Intensity-Duration-Frequency relationships: stochastic modeling and disaggregation of daily rainfall in the lagoa Mirim watershed, Rio Grande do Sul, Brazil

Damé, Rita de C. F; Teixeira-Gandra, Claudia F. A.; Guedes, Hugo A. S.; Silva, Gisele M. da; Silveira, Suélen C. R. da

doi:10.1590/1809-4430-Eng.Agric.v36n3p492-502/2016

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Sumário

Engenharia de Água e Solo • Engenharia Agrícola 36 (3) • May-Jun 2016 • https://doi.org/10.1590/1809-4430-Eng.Agric.v36n3p492-502/2016 copy

Intensity-Duration-Frequency relationships: stochastic modeling and disaggregation of daily rainfall in the lagoa Mirim watershed, Rio Grande do Sul, Brazil

Relações Intensidade-Duração-Frequência: modelagem estocástica e desagregação da chuva diária na bacia hidrográfica da lagoa Mirim/RS/Brasil

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This study aimed to investigate information gain by using rainfall intensity-duration-frequency (IDF) relationships, with data gathered within N+M years from seven rain gauge stations located in the Lagoa Mirim Watershed (South Atlantic basin). After N years of daily rainfall, the transition probabilities of a time homogeneous two-state Markov chain were defined to simulate rainfall occurrence, as well as gamma distribution to measure it; for that, daily rainfall series were composed of N+M years, with M being the generated series. The series were adjusted to Gumbel distribution, being used in annual maximum daily rainfall disaggregation for durations of 10, 20, 30, 40, 50, 60, 120, 360, 720 and 1440 min. Daily rainfall disaggregation was validated through IDF relationships taken from pluviograph records of N years and from N+M years, using the “t” test of relative mean squared error. We can infer that there was information gain using IDF relationships of rainfall occurrence when using N years of observed data and M years of generated data by stochastic modeling compared to those obtained from a composed series of N years.

intense rainfall; hydrologic modeling; pluviographic records; hydrological series

Code	Name	Location	Latitude (S)	Longitude (O)	Altitude (m)	Period
3152003	Canguçu	Canguçu	31°24’16”	52°40’24”	400	1943–2012
3152004	Cascata	Pelotas	31°28’00”	52°31’00”	224	1967–1981
3152005	Vila Freire	Pedro Osório	31°40’10”	52°46’22”	250	1977–2012
3152008	Granja São Pedro	Pelotas	31°40’08”	52°10’50”	3	1967–2012
3152010	Morro Redondo	Morro Redondo	31°38’00”	52°39’00”	245	1966–1981
3252003	Estação do Curtume	Rio Grande	32°26’00”	52°36’00”	4	1964–1976
3252008	Granja Santa Maria	Rio Grande	32°24’16”	52°33’21”	12	1966–2006

Code	Name	Period	Average (mm)	Standard deviation (mm)	CV (%)	Maximum (mm)
3152003	Canguçu	1966–1990	4.43	10.72	24.2	123.30
3152004	Cascata	1976–1980	4.50	11.98	26.6	132.70
3152005	Vila Freire	1977–1998	4.28	11.93	27.9	152.40
3152008	Granja São Pedro	1967–1995	3.50	10.83	31.0	195.20
3152010	Morro Redondo	1971–1975	4.36	11.62	26.7	114.80
3252003	Estação do Curtume	1971–1975	2.90	9.14	31.5	96.00
3252008	Granja Santa Maria	1966–1996	3.53	11.25	31.9	201.00

Station	Transition probabilities				Gamma distribution parameters

	P(0,0)	P(0,1)	P(1,0)	P(1,1)	α	β
3152003	0.79	0.21	0.46	0.54	0.39	8.36
3152004	0.76	0.24	0.46	0.54	0.89	9.34
3152005	0.80	0.20	0.49	0.51	1.09	9.30
3152008	0.84	0.16	0.64	0.36	1.38	8.45
3152010	0.79	0.21	0.52	0.48	0.88	9.06
3252003	0.84	0.16	0.57	0.43	1.21	7.13
3252008	0.83	0.17	0.55	0.45	1.53	8.77

Code	Name	Period	Average (mm)	Standard deviation (mm)	CV (%)	Maximum (mm)
3152003	Canguçu	1943–2012	4.01	11.02	27.5	177.30
3152004	Cascata	1967–2012	2.93	8.05	27.5	132.70
3152005	Vila Freire	1977–2012	4.15	11.82	28.5	152.40
3152008	Granja São Pedro	1966–2012	3.51	10.95	31.2	195.20
3152010	Morro Redondo	1967–2012	2.51	7.56	3.01	114.80
3252003	Estação do Curtume	1964–2012	2.13	6.57	30.9	200.20
3252008	Granja Santa Maria	1966–2012	3.49	11.01	31.6	201.00

Station	Series of N years				Series of N+M years

	λ	γ	KS_calc	KS_crit	λ	γ	KS_calc	KS_crit
3152003	0.0675	66.05	0.56	2.88	0.0417	68.86	0.66	5.58
3152004	0.0459	85.45	0.60	1.44	0.0479	49.27	0.56	3.91
3152005	0.0502	80.84	0.68	3.29	0.0501	79.45	0.61	3.75
3152008	0.0497	80.28	0.59	3.24	0.0491	81.07	0.59	4.16
3152010	0.0939	94.41	0.79	1.92	0.0566	45.76	0.61	4.21
3252003	0.1739	82.67	0.60	1.44	0.0617	39.70	0.51	3.64
3252008	0.0424	86.30	0.63	3.58	0.0421	84.39	0.60	4.16

Code	Tr (years)

	5	10	20	50	100
3152003	101.61/104.19*	113.48/119.17	125.34/134.15	141.02/153.96	152.88/168.94
3152004	110.77/80.56	123.99/90.22	137.20/111.24	154.67/130.68	167.88/145.24
3152005	121.42/111.87	135.79/125.76	150.17/139.64	169.17/158.00	183.55/171.89
3152008	118.72/115.88	134.95/130.90	151.18/145.92	172.63/165.77	188.86/180.79
3152010	105.81/76.38	113.15/89.61	120.49/102.83	130.19/120.31	137.53/133.54
3252003	111.00/55.53	121.48/76.03	131.96/96.53	145.81/123.63	156.29/144.13
3252008	127.69/121.87	143.55/137.92	159.40/153.96	180.35/175.17	196.20/191.22

Code	Tr (years)	PRUSKI et al. (2006) – N years			N – N+M years

		b₀	b₁	t(b₁)	b₀	b₁	t(b₁)
3152003	5	0.2097	1.1318	0.1163	-0.422	1.037	0.0098
	10	0.2301	1.0888	0.0810	-0.213	1.147	0.0061
	20	0.2525	1.0474	0.0452	-0.237	1.122	0.0047
	50	0.2855	0.9951	-0.0491	-0.274	1.089	0.0039
	100	0.3133	0.9573	-0.0430	0.220	1.060	0.0023

3152004	5	-3.7699	1.3322	0.1141	-1.376	0.813	0.00081
	10	-4.1452	1.1615	0.1359	-1.572	0.844	0.00067
	20	-4.5578	1.1916	0.1572	-1.795	0.877	0.00050
	50	-5.1670	1.2326	0.1844	-2.140	0.922	0.00023
	100	-5.6813	1.2645	0.2097	-1.623	0.952	0.00030

3152005	5	-6.2380	1.2641	0.2043	0.090	0.922	0.00256
	10	-6.8533	1.2958	0.2232	0.099	0.925	0.00257
	20	-7.5293	1.3283	0.2417	0.110	0.929	0.00259
	50	-8.5264	1.3725	0.2654	0.125	0.933	0.00262
	100	-9.3675	1.4069	0.2899	0.643	0.982	0.04254

3152008	5	-8.0333	1.2635	0.2041	-2.295	0.740	0.00091
	10	-8.9213	1.3092	0.2311	-2.539	0.737	0.00092
	20	-9.9075	1.3566	0.2572	-2.809	0.734	0.00093
	50	-11.3800	1.4218	0.2903	-3.209	0.731	0.00094
	100	-12.6390	1.4733	0.3257	-3.026	0.725	0.00105

3152010	5	-4.8484	1.0863	0.0780	-0.308	0.742	0.00184
	10	-5.1493	1.0765	0.0690	-0.350	0.792	0.00176
	20	-5.4689	1.0667	0.0610	-0.396	0.845	0.00162
	50	-5.9220	1.0540	0.0501	-0.468	0.921	0.00120
	100	-6.2895	1.0444	0.0412	0.598	0.973	0.06208

3252003	5	2.7943	0.9518	-0.0510	-0.310	0.705	0.00188
	10	3.0217	0.8775	-0.1394	-0.352	0.739	0.00184
	20	3.2675	0.8091	-0.2357	-0.399	0.774	0.00174
	50	3.6235	0.7267	-0.3757	-0.471	0.824	0.00168
	100	3.9183	0.6701	-0.4535	-0.534	0.864	0.00155

3252008	5	3.4070	1.1602	0.1379	-0.490	0.912	0.00127
	10	3.5933	1.0433	0.0415	-0.543	0.958	0.00072
	20	3.7899	0.9382	-0.0658	-0.601	1.006	0.34660
	50	4.0663	0.8154	-0.2262	-0.688	1.073	0.00459
	100	4.2887	0.7332	-0.3269	-0.762	1.127	0.00336

Station	IDF	Tr (years)

		5	10	20	50	100
3152003	Pluvio_N	2.00	2.19	2.40	2.72	3.02
3152003	N_N+M	0.20	0.22	0.25	0.28	0.80
3152004	Pluvio_N	9.00	14.80	10.88	12.33	13.56
3152004	N_N+M	0.38	0.44	0.50	0.60	1.25
3152005	Pluvio_N	9.93	10.90	11.98	13.57	14.46
3152005	N_N+M	0.30	0.15	0.16	0.18	0.52
3152008	Pluvio_N	10.31	11.45	12.71	14.60	16.22
3152008	N_N+M	1.76	1.95	2.16	2.47	2.98
3152010	Pluvio_N	8.55	9.08	9.64	10.44	10.77
3152010	N_N+M	0.20	0.21	0.22	0.24	1.30
3252003	Pluvio_N	1.93	2.09	2.26	2.51	2.71
3252003	N_N+M	0.21	0.22	0.24	0.27	0.29
3252008	Pluvio_N	2.36	2.49	2.62	2.81	2.97
3252008	N_N+M	0.25	0.27	0.28	0.30	0.32

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[TFN2] I – Average maximum rainfall intensity (mm h⁻¹); Tr – Return period (years); t – rainfall duration (min).