Model uncertainty – parameter uncertainty versus conceptual models A.L. Højberg and J.C. Refsgaard Geological Survey of Denmark and Greenland (GEUS), Øster Voldgade 10, DK-1350 Copenhagen (E-mail: alh@geus.dk, jcr@geus.dk) Abstract Uncertainties in model structures have been recognised often to be the main source of uncertainty in predictive model simulations. Despite this knowledge, uncertainty studies are traditionally limited to a single deterministic model and the uncertainty addressed by a parameter uncertainty study. The extent to which a parameter uncertainty study may encompass model structure errors in a groundwater model is studied in a case study. Three groundwater models were constructed on the basis of three different hydrogeological interpretations. Each of the models was calibrated inversely against groundwater heads and streamflows. A parameter uncertainty analysis was carried out for each of the three conceptual models by Monte Carlo simulations. A comparison of the predictive uncertainties for the three conceptual models showed large differences between the uncertainty intervals. Most discrepancies were observed for data types not used in the model calibration. Thus uncertainties in the conceptual models become of increasing importance when predictive simulations consider data types that are extrapolates from the data types used for calibration. Keywords Conceptual uncertainty; groundwater modelling; model structure; Monte Carlo simulation; parameter uncertainty Introduction Uncertainties in groundwater simulations originate from different sources. Assuming the applied numerical code to be error free, the main sources of uncertainty are related to (1) data, for use as input as well as calibration targets, (2) parameter estimation, and (3) model structural error. Methodologies to quantify the uncertainties in model predictions due to input data and model parameter uncertainties have been well developed. These includes Monte Carlo simulations, first-order second moment and the generalized likeli- hood uncertainty estimation methodology (GLUE). For recent applications and discus- sions on the methods see Beven and Binley (1992); James and Oldenburg (1997); Christensen and Cooley (1999); Feyen et al. (2003); Glasgow et al. (2003). Uncertainties due to the model structure have been recognised often to be the most important source of uncertainty (Dubus et al., 2003; Neuman and Wierenga, 2003). The sources of uncertainties in the model structure are manifold, e.g. choice of processes included in the model, the mathematical formulations, boundary conditions, initial con- ditions, and the hydrogeological interpretation. Uncertainties in the model structure have received a growing attention within the last few years and different approaches have been proposed in the literature. The most common approaches are to assess the model structure error from validation tests where the model predictions are compared with independent field data. A limitation of this approach is that the model structure error can only be assessed with respect to the output variables for which field data are available, and often models are used for making extrapolatory predictions. Another approach, advocated by e.g. Neuman and Wierenga (2003), uses multiple alternative model structures (conceptual models) whereby the model structural uncertainties more explicitly can be taken into account in the assessment of predictive uncertainty. The limitation of this approach is Water Science & Technology Vol 52 No 6 pp 177–186 Q IWA Publishing 2005 177 Downloaded from https://iwaponline.com/wst/article-pdf/52/6/177/434131/177.pdf by guest on 02 November 2018