Comparing Nonlinear Regression and Markov Chain Monte Carlo Methods for Assessment of Predic on Uncertainty in Vadose Zone Modeling

In vadose zone modeling, parameter es mates and model predic ons are inherently uncertain, regardless of quality and quan ty of data used in model-data fusion. Accurate quan fi ca on of the uncertainty is necessary to design future data collec on for improving the predic ve capability of models. This study is focused on evalua ng predic ve performance of two commonly used methods of uncertainty quan fi ca on: nonlinear regression and Bayesian methods. The former quan fi es predic ve uncertainty using the regression confi dence interval (RCI), whereas the la er uses the Bayesian credible interval (BCI); neither RCI nor BCI includes measurement errors. When measurement errors are considered, the counterparts of RCI and BCI are regression predic on interval (RPI) and Bayesian predic on interval (BPI), respec vely. The predic ve performance is examined through a cross-valida on study of two-phase fl ow modeling, and predic ve logscore is used as the performance measure. The linear and nonlinear RCI and RPI are evaluated using UCODE_2005. The nonlinear RCI performs be er than the linear RCI, and the nonlinear RPI outperforms the linear RPI. The Bayesian intervals are calculated using Markov Chain Monte Carlo (MCMC) techniques implemented with the diff eren al evolu on adap ve metropolis (DREAM) algorithm. The BCI/BPI obtained from DREAM has be er predic ve performance than the linear and nonlinear RCI/RPI. Diff erent from observa ons in other studies, it is found that es ma ng nonlinear RCI/RPI is not computa onally more effi cient than es ma ng BCI/BPI in this case with low-dimensional parameter space and a large number of predic ons. MCMC methods are thus more appealing than nonlinear regression methods for uncertainty quan fi ca on in vadose zone modeling.