Abstract
In a sustainable urbanisation process, the infrastructure has to be designed taking into consideration the hydrological behaviour of the respective catchment. It is mandatory to predict the climatic events accurately to understand the hydrological impacts of urban developments. It is very challenging for hydrologists to model extreme events when there are limited data available. The current study proposed a methodology to calculate the design rainfalls in the coastal region of Sao Paulo, Brazil. The gamma-function distribution used the annual maximum daily rainfalls in a probabilistic approach. The achieved 24-h-design rainfalls were compared to the results from other intensity–duration–frequency equations in different time-series. The rainfall disaggregation used regional and national conversion ratios. The fluctuation of the annual maxima revealed that the study area was affected by the Noah and Joseph erratic processes. Subsequently, the detected extreme event time-series were also used for the derivation of the 24-h-design rainfalls. The outcomes of the study showed that the gamma-function distribution provides reliable results, enhanced by the use of representative disaggregation ratios and proper time-series.
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Acknowledgements
We gratefully acknowledge UNICAMP and the Brazilian National Council for the Improvement of Higher Education (CAPES) for the study support, and the Australian Government for the Research Training Program (RTP) Fees Offset Scholarship at Swinburne University of Technology.
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Appendices
Appendix A
The calculation of the gamma-function parameters and the test statistic for the rain gauges (see Tables 6, 7, 8 and 9).
Appendix B
The calculation of the gamma-function parameters and the test statistic for the rain gauges during the extreme event time-series (see Tables 10, 11).
Appendix C
Exemplification of the rainfall disaggregation with different ratios
-
(a)
Downscaling the 24 h to 12 h rainfalls for the gamma distribution design rainfall of the E2-046 station (65 years), by the use of the CETESB ratio:
-
From Table 2
CETESB RATIO
Original duration
Final duration
Conversion ratios
1 day
24 h
1.14
24 h
12 h
0.85
-
The gamma distribution values are multiplied by 1.14 (converting the 1 day to a 24 h rainfall) and then by 0.85 (converting the 24 h to a 12 h rainfall)
Gamma-CETESB
Return period (years)
Design rainfall (1 day)
Design rainfall (24 h)
Design rainfall (12 h)
2
100.60
114.69
97.48
5
138.68
158.09
133.03
10
161.87
184.53
155.20
15
174.31
198.72
167.11
20
182.79
208.38
175.21
25
189.19
215.68
181.33
50
208.31
237.47
199.60
100
226.51
258.22
217.00
-
(b)
Downscaling the 24 h to 12 h rainfalls for the gamma distribution design rainfall of the E2-046 station (65 years), by the use of the DAEE-Caraguatatuba (CAR) ratio:
-
From Table 3:
DAEE-CAR RATIO
Original duration
Final duration
Conversion ratios
1 day
24 h
1.14
24 h
12 h
0.88
-
The gamma distribution values are multiplied by 1.14 (converting the 1 day to a 24 h rainfall) and then by 0.88 (converting the 24 h to a 12 h rainfall):
Gamma-CAR
Return period (years)
Design rainfall (1 day)
Design rainfall (24 h)
Design rainfall (12 h)
2
100.60
114.69
100.93
5
138.68
158.09
139.12
10
161.87
184.53
162.38
15
174.31
198.72
174.87
20
182.79
208.38
183.37
25
189.19
215.68
189.80
50
208.31
237.47
208.98
100
226.51
258.22
227.23
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Boulomytis, V.T.G., Zuffo, A.C. & Imteaz, M.A. Derivation of Design Rainfall and Disaggregation Process of Areas with Limited Data and Extreme Climatic Variability. Int J Environ Res 12, 147–166 (2018). https://doi.org/10.1007/s41742-018-0079-x
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DOI: https://doi.org/10.1007/s41742-018-0079-x