A weighted multivariate spatial clustering model to determine irrigation management zones

Management of agricultural fields according to spatial and temporal variability is an important aspect of precision agriculture. Precision management relies on division of a field into areas with homogeneous characteristics, management zones (MZs), which are likely affected by multiple, interrelated factors. We present a method, based on machine learning and spatial statistics, to analyze the spatial relationship between a set of variables and determine management zones in a vineyard. The method involves: (1) fitting a model that quantifies the relationship between multiple variables and yield; (2) fitting a model that quantifies the effect of the spatial variability of multiple variables on yield spatial characteristics; and (3) developing a weighted multivariate spatial clustering model as a method to determine MZs. Twelve variables were sampled for 3893 vines in the wine grape vineyard. These variables included soil properties, terrain characteristics, and environmental impact, as well as crop-condition, using indices calculated from remote sensing images. The predictor variables were spatially characterized using hot-spot analysis (Getis Ord Gi^* Z-score values) to assess their spatial variability. A gradient boosted regression trees (BRT) algorithm was used to analyze the spatial multivariable effect on yield spatial characteristics. MZs were determined using multivariate K-means clustering, with relative weights given to the predictors, based on their relative influence on yield spatial variability provided by the BRT model. This method was compared to ordinary K-means clustering and K-means with spatial representation of the variables without weights using a dissimilarity index and spatial autocorrelation measures. Model performance was found to be very high and demonstrated that among the evaluated predictors, crop condition indices were the most important regressors for yield and its spatial characteristics. The weighted multivariate spatial clustering was found to perform better in terms of separability of the points and their spatial distribution than the other two clustering techniques. Quantifying yield and its within-field spatial variability, ranking the effects of the predictors and their spatial variabilities, and segmentation of MZs through multivariable spatial analysis, are expected to benefit irrigation management and agricultural decision-making processes.