Probabilistic flood hydrographs using Monte Carlo simulation: potential impact to flood inundation mapping

Flood inundation modelling generally involves two steps. The first involves the use of a hydrologic model, such as RORB, to estimate the design flood hydrograph for a given design storm event. These models require several inputs, such as design rainfalls (i.e. duration, intensity & temporal pattern), losses, baseflow and routing parameters; each of which has an associated degree of uncertainty that can affect the shape and magnitude of the estimated design flood hydrograph. The second involves the use of these design flood hydrographs as inputs into a hydraulic model, to estimate the flood inundation extent. Given the uncertainties in hydrologic modelling and their importance in mapping inundation extents, it is of interest to determine the potential impacts of hydrological uncertainties on flood inundation mapping. This paper, therefore, considers how the uncertainties in design losses can affect the hydraulic analysis. The Orara River catchment in north-east NSW was selected for this study, which covers an area of 135 km. The data during the period of 1970 to 2009 was used, with both streamflow (204025) and a pluviograph station (59026) available throughout this period. For 43 storm events, rainfall spatial patterns are produced using ordinary kriging, with 23 daily rainfall stations, and baseflow was separated using a recursive digital filter. The RORB rainfall-runoff model was adopted, with the non-linearity exponent fixed at 0.8 and the routing parameter fixed at 15. Both the initial and continuing losses were calibrated for each event and then examined to find the best fit probability distribution. From the 27 parametric distributions, it was found that the initial loss (IL) can be approximated by the 2-parameter Gamma distribution and the continuing loss (CL) can be approximated by the 3-parameter Weibull distribution. A Monte Carlo framework was adopted to quantify uncertainties in the losses. Ten thousand randomly generated initial and continuing loss values were run through RORB in order to derive confidence limits for the peak flow, flood volume and time to peak flow characteristics. These derived flood frequency curves (DFFC) are then compared to observed floods and an at-site flood frequency analysis (FFA). The median relative errors of the DFFC when compared to the at-site FFA were found to be 13.5% and 23.1%, for the peak flow and flood volumes, respectively. The flood volumes were found to be more consistent across all probabilities with a range of -3.6% to -26.6%, as compared to the peak flows that ranged from 9% to 39.5%. The confidence band (referring to the 5 and 95 percentiles) were found to be smallest about the time to peak flow, which only varied up to 10%, followed by the peak flows which showed around ±55% variability. The flood volumes saw the widest confidence bands, with a median variation of about ±63%, which increased to a maximum of about ±105%. It has been found that the Monte Carlo framework adopted in this study has the ability to produce more accurate and realistic design flood estimates, however, these improvements have not yet been carried through to the hydraulic model. Flood inundation maps are generally still depicted as a single deterministic flood inundation prediction for a given deterministic design hydrograph. As found in a study by Merwade et al. (2008) when the standard errors in peak flows ranged from -36.1% to 56.5%, this caused a shift in the water surface elevation from -0.4 m to 1 m and the extent of floodplain inundation varied in width from 54.3 m to 90.2 m. With peak flows ranging up to ±55% in this study, potentially causing these types of errors in the inundation extents, it is clear that probability-weighted flood inundation extents need to be modelled rather than a single deterministic prediction.