Optimal Sample Size for Furrow Irrigation Design

Optimal sample size for representing spatially varying infiltration and furrow geometry conditions under furrow irrigation was determined for different field sizes considering both the expected monetary loss due to incomplete information and sampling cost. Step and linear sampling cost functions were considered. The sum of expected loss due to incomplete information and sampling cost gave the total expected loss, and its minimum value for a given field size resulted in optimal sample size. Consequently, the minimum value of the total expected loss also corresponded with the maximum return to water including sampling cost. In the case of the step sampling cost function, the optimal sample sizes were 3, 9 and 10 for fields consisting of <500 (11·4 ha), 500-1800 (41·0 ha), and 1800 or more (>41·0 ha) furrows (300 m long spaced at 0·76 m), respectively. The optimal sample size n gradually increased from 1 to 3 with the number of furrows, Nf⩽400 and shifted rapidly to 9 at Nf=500 and it became 10 at 700 furrows in the case of the linear sampling cost function. Index field size (field size at which both sampling cost and expected loss become comparable) was found to be 400 furrows (9·1 ha). Therefore, 3 samples per 9 ha block can be used for representing spatial variability in managing the furrow irrigation for the conditions studied.