Research Paper
Dynamic model for water application using centre pivot irrigation

https://doi.org/10.1016/j.biosystemseng.2010.01.006Get rights and content

The application pattern for single, stationary spray sprinklers exposed to the wind was modelled to simulate water application in a centre pivot-irrigated field. In the model, a dynamic square grid of cells for water application and a static square grid of cells for water collection were defined. The dynamic grid contained the information on the water application pattern of an isolated spray sprinkler, and this followed the motion of the centre pivot lateral. The static grid represented the entire field, and received water from the dynamic grid at fixed time intervals. Model outputs included the applied water distribution pattern and measures of irrigation uniformity (radial, travelling path and global). A series of experiments using pivoted and single spray sprinklers were conducted simultaneously. The results from the model compared well with field observations. The resulting root mean square errors for the Heermann and Hein uniformity coefficient and the average applied water depth were 0.02% and 0.08 mm, respectively. Model simulations were carried out to illustrate the effect of wind on irrigation uniformity.

Introduction

Water is the main yield-determining factor in the majority of agricultural systems. Irrigation systems help growers manage weather related risks by effectively supplementing rainfall (Perry et al., 2002). To sustain agricultural production in the coming years, it is important to optimise irrigation systems, adjusting water application to crop water requirements. This will help protect both the quantitative and qualitative aspects of water conservation. Centre pivots are an interesting technological option for irrigation, since their performance can be very high (Clemmens & Dedrick, 1994).

Centre pivots are commonly used in modern irrigation developments all over the world (Evans et al., 1993, Faci et al., 2001). Consequently, it is important to characterise the relevance of several design and management factors affecting the efficiency and uniformity of these machines (Montero, Valero, & Tarjuelo, 2003). Quality control for centre pivot irrigation involves measuring the levels of irrigation precipitation under the machine (Bremond & Molle, 1995). Centre pivot simulation models have been used to improve the design of new systems and to modify existing systems with the view of improving irrigation performance.

The simulation of centre pivot performance has been the subject of a series of research efforts since the 1960s. Bittinger and Logenbaugh (1962) simulated precipitation under centre pivots with the objective of defining the optimal sprinkler spacing in order to obtain uniform water distribution. They developed an analytical model of precipitation under a sprinkler assuming that its water application pattern was either triangular or elliptical. The model was based on the additional hypotheses of continuous movement and linear or circular sprinkler trajectory. They estimated the irrigation depth by moving the water application pattern at the same velocity of sprinkler movement on the pivot lateral. Heermann and Hein (1968) continued this line of research by taking into account the overlapping effect of neighbouring sprinklers, and introduced the uniformity coefficient that bears their name. This led to the introduction of the CPED (centre pivot evaluation and design) software package (Heermann & Stahl, 2004). CPED input data included sprinkler positions on the lateral, discharge, radial application pattern and time of system revolution. Triangular, elliptical and toroidal application patterns were assumed for single nozzle, dual nozzle impact sprinklers and spray sprinklers, respectively. Model outputs included the applied water depth as a function of radial distance from the pivot point, application intensity under the lateral and a uniformity coefficient. Wind effects were not considered in the model. Evans et al. (1993) developed the CPIM (centre pivot irrigation model) software for water and/or water-nitrate distribution analyses from centre pivots. Their model used an empirical equation relating the water application pattern in the absence of wind to supply pressure. The CPIM software overlapped individual water application patterns and represented water application over the irrigated field. Bremond and Molle (1995) developed a model for the simulation of water application under centre pivots, focusing on irrigation uniformity. The basic model input was the sprinkler application pattern, obtained from field experiments. The overlap between sprinklers and the estimated water application as a function of machine speed were determined numerically.

The above-mentioned models used one-dimensional, geometrical water application profiles for simulation purposes. This can lead to significant errors since water application patterns are not always adequately reproduced by a simple geometrical shape, and even light winds can produce asymmetric water application patterns. Consequently, models were required where water application is related to more than just distance from the sprinkler.

In a direct precedent to the present work, Omary and Sumner (2001) developed a model to simulate water application and irrigation uniformity resulting from overlapping spray nozzles mounted on a centre pivot. Building on a previous effort (Omary, Camp, & Sadler, 1997), their objective was to simulate water application resulting from a moving spray sprinkler using the stationary water application pattern as the main input data. The area under a single spray sprinkler during its movement on a centre pivot was discretised using two regular grids. One grid represented water application (the sprinkler application pattern), whilst the other represented water collection (the soil surface). The grid representing the single spray sprinkler moved along the pivot trajectory, whilst the grid representing the soil was stationary. Taking into account precipitation intensity in each cell of the moving grid, and its time to pass over the fixed grid, water application distribution in the fixed grid was determined. Following the simulation of water application from all spray nozzles, a uniformity coefficient was calculated (Omary & Sumner, 2001). The authors used a moving grid that included experimentally determined application intensities, rather than simple geometric water application patterns. However, the model included simplifications, such as assuming a linear movement of the spray sprinklers (as if the pivot lateral was a linear-moving machine). This assumption can lead to significant errors, particularly near the pivot point. On the other hand, it simplified model design, since each cell of the moving grid applied water over only one line of cells in the fixed grid.

Considering a fixed water application pattern for the whole system operation time may also result in poor model performance since wind speed and direction may significantly vary during pivot irrigation varying the pattern. Thus, the use of wind dependent, variable, two-dimensional sprinkler application patterns appears to be required in order to produce accurate simulation models.

The main objective of this research was to develop an improved model of water application by centre pivot spray sprinklers. The model was designed to improve on previous efforts by (1) taking into account wind effects; (2) considering the real circular path of the spray nozzles in their rotation around the pivot point; (3) characterising the water application pattern as a grid of observed irrigation depths, and rotating this application pattern during pivot rotation; and (4) changing the water application pattern with wind speed and direction. Here, the model is formulated, validated and applied to the simulation of a case study.

Section snippets

Building and moving grids for spray sprinkler application pattern

In the model, the water application pattern of a stationary, isolated spray sprinkler is used to calculate the water depth applied when mounted on a centre pivot. For modelling purposes, the entire field covered by the centre pivot system is divided into square cells to produce a static grid.

A second dynamic grid, composed of regular cells, represents the water application pattern resulting from a single spray sprinkler. In this grid, the water application rate can be determined in each cell as:

Field experiments

A series of experiments were performed to determine the water application pattern of single sprinklers under different wind conditions. The same sprinklers were installed on a centre pivot lateral. Experiments were performed on both configurations at the same time, recording water application using different collector arrangements. The experiments were carried out at the experimental irrigation farm of the University of Tabriz, Iran. A centre pivot and an adjacent area were used for the

Model validation

The experiments reported in this paper concerned two spray sprinkler models, two pressures, two nozzle elevations and two pivot spans. Therefore, there were 16 different experimental conditions. Also, experiments were repeated in order to obtain data under different wind conditions, giving a total of 34 experiments. The experimental data on water application patterns was introduced into the model, and the pivot experiments were computer simulated. As previously explained, the model did not

Model application

A case study was devised to demonstrate the model capacity to simulate uniformity using experimental data. Three water application patterns obtained for Senninger LDN spray sprinklers operating at 103 kPa and installed at a nozzle elevation of 2.25 m were used for input. These experiments were performed under the following wind speeds and directions: (a) 3.3 m s−1 and 311°; (b) 4.9 m s−1 and 342°; and (c) 4.1 m s−1 and 59°.

The model was run counter clockwise from a starting angle of 90°,

Summary and conclusions

A new model of pivot irrigation has been developed. The model is based on the displacement of a moving grid representing each spray sprinkler moving over a static grid. Grid displacement produces circular paths for each of the grid cells. The analysis of the intersecting paths of the dynamic cells during their rotation around the pivot point led to a new concept in pivot irrigation modelling. It was shown that uniform water application along a centre pivot lateral does not fully guarantee the

Acknowledgements

Thanks are due to Dr. A. Hoseinzadeh Dalir, former head of agriculture faculty in University of Tabriz and Engineer. A. Rezaiee, former head of research farms, for their support in the reported experiments. R. Delirhasannia received a scholarship from the Ministry of Science, Research and Technology of Iran to do research at the Aula Dei Experimental Station of CSIC, Zaragoza, Spain.

Please note that mention of a commercial product does not imply endorsement.

References (19)

  • E. Playán et al.

    Assessing sprinkler irrigation uniformity using a ballistic simulation model

    Agricultural Water Management

    (2006)
  • ASAE

    ASAE standard (R2007) S436.1. Test procedure for determining the uniformity of center-pivot and lateral move irrigation machines equipped with spray or sprinkler nozzles

    (1996)
  • ASAE

    ASAE Standard S330.1. Procedure for sprinkler distribution testing for research purpose

    (2003)
  • M.W. Bittinger et al.

    Theoretical distribution of water from a moving sprinkler

    Transactions of the ASAE

    (1962)
  • B. Bremond et al.

    Characterization of rainfall under center-pivot: influence of measuring procedure

    Journal of Irrigation and Drainage Engineering: ASCE

    (1995)
  • P. Carrión et al.

    SIRIAS: a simulation model for sprinkler irrigation: I. Description of the model

    Irrigation Science

    (2001)
  • A.J. Clemmens et al.

    Irrigation techniques and evaluations

  • R.G. Evans et al.

    CPIM- A computer simulation program for center pivot irrigation systems

    (1993)
  • J.M. Faci et al.

    “Comparison of fixed and rotating spray plate sprinklers”

    Journal of Irrigation and Drainage Engineering: ASCE

    (2001)
There are more references available in the full text version of this article.

Cited by (23)

  • Novel approach to evaluate the dynamic variation of wind drift and evaporation losses under moving irrigation systems

    2015, Biosystems Engineering
    Citation Excerpt :

    Also, climate change has already limited water resources for many regions of the world (Bandyopadhayay, Bhadra, Raghuwanshi, & Singh, 2009; Li et al. 2007; McVicar et al., 2007), which has a negative feedback to future agricultural sustainability and food security (Gheysari et al., 2015; Rockström et al., 2009). Optimising agronomic water use efficiency through new irrigation management approaches is one way to mitigate this negative feedback, while at the same time, maximizing economic returns (Delirhasannia, Sadraddini, Nazemi, Farsadizadeh, & Playán, 2010; Evans & Sadler, 2008; Montazar & Behbahani, 2007). Center pivot irrigation systems currently irrigate more than 12.5 million ha around the globe (Spears, 2003; Sadeghi & Peters, 2013), and they are steadily replacing traditional flood irrigation and other types of sprinkler irrigation.

  • Effect of the start-stop cycle of center-pivot towers on irrigation performance: Experiments and simulations

    2015, Agricultural Water Management
    Citation Excerpt :

    The grids representing the sprinklers were computed using ballistic theory as reported in Ouazzaa et al. (2013). Other authors have used experimentally determined water distribution grids (Delirhasannia et al., 2010) or statistically defined water distribution patterns (Le Gat and Molle, 2000). The advantage of the method used in this paper is that model parameters can be extrapolated to non-evaluated nozzle diameters (within the experimental range), wind speeds (from 0 to 8 m s−1) and working pressures (from 15 to 20 psi).

  • Characterising droplets and precipitation profiles of a fixed spray-plate sprinkler

    2014, Biosystems Engineering
    Citation Excerpt :

    Kohl and DeBoer (1984) observed that for low pressure spray type agricultural sprinklers, the geometry of the spray plate surface, rather than the nozzle size and operating pressure, was the dominant variable that influenced drop size distribution. Many research papers reported that the uniformity coefficients ranging from 70% to 90% for the FSPS were lower than those for the RSPS in terms of the same nozzle diameter, nozzle height, sprinkler spacing and working pressure (Clark et al., 2003; Delirhasannia, Sadraddini, Nazemi, Farsadizadeh, & Playán, 2010; Faci et al., 2001; Playán, Garrido, Faci, & Galán, 2004). Kohl, Kohl, and DeBoer (1987) reported that the total droplet evaporation losses from the FSPS would be expected to range from 0.4% to 0.6% (Kohl et al., 1987).

  • DEPIVOT: A model for center-pivot design and evaluation

    2012, Computers and Electronics in Agriculture
    Citation Excerpt :

    Silva (2006) developed a model for estimation of runoff and soil losses for different sprinklers. Delirhasannia et al. (2010) developed, validated and applied a model to predict the radial irrigation uniformity and the water application along the CP systems while López-Mata et al. (2010) developed a model that allows simulating the effect of irrigation uniformity on crop yields profitability. Some models, in addition to ease and improve the design of new systems, may be used to support field evaluation of systems under operation, mainly calculating the water application and performance indicators (Tarjuelo et al., 1999; Rodrigues et al., 2001; Duke and Perry, 2006; Marjang et al., 2011).

  • Optimal Sprinkler Spacing for a Mini Center Pivot System

    2022, Journal of Irrigation and Drainage Engineering
View all citing articles on Scopus
View full text