Recurrent Neural Net Regression Models with space-varying coefficients for pedotransfer function estimation and prediction of soil properties

The paper aim is to propose a new regression model for relating soil variables of difficult or complex measurement with other variables easier to measure, in order to predict the first one based on data about the last ones. The measurements are taken along soil lines called transects. The study of these relations (pedotransfer functions) presents the complexity of simultaneous presence of 3 elements: data spatial dependence, soil non-homogeneity and non-linearity of the relationship. The main models usually considered in the literature for such relations (namely, linear state-space and feedforward neural nets) have the limitation of expressing only two of these 3 characteristics of the problem. In order to overcome such limitations, it is proposed here a regression model for pedotransfer mapping based on recurrent neural nets (the feedback helps to better express the spatial dependence), but with weights varying smoothly along the space in order to incorporate the soil non-homogeneity. The algorithm developed for model estimation and prediction is based on a second order non-linear extension of the Kalman filter in Bayesian form. The comparative advantages of the proposed model in relation to the other ones are shown, considering different prediction performance measures for the transect extremes.