Regionalization of hydrological model parameters for the semi-arid region of the northeast Brazil

Virães, Múcio Valença; Cirilo, José Almir

doi:10.1590/2318-0331.241920180114

Múcio Valença Virães

Companhia de Pesquisa de Recursos Minerais, Serviço Geológico do Brasil, Recife, PE, Brasil

http://orcid.org/0000-0001-9739-7099

José Almir Cirilo

Universidade Federal de Pernambuco, Caruaru, PE, Brasil

http://orcid.org/0000-0002-8672-0898

E-mails: mucio.viraes@cprm.gov.br (MVV), almir.cirilo@gmail.com (JAC)

Múcio Valença Virães: Paper conception, research, literature review, data analysis, results, discussion and paper writing.

José Almir Cirilo: Paper conception, research, literature review, discussion, paper revision and writing.

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Figure 1
Schematic representation of the processes of the hydrological cycle in MODHAC. Source: (Lanna, 1997LANNA, A. E. MAG1 – MODHAC97: modelo hidrológico auto-calibrável. Porto Alegre: Instituto de Pesquisas Hidráulicas da UFRGS, 1997.).

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Figure 2
Study area in northeastern semi-arid boundaries, according to cartographic data of IBGE (2013)IBGE – Instituto Brasileiro de Geografia e Estatística. Base cartográfica. Rio de Janeiro, 2013. Escala 1:250.000. Available from: <http://mapas.ibge.gov.br/bases-e-referenciais/bases-cartograficas/cartas>. Access on: 02 apr. 2013.
http://mapas.ibge.gov.br/bases-e-referen... and INSA (2014)INSA – Instituto Nacional do Semiárido. Acervo digital. Campina Grande, 2014. Available from: <www.insa.gov.br/sigsab/acervoDigital>. Access on: 26 sept. 2017.
www.insa.gov.br/sigsab/acervoDigital... . Fluviometric reference stations: Iguatu (a), Icó (b), Piancó (c), Poço de Pedras (d), Ilha Grande (e), Toritama (f), Capivara (g), Oiticica (h) and Mossoró (i).

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Figure 3
Flow rates calculated in the Iguatu station with MODHAC for evapotranspiration estimated by the INMET Climatological Normals of the station and by the average of 04 stations in the region (Northeast Atlas). Period 1973-1974.

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Figure 4
Modeling of the Icó station, period 1988-1999.

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Figure 5
Permanence curves of the observed and simulated flow for the Floresta station from the parameters calibrated at the Poço de Pedras, Ilha Grande, and Piancó stations: a) larger flows; b) smaller flows.

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Figure 6
Permanence curves of the observed and simulated flow for the Iguatu station from the parameters calibrated at the Icó station: a) higher flows; b) smaller flows.

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Figure 7
Box plot graph of all results obtained between observed flow and simulated flow considering the performance indicators NSE, NSE_sqrtQ, NSE_logQ, PBias, and RSR (first and third quartiles, median and extreme values).

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Table 1
Description of the MODHAC parameters.

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Table 2
Fluviometric stations selected for analysis, where A is the station’s drainage area, Qm is the average annual flow, PMA is the average annual rainfall, C_esc is the surface runoff coefficient, and C_ris is the percentage of the station’s drainage area over the karstic and/or fractured aquifer.

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Table 3
Recommended performance values for monthly simulations.

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Table 4
Best performance indicators for full series data of the reference gauge stations.

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Table 5
Calibrated parameters of Iguatu (a), Icó (b) and Oiticica (h) stations in the state of Ceará, Piancó (c) and Poço de Pedras (d) in the state of Paraíba, Ilha Grande (e), Toritama (f), and Capivara (g) in the state of Pernambuco, and Mossoró (i) in the state of Rio Grande do Norte, which were selected for regionalization.

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Table 6
Evaporimetric data used to estimate the evapotranspiration for modeling the Iguatu station.

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Table 7
Performance indicators for regionalization of parameters concerning the permanence curves: Iguatu and Floresta stations.

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(2)

(3)

(4)

(5)

(6)

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Parameters	Designation
RSPX	Maximum capacity of the surface reservoir [mm].
RSSX	Maximum capacity of the subsurface reservoir [mm].
RSBX	Maximum capacity of the underground reservoir [mm].
RSBY	Minimum storage to occur contribution from the underground reservoir to base flow [mm].
IMAX	Soil permeability [mm].
IMIN	Minimum infiltration [mm].
IDEC	Empirical infiltration coefficient (0-1) [dimensionless].
ASP	Exponent of the surface reservoir emptying law [dimensionless].
ASS	Exponent of the subsurface reservoir emptying law [dimensionless].
ASBX	Exponent of the underground reservoir emptying law [dimensionless].
ASBY	Adjustment of the hydrographic recession curve [dimensionless].
PRED	Precipitation correction [dimensionless].
CEVA	Soil evapotranspiration [dimensionless].
CHET	ETP fraction supplied directly from the rain [dimensionless].

Code	A (km²)	Qm (mm/ano)	PMA (mm)	C_esc	C_ris (%)
34730000	1,031	80.37	654.9	0.123	0.0
34740000	2,216	57.03	791.1	0.072	0.0
34741000	10,730	32.86	682.3	0.048	92.2
35125000	1,498	193.00	989.9	0.195	96.4
35210000	1,563	102.80	758.3	0.136	100.0
35223000	698	214.45	1,011.0	0.212	82.6
35235000	3,653	113.72	844.6	0.135	95.7
35240000	1,530	96.81	747.2	0.130	100.0
35258000	2,375	29.69	736.9	0.040	100.0
35275000	11,273	155.22	811.4	0.191	95.9
35830000	1,599	89.89	809.2	0.111	100.0
36045000	3,454	24.38	684.0	0.036	93.3
36070000	13,671	27.11	649.9	0.042	95.8
36125000	3,632	44.73	739.3	0.061	80.4
36130000	6,183	59.84	826.9	0.072	77.8
36160000	20,824	40.70	717.0	0.057	89.3
36270000	8,910	81.58	885.3	0.092	47.2
36290000	12,203	66.41	894.2	0.074	59.1
36320000	39,689	43.32	787.1	0.055	79.0
36390000	48,283	62.74	780.5	0.080	80.7
36470000	4,525	63.26	780.5	0.081	100.0
36520000	7,038	49.47	656.2	0.075	100.0
36580000	17,237	193.00	705.3	0.274	99.5
37030000	2,197	77.72	709.1	0.110	98.8
37080000	6,588	61.91	728.1	0.085	85.9
37084000	7,690	16.31	718.6	0.023	85.2
37090000	9,786	26.70	698.3	0.038	86.6
37260000	1,451	55.99	826.3	0.068	63.5
37340000	4,555	83.93	704.7	0.119	96.4
37410000	15,212	78.60	725.1	0.108	89.1
37470000	21,639	75.74	686.1	0.110	91.6
37515000	1,868	33.12	497.8	0.067	99.7
37559000	6,316	6.95	504.0	0.014	96.1
37570000	9,714	41.02	517.8	0.079	97.3
37710150	38,061	50.35	616.6	0.082	93.3
38830000	5,033	31.60	597.2	0.053	100.0
38850000	3,181	38.71	537.1	0.072	100.0
38860000	13,648	80.25	520.7	0.154	99.6
39130000	2,443	31.67	529.4	0.060	100.0
39340000	1,973	45.66	582.6	0.078	100.0
39540000	2,628	44.45	592.1	0.075	100.0
48820000	3,537	88.42	617.4	0.143	99.8
48860000	12,276	68.74	622.8	0.110	87.9
48880000	2,263	26.21	583.3	0.045	89.7
49160000	8,241	16.40	589.1	0.028	58.9

Recommended Performance Values for Monthly Simulations	*NSE*	*Pbias (%)*	*RSR*
Very good	0.75 to 1.00	< ±10	0 to 0.5
Good	0.65 to 0.75	±10 to ±15	0.5 to 0.6
Satisfactory	0.50 to 0.65	±15 to ±25	0.6 to 0.7
Insufficient	< 0.50	> ±25	> 0.7

Code	Name	Parameters	NSE	R²	RMSE	AAPE	RSR	PBias	NSE	NSE
Code	Name	“donor basins”	NSE	R²	RMSE	AAPE	RSR	PBias	*sqrtQ*	*logQ*
34741000	Oiticica	Oiticica	0.55	0.64	7.75	1.15	0.67	-5.94	0.54	-5.52
36160000	Iguatu	Icó	0.81	0.81	4.97	19.57	0.44	0.69	0.81	0.53
36290000	Icó	Icó	0.72	0.76	7.26	6.38	0.53	4.49	0.75	0.59
37090000	Mossoró	Mossoró	0.59	0.78	4.50	4.03	0.64	-1.01	0.65	-0.31
37470000	Piancó	Icó	0.66	0.67	11.32	6.09	0.58	-10.95	0.76	0.67
38850000	Poço de Pedras	Piancó	0.60	0.62	7.70	1.46	0.63	-39.33	0.62	-2.42
39130000	Toritama	Capivara	0.39	0.59	7.85	18.02	0.78	25.39	0.41	-0.05
39540000	Capivara	Capivara	-0.66	0.49	11.36	2.84	1.29	37.11	0.34	0.11
48880000	Ilha Grande	Piancó	0.52	0.53	6.15	1.69	0.69	-40.82	0.31	-1.97

Parameters	Stations
Parameters	a	b	c	d	e	f	g	h	i
RSPX	97	121	49.82	40	6.5	8.0	17.3	300	300
RSSX	376.6	519.3	530	300	288	239.2	103	200	300
RSBX	30.05	19.67	0.0	20	0.0	0.0	0.0	0	30
RSBY	145.8	145.8	0.0	20	0.0	0.0	0.0	0	1.0
IMAX	50	78.91	181	24.18	228.5	267.7	100	80	30
IMIN	0.4969	0.4969	2.0	7.0	31.65	8.813	0	0.5	0.5
IDEC	0.3025	0.2275	0.29	0.7964	0.534	0.4546	0.19	0.1	0.3
ASP	3.902	1.668	0.01	0.2525	0.4478	0.1776	0.9	0.5	100
ASS	0.1017	0.1017	0.08	0.9555	0.152	0.1	0.18	0.1	0.035
ASBX	0.4585	0.4585	0.0	0.5	0.0	0.0	0.0	0.0	0.0001
*ASBY (10^-3)**	66,192	37.9	0.0	500	0.0	0.0	0.0	0.0	0.005
PRED	999	999	999	999	999	999.9	999	999	999
CEVA	0.99	1.0	0.7459	0.1	0.3	0.3	0.3	1.0	0.99
CHET	1.0	1.0	0.9	0.8	0.8	0.75	0.9	1.0	1.0

Jan	Feb	Mar	Apr	Mai	Jun	Jul	Aug	Set	Oct	Nov	Dec
Evaporimetric Data (Average of 04 basin stations - Northeast Atlas project)
190.8	138.55	104.15	105.67	136.07	159.90	216.37	265.65	281.47	282.97	262.25	247.47
Evaporimetric Data (INMET Climatic Standard) - 82686 - Iguatu
158.8	103.7	90.2	80.2	95.7	127.9	172.6	205.3	217.5	230.1	215.5	203.1

Code	Name	Parameter	NSE	R²	RMSE	AAPE	RSR	PBias	NSE_sqrtQ	NSE_logQ
36160000	Iguatu	Icó	0.98	0.98	1.63	20.53	0.14	0.69	0.93	0.62
48860000	Floresta	Poço de Pedras	-0.13	0.98	17.82	0.47	1.06	88.41	0.78	0.89
48860000	Floresta	Ilha Grande	0.70	0.96	9.19	0.88	0.55	52.41	0.84	0.82
48860000	Floresta	Piancó	0.93	0.94	4.52	0.82	0.27	-10.11	0.90	-1.16

N S E = 1 - \frac{\sum_{i = 1}^{n} {(Q_{i, o b s} - Q_{i, c a l})}^{2}}{\sum_{i = 1}^{n} {(Q_{i, o b s} - \bar{Q_{o b s}})}^{2}}

N S E_{s q r t Q} = 1 - \frac{\sum_{i = 1}^{n} {(\sqrt{Q_{i, o b s}} - \sqrt{Q_{i, c a l}})}^{2}}{\sum_{i = 1}^{n} {(\sqrt{Q_{i, o b s}} - \sqrt{\bar{Q_{o b s}}})}^{2}}

N S E_{l o g Q} = 1 - \frac{\sum_{i = 1}^{n} {(\log Q_{i, o b s} - \log Q_{i, c a l})}^{2}}{\sum_{i = 1}^{n} {(\log Q_{i, o b s} - \log \bar{Q_{o b s}})}^{2}}

R S R = |\frac{{[\sum_{i = 1}^{n} {(Q_{i, o b s} - Q_{i, c a l})}^{2}]}^{1 / 2}}{{[\sum_{i = 1}^{n} {(Q_{i, o b s} - \bar{Q_{o b s}})}^{2}]}^{1 / 2}}|

[1] E-mails: mucio.viraes@cprm.gov.br (MVV), almir.cirilo@gmail.com (JAC)

Brasil

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Regionalization of hydrological model parameters for the semi-arid region of the northeast Brazil

Regionalização de parâmetros de modelo hidrológico para a região semiárida do nordeste brasileiro

RESUMO