Artificial intelligence-based fast and efficient hybrid approach for spatial modelling of soil electrical conductivity

Expert systems adopted to support modern and rapidly advancing proximal soil sensing technologies can help generate accurately modelled electrical conductivity, as a decision-support parameter defining soil health in terms of the salinity, clay and bulk density compositions, among the other primal soil properties. Electrical conductivity (EC) is expected to correlate with the pertinent factors that regulate the crop yield (i.e., soil texture, cation exchange, drainage conditions, organic matter level, salinity, and the subsoil characteristics), which in turn, can also acts to control the overall health of the crop. Utilizing a fast and efficient artificial intelligence approach, this study designs a hybrid predictive model integrating multilayer perceptron with the Firefly Algorithm (MLP-FFA), and then evaluates its performance in respect to the standalone MLP and the ordinary kriging (OK) model applied in agricultural locality of the Soofiyan, plains in Tabriz, northwest of Iran. To develop a spatial modelling framework, 126 distinct measurements of EC were obtained through a grid sampled at 1000 m × 1000 m spacing, partitioned in training (88) and testing (38) sets. Applying a ratio of nugget to sill to determine the spatial dependence, a spatial modelling strategy was utilized where the spherical, exponential, Gaussian and linear semi-variograms depicting the autocorrelation of the sampled points (latitude × longitude) over the study area were analyzed in ArcGIS to deduce the optimal data characteristics and the respective statistical model. Spherical semi-variogram was the optimal representor for EC, relative to its latitude and longitude, in agreement with the lowest Residual Sums of Squares (RSS) and the highest coefficient of determination (R2). Hybrid MLP-FFA and standalone MLP models were thus developed with latitude, longitude and measured electrical conductivity in the training set and evaluated in respect to the OK method by means of statistical scores: root mean square error (RMSE), mean absolute error (MAE) including the normalized metrics represented by Willmott’s Index (WI), Nash Sutcliffe’s coefficient (ENS) and Legates & McCabe’s Index (ELM). Verified by diagnostic plots and grid-averaged metrics, the results revealed that the hybrid MLP-FFA model performed significantly better than both comparative models, with WI = 0.780 relative to 0.637 (MLP) and 0.714 (OK) models and ENS = 0.725 (vs. 0.511 & 0.589) and ELM = 0.552 (vs. 0.402 & 0.413), respectively. Expanded uncertainty, t-statistic and global performance indicators combining the R2, RMSE and mean bias error and a Taylor plot also confirmed the efficacy of the hybrid MLP-FFA over the standalone MLP and OK model. There was no significant difference between the results of standalone MLP and OK when evaluated through spatial trend maps, while the hybrid MLP-FFA model exhibited a better ability to establishing nonlinear relationships with electrical conductivity data, resulting in a better representation of the spatially modelled EC. Our results ascertain the prodigious performance of a hybrid MLP-FFA over a standalone MLP and ordinary kriging approaches, attributable to a better utility of the Firefly algorithm in improved spatial estimation of electrical conductivity. This study concludes that the hybrid MLP-FFA model should be explored to solve practical problems in soil physics, particularly in designing decision-support systems to attain agricultural precision