Assessing intensity-duration-frequency equations and spatialization techniques across the Grande River Basin in the state of Bahia, Brazil

Barbosa, Alan de Gois; Souza Neto, Izaias Rodrigues de; Costa, Veber Afonso Figueiredo; Mendes, Ludmilson Abritta

doi:10.1590/2318-0331.272220220083

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Scientific/Technical Article • RBRH 27 • 2022 • https://doi.org/10.1590/2318-0331.272220220083 linkcopy

Assessing intensity-duration-frequency equations and spatialization techniques across the Grande River Basin in the state of Bahia, Brazil

Avaliação de equações de intensidade-duração-frequência e técnicas de espacialização na Bacia do Rio Grande no estado da Bahia, Brasil

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Understanding the probabilistic behavior of extreme rainfall on a fine temporal and spatial scales is crucial for design and risk assessment of hydraulic structures. However, information at appropriate resolutions is frequently limited or unavailable at the locations of interest, thereby requiring the estimation of Intensity-Duration-Frequency (IDF) curves at the regional scale. In this paper, we resort to simplified approaches for rainfall disaggregation and spatialization for deriving a regional IDF equation for the Grande River catchment, in the Brazilian state of Bahia. Our results suggest that, at the daily time scale, the maximum rainfall amounts can be reasonably described by the light-tailed Gumbel distribution in the study region. The spatialization procedures indicated that, whereas both the Inverse Distance Weighting (IDW) and the ordinary kriging techniques could capture the spatial variability of rainfall quantiles, for several durations of practical interest, only the former was able to model the spatial variability of the IDF parameters. Finally, despite the simplifying assumptions, we were able to derive smooth spatial surfaces for the aforementioned quantities, which might be useful for the design of hydraulic structures at ungauged sites.

Keywords: Heavy rainfalls; IDF; IDW; Kriging

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

Rain gauge	$λ$	$κ$	$θ$	$η$	RMSE	p-bias (%)	Coefficient of determination (r²)
946003	38.3407	0.1580	0.1971	0.7580	2.48	0.00	0.9979
1042012	31.5480	0.1884	0.1971	0.7580	8.38	-9.80	0.9963
1047004	35.0560	0.2010	0.1971	0.7580	6.04	4.10	0.9945
1142017	29.6207	0.1641	0.1971	0.7580	17.91	-21.30	0.9979
1142020	30.9594	0.1656	0.1971	0.7580	14.63	-17.40	0.9979
1143002	36.8106	0.2028	0.1971	0.7580	10.27	9.90	0.9942
1143010	36.1907	0.1790	0.1971	0.7580	3.02	0.50	0.9972
1144005	37.2851	0.1727	0.1971	0.7580	3.14	1.60	0.9976
1144014	30.8785	0.2098	0.1971	0.7580	6.08	-5.80	0.9928
1144027	37.9695	0.1890	0.1971	0.7580	8.69	8.70	0.9962
1145001	33.3950	0.1761	0.1971	0.7580	6.95	-8.00	0.9974
1145013	33.9834	0.1547	0.1971	0.7580	10.56	-12.20	0.9978
1145014	36.2693	0.1503	0.1971	0.7580	6.93	-7.60	0.9976
1145019	35.5300	0.1735	0.1971	0.7580	3.42	-2.90	0.9976
1146000	35.4630	0.1878	0.1971	0.7580	3.70	1.20	0.9964
1147000	37.3212	0.1493	0.1971	0.7580	5.16	-5.20	0.9975
1147002	36.9048	0.1761	0.1971	0.7580	3.27	1.60	0.9974
1147003	37.3500	0.1459	0.1971	0.7580	5.91	-6.10	0.9973
1242015	27.5183	0.1830	0.1971	0.7580	18.80	-22.60	0.9969
1243000	32.2353	0.1785	0.1971	0.7580	8.95	-10.60	0.9973
1243019	37.3445	0.1768	0.1971	0.7580	4.07	3.00	0.9974
1244011	35.9524	0.1736	0.1971	0.7580	2.91	-1.70	0.9976
1244019	39.7183	0.1888	0.1971	0.7580	12.63	13.70	0.9962
1245004	35.3445	0.1736	0.1971	0.7580	3.68	-3.40	0.9976
1245005	38.5224	0.1415	0.1971	0.7580	4.91	-4.40	0.9968
1245007	37.5838	0.1421	0.1971	0.7580	6.39	-6.50	0.9969
1245015	35.5498	0.1862	0.1971	0.7580	3.53	0.90	0.9965
1246000	37.7133	0.1844	0.1971	0.7580	6.80	6.50	0.9967
1246001	36.0317	0.1714	0.1971	0.7580	3.02	-2.20	0.9977
1247002	32.8359	0.1723	0.1971	0.7580	9.01	-10.60	0.9977
1343008	33.6851	0.1733	0.1971	0.7580	6.94	-8.00	0.9976
1344013	35.8251	0.1757	0.1971	0.7580	2.88	-1.50	0.9975
1344014	34.6589	0.1904	0.1971	0.7580	3.50	-0.30	0.9960
1344015	37.9329	0.1872	0.1971	0.7580	8.07	8.00	0.9964
1344016	35.4643	0.1400	0.1971	0.7580	10.99	-12.40	0.9967
1344017	35.4002	0.1808	0.1971	0.7580	3.01	-1.10	0.9971
1345000	33.2569	0.2411	0.1971	0.7580	13.78	11.70	0.9851
1346000	31.8437	0.1492	0.1971	0.7580	16.31	-19.10	0.9975
1346001	34.9734	0.1673	0.1971	0.7580	5.60	-6.20	0.9979
1346002	34.7456	0.1871	0.1971	0.7580	3.31	-1.10	0.9964
1346004	37.7059	0.1491	0.1971	0.7580	4.53	-4.30	0.9975
1346005	32.1770	0.1908	0.1971	0.7580	6.55	-7.40	0.9960
1346006	35.7780	0.1556	0.1971	0.7580	6.63	-7.40	0.9978
1346007	36.1201	0.1852	0.1971	0.7580	4.02	2.20	0.9967
1347001	32.4031	0.1415	0.1971	0.7580	16.81	-19.60	0.9968

Theoretical model	2-year return period
Theoretical model	SSE	Nugget	Partial sill	Range
Spherical	5.44⋅10^-12	0.00	0.0390	58984.2
Exponential	6.91⋅10^-12	0.00	0.0428	33410.0
Gaussian	3.58⋅10^-12	0.00	0.0396	25808.6
Theoretical model	50-year return period
Theoretical model	SSE	Nugget	Partial sill	Range
Spherical	3.33⋅10^-10	0.00	0.2676	31545.8
Exponential	4.33⋅10^-10	0.00	0.2691	13125.0
Gaussian	1.27⋅10^-10	0.21	0.3928	9289.8

Return period	Step	IDW		Ordinary Kriging
Return period	Step	RMSE	p-bias	RMSE	p-bias
2 - years	Calibration	0.0001	0.00%	0.0017	0.01%
2 - years	Cross-validation	0.1915	-0.29%	0.2348	-0.79%
50 - years	Calibration	0.0003	0.00%	0.1577	-0.01%
50 - years	Cross-validation	0.4699	-1.62%	0.4788	-0.54%

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[1] Source: Departamento de Águas e Energia Elétrica (1980).