An Ensemble Modeling Approach for Estimating Diffusive Tortuosity for Saturated Soils From Porosity

Abstract

Apparent diffusion constants in soil are generally estimated by dividing molecular diffusion coefficient for a solute with soil tortuosity (τ) values. Several models have been proposed to estimate τ from soil porosity (ϕ) alone, but most of these models fail when the variability in observed τ-ϕ pairs increases. Pedotransfer functions can be used to predict τ from easy-to-measure soil properties such soil texture, organic carbon contents, and ϕ, but such an approach requires more measurements to be performed than just measuring ϕ. Here, we show that τ may be estimated from ϕ alone using the ensemble averaging approach. We examined seven different analytical expressions for τ-ϕ and seven different ensemble-modeling approaches to estimate τ for 100 pairs of τ-ϕ collected from a wide geographical area. Modeling results showed that the Bayesian model averaging method was the best ensemble-modeling approach for estimating τ from ϕ. Of 119 different combinations of τ (ϕ) models, three models derived considering (1) packing of square-shaped particles, (2) fractal geometry with particles of different sizes, and (3) percolation theory were identified as the best individual models for ensemble modeling. The coefficient of determination (0.67), root-mean-squared error (0.23), and the Akaike information criterion (94.37) values for this ensemble model were better than those when a single model was used for prediction. Inclusion of these three models that are based on both fractal and regular geometrical shapes for particles of different sizes may be a reason for improved performance of the ensemble approach. These results suggest that τ may be estimated from ϕ using the ensemble approach without the need for additional soil data, as is done in a pedotransfer function approach.