Uniformity Measurements for Turfgrass: What's Best? 
by
D . F. Zoldoske, K. H. Solomon, and E. M. Norum
CATI Publication #941102
© Copyright November 1994, all rights reserved

The basic concept behind irrigation uniformity is to apply water so that every square inch of the turfgrass receives an equal amount. If this were to occur, then we could say the sprinkler system is applying water with 100 percent uniformity. Unfortunately, no sprinkler system (not even rain) is able to apply water with 100 percent (perfect) uniformity. Traditionally, irrigation systems that applied water with uniformity measurements of 80% or better were considered adequate. This paper looks at what measurements have been historically used and suggests new approaches which the authors believe offer significant improvements.
CHRISTIANSEN'S COEFFICIENT OF UNIFORMITY (CU)
One of the most frequently referenced measures is the Uniformity Coefficient as defined by J. E. Christiansen (CU). CU for an irrigated area can be determined from a catch can study and then applying the formula given below. (If the irrigation time at each measurement point is the same, then it does not matter whether the application rate or application amount is measured.) It is assumed that the application measurement points are located so that each point represents the same size area as the others.

CU = 
100 (1  D/M) 
D = 
(1/n) å  Xi  M 
M = 
(1/n) å Xi 
Xi = 
Individual Application Amount 
n = 
Individual Application Amount 
å = 
Symbol for Summation 
  = 
Symbol for Absolute Value of Quantity Between the Bars 

The absolute value of a deviation considers only its magnitude, not its sign. For example, deviations of two units above the mean and two units below the mean both have absolute
deviations of two.
There are a few significant features of Christiansen's CU that should be considered when interpreting CU values. For one thing, the absolute value bars used in computing D treat
over and underwatering (relative to the mean application amount M) the same. Deviations above and below the mean application are judged only by the size of the deviation, not
according to whether they represent cases of excess or deficient water.
Another characteristic of CU is that the computation of D penalizes a deviation in a mathematically "linear" fashion. This means that the decrease in CU caused by any individual
deviation is in direct proportion to the magnitude of that deviation.
To illustrate these points, suppose the mean application is 10, and consider individual application amounts of 8, 12, and 14. The deviations for these amounts are respectively
2, 2 and 4. Because of the absolute value bars, the applications 8 and 12 both contribute absolute deviations of 2 to D. Because of the "linear" feature of D, the 14 contributes
twice as much to D as does the 12, because its deviation from the mean is twice as large.
A third feature of CU is that by design, it is an "average" measure. CU compares the average absolute deviation (D) to the mean or average application (M). Thus CU indicates on
average how uniform the sprinkler application pattern is. CU gives no indication of how bad a particular localized area might be, or how big that critical area might be.
There can be no doubt that CU has been a valuable tool in aiding the design and evaluation of sprinkler systems. But the features of CU noted above have caused some criticisms.
Some people would prefer that over and underwatering not be treated the same. Others argue that large deviations are far more significant than small ones, and the calculation
of D should penalize deviations more than proportionate to their magnitude. Still others complain that average conditions are of no concern, they need to know how bad things are
in some critical area.
Due in part to these criticisms, several other coefficients and uniformity indices have been developed over the years. Many are merely refinements or minor alterations in the
concept embodied in the CU formula. A few, however, are different. The following sections discuss three fundamentally different approaches to uniformity evaluation on turfgrass.

DISTRIBUTION UNIFORMITY (DU)
Another popular method among turfgrass irrigators that emphasizes the underwatered area is DU, for Distribution Uniformity. In using this approach, all the individual application
data points are sorted from high to low values. The lowest 25% of the values are identified, and the average of these (the "low quarter, as it's sometimes referred to) is divided
by the mean application for the entire area, and multiplied by 100 to convert to percent. Thus a DU of, say, 80 means that the low quarter of the applications averaged 20% lower
than the mean application. However, this method does not take into account the location of the low application values, or any benefit which might be derived from higher applications
immediately adjacent to the low values. The "low quarter" might be made up of one relatively large area in deficit, or it might be from several smaller deficit areas. Also DU would
still be considered an average measure, since it describes the average of a relatively large area (25% of the total), rather than describing the worst case situation. The use of the
"lowest 25%" is purely arbitrary and bears no relationship to the crop's growing characteristics.

Figure 1. DensoGram Example

CIT DENSOGRAM
The Center for Irrigation Technology has developed a nonquantitative way to describe and display sprinkler application patterns that many of our clients seem to like.
This method uses a dot matrix printer shading technique to produce what might be called a "densogram." The actual application amounts are transformed into different
intensities (densities) of dots. The application in the wettest area is set to a value of one, and displayed as solid black (solid dots). The value zero represents no
water at all (a dry spot), and is displayed as white (no dots  the paper shows through full white). All other application amounts are scaled between these two points,
and are given shading densities corresponding to their relative position between zero and one. The resulting densogram (Figure 1.) gives an excellent visual description
of where the high and low watering spots are, how wet or dry they are, and in general, how uniform the water application is.

SCHEDULING COEFFICIENT (SC)
An approach that measures specific aspects of irrigation uniformity is the "Scheduling Coefficient" which was developed by CIT in conjunction with industry representatives.
While the densogram gives a good visual impression of the overall uniformity of application, it does not provide a quantitative way to actually measure uniformity.
Conceptually, the Scheduling Coefficient uses a sliding window of a designated size ( e.g.. 2, 5, or 10% of coverage area) that is moved over the sprinkler pattern area.
The application values falling within the window at any particular position are averaged. As the window is moved through the area, the average application within the window
for each position is stored. After the window has passed through the entire sprinkler overlap area, the window averages are reviewed to identify the low values.
The lowest window value is divided into the total area average. This coefficient or ratio is always "1" or greater and is used to increase the run time of the mean application,
thereby providing adequate water to the driest "window" of the coverage area.

Figure 2. Turgrasss quality rating as a function of percent ETc

NEW APPROACHES TO OPTIMIZE SC
CIT is currently attempting to refine this method to base the irrigation application amount directly to the desired appearance of the turfgrass and the size of this "sliding window" dry spot. The basic concept would give a more rational approach to what the irrigation manager is already trying to achieve. That is, apply just enough water to satisfactorily manage the dry spots. Any irrigation beyond this point would be defined as overirrigation.
The approach we are developing is described as follows. Visual quality observations of turfgrasses are made, with ratings values based on color, density, uniformity, and general vigor of growth. The scale used to rate the turfgrass quality ranges from 1 to 9, with 1 to 3 indicating unacceptable quality turfgrass, 4 to 6 indicating acceptable quality turfgrass, and 7 to 9 indicating superior quality turfgrass. These quality ratings are indexed to the amount of water applied and expressed as a percentage of the evapotranspiration crop (ETc) in Figure 2. Thus, the turfgrass manager can select the Minimum Turfgrass Quality (MTR) rating that is acceptable for the situation.
Additionally, a judgment must be made on the Turfgrass Management Area (TMA) or size of the dry spot which is to be managed. With these two pieces of information and basic sprinkler pattern data the turfgrass manager can more accurately predict irrigation run times that will produce the Minimum Turfgrass Quality that the manager has defined. The following example is an attempt to illustrate how this concept would work in the field.
The values found in Figure 3 are precipitation amounts measured in hundredths of an inch per hour. The values are those found between four sprinklers spaced 50 ft apart on a large turf sports area, and for the purpose of this example, the sprinklers and spacing are repeated throughout the turfgrass area. The mean application rate is 0.46 in/hour, and the ETc is 0.30 in. for the day. The Turfgrass Management Area (TMA) that is being managed is approximately 10 ft by 10 ft, or 100 square ft. This represents 4 percent of the coverage area. Say for example, the turf manager wants to maintain a Minimum Turfgrass Quality (MTQ) rating of 5 in this driest part of the field. Using Figure 2 to achieve this rating, a minimum of 50% of the ETc must be applied. The calculations are as follows in the Example given below:
EXAMPLE 
The average amount of water found in the entire coverage area is 0.46 in/hr (sum of the measurements divided by the number of observations). The average amount of water found in the TMA (100 square ft) is 0.28 in/hr. This is the equivalent of a Scheduling Coefficient of 1.64 on a window size of 4 percent.
As stated above, the daily ETc rate for turfgrass is 0.30 in. We know our system delivers an average of 0.46 in/hr. If we divide the required 0.30 in. by .46 in/hr, 39 minutes of daily run time is required to deliver the 0.30 in. of water on average to the TMA or driest 100 square feet of turfgrass. However, we know this unnecessarily over irrigates the largest part of the turfgrass area. Remember, we only want to maintain a minimum quality rating of "5" on the driest area. In this case, we need to be sure 50% of the ETc is applied to the TMA. We take the daily ETc of 0.30 and multiply by 50%, which produces a net required ETc of 0.15 in. The managed dry spot is receiving 0.28 in/hr. The 0.15 in. is multiplied by the SC of 1.64 and then divided by the mean application rate of 0.46 in/hr. The result is a run time of 32 minutes, or a savings of 18 percent of the water required in meeting ETc in the TMA. This water savings is possible while assuring that no "dry spots" exist of any consequence below a turfgrass quality rating of "5" as specified by the turfgrass manager.

Figure 3. Catch Can Values for a Representative Sprinkler Pattern

The calculation can be summarized as follows:
Set Time = (ETc )*(%ETc)*(SC) * (60 minutes )
Where
Etc = Evapotranspiration crop
%Etc = Minimum Turfgrass Rating (MTR) expressed as percentage of ETc
SC = Mean application rate divided by the mean application rate in the
"Sliding Window" or Turfgrass Management Area (TMA), where size is user defined
And based on the given example would be:
32 Minute Set Time = ETc (0.30) * %ETc (50%) * SC (1.64) * (60 minutes)
We are currently refining this method and hope to develop it into a useful turfgrass management practice. It represents a pioneering attempt to finally combine sprinkler uniformity data with turfgrass quality requirements in a more rational and realistic manner.

REFERENCES
Gibeault, V.A., 1983. "Rating Turfgrass Plots," Cooperative Extension, University of California, Riverside, CA, 3 p.
Oliphant, J.C. and D.F. Zoldoske, 1989. "Sprinkler Profile And Coverage Evaluation (SPACE)", Software and Documentation, CATI Publication No. 890403,
Center For Irrigation Technology, California State University, Fresno, CA, 39 p.



