Evaluation of various global solar radiation models for Nigeria

Figures & data

Table 1. Main characteristics of studied models.

Model	Category	Relation	Accuracy	Restrictions
Angstrom–Prescott	Sunshine		High	–
Swartman–Ogunlade	Hybrid		High	–
Badescu	Cloud		High	Sensible to human biasing
Chen et al.	Hybrid		High	Suitable for tropical climate
El-Metwally	Sunshine		High	–
Okundamiya	Hybrid		High	–

Figure 1. Map of Nigeria showing the study sites.

Table 2. Geographical coordinates of study locations and characteristics of sunshine data.

Regions	Geographical coordinates				Characteristics of sunshine data (NIMET 2013)
	Locations	Latitude (°N)	Longitude (°E)	Elevation (m)	Instrument used	Measurement range	Recording resolution
Central	Abuja	9.08	7.53	484	Campbell stokes sunshine recorder	0–24 h	0.1 h
Southern	Benin City	6.34	5.63	135
Northern	Sokoto	13.06	5.25	331

Figure 2. Long-term (22 years) monthly average daily data sets for Nigeria (a) global solar radiation, (b) maximum air temperature, (c) minimum air temperature, (d) cloudiness, (e) relative humidity, and (f) sunshine duration.

Table 3. Calibration results of studied models along with R² and t-stat for Nigeria.

Region	Site	Model	Statistics		Regression coefficients
			R^2	t-stat	a	b	c	d	e
Central	Abuja	Equation 1	0.8059	0.0380	0.2195	0.6143	0	0	0
		Equation 2	0.9467	0.3312	0.4171	0.4252	–0.0015	0	0
		Equation 3	0.7936	0.0543	0.7506	–0.0455	0	0	0
		Equation 4	0.9598	0.0770	–6.8739	0.1167	7.3102	0.0237	0
		Equation 5	0.8145	0.0718	0.7349	0	0	0	0
		Equation 6	0.9793	0.3298	–0.1832	0.2790	0.1704	0.0179	–0.0128
Southern	Benin City	Equation 1	0.6677	0.0270	0.2361	0.6213	0	0	0
		Equation 2	0.8874	0.4260	0.6700	0.4381	–0.0046	0	0
		Equation 3	0.8456	0.0462	0.7374	–0.0528	0	0	0
		Equation 4	0.9532	0.0344	–5.3448	0.2396	5.4894	0.0172	0
		Equation 5	0.6707	0.0038	0.7649	0	0	0	0
		Equation 6	0.9750	0.0067	–0.5700	0.1158	0.4513	0.0285	-0.0345
Northern	Sokoto	Equation 1	0.6702	0.0616	0.4785	0.2465	0	0	0
		Equation 2	0.8332	0.1498	0.7561	–0.0829	–0.0014	0	0
		Equation 3	0.8133	0.1042	0.7231	–0.0265	0	0	0
		Equation 4	0.8154	0.1028	–13.090	0.1149	13.439	–0.0041	0
		Equation 5	0.7573	0.0684	0.7496	0	0	0	0
		Equation 6	0.9087	0.1465	0.5741	–0.3053	0.1922	0.0097	–0.0577

Table 4. Validation results of studied models for different regions in Nigeria using sub-data Set 2.

Region	Location	Model	Statistics
			r-value	Error terms (MJ m^–2 day^–1)
				RMSE	MBE	MABE
Central	Abuja	Equation 1	0.8987	1.3055	0.3464	1.1711
		Equation 2	0.9785	0.9159	0.1930	0.7494
		Equation 3	0.8867	1.4682	0.3156	1.2301
		Equation 4	0.9668	0.8273	0.2044	0.6164
		Equation 5	0.8888	1.3134	0.3596	1.1127
		Equation 6	0.9867	0.6796	0.2736	0.5705
Southern	Benin City	Equation 1	0.6670	1.7513	-0.0630	1.4471
		Equation 2	0.7367	1.6891	-0.8809	1.2665
		Equation 3	0.8600	1.1254	-0.0932	0.9256
		Equation 4	0.8362	7.5463	-7.4307	7.4307
		Equation 5	0.6414	3.1778	-0.0697	2.5651
		Equation 6	0.8774	1.0854	0.0089	0.8160
Northern	Sokoto	Equation 1	0.7731	1.4324	0.2990	1.1706
		Equation 2	0.9128	1.0715	0.5119	0.7433
		Equation 3	0.8535	1.2878	0.2823	1.0614
		Equation 4	0.9109	1.2158	0.7757	0.8920
		Equation 5	0.8329	1.3866	0.2945	1.2025
		Equation 6	0.9377	0.9202	0.5192	0.6282

Figure 3. Comparison of the measured (22 years) and estimated monthly average daily global solar radiations for study locations: (a) Abuja, (b) Benin City, and (c) Sokoto; in Nigeria.

Figure 4. Comparison of the monthly relative percentage error of average daily global solar radiations (22 years) for studied models: (a) Angstrom–Prescott (1940), (b) Swartman and Ogunlade (1967), (c) Badescu (1999), (d) Chen et al. (2004), (e) El-Metwally (2005), and (f) Okundamiya (2014); in Nigeria.

NIMET. 2013. Archives of Nigerian Meteorological (NIMET) agency, Oshodi, Lagos State, Nigeria.

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