Using a parallelized MCMC algorithm in R to identify appropriate likelihood functions for SWAT

Markov Chain Monte Carlo (MCMC) algorithms allow the analysis of parameter uncertainty. This analysis can inform the choice of appropriate likelihood functions, thereby advancing hydrologic modeling with improved parameter and quantity estimates and more reliable assessment of uncertainty. For long-running models, the Differential Evolution Adaptive Metropolis (DREAM) algorithm offers spectacular reductions in time required for MCMC analysis. This is partly due to multiple parameter sets being evaluated simultaneously. The ability to use this feature is hindered in models that have a large number of input files, such as SWAT. A conceptually simple, robust method for applying DREAM to SWAT in R is provided. The general approach is transferrable to any executable that reads input files. We provide this approach to reduce barriers to the use of MCMC algorithms and to promote the development of appropriate likelihood functions. Bayesian MCMC analysis has yet to be successfully applied to the popular SWAT model.An R implementation of DREAM accommodates SWAT's reading of input files.Open source script allows for likelihood function development to advance modeling.

[1]  John F. Joseph Preliminaries to watershed instrumentation system design , 2011 .

[2]  Remegio Confesor,et al.  Automatic Calibration of Hydrologic Models With Multi‐Objective Evolutionary Algorithm and Pareto Optimization 1 , 2007 .

[3]  Tyler Smith,et al.  Development of a formal likelihood function for improved Bayesian inference of ephemeral catchments , 2010 .

[4]  J. Vrugt,et al.  A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors , 2010 .

[5]  Brent M. Troutman,et al.  Runoff prediction errors and bias in parameter estimation induced by spatial variability of precipitation , 1983 .

[6]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[7]  Jing Yang,et al.  Comparing uncertainty analysis techniques for a SWAT application to the Chaohe Basin in China , 2008 .

[8]  John R. Williams,et al.  LARGE AREA HYDROLOGIC MODELING AND ASSESSMENT PART I: MODEL DEVELOPMENT 1 , 1998 .

[9]  George Kuczera,et al.  Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory , 2006 .

[10]  Vijay P. Singh,et al.  The NWS River Forecast System - catchment modeling. , 1995 .

[11]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[12]  Raghavan Srinivasan,et al.  A parallelization framework for calibration of hydrological models , 2012, Environ. Model. Softw..

[13]  Gerald Whittaker,et al.  Use of a beowulf cluster for estimation of risk using swat , 2004 .

[14]  V. Singh,et al.  Computer Models of Watershed Hydrology , 1995 .

[15]  Johan Alexander Huisman,et al.  Hydraulic properties of a model dike from coupled Bayesian and multi-criteria hydrogeophysical inversion , 2010 .

[16]  M. Di Luzio,et al.  Detection of overparameterization and overfitting in an automatic calibration of SWAT. , 2010 .

[17]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[18]  Persi Diaconis,et al.  The Markov chain Monte Carlo revolution , 2008 .

[19]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[20]  Heikki Haario,et al.  DRAM: Efficient adaptive MCMC , 2006, Stat. Comput..

[21]  S. Sorooshian,et al.  Stochastic parameter estimation procedures for hydrologie rainfall‐runoff models: Correlated and heteroscedastic error cases , 1980 .

[22]  Peter M. A. Sloot,et al.  Application of parallel computing to stochastic parameter estimation in environmental models , 2006, Comput. Geosci..

[23]  Ziliang Zong,et al.  Evaluating the Efficiency of a Multi-core Aware Multi-objective Optimization Tool for Calibrating the SWAT Model , 2012 .

[24]  Karline Soetaert,et al.  Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME , 2010 .

[25]  D. Higdon,et al.  Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling , 2009 .

[26]  Shuguang Liu,et al.  Automating calibration, sensitivity and uncertainty analysis of complex models using the R package Flexible Modeling Environment (FME): SWAT as an example , 2012, Environ. Model. Softw..

[27]  Peter Reichert,et al.  Bayesian uncertainty analysis in distributed hydrologic modeling: A case study in the Thur River basin (Switzerland) , 2007 .

[28]  Jasper A. Vrugt,et al.  High‐dimensional posterior exploration of hydrologic models using multiple‐try DREAM(ZS) and high‐performance computing , 2012 .

[29]  Minxue He,et al.  Corruption of parameter behavior and regionalization by model and forcing data errors: A Bayesian example using the SNOW17 model , 2011 .