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Statistical Analysis of Sorghum Yield: A Stochastic Approach¹

ABSTRACT

The spatial variability of the yield of a sorghum (Sorghum vulgare Pers.) crop irrigated by a two line source sprinkler system is analyzed. This system, with two different qualities of irrigation water, produced a uniform water but varying salt application between the irrigation lines. On the outside of the irrigation lines both the amount of applied water and salt varied. Maximum yield was obtained around the low salt line and the yield decreased from the low (EC = 1.50 dS m^–1) to high (EC = 4.02 dS m^–1) salt line. On the outside of the irrigation lines the sorghum yield decreased approximately linearly with distance from each sprinkler line. The sorghum was harvested with 1-m sampling intervals along five 45-m transects normal to the irrigation lines. Sample autocorrelation function (SACF) of the mean yield showed high correlation values at the first two lags and a slow decay thereafter, indicating the nonstationary behavior caused by the controlled water application. A fourth-order polynomial removed the deterministic component of the yield. The sample autocorrelation function of the residuals showed spatial structure with a significant peak at lag 1 and indicated that the stationarity condition is achieved. Further analysis of the residuals using the sample partial autocorrelation function (SPACF) revealed significant peaks at lags 1 and 2. The behavior of SACF and SPACF indicated that the spatial structure of residuals related to the effect of soil salinity variation on the sorghum yield is well described by a second order autoregressive process with a white noise (identically and independently distributed with mean (x) zero and variance ²).

¹ Contribution from Dep. of Land, Air, and Water Resources, Univ. of California, Davis. This research was supported by the Kearney Foundation of Soil Science.

² Graduate Student and Professors, Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA 95616.

Received for publication March 22, 1984. Accepted for publication May 2, 1985.