DECLARATION 2: PUBLICATIONS
5. PERFORMANCE AND SENSITIVITY ANALYSIS OF THE SCS-BASED PEAK
5.3 Methodology
The following methodology was applied in this chapter:
(i) The Flood Hydrograph Extraction Software (EX-HYD) developed by Görgens et al.
(2007), and provided by Gericke (2018) was used to extract complete flood hydrographs from the primary streamflow data of the two catchments selected. The software identifies all significant events above a user defined threshold value. The
default threshold value estimated by the model was used in this study. When applying the default value, the truncation level is set such that on average 5 peak events are selected per year (Denys et al., 2006). The software is designed to estimate the start and end of each event, however, this is often not exact and sometimes single events are broken up into multiple events and thus each event had to be checked manually and adjusted if necessary.
(ii) For Cathedral Peak IV (V1H005), where only a short record of overlapping and consistent streamflow and sub-daily rainfall data were available, i.e. 1974 – 1979 (Table 5.2), the largest event for each year on record was firstly extracted and then the second largest, third largest, and so on, until a reasonable sample of 20 events was obtained. For DeHoek / Ntabamhlope (V1H015), the same procedure was followed, however, the record length was significantly longer, i.e. 1979 – 1993 (Table 5.2), and therefore the majority of the events selected were the annual maximum events and 17 events were finally extracted. It was essential to have both accurate short-duration (e.g.
hourly) rainfall data, and primary streamflow data for each event. For this reason, in many cases events were excluded due to missing, erroneous or inconsistent rainfall or streamflow data. This resulted in the exclusion of the largest events on record for certain years. An additional requirement was that each event had to start and end within the time period from 08:00 to 08:00 the next day, i.e. to be consistent with the daily modelling output from the ACRU model. Consequently, significant time was spent on checking and verifying the data for each event selected. A lack of short-duration rainfall data, particularly consistent and accurate short-duration rainfall data, was a significant challenge to this study. This coupled with time constraints to complete the project resulted in the use of only two case study catchments. These catchments were selected since they were identified to have high quality data, with the short-duration rainfall stations being highly representative of the catchments.
(iii) A Hydrograph Analysis Tool (HAT), developed by Gericke in Microsoft Excel, and implemented by Gericke and Smithers (2017), was used to further analyse and process each of the events extracted using the EX-HYD software. This included: (i) a final check that each event hydrograph fell within the time period 08:00 to 08:00 the next day, i.e. the rise, peak and recession of the hydrograph all occur within this time period, (ii) separation of the event hydrographs into direct surface runoff and baseflow, and (iii) calculation of the time to peak (TP) and corresponding lag time (L). The Nathan
and McMahon (1990) method to separate direct surface runoff and baseflow, as recommended and implemented by Gericke and Smithers (2017), was applied in this study. This was essential in order to determine the actual observed direct surface runoff (stormflow) for each event to use in the ACRU stormflow peak discharge equations.
As recommended and implemented by Gericke and Smithers (2017), the time to peak was calculated from the point on the hydrograph where the streamflow changes from nearly constant or steadily declining values to rapidly increasing values until the point where the peak discharge occurs. For multi-peaked events the total net rise of the hydrograph was used to calculate the time to peak, i.e. only the periods where the hydrograph ordinates are increasing are used, up to the point where the final peak discharge is reached, as detailed by Gericke and Smithers (2017). Applying the assumption defined by Gericke and Smithers (2017) that TP ≈ TC, the observed lag time (L) for each event is calculated using Equation 4.2 (Chapter 4).
(iv) The ACRU simulation results obtained from the assessment of the CSM system in the Chapter 4, i.e. applying the revised peak discharge computation procedure, were used to provide the simulated stormflow volumes, i.e. UQFLOW OTD, required as input to the ACRU stormflow peak discharge equations.
(v) The Schmidt and Schulze (1984) lag equation was used to estimate the average catchment lag time for the two case study catchments, as summarised in Table 5.1.
(vi) Using all of the information above, the performance of the single UH approach, i.e.
the default option in the ACRU model, as implemented in Chapter 4, was firstly investigated (Step 1). The following procedure was followed:
• Step 1.1, the simulated UQFLOW OTD from the ACRU model was used as input to the single UH approach along with the Schmidt and Schulze (1984) estimated lag time, to estimate the stormflow contribution to the peak discharge for the day, i.e.
for each of the events extracted for the two case study catchments.
• Step 1.2, repeat Step 1.1, however, replace the Schmidt and Schulze (1984) estimated lag time, i.e. which remains constant for each event, with the observed lag time estimated for each event extracted from the observed event hydrographs.
• Step 1.3, use both the observed stormflow volume and observed lag time for each event to calculate the stormflow contribution to peak discharge.
(vii) The same procedure was followed to assess the performance of the incremental UH approach (Step 2), however, in this case the temporal distribution of daily rainfall was required. Therefore, the procedure was as follows:
• Step 2.1, the simulated UQFLOW OTD from the ACRU model was disaggregated into incremental stormflow volumes, based on hyetographs generated using the daily rainfall and one of four synthetic regionalised rainfall distributions (Figure 5.1) applicable to each catchment (Table 5.1). Incremental triangular UHs were then generated for each increment of stormflow volume, using the Schmidt and Schulze (1984) estimated lag time. The incremental UHs were then superimposed to provide a composite surface runoff hydrograph and final stormflow peak discharge estimate, as depicted in Figure 5.2. A program written in FORTRAN was used for these computations.
• Step 2.2, repeat Step 2.1, however, replace the synthetic regionalised rainfall distributions with the observed rainfall hyetographs for each event, and replace the Schmidt and Schulze (1984) estimated lag time with the observed lag time for each event.
• Step 2.3, use the observed stormflow volume, the observed rainfall hyetographs, and the observed lag time for each event to calculate the stormflow contribution to peak discharge.
• Step 2.4, use the UQFLOW OTD as the input for stormflow and keep this fixed, then use the observed rainfall hyetographs and Schmidt and Schulze (1984) estimated lag time for one set of computations, then change this to the synthetic regionalised rainfall distributions and the observed lag time. The objective of this assessment is to try to identify if the incremental UH approach is more sensitive to inaccurate estimates of daily rainfall distributions or to catchment lag times.
(viii) The results from each of the above analyses are then summarised for each catchment using both the Mean Relative Error (MRE), Equation 5.1, and the Mean Absolute Relative Error (MARE), Equation 5.2, between observed and simulated peak discharge values, i.e. from all the selected events, as follows:
𝑆𝑆𝑄𝑄𝑄𝑄 =1𝑛𝑛∑ 𝑆𝑆𝑆𝑆𝑆𝑆𝑂𝑂𝑂𝑂𝑂𝑂𝑖𝑖−𝑂𝑂𝑂𝑂𝑂𝑂𝑖𝑖
𝑖𝑖
𝑛𝑛𝑆𝑆=1 (5.1) 𝑆𝑆𝑀𝑀𝑄𝑄𝑄𝑄 =𝑛𝑛1∑𝑛𝑛𝑆𝑆=1|𝑆𝑆𝑆𝑆𝑆𝑆𝑂𝑂𝑂𝑂𝑂𝑂𝑖𝑖−𝑂𝑂𝑂𝑂𝑂𝑂𝑖𝑖| (5.2)
where
MRE = mean relative error (0 - ∞; objective is to minimise MRE),
MARE = mean absolute relative error (0 - ∞; objective is to minimise MARE), 𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆 = simulated stormflow peak discharge, for event i [m3.s-1],
𝑂𝑂𝑂𝑂𝑂𝑂𝑆𝑆 = observed stormflow peak discharge, for event i [m3.s-1].
𝑛𝑛 = number of events.
(ix) The results are then compared and discussed.
(x) An additional investigation was performed using the observed data to identify if there is a relationship between the distribution of daily rainfall, i.e. rainfall intensity, and catchment lag time.
(xi) Conclusions are then drawn from the results and recommendations made for further research.
Figure 5.2 Generation of incremental UH’s which are superimposed to provide a composite surface runoff hydrograph, after Schmidt and Schulze (1987a)