Universal equations for rainfall distributions from SCS and Huff methods

Silveira, André Luiz Lopes da

doi:10.1590/2318-0331.292420230093

André Luiz Lopes da Silveira

Corresponding author

conceptualization

methodology

formal analysis

validation

writing - original draft

review & editing

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

https://orcid.org/0000-0001-9875-879X

E-mail: andre@iph.ufrgs.br (ALLS)

Editor-in-Chief: Adilson Pinheiro

Associated Editor: Priscilla Macedo Moura

Thumbnail

Figure 1
Fitting the 24-hour SCS I and II curves.

Thumbnail

Figure 2
Fitting the 24-hour SCS IA and III curves.

Thumbnail

Figure 3
Fitting the 6-hour SCS I and II curves.

Thumbnail

Figure 4
Fitting the 6-hour SCS IA and III curves.

Thumbnail

Figure 5
Fitting the Huff´s point median curves of dimensionless precipitation from 1st to 4th quartile.

Thumbnail

Figure 6
Fitting the Huff’s median areal curves of dimensionless precipitation from the 1st to the 4th quartile in the range 10 to 50 mi².

Thumbnail

Figure 7
Fitting the Huff’s median areal curves of dimensionless precipitation from the 1st to the 4th quartile in the range 50 to 400 mi².

Thumbnail

Figure 8
Fitting the Huff’s median areal curves of dimensionless precipitation from the 1st quartile 10%, 50% and 90% probabilities.

Thumbnail

Table 1
Parameters b´, n and γ of the SCS curves.

Thumbnail

Table 2
Parameters b´, n and γ of the Huff curves.

Thumbnail

Table 3
Solution of Example 1.

Thumbnail

Table 4
Solution of Example 2.

Thumbnail

Table 5
Solution to Example 3.

Thumbnail

Table 6
Solution to Example 4.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

Type	b´	n	ã	MSPE
I (24h)	0.001466	0.608	0.410	0.017195
IA (24h)	0.129108	0.546	0.293	0.219439
II (24h)	0.001957	0.755	0.493	0.010405
III (24h)	0.022281	0.794	0.500	0.040088
I (6h)	0.025795	0.629	0.383	0.048977
IA (6h)	0.001577	0.415	0.465	0.020974
II (6h)	0.007717	0.762	0.488	0.078862
III (6h)	0.014864	0.694	0.500	0.025629

Huff curve 50%	b´	n	ã	MSPE
1QPt	0.192882	0.898	0.018	0.009850
2QPt	2.058141	0.486	0.295	4.222665
3QPt	0.077070	0.519	0.612	0.170782
4QPt	0.063740	0.590	0.916	0.310243
1Q10-50	0.379444	1.164	0.035	0.286376
2Q10-50	2.866894	3.339	0.295	4.539326
3Q10-50	0.124159	0.653	0.626	0.521046
4Q10-50	0.120152	0.743	0.902	0.771908
1Q50-400	0.233444	1.069	0.087	3.588326
2Q50-400	2.787747	3.530	0.293	3.804585
3Q50-400	0.213556	0.843	0.634	1.354016
4Q50-400	0.054689	0.776	0.864	0.960277
1Q10%	0.118290	1.137	0.032	0.082248
1Q50%	0.233444	1.069	0.087	3.588326
1Q90%	0.000000	0.207	0.085	7.375398

t (min)	t´	P_t´	P calc (mm)	P SCS I (mm)	Error (%)
60	0.042	0.017	4.2	4.4	-4.5
120	0.083	0.035	8.8	8.8	0.0
180	0.125	0.054	13.7	13.5	1.5
240	0.167	0.076	19.0	19.0	0.0
300	0.208	0.100	25.0	25.0	0.0
360	0.250	0.125	31.7	31.3	1.3
420	0.292	0.156	39.7	39.0	1.8
480	0.333	0.194	49.6	48.5	2.3
540	0.375	0.254	63.8	63.5	0.5
600	0.417	0.515	126.1	128.8	-2.1
660	0.458	0.623	157.3	155.8	1.0
720	0.500	0.684	172.7	171.0	1.0
780	0.542	0.732	184.2	183.0	0.7
840	0.583	0.770	193.6	192.5	0.6
900	0.625	0.802	201.6	200.5	0.5
960	0.667	0.832	208.8	208.0	0.4
1020	0.708	0.860	215.3	215.0	0.1
1080	0.750	0.886	221.3	221.5	-0.1
1140	0.792	0.910	226.8	227.5	-0.3
1200	0.833	0.932	232.0	233.0	-0.4
1260	0.875	0.952	236.8	238.0	-0.5
1320	0.917	0.970	241.4	242.5	-0.5
1380	0.958	0.986	245.8	246.5	-0.3
1440	1.000	1.000	250.0	250.0	0.0

t (min)	t´	P_t´	P calc (mm)	P Huff (mm)	Error (%)
10	0.100	0.330	47.1	39.6	19.0
20	0.200	0.600	66.0	72.0	-8.4
30	0.300	0.660	77.6	79.2	-2.0
40	0.400	0.750	86.5	90.0	-3.9
50	0.500	0.820	93.8	98.4	-4.6
60	0.600	0.860	100.2	103.2	-2.9
70	0.700	0.900	105.9	108.0	-2.0
80	0.800	0.940	111.0	112.8	-1.6
90	0.900	0.970	115.7	116.4	-0.6
100	1.000	1.000	120.0	120.0	0.0

t (min)	t´ (=t/t_TOT)	P_t´ (=P_t/P_TOT)	P_t (mm) (=P_t´*P_TOT)
10	0.1111	0.0571	3.67
20	0.2222	0.1425	9.16
30	0.3333	0.3073	19.76
40	0.4444	0.5537	35.59
50	0.5556	0.7025	45.16
60	0.6667	0.8058	51.80
70	0.7778	0.8842	56.85
80	0.8889	0.9473	60.90
90	1.0000	1.0000	64.29

t (min)	t´ (=t/t_TOT)	P_t Euler II (mm)	P_t´ Euler II (=P_t Euler II/P_TOT)	P_t´calc
5	0.1111	1.9	0.114	0.039
10	0.2222	5.3	0.319	0.319
15	0.3333	11.4	0.687	0.667
20	0.4444	12.8	0.771	0.772
25	0.5556	13.8	0.831	0.840
30	0.6667	14.7	0.886	0.891
35	0.7778	15.3	0.922	0.933
40	0.8889	16.0	0.964	0.969
45	1.0000	16.6	1.000	1.000

\frac{P_{t}}{P_{T O T}} = γ - \frac{(γ - \frac{t}{t_{T O T}}) \cdot {(1 + \frac{b}{t_{T O T}})}^{n}}{{(1 + \frac{b}{t_{T O T}} - \frac{1}{γ} \frac{t}{t_{T O T}})}^{n}}

\frac{P_{t}}{P_{T O T}} = γ + \frac{(\frac{t}{t_{T O T}} - γ) \cdot {(1 + \frac{b}{t_{T O T}})}^{n}}{{(\frac{b}{t_{T O T}} + \frac{\frac{t}{t_{T O T}} - γ}{1 - γ})}^{n}}

[1] E-mail: andre@iph.ufrgs.br (ALLS)

Brasil

Brasil

Universal equations for rainfall distributions from SCS and Huff methods

Equações universais para as distribuições de chuva dos métodos SCS e Huff

ABSTRACT