Sampling patterns may influence the evaluation of irrigation uniformity of Center Pivot systems Open Access

Water application uniformity is one of the main technical variables in the evaluation of an irrigation system because it is by this that irrigation management, water and energy saving can be improved, in addition to guaranteeing production (Al-Gaadi et al. 2019; Mohamed et al. 2021). Dwomoh et al. (2013), Zhang et al. (2013), cite that an irrigation system that operates under optimal conditions must apply water to the soil uniformly, to satisfactorily achieve the water needs for crops and their development, which is dependent on the uniformity of water applied to the surface and soil moisture in its subsurface.

Al-Gaadi et al. (2019) and Mohamed et al. (2021) point out that the analysis of uniformity coefficients is essential to evaluate the performance of any irrigation system, in addition, Lecina et al. (2016) and Darko et al. (2017) present that the economic benefits of irrigation increase due to the increase in water distribution uniformity.

However, there are several factors that affect irrigation uniformity and, in the case of Center Pivot systems, there are some related to the equipment (sprinkler type and model, operating pressure, spacing, travel speed, lateral line alignment, and emitter height); climate-related factors (evaporation, air temperature, relative humidity, and wind drift); and factors related to the relief conformation of the irrigated area (Ortiz et al. 2010; Rajan et al. 2015; Li et al. 2016). With all these variables on which the uniformity of irrigation systems depends, it is inferred that there is a spatial dependence of the collected water depths that would lead to a possible link between the sample pattern on the observed uniformity.

The water application uniformity of a Center Pivot is measured by collectors that are positioned radially, from the center to the edge of the equipment (ABNT 1998; ASAE 2020). Additionally, Shaughnessy et al. (2013) and Ouazaa et al. (2015) state that the uniformity in the direction that the Center Pivot moves is not much explored and can be questioned. For example: when a tower has its movement interrupted, its emitters continue to apply water in the same place and, if the water contains a chemical product, such as fertilizers, the plants of this area will receive a greater amount of it, as the dosage is proportional to the applied water. Thus, this fact can affect the development uniformity of the irrigated crop.

Consequently, some manufacturers offer systems equipped with solenoid valves, that open only if the tower is in motion, a technique that has not been effective due to the rapid wear of the valves and is its high cost (Mostacero et al. 2012). Mohamed et al. (2021) mention that several models are developed to assess the impact of mobile tower misalignment on irrigation uniformity. There are also Center Pivots activated by pumping hydraulic oil or variable-frequency drivers. All these solutions are adopted so that the movement of the towers is continuous and so the head on the lateral line is the most uniform, making it possible to obtain a good irrigation uniformity (Ouazaa et al. 2015). However, the poor quality of electricity in rural areas does not allow the proper functioning of this equipment. It is important to emphasize that all these attempts would not exist if the discrete movement of the towers against the general movement was a negligible phenomenon in terms of system performance.

Therefore, it was proposed, with the present article, to study the dependence of the sampling method of the applied water depth over the observed uniformity of a Center Pivot system, when evaluating its effect on the Christiansen (CUC) and Distribution Uniformity Coefficient (DUC).

The tests were carried out on a Tifton 85 grass and hay producing farm, located in Bom Despacho city, state of Minas Gerais, Brazil, at geographic coordinates 19°36′23.88″S; 45°16′14.98″W and 631.5 m altitude, on a flat terrain topography.

The evaluated Center Pivot equipment irrigates an area of 10.95 ha and had three mobile towers plus an overhang with no end gun. Its technical characteristics are revolution time with the percent timer set to 100% of 7.10 hours, 185.7 m of lateral line length (57.1 m in the first span, 51.4 m in the second span, 51.1 m in the third span, and 25.4 m of overhang), which leads to 1,007.19 m of useful perimeter. The average design water depth is 3.59 mm for a flow of 86.58 m³·h⁻¹.

Two types of sprinklers (Superspray and I-Wobler) were installed in spans 1 and 2, alternating along each span. The span 3 and the overhang had only ‘I-Wobler’ type sprinklers. All emitters were connected to a pressure regulating valve with an operating pressure of 10 mca. The combinations of emitters and nozzles used in each span of the evaluated system are listed in Table 1.

Data collection was performed with the equipment operating with the percent time set at 66%. The collectors used had a diameter of 0.08 m and so an area greater than 50 cm², as recommended by ASABE (ASAE 2020), and were placed on fixed rods attached to the ground, keeping them at an elevation of 0.3 m in relation to the surface (ABNT 1998; ASAE 2020).

To determine the application uniformity of sampling in the radial direction, a line of collectors was positioned in the direction of the radius of the Center Pivot, i.e., following the lateral line, with a spacing of 3 m between collectors, with 20 collectors being used in each span, corresponding to a total of 60 collectors for all three spans (ABNT 1998; ASAE 2020).

The center of the equipment and all collectors were georeferenced using a GPS signal receiver equipment, geodesic type, Spectra Precision ProMark 220 (GNSS L1,L2 GLONASS), so that it was possible to measure the location of each collector in the field using the UTM coordinate system, to obtain the surfaces profiles of the water depths over the irrigated area, by span, in the three evaluated sampling patterns.

During the tests, the irrigation system traveled an arc of 120° for a period of 2 hours and 30 minutes. This process occurred simultaneously with the collection of meteorological data, which were recorded at 5-minute intervals by an automatic meteorological station positioned infield, but in an area adjacent to the irrigated one. Wind speed (m·s⁻¹), wind direction, relative humidity (%), solar radiation, and air temperature (°C) were recorded. The wind speed and direction varied during the tests, as they were recorded at two-meter height from the ground level. The average values of the climatic variables observed during the tests are presented in Table 2.

In this equation, the numerator represents the mean applied volume of the smallest quarter of samples (j) in the span. As shown, the calculation of this uniformity coefficient reflects the weighted area represented by each collector. The interpretation of the evaluated coefficients was performed using the limits presented in Table 3.

To evaluate the results, a Completely Randomized Design (CRD) was adopted, in a 3×3 factorial scheme. The treatments were defined as the sampling pattern (three levels: radial, circular and, meshed); and sampling positions (three levels: Span 1, Span 2 and Span 3), with three repetitions.

The Analysis of Variance (ANOVA) was performed using the F test, at 5% statistical probability. When significant differences were verified, the Scott–Knott mean test was used, also at 5% probability. All the statistical analysis were made with the AGROESTAT software (Barbosa & Maldonado 2010).

There is a difference between the distribution profiles of water depths along the surface. The collectors arranged in the radial pattern showed the greatest water depths variation, while the ones arranged in the circular shape showed the smallest. One factor that influenced the variation of the water depths, mainly for the radial pattern, was the use of two sprinkler models arranged alternately along the span. This fact occurs because, in the radial profile, the collectors are positioned parallel to the lateral line of the Center Pivot, and they sample a very small region in the perpendicular direction to the movement. This makes them more sensitive to the effect of the flow variation of the sprinklers along the lateral line and representing a smaller sample surface, producing, therefore, a practically unidirectional sampling. In contrast in the circular profile the collectors are positioned perpendicular to the lateral line, so they sample a very small region between the position of the nozzles, on the direction of the Center Pivot radius, which makes them less sensitive to this variation. For the meshed profile, the collectors are also parallel to the lateral line, however, the perpendicular sampling is greater, which also makes them less sensitive. Studies carried out by Rajan et al. (2015), Li et al. (2016) with collectors in the radial arrangement, also observed that the use of different sprinklers along the lateral line of the pivot, interfered in the irrigation water depth distribution.

The effect of tower movement is also a factor that cannot be neglected because, when they are in motion, the collectors in the circular and meshed patterns receive water applied by the emitters for a longer period, while for the collectors in the radial pattern the sprinklers pass over them for a short period.

With the analysis in Figure 3, it was also possible to notice a difference between the distribution profiles of water depths for the three arrangements of collectors in Span 2, which was more accentuated in relation observations in the first span. It was observed that the meshed type showed less variation of water depths on the surface. The higher variations were verified for the radial and circular patterns. As for Span 1, the arrangement of nozzle diameters in this span (Table 1) did not increase: each larger diameter ‘Super Spray’ nozzle was followed by a smaller diameter ‘I-Wobler’ nozzle, which resulted in flow variation and applied water depths. The variation caused by this installation feature was detected by sampling irrigation water depths at radial patterns.

The wind effect also affected, mainly, the values of water depths obtained for the meshed arrangement of the collectors, regardless of their direction, precisely because in this pattern the collectors are arranged two-dimensionally. In the circular and radial profiles, the collectors are arranged in a unidirectional way and, according to several authors, such as Ortiz et al. (2010) and Shaughnessy et al. (2013), the influence of the wind can be detected only when its direction coincides with the arrangement direction of collectors. Therefore, as the wind direction was not measured at the exact moment that the lateral line passed over the collectors, its effect on the uniformity calculated for the radial and circular patterns cannot be stated with certainty.

When observing Figure 4, it is noted that this span has the worst irrigation water distribution profile for the collectors in the circular pattern but, for the meshed pattern, the best sampling uniformity was obtained. There was also an improvement in the sampling profile for the radial pattern in relation to Spans 1 and 2, as only a single sprinkler model was installed in this area, in addition to an increasing arrangement of nozzle models, except for the first one (Table 1). Additionally, the area relief favored this result, by not presenting great variations, being considered flat.

In addition to the stoppage effect, the velocity of towers also affected, mainly, the circular profile, as the farther away from the equipment center, the linear displacement speed of the mobile towers tends to be higher, which means that tower 3 moves faster. According to several authors such as Rajan et al. (2015), Ouazaa et al. (2015), Mohamed et al. (2021), the higher the equipment displacement velocity, the lower the uniformity, and this fact had more impact on the circular pattern because they were parallel to the movement direction of towers. Furthermore, Al-Gaadi et al. (2019), studying the uniformity within eight spans of a Center Pivot system, observed a decreasing trend in spans farther away from the center.

Considering the results obtained by Shaughnessy et al. (2013) for 5 m·s⁻¹ wind velocity, the effect of wind direction and speed cannot be disregarded for irrigation water depth variation, especially for the meshed profile, as the observed wind speed by the aforementioned authors was between 3.26 and 5.30 m·s⁻¹, similar to the average observed in the present study. Furthermore, Bernardo et al. (2019) present a classification for wind velocity in irrigated areas, with speeds above 3.89 m·s⁻¹ considered ‘high’. Furthermore, Bishaw & Olumama (2016) also observed that both wind intensity and direction, changed the fate of water droplets, drifting them out of the disposition area of collectors.

Differences between water application profiles were also found in a study developed by Jardim et al. (2018), who evaluated the uniformity of water distribution under different collector arrangements. These authors concluded that for different forms of arrangement, the water depth applied by a sprinkler behaves in different ways, mainly due to the difference in overlap zones. The results regarding the ANOVA for the collectors pattern, span, and their interaction, are shown in Table 4.

The ANOVA showed that there is a significant difference due to the effect of collectors patterns, both for CUC and DUC values. The span effect also showed a significant difference at 1% probability. The interaction between factors also showed a significant difference, but at 5% probability. The means comparison between the radial, circular and meshed patterns can be seen in Table 5.

Analyzing Table 5 it could be noted that the radial type of arrangement is statistically different from other patterns. It was obtained with the meshed and circular dispositions higher values of CUC and DUC, being these rated as ‘Excellent’ (Table 3). The radial pattern had lower means, with 84.20% CUC and 74.88% DUC, being rated ‘Good’.

Although the circular and meshed patterns have uniformities rated as excellent, this rating may not be extrapolated to the overall performance of the system. For the meshed, two-dimensional arrangement, the collectors are more concentrated, close together and covering a small area, relative to the total area, and the equipment movement, thus there is no accurate detection of problems that occur between nozzles and on the Center Pivot movement direction. The circular pattern, on the other hand, does not detect problems located between spans but detects possible flowrate variations due to the area relief on the Center Pivot movement direction, thus having the evaluated equipment pressure-regulating valves installed for each emitter and the area being flat, a high uniformity value was expected.

The results obtained for the radial pattern are similar to those found by Bishaw & Olumama (2016) who had a CUC of 79% and a DUC of 70% in wind conditions of 2.5 m·s⁻¹ which, according to these authors, was the main factor that affected the uniformity.

Li et al. (2016), when studying the effect of nozzle arrangement on the uniformity of a Center Pivot with radially arranged collectors, obtained an increase of 8.9% for CUC and 25.67% for DUC along the spans when the nozzle arrangement was increasing. The same authors obtained a decrease of 21.81% for CUC and 43.71% for DUC when their disposition did not follow the ascending order. Al-Gaadi et al. (2019) obtained a variation in CUC from 76.83% to 93.45% over eight pivot spans for which, in addition to the wind, the difference in nozzles installed on the lateral line was also cited as the main factor affecting uniformity.

Based on observations in Table 5 and on the results and conclusions of the aforementioned authors, it is evident that the radial arrangement is an interesting sampling method to detect uniformity problems that occur between sets of nozzles. In the Center Pivot evaluated in this study, neither the pressure variation nor the relief affected, in a relevant way, the uniformity. Mainly, the uniformity was affected by the installation of nozzles that varied along the lateral line incorrectly, which led to a lower uniformity for radial sampling.

Rodrigues et al. (2019) studying the water application uniformity of a solid set sprinkler system for different collector patterns, obtained better coefficients for meshed arrangement, with a CUC of 92.85% and DUC of 86.98%. These authors state that this was due to the better spatial sampling of this arrangement in relation to the overlapping irrigation water depths applied by the sprinklers. These results are similar to those presented in Table 5, in which it can also be seen that the arrangement of the collectors associated with the greater overlap had an influence on the uniformity sampled for the meshed arrangement.

The results referring to the mean comparison test between Spans 1, 2, and 3 can be seen in Table 6.

There is a significant difference between Span 1 in relation to Spans 2 and 3 for both CUC and DUC. In Span 1, higher means were observed with a CUC of 91.80% and DUC of 88.65%, which are rated as ‘Excellent’. In Span 2, there was a CUC of 87.12% and a DUC of 79.52%, classified as ‘Good’; for Span 3, the CUC was 86.46% and the DUC 78.48%, also rated as ‘Good’.

Analyzing these results, it is noted that the further away from the center of the equipment, the values of CUC and DUC, for each span, have decreased. This is due to the tower period of movement because the closer to the center of the system, the towers tend to be, the less time in movement and more time stopped. In addition, the velocity of the towers closer to the center of the pivot is lower, this increases the uniformity of water application mainly in the direction of lateral line movement. During the tests it was observed that the period in which the mobile towers 1, 2, and 3 were functioning was 16, 27, and 46 s respectively, which shows that the first tower moves less time. Moreover, the effect of the wind cannot be neglected, as already explained. Several authors such as Ouazaa et al. (2015) and Mohamed et al. (2021) also observed that the effect of operating cycles, as well as variations in the speed of the towers, affect the uniformity of irrigation on the travel direction.

Another fact to note is that the radial arrangement is always parallel to the meshed in the direction of the Center Pivot radius. As for the circular pattern, as it moves away from the center, it tends to be parallel to the meshed on the equipment direction of movement. This happens due to the increase in the diameter of the circles of each span in the direction of the radius, therefore, to some extent this influenced the fact that Spans 2 and 3 are statistically equal in terms of uniformity.

The comparison of the uniformity coefficients means for each of the patterns along the evaluated spans is presented in Table 7.

Observing the results within each span, it is noted that in Spans 1 and 2, the uniformity values for the radial pattern were statistically different from the circular and meshed. On Span 3, all sampling patterns are statistically equal and are rated as ‘Excellent’. With this result, it is evident that for terrains with flat topography, constant pressure on the nozzles, and adequate sequencing of the nozzles along the lateral line, any sample pattern can be adopted to evaluate the uniformity performance of a Center Pivot.

Note that the radial pattern showed a higher CUC, of 91.62%, and DUC of 86.96%, in relation to the first two spans. For the third span, the water depths uniformity sampled on radial pattern could be classified as ‘Excellent’, while the rating for the first ones was considered as ‘Good’.

The circular pattern generated statistically equal uniformities along the spans, with CUC and DUC values rated as ‘Excellent’, except in Span 2, where CUC was 87.23% and DUC 79.70%, rated as ‘Good’. The meshed pattern was also statistically equal for all spans, with CUC and DUC rated as ‘Excellent’ mostly, but not in Span 1 where CUC and DUC were ‘Good’.

Shaughnessy et al. (2013) studying CUC and DUC in a six-span Center Pivot system observed variations along the spans in the order of 3% for circular and meshed layout, 9% for radial, where the wind was pointed out as the main factor affecting uniformity. Ortiz et al. (2010) studying the application uniformity of a Center Pivot for different application rates with collectors arranged in two radial lines, obtained a variation of CUC around 73.80% to 81.00% along the spans, where the wind was also cited as the factor that influenced most the results. The results of the aforementioned authors show how sensitive the radial type of arrangement is.

In general, radial sampling characterizes the longitudinal profile and better represents the influence of emitters on the behavior of the applied irrigation water depths. In this way, with few collectors, it is possible to observe the water depth behavior along with the irrigation lateral, which makes possible to make an inference about the need for changes in the system regarding the emitters. However, the fact that the sample width is smaller is a limitation, so it does not accurately express the behavior of the water depths along the entire irrigated circle, on the system movement direction.

The circular-type sampling pattern characterizes the behavior of the irrigation depths over the movement direction of the Center Pivot, along the circle irrigated by the equipment. Its limitation is that it does not cover all emitters installed along the lateral line, presenting only the behavior of the water depths applied by the emitters close to the line of collectors.

The meshed pattern sampling characterizes the irrigation depths applied both in the radial and on the movement direction of the Center Pivot. It provides coverage of a two-dimensional area in each span; however, its limitation is linked to the sample range, narrow in both directions, that is, it does not allow observing the behavior of the water depths in the entire irrigated circle. Thus, to have a larger area of coverage with this sample pattern, a high number of collectors is necessary.

In practical terms, it was possible to evaluate that, for areas with flat or slightly undulating topography and when using pressure regulating valves for the emitters, sampling in a radial pattern is sufficient, as causes of reduction in water uniformity application due to installed emitters and nozzles will be detected.

The combined use of the radial and circular sampling pattern is interesting for the evaluation of the uniformity of Center Pivots on situations of terrain with irregular topography and when there are sensitive variations in the dynamic operation pressure of the emitters.

Meshed-type sampling detects the effect of wind in any direction, as well as tower stoppage during the system operation. The radical and circular sampling patterns are only effective for detecting wind drift of sprayed drops when the wind direction coincides with the collector arrangement direction.

Finally, based on the results obtained in this article, it is recommended to investigate the spatial and temporal dependence between the applied water depth and the movement of the Center Pivot irrigation towers, in future works.

This research was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) – no grant number awarded.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.