## Abstract

Reliability of groundwater flow and transport predictions obtained from numerical models depends on how well the model represents the aquifer system it is simulating. An inevitable part of obtaining a satisfactory representation is the process of model calibration whereby parameters are estimated. There exists two techniques for calibration: trial-and-error where the parameters are updated manually until a satisfactorily match to measurement values is obtained and inverse methods where the parameter estimation procedure is automated. The problem to be solved in the latter case is: Given point measurement, obtain realistic parameter values, which lead to an optimum match between measured and simulated point values. This thesis reviews the current knowledge on inverse groundwater parameter estimation. Focus is on statistical methods, coupling of flow and transport modelling, and field applications to three-dimensional aquifers. The demand for quantification of confidence in estimates and predictions has been increasing rapidly over the last years. This has resulted in posing the inverse groundwater problem in a statistic or stochastic (geostatistical) framework. Calculation of parameter correlation, parameter uncertainty, and prediction uncertainty is now a natural part of inverse modelling. However, despite the nonlinearity of the inverse problem most common the statistics are calculated using first-order analysis. Results with the latter approach have proven successful in many cases but caution is advised. Originally, inverse groundwater methods were only developed for optimization of parameters describing the flow field (mainly hydraulic conductivities) based on measurements of e.g. hydraulic heads. Due to problems with ill-posedness resulting in meaningless solutions new and improved techniques have been proposed to constrain the inverse problem. Among them is coupling of flow and transport modelling whereby it is possible to include the information about the flow system given by available concentration data in the optimization of the flow field. The most valuable way of using measured concentrations is by including them directly in the objective function. This is obtained by adding an additional term. Results from coupling are successful. The obtained flow field is in better agreement with measured values and parameters are more certain (i.e. smaller standard deviations). Initially, inverse methods were developed for one- or two-dimensional problems. Increase in computer capacity has made applications of inverse methods to three-dimensional real aquifers possible. Especially applications of statistical methods have been reported; recently including coupling of flow and transport modelling. Results show that the inverse approaches provide valuable information about the aquifer systems and realistic parameter values are obtained. An increase in applications using statistical inverse methods is expected due to recent commercially available computer codes. The ability of geostatistical methods in three-dimensional field cases is to be studied in the future.

Original language | English |
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Article number | 75 |

Pages (from-to) | 86-103 |

Number of pages | 18 |

Journal | Series Paper - Technical University of Denmark, Institute of Hydrodynamics and Water Resources |

Issue number | 75 |

Publication status | Published - 2000 |

Externally published | Yes |

## Programme Area

- Programme Area 2: Water Resources