## 3 System Development: Methodologies and Analysis
### Peak Flow Estimation  
Forecasts of peak flows estimated using the relationships described in Sections 3.1 and 3.2 for the Alaoa East gauged site were used to provide short-term warnings of potential high flows at this location; based on observed/nowcast rainfall and stage-flow as well as forecast rainfall sourced from the WRF model (see Figure 2). This site is particularly important due to the absence of reliable gauged data at the Lelata and Alaoa West sites. A unit hydrograph approach was used to predict the flood hydrograph at this site using the procedure adapted from [34]. This approach was used because of the lack of detailed soil or vegetations maps at the site that could be used to inform a more physically based model. Also, as the model was to be hosted by a web-based service, it was more convenient to use an empirical-based model that could be hard-coded into the system. The key steps involved in developing the model included:  
* Identifying observed flow data for the given catchment. These data should be available in the required temporal resolution (duration) of the unit hydrograph (e.g., 10-min, 1 h or 3 h);
* Identifying an appropriate flow event (i.e., where river flow starts and ends at a common baseflow value and exhibits a standard hydrograph shape);
* Plotting the direct runoff hydrograph (i.e., observed flow/baseflow) and then calculate the area under the hydrograph curve to determine the volume of runoff for the event (trapezoidal method);
* Calculating the rainfall excess (mm) by dividing the volume of runoff by the catchment area (m\({}^{2}\)); and
* Calculating each temporal ordinate of the unit hydrograph by dividing each observed discharge ordinates (t1, t2, t3,..., tx) by the excess rainfall figure described above. To use the unit hydrograph to predict the direct runoff resulting from each 1 mm of rainfall, the following steps were used:  
* Subtract the estimated 'rainfall loss' from the rainfall timeseries to get 'effective rainfall';
* Multiply each rainfall value by the unit hydrograph to obtain multiple direct runoff hydrographs (one for each rainfall increment, and each lagged by a successive time increment); and \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Return Period Event**} & \multirow{2}{*}{**Source**} \\ \cline{3-6}  & & **5-Year** & **20-Year** & **100-Year** & **1000-Year** & \\ \hline Rainfall & Total (mm) & 93.5 & 127.0 & 133.7 & 337.3 & [33] \\  & Duration & 45.0 & 60.0 & 45.0 & 45.0 & [22] \\  & & & & & & [32], estimated from 30 and 60 min for the 45 min critical duration & \\  & Intensity & 133.2 & 127.0 & 190.5 & 240.4 & \\  & (mm/h) & & & & & \\  & & & & & & events \\ \cline{2-6} Flow & Lelata (m\({}^{3}\)/s) & Bridge & 550.0 & 690.0 & 862.0 & 1137.0 & [22] \\  & & & & & & & Scaled by area from the \\  & Alaoa East & 292.0 & 366.0 & 458.0 & 604.0 &
\begin{tabular}{c} Lelata Bridge \\ model in [22] \\ \end{tabular} \\  & & & & & & Scaled by area from the \\  & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\ \end{tabular}
\end{table} 
Table 5: Predicted critical rainfall characteristics for 5-, 20-, 100- and 1000-year return period and associated predicted flows at Lelata Bridge and re-scaled critical flows for Alaoa East and Alaoa West using catchment areas. Calculate the sum of all the direct runoff hydrographs and add the baseflow component of observed data to obtain the flow timeseries. Implementation of the unit hydrograph method in the FDSS allowed the starting condition (baseflow) to be determined from observed conditions. In addition, the rainfall loss factor was made dependent on antecedent rainfall conditions, thus acting as a surrogate for the extent of soil saturation at the start of each storm event. Flow event data, which captured the extreme flood in 2012, were used to calculate the 10-min unit hydrograph at Alaoa East, as both the rainfall and flow data were available in 10-min increments during this period.