Estimation of daily global solar irradiance from the air temperature in the state of Paraná, Brazil

Sgarbossa, Carolina K.; Virgens Filho, Jorim S. das

doi:10.1590/1807-1929/agriambi.v24n8p512-519

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Articles • Rev. bras. eng. agríc. ambient. 24 (8) • Aug 2020 • https://doi.org/10.1590/1807-1929/agriambi.v24n8p512-519 copy

Estimation of daily global solar irradiance from the air temperature in the state of Paraná, Brazil

Estimativa da irradiância solar global diária a partir da temperatura do ar no Estado do Paraná, Brasil

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Global solar irradiance (GSI) is a fundamental source of energy on Earth. Despite its importance, sunshine or solar irradiance data are rarely available from weather stations. In the absence of available data, there are empirical methods that can be used to estimate solar irradiance. The objective of this study is to calibrate the parameters and to evaluate the performance of four empirical models of solar irradiance estimation (those of Chen, Hargreaves, Hunt, and Richardson) from air temperature data for eight localities in the state of Paraná, Brazil. Data were obtained from the Meteorological Database for Teaching and Research (BDMEP). For the comparison of means among the models, the Kruskal-Wallis non-parametric test was used. Dunn’s multiple comparison tests were used to analyze which models presented different means from the others. The performance of each model was assessed using the indices Pearson correlation coefficient (r), mean bias error (MBE), root mean square error (RMSE), Wilmott concordance index (d), performance index (c) and the Nash-Sutcliffe efficiency (NSE) coefficient. It was observed that the models proposed by Chen and Hunt presented the best performances in the estimation of GSI for the studied Paraná state localities, given that they yielded results which are closer to the observed historical data.

Key words:
empirical models; model calibration; sunshine hours

ID	Locality	Latitude (S)	Longitude (W)	Altitude (m)
L1	Campo Mourão	24º 5’	52º 36’	616
L2	Curitiba	24º 78’	50º 0’	1009
L3	Castro	25º 43’	49º 26’	924
L4	Irati	25º 46’	50º 63’	837
L5	Ivaí	25º 0’	50º 85’	808
L6	Londrina	23º 31’	51º 13’	566
L7	Maringá	23º 40’	51º 91’	542
L8	Paranaguá	25º 53’	48º 51’	5

ID	Model	Equation	Reference
Hg	Hargreaves	$R_{G} = R_{A} \times (a + b \sqrt{Δ T})$	Hargreaves & Samani (1982)Hargreaves, G. H.; Samani, Z. A. Estimating potencial evapotranspiration. Journal of Irrigation and Drainage Engineering, v.108, p.225-230, 1982.
R	Richardson	$R_{G} = R_{A} \times (a + Δ T^{b})$	Richardson (1985)Richardson, C. W. Weather simulation for crop management models. Transactions of the American Society of Agricultural Engineers, v.28, p.1602-1606, 1985. https://doi.org/10.13031/2013.32484 https://doi.org/10.13031/2013.32484...
Hu	Hunt	$R_{G} = (b \times \sqrt{Δ T} \times R_{A}) + a$	Hunt (1998)Hunt, L. A. Estimation of solar irradiance for use in crop modeling. Agricultural and Forest Meteorology , v.91, p.293-300, 1998. https://doi.org/10.1016/S0168-1923(98)00055-0 https://doi.org/10.1016/S0168-1923(98)00...
Ch	Chen	$R_{G} = R_{A} \times (b \ln Δ T + a)$	Chen et al. (2004)Chen, R.; Ersi, K.; Yang, J.; Lu, S.; Zhao, W. Validation of five global irradiance models with measured daily data in China. Energy Conversion and Management, v.45, p.1759-1769, 2004. https://doi.org/10.1016/j.enconman.2003.09.019 https://doi.org/10.1016/j.enconman.2003....

Initials	Index	Equation
r	Pearson correlation coefficient	$r = \frac{\sum_{i = 1}^{n} (x \times y) - (Σ x) \times (Σ y)}{\sqrt{n Σ x^{2} - {(Σ x)}^{2}} \times \sqrt{n Σ y^{2} - {(Σ y)}^{2}}}$
MBE	Mean bias error	$M B E = \frac{1}{n} \sum_{i = 1}^{n} (P i - O i)$
RMSE	Square root mean square	$R M S E = \sqrt{\frac{1}{n}} \sum_{i = 1}^{n} {(P i - O i)}^{2}$
d	Wilmott's concordance index
c	Performance index “c”	$d = 1 - [\frac{\sum_{i = 1}^{n} {(P i - O i)}^{2}}{\sum_{i = 1}^{n} {(\|P i - \bar{O}\| + \|O i - \bar{O}\|)}^{2}}]$
NSE	Nash-Sutcliffe efficiency coefficient	$N S E = 1 - [\frac{\sum_{i = 1}^{n} {(O i - P i)}^{2}}{\sum_{i = 1}^{n} {(\|O i - \bar{O}\|)}^{2}}]$

Localities	Models
	Ch		Hg		Hu		R
	a	b	a	b	a	b	a	b
L1	-0.159	0.288	-0.063	0.176	-2.50	0.177	0.119	0.626
L2	-0.026	0.194	-0.006	0.132	0.699	0.129	0.214	0.513
L3	-0.117	0.261	-0.089	0.178	-3.806	0.178	0.121	0.601
L4	-0.059	0.227	-0.049	0.159	-2.136	0.158	0.140	0.533
L5	0.115	0.158	0.103	0.116	4.184	0.115	0.250	0.362
L6	0.309	0.098	0.363	0.054	11.942	0.053	0.356	0.214
L7	-0.061	0.263	0.003	0.169	-0.235	0.169	0.204	0.543
L8	0.340	0.037	0.359	0.019	12.429	0.021	0.305	0.177

	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
L1 - Campo Mourão
Ch	b	b	a	a	b	a	b	a	b	b	a	b
Hg	a	a	b	b	a	a	a	b	a	a	c	a
Hu	b	b	a	a	b	a	b	a	b	b	a	b
Obs	b	b	a	a	b	a	b	a	b	b	a	b
R	b	b	a	a	b	a	b	a	b	b	b	b
L2 - Curitiba
Ch	b	a	b	a	b	b	a	b	a	a	b	b
Hg	a	b	a	b	a	a	b	a	b	ab	a	a
Hu	b	a	b	a	b	b	a	b	a	a	b	b
Obs	b	a	b	a	b	b	a	b	a	a	b	b
R	b	a	b	a	b	b	a	b	a	b	b	b
L3 - Castro
Ch	b	b	b	b	a	a	b	a	b	a	b	b
Hg	a	a	a	a	b	c	a	c	a	b	a	a
Hu	b	b	b	b	a	a	b	a	b	a	b	b
Obs	b	b	b	b	a	a	b	a	b	a	b	b
R	b	b	b	b	a	b	b	b	b	a	b	b
L4 - Irati
Ch	b	b	b	a	a	a	b	a	a	b	b	a
Hg	a	a	a	a	b	a	a	c	b	a	a	b
Hu	b	b	b	a	a	a	b	a	a	b	b	a
Obs	b	b	b	a	a	a	b	a	a	b	b	a
R	b	b	b	a	a	a	b	b	a	b	b	ab
L5 - Ivaí
Ch	a	b	b	ab	a	b	b	a	ab	a	a	a
Hg	c	a	a	a	c	a	a	b	c	c	c	c
Hu	a	b	b	ab	a	b	b	a	ab	a	a	a
Obs	a	b	b	ab	a	b	b	a	a	a	a	a
R	b	b	b	b	b	b	b	ab	b	b	b	b
L6 - Londrina
Ch	b	a	a	a	b	a	a	a	a	a	a	a
Hg	a	c	c	c	a	c	c	c	c	c	c	c
Hu	b	a	a	a	b	a	a	a	a	a	a	a
Obs	b	a	a	a	b	a	a	a	a	a	a	a
R	b	b	b	b	b	b	b	b	b	b	b	b
L7 - Maringá
Ch	b	a	b	a	a	ab	a	b	b	b	a	a
Hg	a	b	a	c	c	a	c	a	a	a	c	b
Hu	b	a	b	a	a	ab	a	b	b	b	a	a
Obs	b	a	b	a	a	ab	a	b	b	b	a	a
R	b	a	b	b	b	b	b	b	b	b	b	a
L8 - Paranaguá
Ch	a	a	a	a	a	a	a	a	a	a	a	a
Hg	c	c	c	c	c	c	c	c	b	c	c	c
Hu	a	a	a	a	a	a	a	a	a	a	a	a
Obs	a	a	a	a	a	a	a	a	a	a	a	a
R	b	b	b	b	b	b	b	b	a	b	b	b

	Localities
	L1	L2	L3	L4	L5	L6	L7	L8
Ch - Chen
r	0.707	0.410	0.759	0.715	0.351	0.416	0.561	0.153
MBE	0.001	-0.037	-0.003	-0.005	-0.006	-0.028	-0.028	-0.021
RMSE	1.037	1.377	0.911	0.930	1.002	1.148	1.324	1.296
d	0.801	0.721	0.831	0.809	0.762	0.778	0.786	0.746
c	0.571	0.303	0.635	0.582	0.275	0.333	0.448	0.115
NSE	0.457	0.082	0.570	0.489	0.433	0.226	0.324	0.011
Hg - Hargreaves
r	0.701	0.441	0.759	0.720	0.356	0.327	0.571	0.159
MBE	2.412	3.423	3.740	2.120	-4.081	-11.44	0.275	-12.27
RMSE	4.792	5.729	5.064	4.456	6.695	12.26	8.203	12.36
d	0.446	0.383	0.438	0.461	0.389	0.217	0.367	0.198
c	0.317	0.168	0.336	0.350	0.199	0.119	0.221	0.049
NSE	-10.84	-21.43	-14.47	-14.16	-45.57	-123.0	-37.85	-105.2
Hu - Hunt
r	0.701	0.417	0.759	0.720	0.466	0.257	0.571	0.159
MBE	0.010	-0.032	-0.003	-0.009	0.002	-0.024	-0.027	-0.011
RMSE	1.044	1.383	0.907	0.919	0.973	1.169	1.323	1.296
d	0.801	0.731	0.832	0.810	0.765	0.773	0.786	0.748
c	0.565	0.311	0.635	0.587	0.360	0.216	0.455	0.121
NSE	0.449	0.076	0.571	0.501	0.474	0.177	0.327	0.013
R - Richardson
r	0.697	0.416	0.759	0.720	0.353	0.347	0.567	0.240
MBE	-0.433	-0.404	-0.465	-0.386	-0.566	-0.807	-0.599	-0.884
RMSE	1.173	1.477	1.037	1.034	1.182	1.402	1.458	1.560
d	0.769	0.701	0.797	0.778	0.710	0.707	0.756	0.673
c	0.539	0.298	0.609	0.564	0.262	0.260	0.434	0.162
NSE	0.297	-0.053	0.423	0.351	0.175	-0.173	0.191	-0.449

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[1] Carolina K. Sgarbossa - E-mail: carolina.sgarb@gmail.com (Corresponding author)