5.3.2: Application Uniformity

Irrigation systems are not capable of applying exactly the same depth of water to every location in the field. The distribution of applied water varies because of factors such as wind drift, improper pipeline pressure, poor design, and inappropriate system management. For many irrigation systems, the depth of water applied at a point is nearly the same as the depth entering the soil (infiltration) at the point. Thus, nonuniform applications lead to nonuniform depths of infiltration and ultimately to varying amounts of soil water in the root zone. This nonuniformity adversely affects plant performance so information about the uniformity of application is needed to manage irrigation systems effectively. Illustrations of the effects of poor water distribution on plant health are shown in Figure 5.5. The center pivot pictures (Figures 5.5a and 5.5b) are in Nebraska soybean fields during a drought year (August 2012), which exacerbated the effect of poor uniformity. Further, nonuniform application leads to more deep percolation which results in lower application efficiencies and sometimes to chemical leaching. Uniformity can be measured for all irrigation systems. For sprinkler systems collection containers (catch cans) or rain gauges are placed in a grid pattern in the field. The irrigation system is then operated for a period of time and the depth of water caught in each container is measured. For microirrigation systems, the volume of water emitted in a given time is measured for all emitters on a lateral. For surface irrigation, experiments can be conducted to determine the depth of water that infiltrates at various points within the field. To evaluate uniformity, a method is needed to compute a performance value from field test data. The two most commonly used methods are the distribution uniformity (DU) and the Christiansen uniformity coefficient. The DU is a relatively simple method where:

\(DU = \frac{d_{LQ}}{d_z}\) (5.2)

where: d_LQ = average low-quarter depth of water infiltrated, and

d_z = mean depth infiltrated for all observations.

The value of d_LQ is the average depth of application for the lowest one-quarter of all measured values when each value represents an equal area of the field. You can determine the low-quarter depth by ranking observed depths and computing the average for the smallest 25% of the values. Since DU is a ratio with the value of the denominator always being larger than the numerator, DU is always between 0 and 1. The larger the value of DU, the better the uniformity.

Figure 5.5. Irrigation system having poor water distribution: (a) center pivot irrigation system with large leaks, (b) center pivot with end gun providing a larger application depth than the rest of the system, (c) furrow irrigation, and (d) underground sprinkler system for turfgrass. (Photos a and b courtesy of Gary Zoubek, Nebraska Extension; photo c courtesy of Richard Ferguson, Nebraska Extension.)

The Christiansen uniformity coefficient (CU) is another index to indicate application uniformity. When each observation represents the same area, the CU is determined as:

\(CU = 100\% \left( 1 - \sum_{i=1}^{n} \frac{|d_i - d_z|}{n d_z} \right)\) (5.3)

where: d_i = depth of observation i,

d_z = mean depth infiltrated for all observations, and

n = number of observations.

The calculated value is multiplied by 100 to provide an index value between 0 and 100. Note that \(\sum_{i=1}^{n} \frac{|d_i - d_z|}{n}\) is the average deviation from the mean. Thus, another way to write Equation 5.3 is: 100% (1 – average deviation ÷ mean depth infiltrated). Equation 5.3 was developed to interpret data collected with catch cans placed under sprinkler irrigation system. Typically, water depths in the equation are amounts caught in the cans, not infiltrated water. Since the distribution of infiltration is really what is of interest, the depth of water caught in the can used in Equation 5.3 will indicate infiltrated water only if no surface runoff occurs.

Example 5.1

Given: A sprinkler system was evaluated using 20 catch can containers. The depth caught in each container is given below.

#	di (in)
1	1.2
2	2.6
3	1.8
4	2.1
5	2.2
6	1.7
7	2.9
8	2.7
9	1.6
10	2.0
11	2.1
12	1.7
13	1.9
14	1.4
15	2.4
16	2.0
17	1.6
18	2.3
19	1.8
20	2.0

Finds: Compute the distribution uniformity (DU) and Christiansen’s uniformity coefficient (CU).

Solution: Rank the data in descending order, compute d_z and then calculate d_LQ.

#	di (in)	|di-dz|
1	2.9	0.9
2	2.7	0.7
3	2.6	0.6
4	2.4	0.4
5	2.3	0.3
6	2.2	0.2
7	2.1	0.1
8	2.1	0.1
9	2.0	0.0
10	2.0	0.0
11	2.0	0.0
12	1.9	0.1
13	1.8	0.2
14	1.8	0.2
15	1.7	0.3
16	1.7	0.3
17	1.6	0.4
18	1.6	0.4
19	1.4	0.6
20	1.2	0.8

d_LQ== average of #16 to 20 = 1.5 in

d_z=average of #1 to 20 = 2.0 in

Then compute the individual deviations \(|d_i - d_z|\) and the sum of deviations \(\sum|d_i - d_z| = 6.6\)

Then: \(DU = \frac{d_{LQ}}{d_z}\) \(DU = \frac{1.5}{2.0} = 0.75\) (Eq. 5.2)

\(CU = 100\% \left( 1 - \sum_{i=1}^{n} \frac{|d_i - d_z|}{n d_z} \right)\) (Eq. 5.3)

\(CU = 100\% \left( 1 - \frac{6.6}{20 \times 2.0} \right) = 84\%\)

1

Typically, CU values are used for sprinkler and microirrigation systems while DU has become more popular for surface systems. However, some organizations use DU exclusively for all irrigation systems. Methods used to measure the uniformity of center pivot irrigation systems are unique and a modified CU is normally used. The uniformity of a center pivot is measured by placing containers along two radial lines. The cans are usually placed with uniform spacing from 5 to 15 ft apart along each line. Then the pivot is operated so that the lateral passes over the containers. Since the pivot operates in a circular fashion, a container located far from the pivot point represents more area than one close to the pivot point. Therefore, the Heermann and Hein coefficient of uniformity (CU_H) is ordinarily used for pivots (Heermann and Hein, 1968):

\(CU_H = 100\% \left( 1 - \frac{\sum_{i=1}^{n}|d_i - d_z^*| S_i}{\sum_{i=1}^{n} d_i S_i} \right)\) (5.4)

where: \(S_i\) = distance from the pivot point to the container, and

\(d_z^*\) = weighted mean infiltration, which is equal to:

\(d_z^* = \frac{\sum_{i=1}^{n} d_i S_i}{\sum_{i=1}^{n} S_i}\) (5.5)

Uniformity values are not used like efficiency terms; rather they provide an index of performance. The optimal value of CU or DU depends on the price of irrigation water, the value of the irrigated crop, the costs of drainage or water quality impacts on the environment, and the cost of system renovation and/or management changes. Guidelines to judge whether uniformity is acceptable have been established. For moved lateral sprinkler systems, a CU of 80 (or DU of 0.7) is commonly the lowest acceptable uniformity. For center pivots, a CU_H = 90 is often achieved. For furrow systems, a DU of 0.6 is frequently the lowest acceptable value. The DU for microirrigation systems (also known as emission uniformity) should be at least 0.8.