Sensor-directed response surface sampling designs for characterizing spatial variation in soil properties

Abstract

In many applied precision farming applications, remotely sensed survey data are collected specifically because these data correlate well with some soil property of interest. Additionally, a general model for the functional relationship between the soil property and the sensor data is often known a priori, but the exact parameter estimates associated with the model must still be determined via some type of site-specific sampling strategy. The main objective of this paper is to present an objective sampling and simplified modeling strategy for predicting soil property information from such spatially referenced sensor data. Some common types of spatial linear prediction models and linear geostatistical models are reviewed, and the assumptions needed to reduce these more complicated models to a spatially referenced, ordinary linear regression model (LR) are discussed. Next, a model-based sampling strategy for estimating an ordinary linear regression model in the spatial setting is described. This sampling strategy incorporates a traditional response surface design into an iterative, space-filling type algorithm for purposes of selecting sample site locations that are (i) nearly optimal with respect to matching the selected response surface design levels and (ii) physically separated far apart as possible to ensure the best chance that the independent error assumption is adequately met. This strategy can in principal be used to select a minimal number of optimal sample site locations that satisfy the residual independence assumptions in the ordinary model. A detailed case study of a salinity survey using electromagnetic induction (EM) and four-electrode sensor data is then presented. These case study results confirm that the sampling strategy was highly effective at ensuring efficient regression model parameter estimates and a reliable salinity prediction map. An additional simulation study confirmed the effectiveness of this model-based strategy over a more traditional simple random sampling strategy with respect to four regression model design criteria. Under the right conditions, this methodology should be applicable to many types of precision farming survey applications where soil property/sensor data prediction models need to be fitted using only a limited number of soil samples.