Parameter sensitivity and uncertainty analysis in simplified conceptual urban drainage models

Stormwater models are powerful tools to aid the planning, design and performance of different stormwater management strategies. Although these models provide a great platform for decision making, they all have an intrinsic level of uncertainty. Little is understood about the sources and magnitude of this uncertainty, which could be due to the errors in measured data (input and calibration data) and/or due to the model itself. To better understand these sources and their impacts on the model predictions, robust model calibration and sensitivity analysis should be performed. The methodologies used for such an exercise should not only be able to provide an assessment of the uncertainties in the model’s parameter values and an evaluation of the confidence level of the model’s predictions, but also be able to identify and propagate the different sources of uncertainties. The main aim of this research project is to assess uncertainties in conceptual urban stormwater flow and pollution generation models, with different levels of complexity, by evaluating the impact of different sources of uncertainties on the model predictions and parameter sensitivity. The research focuses on three main steps: (i) identifying suitable global sensitivity analysis method(s) to perform parameter calibration, model sensitivity and uncertainty analysis in stormwater models; (ii) exploring parameter calibration, model sensitivity and the resulting predictive uncertainties in models with different level of complexities; and, (iii) investigating the impact of measured input and calibration data uncertainty on the performance, sensitivity and predictive uncertainty of stormwater models. Four methods were applied for calibration, sensitivity and uncertainty analysis of a simple stormwater (quantity and quality) model: one is a formal Bayesian approach, and three are methods based on Monte Carlo simulations coupled with different sampling and acceptance criteria. While the application of the four methods generated similar posterior parameter distributions and predictive uncertainty, results indicated that the selection of the most appropriate method is a trade-off between the need for a strong theory-based description of uncertainty (but limited by the requirements on prior knowledge), simplicity (but limited by the subjectivity) and computational efficiency (also affected by subjectivity). The results also suggested that modellers should select the method which is most suitable for the system they are modelling, their skill/knowledge level, the available information, and the purpose of their study. Further analysis of the application of the Bayesian approach verified the potential of the method to assess urban drainage models (with different level of complexities) in urban catchments of different sizes and land-use types. The tested Bayesian approach was selected to be used in the remaining activities of this research. The likelihood function in the applied Bayesian approach assumes that the model errors (residuals) are normally distributed. This study demonstrated that this assumption is often not met in stormwater modelling (i.e. model residuals are not normally distributed), and therefore, the data was transformed (Box-Cox) to ensure the normality of the model residuals. The main finding was that the parameter sensitivity varied significantly between the scenarios in which the normality assumption of the residuals was verified or not. The main reason for this being the fact that the data transformation method to meet the assumption altered the intrinsic content of the measured data, which then influenced the emphasis on various parts of the hydrograph. The Bayesian approach was used to assess two conceptual catchment rainfall runoff models (MUSIC, which simulates runoff from both impervious and pervious areas as a series of reservoirs; and, KAREN that simulates runoff from impervious surfaces using the time-area method) and few simple stormwater quality models (empirical regressions and build-up/wash-off based models). Results from parameter calibration and sensitivity analysis of the rainfall runoff models demonstrated that the effective impervious fraction is the main parameter governing the prediction of runoff in urbanised catchments. Other key parameters are those related to the time of concentration. Indeed, the analysis indicated that the pervious area parameters play a secondary role when modelling highly urbanised catchments, which implies that the tested models could be simplified. The uncertainty analysis showed that the total predictive uncertainty bands (i.e. the total uncertainty derived from the specific modelling application) was considerably larger than the uncertainty bands contributed from parameter uncertainty alone, indicating that there are other prominent sources of uncertainty for these models. The water quality models were shown to be ‘ill-posed’ and unable to reproduce the pollutant processes in the catchment. The impact of both input and calibration data errors on the parameter sensitivity and predictive uncertainty was evaluated by means of propagating these errors through the selected urban stormwater model (rainfall runoff model KAREN coupled with a build-up/wash-off water quality model). It was found that random errors in measured data had minor impact on the model performance and sensitivity. Systematic errors in input and calibration data impacted the parameter distributions (e.g. changed their shapes and location of peaks). In most of the systematic error scenarios (especially those where uncertainty in input and calibration data was represented using ‘best-case’ assumptions), the errors in measured data were fully compensated by the parameters. For example, when rainfall was systematically under or overestimated, the effective impervious area parameter varied systematically to compensate for the changes in the input data. Parameters were unable to compensate in some of the scenarios where the systematic uncertainty in the input and calibration data were represented using extreme worst-case scenarios. As such, in these few worst case scenarios, the model’s performance was reduced considerably. Systematic errors in the calibration data error did not significantly impact the parameter probability distributions of the water quality model, mainly because the model cannot even reproduce TSS concentrations when the ‘true’ data is used. This finding suggested that the current main limitation in water quality modelling is related to poor model structure, and not to errors in measured data. This research provides a comprehensive study of the propagation of different sources of uncertainties through stormwater models. It identifies how the different uncertainty sources impact on parameter sensitivity and the predictive uncertainty. In addition, the analysis of model parameters and their interactions provides practical recommendations for refining and further developing stormwater rainfall runoff and pollution generation models.