Alternative model of intense rainfall equation obtained from daily rainfall disaggregation

Back, Álvaro José

doi:10.1590/2318-0331.252020190031

Álvaro José Back

Empresa de Pesquisa Agropecuária e Extensão Rural de Santa Catarina, Urussanga, SC, Brasil E-mail: ajb@epagri.sc.gov.br (AJB)

http://orcid.org/0000-0002-0057-2186

Author contribution

Álvaro José Back: Responsible for the paper.

Thumbnail

Figure 1
Location of rainfall station.

Thumbnail

Figure 2
Schematization of the algorithm that generates the IDF equations by daily rainfall disaggregation.

Thumbnail

Figure 3
Relationship between rainfall durations given by CETESB (Companhia de Tecnologia de Saneamento Ambiental, 1986Companhia de Tecnologia de Saneamento Ambiental – CETESB. (1986). Drenagem urbana: manual de projetos (466 p.). São Paulo: DAEE/CETESB.) and the fitted model.

Thumbnail

Figure 4
Logarithmic regression between maximum one-day rainfall estimated by Log-Pearson type III with parameters estimated by de L-moments method (MML) and return period.

Thumbnail

Figure 5
Schematization of the algorithm that generates the proposed equations by daily rainfall disaggregation.

Thumbnail

Table 1
Rainfall disaggregation coefficients.

Thumbnail

Table 2
Parameters of the distributions adjusted with the respective values of the Kolmogorov-Smirnov (Dmax) and Anderson-Darling (AD) adhesion tests).

Thumbnail

Table 3
Values of maximum rainfall with durations of 1 day estimated by the probability distributions.

Thumbnail

Table 4
Rainfall intensity (mm h^-1) obtained by the rainfall disaggregation with the Cetesb coefficients.

Thumbnail

Table 5
Squares of the deviations between the intensities obtained with the disaggregation and intensities from IDF equation.

Thumbnail

Table 6
Squares of the deviations between the intensities obtained with the disaggregation and intensities from proposed equation.

Thumbnail

Table 7
Values of logarithmic regression adjustment coefficients d and e for various distributions.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Relationships between rainfall durations	Coefficients
24h/1 day	1.14
12h/24h	0.85
10h/24h	0.82
8h/24h	0.78
6h/24h	0.72
1h/ 24h	0.42
30 min/1h	0.74
25 min/30min	0.91
20 min/30min	0.81
15 min/30min	0.70
10 min/30min	0.54
5 min/30min	0.34

Distribution ¹ 1 Log-Normal with two parameters (LN2); Log-Normal with three parameters (LN3); Pearson type III (PIII); Log Pearson type III (LPIII) Gumbel distribution (Gb); Generalizes Distribution of Extreme Values (GEV); Method of moments (MM); Maximum likelihood method of (ML); Method of L-moments (MML);Chow method (Ch);	Parameters ² 2 α is the scale parameter; β is the form parameter; k is the location parameters;			Adhesion test ³ 3 Dmax is the Kolmogorov-Smirnov value test; AD is de Anderson-Darling value test.
	α	β	k	D_max	AD
LN2-MM	4.364	0.268		0.0877	0.4876
LN2-ML	4.365	0.262		0.0942	0.6308
LN2-MML	4.362	0.275		0.0800	0.5379
LN3-MM	4.5282	0.2308	13.680	0.0851	0.4995
LN3-ML	3.6886	0.5119	36.224	0.0873	0.4742
LN3-MML	4.1559	0.333	13.968	0.0809	0.4362
PIII–MM	11.274	4.139	34.751	0.0828	0.4718
PIII-ML	8.362	6.334	28.56	0.0828	0.5362
PIII-MML	11.274	4.139	34.751	0.0770	0.3963
LPIII-MM	0.032	70.730	2.133	0.0843	0.4508
LPIII-ML	0.030	73.276	2.133	0.0743	0.4508
LPIII-MML	0.174	3.992	3.727	0.0628	0.3205
Gb-MM	17.347	71.403		0.0990	0.5560
Gb-ML	17.440	71.203		0.0966	0.5584
Gb-MML	18.116	70.954		0.0839	0.4542
Gb-Ch	19.348	70.856		0.0715	0.4233
GEV-MM	19.088	71.839	0.082	0.0857	0.4880
GEV-MML	18.327	71.065	0.013	0.0832	0.4511

Probability	Return period (years)
Distribution ¹ 1 Log-Normal with two parameters (LN2); Log-Normal with three parameters (LN3); Pearson type III (PIII);Log Pearson type III (LPIII) Gumbel distribution (Gb); Generalizes Distribution of Extreme Values (GEV); Method of moments (MM); Maximum likelihood method of (ML); Method of L-moments (MML);Chow method (Ch).	2	5	10	15	20	25	50	100
LN2-MM	78.6	98.5	110.8	117.5	122.1	125.6	136.2	146.6
LN2-ML	78.6	98.1	110.0	116.5	121.0	124.4	134.7	144.7
LN2-MML	78.4	98.8	111.5	118.5	123.3	126.9	137.9	148.7
LN3-MM	78.9	98.8	110.8	117.3	121.7	125.0	135.1	144.8
LN3-ML	76.2	97.7	113.3	122.4	129.0	134.2	150.6	167.7
LN3-MML	77.8	98.4	111.8	119.2	124.3	128.3	140.4	152.4
PIII–MM	77.8	98.8	112.0	119.3	124.3	128.1	139.6	150.8
PIII-ML	78.8	97.9	109.6	115.9	120.2	123.4	133.1	142.4
PIII-MML	77.8	98.8	112	119.3	124.3	128.1	139.6	150.7
LPIII-MM	81.0	101.7	114.7	121.9	126.7	130.5	141.9	153.0
LPIII-ML	75.9	94.3	105.8	112.0	116.3	119.6	129.5	139.2
LPIII-MML	78.4	98.8	111.6	118.7	123.6	127.3	138.7	149.9
Gb-MM	77.8	97.4	110.4	117.8	122.9	126.9	139.1	151.2
Gb-ML	77.5	97.1	110.0	117.3	122.4	126.3	138.5	150.5
Gb-MML	77.6	98.1	111.7	119.4	124.8	128.9	141.6	154.3
Gb-Ch	77.9	99.9	114.4	122.6	128.3	132.7	146.3	159.9
GEV -MM	78.7	98.8	111.1	117.7	122.2	125.5	135.6	145.0
GEV -MML	77.8	98.3	111.7	119.2	124.5	128.5	140.8	152.9

Duration t (min)	Return period (years)
Duration t (min)	2	5	10	15	20	25	50	100
5	113.3	142.8	161.3	171.6	178.7	184.0	200.5	216.7
10	90.0	113.4	128.1	136.3	141.9	146.1	159.2	172.1
15	77.8	98.0	110.7	117.8	122.6	126.3	137.6	148.7
20	67.5	85.1	96.1	102.2	106.4	109.6	119.4	129.1
25	60.7	76.5	86.4	91.9	95.6	98.5	107.3	116.0
30	55.6	70.0	79.1	84.1	87.6	90.2	98.3	106.2
60	37.5	47.3	53.4	56.8	59.2	61.0	66.4	71.8
360	10.7	13.5	15.3	16.2	16.9	17.4	19.0	20.5
480	8.7	11.0	12.4	13.2	13.7	14.1	15.4	16.7
600	7.3	9.2	10.4	11.1	11.6	11.9	13.0	14.0
720	6.3	8.0	9.0	9.6	10.0	10.3	11.2	12.1
1440	3.7	4.7	5.3	5.6	5.9	6.0	6.6	7.1

Duration (min)	Return period (years)
Duration (min)	2	5	10	15	20	25	50	100
5	91.7	3.0	22.0	25.8	22.9	17.6	0.8	24.2
10	90.8	0.7	1.6	2.0	1.2	0.3	5.9	54.4
15	45.8	0.9	8.8	10.4	9.1	6.7	0.1	13.9
20	42.4	0.0	3.1	3.7	2.9	1.7	0.6	19.2
25	30.0	0.3	4.3	5.0	4.3	3.0	0.0	10.6
30	19.9	1.2	6.8	7.9	7.2	5.8	0.7	3.9
60	5.8	2.1	6.4	7.4	7.1	6.3	2.3	0.1
360	1.5	0.0	0.0	0.0	0.0	0.0	0.2	1.0
480	1.1	0.0	0.0	0.0	0.0	0.0	0.2	0.8
600	1.0	0.1	0.0	0.0	0.0	0.1	0.3	1.0
720	0.9	0.2	0.1	0.1	0.1	0.2	0.4	1.1
1440	0.5	0.2	0.1	0.1	0.2	0.2	0.4	0.8

Duration (min)	Return period (years)
Duration (min)	2	5	10	15	20	25	50	100
5	0.2	0.3	0.3	0.4	0.4	0.5	0.5	0.6
10	1.0	1.5	1.9	2.2	2.4	2.5	3.0	3.5
15	0.1	0.1	0.2	0.2	0.2	0.2	0.3	0.3
20	0.3	0.5	0.7	0.7	0.8	0.9	1.0	1.2
25	0.1	0.2	0.3	0.3	0.3	0.4	0.4	0.5
30	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
60	0.1	0.1	0.2	0.2	0.2	0.2	0.2	0.3
360	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
480	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
600	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
720	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1440	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

Probability Distribution ¹ 1 Log-Normal with two parameters (LN2); Log-Normal with three parameters (LN3); Pearson type III (PIII); Log Pearson type III (LPIII) Gumbel distribution (Gb); Generalizes Distribution of Extreme Values (GEV); Method of moments (MM); Maximum likelihood method of (ML); Method of L-moments (MML);Chow method (Ch).	Coefficients of regression
	d	e	R²
LN2-MM	36.62	52.7	0.9995
LN2-ML	15.31	73.2	0.9943
LN2-MML	16.42	72.3	0.9951
LN3-MM	14.99	74.7	0.9918
LN3-ML	24.70	52.2	0.9981
LN3-MML	18.06	69.0	0.9981
PIII–MM	16.94	71.6	0.9946
PIII-ML	14.40	74.9	0.9911
PIII-MML	16.94	71.6	0,9947
LPIII-MM	27.18	65.6	0,9996
LPIII-ML	16.94	71.6	0.9947
LPIII-MML	16.96	71.2	0.9966
Gb-MM	17.96	68.2	0.9989
Gb-ML	17.85	68.0	0.9988
Gb-MML	18.76	67.6	0.9989
Gb-Ch	20.04	67.3	0.9988
GEV-MM	14.62	75.8	0.9867
GEV-MML	18.07	69.1	0.9979

[1] Author contribution

Álvaro José Back: Responsible for the paper.

Brasil

Brasil

Alternative model of intense rainfall equation obtained from daily rainfall disaggregation

Modelo alternativo de equação de chuvas intensas obtida a partir da desagregação da chuva diária

ABSTRACT