Calibration methods for the Hargreaves-Samani equation

Ferreira, Lucas Borges; Cunha, Fernando França da; Duarte, Anunciene Barbosa; Sediyama, Gilberto Chohaku; Cecon, Paulo Roberto

doi:10.1590/1413-70542018421017517

ABSTRACT

The estimation of the reference evapotranspiration is an important factor for hydrological studies, design and management of irrigation systems, among others. The Penman Monteith equation presents high precision and accuracy in the estimation of this variable. However, its use becomes limited due to the large number of required meteorological data. In this context, the Hargreaves-Samani equation could be used as alternative, although, for a better performance a local calibration is required. Thus, the aim was to compare the calibration process of the Hargreaves-Samani equation by linear regression, by adjustment of the coefficients (A and B) and exponent (C) of the equation and by combinations of the two previous alternatives. Daily data from 6 weather stations, located in the state of Minas Gerais, from the period 1997 to 2016 were used. The calibration of the Hargreaves-Samani equation was performed in five ways: calibration by linear regression, adjustment of parameter “A”, adjustment of parameters “A” and “C”, adjustment of parameters “A”, “B” and “C” and adjustment of parameters “A”, “B” and “C” followed by calibration by linear regression. The performances of the models were evaluated based on the statistical indicators mean absolute error, mean bias error, Willmott’s index of agreement, correlation coefficient and performance index. All the studied methodologies promoted better estimations of reference evapotranspiration. The simultaneous adjustment of the empirical parameters “A”, “B” and “C” was the best alternative for calibration of the Hargreaves-Samani equation.

Index terms:
Evapotranspiration; irrigation; temperature; agrometeorology

[1] ^*Corresponding author: contato.lucasbf@gmail.com

Station	Latitude (°)	Longitude (°)	Altitude (m)
Januária	15.45 S	44.00 W	474
Lavras	21.75 S	45.00 W	919
Paracatu	17.24 S	46.88 W	712
Sete Lagoas	19.46 S	44.25 W	732
Uberaba	19.73 S	47.95 W	737
Viçosa	20.76 S	42.86 W	712

Station	Tmax (°C)	Tmin (°C)	n (h)	RH (%)	U₂ (m s^-1)	ET_o (mm d^-1)
Januária	31.7	18.4	8.1	66.2	1.5	4.5
Lavras	27.5	15.5	6.9	70.7	1.8	3.7
Paracatu	30.2	18.5	7.5	69.6	1.6	4.2
Sete Lagoas	28.7	16.5	7.3	67.1	1.0	3.7
Uberaba	30.0	17.1	7.4	66.8	1.3	4.0
Viçosa	27.0	15.7	5.7	79.8	0.9	3.1

Value of “PI”	Performance
> 0.85	Great
0.76 a 0.85	Very Good
0.66 a 0.75	Good
0.61 a 0.65	Medium
0.51 a 0.60	Not Good
0.41 a 0.50	Bad
≤ 0.40	Terrible

Calibration	A	AC		ABC			Lin		ABC+Lin
Parameter	A	A	C	A	B	C	a	b	a	b
Januária	0.0021	0.0013	0.6841	0.0019	2.8987	0.6943	-0.75	1.04	0.18	0.96
Lavras	0.0020	0.0011	0.7521	0.0011	15.5731	0.7542	-0.16	0.91	0.16	0.96
Paracatu	0.0021	0.0009	0.8311	0.0013	4.2191	0.8312	-0.40	0.98	0.39	0.91
Sete Lagoas	0.0019	0.0013	0.6379	0.0015	12.8973	0.6427	-0.28	0.90	0.04	1,00
Uberaba	0.0019	0.0011	0.7176	0.0015	7.3803	0.7199	-0.13	0.88	0.36	0.93
Viçosa	0.0018	0.0014	0.5881	0.0023	1.1669	0.6128	-0.52	0.89	0.08	0.98

Municipality	Index	HS	Lin	A	AC	ABC	ABC+Lin
Januária	MAE (mm d^-1)	0.74	0.62	0.64	0.61	0.61	0.61
	MBE (mm d^-1)	0.45	-0.08	-0.06	-0.09	-0.03	-0.03
	d	0.85	0.88	0.86	0.88	0.90	0.89
	r	0.81	0.81	0.81	0.82	0.82	0.82
	PI	0.69	0.72	0.70	0.72	0.74	0.73
	Classification	Good	Good	Good	Good	Good	Good
Lavras	MAE (mm d^-1)	0.62	0.47	0.48	0.44	0.44	0.44
	MBE (mm d^-1)	0.50	-0.06	-0.04	-0.12	-0.12	-0.08
	d	0.91	0.94	0.93	0.95	0.95	0.95
	r	0.89	0.89	0.89	0.91	0.91	0.91
	PI	0.81	0.84	0.83	0.86	0.86	0.86
	Classification	V. Good	V. Good	V. Good	Great	Great	Great
Paracatu	MAE (mm d^-1)	0.67	0.67	0.66	0.57	0.57	0.57
	MBE (mm d^-1)	0.30	-0.18	-0.13	-0.18	-0.18	-0.16
	d	0.87	0.87	0.86	0.90	0.91	0.90
	r	0.80	0.80	0.80	0.84	0.85	0.85
	PI	0.69	0.70	0.69	0.76	0.77	0.77
	Classification	Good	Good	Good	V. Good	V. Good	V. Good
Sete Lagoas	MAE (mm d^-1)	0.98	0.50	0.51	0.52	0.52	0.53
	MBE (mm d^-1)	0.94	0.17	0.16	0.22	0.22	0.25
	d	0.82	0.92	0.92	0.92	0.92	0.92
	r	0.87	0.87	0.87	0.87	0.87	0.87
	PI	0.71	0.80	0.80	0.81	0.81	0.80
	Classification	Good	V. Good	V. Good	V. Good	V. Good	V. Good
Uberaba	MAE (mm d^-1)	0.95	0.58	0.57	0.57	0.56	0.57
	MBE (mm d^-1)	0.85	0.12	0.06	0.07	0.06	0.14
	d	0.81	0.89	0.89	0.90	0.90	0.90
	r	0.82	0.82	0.82	0.82	0.82	0.82
	PI	0.66	0.73	0.72	0.73	0.74	0.74
	Classification	Good	Good	Good	Good	Good	Good
Viçosa	MAE (mm d^-1)	0.90	0.40	0.43	0.41	0.39	0.39
	MBE (mm d^-1)	0.89	-0.09	-0.10	-0.10	-0.08	-0.07
	d	0.86	0.95	0.94	0.94	0.96	0.95
	r	0.92	0.92	0.92	0.92	0.92	0.92
	PI	0.79	0.88	0.86	0.87	0.88	0.88
	Classification	V. Good	Great	Great	Great	Great	Great

Brasil

Brasil

Calibration methods for the Hargreaves-Samani equation

Métodos de calibração para a equação de Hargreaves-Samani

ABSTRACT