Direct and Inverse Problems for PDEs with Random Coefficients - Abstract
Hydrological models are only constructs of a real problem and are realizations of schematic representations that the modelers perceive as reality. Also, it is rarely possible to observe a hydrological variable without errors. Hydrological models, in particular, are known to have large spatial and temporal variability, and only describe a part of reality as they are restricted to a specific region of interest. Moreover, the boundaries of the model values, such as groundwater heads, infiltration, recharge/discharge time series etc., which are not exactly known, have to be imposed on the physical equations that are used to describe the process. These are just a few challenges that the modeler tries to handle in the face of uncertainty. Moreover, the simulations and predictions are based on the model response followed by a risk analysis for high consequences decision making. Strictly speaking, the simulation results are valid only on the model and a meaningful transfer of results to reality require uncertainties on the data to appear as uncertainties on the results. It is mainly the lack of clarity, detail and data that are the cause of both variability and ambiguity in hydrological applications. Hydrological variability together with ambiguity contribute to uncertainty in water resources systems and associated hydrological applications. par The talk aims to address a systematic framework for incorporating water resources uncertainty, particularly hydrological variability, to do meaningful predictive simulations. It also aims to illustrate the possibility of using different methods together, such as the Turning Band method and Distance Kernel Method, to generate stochastic fields and better understand the input/output space of spatial variability. Some further processing may reduce redundancies in the input for reducing the Monte Carlo input sample set and/or help correlating the input and output. A set of selected examples are presented to illustrate the effect of uncertainty on simulations on hydrological models, mainly in a Monte-Carlo framework, using the FEFLOW software, a development of DHI-WASY GmbH.