A framework for recalibrating pedotransfer functions using nonlinear least squares and estimating uncertainty using quantile regression

Abstract

Pedotransfer functions (PTFs) have been developed for many regions to estimate values missing from soil profile databases. However, globally there are many areas without existing PTFs, and it is not advisable to use PTFs outside their domain of development due to poor performance. Further, developed PTFs often lack accompanying uncertainty estimations. To address these issues, a framework is proposed where existing equation-based PTFs are recalibrated using a nonlinear least squares (NLS) approach and validated on two regions of Canada; this process is coupled with the use of quantile regression (QR) to generate uncertainty estimates. Many PTFs have been developed to predict soil bulk density, so this variable is used as a case study to evaluate the outcome of recalibration. New coefficients are generated for existing soil bulk density PTFs, and the performance of these PTFs is validated using three case study datasets, one from the Ottawa region of Ontario and two from the province of British Columbia, Canada. The improvement of the performance of the recalibrated PTFs is evaluated using root mean square error (RMSE) and the concordance correlation coefficient (CCC). Uncertainty estimates produced using QR are communicated through the mean prediction interval (MPI) and prediction interval coverage probability (PICP) graphs. This framework produces dataset-specific PTFs with improved accuracy and minimized uncertainty, and the method can be applied to other regional datasets to improve the estimations of existing PTF model forms. The methods are most successful with large datasets and PTFs with fewer variables and minimal transformations; further, PTFs with organic carbon (OC) as one of or the sole input variable resulted in the highest accuracy.