Developments in Informal Multi-Criteria Calibration and Uncertainty Estimation in Hydrological Modelling

Abstract

Hydrologic modelling has benefited from significant developments over the past two decades, which has led to the development of distributed hydrologic models. Parameter adjustment, or model calibration, is extremely important in the application of these hydrologic models. Multi-criteria calibration schemes and several formal and informal predictive uncertainty estimation methodologies are among the approaches to improve the results of model calibration. Moreover, literature indicates a general agreement between formal and informal approaches with respect to the predictive uncertainty estimation in single-criterion calibration cases. This research extends the comparison between these techniques to multi-criteria calibration cases, and furthermore, proposes new ideas to improve informal multi-criteria calibration and uncertainty estimation in hydrological modelling. GLUE is selected as a candidate informal methodology due to its extreme popularity among hydrological modellers, i.e., based on the number of applications in the past two decades. However, it is hypothesized that improvements can be applied to other certain types of informal uncertainty estimation as well.

The first contribution of this research is an in-depth comparison between GLUE and Bayesian inference in the multi-criteria context. Such a comparison is novel because past literature has focused on comparisons for only single criterion calibration studies. Unlike the previous research, the results show that there can be considerable differences in hydrograph prediction intervals generated by traditional GLUE and Bayesian inference in multi-criteria cases. Bayesian inference performs more satisfactorily than GLUE along most of the comparative measures. However, results also reveal that a standard Bayesian formulation (i.e., aggregating all uncertainties into a single additive error term) may not demonstrate perfect reliability in the prediction mode. Furthermore, in cases with a limited computational budget, non-converged MCMC sampling proves to be an appropriate alternative to GLUE since it is reasonably consistent with a fully-converged Bayesian approach, even though the fully-converged MCMC requires a substantially larger number of model evaluations.

Another contribution of this research is to improve the uncertainty bounds of the traditional GLUE approach by the exploration of alternative behavioural solution identification strategies. Multiple behavioural solution identification strategies from the literature are evaluated, new objective strategies are developed, and multi-criteria decision-making concepts are utilized to select the best strategy. The results indicate that the subjectivity involved in behavioural solution identification strategies impacts the uncertainty of model outcome. More importantly, a robust implementation of GLUE proves to require comparing multiple behavioural solution identification strategies and choosing the best one based on the modeller’s priorities. Moreover, it appears that the proposed objective strategies are among the best options in most of the case studies investigated in this research. Thus, it is recommended that these new strategies be considered among the set of behavioural solution identification strategies in future GLUE applications.

Lastly, this research also develops a full optimization-based calibration framework that is capable of utilizing both standard goodness-of-fit measures and many hydrological signatures simultaneously. These signatures can improve the calibration results by constraining the model outcome hydrologically. However, the literature shows that to simultaneously apply a large number of hydrological signatures in model calibration is challenging. Therefore, the proposed research adopts optimization concepts to accommodate many criteria (including 13 hydrologic signature-based objectives and two standard statistical goodness-of-fit measures). In the proposed framework, hydrological consistency is quantified (based on a set of signature-based measures and their desired level of acceptability) and utilized as a criterion in multiple calibration formulations. The results show that these formulations perform better than the traditional approaches to locate hydrologically consistent parameter sets in the search space.

Different hydrologic models, most of which are conceptual rainfall-runoff models, are used throughout the thesis to evaluate the performance of the developed strategies. However, the developments explored in this research are typically simulation-model-independent and can be applied to calibration and uncertainty estimation of any environmental model. However, further testing of these methods is warranted for more computationally intensive simulation models, such as fully distributed hydrologic models.