Inverse groundwater flow modelling

The prediction of groundwater flow, heat transport and solute transport in aquifers is strongly affected by the heterogeneity of hydraulic conductivity and other aquifer properties like for example porosity. The use of time series of state measurements (especially piezometric heads but also solute concentrations) in inverse modelling techniques allows the estimation of the spatially variable fields of the unknown aquifer properties. In the past different inverse modelling methods have been proposed and the 1980´s saw a shift towards stochastic methods, which involved geostatistics. In the 1990´s new methods were proposed that involved the estimation of many equally likely solutions to the groundwater inverse problem, instead of one unique solution. This philosophy became more popular afterwards, but it was especially the Ensemble Kalman Filter, introduced in the groundwater inverse modelling literature in 2006, which was used and further developed in research. Since then, many different variants of the EnKF-algorithm have been proposed and tested.

Harrie-Jan Hendricks-Franssen contributed in the past to the development of inverse modelling methods, like the sequential calibration method, and the extension of this method towards 3D-flow problems, transient flow and solute transport. Later he worked on estimation of spatially distributed parameter fields in combination with the Ensemble Kalman Filter, and handling non-Gaussian distributions of states and parameters with the EnKF.

Currently, in the group there are two main DFG-projects related to groundwater inverse modelling. In a first project, which runs until spring 2018, inverse modelling focuses on the estimation of properties of geothermal reservoirs. In a first study, it is evaluated how robust inverse modelling comparison studies are. It is argued that in the literature often two inverse modelling methods are compared on the basis of limited cases, and we conclude that it is important to perform a large number of synthetic tests. It is needed to have 10, and sometimes even 100 synthetic tests for a sound comparison of methods. Subsequent work in the context of this project focused on the development of a hybrid data assimilation method, which combines advantages of the Ensemble Kalman Filter and the sequential self- calibration method.

Inverse groundwater flow modelling
Figure 1: Comparison of seven different EnKF-variants for inverse estimation of aquifer parameters. In total 1000 synthetic experiments, in each of them using 250 ensemble members, were performed for each data assimilation method. Next, it was compared how often one data assimilation method outperforms another data assimilation method. The figure indicates how often (in %) one method outperforms another method (in black: method on horizontal axis shows better performance; in white: method on vertical axis shows better performance). It can be seen that only exceptionally one method outperforms another method in more than 90% of the synthetic tests.

A new funded DFG-project will focus on the comparison of inverse modelling methods on the basis of a benchmark. This benchmark inverse solution will be calculated with very efficient Markov Chain Monte Carlo methods. This project is together with Prof. Wolfgang Nowak from the University of Stuttgart and various international partners.

Contact persons:
Harrie-Jan Hendricks Franssen
Agrosphere (IBG-3)
Forschungszentrum Jülich GmbH
Leo Brandtstrasse
52425 Jülich
Tel. 02461 / 61-4462

Johannes Keller

Link to project partners:

Relevant publications:

Zovi, F., M. Camporese, H.J. Hendricks Franssen, J.A. Huisman, and P. Salandin, 2017. Identification of high permeability subsurface structures with multiple point geostatistics and normal score ensemble Kalman filter. Journal of Hydrology, 548, 208-224.

Schöniger, A., W. Nowak and H.J. Hendricks Franssen. 2012. Parameter estimation by Ensemble Kalman filters with transformed data: Approach and application to hydraulic tomography. Water Resources Research 48, W04502, doi:10.1029/2011WR010462.

Li, L., H. Zhou, J. Gomez-Hernandez and H.J. Hendricks Franssen. 2012. Jointly mapping hydraulic conductivity and porosity by assimilating concentration data via Ensemble Kalman Filter. Journal of Hydrology, 428-429, 152-168. doi:10.1016/j.hydrol.2012.01.037.

Li, L., H. Zhou, H.J. Hendricks Franssen and J. Gomez-Hernandez. 2012. Groundwater flow inverse modeling in non-multiGaussian media: performance assessment of the normal-score Ensemble Kalman filter. Hydrol. Earth Syst. Sci. 16(2), 573-590.

Zhou, H., L. Li, H.J. Hendricks Franssen and J. Gomez-Hernandez. 2012. Pattern recognition in a bimodal aquifer using the normal-score Ensemble Kalman Filter. Mathematical Geosciences 44, 169-185. doi:10.1007/s11004-011-9372-3.

Li, L., H. Zhou, H.J. Hendricks Franssen and J. Gomez-Hernandez. 2012. Modeling transient groundwater flow by coupling Ensemble Kalman filtering and upscaling. Water Resources Research 48, W01537. doi:10.1029/2010WR010214.

Huber, E., H.J. Hendricks Franssen, H.P. Kaiser and F. Stauffer. 2011. The role of prior model calibration on predictions with Ensemble Kalman Filter. Ground Water 49(6), 845-858, DOI: 10.1111/j.1745-6584.2010.00784.x.

Zhou, H., J. Gomez-Hernandez, H.J. Hendricks Franssen and L. Li. 2011. An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering. Advances in water Resources 34(7), 844-864, doi: 10.1016/j.advwatres.2011.04.014.
Hendricks Franssen, H.J., A. Alcolea, M. Riva, M. Bakr, N. van de Wiel, F. Stauffer and A. Guadagnini. 2009. A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments. Advances in Water Resources. doi:10.1016//j.advwatres.2009.02.011.

Hendricks Franssen, H.J. and W. Kinzelbach. 2009. Ensemble Kalman filtering versus sequential self-calibration for transient inverse modeling of dynamic groundwater flow systems. Journal of Hydrology 365, 261-274, doi:10.1016/j.jhydrol.2008.11.033.

Hendricks Franssen, H.J. and W. Kinzelbach. 2008. Real-time groundwater flow modelling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem. Water Resources Research, doi:10.1029/2007WR006505.

Kerrou, J., P. Renard, H.J. Hendricks Franssen and I. Lunati. 2008. Issues in characterizing connectivity and heterogeneity in non-multi-Gaussian media. Advances in Water Resources 31, 147-159. doi:10.1016/j.advwatres.2007.07.002.

Stauffer, F., H.J. Hendricks Franssen and W. Kinzelbach 2004. Semi-analytical uncertainty estimation of well catchments: conditioning by head and transmissivity data. Water Resources Research 40, W08305, doi: 10.1029/2004WR003320.

Hendricks Franssen, H.J., F. Stauffer and W. Kinzelbach. 2004. Joint estimation of transmissivities and recharges – stochastic characterization of well capture zones. Journal of Hydrology, 294 (1-3), p. 87-102.

Gómez-Hernández, J.J., H.J. Hendricks Franssen and A. Sahuquillo. 2003. Stochastic conditional inverse modelling of subsurface mass transport: a brief review and the self-calibrating method. Stochastic Environmental Research and Risk Assessment 17(5), p. 319-328.

Hendricks Franssen, H.J., J.J. Gómez-Hernández and A. Sahuquillo. 2003. Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data. Journal of Hydrology, 281(4), p. 281-295. Hendricks Franssen, H.J. and J.J. Gómez-Hernández. 2003. Impact of measurement errors in the sequential self-calibrated approach. Advances in Water Resources 26(5), p. 501-511.

Hendricks Franssen, H.J. and J.J. Gómez-Hernández. 2002. 3D Inverse modelling of groundwater flow at a fractured site using a stochastic continuum model with multiple statistical populations. Stochastic Environmental Research and Risk Assessment 16, p. 155-174.

Gómez-Hernández, J.J., H.J. Hendricks Franssen and E.F. Cassiraga. 2001. Stochastic analysis of flow response in a three-dimensional fractured rock mass block. International Journal of Rock Mechanics & Mining Sciences 38, p. 31-44.

Hendricks Franssen, H.J. 2001. Inverse stochastic modelling of groundwater flow and mass transport. Ph.D. dissertation Technical University of Valencia. Department of Hydraulic and Environmental Engineering. ISBN 0-493-16707-2. UMI 3007628.

Hendricks Franssen, H.J., J.J. Gómez-Hernández, A. Sahuquillo and J.E. Capilla. 1999. Joint simulation of transmissivity and storativity fields conditional to hydraulic head data. Advances in Water Resources 23, p. 1-13.

Last Modified: 25.05.2022