation average, 106 mm, and the strongest residuale�ect on yield, 275 kg/ha. These results may indicate thathigher seasonal irrigation amounts caused increasedlevels of nitrogen leaching from the soil pro®le ± eitherduring the season or during the o�-season. For example,the higher irrigation amounts may have produced lesscapacity in the soil pro®le to store o�-season precipita-tion, thereby causing increased o�-season leaching ofnitrogen from the soil pro®le and, subsequently, loweryields the next season. Nitrogen fertility and lysimeterstudies were conducted concurrently with this study atthe site and may provide insight into these phenomena,but are beyond the scope of this paper.

The e�ects of the irrigation methods on seasonal ir-rigation amounts and corn grain yields were analyzed inmore detail using pairwise comparisons. The compari-sons were made using the variance±covariance matrix ofthe estimators ci and a t-statistic with 9 degrees offreedom at the 0.05 level of signi®cance. The results in-dicate that the irrigation scheduling methods were not

statistically di�erent in terms of seasonal irrigationamount (Table 8), while Method B had a signi®cantlystronger positive impact on yield than the negative im-pact on yield exhibited by Method A. The estimatorc2 � 247 kg/ha (Table 7) indicates that the water bal-ance Method B produced the strongest positive in¯uenceon yields. Methods B and C were in the highest statis-tical grouping for yield (Table 8).

The overall experiment produced an average seasonalirrigation application of 134 mm, compared to an av-erage of 192 mm for other commercial irrigated corngrown in the OTA. The saving of 58 mm per seasontranslates into savings of US $7.12 ha)1 year)1 during1990±1992 and US $8.53 ha)1 year)1 during 1993±1995(D. Esser, personal communication 1997). These savingsare based on water service charges of US $19.77 ha)1

each year and energy charges of US $0.0122 m)3 during1990±1992 and US $0.0146 m)3 during 1993±1995. Thesavings do not include operating costs such as energyand labor to run the irrigation machine.

Stegman (1982) used an irrigation e�ciency (IE)values, de®ned as yield divided by seasonal irrigationamount, to compare irrigation methods. For a prelimi-nary analysis, the procedure of Cochran and Cox (1957,pp. 133±143) was used to analyze IE values for the1991±1995 seasons. No signi®cant di�erences werefound due to years, quadrants, direct e�ects of irrigationmethods, or residual e�ects of irrigation methods. Fur-ther statistical analyses of IE values, such as by using thelinear model of Eq. 1, were not conducted.

Conclusions

This 6-year, ®eld-scale study of four irrigation schedulingmethods for continuous corn indicates that compared toother commercial corn growers in the OTA of ND, sig-ni®cant savings in seasonal irrigation water amounts canbe achieved while maintaining yields at slightly higherlevels. All the irrigation scheduling methods producedstatistically similar seasonal irrigation amounts, whileMethod B's positive e�ect on yield was signi®cantlylarger than Method A's negative e�ect on yield. Thus,in terms of yield, Method B was distinctly betterthan Method A. Year-to-year variations in climatic

Table 8 Pairwise comparisons of estimators for the e�ects of irri-gation scheduling methods on seasonal irrigation amounts andcorn grain yields

Estimator Method E�ect onirrigationamount (mm)

Estimator Method E�ecton yield(kg/ha)

c1 A 15.8a* c2 B 247a

c2 B 2.5a c4 D 28ab

c4 D 1.5a c3 C 18ab

c3 C )19.8a c1 A )293b

* Values followed by the same letter in the respective columns arenot signi®cantly di�erent at the 0.05 level.

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conditions signi®cantly a�ected both seasonal irrigationrequirement and yield, meaning that a preprogrammedirrigation scheduling regime will not work in this climaticsetting. In other words, irrigation scheduling must followreal-time monitoring or modeling of crop water use.Field quadrant had a signi®cant e�ect on yield but noton seasonal irrigation requirement. Residual e�ects, i.e.,the e�ects of the previous season's irrigation schedulingon the current season's irrigation requirement or yield,were not statistically signi®cant for irrigation amountsbut were signi®cant for yield. For each irrigationscheduling method, seasonal averages for irrigationamounts appeared inversely correlated with yield thenext year, but detailed analyses based on data fromconcurrent nitrogen fertility and lysimeter studies at thesite were beyond the scope of this study.

We recommend either Method B or Method C be-cause they are similar to a commonly used Checkbookmethod for irrigation scheduling. These methods' simi-larity to the Checkbook method is an advantage becauseit builds upon irrigators' prior knowledge of the lattermethod. Methods B and C produced statisticallyequivalent e�ects on yield. Method B is suited for larger-capacity irrigation systems and soils with largerwaterholding capacities, while Method C is suited forsmaller-capacity irrigation systems and soils with smallerwater-holding capacities. However, Method C usessmaller irrigation amounts at each irrigation event, so itsincreased risk of yield-reducing soil moisture de®citscaused by possible breakdown of the irrigation systemmust be weighed into the selection of a method.

Acknowledgments The research was supported by North DakotaAgricultural Experiment Station Project 5041 and by the U.S.Department of Interior, Bureau of Reclamation. Use of equipmentand trade names does not constitute endorsement by NorthDakota State University or the U.S. Bureau of Reclamation;names are provided for information only. The authors gratefullyacknowledge the assistance of Nathan Derby, Dale Coe, WalterAlbus, James Moos, Wade Kuehl, and Dale Esser for ®eld oper-ations and Je�rey Terpstra, Marepalli Rao, Surekah Mudivarphy,Richard Horsley, James Hammond, and Curt Doetkott forstatistical consultations.

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