Implications of discontinuous IDF equations in generation of runoff hydrographs. Case study: IDF-Porto Alegre (8º DISME)

Helfer, Ana Luiza; Dornelles, Fernando; Goldenfum, Joel Avruch

doi:10.1590/2318-0331.0217170004

Ana Luiza Helfer

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil

Fernando Dornelles

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil

Joel Avruch Goldenfum

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil

E-mails: anahelfer@hotmail.com (ALH), fernando.dornelles@ufrgs.br (FD), joel@iph.ufrgs.br (JAG)

Ana Luiza Helfer: Performed the methodology, obtained the results and wrote the text.

Fernando Dornelles: Defined the objectives, purposes and revised the text.

Joel Avruch Goldenfum: Contributed with technical discussions and revised the text.

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Figure 1
IDF curves at the 8^th DISME meteorological station in Porto Alegre, Brazil (CPRM, 2015SERVIÇO GEOLÓGICO DO BRASIL – CPRM. Atlas Pluviométrico do Brasil: equações intensidade-duração-frequência. Município: Porto Alegre. Estação Pluviográfica: Porto Alegre, Códigos 03051011 (ANA) e 83967 (OMM). Porto Alegre: CPRM, 2015. 14 p.).

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Figure 2
Total rainfall (dotted line) and effective rainfall (solid line) calculated by the alternating block method using the discontinuous IDF equation, considering various CN and return period.

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Figure 3
Surface runoff hydrographs obtained from the discontinuous IDF equation for a hypothetical basin with an area of 10 km² and time of concentration of 20 minutes, considering various CN and return period.

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Figure 4
IDF curves at the 8^th DISME meteorological station fitted by a single equation.

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Figure 5
Visual comparison between the runoff hydrographs obtained using the discontinuous IDF equation and those obtained using the single IDF equation for a hypothetical basin with an area of 10 km² and time of concentration of 20 minutes.

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Table 1
Parameters of the 8^th DISME IDF equation (CPRM, 2015SERVIÇO GEOLÓGICO DO BRASIL – CPRM. Atlas Pluviométrico do Brasil: equações intensidade-duração-frequência. Município: Porto Alegre. Estação Pluviográfica: Porto Alegre, Códigos 03051011 (ANA) e 83967 (OMM). Porto Alegre: CPRM, 2015. 14 p.).

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Table 2
Rainfall intensity (mm/h) at the transition point between the two 8º DISME IDF equations.

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Table 3
Rainfall depth calculated by using the discontinuous IDF equation for rainfall duration between 110 and 125 minutes considering a 5-year return period.

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Table 4
Relative difference between the rainfall intensity calculated using the single IDF equation and the rainfall intensity observed at the 8^th DISME station, for several return periods and rainfall duration.

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Table 5
Relative difference between the rainfall intensity calculated using the discontinuous IDF equation and the rainfall intensity observed at the 8^th DISME station, for several return periods and rainfall duration.

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Table 6
Absolute difference between the rainfall intensity (mm/h) calculated using the single IDF equation and the rainfall intensity observed at the 8^th DISME station, for several return periods and rainfall duration.

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Table 7
Absolute difference between the rainfall intensity (mm/h) calculated using the discontinuous IDF equation and the rainfall intensity observed at the 8^th DISME station, for several return periods and rainfall duration.

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Table 8
Relative difference (%) between the peak flow obtained using the single IDF equation and the peak flow obtained using the discontinuous IDF equation.

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Table 9
Relative difference (%) between the runoff volume obtained using the single IDF equation and the runoff volume obtained using the discontinuous IDF equation.

(1)

(2)

(3)

(4)

(5)

Duration	a	b	c	d
5 ≤ t < 120 min	4,247.90	0.2097	25.20	1.1199
120 ≤ t ≤ 1440 min	573.10	0.1889	0	0.7256

Return Period (years)	Duration (min)		Difference (mm/h)
	119.9999	120.0000
	Rainfall Intensity (mm/h)
2	18.63	20.25	1.62
5	22.57	24.08	1.51
10	26.10	27.45	1.34
25	31.63	32.63	1.00
50	36.58	37.20	0.62
100	42.30	42.40	0.10

Duration (min)	Cumulative Depth (mm)	Incremental Depth (mm)
...	...	...
110	44.82	...
115	44.99	0.17
120	48.16	3.16
125	48.70	0.54
...	...	...

	T (years)	Duration (min)
	T (years)	5	10	15	30	45	60	120	180	240	480	840	1440
Relative Difference (%)	2	6.3%	11.5%	9.0%	2.9%	2.4%	5.1%	8.3%	8.5%	7.8%	1.6%	-3.0%	-4.1%
	5	0.0%	2.3%	0.0%	-6.4%	-7.5%	-6.1%	0.8%	4.2%	3.9%	0.0%	-7.0%	-9.1%
	10	-1.2%	-0.2%	-2.4%	-9.1%	-10.4%	-9.6%	-0.9%	4.0%	3.8%	1.1%	-7.2%	-9.9%
	15	-1.0%	-0.5%	-2.7%	-9.6%	-11.0%	-10.4%	-0.9%	4.8%	4.7%	2.4%	-6.6%	-9.5%
	20	-0.4%	-0.4%	-2.6%	-9.5%	-11.0%	-10.5%	-0.5%	5.7%	5.7%	3.7%	-5.8%	-8.9%
	25	0.2%	0.0%	-2.2%	-9.2%	-10.8%	-10.4%	0.0%	6.6%	6.6%	4.9%	-5.0%	-8.2%
	50	3.0%	2.2%	-0.1%	-7.5%	-9.2%	-9.0%	2.5%	10.2%	10.4%	9.3%	-1.8%	-5.4%
	75	5.3%	4.1%	1.8%	-5.8%	-7.6%	-7.6%	4.7%	13.0%	13.2%	12.5%	0.7%	-3.2%
	100	7.2%	5.8%	3.4%	-4.4%	-6.3%	-6.3%	6.4%	15.2%	15.5%	15.0%	2.7%	-1.4%

	T (years)	Duration (min)
	T (years)	5	10	15	30	45	60	120	180	240	480	840	1440
Relative Differene (%)	2	-4.1%	8.3%	10.0%	7.0%	5.1%	5.2%	6.0%	6.6%	6.6%	2.8%	0.5%	1.9%
	5	-9.3%	-0.1%	1.4%	-2.2%	-4.6%	-5.5%	-2.7%	0.9%	1.3%	-0.3%	-5.0%	-4.7%
	10	-10.1%	-2.2%	-0.7%	-4.7%	-7.2%	-8.6%	-5.4%	-0.3%	0.2%	-0.2%	-6.2%	-6.5%
	15	-9.7%	-2.3%	-0.8%	-4.9%	-7.6%	-9.2%	-6.0%	-0.2%	0.4%	0.5%	-6.1%	-6.7%
	20	-9.0%	-1.9%	-0.4%	-4.7%	-7.5%	-9.2%	-6.0%	0.2%	0.9%	1.4%	-5.7%	-6.5%
	25	-8.3%	-1.4%	0.1%	-4.3%	-7.1%	-9.0%	-5.9%	0.7%	1.4%	2.1%	-5.3%	-6.1%
	50	-5.4%	1.1%	2.7%	-2.1%	-5.1%	-7.2%	-4.5%	3.1%	3.9%	5.3%	-3.1%	-4.3%
	75	-3.0%	3.2%	4.9%	-0.1%	-3.3%	-5.5%	-3.1%	5.1%	5.9%	7.7%	-1.3%	-2.6%
	100	-1.1%	5.0%	6.7%	1.6%	-1.7%	-4.1%	-1.9%	6.7%	7.6%	9.6%	0.2%	-1.3%

	T (years)	Duration (min)
	T (years)	5	10	15	30	45	60	120	180	240	480	840	1440
Absolute Difference (mm/h)	2	7.1	9.7	6.4	1.5	1.0	1.6	1.6	1.2	0.9	0.1	0.1	0.1
	5	0.0	2.5	0.0	4.4	4.0	2.7	0.2	0.7	0.6	0.0	0.4	0.4
	10	2.1	0.3	2.7	7.4	6.6	5.0	0.3	0.8	0.6	0.1	0.5	0.5
	15	1.8	0.8	3.3	8.5	7.6	5.9	0.3	1.1	0.8	0.3	0.5	0.5
	20	0.8	0.5	3.3	8.9	8.1	6.3	0.2	1.3	1.1	0.4	0.5	0.5
	25	0.4	0.0	2.9	9.0	8.3	6.6	0.0	1.6	1.3	0.6	0.4	0.5
	50	6.8	3.9	0.1	8.3	8.0	6.5	1.0	2.8	2.2	1.2	0.2	0.3
	75	12.7	7.8	2.9	6.9	7.1	5.8	1.9	3.7	3.0	1.7	0.1	0.2
	100	17.9	11.3	5.7	5.4	6.1	5.1	2.8	4.5	3.7	2.1	0.3	0.1

	T (years)	Duration (min)
	T (years)	5	10	15	30	45	60	120	180	240	480	840	1440
Absolute Difference (mm/h)	2	4.6	7.0	7.1	3.6	2.0	1.7	1.1	0.9	0.8	0.2	0.0	0.1
	5	13.5	0.1	1.3	1.5	2.4	2.4	0.7	0.2	0.2	0.0	0.3	0.2
	10	17.0	2.9	0.8	3.8	4.6	4.5	1.6	0.1	0.0	0.0	0.4	0.3
	15	17.6	3.2	0.9	4.4	5.3	5.2	1.9	0.0	0.1	0.1	0.5	0.4
	20	17.4	2.9	0.5	4.4	5.5	5.5	2.0	0.1	0.2	0.2	0.5	0.4
	25	16.7	2.3	0.1	4.2	5.5	5.7	2.0	0.2	0.3	0.2	0.4	0.4
	50	12.0	1.9	4.0	2.3	4.4	5.2	1.7	0.8	0.9	0.7	0.3	0.3
	75	7.2	6.1	7.8	0.1	3.0	4.2	1.3	1.4	1.4	1.1	0.1	0.2
	100	2.8	9.9	11.2	1.9	1.6	3.3	0.8	2.0	1.8	1.4	0.0	0.1

CN=70
Area (km²)	tc (min)	Return Period (years)
Area (km²)	tc (min)	5	10	25	50	100
5	20	-5.1%	-4.8%	-4.6%	-4.6%	-4.8%
	40	-4.6%	-4.1%	-3.8%	-3.7%	-3.8%
	60	-2.0%	-2.0%	-1.7%	-1.6%	-1.6%
	100	-1.3%	-0.1%	1.2%	1.6%	1.9%
	200	-2.4%	-0.4%	1.8%	3.1%	4.4%
20	20	-5.1%	-4.8%	-4.6%	-4.6%	-4.8%
	40	-4.6%	-4.1%	-3.8%	-3.7%	-3.8%
	60	-2.0%	-2.0%	-1.7%	-1.6%	-1.6%
	100	-1.3%	-0.1%	1.2%	1.6%	1.9%
	200	-2.4%	-0.4%	1.8%	3.1%	4.4%
80	20	-5.1%	-4.8%	-4.6%	-4.6%	-4.8%
	40	-4.6%	-4.1%	-3.8%	-3.7%	-3.8%
	60	-2.0%	-2.0%	-1.7%	-1.6%	-1.6%
	100	-1.3%	-0.1%	1.2%	1.6%	1.9%
	200	-2.4%	-0.4%	1.8%	3.1%	4.4%
CN=80
Area (km²)	tc (min)	Return Period (years)
Area (km²)	tc (min)	5	10	25	50	100
5	20	-4.2%	-4.2%	-4.4%	-4.5%	-4.8%
	40	-3.4%	-3.3%	-3.4%	-3.5%	-3.7%
	60	-1.2%	-1.1%	-1.1%	-1.2%	-1.3%
	100	0.5%	1.2%	1.7%	2.0%	2.3%
	200	-0.9%	0.7%	2.5%	3.6%	4.5%
20	20	-4.2%	-4.2%	-4.4%	-4.5%	-4.8%
	40	-3.4%	-3.3%	-3.4%	-3.5%	-3.7%
	60	-1.2%	-1.1%	-1.1%	-1.2%	-1.3%
	100	0.5%	1.2%	1.7%	2.0%	2.3%
	200	-0.9%	0.7%	2.5%	3.6%	4.5%
80	20	-4.2%	-4.2%	-4.4%	-4.5%	-4.8%
	40	-3.4%	-3.3%	-3.4%	-3.5%	-3.7%
	60	-1.2%	-1.1%	-1.1%	-1.2%	-1.3%
	100	0.5%	1.2%	1.7%	2.0%	2.3%
	200	-0.9%	0.7%	2.5%	3.6%	4.5%
CN=90
Area (km²)	tc (min)	Return Period (years)
Area (km²)	tc (min)	5	10	25	50	100
5	20	-3.6%	-3.8%	-3.9%	-4.0%	-4.1%
	40	-2.6%	-2.8%	-3.1%	-3.4%	-3.7%
	60	-0.1%	-0.3%	-0.6%	-0.8%	-1.1%
	100	2.1%	2.3%	2.5%	2.6%	2.6%
	200	1.2%	2.2%	3.3%	4.2%	4.9%
20	20	-3.6%	-3.8%	-3.9%	-4.0%	-4.1%
	40	-2.6%	-2.8%	-3.1%	-3.4%	-3.7%
	60	-0.1%	-0.3%	-0.6%	-0.8%	-1.1%
	100	2.1%	2.3%	2.5%	2.6%	2.6%
	200	1.2%	2.2%	3.3%	4.2%	4.9%
80	20	-3.6%	-3.8%	-3.9%	-4.0%	-4.1%
	40	-2.6%	-2.8%	-3.1%	-3.4%	-3.7%
	60	-0.1%	-0.3%	-0.6%	-0.8%	-1.1%
	100	2.1%	2.3%	2.5%	2.6%	2.6%
	200	1.2%	2.2%	3.3%	4.2%	4.9%

CN=70
Area (km²)	tc (min)	Return Period (years)
Area (km²)	tc (min)	5	10	25	50	100
5, 20, 80	20, 40, 60, 100, 200	-8.70%	-6.30%	-3.50%	-1.50%	0.30%
CN=80
Area (km²)	tc (min)	Return Period (years)
Area (km²)	tc (min)	5	10	25	50	100
5, 20, 80	20, 40, 60, 100, 200	-7.00%	-5.10%	-2.90%	-1.30%	0.20%
CN=90
Area (km²)	tc (min)	Return Period (years)
Area (km²)	tc (min)	5	10	25	50	100
5, 20, 80	20, 40, 60, 100, 200	-5.60%	-4.20%	-2.40%	-1.10%	0.20%

[1] E-mails: anahelfer@hotmail.com (ALH), fernando.dornelles@ufrgs.br (FD), joel@iph.ufrgs.br (JAG)

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Implications of discontinuous IDF equations in generation of runoff hydrographs. Case study: IDF-Porto Alegre (8º DISME)

Implicações da utilização de equações IDF descontínuas na geração de hidrogramas de escoamento superficial. Estudo de caso: IDF-Porto Alegre (8º DISME)

ABSTRACT