The effects of pressure, nozzle diameter and meteorological conditions on the performance of agricultural impact sprinklers

Agricultural Water Management 102 (2011) 13–24

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The effects of pressure, nozzle diameter and meteorological conditions on the performance of agricultural impact sprinklers I. Sanchez a,∗ , J.M. Faci a , N. Zapata b a b

Unidad de Suelos y Riegos (asociada al CSIC), Centro de Investigación y Tecnología Agroalimentaria (CITA), Gobierno de Aragón, Avenida Monta˜ nana 930, 50059 Zaragoza, Spain Dept. Soil and Water, Estación Experimental de Aula Dei (EEAD), CSIC, Apdo. 202, 50080 Zaragoza, Spain

a r t i c l e

i n f o

Article history: Received 14 December 2010 Accepted 6 October 2011 Available online 1 November 2011 Keywords: Sprinkler irrigation Evaluation Wind Uniformity Water-losses

a b s t r a c t This study evaluates agricultural impact sprinklers under different combinations of pressure (p), nozzle diameter (D) and meteorological conditions. The radial curve (Rad) of an isolated sprinkler, i.e., the water distribution along the wetted radius, was evaluated through 25 tests. Christiansen’s uniformity coefficient (CUC) and the wind drift and evaporation losses (WDEL) were evaluated for a solid-set system using 52 tests. The Rad constitutes the footprint of a sprinkler. The CUC is intimately connected to the Rad. The Rad must be characterized under calm conditions. Very low winds, especially prevailing winds, significantly distort the water distribution. The vector average of the wind velocity (V’) is recommended as a better explanatory variable than the more popular arithmetic average (V). We recommend characterizing the Rad under indoor conditions or under conditions that meet V’ < 0.6 m s−1 in open-air conditions. The Rad was mostly affected by the sprinkler model. V’ was the main explanatory variable for the CUC; p was significant as well. V was the main variable explaining the WDEL; the air temperature (T) was significant, too. Sprinkler irrigation simulators simplify the selection of a solid-set system for farmers, designers and advisors. However, the quality of the simulations greatly depends on the characterization of the Rad. This work provides useful recommendations in this area. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Sprinkler irrigation depends on many operating, environmental and agronomic factors. The uniformity of the water distribution mainly depends on the spacing and arrangement of the sprinklers, the environmental conditions, the number and diameter of the nozzles, the sprinkler model and the operating pressure (Carrión et al., 2001; Keller and Bliesner, 1990; Playán et al., 2006) and on the crop irrigated (Sanchez et al., 2010a,b). Among these variables, those controlled by design are particularly interesting to people involved with irrigation technology. Playán et al. (2005) reported that the wind velocity is the meteorological variable most directly related to irrigation performance through its effects on Christiansen’s uniformity coefficient (CUC, Christiansen, 1942) and on the wind drift and evaporation losses (WDEL). The evaluation of a solid-set system ranges from the assessment of the distribution pattern of an isolated sprinkler in no-wind conditions (Tarjuelo et al., 1999a) to the study of the whole-field

∗ Corresponding author. Tel.: +34 976 71 6324; fax: +34 976 71 6335. E-mail address: [email protected] (I. Sanchez). 0378-3774/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.agwat.2011.10.002

irrigation in real conditions (Mateos, 1998). The operational, atmospheric and agronomic conditions in which sprinkler irrigation can be used are vast. To study all the cases with field experiments is cost prohibitive. Therefore, sprinkler simulators have been developed and used to analyze an ample range of conditions, with minimal experimental effort. Most of these models have been developed using the ballistic approach first proposed during the 1980s (Fukui et al., 1980; Von Bernuth and Gilley, 1984; Vories and von Bernuth, 1987). In these models, the superposition of the water distribution of an isolated sprinkler can provide an acceptable approximation to simulate the distribution of a group of sprinklers on a field scale when adjustments for wind drift and evaporation losses are correctly made (Carrión et al., 2001). Experimental irrigation evaluations were performed under isolated and blocksprinkler configurations for calibration and validation processes. The procedure for the evaluation of an agricultural impact sprinkler, conducted by the calibration and validation of an irrigation simulator, has been described in numerous studies (Carrión et al., 2001; Dechmi et al., 2004a,b; Playán et al., 2006; Seginer et al., 1991a,b). The radial curve (Rad) for an isolated sprinkler, i.e., the irrigation depth (ID) as a function of the distance from the sprinkler, is the basis for the characterization of the drop-size

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I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

population from which the irrigation performance of a solid set can be simulated under different conditions. This study analyzes the effects of the sprinkler model and of the solid-set arrangement on irrigation performance under different technical (nozzle diameter and operating pressure) and meteorological (wind velocity and direction, temperature and relative humidity of the air) conditions. The paper discusses the drawbacks of the common procedures used to evaluate sprinklers and to calibrate and validate the empirical models for the simulation of irrigation performance.

2. Material and methods Two experiments designed to evaluate the irrigation performance of agricultural impact sprinklers were conducted at the experimental farm of the Agricultural and Food Research and Technology Centre in Zaragoza, Spain (41◦ 43 N, 0◦ 48 W, 225 m altitude) during the years 2003 and 2004. One experiment was performed using an isolated sprinkler. The other experiment was performed using a rectangular 15 m × 15 m (R15 × 15) solid-set arrangement. The isolated sprinkler experiment was designed to evaluate the Rad. It was performed on bare soil and under calm conditions as specified by the most relevant international standards. The solid-set experiment was designed to evaluate the irrigation performance using the CUC and the WDEL parameters under different wind conditions. This experiment was also conducted on bare soil. Both experiments were designed according to the recommendations of Merriam and Keller (1978) and the relevant International Standards (ANSI/ASAE, 2003; ISO, 1990, 1995). In the isolated sprinkler experiment, the ID emitted by a model Somlo 30C sprinkler (Zaragoza, Spain), assembled in a riser tube at 2 m above the ground level (a.g.l), was collected into pluviometers located at 0.25 m a.g.l. along four radii at distances from the sprinkler ranging from 0.75 to 16.75 m, in increments of 0.5 m (Fig. 1). The radii faced north (N), west (W), south (S) and east (E), respectively. The evaluated sprinkler was an agricultural impact sprinkler made of brass and equipped with a drive nozzle that included a straightening vane (SV). Three diameters of the main nozzle (D) were tested: 4, 4.4 and 4.8 mm. The sprinkler also included a spreader nozzle, 2.4 mm in diameter (d). An ample range of operating pressures (p) from 180 to 420 kPa was tested. All the tests were performed for 2 h under low wind conditions. The wind velocity (V) and direction (WD) and the temperature (T) and relative humidity (RH) of the air were monitored by an automatic weather station located in the same plot. The average records were collected every 5 min using a model CR10X data logger (Campbell Scientific Ltd, UK). A set up with 24 sprinklers was used in the solid-set experiment (Fig. 1). The distance between the laterals was 15 m, and the distance between the sprinklers along the lateral was 15 m. The sprinklers were arranged according to a rectangular layout (R15 × 15). The sprinkler model and the combination of nozzles were the same as used for the isolated sprinkler test. The experimental area was located between the four central sprinklers. A matrix of 25 pluviometers was installed at 0.25 m a.g.l. using a 3 m × 3 m grid that covered the experimental area of the four central sprinklers. One manometer was installed at each of the four sprinklers. Three p were evaluated: 240, 320 and 420 kPa. Meteorological factors cannot be controlled, but we sought low, medium and strong winds. For the solid-set experiment, all the tests lasted 3 h. For each test of the solid-set experiment, the CUC and the WDEL were assessed from the ID collected in the pluviometers. The WDEL was estimated as the percentage of the water emitted by the sprinklers (IDe ) but not collected inside the pluviometers (Dechmi et al.,

2003; Playán et al., 2005; Sanchez et al., 2010a) according to the following formula: WDEL = IDe =

IDe − ID × 100 IDe

Q ×t 15 × 15

(1)

(2)

where Q was the water discharge (l s−1 ), t (s) the operating time and 15 × 15 the area (m2 ) assigned to each sprinkler. Q was assessed by collecting the water emitted by the sprinkler into a tared container. The discharge was calculated by dividing the weight of the collected volume by the time of filling. This operation was repeated twice for each combination of D and p (nine combinations in total). The discharge was estimated using the equation: Q = CD × A × (2gp)n

(3)

where CD is the discharge coefficient, A is the area of the nozzle orifice, g is the gravity acceleration, and n is the discharge exponent. A meteorological station similar to the one used during the isolated-sprinkler experiment was located at an adjoining plot during the solid-set experiment (Fig. 1). The experiment was performed under an ample range of meteorological conditions in an attempt to characterize the CUC and the WDEL resulting from different combinations of D, p and V. The variation of the CUC and of the WDEL with several meteorological and technical variables was analyzed using multiple regression analysis. Traditionally, the average wind velocity during an irrigation event is calculated as the arithmetic mean considering the records as positive rational numbers. This will be called the arithmetic average (V). In addition, we assessed the vector average (V’) considering each 5-min record a Euclidean vector endowed with magnitude and direction. Fig. 1 shows the Cartesian coordinate systems used for each experiment. The projections of each 5-min vector on the X and Y axes (Vx and Vy , respectively) were calculated and averaged separately. The resultant of the axial components was calculated. Its magnitude was considered the vector average (V’), and the direction of the resultant was the WD during the irrigation event. For each isolated sprinkler test, the Rads resulting from each radius were compared. The tests in which the differences between the radii were the smallest were used to characterize the Rad. For each test, we calculated the average deviation of the volume collected along the four radii (AD, %), the ratio of the volume of water collected along the leeward radius to the volume collected along the windward radius, and the fraction of the water drifted from the leeward radius to the windward radius. The average Rad was calculated for each test from the four Rads corresponding to each radius. Then the CUC was calculated from the average Rad as follows: the ID of each position on the grid of pluviometers was assessed by interpolation from the average Rad as a function of the distance from each position to each sprinkler. This was calculated for a R15 × 15 solid set. The values of the CUC evaluated under low winds during the solid-set experiment and the CUC calculated from the Rad were compared. Four sprinkler models were compared: the Somlo 30C, the VYR 70 (VYRSA, Burgos, Spain) and the RC 130 (Riegos Costa, Lleida, Spain) evaluated by Playán et al. (2006) and the VYR 35 evaluated by Zapata et al. (2009). All are widely used in the Ebro Valley (Spain). A comparison was made for calm and windy conditions. For the calm conditions, we compared the average Rad and the CUC calculated from the average Rad for two solid sets (R15 × 15 and R18 × 15). For the windy conditions, we compared the CUC for the same combination of D, p and V evaluated during the solid-set experiment. The latter was assessed using the Ador-sprinkler simulator for the VYR 70, the RC 130 and the VYR 35.

I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

15

Fig. 1. Arrangement of the pluviometers (upper part on the left) and facilities (bottom part on the left) for the isolated sprinkler experiment. Arrangement of the sprinklers, situation of the experimental plot, facilities (upper part on the right) and matrix of pluviometers in the experimental plot (bottom part on the right) for the solid-set experiment. The Cartesian coordinate systems used for each experiment are shown.

The results from the isolated and solid-set experiments will be used to calibrate and validate the Ador-sprinkler simulator for the Somlo 30C sprinkler.

3. Results and discussion 3.1. Isolated sprinkler experiment The discharge of the evaluated sprinkler increased with D and p. With regard to the discharge equation (Eq. (3)), several studies applied to agricultural sprinklers interpreted that CD is essentially independent of p for a given nozzle and that n is constant and equal to 0.5 (Li, 1996; Li and Kawano, 1998; Tarjuelo et al., 1999a). We also assumed n to be equal to 0.5. The CD was assessed by a nonlinear regression analysis of the evaluated values of Q fitted to a power curve. For D equal to 4, 4.4 and 4.8 mm, the CD was 0.952, 0.958 and 0.942, respectively. Eq. (3) and CD values allowed us to calculate Q for every p. During the isolated sprinkler experiment, 25 tests were performed to assess the Rad for different combinations of D and p (Table 1). The Rad must be evaluated under calm conditions. This becomes almost impossible in open air, given that the wind always blows, even imperceptibly. The Rad is calculated as the average between the four radii, assuming that the curves must be alike under calm conditions. In contrast, the Rad noticeably differed between radii for many of the tests, both in shape and in the total volume of water collected. Special attention was paid to the differences at the longest distances from the sprinkler; they imply greater differences in the volume collected along each radius because the area watered by the sprinkler increases with the distance.

Fig. 2 shows the results for several tests. For the tests I/4/230.a and I/4/230.b, the Rads resulting from each radius were acceptably alike, and the tests resulted in a similar average Rad; the AD was 8% for both tests. For the test I/4.4/400, each radius resulted in a similar Rad as well (the AD was 8%, too). However, for the test I/4.4/420, the Rad from each radius greatly differed, and the AD increased to 31%. The former was accepted (suitable), and the latter was rejected. The wind conditions during the tests explained the results. Prevailing winds, even very low in velocity, caused a significant volume of water to drift. Fig. 2 shows that the water collected along the leeward radius exceeded that collected along the other radii. The experiment was limited in this sense because we only used four radii, and the wind blew from all directions. The distortion of the irrigation pattern by the wind is connected with the magnitude and the prevalence of the wind (Fig. 2). V’ considers both features while V considers only the magnitude. We recommend V’ as the explanatory variable rather than the more widely used V. The differences between V’ and V are greater when the wind directions are changeable because the resultant vector decreases, thus decreasing V’, when the wind blows in opposite directions, but this has no influence in the calculation of V. Changeable directions happen more frequently with low winds, while strong winds generally blow in a prevailing direction (Tables 1 and 2, Fig. 3). The water drift was linearly proportional to V’. We estimated the water drift as the ratio of the volume collected along the leeward radius to the water collected along the windward radius. The drift increased 3.675% for every increase of 0.1 m s−1 in V’ (Fig. 4). This relationship was true for every D and p. This ratio may differ with the riser height of the sprinkler. ratio = 0.3675V  + 1

(4)

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I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

Fig. 2. Results for several tests during the isolated sprinkler experiment (Table 1): radial curve of the irrigation depth [(ID, mm h−1 ) vs. range (m)] for each radius (left), volume of water (l h−1 ) collected along each radius (middle) and frequency of the wind direction from which the wind blew during the test (right).

Isolated experiment

Solid-set experiment 9

Vectorial average (m s-1)

3

8 7 2

6 5 4

1

3 2 1

0

0 0

1

2

3 -1

Arithmetic average (m s )

0

1

2

3

4

5

6

7

8

9

-1

Arithmetic average (m s )

Fig. 3. Comparison between the arithmetic and vectorial averages of the wind velocity from values recorded every 5 min during each irrigation test. The vectorial average (y-axis) considers each record as a vector. The arithmetic average (x-axis) considers each record as a positive rational number.

I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

17

Table 1 Characteristics and conditions of the tests performed in the isolated sprinkler experiment: diameter of the main and secondary nozzles (D + d, mm), operating pressure (p, kPa), sprinkler discharge (Q, l h−1 ), temperature (T, ◦ C) and relative humidity (RH, %) of the air, arithmetic (V, m s−1 ) and vectorial (V’, m s−1 ) average velocity of the wind and wind direction (WD,◦ ). Test

D+d

p

Q

T

RH

V

V’

WD

I/4/230.a I/4/230.b* I/4/240.a I/4/240.b I/4/260 I/4/300 I/4/350 I/4.4/180 I/4.4/210 I/4.4/230* I/4.4/270 I/4.4/290 I/4.4/320 I/4.4/380* I/4.4/390 I/4.4/400* I/4.4/420 I/4.8/190.a I/4.8/190.b I/4.8/230.a I/4.8/230.b* I/4.8/230.c I/4.8/260 I/4.8/340* I/4.8/350

4 + 2.4 4 + 2.4 4 + 2.4 4 + 2.4 4 + 2.4 4 + 2.4 4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.4 + 2.4 4.8 + 2.4 4.8 + 2.4 4.8 + 2.4 4.8 + 2.4 4.8 + 2.4 4.8 + 2.4 4.8 + 2.4 4.8 + 2.4

230 230 240 240 260 300 350 180 210 230 270 290 320 380 390 400 420 190 190 230 230 230 260 340 350

1273 1256 1264 1281 1330 1443 1571 1294 1399 1470 1594 1667 1743 1879 1908 1930 1968 1575 1576 1658 1673 1677 1743 1962 1980

23 12 12 15 20 14 30 19 11 17 12 11 17 13 21 18 16 26 23 22 19 30 22 13 23

59 70 80 69 47 75 44 56 55 62 60 68 64 68 70 71 71 66 73 61 63 28 73 90 76

0.9 0.6 1.0 0.8 1.2 0.7 1.1 1.1 1.2 0.9 2.8 0.4 1.3 0.6 2.6 0.8 1.3 1.4 1.4 0.9 0.4 1.5 1.2 0.8 0.8

0.5 0.5 0.9 0.5 1.1 0.6 0.8 0.7 1.1 0.7 2.5 0.2 1.2 0.5 2 0.4 1.3 1.3 1.1 0.7 0.1 1.2 1.0 0.8 0.8

158 181 10 297 20 182 190 173 218 157 276 155 189 61 143 20 257 173 196 173 194 192 201 13 199

*

Tests considered suitable for the characterization of the Rad and used in this paper.

The water drift can be also estimated in terms of the fraction of the water drifted from the windward radius to the leeward radius (f, %): ratio =

100 + f 100 − f

f therefore becomes f =

0.3675V  × 100 2 + 0.3675V 

(5)

Table 3 shows the increase of f with V’. These results can be used to provide recommendations for the evaluation of isolated sprinklers. The authors recommend that the value of f should not exceed

Ratio S to N

2.0

Ratio W to E

Ratio between radii

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

-3

-2

-1

0

1

2

Cartesian proyection of the wind velocity (m s-1)

3

ratio = 0.3675Vi + 1 (R 2 = 0.75) Fig. 4. For each test in the isolated sprinkler experiment, the y-axis shows the total volume of the water collected along one radius (the radius facing south or that facing west) divided by the total volume collected along the opposite radius (that facing north, or east, respectively). The x-axis shows the component of the vectorial average wind velocity during the test in the direction of the corresponding radii: the ratio between the radii facing west and east is referred to Vx and the ratio between the radii facing south and north is referred to Vy .

10%, and consequently, that the values of V’ should not exceed 0.6 m s−1 . For tests I/4/230.a, I/4/230.b and I/4.4/400 (Fig. 2), f was 11.1, 11.9 and 10.7% respectively. Fig. 5 shows the Rad resulting from the tests found suitable. For every distance from the sprinkler, increasing D and increasing p increased the ID along the curve. In addition, D and p affected the shape of the curve. For D equal to 4.8 mm, the Rad bulged along the final third. This might be related to the atomization process. For the largest diameter of the jet, complete atomization was delayed, and the number of drops reaching the longest distances increased. The curve tended to become triangular as p increased (from the top to the bottom in the central column, Fig. 5). According to our previous reasoning, when p increased, atomization was enhanced, and the distribution became more homogenous. The average Rad resulting from the rejected tests departed in shape and magnitude from the average Rad resulting from the suitable tests (Fig. 5). The deformation pattern was not clear. The results demonstrate that it is incorrect to assess the average Rad from tests performed under unfavorable wind conditions under the assumption that there is a compensatory effect between the windward and the leeward radii. The suitability of the selected tests was illustrated by comparing the values of the CUC calculated from the average Rad and the values of the CUC evaluated under very low wind conditions during the solid-set experiment. Fig. 6 shows that the selection of the suitable tests made good sense. The proper Rad can be used to assess the CUC for different arrangements of the sprinklers. We advise evaluating the Rad in indoor conditions with still air. Evaluations conducted in open-air conditions must pay special attention to the wind, even if the wind is very low. The recommendations in this paper will help to improve the results. Fig. 7 shows the average Rad for the different sprinkler models and combinations of D and p (note some differences in p between the models). The angle of insertion of the drive nozzle was 26–27◦ for all the models. The angle of insertion of the spreader nozzle was 20–22◦ for all the models except the VYR 35, which was 26◦ . All the models included the SV.

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I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

Table 2 Characteristics and conditions of the tests performed in the solid-set sprinkler experiment: diameter of the main and secondary nozzles (D + d, mm), operating pressure (p, kPa), arithmetic (V, m s−1 ) and vectorial (V’, m s−1 ) average of the wind velocity, temperature (T, ◦ C) and relative humidity (HR, %) of the air, average irrigation depth collected into the pluviometers (ID, mm h−1 ), wind drift and evaporation losses (WDEL, %) and Christiansen’s uniformity coefficient (CUC, %). Test

D+d

p

V

V’

T

HR

S/4/240.a S/4/240.b S/4/240.c S/4/240.d S/4/240.e S/4/240.f S/4/240.g S/4/320.a S/4/320.b S/4/320.c S/4/320.d S/4/320.e S/4/320.f S/4/420.a S/4/420.b S/4/420.c S/4/420.d S/4/420.e S/4.4/240.a S/4.4/240.b S/4.4/240.c S/4.4/240.d S/4.4/240.e S/4.4/240.f S/4.4/320.a S/4.4/320.b S/4.4/320.c S/4.4/320.d S/4.4/320.e S/4.4/420.a S/4.4/420.b S/4.4/420.c S/4.4/420.d S/4.4/420.e S/4.4/420.f S/4.8/240.a S/4.8/240.b S/4.8/240.c S/4.8/240.d S/4.8/240.e S/4.8/320.a S/4.8/320.b S/4.8/320.c S/4.8/320.d S/4.8/320.e S/4.8/320.f S/4.8/420.a S/4.8/420.b S/4.8/420.c S/4.8/420.d S/4.8/420.e S/4.8/420.f

4 + 2.4

240

0.4 1.1 1.1 1.5 2.9 4.3 8.0 0.5 0.8 0.9 3.4 5.2 6.5 0.8 0.8 3.0 3.5 5.8 0.8 1.8 3.4 3.7 4.9 5.9 0.9 1.0 2.7 6.4 7.1 1.0 1.5 2.5 3.7 5.1 6.8 1.1 1.7 4.4 4.9 6.7 1.3 1.7 3.6 3.7 7.4 7.6 0.8 0.8 3.6 4.6 6.5 6.7

0.1 0.4 0.6 0.9 2.7 4.2 8.0 0.1 0.3 0.4 3.5 5.1 6.4 0.1 0.6 3.0 3.4 5.8 0.2 1.8 3.3 3.6 4.9 5.8 0.5 0.7 2.5 6.4 7.1 0.7 1.4 2.3 3.4 5.0 6.8 0.7 1.7 4.3 3.7 6.7 0.9 1.5 3.5 3.1 7.4 7.5 0.4 0.1 3.4 4.6 6.5 6.7

14 20 7 10 24 10 21 9 7 5 10 11 16 13 19 10 19 15 22 17 21 21 20 22 23 17 13 13 22 23 16 17 11 21 14 27.1 21.9 12.3 5.6 10.5 19.4 17.4 17.1 18.9 15.2 10.8 21.2 20.6 15.3 16.6 14.7 14.2

80 67 71 57 43 69 54 84 85 76 58 57 49 72 62 68 56 44 64 62 47 46 58 45 62 66 56 54 54 60 71 43 67 45 40 48.6 66.7 47.5 46.9 55.8 86.0 68.0 49.3 43.5 55.3 62.1 62.9 70.9 52.5 48.1 60.2 65.7

a

320

420

4.4 + 2.4

240

320

420

4.8 + 2.4

240

320

420

ID 4.9 4.6 5.3 5.4 4.2 5.1 3.7 6.4 6.5 6.1 5.8 5.7 5.0 6.9 6.4 7.8 6.2 5.6 6.5 5.6 5.5 5.8 5.1 4.5 7.0 7.0 7.0 5.7 5.5 7.8 8.1 6.6 7.8 7.1 6.0 6.9 7.0 6.3 5.8 6.0 8.0 8.0 7.5 7.2 6.7 6.9 9.0 9.2 8.7 8.2 7.7 7.8

WDEL

CUC

16.2 21.2 9.5 6.6 27.2 12.9 35.6 4.0 3.5 8.5 13.1 14.6 25.3 10.5 16.6 0a 20.8 27.4 2.4 16.7 18.4 13.8 23.4 32.9 9.1 7.2 9.3 23.7 31.6 12.3 8.7 23.9 12.3 20.5 30.2 10.1 9.6 18.0 25.1 22.2 10.2 10.2 15.8 19.3 24.1 22.1 11.6 10.0 14.9 19.9 24.6 22.9

84 88 89 89 87 81 75 88 87 93 82 87 83 90 93 86 86 81 86 84 83 85 80 78 91 89 89 84 81 91 88 90 86 83 85 87 85 81 84 82 89 89 85 88 82 82 92 92 89 82 84 82

Negative value replaced by zero.

The Rad noticeably differed between models (Fig. 7). Because the sprinklers presented a similar configuration of nozzles, we suggest that the shape of the Rad was mainly affected by the inner design of the sprinklers. Three typical shapes of Rad have been reported: triangular, rectangular and donut. Respectively, they correspond to a combination of two nozzles, one nozzle without the SV and one nozzle with the SV and lower pressure (Tarjuelo et al., 1999a). The Rad for the presented models did not match the three typical shapes, but were instead combinations of these shapes. Fig. 8 shows the CUC calculated from the average Rad (Fig. 7) according to two sprinkler arrangements: R15 × 15 and R18 × 15. The calculations apply to calm conditions. The CUC ranged between 87% and 92%. The CUC depended on the shape of the Rad and therefore on the sprinkler model. The triangular Rad corresponding to the model VYR 35 yielded the greatest CUC for both arrangements.

The VYR 70 and the RC 130 presented a similar Rad with a rectangular shape close to the sprinkler that changed to a triangular shape further from the sprinkler. These models yielded a similar CUC. The Somlo 30C presented the most irregular Rad, and the CUC was slightly smaller for this model. The arrangement also influenced the CUC. The CUC decreased with the spacing for the VYR 70 and the RC 130, but the opposite was true for the Somlo 30C (the arrangement had no relevance for the VYR 35). Consequently, the differences in the CUC between sprinklers decreased for the R18 × 15 compared to the R15 × 15. Many manufacturers of agricultural sprinklers only provide information about the discharge and the range of their models. According to our results, this information is inadequate because the water distribution greatly depends on the shape of the Rad.

I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

D=4mm

D=4.4mm

I/4/240.b

I/4.4/210

I/4/230.b

D=4.8mm I/4.8/230.a

I/4.4/230

I/4.8/230.b

.7 5

.2 5

I/4.8/230.c

8 7 6 5 4 3 2 1 0 -1 -2

15

.7 5

14

12

75

.2 5

9.

11

25

75 6.

8.

75

25 5.

25

8 7 6 5 4 3 2 1 0 -1 -2 3.

0.

75

8 7 6 5 4 3 2 1 0 -1 -2 2.

ID (mm h )

I/4/240.a

19

9. 75 11 .2 5 12 .7 5 14 .2 5 15 .7 5

75

25 8.

25

I/4.8/340

6.

5.

0.

25

I/4.8/350

8 7 6 5 4 3 2 1 0 -1 -2

75

I/4.4/380

3.

I/4.4/390

75

8 7 6 5 4 3 2 1 0 -1 -2

2.

ID (mm h )

Range (m)

.2 5

.7 5

15

.7 5

14

.2 5

Range (m)

12

11

9. 75

I/4.4/400

6. 75 8. 25

3. 75 5. 25

I/4.4/420

2. 25

0. 75

ID (mm h )

Range (m) 8 7 6 5 4 3 2 1 0 -1 -2

Fig. 5. Average radial curves (average between the four radii) of the irrigation depth (ID, mm h−1 ) for different combinations of drive nozzle and pressure tested during the isolated sprinkler experiment (Table 1). The lines show the curves for the tests selected as suitable. The bars show the differences between the curves resulting from the rejected tests and the curves resulting from the suitable tests.

3.2. Solid-set experiment Fifty-two tests corresponding to different combinations of D, p and wind conditions were performed for the solid-set experiment to analyze the effects of these variables on the CUC and on the WDEL (Table 2).

Table 3 Fraction (%) of the water emitted towards the windward radius and drifted to the leeward radius according to the vectorial average of the wind velocity (V’ m s−1 ) during the isolated sprinkler test. V’ (m s−1 )

Fraction (%)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

1.8 3.5 5.2 6.8 8.4 9.9 11.4 12.8 14.2 15.5 16.8 18.1 19.3 20.5 21.6 22.7 23.8 24.9 25.9 26.9

Many studies have shown that the wind is the main environmental factor affecting sprinkler irrigation (Beskow et al., 2008; Dechmi et al., 2003, 2004b; Kincaid et al., 1996; Playán et al., 2005; Sanchez et al., 2010a,b; Seginer et al., 1991a,b; Tarjuelo et al., 1999c; Yu et al., 2009). In agreement with these studies, in our study, the wind velocity decreased the CUC (Fig. 9) and increased the WDEL (Fig. 10).

Suitable

Rejected

1:1

100

CUC calculated from the Rad (%)

Thus far, the analysis has been conducted under calm conditions and very low winds. The next analysis was performed under windy conditions.

95

90

85

80 80

85

90

95

100

CUC evaluated under very low wind (%) Fig. 6. Comparison between the Christiansen’s Uniformity Coefficient (CUC, %) calculated from the average radial curves (Rad) in the isolated sprinkler experiment (y-axis) and the CUC evaluated in the solid-set experiment under very low winds and (x-axis). The CUC are calculated for the arrangement used in the solid-set experiment (R15 × 15). The nozzle and the operating pressure matched for the tests in the comparison.

4.8 + 2.4

Somlo30C 230kPa

8 7 6 5 4 3 2 1 0

VYR70 300kPa

RC130 300kPa

240 kPa

4 +2.4 mm

8 7 6 5 4 3 2 1 0

4.4 +2.4 mm

Somlo30C 340kPa

8 7 6 5 4 3 2 1 0

320 kPa

420 kPa

90

80

70 100

RC130 300 kPa

CUC (%)

Somlo30C 230kPa

CUC (%)

100

90

80

70 100

VYR35 350kPa

4.8 +2.4 mm

CUC (%)

mm h-1

4.4 + 2.4

mm h-1

4 + 2.4

I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

mm h-1

20

90

80

70 0

0

2

4

6

8

10

Range (m)

12

14

16

18

Fig. 7. Radial curves of the irrigation depth (mm h−1 ) for various models of impact sprinklers. Left column shows the diameters of the main and spreader nozzles (mm).

Sprinkler irrigation has been evaluated using combinations of D and p (Playán et al., 2006; Tarjuelo et al., 1999b,c). Some studies like that by Kincaid (1982) analyzed the combined effect of p and D on the discharge of the sprinklers. However, other studies have analyzed the effects of D and p separately rather than together. Kohl (1974) reported that the effect of D on the drop-size distribution is smaller than the effect of p. At first sight, the relationship of the CUC and WDEL with the wind velocity was affected by D and p (Figs. 9 and 10). Apparently, these relationships differed depending on p, and the differences due to p decreased as D increased. The effects of these variables on the CUC and the WDEL were assessed using multiple regression analysis. Table 4 shows the steps taken towards a satisfactory explanatory function (from the top to the bottom obviating the intermediate steps). In multiple linear regressions, it is fundamental to detect the existence of a correlation among the prediction variables. The variance inflation factor (vif) was used to detect multi-collinearity among the variables. If the variables are orthogonal to each other, vif equals 1. In contrast, vif greatly increases with the relationship

4 +2.4 mm Somlo30C 230kPa 100

VYR70 300kPa

Somlo30C 230kPa

2 3 4 5 6 7 Vectorial average velocity (m s-1)

8

Fig. 9. Variation of the evaluated CUC with the wind velocity for sprinklers model Somlo 30C arranged in a rectangular solid-set (15 × 15). The figure shows the results for different combinations of nozzle diameter and operating pressure.

between the variables (Bowley, 2004). There are no formal criteria to decide the cut-off for the vif, but the vif was sufficiently similar to 1 for the resulting explanatory functions to consider that the independent variables were not correlated (Table 4). V’ was better than V in predicting the CUC. V was better than V’ in predicting the WDEL. This was assessed for each dependent variable by comparing the values of R2 adj. and RMSE that corresponded to V’ and to V (values not shown). The results make sense. We proved in the first section that the CUC is connected with the WD. In contrast, the wind increases the evaporation (therefore the WDEL) through the wind intensity and the time of exposure, independently of the WD. The variation of the CUC was mainly explained by V’, and by p to a lesser extent (Table 4, Fig. 11). From the multiple regression analysis, the explanatory model for the CUC was CUC = 83.4 − 1.274 V  + 0.019 p (RMSE = 1.98; R2 adj. = 0.75) (6) According to the model, the CUC decreased with V’ and increased with p. To the best of our knowledge, this is the first time that

4.4 +2.4 mm RC130 300kPa

1

RC130 300kPa

4.8 +2.4 mm Somlo30C 340kPa

VYR35 350kPa

CUC (%)

90 80 70 60 50 15x15

18x15

15x15

18x15

15x15

18x15

Fig. 8. Values of the CUC calculated from the radial curves of various models of impact sprinklers and different combinations of nozzles and pressures (Fig. 7). Values are shown for two spacings between sprinklers (rectangular arrangements).

I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

21

Table 4 Multiple regression analysis to explain the variation of the Christiansen’s uniformity coefficient (CUC, %) and of the wind drift and evaporation losses (WDEL, %). The independent variables are: the vectorial and arithmetic averages of the wind velocity (V’ and V, m s−1 ), the diameter of the drive nozzle (D, mm), the pressure (p, kPa) and the temperature (T,◦ C) and the relative humidity of the air (%). CUC = ˇ0 + ˇ1 X1 + · · · + ˇn Xn D All

WDEL = ˇ0 + ˇ1 X1 + · · · + ˇn Xn p > [t]

vifa

ˇi b

D

X

p > [t]

vif

ˇi

int. V’ D p T RH

<0.0001 <0.0001 0.1653 <0.0001 0.1318 0.1145

int. V D p T RH

0.0217 <0.0001 0.0830 0.6792 0.0055 0.0990

<0.0001 <0.0001

83.0 −1.444 1.222 0.019 −0.090 −0.049 1.94 0.76 89.6 −1.255 2.44 0.62

All

int. V’

0 1.60 1.12 1.01 1.29 1.73 RMSE d R2 adj. e 0 1.00 RMSE R2 adj.

int. V

<0.0001 <0.0001

int. V’ p

<0.0001 <0.0001 <0.0001

0 1.00 1.00 RMSE R2 adj.

83.4 −1.274 0.019 1.98 0.75

int. V T

0.8078 <0.0001 <0.0001

0 1.66 1.13 1.01 1.32 1.77 RMSE R2 adj. 0 1.00 RMSE R2 adj. 0 1.01 1.01 RMSE R2 adj.

V T

<0.0001 <0.0001

25.8 2.625 −3.700 −0.004 0.416 −0.013 4.65 0.69 7.1 2.776 5.33 0.59 −0.600 2.869 0.460 4.80 0.67 2.835 0.433 4.75 0.93 1.655 0.833 4.82 0.93 3.606 0.270 4.50 0.95 2.949 0.316 2.91 0.97

X c

RMSE R2 adj. 4

V T

0.0062 <0.0001 RMSE R2 adj.

4.4

V T

<0.0001 0.0176 RMSE R2 adj.

4.8

V T

<0.0001 <0.0001 RMSE R2 adj.

The significance of bolded values in Table 4 is that the p-value is less than the significance level alpha (0.05). a Variance inflation factor (vif). b Partial regression coefficients corresponding to each independent variable. c Intercept (int.). d Root mean square error (RMSE). e Coefficient of determination adjusted by the number of parameters in the model (R2 adjust.).

experimental results have improved the explanation of the CUC by considering the prevalence of the wind direction and the operating pressure. The selection of the predictor variables was more complicated in the case of the WDEL. When all the variables were included, only V and T were found significant (Table 4). Both variables have been previously selected among the predictor variables of the WDEL (Faci et al., 2001; Frost and Schwalen, 1955; Hermsmeier, 1973; Seginer, 1971; Silva and James, 1988; Tarjuelo, 1995; Yazar, 1984; Playán et al., 2005). D has been included as a predictor variable in former studies (Faci et al., 2001; Frost and Schwalen, 1955; Keller and Bliesner, 1990; Tarjuelo et al., 2000; Trimmer, 1987). An explanatory function considering V and D as the predictor variables, both significant, yielded acceptable results: RMSE = 5.41 and R2 adj. = 0.91 (not included in Table 4). However, considering V, D and T, the variable D was not significant, and the model was improved by considering V and T instead of V and D. The variable p was not significant although it has been included in many previous studies (Frost and Schwalen, 1955; Keller and Bliesner, 1990; Montero, 1999; Tarjuelo et al., 2000; Trimmer, 1987; Yazar, 1984). The most suitable model for the WDEL was one using V and T as the predictor variables (Table 4). The intercept was not significant, and it was deleted from the model (noint statement in SAS): WDEL = 2.835V + 0.433 T

(RMSE = 4.75; R2 adj. = 0.93)

(7)

In addition, the influence of D on the WDEL was considered by assessing the explanatory functions based on V and T for each D. The results show that R2 adj. increased and RMSE decreased with an increase in D. However, the rates of change assigned to V and T through the partial regression coefficients were not proportionate with the variation of D (Table 4). The empirical model proposed to explain the variation of the WDEL (one function for each D) was statistically satisfactory (Fig. 11). The accuracy of the prediction was greater for the CUC than for the WDEL. For the CUC, the values ranged between 75 and 93%, and the RMSE was 1.98%, while for the WDEL, the values ranged between 2 and 36%, and the RMSE was 4.75%. This trend is recurrent in the bibliography. The importance of D and p in the performance of the sprinkler irrigation system (Eqs. (6) and (7)) is explained through their effects on the atomization process. Recent and current investigations have focused on the atomization of the water jet released by agricultural sprinklers (Salvador et al., 2009; Bautista-Capetillo et al., 2009; King et al., 2010; Playán et al., 2010). The presented results prove the suitability of this line of research and point out that D and p must be analyzed together. Beskow et al. (2008) concluded that the application of empirical models must be limited to working conditions (nozzle size, operational pressure, etc.) similar to the ones in which they were developed. The empirical models proposed in this study are most

I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

240 kPa

4 +2.4 mm

WDEL (%)

40

320 kPa

420 kPa

Somlo30C

100

30

4.4 + 2.4 mm p = 240 kPa

20

CUC (%)

22

VYR70

RC130

90

80

10

WDEL (%)

4.4 +2.4 mm

30

4.4 + 2.4 mm p = 320 kPa

20 10

CUC (%)

70 100

0 40

90

80

70 100

4.8 +2.4 mm

30

4.4 + 2.4 mm p = 420 kPa

20

CUC (%)

WDEL (%)

0 40 90

80

70

10

0

0 0

1 2 3 4 5 6 7 Arithmetic average velocity (m s-1)

8

Fig. 10. Variation of the evaluated WDEL with the wind velocity for the sprinkler model Somlo 30C arranged in a rectangular solid-set (15 × 15). The figure shows the results for different combinations of nozzle diameter and operating pressure.

likely limited to the conditions of the experiment. Discrepancies are expected, mostly depending on the solid-set arrangement and spacing and on the surface conditions, especially when tall crops are irrigated (Sanchez et al., 2010b). Fig. 12 shows the variation of the CUC with V for three sprinkler models. The values of the CUC for the Somlo 30C correspond to the tests conducted during the solid-set experiment. For the VYR 70 and

8

the RC 130, the CUC was simulated with the Ador-sprinkler model (Dechmi et al., 2004a,b; Playán et al., 2006). V was used in this comparison because the Ador-sprinkler simulator has been calibrated and validated according to this variable. The shape of the curves in Fig. 12 depended on the sprinkler model (as was proven in the previous section) and on p (in accordance with Eq. (6)). According to the results, the choice of the most suitable sprinkler is based on how the CUC is connected with p,

W D EL WDEL = f (V) 40

CUC = f (V',p)

Calculated WDEL (%)

Calculated CUC (%)

2 3 4 5 6 7 Arithmetic average velocity (m s-1)

Fig. 12. Effect of the sprinkler model on the variation of the CUC (%) with the wind velocity. The values for the model Somlo 30C stem from Fig. 9 (central column). The values for the models VYR 70 and RC 130C are simulated for the same arrangement using Ador-sprinkler.

CUC CUC = f (V')

1

90

80

WDEL =f(V,T); by D

30

20

10

0

70

70

80 90 Evaluated CUC (%)

0

10 20 30 Evaluated WDEL (%)

40

Fig. 11. Comparison of the values of the Christiansen’s uniformity coefficient (CUC, %) and of the wind drift and evaporation losses (WDEL, %) evaluated in the solid-set experiment with the values calculated using models comprising different variables.

I. Sanchez et al. / Agricultural Water Management 102 (2011) 13–24

with the solid-set arrangement and with the wind conditions under which the irrigation will be conducted.

4. Conclusions The curve of the distribution of the irrigation depth along the wetted radius (Rad) is crucial to characterize the water distribution of a sprinkler. The water distribution closely depends on the shape of the Rad. The discharge and the range of a sprinkler are insufficient by themselves to select a sprinkler adequately. However, this is the only information provided by the manufacturers in most cases. The shape of the Rad is mainly affected by the sprinkler design. The nozzle diameter (D) and the pressure (p) also modify the shape but to a lesser extent. The characterization of the Rad with isolated sprinkler tests requires several precautions because the wind, however low it blows, significantly distorts the water distribution. When the tests cannot be performed under indoor conditions, the wind must be observed meticulously to ensure that the vector average of the wind velocity (V’) during the tests does not exceed 0.6 m s−1 . Otherwise, the resulting Rad will not be suitable and will lead to erroneous results. The authors firmly propose the use of V’ rather than the widely used arithmetic average (V). V’ considers both the wind speed and the prevalence of the wind direction, which are both crucial in sprinkler irrigation. The V is preferred to the V’ when evaluating the WDEL because the wind, irrespective of its direction, increases the WDEL. For every solid-set system, Christiansen’s Uniformity Coefficient (CUC) can be calculated in calm conditions directly from the Rad. For every wind condition, the CUC can be calculated using sprinkler simulators, but a suitable characterization of the Rad is necessary. The CUC depends on the Rad and consequently varies depending on the sprinkler design. The differences in the CUC between sprinkler designs vary with the wind conditions, the solid-set arrangement and p. The wind velocity makes the greatest relative contribution to explain the CUC and WDEL. However, including V’ (instead of V) and p as the explanatory variables, the assessment of the CUC can be noticeably improved. The WDEL was best assessed using specific functions based on V and the temperature (T) for each D. Nonetheless, the effect of D was not found to be sound. These functions were obtained for a specific sprinkler and solid-set arrangement. The presented results prove that the choice of the sprinkler model is very complicated because it depends on many factors, and many of these factors are out of the control of the farmer. Simulators based on ballistics are extremely useful tools for decision making because they allow the simulation of the sprinkler irrigation performance under very different operational and meteorological conditions. However, thorough investigations are needed to understand the processes involved in the formation and the atomization of the jet and the evaporation and drift of the resulting water drops. By following this path, physical models can be developed that are valuable for the manufacturers, advisors, farmers, and for the entire society that needs and demands an efficient use of water.

Acknowledgements This research was funded by the Government of Spain through grants AGL2004-06675-C03-03/AGR, AGL2007-66716-C03 and AGL2010-21681, by the Government of Aragón through grant PIP090/2005, and by the INIA and CITA through the PhD grants program. We are very grateful to the colleagues and friends of the Dept. of Soils and Irrigation (CITA-DGA) and of the Dept. of Soil and Water (EEAD-CSIC), for their support and co-operation in the fieldwork.

23

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