Reply to comment by Chu et al. on “High‐dimensional posterior exploration of hydrologic models using multiple‐try DREAM (ZS) and high‐performance computing”

Abstract

PUBLICATIONS Water Resources Research COMMENTARY 10.1002/2013WR014425 This article is a reply to Chu et al. [2014] doi:10.1002/2012WR013341. Reply to comment by Chu et al. on ‘‘High-dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing’’ Jasper A. Vrugt 1,2,3 and Eric Laloy 4 Correspondence to: J. A. Vrugt, jasper@uci.edu Citation: Vrugt, J. A., and E. Laloy (2014), Reply to comment Chu et al. on ‘‘High- dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing,’’ Water Resour. Res., 50, 2781–2786, doi:10.1002/ 2013WR014425. Received 15 JULY 2013 Accepted 8 FEB 2014 Accepted article online 15 FEB 2014 Published online 21 MAR 2014 Department of Civil and Environmental Engineering, University of California, Irvine, California, USA, 2 Department of Earth System Science, University of California, Irvine, California, USA, 3 Institute for Biodiversity and Ecosystems Dynamics, University of Amsterdam, Amsterdam, Netherlands, 4 Institute for Environment, Health and Safety, Belgian Nuclear Research Centre, Mol, Belgium 1. Introduction The comment of Chu et al. [2014], hereafter referred to as CYG, raises questions about some of the results presented in our paper (Laloy and Vrugt [2012], hereinafter LV, which is not to be confused with Las Vegas, although appropriate concerning the subject of this work on Monte Carlo simulation). As a preamble, we would like to remark that the work presented in Chu et al. [2010] and LV (2012) concern two different fields of study. CYG view the model calibration as an optimization problem, and use common concepts to efficiently find a single realization of the parameter values that minimizes (or maximizes, if appropriate) some user-defined objective function. Our work, on the contrary, uses Bayesian principles coupled with MCMC simulation to derive a distribution of parameter values that honor the observed data. This distribution summarizes parameter and model predictive (simulation) uncertainty, a requirement for probabilistic analysis, operational forecasting, disentangling error sources, and decision making. The maxi- mum a posteriori density (MAP) parameter values derived with MCMC simulation should reside in close vicinity of the ‘‘best’’ solution found with an optimization algorithm, if the exact same data set, prior distribu- tion, and likelihood (objective) function are used. In this reply, we assume that CYG used a correct imple- mentation of the MT-DREAM (ZS) algorithm and similar data set, prior and likelihood function as LV. Otherwise, the comparative analysis is meaningless. We emphasize this for three reasons. First, the results presented herein contradict CYG and are similar to those reported in LV but now with more trials plotted. Second, contributions in physics [Horowitz et al., 2012; Toyli et al., 2012; Yale et al., 2013] and geophysics [Linde and Vrugt, 2013; Laloy et al., 2012, Rosas-Carbajal et al., 2014; T. Lochbuehler et al., Summary statistics from training images as model constraints in probabilistic inversion, Geophysical Journal International, in review, 2014] demonstrate proper convergence behavior of MT-DREAM (ZS) on complex and high- dimensional targets involving hundreds of parameters. Third, to justify their SP-UCI algorithm the original paper of Chu et al. [2010] portrays misleading results of the predecessor of DREAM, called SCEM-UA. Section 4 of this reply will address this latter issue in more detail. We now respond to the comments of CYG. We use different sections with numbering corresponding to CYG. 2. Computational Time Unit CYG find the Computational Time Unit (CTU) diagnostic to be a poor indicator of the performance of MT- DREAM (ZS) . They suggest using the number of function evaluations or clock time instead. The CPU-time (s) scales linearly with CTU, or CPU 5 aCTU, where a (s) denotes the average time it takes to complete a sin- gle function (model) evaluation. As a is dependent on the processor speed (hardware), LV purposely reported the CTU values. Note that we neglect the actual run time of MT-DREAM (ZS) , in the determination of a, which is appropriate given the intended application of this algorithm to CPU-intensive forward models. We purposely do not use the number of function evaluations as performance diagnostic. This metric does not properly convey the CPU-time (CTU) of parallel algorithms such as DREAM (ZS) or MT-DREAM (ZS) . These VRUGT AND LALOY C 2014. American Geophysical Union. All Rights Reserved. V