Uncertainty Characterization Of A Conceptual Rainfall-Runoff Model By Using Grey Numbers

A procedure for characterizing global uncertainty of a rainfall-runoff simulation model based on using grey numbers is presented. By using the grey numbers technique the uncertainty is characterized by an interval; once the parameters of the rainfall-runoff model have been properly defined as grey numbers, by using the grey mathematics and functions it is possible to obtain simulated discharges in the form of grey numbers whose envelope defines a band which represents the vagueness/uncertainty associated with the simulated variable. The grey numbers representing the model parameters are estimated in such a way that the band obtained from the envelope of simulated grey discharges includes an assigned percentage of observed discharge values and is at the same time as narrow as possible. The approach is applied to a real case study highlighting that a rigorous application of the procedure for direct simulation through the rainfall-runoff model with grey parameters involves long computational times. However, these times can be significantly reduced using a simplified computing procedure with minimal approximations in the quantification of the grey numbers representing the simulated discharges. Relying on this simplified procedure, the conceptual rainfall-runoff grey model is thus calibrated and the uncertainty bands obtained both downstream of the calibration process and downstream of the validation process are compared with those obtained by using a well-established approach, like the GLUE approach, for characterizing uncertainty. The results of the comparison show that the proposed approach may represent a valid tool for characterizing the global uncertainty associable with the output of a rainfall-runoff simulation model.