Evaluating the prediction of two unsaturated hydraulic conductivity models by considering parameters uncertainty

Unsaturated hydraulic conductivity (K(θ)) is proportional to volumetric water content in vadose zone and the obtained K(θ) curve is crucial for modeling the soil water movement. Numerous theories and models have been recently proposed regarding the estimation of K(θ) that despite improving model predictions, each has a disadvantage of its own. The critical path analysis from percolation theory attempts to improve the prediction of K(θ) by simplifying the complex geometry of the porous medium. In addition, the recently developed Peters-Durner-Iden model (PDI) has shown high potential for prediction of K(θ). In this research, both percolation theory and PDI models are evaluated. Also, by using Monte Carlo- Markov chain method, the uncertainty of the simulated parameters is assessed. In this study, the Hybrid-Evolution Monte Carlo-Markov chain algorithm has been utilized, that employs adaptive metropolis, differential-evolution, and Snooker update algorithms, which minimizes the number of iterations required to search parametric space. Goodness of fit measures shows higher results for prediction of K(θ) by percolation theory and in every case except for a single soil, the Nash–Sutcliffe criterion was higher than 0.9. In addition, the number of parameters required for the PDI model is more than percolation theory, which leads to an increase in parameter- associated uncertainty. It is also discussed that it is possible to reduce the number of parameters required by PDI model by applying several constraints. But this method is not applicable to all soil textures. Comparison of the convergence rate of the two models showed that parameters of PDI model in all cases require close to 300 iterations to converge while, percolation theory requires up to 2000 iterations to converge. Therefore, the results indicate that the percolation theory with fewer number of parameters can provide more accurate and reliable estimates of K(θ) and water retention.