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Assessing Spatial Variation of Corn Response to Irrigation Using a Bayesian Semiparametric Model

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan www.asabe.org

Citation:  Transactions of the ASABE. 59(1): 251-261. (doi: 10.13031/trans.59.10942) @2016
Authors:   Kenneth C. Stone, E. John Sadler
Keywords:   Additive models, Bivariate smoothing, Penalized splines, Response curves, Semiparametric regression, Site-specific agriculture, Varying coefficient models.

Abstract. Spatial irrigation of agricultural crops using site-specific variable-rate irrigation (VRI) systems is beginning to have widespread acceptance. However, optimizing the management of these VRI systems to conserve natural resources and increase profitability requires an understanding of the spatial crop responses. In this research, we utilize a recently developed spatially explicit analysis model to reanalyze spatial corn yield data. The specific objectives of this research were to (1) calculate a suite of estimates (estimated yield, rainfed yield, maximum yield, and irrigation at maximum yield) and provide credible intervals (measures of uncertainty) around these estimates for comparing with the previous analysis, and (2) examine whether the conclusions from this rigorous re-analysis were different from the prior analysis and if the results would force any modifications to the conclusions obtained with the prior analyses. The spatially explicit analysis was achieved using a mixed model formulation of bivariate penalized smoothing splines and was implemented in a Bayesian framework. This model simultaneously accounted for spatial correlation as well as relationships within the treatments and had the ability to contribute information to nearby neighbors. The model-based yield estimates were in excellent agreement with the observed spatial corn yields and were able to estimate the high and low yields more accurately than the previous analysis. Credible intervals were calculated around the estimates, and the majority encompassed the observed yields. After calculating estimates of yield, we then calculated estimates of other response variables, such as rainfed yield, maximum yield, and irrigation at maximum yield. These estimated response variables were then compared with previous results from a classical statistical analysis. Our conclusions supported the original analysis in identifying significant spatial differences in crop responses across and within soil map units. These spatial differences were great enough to be considered in irrigation system design and management. The major improvement in the 2014 re-analysis is that the model explicitly considered spatial dependence in calculating the estimated yields and other variables and thus should provide improved estimates of the impact of spatial differences for use in irrigation system design and management.

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