A conceptual grey rainfall-runoff model for simulation with uncertainty

This paper presents an approach based on grey numbers to represent the total uncertainty of a conceptual rainfall-runoff model. Using this approach, once the grey numbers representing the model parameters have been properly defined, it is possible to obtain simulated discharges in the form of intervals (grey numbers) whose envelope defines a band which represents the total model uncertainty. The application to a real case showed that the construction of this band, according to a rigorous application of grey number theory, involves long computational times. However, these times can be significantly reduced using a simplified computing procedure with minimal approximations in the quantification of the simulated grey discharge. Relying on this simplified procedure, the conceptual rainfall-runoff grey model was then calibrated in order to respect a predefined level of model uncertainty, i.e. the band obtained from the envelope of simulated grey discharges had to include an assigned percentage of observed discharges and was at the same time as narrow as possible. Finally, the uncertainty bands were compared with the ones obtained using a well-established approach for characterising uncertainty, the Generalised Likelihood Uncertainty Estimation (GLUE) method. The results of the comparison showed that the proposed approach may represent a valid tool for characterising the total uncertainty of a rainfall-runoff model.