It is also one of the primary inputs to hydrologic models used for hydraulic planning purposes. The primary part of the model is the R distribution, which is the fraction of the daily total that occurs during the hour of peak precipitation.
METHODS TO ESTIMATE THE TEMPORAL DISTRIBUTION OF RAINFALL
TEMPORAL DISTRIBUTION OF RAINFALL
Design Hyetographs Derived from Intensity-Duration-Frequency Relationships
- Temporal storm distributions
A simple means of developing a design hyetograph from an IDF curve is by the alternating block method (Chow et al., 1988). The types of time distributions used in the SCS model have evolved somewhat over the years. Initially, two 24-h storm distributions (Type I and Type II) were developed in the USA (Chow et al., 1988).
Hyetographs Derived from Observed Rainfall Data
- Triangular rainfall distribution
- Sampling from historical records
Their results showed that Huff curves were the most flexible of the four hyetograph representations studied. Results from this study indicated that a set of Huff curves could be used to represent a large part of the South African highlands (Walker and Tsubo, 2003).
Rainfall Disaggregation Models
- Neural network applications
Tests of the model performance have shown that the methodology is sufficient to reproduce IFD statistics at each of the tested stations (Boughton, 2000b). Stochastic rainfall models based on point processes have been one of the most widespread and useful tools in the analysis and modeling of rainfall (Koutsoyiannis and Mamassis, 2001).
Discussion and Conclusions
However, these adjustments caused a further problem in that the actual daily rainfall no longer corresponds to the daily rainfall sums of the generated rainfall intensities. ANNs are powerful tools with the potential to solve complex problems in hydrology, such as rainfall disaggregation.
DATA UTILISED IN THE STUDY
- Selection of Hidden Stations for Model Testing
- Data Selection
In contrast to the work done by Boughton (2000b), which was to disaggregate only the larger daily rainfall amounts considered important in flood studies, the aim of this study was to disaggregate all daily rainfall. In Boughton's (2000b) study, only rainfall data greater than or equal to 15 mm were used to develop his model. However, Boughton (2005) states that the method can be applied to all non-zero daily rainfall amounts.
For the purpose of this study, it was decided to develop the model to partition all non-zero daily rainfall amounts. All hourly data from the remaining 157 stations for which total daily precipitation was greater than or equal to 1 mm were used in the development of the disaggregation model, i.e. the choice to use all data where total daily rainfall was greater than or equal to 1 mm to develop the model is justified in section 6.1.
Furthermore, only data were used where all 24 hours of the day were successfully recorded, i.e. all days containing missing hours or completed data were excluded. Boughton (2000b) states that the model treats each day as an independent event for analysis, so that selecting days for analysis does not require whole months or whole years of data.
THE DISAGGREGATION MODEL
- Structure of the Model
- Distribution of R
- Calculating the Other 23 Hourly Fractions
- Daily Temporal Patterns of Hourly Rainfalls
- Chapter Conclusions
The distribution of Rot Ntabamhlope (mean R = 0.537) shows a greater proportion of days with larger values for R. If R= 1.0 then all the rainfall fell in a single hour, so the other 23 hourly fractions must be O . to group the 24 hour fractions, the data from all stations were reprocessed to obtain the highest 2-hour fraction of the daily total (r;i~»), the highest 3-hour fraction (r;~»), the highest to calculate 6-hour fraction (r;i~») and the highest 12-hour fraction (r;~)2») on each day.
Furthermore, the peak intensity can occur at all hours of the day, increasing the variability in temporal rainfall patterns. The hour of the day when the highest intensity rain fell was determined for each day that precipitation fell at each of the 157 stations. In the application, a random number is used to select the hour of maximum rainfall from the distribution of the hour of maximum rain for the location of interest.
These range from uniform to non-uniform with the possibility of the hour of maximum rainfall occurring at any hour of the day. Modifications made to the Boughton (2000b) methodology in this study relate to the decomposition of all daily precipitation, as opposed to only the decomposition of the largest events and the time distribution when the hour of maximum precipitation occurred. The distribution of the hour of maximum rainfall at each station was calculated and random sampling was done along the respective distributions.
REGIONALISATION
Once all 157 stations had been divided according to their respective Rrnean values using Table 5-1, an average distribution of R was calculated using all the stations in each Rrnean range. This resulted in 4 mean distributions of R, which are shown in Figure 5 -5. Correspondingly, 4 average distributions were calculated for the hour with maximum rainfall and are shown in Figures 5-6. To establish which distribution of R should be used for a site of interest throughout South Africa, it was necessary to develop a regionalized map of the mean value of R.
In the application, the range over which the average value of R for the site of interest must be determined to select the appropriate distribution of R. Once the average value of R for the site of interest has been determined, the distribution model as presented in Chapter 4 is run. In this study, the approach differs from the method developed by Boughton (2000b) by using regionalized distributions for R, and hourly distributions of maximum rainfall.
However, a shortcoming of the technique used to regionalize the methodology is that certain distributions of when the hour of maximum rainfall occurs are lost during the regionalization, which can be seen when comparing the regionalized distributions in Figure 5-6 with that of Station Jnk19a in Figure 5.6. 4-4.We have yet to discover what effect this will have on the resulting output of the model, which will be presented and discussed in the next chapter.
MODEL TESTING AND RESULTS
- Moments and Statistics Using At-site Short Duration Data
- Extreme Rainfall Events Using At-site Short Duration Data
- Extreme Rainfall Events When Using Regionalised Information
- Chapter Conclusions
In order to objectively assess the overall performance of the models, the Mean Absolute Relative Error of hourly rainfall (MARE), calculated as shown in Equation 6.1, is contained in Table 6-1. Therefore, this version of the model was chosen to be used for the rest of the study. Similar to the procedures used by Smithers and Schulze (2000a), design rainfall depths were calculated using the Generalized Extreme Value (GEV) distribution fitted to the Annual Maximum Series (AMS) by L-moments, for the observed data and for each of the 100 disaggregated series generated from the distribution model.
It is hypothesized that using different distributions of R to represent rainfall of different sizes will improve the performance of the rainfall distribution model. The following sections evaluate the performance of the partition model when regionalized input is used. The performance of the model at the "unsuitable" test stations was evaluated in exactly the same way as described in Section 6.2.
The values of the mean absolute relative error for hourly rainfall (MARE) and the mean absolute relative error for all durations (MARE_AD), as calculated in Equation 6.1 and Equation 6.2, respectively, are shown in Tables 6-8. This facilitated the comparison of the results from the partitioning model when short-term on-site information was available and when regionalized input was used. The performance of the regionalized method in terms of design rainfall was assessed using the same method as described in Section 6.3.
The values of the mean absolute relative error for the l-hour duration (MARE) and the mean absolute relative error for all durations (MARE_AD), as calculated in Equation 6.4 and Equation 6.5 respectively, are summarized in Table 6-9. The performance of the disaggregation model was analyzed first by comparing moments and event characteristics calculated for the observed and disaggregated data, and second by comparing design rainfall values calculated from the observed and disaggregated data.
DISCUSSION, CONCLUSIONS AND RECOMMENDATIONS
- Short Duration Data Used
- Application of the Disaggregation Model
- Application of the Model Using At-Site Short Duration Data
- Application of the Model Using Regionalised Input
- Summary
Further changes have been made to the methodology regarding the distribution of the time at which the hour of maximum rainfall occurred. The distribution of R and the distribution of the hour of maximum precipitation for each station determine which of the 480 possible temporal patterns to select for a given day's precipitation. This allows for the breakdown of daily rainfall for a given location where daily rainfall data is available and where short rainfall data is not available. A regionalized map of the mean value of R (Rmean) was developed for South Africa.
Due to the stochastic nature of the distribution patterns, 100 separate series were generated for each test site and a frequency analysis was performed. Although the use of regionalized inputs is able to adequately represent the distribution of R at the different test sites, the regionalization method fails to adequately capture the distribution of peak rainfall hours. Therefore, the direct application of the model developed in this study may not provide satisfactory results when applied to the daily rainfall totals for the 08:00–08:00 periods.
If testing shows that the direct application of the model is unsatisfactory, it is recommended that the model be redeveloped using 8:00 to 8:00 periods. It is postulated that the model's weakness in simulating both extremes of the rainfall spectrum (dry probabilities and design rainfall) is a consequence of using a single distribution of R to represent an entire range of magnitudes within a rainfall record set. It is recommended that this not be done in the future, as it becomes confusing when trying to distinguish between the composition R and the composition Rmean. Furthermore, it was noted in Section 7.4.2 that the distribution of the hour of maximum rainfall for certain stations is lost with this method of regionalization.
Design Flood Hydrology. Design and rehabilitation of dams, Department of Water and Environmental Engineering, Department of Building and Construction. Stochastic generation and disaggregation of hourly rainfall series for continuous hydrologic modeling and flood control reservoir design. A computer program for temporal partitioning of precipitation using adjustment procedures.XXV General Assembly ofEuropean Geophysical Society, Geophysical Research Abstracts, 2, European Geophysical Society.
Improvements to British rainfall modeling using a Bartlett-Lewis rectangular impulse model with a modified random parameter. Journal of Hydrology. Monte Carlo simulation of rainfall frequency curves. Cooperative Research Center for Catchment Hydrology, Monash University, Clayton, Victoria, Australia. Report, p. 1979. Estimation of runoff volume and rate in small catchments in South Africa based on the SCS technique. University of Natal, Pietermaritzburg, RSA ACRU Report No.
APPENDIX A
SITE CHARACTERISTICS OF STATIONS USED IN MODEL DEVELOPMENT
APPENDIXB
AVERAGE RANKED SERIES OF HOURLY FRACTIONS
APPENDIXC
CLUSTERED SEQUENCES OF HOURLY FRACTIONS
