Nonlinear parametric modelling to study how soil properties affect crop yields and NDVI

This paper explores the use of a novel nonlinear parametric modelling technique based on a Volterra Non-linear Regressive with eXogenous inputs (VNRX) method to quantify the individual, interaction and overall contributions of six soil properties on crop yield and normalised difference vegetation index (NDVI). The proposed technique has been applied on high sampling resolution data of soil total nitrogen (TN) in %, total carbon (TC) in %, potassium (K) in cmol kg−1, pH, phosphorous (P) in mg kg−1 and moisture content (MC) in %, collected with an on-line visible and near infrared (VIS-NIR) spectroscopy sensor from a 18 ha field in Bedfordshire, UK over 2013 (wheat) and 2015 (spring barley) cropping seasons. The on-line soil data were first subjected to a raster analysis to produce a common 5 m by 5 m grid, before they were used as inputs into the VNRX model, whereas crop yield and NDVI represented system outputs. Results revealed that the largest contributions commonly observed for both yield and NDVI were from K, P and TC. The highest sum of the error reduction ratio (SERR) of 48.59% was calculated with the VNRX model for NDVI, which was in line with the highest correlation coefficient (r) of 0.71 found between measured and predicted NDVI. However, on-line measured soil properties led to larger contributions to early measured NDVI than to a late measurement in the growing season. The performance of the VNRX model was better for NDVI than for yield, which was attributed to the exclusion of the influence of crop diseases, appearing at late growing stages. It was recommended to adopt the VNRX method for quantifying the contribution of on-line collected soil properties to crop NDVI and yield. However, it is important for future work to include additional soil properties and to account for other factors affecting crop growth and yield, to improve the performance of the VNRX model.