Irrig Sci (2013) 31:507–521 DOI 10.1007/s00271-012-0326-4

ORIGINAL PAPER

Analysis of water application costs with a centre pivot system for irrigation of crops in Spain J. Montero • A. Martı´nez • M. Valiente M. A. Moreno • J. M. Tarjuelo

•

Received: 5 June 2011 / Accepted: 13 February 2012 / Published online: 29 February 2012  Springer-Verlag 2012

Abstract The aim of this study was to present a methodology to analyse the main factors that influence annual water application costs in centre pivot irrigation systems and to determine the most cost-effective centre pivot design, given the variables of machine length, lateral pipe diameter, sprinkler type (LEPA and fixed and rotating spray plate sprinklers (FSPS and RSPS)), system capacity, application efficiency, and water and energy costs for the irrigation of crops such as maize under conditions in Spain. Annual water application costs were calculated as the sum of the investment (Ca), energy (Ce), water (Cw), and equipment maintenance costs (Cm). Parameters used to assess the influences on pivot design were system capacity Sc = 1.25 L s-1 ha-1; application efficiency Ea = 80% for FSPS, Ea = 85% for RSPS, and Ea = 90% for LEPA; water price Pw = 0.06 € m-3 (0.081 US dollars); energy price Ene = 0.10 € kWh-1 (0.135 US dollars); net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1; and net daily peak crop water requirement Nnmax = 7.63 mm d-1 for maize. Results indicate that for plots smaller than 30 ha, the recommended pipeline diameter is 127.0 mm (5 in); for 30–40 ha, 168.3 mm (6 5/8 in); for 40–75 ha, 219.1 mm (8 5/8 in); and for 75–100 ha, 254.0 mm (10 in). A multidiameter pipe solution only slightly reduced water application costs in most cases Communicated by S. O. Shaughnessy. J. Montero  A. Martı´nez  M. Valiente  M. A. Moreno  J. M. Tarjuelo (&) Centro Regional de Estudios del Agua, Universidad de Castilla-La Mancha, Campus Universitario, s/n, 02071 Albacete, Spain e-mail: [email protected] J. Montero e-mail: [email protected]

studied. It was also determined that water costs and irrigation efficiency have a major influence on the total annual cost of water application; however, system capacity and energy price did not strongly affect total cost. For this reason, water application uniformity is very important and can be accomplished using a proper nozzle package and regular maintenance. The paper helps farmers determine the most cost-effective centre pivot design and management.

Introduction Efficient water and energy use takes on great importance in agriculture due to the widespread tendency of reduced water availability and increasing energy costs, which determine the viability of irrigated agriculture in many areas of the world. In Spain, 24% of the 3.4 Mha of irrigated land is managed with sprinkler irrigation systems, with a preference for two methods: centre pivot and set systems (MARMA 2008). Centre pivot systems are replacing surface and other sprinkler irrigation systems due to the ability to programme them, coverage of a large area, reliability, high application uniformity, and the ability to operate these systems on relatively rough topography. In Spain, a centre pivot field size varies between 15 and 165 ha, with a system capacity of 1.2–1.4 L s-1 ha-1, for irrigating crops such as cereals (wheat, barley, and maize), onion, garlic, alfalfa, or sugar beet. In regions like Castilla-La Mancha, more than 60% of irrigation water is groundwater, with a well capacity of 20–250 L s-1. Centre pivot systems generally entail a larger upfront investment but require less labour to operate and have a lower water application cost than a solid set system (Tarjuelo 2005, Ortiz et al. 2006) and therefore is the most

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commonly used sprinkler irrigation system in plots greater than 10–15 ha when there is no restriction on factors such as shape, layout, and size of the field. Water application uniformity with an irrigation system helps optimize energy and water consumption and crop yield and minimize the environmental impact of irrigation when additional water is applied to compensate for the non-uniformity of irrigation (Louis and Selker 2000). The application rate and water application uniformity with centre pivots depend mainly on sprinkler type, spacing along the lateral pipe, height above the ground, and nozzle pressure and size (Allen et al. 2000; Keller and Bliesner 1990; Duke et al. 1991; Faci et al. 2001; Montero et al. 1997, 2003; Tarjuelo 2005). Ortiz et al. (2009), in an experiment with sugar beets, reported that wind drift and evaporation losses (WDELs) were significantly higher with the fixed spray plate sprinklers (FSPS) placed 2.5 m above the ground (FSPS 2.5) than with the rotating spray plate sprinkler (RSPS) placed 1 m above the ground (RSPS 1). The WDELs obtained for the FSPS 2.5 combination were 8% for night irrigation events and 13.7% for daytime irrigation events. The lowest WDELs were registered with RSPS 1, ranging from 3.3 to 8.2% under night and day operation conditions, respectively. These results were obtained for an average wind speed of 1.3 m s-1 at night and 3.5 m s-1 during the day. Application efficiency also impacts total water application costs. Schneider and Howell (1990) reported an application efficiency of 95–98% using a linear move with LEPA over 9-m2 weighing lysimeters. Efficiency was aided because the evaporation and drift losses were very low. However, although the reported application efficiencies for LEPA irrigation are 10% greater than for spray irrigation (low-elevation spray application, LESA, or medium-elevation spray application, MESA), the on-farm efficiency of the LESA and MESA may be nearly equal because runoff with LEPA significantly reduces its efficiency (Buchleiter 1990; Spurgeon et al. 1995; Schneider and Howell 1999). In sprinkler irrigation systems, the main innovations have occurred in the spray plate designs, resulting in sprinklers that work under low pressure (between 100 and 200 kPa), with a higher proportion of average nozzle sizes between 1.5 and 4.5 mm in diameter and a greater wetted area (Sourell et al. 2003; Playa´n et al. 2004; Tarjuelo 2005). In this regard, it is important to advise farmers on the design and management of centre pivot systems, which can lead to lower water application costs. These costs include expenses for equipment (e.g. pumps, pipes, sprinklers), energy, labour, maintenance, and water (Montero et al. 2004; Ortiz et al. 2006). The cost of the sprinkler irrigation system depends on the equipment and its design, materials, and level of automation. Cost is also influenced by other factors such as shape, layout, and size of the field;

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distance between the water source and the field; and pumping requirements (Van der Gulik 2003). Water as a production factor has a cost and therefore should have an assigned price. A first approximation of irrigation water price is the cost of obtaining it (Caballer and Guadalajara 1998). The assigned price corresponds to the water available at the intake of the machine, with a flow rate appropriate for centre pivot operation. Annual investment in pumping station, pipes, and other regulation and control elements (automatic valves, flow meter, air relief valve, etc.); maintenance; and labour are also included within the water price. Maize (Zea Mays L.) achieves high yields under semiarid conditions but with high water requirements, which in many areas around the world means an important restriction due to water scarcity (Plan Bleu 2004; Martı´n de Santa Olalla et al. 2007; Iba´n˜ez et al. 2008). As this crop is one of the most important cereals in terms of production (FAO 2011), more efforts have been dedicated to both improving water use efficiency through regulated deficit irrigation (RDI) techniques (Eck 1984; English and Raja 1996; Kang et al. 2000; Payero et al. 2006; Farre´ and Faci 2009) and minimizing irrigation water application costs by improving the design and management of irrigation systems. Throughout the history of sprinkler irrigation, there has always been interest in finding those system characteristics that yield the least expensive results with irrigation (Kumar et al. 1992; Esquiroz and Puig 2001; Montero et al. 2004; Ortiz et al. 2006). Also, numerous cost-benefit analyses have been performed for optimal water use with different irrigation systems (Khanjani and Busch 1982; Ortega et al. 2004b). In Spain and other regions, centre pivot systems with a lateral pipe diameter of 168.3 mm (6 5/8 in) and a system capacity of 1.25 L s-1 ha-1 have been widely used to irrigate fields of 60–70 ha. This design, which was once costeffective (Tarjuelo 2005), may no longer be the optimal design with increasing energy prices. The aim of this study was to analyse the main factors that influence annual water application costs in centre pivot irrigation systems and determine the most cost-effective centre pivot design. The methodology has been applied to the case of the Castilla La Mancha Region in Spain, where corn has been selected as an example to quantify irrigation water needs.

Methodology To identify the most cost-effective centre pivot sprinkler irrigation design, the annual water application cost was calculated. This is defined as the cost of applying a cubic metre of water to the soil for crop use, calculated as the

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sum of investment, maintenance, energy, and water. Because this study only aimed to select the machine characteristics that imply low cost water application, a circular field irrigated by a centre pivot was selected. The following equipment was considered: sprinkler package, lateral pipe diameter, spans, towers, and overhangs necessary according to lateral length, control panel, alignment and security systems. The infrastructure necessary for water delivery to the pivot was not taken into account, and runoff problems were not considered. Since the size of the machine was the main variable analysed, water application costs were obtained from lateral pipes ranging in length from 55 m (1 ha of irrigated area) to 780 m (190 ha of irrigated area). For optimizing the length of the centre pivot lateral pipeline, multiple pipe diameters were used (Allen et al. 2000; Valiantzas and Dercas 2004): 127.0 mm (5 in), 168.3 mm (6 5/8 in), 219.1 mm (8 5/8 in), and 254.0 mm (10 in). In this study, 2.8, 3.0, 3.2, and 3.5 mm thicknesses were considered for diameters of 127.0, 168.3, 219.1, and 254.0 mm, respectively. To select the length of each machine, span lengths of 43, 49, 55, and 61 m were considered with lateral diameters of 127.0 and 168.3 mm (Table 1), span lengths of 43 and 49 m were considered for pipelines with a diameter of 219.1 mm, and a 36-m span length was considered with a pipeline diameter of 254.0 mm. Four lengths of overhang were considered (6, 11, 17, and 25 m), and no gun was used in the far end of the lateral for all pipeline diameters. Three sprinkler types, one FSPS and two RSPS (Rotator or Wobbler), were located 2.5 m above the ground. Information regarding the working pressure, sprinkler spacing, and width of coverage recommended by the manufacturer (Table 2) were applied to obtain proper water distribution uniformity. In addition, the LEPA system was analysed with a discharge point 0.2 m above the soil surface and an operating pressure of 40 kPa. To analyse the influence of each factor in irrigation water application cost, the following reference values of the different parameters were considered: system capacity Sc = 1.25 l s-1 ha-1; application efficiency Ea = 80% for FSPS, Ea = 85% for RSPS, and Ea = 90% for LEPA; water price Pw = 0.06 € m-3 ($94 acre-feet); energy price Ene = 0.10 € kWh-1 (0.135 US dollars); net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1; and daily peak net crop water requirement Nnmax = 7.63 mm day-1 (representative data for maize in the Albacete area, Spain) (Martin de Santa Olalla et al. 2003; De Juan et al. 2008). The water application costs using centre pivots, expressed as total annual cost per unit irrigated area (CT, € ha-1 year-1), were determined as the sum of investment, energy, water, and maintenance costs.

509 Table 1 Cost summary of the main components of a centre pivot Component Span and tower Diameter (mm)

Length (m)

Cost (€)

127 (5 in)

61

4,933

55

4,681

49

4,415

43

4,196

168.3 (6 5/8 in)

61

5,712

55

5,394

49

5,075

43

4,937

219.1 (8 5/8 in)

49

6,002

254.0 (10 in)

43 36

5,636 5,713

Overhang Diameter (mm)

Cost (€ m-1)

101.6 (4 in)

70

168.3 (6 5/8 in)

75

Component

Cost

Drops hose

2.2 € m-1

Pressure regulator and counterweight

9€

Sprinkler type spray

3€

Sprinkler type rotator or wobbler

15.7 €

LEPA quad spray

1€

Transport and assembly

780 € span-1

Additional equipment (control panel, alignment and security systems, central base of concrete, high flotation wheels, etc.)

5.500 €

Investment costs The investment annuity (A = CRF Ci, € year-1) for the total investment cost of the centre pivot (Ci, €) was computed considering a useful life (n = 15) (Scherer and Weigel 1993) and an interest rate (1) of 6%. The capital recovery factor (CRF) and the investment annuity per unit of irrigated area (Ca, en € ha-1year-1) were calculated using Eqs. 1 and 2: CRF ¼ Ca ¼

ið1 þ iÞn ð1 þ iÞn  1

A CRFCi ¼ S S

ð1Þ ð2Þ

where S is the area irrigated by the centre pivot (ha). To determine the total investment cost (Ci, €), the average prices of equipment from different manufacturers and distributors in Spain were considered (Table 1). In

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addition, the following equipment was considered: the diameter of the lateral pipe (127.0; 168.9; 219.1; 254.0 mm) and its corresponding triangular structure, the number of spans, towers, and overhangs necessary according to lateral length, control panel, alignment and security systems, central base of concrete for the pivot foundation and high flotation wheels. We also took into account the cost of the sprinkler packages, using drop hoses to place the sprinkler 2.5 m above the ground (or 0.2 m for LEPA), the counterweight, pressure regulators, and drains by considering the number of exits as well as transport and assembly costs. Considering that span length selection is conditioned by the radial and tangential (in the circular direction) slope of the field, as well as the soil texture and structure, the investment costs of equipment with three different pivot configurations were calculated to analyse the influence of these factors: (a) all spans of 61 m plus overhangs of 6 or 25 m; (b) all spans of 43 m, plus overhangs of 6 or 25 m; and (c) a combination of long and short span lengths, plus an overhang with a length selected by considering the total length. For example, with pipeline diameter 168.3 mm and lateral length between 300 and 500 m, the spans of 54.86 m in length were used, except in the last three spans, where lengths of 43 and 37 m were considered. Energy cost The annual energy cost per unit of irrigated area (Ce, € year-1 ha-1) was calculated using Eq. 3: Ce ¼

POt Enc S

9:81Q0 H0 Ep

Working pressure (kPa)

Width of coverage (m)

Sprinkler spacing (m)

Sprinkler height (m)

Spray

120

12

2.88

2.50

Wobbler

150

16

2.88

2.50

Rotator

180

20

3.84

2.50

LEPA

40

1.50

0.20

considering the necessary sprinkler pressure and discharge, as well as losses due to friction in the lateral pipe (Eqs. 5 and 6). The efficiency of the pumping system was calculated from field data and shown to be 0.65 based on an energy analysis of irrigation systems in the Castilla-La Mancha Region (Moreno et al. 2010). Pressure (H0) is calculated by using Eq. 5: H0 ¼ He þ hr þ hs þ Hg þ DZ

ð5Þ

where He = the nominal sprinkler operating pressure (m) (Table 2); hs = singular head losses (m) (8 m was considered due to the pressure regulator, singular loss in drops, gates, bend, and regulation valve); Hg = height of the sprinkler above the ground (m) (2.5 or 0.2 m, in this study); Z = difference in elevation for slope (m) (a slope of 1% in this study); and hr = friction losses in the pipe, calculated using the Hazen-Williams equation: !  1:852 Q0 4:87 hr ¼ 0:548 hro ¼ 0:548  10:646  D R C0 ð6Þ 3

ð4Þ

where Ep = efficiency of the pumping system, Qo was determined from Eq. 9, and H0 was determined by

123

Sprinkler type

ð3Þ

where P is the power necessary (in kW (Eq. 4)) for water application, Ot the annual number of system operating hours (Eq. 7), considering water requirement of maize in Spain as example of application, Enc the energy rates (in € kW h-1), and S the irrigated area (ha). In order to analyse the effect of average energy rate, the following energy rates were considered: 0.05, 0.10, and 0.15 € kW h-1 (0.067, 0.135, and 0.202 US dollars kW h-1). These energy rates cover a wide range, representing real conditions over time in Spain and in many regions in the world. The power consumed for irrigation water application (P) was calculated according to the pressure (H0, m) and discharge (Q0, m3 s-1) necessary at the intake of the centre pivot: P¼

Table 2 Sprinkler types and working conditions considered

-1

where Q0 = flow rate in the origin of pipe (m s ); C0 friction coefficient (115 for the galvanized steel pipe used); D = internal diameter of the pipe (m); R = radius of area sufficiently irrigated (m). The number of operating hours per year (Ot) was calculated with Eq. 7: Ot ¼

Nn Ea Sc3:6

ð7Þ

where Nn = net crop water requirement per year (m3 ha-1 year-1) (7,000 m3 ha-1 year-1 in this study); Ea = general application efficiency for the irrigation system (decimal); Sc = system capacity (l s-1 ha-1). The general application efficiency (Ea) for a defined percentage a of adequately irrigated area can be calculated as (Keller and Bliesner 1990) Ea ¼ EDa Pef

ð8Þ

where EDa = distribution efficiency (ratio of net crop requirement, Nn, to gross average water depth that reaches the soil surface, Drs) and Pef is the effective proportion of

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511

water from the sprinklers that reaches the soil surface, Pef = Drs/Nb; Nb is the gross crop water requirement per year (Nn/Ea). Assuming water distribution through the irrigation system follows a normal distribution (Keller and Bliesner 1990), the EDa value can be easily deduced as a function of the irrigation uniformity coefficient (CU) and the percentage of adequately irrigated area (a). In this study, for the FSPS, Ea = 0.80 was considered, which corresponds to a soil water uniformity during the irrigation season of CU = 88% (Ortiz et al. 2010) at an adequately irrigated area of a = 80% (Keller and Bliesner 1990) (equivalent to EDa = 87.3%) and a Pef = 92% (with wind drift and evaporation losses WDELs = 8%) (Ortiz et al. 2009). For the RSPS (Rotator and Wobbler), Ea = 0.85 was used, which corresponds to CU = 92% (Ortiz et al. 2010), a = 80% (equivalent to EDa = 91.5%), and Pef = 0.93% (with WDELs = 7%) (Ortiz et al. 2009). In order to analyse the effect of irrigation efficiency (Ea) on water application costs, several efficiencies were considered (70, 75, 80, 85, 90 and 100%) where 70–75% represents inadequate irrigation design and management, 80-85% represents adequate management, and 90% represents excellent management. The case of 100% irrigation efficiency was also analysed to establish a reference of maximum potential efficiency of the systems. The required system capacity (Sc, L s-1 ha-1) was calculated using Eq. 9: N

Q0 0:116 Enamax Fd ¼ Sc ¼ S S

S

ð9Þ

where Nnmax = maximum net daily peak crop water required for maize (7.63 mm day-1) and Fd = fraction of hours in a day employed for irrigation (normally 20/24). This gives a system capacity of 1.25 L s-1 ha-1. The analysis of the influence of system capacity on water application cost also included Sc values = 1.0 and 1.5 L s-1 ha-1. Water costs Irrigation water price is the cost of obtaining it. Four water prices (Pw) were considered: 0.03, 0.06, 0.09, and 0.12 € m-3 ($47, $94, $141, $188 acre-feet) (Ortega et al. 2004a). The differences in water price mostly depend on water availability and the initial water energy (groundwater or superficial).Thus, the cost of the irrigation water (Cw, € year-1 ha-1) is Cw ¼

Nn Pw : Ea S

ð10Þ

Maintenance costs An additional cost of 5% of the investment costs was considered to take into account the maintenance needs of the centre pivot (Cm), to reach a useful life of 15 years. Consideration of multidiameter lateral pipes in the centre pivot Sometimes, it is more affordable to design a centre pivot with a multidiameter lateral pipe (Allen et al. 2000; Valiantzas and Dercas 2004). For this, the cost of energy per each metre of additional friction loss in the pipe over the life of the system, CDe, was calculated using Eq. 11 CDe ¼

9:81  QEpo Ot Enc CRF

ð11Þ

where Qo = the total centre pivot discharge (m3 s-1); Ot = average operation time per year (h); Enc = energy rate (€ kW h-1); Ep = efficiency of the pumping system (decimal); and CRF = capital recovery factor. The CRF was calculated using Eq. 1, assuming an interest rate (i) of 6% and a useful life (n) of 15 years. The second step was to calculate the difference in cost per 1 m of pipe, CDd, for larger and smaller pipes by using Eq. 12: CDd ¼

CDl  CDs L

ð12Þ

where CDl = cost for a lateral of length L that is comprised totally of the larger pipe size; CDs = cost for a lateral of length L that is comprised totally of the smaller pipe size; L = length of the centre pivot lateral (m). The third step required the calculation of necessary flow, flow change (Qc), that produces head losses hc (m) equal to the reduction in pipe cost (CDd) with an increase in energy costs (CDe). This flow was calculated with Eq. 13, which uses the Hazen–Williams equation for calculating friction losses:    CDd Qc 1:852  4:87 ð13Þ ¼ hc ¼ 10:646  Ds  D4:87 l CDe 115 where Ds = diameter of the smaller pipe size and Dl = diameter of the larger pipe size. After obtaining Qc, two alternatives appear: •

If Qc [ Qo, the entire centre pivot lateral can be comprised of the smaller pipe to save on costs. • If Qc \ Qo, the distance from the centre pivot intake to the transition in pipe size (r) can be calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffi Qc r ¼R 1 ð14Þ Qo

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where r = the distance to the centre of the pivot for the diameter pipe change and R is the radius of area sufficiently irrigated, with R C L. The value for r calculated above must be rounded up or down to match a span length combination available for the larger pipe size. The method for calculating head losses in multidiameter pipes is based on the iterative application of the regular procedure with zero flow in the end. Thus, head loss in a pipe with two diameters (hrd) is calculated by adding the head loss of the first pipe diameter (h1 = hf - hc) to the second (h2), using Eq. 15: hrd ¼ h1 þ h2 ¼ hf ðQ0 ; R; Dl Þ  hc ðQc ; L2 ; Dl Þ þ h2 ðQc ; L2 ; Ds Þ

Table 3 Prices of the power (Ep) and energy (En) for the three billing rates considered in the study Energy period Low

2.13

0.0754

Medium

9.31

0.1071

15.09

0.1211

High

Ep fixed cost for having a power available, En cost of kW h consumed

Table 4 Long-term average monthly net water requirements for maize crop Month

ð15Þ where Qc is flow in the pipe section in which the pipe diameter changes from D1 to Ds; L2 = R–r is the length of pipe with the second diameter; hf is the head loss of the pipe with diameter D1, total flow (Q0), and length (R); hc is the head loss of the pipe with diameter D1, flow Qc, and length L2; and h2 is the head loss of the pipe with diameter D2, flow Qc, and length L2. Analysis of the effects of energy price on machine design

Ce ¼

Cem ¼

i¼1

12 X k X

ðPi Oij Enij þ Epi Þ 1:26 S1

ð16Þ

i¼1 j¼1

where Pi = power necessary for water application in month i (kW mo-1) (Eq. 4); Oij is the operating hours during month i (h mo-1) and billing rate j; Enij is the energy rate during month i and billing rate j (€ kW h-1); Epi is the cost of the power contracted for month i (power access); 1.26 corresponds to the energy tax (26% in this case); and S is the irrigated area (ha). In this case, the prices in Table 3 were considered for power (Ep) and energy consumption (En). The electric billing rate corresponded to 8 h day-1 for the low-cost period (12:00 am–8:00 am), 10 h day-1 for the mediumcost period (8:00 am–10:00 am and 4.00 pm–12:00 am), and 6 h day-1 (10:00 am–4:00 pm) for the high-cost period. On weekends and national festivities, the rates were 18 h day-1 for the low-cost period and 6 h day-1 for the

123

Nnm (mm month-1)

Total

Apr

May

Jun

Jul

Aug

Sept

34

61

166

236

193

10

700

medium-cost period. The criteria of using cheap, medium, and high energy rates sequentially were considered. For calculations of monthly water requirements considering a maize crop, Table 4 shows the long-term average net requirements during each month, Nnm. Total cost

As an alternative to calculate the annual energy cost per unit of irrigated area (Ce, € year-1 ha-1) using the average energy rates (Enc) (Eq. 3), Ce can be calculated as the sum of the monthly costs (Cem) using Eq. 16, since energy (En) prices are different depending on time of day and month of the year: 12 X

Energy consumption (En) (€ kW h-1)

Power access (Ep) (€ kW-1)

The total cost of water application with a centre pivot (CT, € ha-1 year-1) is the sum of the four previously defined costs CT ¼ Ca þ Ce þ Cw þ Cm :

ð17Þ

Results Investment costs of equipment The methodology was first applied to a centre pivot with a 127.0 mm (5 in) pipeline diameter and then to a system with a 168.3 mm (6 5/8 in) pipeline diameter, with FSPS sprinklers. Reference values were considered for the remaining parameters. Results for the pipeline diameter of 168.3 mm show (Fig. 1) that investment cost per unit length Cil (€/m) decreased with lateral length. In addition, the cost was lower with a longer span length. The overhang length had less influence on the unitary cost. The decrease in cost per unit length using only long spans was approximately 22% for laterals between 200 and 600 m long. However, structural or wheel track issues can occur when using long spans for the entire system length. The cost is intermediate for machines that combine long and short spans. The combination of span lengths became the

Irrig Sci (2013) 31:507–521

513

200 61m+6m 61m+25m

Investment costs (€ m-1)

43m+6m 43m+25m

175

Combination of span and overhangs

150

125

costs per unit length of 11–18% (for machines of 200 and 600 m length) (Fig. 2). A similar cost increase (13–15%) was produced when installing a diameter of 168.3 mm (6 5/8 in) or 219.1 mm (8 5/8 in). However, when installing a diameter of 254.0 mm (10 in) instead of 219.1 mm, there was a greater increase in investment cost per unit length (18–25%). This is because the 254.0-mm pipe is not commonly used, and therefore, it has a higher manufacturing cost. In addition, it requires the design of short spans between towers to avoid increased weight on the wheels and sinking problems.

100 0

100

200

300

400

500

600

700

Length (m)

Fig. 1 Investment costs per unit length (Cil) of centre pivot lateral with different span and overhang lengths (pipeline diameter of 168.3 mm)

configuration adopted in this study. The same trends were obtained with the 127.0 mm pipeline diameter. Investment cost per unit length Cil (in €/m) was estimated using the equation C = aL-b, where L is the length of lateral (m) and a and b were adjustment factors. This type of equation does not have a good fit for short machines (less than 100 m), as it underestimates unit cost. Table 5 shows these equations for different pipeline diameters and sprinkler types. Figure 2 shows how total investment costs increase with machine size for the four pipeline diameters and sprinkler types using the equations from Table 5. Results show that the effect of lateral pipe diameter is much more important than sprinkler type. The more expensive system often is the LEPA, the least costly is FSPS, and RSPS (rotators) represents intermediate costs. The difference ranges between 3 and 6% for machines with a pipeline diameter of 127.0 mm (5 in) and is somewhat lower for larger diameters. This highlights the limited influence of sprinkler type on the investment cost of the centre pivot. Installing a lateral with a 127.0 mm (5 in) or 168.3 mm (6 5/8 in) pipe diameter leads to an increase in investment

Total water application cost as a function of centre pivot size Figure 3 presents the annual investment, energy, maintenance, and water costs for an FSPS with a 168.3 mm (6 5/ 8 in) pipeline diameter under the reference working conditions (Ea = 0.8; Nnmax = 7.63 mm/day; energy price Enc = 0.1 € kW h-1 (0.135 US dollars kW h-1), system capacities 1.25 L s-1 ha-1 and water price = 0.06 € m-3 ($94 acre-fee). The annual investment and maintenance costs per unit area decreased with increasing length of the machine. Annual energy cost per unit area increased exponentially with machine length. Annual water cost remained constant regardless of machine length. Effect of sprinkler type and pipeline diameter on total water application cost per unit area Total water application cost was calculated for different combinations of pipeline diameters, lateral length, and sprinkler types. Table 6 shows the centre pivot size that minimizes annual water application cost per unit area for the four pipe diameters of the four sprinkler types under reference conditions. The results show that the machine with the minimum cost under reference conditions had a length of 485 m (74 ha irrigated), with a pipeline diameter of 219.1 mm (8 5/8 in) and an LEPA system.

Table 5 Equations that relate investment cost per unit length (Cil, €/m) with machine length (L, m) for the four pipe diameters and the types of sprinklers Pipe diameter

FSPS

RSPS (rotator)

RSPS (wobbler)

LEPA

127.0 mm (5 in)

Cil = 511.85 L-0.232 (R2 = 0.934)

Cil = 510.20 L-0.229 (R2 = 0.935)

Cil = 510.64 L-0.226 (R2 = 0.933)

Cil = 507.78 L-0.221 (R2 = 0.933)

168.3 mm (6 5/8 in)

Cil = 425.96 L-0.177 (R2 = 0.864)

Cil = 426.16 L-0.175 (R2 = 0.865)

Cil = 428.18 L-0.173 (R2 = 0.864)

Cil = 427.77 L-0.169 (R2 = 0.864)

219.1 mm (8 5/8 in)

Cil = 463.43 L-0.168 (R2 = 0.904)

Cil = 464.25 L-0.167 (R2 = 0.903)

Cil = 465.77 L-0.165 (R2 = 0.903)

Cil = 465.62 L-0.161 (R2 = 0.903)

254.0 mm (10 in)

Cil = 431.43 L-0.123 (R2 = 0.905)

Cil = 433.05 L-0.122 (R2 = 0.905)

Cil = 435.11 L-0.120 (R2 = 0.905)

Cil = 437.05 L-0.118 (R2 = 0.904)

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514

Irrig Sci (2013) 31:507–521

Fig. 2 Total investment costs (in €) as a function of machine length (L, m) for the four pipeline diameters and sprinkler types

160000 SPRAY

ROTATOR

WOBBLER

254.0 mm

LEPA

Investment total costs (€)

140000 120000

219.1 mm

100000

168.3 mm 127.0 mm

80000 60000 40000 20000 0 0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

Length (m)

In the case of an LEPA system with pipeline diameters of 168, 219.1, and 254 mm, the water application costs, on average, were 10% lower than the other sprinkler and pipeline diameter combinations. This was due to the higher energy savings and higher general application efficiency (Ea = 90%) that was considered when utilizing the LEPA system. For the FSPS, the trend of investment annuity (Ca) and energy (Ce) costs as a function of the area irrigated by the machine for the four pipeline diameters (127.0 mm (5 in), 168.3 mm (6 5/8 in), 219.1 mm (8 5/8 in), and 254.0 mm (10 in)) was analyzed (Fig. 4). The results show that the differences between investment annuity costs decreased with increasing size of the irrigated field. However, differences in energy costs increased with the size of machine as a consequence of the increase in head losses in the lateral. The trend of the annual cost of water application per unit area irrigated as a function of the machine length for a pipeline diameter of 168.3 mm (6 5/8 in) for the four types of sprinklers was also analysed (Fig. 5). The results show that water application cost for the Rotator and Wobbler type RSPS sprinklers were similar, but the solution corresponding to FSPS was more expensive (3–6%) than RSPS. The differences increased slightly with the size of the area

irrigated. This was not due to the effect of lower operating pressure, but to lower water application efficiency of FSPS, as indicated in the methodology, which required a higher flow rate and greater pumping power. As an example, Fig. 6 shows the trend of the total cost of water application as a function of machine length for the four pipeline diameters using the FSPS sprinkler at reference conditions. The cost curves for the FSPS and RSPS type of sprinklers were similar. The results showed that the total cost curves are wider with increasing machine length for the different pipe diameters. Table 7 summarizes the range of lengths and irrigated areas with the most cost-effective design for the four pipeline diameters and the types of sprinkler spray plates, using the working reference conditions. These results contrast with the widespread use of centre pivots in Spain and other regions, which are designed with a lateral pipeline diameter of 168.3 mm (6 5/8 in) to irrigate fields of 60–70 ha and a system capacity of 1.2 L s-1 ha-1. Centre pivots operating under the specified reference conditions, designed with a 168.3 mm pipeline diameter are most costeffective when irrigating smaller fields (21–41 ha), while those irrigating plots in the range of 60–70 ha should be designed with a pipeline diameter of 219.1 mm.

Annual Costs (€ ha-1 y-1)

1500 Investment costs Energy costs Water costs Maintenance costs Total costs

1250

Comparison of results with multidiameter pipe in the centre pivot

1000 750 500 250 0 0

100

200

300

400

500

600

700

Length (m)

Fig. 3 Annual costs per unit area for an FSPS with a pipeline diameter of 168.3 mm (6 5/8 in)

123

The trend of the total water application cost (CT, € ha-1 year-1) as a function of irrigated area when using a single lateral pipe diameter was also compared with the option of using a multidiameter lateral pipe. The dashed line represents the limit of minimum water application cost. The potential savings that could be achieved with the option of a multidiameter pipe versus a single pipe size solution is only slightly more cost-effective for each irrigated area (Table 8).

Irrig Sci (2013) 31:507–521

515

Table 6 Length (L, m) and area (S, ha) of centre pivot that minimizes the annual cost of water application per unit area (CT, in € ha-1 year-1) for four pipe diameters and four sprinkler types under reference conditions Pipe diameter

FSPS L (m)

RSPS (rotator) S (ha)

CT (€ ha year-1)

-1

L (m)

S (ha)

RSPS (wobbler) CT (€ ha year-1)

-1

L (m)

S (ha)

LEPA CT (€ ha year-1)

-1

L (m)

S (ha)

CT (€ ha-1 year-1)

127.0 mm (5 in)

315

31

908

315

31

882

315

31

876

315

31

908

168.3 mm (6 5/8 in)

361

41

858

361

41

839

361

41

832

416

54

751

219.1 mm (8 5/8 in)

485

74

833

485

74

812

485

74

804

485

74

725

254.0 mm (10 in)

562

842

562

99

821

562

99

813

599

113

733

99 -1

-1

System capacity Sc = 1.25 L s ha ; application efficiency Ea = 80% for FSPS, Ea = 85% for RSPS and Ea = 90% for LEPA; water price Pw = 0.06 € m-3; energy price Ene = 0.10 € kW h-1; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1

The length of the machine for which the water application cost is minimum for each pipeline size is presented. The results indicate that when pipeline diameter is increased, the length of the centre pivot lateral that minimizes the water application cost increases, from 290 m for the 127.0 mm (5 in) pipeline diameter, up to 550 m for the 254.0 mm (10 in) pipeline diameter. There is financial savings with the multiple pipe size solution in small diameters (over 2% in 127.0 and 168.3 mm), but the saving is not significant in the 219.1 mm pipeline diameter. Influence of system capacity and water application efficiency To study the influence of system capacity and irrigation efficiency on total water application cost, the following parameters were considered: an FSPS, a pipeline diameter of 168.3 mm (6 5/8 in), different system capacities (1.0, 1.25, and 1.5 L s-1 ha-1), and different general application efficiencies (from 70 to 100%) (Fig. 7).

Ca 127.0 mm Ca 168.3 mm Ca 219.1 mm Ca 254.0 mm

600

The results show that for up to 350 m of machine length, the costs are similar for the three system capacities considered (differences of less than 1%), with increasing differences for greater lateral lengths. This coincides with the range of length limited to the most cost-effective length for a pipeline diameter of 168.3 mm (6 5/8 in) (265–360 m in length, Table 7). Increasing the system capacity from 1.0 to 1.5 L s-1 ha-1, within the more cost-effective range for the 168.3 mm (6 5/8 in) pipe, would increase costs a maximum of 3%, but the machine would have a higher discharge capacity. This result may be useful for arid areas or crops with high water requirements, and energy prices are high in peak periods. Figure 7 shows that variation in water application efficiency has a greater impact than the system capacity on total water application cost. Within the cost-effective range for a lateral of pipe diameter of 168.3 mm (6 5/8 in) (265–360 m in length), a slight improvement in efficiency (80–85%) leads to a reduction of 4–5% in the total cost of

Ce 127.0 mm Ce 168.3 mm Ce 219.1 mm Ce 254.0 mm

1200

ROTATOR WOBBLER

1000

Annual Costs (€ ha-1 y-1)

Annual Costs (€ ha-1 y-1)

500

400

300

200

SPRAY

LEPA

Total Costs

800

600

Energy Costs

400

200 Investment Costs

100

0 0

0 0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

10 20

30

40

50 60

70

80

90 100 110 120 130 140 150

Area (ha)

Area (ha)

Fig. 4 Annual investment and energy costs per unit area for the four pipeline diameters, using FSPS

Fig. 5 Annual cost of water application per unit area as a function of machine length, for the four types of sprinklers, with pipeline diameter of 168.3 mm (6 5/8 in)

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Irrig Sci (2013) 31:507–521

Fig. 6 Total annual cost per unit area as a function of irrigated area for the four pipeline diameters and multidiameter pipeline, with an FSPS, under reference conditions (system capacity Sc = 1.25 L s-1 ha-1; application efficiency Ea = 80% for FSPS; water price Pw = 0.06 € m-3; energy price Ene = 0.10 € kW h-1; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1)

water application. The savings are higher with greater length of the centre pivot. On the other hand, it is important to note that, for all water application efficiencies, when lateral length is increased up to 400 m, the water application cost decreases. Effect of energy and water prices The effect of energy and water prices on water application costs were evaluated using a system equipped with 168.3-mm pipeline and an FSPS, under reference working conditions (Ea = 0.8 for FSPS; system capacities 1.25 L s-1 ha-1; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1; Nnmax = 7.63 mm/day). Energy prices ranged from 0.05 to 0.15 € kW h-1 (0.08 to 0.20 US dollars kW h-1), and water prices were varied between 0.03 and 0.12 € m-3 (0.040 and 0.162 US dollars m-3). The results (Fig. 8) show that water prices have a greater influence on the total water application cost than energy prices. For the same energy price (Fig. 8), increasing the water price from 0.03 to 0.09 € m-3 (0.04–0.12 US dollars m-3) (300%) results in an increase in annual water application

cost of 80–90% within the range of use of the 168.3 mm (6 5/8 in) pipe (265–360 m in length). Similarly, for the same price of water, and in the same range of use of the 168.3 mm pipe, increasing the energy cost from 0.05 to 0.15 € kW h-1 (0.067–0.202 US dollars kW h-1)(300%) represents only a 10–18% increase in annual water application cost.

Influence of electricity rates and use of multidiameter pipe on water application cost The trend of water application cost as a function of machine length, multidiameter pipe lateral design, and electricity rates, under reference conditions (application efficiency Ea = 80% for FSPS; system capacity Sc = 1.15 L s-1 ha-1 for irrigation time by day (ITD) of 24 h day-1; water price Pw = 0.06 € m-3; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1), is that total water application cost (TCs) decreases as pivot lateral length increases to

Table 7 Recommended lateral length and irrigated area for lower water application cost for four pipe diameters and types of sprinklers, under reference conditions Pipe diameter

FSPS

RSPS (rotator and wobbler)

LEPA

Length (m)

Area (ha)

Length (m)

Area (ha)

Length (m)

Area (ha)

127.0 mm (5 in)

\265

\22

\275

\24

\280

\25

168.3 mm (6 5/8 in)

265–360

22–41

275–375

24–44

280–385

25–47

219.1 mm (8 5/8 in)

360–535

41–90

375–555

44–97

385–570

47–102

254.0 mm (10 in)

[535

[90

[555

[97

[570

[102

-1

-1

System capacity Sc = 1.25 L s ha ; application efficiency Ea = 80% for FSPS, Ea = 85% for RSPS and Ea = 90% for LEPA; water price Pw = 0.06 € m-3; energy price Ene = 0.10 € kW h-1; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1

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517

Table 8 Length of centre pivot lateral that minimizes water application costs under reference conditions for each pipeline diameter, with FSPS, and possible savings from using multidiameter pipe Pipeline diameter

Length (m)

TCs (€ ha-1 year-1)

TCv (€ m-3)

Estimated savings (%)

127 mm (5 in)

292.6

904

0.1291

-2.12

Multidiameter pipe

292.6

885

0.1264

168.3 mm (6 5/8 in)

376.0

860

0.1228

Multidiameter pipe

376.0

846

0.1209

219.1 mm (8 5/8 in)

478.3

830

0.1186

Multidiameter pipe

478.3

830

0.1185

254.0 mm (10 in) Multidiameter pipe

556.3 556.3

839 829

0.1198 0.1185

-1.62 -0.07 -1.10

System capacity Sc = 1.25 L s-1 ha-1; application efficiency Ea = 80% for FSPS; water price Pw = 0.06 € m-3; energy price Ene = 0.10 € kW h-1; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1 TCs total costs per unit area, TCv total costs per unit volume

1500

1.5 L s-1ha-1

1900

1400

Annual Costs (€ ha-1 y-1)

1.25 L s-1ha-1

1200 1100 1.0 L s-1ha-1

1000 900 800

Cost -effective range

700

Total Annual Costs (€ ha-1 y-1)

1300

70%

1700

75% 1500

80% 1300

85% 90%

1100

100%

900 700

Cost -effective range

600 500

500 0

100

200

300

400

500

600

700

800

Length (m)

0

100

200

300

400

500

600

700

800

Length (m)

Fig. 7 Annual cost of water application per unit area as a function of the irrigated area with an FSPS, and 168.3 mm (6 5/8 in) pipeline diameter, for different system capacities (left) and water application efficiency (right), under reference working conditions (water price

Pw = 0.06 € m-3; energy price Ene = 0.10 € kW h-1; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1)

500 m (Fig. 9). The optimal proportional length of each different pipe diameter used for the length of the machine is described. Results indicate that with a length of 500 m (78.54 ha irrigated) and an ITD of 24 h day-1, the minimum cost of irrigation water application is obtained (844 € ha-1 year-1) (1,140 US dollars ha-1 year-1). This cost is slightly greater than the water application cost with multidiameter pipes and with a single pipe diameter of 219.1 (8 5/8 in) (830 € ha-1 year-1 with a length of 478.3 m and 72 ha irrigated) (Table 8) under reference conditions (with average energy price Ene = 0.10 € kW h-1). The increase in cost is mainly due to increased energy cost when using electricity rate periods (Fig. 11).

Machine length (100–700 m) and ITD length (8–24 h day-1) determine system capacity and influence water application cost per unit volume (€ m-3). Results in Fig. 10 indicate a significant decrease in water application cost with increasing machine length, using multidiameter pipe design with the combination corresponding to the most cost-effective centre pivot design (Fig. 9). This cost remains practically constant for different ITDs, except for lateral lengths over 500 m. The increase in water application cost at a lower ITD in long lengths (over 500 m) is due to a large increase in energy costs in these cases because of the large flow rate that is necessary for transport when system capacity exceeds 3 L s-1 ha-1 using pipe diameter (254.0 mm (10 in) (the biggest considered in this study).

123

518

Irrig Sci (2013) 31:507–521 2500

2000 0.12 € m-3 0.09 € m-3

1500

0.06 € m-3 0.03 € m-3

1000

500

Total Annual Costs (€ ha-1 y-1)

Total Annual Costs (€ ha-1 y-1)

2500

2000 0.15 € kW h-1

1500 0.10 € kW h-1

1000 0.05 € kW h-1

500

0

0 0

100

200

300

400

500

600

700

800

0

100

Length (m)

200

300

400

500

600

700

800

Length (m)

Fig. 8 Influence of water price (left) and energy price (right) on the annual water application cost per unit irrigated area using an FSPS and 168.3 mm (6 5/8 in) pipeline diameter, under reference working

conditions (Ea = 0.8 for FSPS; system capacities 1.25 L s-1 ha-1; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1; Nnmax = 7.63 mm/day)

Table 9 shows the ITD (h day-1) that minimizes total water application costs according to lateral length and pipe diameter, including the multidiameter pipe solution. Shaded numbers show the machine length that minimizes the water application cost for a given diameter. This length varies from 300 m for 127.0 mm (5 in) pipeline diameter to 600 m for 254.0 mm (10 in). In all cases, the minimum cost is obtained with an ITD of 24 h day-1, with a system capacity of about 1.15 L s-1 ha-1 (Fig. 11). In the case of using multidiameter pipe, the minimum water application cost for all the cases studied corresponds to a length of 500 m (78.54 ha irrigated) and ITD = 24 h day-1. However, designing irrigation machines to function for over 20 h day-1 is not recommended in anticipation of

possible failures in the equipment and maintenance requirements. When this condition is imposed, the lowest water application cost solution is obtained with ITD of 18 h day-1 instead of 20 h day-1 (Fig. 10). This indicates that it is not advisable to irrigate during the 6 h corresponding to peak periods of high energy cost.

Fig. 9 Influence of machine length (L) on water application cost (TCs), using electricity rates and multidiameter pipe lateral, proportional length of each pipe diameter is shown for the length of the machine, with FSPS and an irrigation time per day (ITD) of 24 h day-1, under reference conditions (application efficiency Ea = 80% for FSPS, water price Pw = 0.06 € m-3; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1)

123

Conclusions In this study, variables of machine length, lateral pipeline diameter, sprinkler type (with corresponding application efficiency), system capacity, irrigation time per day, and water and energy costs were analysed to determine the

Irrig Sci (2013) 31:507–521

519

Fig. 10 Influence of machine length (100–700 m) and irrigation time per day (ITD) (8–24 h day-1) on water application costs per unit volume, using a multidiameter pipeline and electricity rates, with FSPS, under reference conditions (application efficiency Ea = 80% for FSPS; water price Pw = 0.06 € m-3; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1)

Table 9 Irrigation time by day (ITD) (h day-1) that minimizes total water application costs according to lateral length and pipe diameter, including the multidiameter pipeline solution

The shaded box shows the minimum ITD for each pipeline length and diameter

ITD (h day-1)

Pipe diameter in centre pivot lateral

L (m)

127.0 mm (5 in)

168.3 mm (6 5/8 in)

219.1 mm (8 5/8 in)

254.0 mm (10 in)

Multidiameter pipe

100

8

8

8

8

8

200

18

18

8

8

18

300

24

18

18

8

18

400

24

24

18

18

18

500

24

24

24

18

24

600

24

24

24

24

24

700

24

24

24

24

24

most cost-effective centre pivot design. The analysis was based on typical pump efficiency, crop water requirements for maize, and material and energy costs specific to the La Mancha region in Spain. The intervals of lengths and irrigated areas recommended for each pipeline diameter to achieve the most cost-effective centre pivot design have been identified. For plots smaller than 30 ha, the recommended pipeline diameter is 127.0 mm (5 in); for 30–40 ha, 168.3 mm (6 5/ 8 in); for 40–75 ha, 219.1 mm (8 5/8 in); and for 75–100 ha, 254.0 mm (10 in). The multidiameter pipe solution in the centre pivot system reduces water application costs, although only slightly in most cases studied. Centre pivots in Spain and other regions, which are designed with a lateral pipeline diameter of 168.3 mm (6 5/8 in) to irrigate fields of 60–70 ha and with a system capacity of 1.25 l s-1 ha-1, do not currently represent the most cost-effective design. The investment cost variation is small for the different types of sprinkler spray plate systems used. The use of

RSPS type is more highly recommended than the FSPS type when taking into account that the latter has a higher water application cost. This is due to lower water application uniformity, with higher evaporation and drip losses. Moreover, FSPS has a higher probability of obstructions with particles carried by irrigation water, especially organic matter (Ortiz et al. 2010). A more cost-effective design (725 € ha-1 year-1) (979 US dollars ha-1 year-1) is obtained with a centre pivot 485 m long (74 ha), a pipe diameter of 219.1 mm (8 5/8 in), and an LEPA system; however, an LEPA system requires land with minimal slope or laborious soil surface preparation. The cost of water application with centre pivot machines is quite sensitive to the efficiency of water application and not as sensitive to system capacity or energy price. Therefore, it is very important to control the application water uniformity by using a proper nozzle package and to perform regular maintenance. The consideration of variable energy price at different times of day shows that the ITD of 24 h day-1 leads to

123

520

Irrig Sci (2013) 31:507–521

Fig. 11 Average energy cost (€ kW h-1) and system capacity (L s-1 ha-1) with irrigation time per day (ITD) (08–24 h day-1) using a multidiameter pipeline and electricity rates, with FSPS, under reference conditions (application efficiency Ea = 80% for FSPS; water price Pw = 0.06 € m-3; net annual crop irrigation water requirement Nn = 7,000 m3 ha-1 year-1 and net crop water requirements in the peak period Nnmax = 7.63 mm day-1)

lower water application costs. However, irrigation equipment should not be designed to work over 20 h day-1 in anticipation of possible failures in the equipment and maintenance requirements. When this condition is imposed, the lowest water application cost solution is obtained with an ITD of 18 h day-1, avoiding the use of more expensive energy during peak periods. Acknowledgments The authors wish to express their gratitude to the Spanish Ministry of Education and Science (MEC) for funding the AGL2007-66716-C03-03 project. They also wish to thank Aisco Equipment Europe, Ltd., Valmont Irrigation, Albarrain enterprise and the Agro-environmental Training Centre (‘‘Centro de Formacio´n Agroambiental’’) in Albacete for their support of this work by providing the products and facilities needed to carry out the experiment.

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