Data description

The factors in the database included data source (study period or historic), site type (controlled or producer), system type (traveling or stationary), software (excel, R, or none), nozzle diameter, nozzle type (ring, taper ring, taper bore, or Senninger), gun model (100, 150, 200, or 7025), nozzle pressure, gun angle, wetted diameter, sprinkler spacing, sprinkler spacing in percent of wetted diameter, wind speed, and relative wind direction. The records of the study period are those collected after 2007 and the historic records are those collected in 1997 and 1998. The factor “software” represents the way of calculating CU. “excel” was used to calculate the CU of traveling gun systems from profile data, “R” was used to calculate the CU of stationary systems from profile data, and “none” meant that the CU of traveling gun systems was calculated from transect data. Relative wind direction was the angle between the wind direction and the rain gauges. The database contained 722 observations and pseudo-observations (those generated from superpositioning field data to simulate different sprinkler spacings), including those generated from profile data of traveling gun systems using gun angles of 180 degrees, 260 degrees, and 320 degrees, and those generated from Winsipp (Senninger Irrigation, Inc., Clermont, FL). Table 3-1 summarizes the data composition.

Tab le 3-1 Data composition

Number of Records

system type site type data source traveling 529 produced 267 current 586 stationary 193 controlled 405 historic 136

Although various factors were contained in the database, not all of them could be used in the regression analysis. As the sprinkler spacing in percent of wetted diameter was calculated by

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dividing the sprinkler spacing by the wetted diameter, those three variables would likely cause collinearity if they all were retained in the model. Sprinkler spacing in percent o f wetted diameter is a widely used term in irrigation design and analysis and the wetted diameter tends to change with the system age, thus those two variables were selected for the regression analysis and sprinkler spacing was omitted. The variable “tool” was also dropped from the regression analysis, since much of the information provided by “tool” had already been represented by other variables. For example, if the “tool” was “excel”, it was a pseudo- observation from a traveling gun system and if the “tool” was “R”, it was a pseudo- observation from a stationary system. The variable “gun angle” was excluded because of the many missing gun angle values from historic field trials. Since relative wind direction was not measured or not recorded in many of the historic field trial and previous research has shown that the wind direction is not significant in affecting the application uniformity, the relative wind direction was not introduced into the regression analysis.

Since there were some missing values (fields) in the database and some incorrect data, not all the observations and pseudo-observations could be used in the regression analysis. For instance, a negative CU indicates a severe uniformity problem with the irrigation system, thus the record of negative CU was dropped from the analysis. In another instance, trials performed at a training session at LATDU had an obviously lower CU (30 to 56) than others. The trial log recorded that there was a sprinkler malfunction, so those pseudo-observations from that trial were also dropped. A number of pseudo-observations were generated with the excel program using a range of gun angels with each field collected profile data. However, since “gun angle” would not be a variable in the model and a gun angle of 220 degrees was used for the traveler trials using transect gauge setups at LATDU, only pseudo-observations from a gun angle of 220 degrees were retained to reduce mode l variance. Some historic observations or pseudo-observations lacked information on nozzle type, sprinkler spacing or others, and they were retained or dropped for the regression analysis based upon the variables used in the model. Figure3-1 shows the histogram of the CU values of all the observations

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and pseudo-observations. This figure indicates some possible outliers. Figure 3-2 shows the histogram of the CU values after the records mentioned above were dropped. This histogram of CU indicates fewer possible outliers and a more normal distribution.

-20 -10 0 10 20 30 40 50 60 70 80 90 100

Figure 3-1 Data distribution of CU fo r all data

50 60 70 80 90

Figure 3-2 Data distribution of CU after dropping bad data

The regression analysis was first conducted with all the observations and pseudo- observations (combined data of both traveler and stationary systems) except for those excluded by the reasons stated above. Afterwards, those observations and pseudo- observations were split into two subsets depending on the system type, traveling gun systems

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or stationary systems, and the regression analysis was conducted on the separated datasets. Candidate models were then evaluated by R2, CLM (confidence limits of the mean predicted value), and CLI (confidence limits of the mean individual value). Other criteria, such as AIC, AICC, and SBC, were also checked. After initial investigation of significant factors in the model, including factors investigating the effects of system type and data source (historic or current trials), final models were formulated giving consideration to ease of field measurement and the ability to construct user tables for field use.

3.2. Combined data regression model development