Calibration of Methods to Estimate Solar Irradiance in Northeastern Pará

Pinto, João Vitor de Nóvoa; Nunes, Hildo Giuseppe Garcia Caldas; Souza, Daniely Florencia Silva de; Costa, Deborah Luciany Pires; Souza, Paulo Jorge de Oliveira Ponte de

doi:10.1590/0102-7786352002

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Article • Rev. bras. meteorol. 35 (2) • Apr-Jun 2020 • https://doi.org/10.1590/0102-7786352002 copy

Calibration of Methods to Estimate Solar Irradiance in Northeastern Pará

Calibração de Métodos para Estimativa da Irradiância Solar no Nordeste do Pará

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Two models aimed to estimate solar irradiance were calibrated in six locations in Northeastern Pará (Belém, Cametá, Conceição do Araguaia, Marabá, Soure, and Tucuruí). The first one is the equation of Angström-Prescott (AP), which requires observations of sunshine duration hours. The second model is a modified version of Hargreaves' radiation formula (MH), which requires observations of daily maximum and daily minimum air temperatures. Both models were calibrated to estimate daily and monthly solar radiation. The calibration of both equations for each season (i.e., dry season and wet season) in each location was also tested. AP has an average performance about 74% higher than MH for daily estimates (excluding Soure) and 83% higher than MH for monthly estimates (excluding Soure and Tucuruí). The use of seasonally calibrated equations slightly improves the performance of AP, measured by the performance index, by 0.68% and improves the performance of MH in most locations, when estimating daily solar radiation. The performance of both models is much higher when estimating monthly solar radiation than daily solar radiation, with an increase of the performance index of 10.95% for AP.

Keywords:
global radiation; evapotranspiration; Angström-Prescott; temperature; sunshine duration hours

Location	Latitude	Longitude	Period	Dry season
BEL	-1.4112	-48.4395	From 01-20-2003 to 12-31-2016	Aug-Nov
CAM	-2.2397	-49.4998	From 06-22-2008 to 12-31-2016	Aug-Nov
CON	-8.3036	-49.2828	From 09-04-2008 to 12-31-2016	May-Sep
MAR	-5.3664	-49.0512	From 06-25-2009 to 12-31-2016	May-Oct
SOU	-0.7278	-48.5158	From 04-27-2008 to 12-31-2016	Aug-Dec
TUC	-3.8228	-49.6750	From 03-01-2008 to 12-31-2016	Jun-Nov

Location	Season	AP			MH
Location	Season	Calibration	Validation	Total	Calibration	Validation	Total
BEL	Wet	1339	540	1879	1287	576	1863
BEL	Dry	672	324	996	697	291	988
CAM	Wet	1145	459	1604	1139	476	1615
CAM	Dry	688	298	986	663	276	939
CON	Wet	1020	416	1436	1038	435	1473
CON	Dry	738	321	1059	806	371	1177
MAR	Wet	710	289	999	771	324	1095
MAR	Dry	771	340	1111	935	397	1332
SOU	Wet	1185	518	1703	1155	489	1644
SOU	Dry	768	344	1112	844	370	1214
TUC	Wet	1006	451	1457	1101	474	1575
TUC	Dry	970	419	1389	1081	457	1538
Total	-	11012	4719	15731	11516	4937	16753

Location	AP			MH
Location	Calibration	Validation	Total	Calibration	Validation	Total
BEL	64	28	92	64	27	91
CAM	59	26	85	58	25	83
CON	54	23	77	57	25	82
MAR	46	20	66	53	23	76
SOU	62	26	88	66	28	94
TUC	62	27	89	71	30	101

Location	Angström-Prescott			Modified Hargreaves' equation
Location	a_s	b_s	a_s + b_s	a_h	b_h
BEL	0.227** ± 0.009	0.352** ± 0.015	0.579	-0.308** ± 0.060	0.244** ± 0.020
CAM	0.290** ± 0.008	0.434** ± 0.013	0.720	-0.199** ± 0.069	0.268** ± 0.024
CON	0.258** ± 0.008	0.455** ± 0.012	0.712	-0.176** ± 0.032	0.202** ± 0.009
MAR	0.305** ± 0.008	0.390** ± 0.014	0.695	-0.198** ± 0.035	0.229** ± 0.011
SOU	0.329** ± 0.007	0.385** ± 0.012	0.716	0.517** ± 0.069	0.015 ± 0.029
TUC	0.284** ± 0.008	0.363** ± 0.014	0.643	-0.088** ± 0.047	0.200** ± 0.017
For all locations	0.276** ± 0.004	0.407** ± 0.007	0.682	0.270** ± 0.018	0.081** ± 0.006

City	Season	AP	MH
BEL	Wet	0.658	0.336
	Dry	0.463	0.107
	-	0.652	0.334
CAM	Wet	0.822	0.389
	Dry	0.707	0.088
	-	0.812	0.311
CON	Wet	0.807	0.628
	Dry	0.800	0.427
	-	0.840	0.641
MAR	Wet	0.713	0.641
	Dry	0.735	0.489
	-	0.781	0.625
SOU	Wet	0.766	0.051
	Dry	0.750	0.022
	-	0.788	0.001
TUC	Wet	0.664	0.393
	Dry	0.661	0.135
	-	0.689	0.305
For all locations	-	0.693	0.098

Location	Season	Seasonal Angström-Prescott equation (S-AP)			Seasonal modified Hargreaves equation (S-MH)¹
Location	Season	a_s	b_s	a_s + b_s	a_h	b_h
BEL	Wet	0.232** ± 0.010	0.340** ± 0.018	0.572	-0.304** ± 0.071	0.239** ± 0.024
BEL	Dry	0.209** ± 0.028	0.383** ± 0.041	0.592	-0.007 ± 0.136	0.153** ± 0.044
CAM	Wet	0.285** ± 0.010	0.449** ± 0.016	0.734	-0.353** ± 0.086	0.318** ± 0.030
CAM	Dry	0.295** ± 0.020	0.418** ± 0.027	0.713	0.284** ± 0.101	0.109** ± 0.035
CON	Wet	0.247** ± 0.010	0.496** ± 0.020	0.743	-0.349** ± 0.051	0.258** ± 0.016
CON	Dry	0.243** ± 0.017	0.460** ± 0.022	0.703	0.026 ± 0.061	0.149** ± 0.016
MAR	Wet	0.297** ± 0.012	0.407** ± 0.025	0.704	-0.430** ± 0.062	0.310** ± 0.022
MAR	Dry	0.323** ± 0.014	0.364** ± 0.020	0.687	-0.045* ± 0.054	0.183** ± 0.016
SOU	Wet	0.324** ± 0.009	0.415** ± 0.017	0.739	0.205** ± 0.100	0.128** ± 0.041
SOU	Dry	0.325** ± 0.015	0.374** ± 0.020	0.699	0.714** ± 0.065	-0.049** ± 0.029
TUC	Wet	0.288** ± 0.010	0.360** ± 0.021	0.648	-0.231** ± 0.066	0.248** ± 0.024
TUC	Dry	0.269** ± 0.015	0.381** ± 0.023	0.650	0.138** ± 0.074	0.127** ± 0.025

Location	Model¹ 1Different letters indicate statistically different average of residuals.		r	d	c	me	rmse	pbias
BEL	AP	a	0.796	0.877	0.698	-0.067	2.095	-0.4
	S-AP	a	0.798	0.879	0.702	-0.065	2.083	-0.4
	MH	a	0.571	0.710	0.406	0.069	2.858	0.5
	S-MH	a	0.594	0.735	0.437	0.073	2.804	0.5
	R-AP	b	0.796	0.765	0.609	2.770	3.493	18.1
	R-MH	c	0.382	0.494	0.189	3.321	4.626	21.8
	AP-FAO	c	0.794	0.718	0.570	3.714	4.412	24.2
	AP-LAT	d	0.795	0.604	0.480	5.555	6.073	36.3
CAM	AP	c	0.911	0.952	0.867	-0.036	1.490	-0.2
	S-AP	c	0.913	0.952	0.870	-0.045	1.473	-0.2
	MH	c	0.484	0.663	0.321	-0.003	3.107	0.0
	S-MH	c	0.561	0.726	0.408	0.054	2.942	0.3
	R-AP	b	0.911	0.920	0.838	-1.170	1.905	-5.7
	R-MH	a	0.331	0.475	0.157	-2.262	4.008	-11.1
	AP-FAO	c	0.911	0.953	0.869	0.047	1.570	0.2
	AP-LAT	d	0.911	0.893	0.814	1.932	2.525	9.5
CON	AP	ab	0.893	0.938	0.838	-0.060	2.072	-0.3
	S-AP	b	0.899	0.944	0.849	-0.035	2.009	-0.2
	MH	ab	0.757	0.851	0.644	-0.058	2.982	-0.3
	S-MH	b	0.782	0.873	0.683	-0.033	2.852	-0.2
	R-AP	a	0.894	0.924	0.826	-0.400	2.182	-2.1
	R-MH	c	0.530	0.563	0.298	1.094	4.069	5.9
	AP-FAO	c	0.892	0.938	0.836	0.597	2.175	3.2
	AP-LAT	d	0.893	0.884	0.789	2.331	3.141	12.5
MAR	AP	b	0.850	0.913	0.776	0.049	2.097	0.3
	S-AP	b	0.853	0.915	0.780	0.062	2.082	0.3
	MH	b	0.752	0.846	0.636	0.067	2.726	0.4
	S-MH	b	0.780	0.870	0.679	0.011	2.589	0.1
	R-AP	a	0.852	0.911	0.776	-0.664	2.191	-3.6
	R-MH	b	0.479	0.499	0.239	0.456	3.701	2.5
	AP-FAO	b	0.853	0.920	0.785	0.218	2.299	1.2
	AP-LAT	c	0.853	0.869	0.741	1.987	3.086	10.8
SOU	AP	d	0.882	0.936	0.825	-0.095	2.081	-0.5
	S-AP	d	0.888	0.939	0.834	-0.084	2.026	-0.4
	MH	d	0.013	0.191	0.003	0.136	4.749	0.7
	S-MH	d	0.450	0.581	0.262	0.142	4.188	0.7
	R-AP	b	0.883	0.907	0.801	-1.577	2.621	-7.9
	R-MH	a	0.022	0.418	0.009	-3.096	5.671	-15.7
	AP-FAO	c	0.883	0.929	0.820	-0.549	2.504	-2.8
	AP-LAT	e	0.883	0.911	0.805	1.302	2.874	6.5
TUC	AP	a	0.829	0.896	0.742	0.006	2.019	0.0
	S-AP	a	0.830	0.897	0.744	0.006	2.012	0.0
	MH	a	0.541	0.705	0.382	-0.055	3.120	-0.3
	S-MH	a	0.552	0.715	0.395	-0.068	3.094	-0.4
	R-AP	b	0.826	0.898	0.742	0.522	2.111	3.1
	R-MH	b	0.380	0.512	0.194	0.857	3.506	5.0
	AP-FAO	c	0.819	0.874	0.716	1.302	2.649	7.7
	AP-LAT	d	0.821	0.777	0.638	3.091	3.891	18.3

Location	Angström-Prescott			Modified Hargreaves' equation
Location	a_s	b_s	a_s + b_s	a_h	b_h
BEL	0.234** ± 0.034	0.338** ± 0.059	0.572	-0.408** ± 0.356	0.278** ± 0.118
CAM	0.321** ± 0.026	0.384** ± 0.040	0.705	-0.565** ± 0.464	0.394** ± 0.161
COM	0.291** ± 0.031	0.397** ± 0.050	0.687	-0.044 ± 0.135	0.163** ± 0.038
MAR	0.298** ± 0.019	0.401** ± 0.033	0.699	-0.085 ± 0.135	0.194** ± 0.043
SOU	0.345** ± 0.015	0.360** ± 0.026	0.705	1.121** ± 0.530	-0.247** ± 0.225
TUC	0.299** ± 0.025	0.333** ± 0.048	0.632	0.292** ± 0.246	0.065 ± 0.087
For all locations	0.284** ± 0.022	0.391** ± 0.037	0.676	0.410** ± 0.075	0.034** ± 0.025

Location	Model		r	d	c	me	rmse	pbias
BEL	AP	a	0.848	0.909	0.771	-0.081	1.106	-0.5
	MH	a	0.506	0.651	0.329	0.394	1.681	2.6
	R-AP	b	0.847	0.639	0.541	2.795	3.013	18.2
	R-MH	b	0.040	0.419	0.017	3.122	3.723	20.6
	FAO	b	0.855	0.575	0.492	3.709	3.930	24.2
	LAT	c	0.853	0.456	0.389	5.558	5.722	36.3
CAM	AP	b	0.973	0.986	0.959	0.029	0.455	0.1
	MH	b	0.705	0.822	0.580	0.032	1.240	0.2
	R-AP	a	0.974	0.908	0.885	-1.126	1.211	-5.5
	R-MH	a	0.316	0.478	0.151	-2.023	2.629	-10.0
	FAO	b	0.972	0.976	0.949	0.224	0.656	1.1
	LAT	c	0.973	0.795	0.773	2.124	2.231	10.3
CON	AP	a	0.886	0.928	0.822	-0.105	0.887	-0.6
	MH	a	0.695	0.821	0.570	0.154	1.558	0.8
	R-AP	a	0.885	0.910	0.806	-0.449	0.993	-2.4
	R-MH	a	0.006	0.400	0.002	0.189	2.367	1.0
	FAO	a	0.857	0.913	0.782	0.425	1.111	2.3
	LAT	b	0.865	0.720	0.623	2.173	2.399	11.7
MAR	AP	b	0.978	0.988	0.966	0.015	0.352	0.1
	MH	ab	0.655	0.783	0.513	0.011	1.249	0.1
	R-AP	a	0.978	0.948	0.928	-0.650	0.732	-3.5
	R-MH	ab	-0.169	0.268	-0.045	-0.091	1.860	-0.5
	FAO	b	0.972	0.953	0.927	0.315	0.796	1.7
	LAT	c	0.976	0.745	0.727	2.078	2.217	11.2
SOU	AP	b	0.971	0.985	0.957	0.045	0.666	0.2
	MH	ab	0.172	0.388	0.067	-0.069	2.683	-0.3
	R-AP	a	0.974	0.916	0.892	-1.595	1.731	-8.3
	R-MH	a	-0.237	0.390	-0.092	-2.122	3.550	-10.8
	FAO	a	0.975	0.948	0.924	-0.857	1.499	-4.5
	LAT	b	0.975	0.939	0.916	0.964	1.666	5.0
TUC	AP	a	0.860	0.915	0.787	0.098	0.704	0.6
	MH	a	0.188	0.529	0.099	0.031	1.699	0.2
	R-AP	ab	0.824	0.854	0.704	0.666	1.034	3.9
	R-MH	ab	0.152	0.482	0.073	1.110	2.062	6.6
	FAO	b	0.762	0.709	0.540	1.454	1.812	8.6
	LAT	c	0.779	0.459	0.357	3.257	3.432	19.2

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[1] Corresponding author: João Vitor de Nóvoa Pinto, jvitorpinto@gmail.com.