Multivariate adaptive regression splines (MARS) applied to daily reference evapotranspiration modeling with limited weather data

Ferreira, Lucas Borges; Duarte, Anunciene Barbosa; Cunha, Fernando França da; Fernandes Filho, Elpídio Inácio

doi:10.4025/actasciagron.v41i1.39880

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Acta Scientiarum. Agronomy

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AGRICULTURAL ENGINEERING • Acta Sci., Agron. 41 • 2019 • https://doi.org/10.4025/actasciagron.v41i1.39880 copy

Multivariate adaptive regression splines (MARS) applied to daily reference evapotranspiration modeling with limited weather data

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT.

Estimation of reference evapotranspiration (ET_o) is very relevant for water resource management. The Penman-Monteith (PM) equation was proposed by the Food and Agriculture Organization (FAO) as the standard method for estimation of ET_o. However, this method requires various weather data, such as air temperature, wind speed, solar radiation and relative humidity, which are often unavailable. Thus, the objective of this study was to compare the performance of multivariate adaptive regression splines (MARS) and alternative equations, in their original and calibrated forms, to estimate daily ET_o with limited weather data. Daily data from 2002 to 2016 from 8 Brazilian weather stations were used. ET_o was estimated using empirical equations, PM equation with missing data and MARS. Four data availability scenarios were evaluated as follows: temperature only, temperature and solar radiation, temperature and relative humidity, and temperature and wind speed. The MARS models demonstrated superior performance in all scenarios. The models that used solar radiation showed the best performance, followed by those that used relative humidity and, finally, wind speed. The models based only on air temperature had the worst performance.

Keywords:
data driven; irrigation scheduling; agrometeorology; artificial intelligence

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E-mail: actaagron@uem.br

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[1] *Author for correspondence. E-mail: contato.lucasbf@gmail.com

Station	Latitude (°)	Longitude (°)	Altitude (m)	Köppen classification
Araxá - MG	-19.60	-46.94	1024	Cwb
Cabrobó - PE	-8.51	-39.33	341	Bsh
Curitiba - PR	-25.43	-49.26	924	Cfb
Eirunepé - AM	-6.66	-69.86	104	Af
Lages - SC	-27.81	-50.33	937	Cfb
Macapá - AP	-0.05	-51.11	14	Am
Palmas - TO	-10.19	-48.30	280	Aw
Santa Maria - RS	-29.70	-53.70	95	Cfa

Station	Tmax	Tmin	n	RH	U₂	ET_o
Araxá - MG	27.8 (±2.8)	17.0 (±2.5)	6.9 (±3.4)	67.8 (±15.2)	1.9 (±0.7)	3.9 (±1.1)
Cabrobó - PE	32.6 (±2.5)	22.2 (±1.7)	8.0 (±3.0)	59.8 (±13.9)	3.1 (±1.2)	5.9 (±1.7)
Curitiba - PR	24.0 (±4.7)	13.7 (±4.0)	5.1 (±3.6)	80.3 (±9.4)	1.6 (±0.6)	2.9 (±1.3)
Eirunepé - AM	33.5 (±2.5)	21.7 (±1.7)	3.9 (±2.9)	86.0 (±5.1)	0.1 (±0.2)	3.2 (±0.8)
Lages - SC	22.3 (±5.2)	11.9 (±4.8)	5.4 (±3.7)	81.3 (±9.3)	0.9 (±0.6)	2.7 (±1.3)
Macapá - AP	32.1 (±1.8)	24.0 (±0.8)	6.8 (±3.2)	80.5 (±7.9)	1.5 (±0.8)	4.3 (±1.2)
Palmas - TO	33.8 (±2.8)	22.3 (±1.8)	6.9 (±3.3)	66.6 (±17.1)	0.9 (±0.7)	4.3 (±1.2)
Santa Maria - RS	25.5 (±6.1)	14.7 (±5.5)	6.2 (±4.1)	77.7 (±11.6)	1.5 (±0.7)	3.1 (±1.7)

Model basis	Model	Tmax	Tmin	Ra	Rs	RH	U₂
Temperature	MARS1	✓	✓	✓
	PMT	✓	✓	✓
	HS	✓	✓	✓
	OUD	✓	✓	✓
Temperature and solar radiation	MARS2	✓	✓		✓
	PMR	✓	✓	✓	✓
	MAK	✓	✓		✓
	JH	✓	✓		✓
Temperature and relative humidity	MARS3	✓	✓	✓		✓
	PMH	✓	✓	✓		✓
	ROM	✓	✓			✓
	VLT	✓	✓	✓		✓
Temperature and wind speed	MARS4	✓	✓	✓			✓
	PMW	✓	✓	✓			✓

Station	Index	MARS1	PMT	PMTcal	HS	HScal	OUD	OUDcal
Araxá	RMSE	0.66	0.70	0.70	0.79	0.74	1.04	1.02
	MAE	0.53	0.56	0.56	0.63	0.59	0.86	0.82
	R²	0.71	0.68	0.68	0.65	0.65	0.33	0.33
Cabrobó	RMSE	0.88	1.90	0.92	1.57	0.94	1.85	1.20
	MAE	0.70	1.69	0.73	1.37	0.76	1.62	0.98
	R²	0.68	0.66	0.66	0.65	0.65	0.43	0.43
Curitiba	RMSE	0.53	0.67	0.55	0.86	0.56	0.96	0.84
	MAE	0.39	0.55	0.41	0.71	0.42	0.76	0.70
	R²	0.84	0.83	0.83	0.83	0.83	0.59	0.59
Eirunepé	RMSE	0.51	1.76	0.54	2.12	0.56	1.71	0.73
	MAE	0.39	1.66	0.43	2.03	0.45	1.54	0.62
	R²	0.61	0.56	0.56	0.53	0.53	0.21	0.21
Lages	RMSE	0.52	0.89	0.52	1.10	0.53	0.89	0.76
	MAE	0.39	0.75	0.40	0.94	0.39	0.68	0.61
	R²	0.84	0.84	0.84	0.84	0.84	0.64	0.64
Macapá	RMSE	0.62	0.90	0.77	0.82	0.78	1.12	0.90
	MAE	0.47	0.75	0.61	0.68	0.61	0.88	0.76
	R²	0.71	0.55	0.55	0.55	0.55	0.39	0.39
Palmas	RMSE	0.87	1.10	1.00	1.32	1.05	1.41	1.34
	MAE	0.65	0.91	0.72	1.16	0.76	1.12	1.02
	R²	0.61	0.47	0.47	0.41	0.41	0.05	0.05
Santa	RMSE	0.64	0.85	0.75	1.01	0.73	1.05	1.00
Maria	MAE	0.45	0.67	0.54	0.81	0.51	0.79	0.77
	R²	0.86	0.81	0.81	0.82	0.82	0.67	0.67
Mean	RMSE	0.65	1.10	0.72	1.20	0.74	1.25	0.97
	MAE	0.50	0.94	0.55	1.04	0.56	1.03	0.78
	R²	0.73	0.67	0.67	0.66	0.66	0.41	0.41

Station (a)	Index	MARS2	PMR	PMRcal	MAK	MAKcal	JH	JHcal
Araxá	RMSE	0.37	0.41	0.41	0.84	0.42	1.17	0.40
	MAE	0.28	0.33	0.32	0.71	0.30	1.02	0.30
	R²	0.91	0.89	0.89	0.89	0.89	0.90	0.90
Cabrobó	RMSE	0.69	1.38	0.69	2.35	0.72	1.04	0.70
	MAE	0.55	1.20	0.55	2.22	0.56	0.84	0.55
	R²	0.81	0.82	0.82	0.80	0.80	0.81	0.81
Curitiba	RMSE	0.24	0.41	0.30	0.51	0.34	0.93	0.25
	MAE	0.17	0.35	0.21	0.41	0.25	0.74	0.18
	R²	0.97	0.95	0.95	0.93	0.93	0.96	0.96
Eirunepé	RMSE	0.08	1.05	0.22	0.47	0.11	1.72	0.08
	MAE	0.06	1.01	0.17	0.46	0.08	1.61	0.06
	R²	0.99	0.92	0.92	0.98	0.98	0.99	0.99
Lages	RMSE	0.20	0.58	0.25	0.33	0.28	0.86	0.22
	MAE	0.15	0.53	0.19	0.27	0.22	0.67	0.17
	R²	0.98	0.96	0.96	0.95	0.95	0.97	0.97
Macapá	RMSE	0.25	0.36	0.29	0.82	0.29	2.07	0.27
	MAE	0.18	0.31	0.23	0.75	0.23	1.99	0.21
	R²	0.95	0.93	0.93	0.94	0.94	0.95	0.95
Palmas	RMSE	0.73	0.87	0.78	1.27	0.81	1.92	0.76
	MAE	0.44	0.71	0.50	0.97	0.49	1.75	0.46
	R²	0.72	0.67	0.67	0.67	0.67	0.70	0.70
Santa	RMSE	0.40	0.63	0.50	0.71	0.54	1.33	0.43
Maria	MAE	0.26	0.50	0.33	0.51	0.36	1.07	0.28
	R²	0.95	0.91	0.91	0.90	0.90	0.94	0.94
Mean	RMSE	0.37	0.71	0.43	0.91	0.44	1.38	0.39
	MAE	0.26	0.62	0.31	0.79	0.31	1.21	0.28
	R²	0.91	0.88	0.88	0.88	0.88	0.90	0.90

Station (b)	Index	MARS3	PMH	PMHcal	ROM	ROMcal	VLT	VLTcal
Araxá	RMSE	0.46	0.51	0.51	1.79	0.84	0.75	0.50
	MAE	0.35	0.41	0.40	1.37	0.70	0.60	0.40
	R²	0.86	0.83	0.83	0.54	0.54	0.83	0.83
Cabrobó	RMSE	0.71	1.29	0.76	2.36	0.94	1.98	0.75
	MAE	0.55	1.10	0.60	1.99	0.76	1.78	0.59
	R²	0.80	0.76	0.76	0.72	0.72	0.77	0.77
Curitiba	RMSE	0.38	0.46	0.45	0.91	0.72	0.57	0.45
	MAE	0.29	0.35	0.34	0.76	0.58	0.41	0.34
	R²	0.92	0.89	0.89	0.70	0.70	0.89	0.89
Eirunepé	RMSE	0.49	1.09	0.52	1.21	0.64	0.58	0.52
	MAE	0.38	0.96	0.42	1.01	0.50	0.47	0.41
	R²	0.64	0.59	0.59	0.39	0.39	0.59	0.59
Lages	RMSE	0.37	0.50	0.43	1.14	0.75	0.48	0.42
	MAE	0.28	0.36	0.32	0.95	0.59	0.35	0.32
	R²	0.92	0.88	0.88	0.70	0.70	0.89	0.89
Macapá	RMSE	0.46	0.78	0.54	0.94	0.51	1.33	0.55
	MAE	0.34	0.66	0.41	0.78	0.39	1.16	0.42
	R²	0.85	0.79	0.79	0.83	0.83	0.78	0.78
Palmas	RMSE	0.79	0.95	0.82	2.89	0.87	0.87	0.82
	MAE	0.56	0.76	0.58	2.13	0.68	0.62	0.59
	R²	0.68	0.64	0.64	0.61	0.61	0.64	0.64
Santa	RMSE	0.49	0.54	0.54	0.99	0.86	0.73	0.56
Maria	MAE	0.37	0.38	0.37	0.78	0.68	0.52	0.40
	R²	0.92	0.90	0.90	0.76	0.76	0.89	0.89
Mean	RMSE	0.52	0.76	0.57	1.53	0.77	0.91	0.57
	MAE	0.39	0.62	0.43	1.22	0.61	0.74	0.43
	R²	0.82	0.78	0.78	0.65	0.65	0.79	0.79