Performance evaluation of flow duration curves regionalization methods

Piol, Marcos Vinícius Alpoin; Reis, José Antonio Tosta dos; Caiado, Marco Aurélio Costa; Mendonça, Antonio Sérgio Ferreira

doi:10.1590/2318-0331.241920170202

Marcos Vinícius Alpoin Piol

Universidade Federal do Espírito Santo, Vitória, ES, Brasil

José Antonio Tosta dos Reis

Universidade Federal do Espírito Santo, Vitória, ES, Brasil

http://orcid.org/0000-0001-9916-1469

Marco Aurélio Costa Caiado

Instituto Federal de Educação, Ciência e Tecnologia do Espírito Santo‎, Vitória, ES, Brasil

Antonio Sérgio Ferreira Mendonça

Universidade Federal do Espírito Santo, Vitória, ES, Brasil

E-mails: viniciuspiol@hotmail.com (MVAP), jatreis@gmail.com (JATR), maccaiado@gmail.com (MACC), anserfm@terra.com.br (ASFM)

Authors contributions Marcos Vinícius Alpoin Piol: Acquisition of data, selection and application of methods for flow permanence curves hydrological regionalization, analysis and interpretation of results, drafting of manuscript and critical revision.

José Antonio Tosta dos Reis: Selection of methods for flow permanence curves hydrological regionalization, analysis and interpretation of results, drafting of manuscript and critical revision.

Marco Aurélio Costa Caiado: Analysis and interpretation of results, drafting of manuscript and critical revision.

Antonio Sérgio Ferreira Mendonça: Analysis and interpretation of results, drafting of manuscript and critical revision.

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Figure 1
Itapemirim and Itabapoana River Basins location.

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Figure 2
Flowchart presenting steps for the definition of regional functions.

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Figure 3
Comparison between the real permanence curve and those obtained by Characteristic Values and Exponential Curve methods for the Coutinho station.

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Figure 4
Comparison between the real permanence curve and those obtained by Characteristic Value and Exponential Curve methods for the Usina São Miguel station.

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Figure 5
Comparison between the real Q₉₀ flow values, obtained through Regional Indicators, Exponential Curve and Characteristic Values methods.

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Table 1
Fluviometric stations installed and operated in the area considered in the study.

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Table 2
Combinations of independent variables that presented collinearity.

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Table 3
Regional functions obtained by the Characteristic Values method.

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Table 4
Regional functions for Q₅₀ and Q₉₅ flow rates estimation.

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Table 5
Average relative errors and Nash-Sutcliffe coefficients established by the use of the regional function selected for the application of the Characteristic Values method.

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Table 6
Average relative errors and Nash-Sutcliffe coefficient established by the use of the regional function selected for the application of the Exponential Curve method.

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Table 7
Regional flow indicators used to estimate reference flows for the study region.

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Independent Variables k+1 Q50 Q55 Q60 Q65 Q70 Q75 Q80 Q85 Q90 Q95 A 2 0.80 0.72 0.91 0.99 1.15 1.40 2.03 2.32 2.71 4.37 P 2 -0.29 -0.32 -0.23 -0.19 -0.11 -0.03 0.28 0.49 0.74 1.51 L 2 4.94 5.01 4.99 5.13 5.43 5.43 5.89 6.34 6.84 8.07 I 2 79.19 78.67 79.53 80.10 83.85 87.13 94.13 94.87 99.36 112.68 R 2 84.73 84.09 85.33 85.98 89.93 93.64 101.55 102.63 107.74 122.76 A, P 3 1.60 1.56 1.67 1.72 1.80 1.90 2.24 2.45 2.71 3.51 A, L 3 2.62 2.57 2.71 2.80 2.95 3.11 3.60 3.91 4.27 5.61 A, I 3 2.18 2.13 2.24 2.31 2.45 2.64 3.12 3.29 3.56 4.91 A, R 3 2.71 2.63 2.84 2.92 3.07 3.34 3.99 4.27 4.66 6.34 P, L 3 1.41 1.33 1.47 1.50 1.56 1.72 2.08 2.24 2.48 3.30 P, I 3 0.15 0.16 0.13 0.14 0.16 0.14 0.16 0.20 0.23 0.46 P, R 3 1.69 1.66 1.73 1.78 1.86 1.92 2.20 2.41 2.65 3.36 L, I 3 3.72 3.86 3.67 3.75 3.92 3.73 3.72 3.92 4.06 4.37 L, R 3 6.93 7.00 6.98 7.12 7.42 7.43 7.89 8.34 8.84 10.06 I, R 3 75.91 75.43 76.36 76.86 80.33 83.59 90.30 90.87 95.07 107.83 A, P, L 4 3.36 3.28 3.43 3.46 3.53 3.70 4.07 4.23 4.48 5.30 A, P, I 4 2.13 2.15 2.11 2.12 2.13 2.08 2.06 2.07 2.07 2.03 A, P, R 4 3.60 3.56 3.66 3.71 3.79 3.88 4.18 4.40 4.64 5.35 A, L, I 4 3.57 3.59 3.59 3.65 3.75 3.75 3.91 4.09 4.23 4.86 A, L, R 4 4.55 4.50 4.67 4.75 4.89 5.07 5.58 5.89 6.25 7.61 A, I, R 4 3.76 3.72 3.86 3.92 4.03 4.25 4.73 4.87 5.12 6.46 P, L, I 4 2.10 2.09 2.09 2.10 2.11 2.12 2.16 2.20 2.23 2.46 P, L, R 4 3.36 3.28 3.41 3.44 3.50 3.64 3.97 4.13 4.36 5.11 P, I, R 4 2.03 2.04 2.03 2.04 2.04 2.04 2.08 2.10 2.13 2.37 L, I, R 4 5.07 5.21 5.06 5.13 5.26 5.11 5.10 5.26 5.36 5.67 A, P, L, I 5 4.08 4.07 4.06 4.06 4.07 4.06 4.05 4.05 4.05 4.03 A, P, L, R 5 5.34 5.26 5.39 5.42 5.49 5.64 5.97 6.13 6.36 7.05 A, P, I, R 5 4.02 4.04 4.02 4.03 4.03 4.01 4.00 4.01 4.00 4.00 A, L, I, R 5 5.11 5.14 5.16 5.21 5.28 5.30 5.46 5.60 5.71 6.32 P, L, I, R 5 4.01 4.00 4.01 4.02 4.02 4.03 4.08 4.10 4.13 4.36 A, P, L, I, R 6 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00

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Station	Code	Latitude	Longitude
Usina Fortaleza	57350000	–20º22’17”	–41º24’25”
Iúna	57360000	–20º21’08”	–41º31’58”
Terra Corrida	57370000	–20º25’49”	–41º30’10”
Itaici	57400000	–20º31’42”	–41º30’41”
Ibitirama	57420000	–20º32’26”	–41º39’56”
Rive	57450000	–20º44’49”	–41º27’58”
Castelo	57490000	–20º36’22”	–41º11’59”
Usina São Miguel	57550000	–20º42’09”	–41º10’25”
Coutinho	57555000	–20º45’30”	–41º10’25”
Caiana	57700000	–20º41’38”	–41º55’19”
Dores do Rio Preto	57720000	–20º41’09”	–41º50’46”
Guaçuí	57740000	–20º46’25”	–41º40’54”
São José do Calçado	57770000	–21º02’12”	–41º39’08”
Ponte do Itabapoana	57830000	–21º12’22”	–41º27’46”
Mimoso do Sul	57880000	–21º03’53”	–41º21’45”
Santa Cruz	57930000	–21º13’21”	–41º18’31”

Variables Independent	VIF	Variables Independent	VIF
A, P	47.32	I, A, P, R	23.97
A, L	13.51	I, P, A, R	24.03
P, L	31.97	I, P, L, R	17.20
A, P, L	16.24	I, L, P, R	17.04
P, A, L	7.01	I, A, L, R	7.13
L, A, P	23.91	I, L, R, A	7.08
I, A, P	23.91	R, A, P, L	29.63
I, A, L	7.01	R, P, A, L	68.63
I, P, L	16.24	R, L, A, P	20.13
R, A, P	23.91	R, A, P, I	24.58
R, A, L	7.01	R, P, A, I	24.22
R, P, L	16.24	R, P, I, L	16.33
A, P, L, I	16.33	R, L, P, I	16.24
A, L, I, P	16.24	R, A, L, I	7.18
A, P, L, R	17.20	R, L, A, I	7.03
A, L, P, R	17.04	A, P, L, I, R	17.75
P, A, L, I	7.18	A, L, P, I, R	17.24
P, L, A, I	7.03	P, A, L, I, R	7.47
P, A, L, R	7.13	P, L, A, I, R	7.15
P, L, A, R	7.08	L, P, A, I, R	24.24
L, P, A, I	24.58	L, A, P, I, R	24.58
L, I, P, A	24.22	I, P, A, L, R	73.52
L, P, A, R	23.97	I, A, P, L, R	30.47
L, R, P, A	24.03	I, L, P, A, R	21.66
I, A, P, L	29.63	R, P, A, L, I	69.59
I, P, A, L	68.63	R, A, P, L, I	30.57
I, L, A, P	20.13	R, L, P, A, I	20.21

Independent Variables	Flows	Regional Function	R²
Area	₀	$Q_{50} =0 {.01922xA}^{0 .9338}$	0.96
	Q₅₅	$Q_{55} =0 {.01804xA}^{0 .9309}$	0.96
	Q₆₀	$Q_{60} =0 {.01702xA}^{0 .9285}$ .	0.96
	Q₆₅	$Q_{65} =0 {.01534xA}^{0 .9332}$	0.96
	Q₇₀	$Q_{70} =0 {.014724xA}^{0 .9290}$	0.96
	Q₇₅	$Q_{75} =0 {.01350xA}^{0 .9315}$	0.96
	Q₈₀	$Q_{80} =0 {.01239xA}^{0 .9321}$	0.96
	Q₈₅	$Q_{85} =0 {.01113xA}^{0 .9350}$	0.96
	Q₉₀	$Q_{90} =0 {.010281xA}^{0 .9316}$	0.95
	Q₉₅	$Q_{95} =0 {.009018xA}^{0 .9299}$	0.95
Perimeter	Q₅₀	$Q_{50} =0 {.001211xP}^{1 .75505}$	0.96
	Q₅₅	$Q_{55} =0 {.001143xP}^{1 .75013}$	0.96
	Q₆₀	$Q_{60} =0 {.001084xP}^{1 .74596}$	0.96
	Q₆₅	$Q_{65} =0 {.0009620xP}^{1 .7551}$	0.96
	Q₇₀	$Q_{70} =0 {.0009341xP}^{1 .7474}$	0.96
	Q₇₅	$Q_{75} =0 {.0008501xP}^{1 .7522}$	0.97
	Q₈₀	$Q_{80} =0 {.0007749xP}^{1 .7543}$	0.96
	Q₈₅	$Q_{85} =0 {.0006914xP}^{1 .7594}$	0.96
	Q₉₀	$Q_{90} =0 {.0006489xP}^{1 .7518}$	0.96
	Q₉₅	$Q_{95} =0 {.0005313xP}^{1 .7524}$	0.95
Perimeter and Slope	Q₅₀	$Q_{50} =0 {.0005434xP}^{1 .7395} {xS}^{-0 .7194}$	0.96
	Q₅₅	$Q_{55} =0 {.0005134xP}^{1 .7349} {xS}^{-0 .7189}$	0.96
	Q₆₀	$Q_{60} =0 {.0004547xP}^{1 .7294} {xS}^{-0 .7807}$	0.96
	Q₆₅	$Q_{65} =0 {.0003865xP}^{1 .7378} {xS}^{-0 .8186}$	0.96
	Q₇₀	$Q_{70} =0 {.0003702xP}^{1 .7299} {xS}^{-0 .8308}$	0.96
	Q₇₅	$Q_{75} =0 {.0003321xP}^{1 .7344} {xS}^{-0 .8438}$	0.96
	Q₈₀	$Q_{80} =0 {.0002798xP}^{1 .7350} {xS}^{-0 .9145}$	0.97
	Q₈₅	$Q_{85} =0 {.0002189xP}^{1 .7375} {xS}^{-1 .0326}$	0.96
	Q₉₀	$Q_{90} =0 {.0001893xP}^{1 .7282} {xS}^{-1 .1173}$	0.96
	Q₉₅	$Q_{95} =0 {.0001541xP}^{1 .7279} {xS}^{-1 .1600}$	0.96
Perimeter, Slope and Precipitation	Q₅₀	$Q_{50} =7 .383 {.10}^{-9} {xP}^{1 .7214} {xS}^{-0 .9643} {xR}^{1 .5172}$	0.96
	Q₅₅	$Q_{55} =2 .786 {.10}^{-8} {xP}^{1 .7188} {xS}^{-0 .9335} {xR}^{1 .3297}$	0.96
	Q₆₀	$Q_{60} =6 .515 {.10}^{-8} {xP}^{1 .7149} {xS}^{-0 .9741} {xR}^{1 .1983}$	0.96
	Q₆₅	$Q_{65} =7 .122 {.10}^{-8} {xP}^{1 .7237} {xS}^{-1 .0065} {xR}^{1 .1642}$	0.96
	Q₇₀	$Q_{70} =7 .332 {.10}^{-8} {xP}^{1 .7155} {xS}^{-1 .0172} {xR}^{1 .1545}$	0.96
	Q₇₅	$Q_{75} =2 .021 {.10}^{-7} {xP}^{1 .7222} {xS}^{-1 .0056} {xR}^{1 .0025}$	0.96
	Q₈₀	$Q_{80} =2 .628 {.10}^{-7} {xP}^{1 .7236} {xS}^{-1 .0668} {xR}^{0 .9437}$	0.96
	Q₈₅	$Q_{85} =6 .390 {.10}^{-8} {xP}^{1 .7242} {xS}^{-1 .2104} {xR}^{1 .1020}$	0.96
	Q₉₀	$Q_{90} =6 .283 {.10}^{-8} {xP}^{1 .7151} {xS}^{-1 .2921} {xR}^{1 .0829}$	0.96
	Q₉₅	$Q_{95} =2 .067 {.10}^{-7} {xP}^{1 .7170} {xS}^{-1 .3046} {xR}^{0 .8956}$	0.95

Independent Variables	Regional Function
Flow Q₅₀
Area	$Q_{50} =0 {.01922xA}^{0 .9338}$
Perimeter	$Q_{50} =0 {.001211xP}^{1 .75505}$
Perimeter and Slope	$Q_{50} =0 {.0005434xP}^{1 .7395} {xS}^{-0 .7194}$
Perimeter, Slope and Precipitation	$Q_{50} =7 .383 {.10}^{-9} {xP}^{1 .7214} {xS}^{-0 .9643} {xR}^{1 .5172}$
Flow Q₉₅
Area	$Q_{95} =0 {.009018xA}^{0 .9299}$
Perimeter	$Q_{95} =0 {.0005313xP}^{1 .7524}$
Perimeter and Slope	$Q_{95} =0 {.0001541xP}^{1 .7279} {xS}^{-1 .1600}$
Perimeter, Slope and Precipitation	$Q_{95} =2 .067 {.10}^{-7} {xP}^{1 .7170} {xS}^{-1 .3046} {xR}^{0 .8956}$

Stations	Average relative error (absolute values)	Nash-Sutcliffe coefficient
Usina Fortaleza	0.05	0.95
Iuna	0.28	0.36
Terra Corrida	0.08	0.88
Itaici	0.19	0.55
Ibitirama	0.29	0.17
Rive	0.03	0.98
Castelo	0.04	0.96
Usina São Miguel	0.02	0.99
Coutinho	0.04	0.95
Caiana	0.02	0.99
Dores do Rio Preto	0.15	0.75
Guaçui	0.12	0.77
São José do Calçado	0.37	0.22
Ponte do Itabapoana	0.12	0.77
Mimoso do Sul	0.05	0.95
Santa Cruz	0.21	0.51
Average	0.13	P1: 69%
		P2: 12%
		P3: 19%

Stations	Average relative error (absolute values)	Nash-Sutcliffe coefficient
Usina Fortaleza	0.09	0.85
Iuna	0.32	0.33
Terra Corrida	0.13	0.76
Itaici	0.27	0.41
Ibitirama	0.26	0.37
Rive	0.06	0.94
Castelo	0.11	0.84
Usina São Miguel	0.05	0.96
Coutinho	0.06	0.95
Caiana	0.08	0.91
Dores do Rio Preto	0.14	0.79
Guaçui	0.12	0.80
São José do Calçado	0.35	0.26
Ponte do Itabapoana	0.08	0.88
Mimoso do Sul	0.12	0.82
Santa Cruz	0.17	0.63
Average	0.15	P1: 69%
		P2: 6%
		P3: 25%

Stations	Regional indicators
Stations	Q	rcp₅₀	rcp₉₀	rcp₉₅
Usina Fortaleza	0.0244	0.6443	0.3035	0.2474
Iúna	0.0205	0.6753	0.4108	0.3566
Terra Corrida	0.0181	0.7276	0.3994	0.3597
Itaici	0.0185	0.6750	0.3515	0.3019
Ibitirama	0.0360	0.5477	0.2297	0.1972
Rive	0.0192	0.6546	0.3423	0.3010
Castelo	0.0153	0.6471	0.3260	0.2730
Usina São Miguel	0.0154	0.6795	0.3657	0.3119
Coutinho	0.0160	0.6622	0.3295	0.2766
Caiana	0.0162	0.7111	0.4107	0.3701
Dores do Rio Preto	0.0204	0.6297	0.2841	0.2298
Guaçuí	0.0255	0.6686	0.4389	0.4066
São José do Calçado	0.0131	0.6060	0.3445	0.3041
Ponte do Itabapoana	0.0162	0.7015	0.3576	0.3115
Mimoso do Sul	0.0192	0.7179	0.4088	0.3872
Santa Cruz	0.0154	0.6910	0.3722	0.3240
Average	0.0193	0.6650	0.3547	0.3099

[1] E-mails: viniciuspiol@hotmail.com (MVAP), jatreis@gmail.com (JATR), maccaiado@gmail.com (MACC), anserfm@terra.com.br (ASFM)

Brasil

Brasil

Performance evaluation of flow duration curves regionalization methods

Avaliação do desempenho de diferentes métodos de regionalização de curvas de permanência de vazões

ABSTRACT