# Ensemble Radar-Based Rainfall Forecasts for Urban Hydrological Applications
## 3 Results
### Forecasting Sewer Flows  
The sewer flow simulation results obtained by using radar rainfall, rain gauge measurements and rainfall forecasts were compared against the sewer-measured flows. Because the forecasted peak flow sometimes appeared a few minutes later (or earlier) compared to the flow observations, it was decided to compare the peak flows within a particular time window (e.g., 30 min or 1 h). The results are presented in Figures 11-13.  
RMSE calculations were carried out to assess the performance of the ensembles. Due to the time lag present between the measured peak flow and the ensemble-simulated peak flows, a cross-correlation correction was performed between the measured flows and ensemble flows. As the lags are not consistent, the cross-correlation was adjusted for each case. RMSE for each ensemble member was calculated for measured flows higher than 0.1 m\({}^{3}\)/s. (Figure 14). Table 2 presents the mean of the RMSE for both STEPS and Radar ensembles. Given the fact that there is a significant loss of forecast efficiency after 1 h lead-time, the RMSE is only shown for this period. In most events, the time lags between measured flow and forecasts are less than 15 min.  
The forecasted flow in Ilkley only produced reliable forecasts with lead-times up to 30 min, although in some cases the predictability maintained up to 1 h ahead depending upon the nature of the rainfall event.  
Figure 11: Flows (**a**) and peak flows (**b**) for events on 07 July 2008 starting at 15:00. Q\({}_{\text{F}}\) Ens Radar, Q\({}_{\text{F}}\) Ens STEPS, Q\({}_{\text{F}}\) Det, Q\({}_{\text{m}}\), Q\({}_{\text{G}}\) and Q\({}_{\text{R}}\) are, respectively, forecasted radar ensemble flows, forecasted STEPS ensemble flows, forecasted deterministic flow, measured flow, estimated gauge flow and estimated radar flow.  
Figure 12: Flows (**a**) and peak flows (**b**) for events on 09 November 2008 starting at 14:00. Q\({}_{\text{F}}\) Ens Radar, Q\({}_{\text{F}}\) Ens STEPS, Q\({}_{\text{F}}\) Det, Q\({}_{\text{m}}\), Q\({}_{\text{G}}\) and Q\({}_{\text{R}}\) are, respectively, forecasted radar ensemble flows, forecasted STEPS ensemble flows, forecasted deterministic flow, measured flow, estimated gauge flow and estimated radar flow.  
Figure 14: RMSE for radar and STEPS ensembles and 0–1 h after the start of the forecast.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**RMSE Mean (m3/s)**} \\ \hline
**Event Date** & **Starting Time** & **Radar Ensembles** & **STEPS Ensembles** \\ \hline
7 July 2008 & 15:00 & 0.170 & 0.200 \\
1 August 2008 & 02:30 & 0.405 & 0.430 \\
1 August 2008 & 03:00 & 0.140 & 0.166 \\
9 November 2008 & 14:00 & 0.287 & 0.169 \\ \hline \hline \end{tabular}
\end{table}
Table 2: RMSE mean for radar and STEPS ensembles for 0–1 h after the start of the forecast.  
Figure 13: Flows (**a**) and peak flows (**b**) peak flows for events on 1 August 2008 starting at 02:30 and flows (**c**) and peak flows (**d**) for events on 1 August 2008 starting at 03:00. \(Q_{F}\) Ens Radar, \(Q_{F}\) Ens STEPS, \(Q_{F}\) Det, \(Q_{m}\), \(Q_{G}\) and \(Q_{R}\) are, respectively, forecasted STEPS ensemble flows, forecasted deterministic flow, measured flow, estimated gauge flow and estimated radar flow.