Articles | Volume 28, issue 24
https://doi.org/10.5194/hess-28-5375-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-28-5375-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
17 Dec 2024
Research article |
| 17 Dec 2024
| 17 Dec 2024
Towards a community-wide effort for benchmarking in subsurface hydrological inversion: benchmarking cases, high-fidelity reference solutions, procedure, and first comparison
Teng Xu
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, China
Sinan Xiao
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom
Sebastian Reuschen
Institute for Modelling Hydraulic and Environmental Systems, University of Stuttgart, 70569 Stuttgart, Germany
Nils Wildt
Institute for Modelling Hydraulic and Environmental Systems, University of Stuttgart, 70569 Stuttgart, Germany
Harrie-Jan Hendricks Franssen
Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
Centre for High-Performance Scientific Computing in Terrestrial Systems (HPSC-TerrSys), Geoverbund ABC/J, Leo Brandt Strasse, Jülich, Germany
Wolfgang Nowak
CORRESPONDING AUTHOR
Institute for Modelling Hydraulic and Environmental Systems, University of Stuttgart, 70569 Stuttgart, Germany
Related authors
Qiaoyu Wang, Jie Yang, Ingo Heidbüchel, Teng Xu, and Chunhui Lu
EGUsphere, https://doi.org/10.5194/egusphere-2025-676, https://doi.org/10.5194/egusphere-2025-676, 2025
Short summary
Short summary
Extreme storms and droughts had profound impacts on water quality. We adapted a stochastic rainfall generator to examine how rainfall changes affect the transformation and transport of nitrogen (N) and its potential effects on water quality. We found that annual precipitation is an important factor impacting the transport of N. Wet/dry conditions of a year can significantly affect the transformation of N. Different dry-wet patterns during a year can change water quality in terms of nitrate.
Loudi Yap, Jürgen Kusche, Bamidele Oloruntoba, Helena Gerdener, and Harrie-Jan Hendricks Franssen
EGUsphere, https://doi.org/10.5194/egusphere-2025-4600, https://doi.org/10.5194/egusphere-2025-4600, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
Rainfall shifts in West Africa strongly affect the agricultural productivity, making it vital to understand how much water is stored in the soil. We investigated soil moisture from 2003 to 2019 using satellite, models and in-situ data. Results show that ESA CCI v0.81 tracks local conditions best, while CLM5.0 and GLWS2.0 capture broader climate patterns. By linking surface signals to deeper layers, we improved insight into root-zone water, helping to guide farming and water planning.
Fang Li, Heye Reemt Bogena, Johannes Keller, Bagher Bayat, Rahul Raj, and Harrie-Jan Hendricks-Franssen
EGUsphere, https://doi.org/10.5194/egusphere-2025-2124, https://doi.org/10.5194/egusphere-2025-2124, 2025
Short summary
Short summary
We developed a new method to improve hydrological modeling by jointly using soil moisture and groundwater level data from field sensors in a catchment in Germany. By updating the model separately for shallow and deep soil zones, we achieved more accurate predictions of soil water, groundwater depth, and evapotranspiration. Our results show that combining both data types gives more balanced and reliable outcomes than using either alone.
Bamidele Oloruntoba, Stefan Kollet, Carsten Montzka, Harry Vereecken, and Harrie-Jan Hendricks Franssen
Hydrol. Earth Syst. Sci., 29, 1659–1683, https://doi.org/10.5194/hess-29-1659-2025, https://doi.org/10.5194/hess-29-1659-2025, 2025
Short summary
Short summary
We studied how soil and weather data affect land model simulations over Africa. By combining soil data processed in different ways with weather data of varying time intervals, we found that weather inputs had a greater impact on water processes than soil data type. However, the way soil data were processed became crucial when paired with high-frequency weather inputs, showing that detailed weather data can improve local and regional predictions of how water moves and interacts with the land.
Qiaoyu Wang, Jie Yang, Ingo Heidbüchel, Teng Xu, and Chunhui Lu
EGUsphere, https://doi.org/10.5194/egusphere-2025-676, https://doi.org/10.5194/egusphere-2025-676, 2025
Short summary
Short summary
Extreme storms and droughts had profound impacts on water quality. We adapted a stochastic rainfall generator to examine how rainfall changes affect the transformation and transport of nitrogen (N) and its potential effects on water quality. We found that annual precipitation is an important factor impacting the transport of N. Wet/dry conditions of a year can significantly affect the transformation of N. Different dry-wet patterns during a year can change water quality in terms of nitrate.
Christian Poppe Terán, Bibi S. Naz, Harry Vereecken, Roland Baatz, Rosie A. Fisher, and Harrie-Jan Hendricks Franssen
Geosci. Model Dev., 18, 287–317, https://doi.org/10.5194/gmd-18-287-2025, https://doi.org/10.5194/gmd-18-287-2025, 2025
Short summary
Short summary
Carbon and water exchanges between the atmosphere and the land surface contribute to water resource availability and climate change mitigation. Land surface models, like the Community Land Model version 5 (CLM5), simulate these. This study finds that CLM5 and other data sets underestimate the magnitudes of and variability in carbon and water exchanges for the most abundant plant functional types compared to observations. It provides essential insights for further research into these processes.
Lukas Strebel, Heye Bogena, Harry Vereecken, Mie Andreasen, Sergio Aranda-Barranco, and Harrie-Jan Hendricks Franssen
Hydrol. Earth Syst. Sci., 28, 1001–1026, https://doi.org/10.5194/hess-28-1001-2024, https://doi.org/10.5194/hess-28-1001-2024, 2024
Short summary
Short summary
We present results from using soil water content measurements from 13 European forest sites in a state-of-the-art land surface model. We use data assimilation to perform a combination of observed and modeled soil water content and show the improvements in the representation of soil water content. However, we also look at the impact on evapotranspiration and see no corresponding improvements.
Denise Degen, Daniel Caviedes Voullième, Susanne Buiter, Harrie-Jan Hendricks Franssen, Harry Vereecken, Ana González-Nicolás, and Florian Wellmann
Geosci. Model Dev., 16, 7375–7409, https://doi.org/10.5194/gmd-16-7375-2023, https://doi.org/10.5194/gmd-16-7375-2023, 2023
Short summary
Short summary
In geosciences, we often use simulations based on physical laws. These simulations can be computationally expensive, which is a problem if simulations must be performed many times (e.g., to add error bounds). We show how a novel machine learning method helps to reduce simulation time. In comparison to other approaches, which typically only look at the output of a simulation, the method considers physical laws in the simulation itself. The method provides reliable results faster than standard.
Theresa Boas, Heye Reemt Bogena, Dongryeol Ryu, Harry Vereecken, Andrew Western, and Harrie-Jan Hendricks Franssen
Hydrol. Earth Syst. Sci., 27, 3143–3167, https://doi.org/10.5194/hess-27-3143-2023, https://doi.org/10.5194/hess-27-3143-2023, 2023
Short summary
Short summary
In our study, we tested the utility and skill of a state-of-the-art forecasting product for the prediction of regional crop productivity using a land surface model. Our results illustrate the potential value and skill of combining seasonal forecasts with modelling applications to generate variables of interest for stakeholders, such as annual crop yield for specific cash crops and regions. In addition, this study provides useful insights for future technical model evaluations and improvements.
Cosimo Brogi, Heye Reemt Bogena, Markus Köhli, Johan Alexander Huisman, Harrie-Jan Hendricks Franssen, and Olga Dombrowski
Geosci. Instrum. Method. Data Syst., 11, 451–469, https://doi.org/10.5194/gi-11-451-2022, https://doi.org/10.5194/gi-11-451-2022, 2022
Short summary
Short summary
Accurate monitoring of water in soil can improve irrigation efficiency, which is important considering climate change and the growing world population. Cosmic-ray neutrons sensors (CRNSs) are a promising tool in irrigation monitoring due to a larger sensed area and to lower maintenance than other ground-based sensors. Here, we analyse the feasibility of irrigation monitoring with CRNSs and the impact of the irrigated field dimensions, of the variations of water in soil, and of instrument design.
Olga Dombrowski, Cosimo Brogi, Harrie-Jan Hendricks Franssen, Damiano Zanotelli, and Heye Bogena
Geosci. Model Dev., 15, 5167–5193, https://doi.org/10.5194/gmd-15-5167-2022, https://doi.org/10.5194/gmd-15-5167-2022, 2022
Short summary
Short summary
Soil carbon storage and food production of fruit orchards will be influenced by climate change. However, they lack representation in models that study such processes. We developed and tested a new sub-model, CLM5-FruitTree, that describes growth, biomass distribution, and management practices in orchards. The model satisfactorily predicted yield and exchange of carbon, energy, and water in an apple orchard and can be used to study land surface processes in fruit orchards at different scales.
Lukas Strebel, Heye R. Bogena, Harry Vereecken, and Harrie-Jan Hendricks Franssen
Geosci. Model Dev., 15, 395–411, https://doi.org/10.5194/gmd-15-395-2022, https://doi.org/10.5194/gmd-15-395-2022, 2022
Short summary
Short summary
We present the technical coupling between a land surface model (CLM5) and the Parallel Data Assimilation Framework (PDAF). This coupling enables measurement data to update simulated model states and parameters in a statistically optimal way. We demonstrate the viability of the model framework using an application in a forested catchment where the inclusion of soil water measurements significantly improved the simulation quality.
Yafei Huang, Jonas Weis, Harry Vereecken, and Harrie-Jan Hendricks Franssen
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-569, https://doi.org/10.5194/hess-2021-569, 2021
Manuscript not accepted for further review
Short summary
Short summary
Trends in agricultural droughts cannot be easily deduced from measurements. Here trends in agricultural droughts over 31 German and Dutch sites were calculated with model simulations and long-term observed meteorological data as input. We found that agricultural droughts are increasing although precipitation hardly decreases. The increase is driven by increase in evapotranspiration. The year 2018 was for half of the sites the year with the most extreme agricultural drought in the last 55 years.
Mengna Li, Yijian Zeng, Maciek W. Lubczynski, Jean Roy, Lianyu Yu, Hui Qian, Zhenyu Li, Jie Chen, Lei Han, Han Zheng, Tom Veldkamp, Jeroen M. Schoorl, Harrie-Jan Hendricks Franssen, Kai Hou, Qiying Zhang, Panpan Xu, Fan Li, Kai Lu, Yulin Li, and Zhongbo Su
Earth Syst. Sci. Data, 13, 4727–4757, https://doi.org/10.5194/essd-13-4727-2021, https://doi.org/10.5194/essd-13-4727-2021, 2021
Short summary
Short summary
The Tibetan Plateau is the source of most of Asia's major rivers and has been called the Asian Water Tower. Due to its remoteness and the harsh environment, there is a lack of field survey data to investigate its hydrogeology. Borehole core lithology analysis, an altitude survey, soil thickness measurement, hydrogeological surveys, and hydrogeophysical surveys were conducted in the Maqu catchment within the Yellow River source region to improve a full–picture understanding of the water cycle.
Bernd Schalge, Gabriele Baroni, Barbara Haese, Daniel Erdal, Gernot Geppert, Pablo Saavedra, Vincent Haefliger, Harry Vereecken, Sabine Attinger, Harald Kunstmann, Olaf A. Cirpka, Felix Ament, Stefan Kollet, Insa Neuweiler, Harrie-Jan Hendricks Franssen, and Clemens Simmer
Earth Syst. Sci. Data, 13, 4437–4464, https://doi.org/10.5194/essd-13-4437-2021, https://doi.org/10.5194/essd-13-4437-2021, 2021
Short summary
Short summary
In this study, a 9-year simulation of complete model output of a coupled atmosphere–land-surface–subsurface model on the catchment scale is discussed. We used the Neckar catchment in SW Germany as the basis of this simulation. Since the dataset includes the full model output, it is not only possible to investigate model behavior and interactions between the component models but also use it as a virtual truth for comparison of, for example, data assimilation experiments.
Theresa Boas, Heye Bogena, Thomas Grünwald, Bernard Heinesch, Dongryeol Ryu, Marius Schmidt, Harry Vereecken, Andrew Western, and Harrie-Jan Hendricks Franssen
Geosci. Model Dev., 14, 573–601, https://doi.org/10.5194/gmd-14-573-2021, https://doi.org/10.5194/gmd-14-573-2021, 2021
Short summary
Short summary
In this study we were able to significantly improve CLM5 model performance for European cropland sites by adding a winter wheat representation, specific plant parameterizations for important cash crops, and a cover-cropping and crop rotation subroutine to its crop module. Our modifications should be applied in future studies of CLM5 to improve regional yield predictions and to better understand large-scale impacts of agricultural management on carbon, water, and energy fluxes.
Cited articles
Aanonsen, S., Nævdal, G., Oliver, D., Reynolds, A., and Vallès, B.: The Ensemble Kalman Filter in Reservoir Engineering – a Review, SPE J., 14, 393–412, 2009. a
Altekar, G., Dwarkadas, S., Huelsenbeck, J. P., and Ronquist, F.: Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference, Bioinformatics, 20, 407–415, 2004. a
Bear, J.: Dynamics of fluids in porous media, American Elsevier Pub. Co., New York, 764 pp., ISBN 9780444001146, 1972. a
Berg, S. J. and Illman, W. A.: Comparison of hydraulic tomography with traditional methods at a highly heterogeneous site, Groundwater 53, 71–89, https://doi.org/10.1111/gwat.12159, 2015.
Bertino, L., Evensen, G., and Wackernagel, H.: Sequential data assimilation techniques in oceanography, Int. Stat. Rev., 71, 223–241, 2003. a
Brooks, S. P. and Gelman, A.: General methods for monitoring convergence of iterative simulations, J. Comput. Graph. Stat., 7, 434–455, 1998. a
Cary, P. W. and Chapman, C. H.: Automatic 1-D waveform inversion of marine seismic refraction data, Geophys. J.+, 93, 527–546, 1988. a
Chen, Y. and Zhang, D.: Data assimilation for transient flow in geologic formations via ensemble Kalman filter, Adv. Water Resour., 29, 1107–1122, 2006. a
ChooseALicense: Choose an open source license, https://choosealicense.com/ (last access: 9 December 2023), 2023. a
Congdon, P.: Applied Bayesian Modelling, John Wiley & Sons, Ltd., Chichester, ISBN 1119951518, 2003. a
Cotter, S. L., Roberts, G. O., Stuart, A. M., and White, D.: MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster, Stat. Sci., 28, 424–446, 2013a. a
de Marsily, G.: De l'identification des systèmes hydrogéologiques, PhD thesis, https://documentation-beauvais.unilasalle.fr/index.php?lvl=notice_display&id=10179 (last access: 9 July 2023), 1978. a
Deutsch, C. and Journel, A.: GSLIB: Geostatistical software library and user's guide, New York, 369 pp., ISBN 0195100158, 1998. a
Duijndam, A. J. W.: Bayesian estimation in seismic inversion. Part I: Principles, Geophys. Prospect., 36, 878–898, 1988. a
Earl, D. J. and Deem, M. W.: Parallel tempering: Theory, applications, and new perspectives, Phys. Chem. Chem. Phys., 7, 3910–3916, 2005. a
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 143–10, 1994. a
Gelman, A. and Rubin, D. B.: Inference from iterative simulation using multiple sequences, Stat. Sci., 7, 457–472, 1992. a
Gelman, A., Roberts, G. O., and Gilks, W. R.: Efficient Metropolis jumping rules, Bayesian Statistics, 5, 599–607, 1996. a
Gelman, A., Gilks, W. R., and Roberts, G. O.: Weak convergence and optimal scaling of random walk Metropolis algorithms, Ann. Appl. Probab., 7, 110–120, 1997. a
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B.: Bayesian data analysis, CRC Press, https://doi.org/10.1002/2016WR019111, 2013. a
Gharamti, M., Ait-El-Fquih, B., and Hoteit, I.: An iterative ensemble Kalman filter with one-step-ahead smoothing for state-parameters estimation of contaminant transport models, J. Hydrol., 527, 442–457, 2015. a
Gómez-Hernández, J. J., Sahuquillo, A., and Capilla, J. E.: Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data – 1. Theory, J. Hydrol., 203, 167–174, 1997. a
Gómez-Hernández, J. J., Hendricks Franssen, H. J., and Cassiraga, E. F.: Stochastic analysis of flow response in a three-dimensional fractured rock mass block, Int. J. Rock Mech. Min., 38, 31–44, 2001. a
Grandis, H., Menvielle, M., and Roussignol, M.: Bayesian inversion with Markov chains – I. The magnetotelluric one-dimensional case, Geophys. J. Int., 138, 757–768, 1999. a
Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, Bernoulli, 7, 223–242, 2001. a
Hastings, W. K.: Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97–109, 1970. a
Hendricks Franssen, H.-J. and Kinzelbach, W.: Real-time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem, Water Resour. Res., 44, W09408, https://doi.org/10.1029/2007WR006505, 2008. a
Hendricks Franssen, H.-J., Gómez-Hernández, J. J., Capilla, J. E., and Sahuquillo, A.: Joint simulation of transmissivity and storativity fields conditional to steady-state and transient hydraulic head data, Adv. Water Resour., 23, 1–13, 1999. a
Hendricks Franssen, H.-J., Gómez-Hernández, J., and Sahuquillo, A.: Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data, J. Hydrol., 281, 281–295, 2003. a
Houtekamer, P. L., He, B., and Mitchell, H. L.: Parallel Implementation of an Ensemble Kalman Filter, Mon. Weather Rev., 142, 1163–1182, https://doi.org/10.1175/MWR-D-13-00011.1, 2014. a
Kalman, R.: A new approach to linear filtering and prediction problems, J. Basic Eng.-T. ASME, 82, 35–45, 1960. a
Keating, E. H., Doherty, J., Vrugt, J. A., and Kang, Q.: Optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality, Water Resour. Res., 46, W10517, https://doi.org/10.1029/2009WR008584, 2010. a
Keidser, A. and Rosbjerg, D.: A comparison of four inverse approaches to groundwater flow and transport parameter identification, Water Resour. Res., 27, 2219–2232, 1991. a
Keller, J., Hendricks Franssen, H.-J., and Nowak, W.: Investigating the pilot point ensemble Kalman filter for geostatistical inversion and data assimilation, Adv. Water Resour., 155, 104010, https://doi.org/10.1016/j.advwatres.2021.104010, 2021. a, b
Kuiper, L. K.: A comparison of several methods for the solution of the inverse problem in two-dimensional steady state groundwater flow modeling, Water Resour. Res., 22, 705–714, 1986. a
Kurtz, W., He, G., Kollet, S. J., Maxwell, R. M., Vereecken, H., and Hendricks Franssen, H.-J.: TerrSysMP–PDAF (version 1.0): a modular high-performance data assimilation framework for an integrated land surface–subsurface model, Geosci. Model Dev., 9, 1341–1360, https://doi.org/10.5194/gmd-9-1341-2016, 2016. a
Laloy, E., Rogiers, B., Vrugt, J. A., Mallants, D., and Jacques, D.: Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov chain Monte Carlo simulation and polynomial chaos expansion, Water Resour. Res., 49, 2664–2682, 2013. a
Laloy, E., Linde, N., Jacques, D., and Mariethoz, G.: Merging parallel tempering with sequential geostatistical resampling for improved posterior exploration of high-dimensional subsurface categorical fields, Adv. Water Resour., 90, 57–69, 2016. a
Lamprecht, A.-L., Garcia, L., Kuzak, M., Martinez, C., Arcila, R., Martin Del Pico, E., Dominguez Del Angel, V., Van De Sandt, S., Ison, J., and Martinez, P. A.: Towards FAIR principles for research software, Data Science, 3, 37–59, 2020. a
Li, L., Srinivasan, S., Zhou, H., and Gómez-Hernández, J. J.: Two-point or multiple-point statistics? A comparison between the ensemble Kalman filtering and the ensemble pattern matching inverse methods, Adv. Water Resour., 86, 297–310, 2015. a
Liu, B., Gharamti, M., and Hoteit, I.: Assessing clustering strategies for Gaussian mixture filtering a subsurface contaminant model, J. Hydrol., 535, 1–21, 2016. a
Martinez, P. A., Erdmann, C., Simons, N., Otsuji, R., Labou, S., Johnson, R., Castelao, G., Boas, B. V., Lamprecht, A.-L., Ortiz, C. M., Garcia, L., Kuzak, M., Stokes, L., Honeyman, T., Wise, S., Quan, J., Peterson, S., Neeser, A., Karvovskaya, L., Lange, O., Witkowska, I., Flores, J., Bradley, F., Hettne, K., Verhaar, P., Companjen, B., Sesink, L., Schoots, F., Schultes, E., Kaliyaperumal, R., Tóth-Czifra, E., de Miranda Azevedo, R., Muurling, S., Brown, J., Chan, J., Quigley, N., Federer, L., Joubert, D., Dillman, A., Wilkins, K., Chandramouliswaran, I., Navale, V., Wright, S., Giorgio, S. D., Fasemore, M., Förstner, K., Sauerwein, T., Seidlmayer, E., Zeitlin, I., Bacon, S., Hannan, K., Ferrers, R., Russell, K., Whitmore, D., Dennis, T., Bangert, D., Peñuela, A. M., Daga, E., Ryder, G., Narayanan, A., Kuchma, I., Patron, J. M., Mehnert, A., Liffers, M., Siebes, R., Coen, G., Gregory, K., Scharnhorst, A., Cruz, M., Genova, F., Kenworthy, M., Meyers, N., Rol, E., Santander-Vela, J., Yeomans, J., Papadopoulou, E., Lazzeri, E., Mouchliadis, L., Lenaki, K., Zoupanos, S., Hristozov, D., Stoycheva, S., Leenarts, E., Grootveld, M., Huigen, F., and Fankhauser, E.: Top 10 FAIR Data & Software Things, Zenodo, https://doi.org/10.5281/zenodo.3409968, 2019. a
McDonald, M. G. and Harbaugh, A. W.: A modular three-dimensional finite-difference ground-water flow model, vol. 6, US Geological Survey Reston, VA, https://doi.org/10.3133/ofr83875, 1988. a
McElhoe, B. A.: An Assessment of the Navigation and Course Corrections for a Manned Flyby of Mars or Venus, in: IEEE Transactions on Aerospace and Electronic Systems, Supplement, vol. AES-2, IEEE, 613–623, ISBN 15579603, https://doi.org/10.1109/TAES.1966.4501892, 1966. a
Nowak, W.: Best unbiased ensemble linearization and the quasi-linear Kalman ensemble generator, Water Resour. Res., 45, W04431, https://doi.org/10.1029/2008WR007328, 2009. a, b
Nowak, W. and Cirpka, O. A.: Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads and tracer data, Water Resour. Res., 42, W08416, https://doi.org/10.1029/2005WR004832, 2006. a
Predescu, C., Predescu, M., and Ciobanu, C. V.: On the efficiency of exchange in parallel tempering Monte Carlo simulations, J. Phys. Chem. B, 109, 4189–4196, 2005. a
RamaRao, B., LaVenue, A., De Marsily, G., and Marietta, M.: Pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields: 1. Theory and computational experiments, Water Resour. Res., 31, 475–493, 1995. a
Roberts, G. O. and Rosenthal, J. S.: Optimal scaling for various Metropolis-Hastings algorithms, Statistical science, 16, 351–367, 2001. a
Schöniger, A., Nowak, W., and Hendricks Franssen, H.-J.: Parameter estimation by ensemble Kalman filters with transformed data: Approach and application to hydraulic tomography, Water Resour. Res., 48, W04502, https://doi.org/10.1029/2011WR010462, 2012. a
Schott, J.-J., Roussignol, M., Menvielle, M., and Nomenjahanary, F. R.: Bayesian inversion with Markov chains – II. The one-dimensional DC multilayer case, Geophys. J. Int., 138, 769–783, 1999. a
Schoups, G. and Vrugt, J. A.: A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors, Water Resour. Res., 46, W10531, https://doi.org/10.1029/2009WR008933, 2010. a
Schwede, R. L. and Cirpka, O. A.: Use of steady-state concentration measurements in geostatistical inversion, Adv. Water Resour., 32, 607–619, 2009. a
Smith, T. J. and Marshall, L. A.: Bayesian methods in hydrologic modeling: A study of recent advancements in Markov chain Monte Carlo techniques, Water Resour. Res., 44, W00B05, https://doi.org/10.1029/2007WR006705, 2008. a
Sun, A., Morris, A., and Mohanty, S.: Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques, Water Resour. Res., 45, W07424, https://doi.org/10.1029/2008WR007443, 2009. a
Swendsen, R. H. and Wang, J.-S.: Replica Monte Carlo simulation of spin-glasses, Phys. Rev. Lett., 57, 2607, https://doi.org/10.1103/PhysRevLett.57.2607, 1986. a
ter Braak, C. J. F.: A Markov chain Monte Carlo version of the genetic algorithm differential evolution: Easy Bayesian computing for real parameter spaces, Stat. Comput., 16, 239–249, 2006. a
Tierney, L.: Markov Chains for Exploring Posterior Distributions, Ann. Stat., 22, 1701–1728, 1994. a
Tierney, L. and Mira, A.: Some adaptive Monte Carlo methods for Bayesian inference, Stat. Med., 18, 2507–2515, 1999. a
Van Leeuwen, P. J. and Evensen, G.: Data assimilation and inverse methods in terms of a probabilistic formulation, Mon. Weather Rev., 124, 2898–2913, 1996. a
Wilkinson, M. D., Dumontier, M., Aalbersberg, I. J., Appleton, G., Axton, M., Baak, A., Blomberg, N., Boiten, J.-W., da Silva Santos, L. B., and Bourne, P. E. E. M.: The FAIR Guiding Principles for scientific data management and stewardship, Scientific Data, 3, 1–9, https://www.go-fair.org/fair-principles/ (last access: 12 October 2023), 2016. a
Xiao, S., Xu, T., Reuschen, S., Nowak, W., and Hendricks Franssen, H.-J.: Bayesian Inversion of Multi-Gaussian Log-Conductivity Fields With Uncertain Hyperparameters: An Extension of Preconditioned Crank-Nicolson Markov Chain Monte Carlo With Parallel Tempering, Water Resour. Res., 57, e2021WR030313, https://doi.org/10.1029/2021WR030313, 2021. a
Xu, T.: hydrological-inversion-benchmarking, DaRUS [code], https://doi.org/10.5281/zenodo.14377882, 2023a. a
Xu, T. and Gómez-Hernández, J. J.: Inverse sequential simulation: A new approach for the characterization of hydraulic conductivities demonstrated on a non-Gaussian field, Water Resour. Res., 51, 2227–2242, 2015. a
Xu, T. and Gómez-Hernández, J. J.: Simultaneous identification of a contaminant source and hydraulic conductivity via the restart normal-score ensemble Kalman filter, Adv. Water Resour., 112, 106–123, 2018. a
Xu, T., Gómez-Hernández, J. J., Li, L., and Zhou, H.: Parallelized ensemble Kalman filter for hydraulic conductivity characterization, Comput. Geosci., 52, 42–49, 2013a. a
Xu, T., Gómez-Hernández, J. J., Zhou, H., and Li, L.: The power of transient piezometric head data in inverse modeling: an application of the localized normal-score EnKF with covariance inflation in a heterogenous bimodal hydraulic conductivity field, Adv. Water Resour., 54, 100–118, 2013b. a
Xu, T., Reuschen, S., Nowak, W., and Hendricks Franssen, H.-J.: Preconditioned Crank-Nicolson Markov Chain Monte Carlo Coupled With Parallel Tempering: An Efficient Method for Bayesian Inversion of Multi-Gaussian Log-Hydraulic Conductivity Fields, Water Resour. Res., 56, e2020WR027110, https://doi.org/10.1029/2020WR027110, 2020. a, b, c, d, e, f, g, h, i, j
Xu, T., Gómez-Hernández, J. J., Chen, Z., and Lu, C.: A comparison between ES-MDA and restart EnKF for the purpose of the simultaneous identification of a contaminant source and hydraulic conductivity, J. Hydrol., 595, 125681, https://doi.org/10.1016/j.jhydrol.2020.125681, 2021. a
Zimmerman, D. A., de Marsily, G., Gotway, C. A., Marietta, M. G., Axness, C. L., Beauheim, R. L., Bras, R. L., Carrera, J., Dagan, G., Davies, P. B., Gallegos, D. P., Galli, A., Gomez-Hernandez, J., Grindrod, P., Gutjahr, A. L., Kitanidis, P. K., Lavenue, A. M., McLaughlin, D., Neuman, S. P., RamaRao, B. S., Ravenne, C., and Rubin, Y.: A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow, Water Resour. Res., 34, 1373–1413, 1998. a, b, c
Short summary
We provide a set of benchmarking scenarios for geostatistical inversion, and we encourage the scientific community to use these to compare their newly developed methods. To facilitate transparent, appropriate, and uncertainty-aware comparison of novel methods, we provide some accurate reference solutions, a high-end reference algorithm, and a diverse set of benchmarking metrics, all of which are publicly available. With this, we seek to foster more targeted and transparent progress in the field.
We provide a set of benchmarking scenarios for geostatistical inversion, and we encourage the...
