HYDROLOGICAL PROCESSES Hydrol. Process. 25, 2642–2653 (2011) Published online 23 February 2011 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hyp.8006 Comparison of model structural uncertainty using a multi-objective optimisation method Giha Lee, 1 * Yausto Tachikawa 2 and Kaoru Takara 3 1 Research Associate, Construction & Disaster Research Center, Department of Civil Engineering, Chungnam National University, Daejeon 305-764, Korea 2 Associate Professor, Department of Urban and Environmental Engineering, Kyoto University, Kyoto 615-8540, Japan 3 Professor, Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto 611-0011, Japan Abstract: This study aims to propose a method for effectively recognising and evaluating model structural uncertainty. It began with a comparative assessment of various model structures that have differing features regarding the rainfall-runoff mechanism and DEM spatial resolution. The assessment applied a multi-objective optimisation method (MOSCEM-UA) with two objective functions (simple least-squares and the heteroscedastic maximum likelihood estimator), and focused on five historical flood events. The study was based on the assumptions that a structurally sound model assures improved prediction results (either minimized or maximized model performance measure), allows constant model performance with regard to objective functions (a small Pareto solution set), and yields good applicability of a calibrated parameter set to various events (good parameter stability). The results indicated that KWMSS, a distributed model, was superior to SFM, a simple lumped model, when estimating a Pareto solution set and assessing parameter stability for the applied events. In addition, three different spatial resolutions (250 m, 500 m, and 1 km) were compared to assess the structural uncertainty due to changes in the topographical representation in distributed rainfall-runoff modelling. The results indicated that the 250 and 500 m models were Pareto- equivalent, containing similar Pareto fronts, and both produced Pareto results superior to the 1 km model. Both models also yielded parameter stability values that were much more superior to the model based on a 1 km DEM. As the topographic representation became more detailed, the model showed a tendency to have less structural uncertainty in terms of guarantying better performance, better parameter stability, and a smaller Pareto solution set. On the other hand, the output of a spatially detailed model was likely to be insensitive to the variation of model parameters (i.e. equifinality). Copyright  2011 John Wiley & Sons, Ltd. KEY WORDS equifinality; model structural uncertainty; multi-objective optimisation method; parameter stability; Pareto solution set Received 22 September 2008; Accepted 21 August 2009 INTRODUCTION A basic and principal task in hydrological modelling is identifying a suitable model and its corresponding opti- mal parameters under given conditions, such as the mod- elling purpose, catchment characteristics, and available data (Wagener and Gupta, 2005). However, the quan- tifiable and/or unquantifiable uncertainties involved in modelling procedures make model identification diffi- cult. Uncertainty can propagate into model predictions and, in turn, produce unreliable prediction results. Refs- gaard and Knudsen (1996) and Uhlenbrook et al. (1999) demonstrated that different conceptualisations of a catch- ment runoff system can produce equally good numerical outcomes, even if some models are overly simplified or outside a hydrologist’s experience/expertise (i.e. struc- tural uncertainty). Beven and Binely (1992) also showed that despite having differing values, a number of param- eter sets were capable of yielding quite similar model * Correspondence to: Giha Lee, Research Associate, Construction & Disaster Research Center, Department of Civil Engineering, Chungnam National University, Daejeon 305-764, Korea. E-mail: leegiha@gmail.com performance measures from the best-performing param- eter set (i.e. equifinality). A great deal of research has focused on recognising the propagation of various uncertainty components into model predictions (e.g. Beven and Binely, 1992; Jakeman and Hornberger, 1993; Kuczera and Mroczkowksi, 1998; Gupta et al., 1998; Kavetski et al., 2003). In particular, recent research has increasingly focused on model struc- tural uncertainty (Gupta et al., 1998; Yapo et al., 1998; Boyle et al., 2000, 2001; Wagener et al., 2001; Vrugt et al., 2003; Lee et al., 2007). This is a fundamental problem in hydrological modelling because a model is a simplification of reality, so conceptually, it represents only some aspects of the actual hydrological system, no matter how spatiotemporally sophisticated it may be. Although the structural uncertainty of a model has a significant effect on prediction uncertainty, the former is difficult to assess due to problems with quantifica- tion related to model structural error. Gupta et al. (2003) pointed out that a major consequence of model struc- tural inadequacy is the lack of ability to reproduce entire (or global) hydrological behaviour with a single optimal parameter set estimated using traditional single-objective Copyright  2011 John Wiley & Sons, Ltd.