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Multiresponse multilayer vadose zone model calibration using Markov chain Monte Carlo simulation and field water retention data
Author(s) -
Wöhling Thomas,
Vrugt Jasper A.
Publication year - 2011
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2010wr009265
Subject(s) - vadose zone , markov chain monte carlo , hydraulic conductivity , monte carlo method , calibration , algorithm , computer science , mathematical optimization , mathematics , soil science , geology , statistics , soil water
In the past two decades significant progress has been made toward the application of inverse modeling to estimate the water retention and hydraulic conductivity functions of the vadose zone at different spatial scales. Many of these contributions have focused on estimating only a few soil hydraulic parameters, without recourse to appropriately capturing and addressing spatial variability. The assumption of a homogeneous medium significantly simplifies the complexity of the resulting inverse problem, allowing the use of classical parameter estimation algorithms. Here we present an inverse modeling study with a high degree of vertical complexity that involves calibration of a 25 parameter Richards'‐based HYDRUS‐1D model using in situ measurements of volumetric water content and pressure head from multiple depths in a heterogeneous vadose zone in New Zealand. We first determine the trade‐off in the fitting of both data types using the AMALGAM multiple objective evolutionary search algorithm. Then we adopt a Bayesian framework and derive posterior probability density functions of parameter and model predictive uncertainty using the recently developed differential evolution adaptive metropolis, DREAM ZS adaptive Markov chain Monte Carlo scheme. We use four different formulations of the likelihood function each differing in their underlying assumption about the statistical properties of the error residual and data used for calibration. We show that AMALGAM and DREAM ZS can solve for the 25 hydraulic parameters describing the water retention and hydraulic conductivity functions of the multilayer heterogeneous vadose zone. Our study clearly highlights that multiple data types are simultaneously required in the likelihood function to result in an accurate soil hydraulic characterization of the vadose zone of interest. Remaining error residuals are most likely caused by model deficiencies that are not encapsulated by the multilayer model and can not be accessed by the statistics and likelihood function used. The utilization of an explicit autoregressive error model of the remaining error residuals does not work well for the water content data with HYDRUS‐1D prediction uncertainty bounds that become unrealistically large.