000890096 001__ 890096 000890096 005__ 20230815122840.0 000890096 0247_ $$2doi$$a10.1029/2020WR027110 000890096 0247_ $$2ISSN$$a0043-1397 000890096 0247_ $$2ISSN$$a0148-0227 000890096 0247_ $$2ISSN$$a1944-7973 000890096 0247_ $$2ISSN$$a2156-2202 000890096 0247_ $$2altmetric$$aaltmetric:93417004 000890096 0247_ $$2WOS$$aWOS:000582701700068 000890096 037__ $$aFZJ-2021-00685 000890096 082__ $$a550 000890096 1001_ $$00000-0002-0207-9061$$aXu, Teng$$b0$$eCorresponding author 000890096 245__ $$aPreconditioned Crank‐Nicolson Markov Chain Monte Carlo Coupled With Parallel Tempering: An Efficient Method for Bayesian Inversion of Multi‐Gaussian Log‐Hydraulic Conductivity Fields 000890096 260__ $$a[New York]$$bWiley$$c2020 000890096 3367_ $$2DRIVER$$aarticle 000890096 3367_ $$2DataCite$$aOutput Types/Journal article 000890096 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1611653210_21744 000890096 3367_ $$2BibTeX$$aARTICLE 000890096 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000890096 3367_ $$00$$2EndNote$$aJournal Article 000890096 500__ $$aKein Post-print verfügbar 000890096 520__ $$aGeostatistical inversion with quantified uncertainty for nonlinear problems requires techniques for providing conditional realizations of the random field of interest. Many first‐order second‐moment methods are being developed in this field, yet almost impossible to critically test them against high‐accuracy reference solutions in high‐dimensional and nonlinear problems. Our goal is to provide a high‐accuracy reference solution algorithm. Preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐MCMC) has been proven to be more efficient in the inversion of multi‐Gaussian random fields than traditional MCMC methods; however, it still has to take a long chain to converge to the stationary target distribution. Parallel tempering aims to sample by communicating between multiple parallel Markov chains at different temperatures. In this paper, we develop a new algorithm called pCN‐PT. It combines the parallel tempering technique with pCN‐MCMC to make the sampling more efficient, and hence converge to a stationary distribution faster. To demonstrate the high‐accuracy reference character, we test the accuracy and efficiency of pCN‐PT for estimating a multi‐Gaussian log‐hydraulic conductivity field with a relative high variance in three different problems: (1) in a high‐dimensional, linear problem; (2) in a high‐dimensional, nonlinear problem and with only few measurements; and (3) in a high‐dimensional, nonlinear problem with sufficient measurements. This allows testing against (1) analytical solutions (kriging), (2) rejection sampling, and (3) pCN‐MCMC in multiple, independent runs, respectively. The results demonstrate that pCN‐PT is an asymptotically exact conditional sampler and is more efficient than pCN‐MCMC in geostatistical inversion problems. 000890096 536__ $$0G:(DE-HGF)POF3-255$$a255 - Terrestrial Systems: From Observation to Prediction (POF3-255)$$cPOF3-255$$fPOF III$$x0 000890096 536__ $$0G:(GEPRIS)359880532$$aDFG project 359880532 - Computergestützter Ansatz zur Kalibrierung und Validierung mathematischer Modelle für Strömungen im Untergrund - COMPU-FLOW $$c359880532$$x1 000890096 588__ $$aDataset connected to CrossRef 000890096 7001_ $$00000-0001-7331-8237$$aReuschen, Sebastian$$b1 000890096 7001_ $$00000-0003-2583-8865$$aNowak, Wolfgang$$b2 000890096 7001_ $$0P:(DE-Juel1)138662$$aHendricks Franssen, Harrie‐Jan$$b3 000890096 773__ $$0PERI:(DE-600)2029553-4$$a10.1029/2020WR027110$$gVol. 56, no. 8$$n8$$p1-19$$tWater resources research$$v56$$x1944-7973$$y2020 000890096 8564_ $$uhttps://juser.fz-juelich.de/record/890096/files/2020WR027110.pdf 000890096 909CO $$ooai:juser.fz-juelich.de:890096$$pVDB:Earth_Environment$$pVDB 000890096 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)138662$$aForschungszentrum Jülich$$b3$$kFZJ 000890096 9131_ $$0G:(DE-HGF)POF3-255$$1G:(DE-HGF)POF3-250$$2G:(DE-HGF)POF3-200$$3G:(DE-HGF)POF3$$4G:(DE-HGF)POF$$aDE-HGF$$bErde und Umwelt$$lTerrestrische Umwelt$$vTerrestrial Systems: From Observation to Prediction$$x0 000890096 9141_ $$y2020 000890096 915__ $$0StatID:(DE-HGF)3001$$2StatID$$aDEAL Wiley$$d2020-09-03$$wger 000890096 915__ $$0StatID:(DE-HGF)0200$$2StatID$$aDBCoverage$$bSCOPUS$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)0300$$2StatID$$aDBCoverage$$bMedline$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)0100$$2StatID$$aJCR$$bWATER RESOUR RES : 2018$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)0199$$2StatID$$aDBCoverage$$bClarivate Analytics Master Journal List$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)0160$$2StatID$$aDBCoverage$$bEssential Science Indicators$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)1160$$2StatID$$aDBCoverage$$bCurrent Contents - Engineering, Computing and Technology$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)1060$$2StatID$$aDBCoverage$$bCurrent Contents - Agriculture, Biology and Environmental Sciences$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)0113$$2StatID$$aWoS$$bScience Citation Index Expanded$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)0150$$2StatID$$aDBCoverage$$bWeb of Science Core Collection$$d2020-09-03 000890096 915__ $$0StatID:(DE-HGF)9900$$2StatID$$aIF < 5$$d2020-09-03 000890096 920__ $$lyes 000890096 9201_ $$0I:(DE-Juel1)IBG-3-20101118$$kIBG-3$$lAgrosphäre$$x0 000890096 980__ $$ajournal 000890096 980__ $$aVDB 000890096 980__ $$aI:(DE-Juel1)IBG-3-20101118 000890096 980__ $$aUNRESTRICTED