Assessing spatial variation of corn response to irrigation using a bayesian semiparametric model

Authors: Stone, Kenneth - Ken; Sadler, Edward

Submitted to: Transactions of the ASABE
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 1/22/2015
Publication Date: 2/23/2016
Citation: Stone, K.C., Sadler, E.J. 2016. Assessing spatial variation of corn response to irrigation using a bayesian semiparametric model. Transactions of the ASABE. 59(1): 251-261.

Interpretive Summary: Site-specific variable rate irrigation (VRI) is beginning to be widely accepted. These systems have the ability to apply water spatially within a field to meet spatial crop water requirements. These VRI systems require a higher level of management than classical irrigation systems that apply water uniformly through a field. These VRI systems require spatial knowledge of the soil and crop responses throughout the field to determine when and where to apply irrigation. In this research we investigated how to calculate and estimate the variables that irrigation managers would need to make informed decisions for managing spatial irrigation. Traditionally, these estimates were calculated using classical statistical methods. In our current research, we utilized a new approach using a spatially explicit analysis model to estimated spatial crop responses throughout the entire field. The new model calculated the estimated yield in good agreement with the observed yields and more accurately accounted for the low and high yields. The new model also was used to calculate other response variables such as rainfed yield, maximum yield, and irrigation at maximum yield. These variables would be useful for design and management of both conventional irrigation and VRI systems. Overall, our conclusions supported the original classical statistical analysis in identifying significant spatial differences in crop responses across and within soil map units. The major improvement in the current analysis is that the system explicitly considered the spatial dimension in calculation of the estimated yields and response variables and should provide better estimates of their impact in system design and management.

Technical Abstract: Spatial irrigation of agricultural crops using site-specific variable-rate irrigation (VRI) systems is beginning to have wide-spread 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) to 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) to 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 did 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 the spatial dependence in calculation of the estimated yields and other variables and, thus, should provide improved estimates of their impact useful in system design and management.