Discussion
The performance of a border irrigation event was evaluated by taking soil moisture measurements at 12 locations along the border from the upstream end. The computed irrigation depths at those locations were 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, and 39 mm. The Christiansen Uniformity Coefficient (CU) for the event, in %, is __________. (Rounded off to 2 decimal places)
Answer: A
The Christiansen Uniformity Coefficient is 93.26%.
Christiansen's coefficient is
\[ CU = 100\left(1 - \frac{\sum|x_i - m|}{n\,m}\right) \]
where m is the mean depth. The 12 depths run evenly from 50 to 39 mm, so \(m = (50 + 39)/2 = 44.5\) mm. The absolute deviations are 5.5, 4.5, 3.5, 2.5, 1.5, 0.5 on each side, totalling \(2 \times 18 = 36\) mm:
\[ \begin{aligned} CU &= 100\left(1 - \frac{36}{12 \times 44.5}\right) \\ &= 100(1 - 0.0674) = 93.26\% \end{aligned} \]
91.66 and 89.70 do not follow from Christiansen's formula with these depths, and 36.28 is far too low for depths that vary by only about ±12% around the mean.
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