Table 13.
Evaluation of annual optimum tilt angles and maximum global solar radiation in metropolitan towns in Nigeria using Liu and Jordan [50] Isotropy model (L & J), theoretical models – Observed data, model 14 (M14), model 15 (M15), models from literature – Talebizadeh et al. [67] model (M23) and Jamil et al. [54] model (M24). Yearly maximum incident solar radiation and global radiation index with associated evaluation parameters.
| Station | Lat | Long | β Observed | β NASA | β (L&J) [50] | β M14 | β M15 | B M23 [67] | β M24 [54] | H NASA | NASA | (L&J) model [50] | model 38 | model 22 | GRI NASA | GRI Model 38 | GRI Model 22 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Port Harcourt | 4.4 | 7.2 | 8.8 | 4.5 | 8.5 | 7.5 | 11.5 | 10.2 | 12.0 | 172.8 | 179.2 | 177.0 | 178.9 | 179.6 | 0.037 | 0.040 | 0.045 |
| Uyo | 5.1 | 8.0 | 10.1 | 5.5 | 9.3 | 8.1 | 12.1 | 10.6 | 12.5 | 193.4 | 202.1 | 199.9 | 182.2 | 184.2 | 0.045 | 0.041 | 0.053 |
| Asaba | 6.8 | 6.8 | 12.0 | 7 | 9.8 | 9.6 | 13.6 | 11.9 | 13.7 | 197.3 | 207.4 | 204.3 | 207.5 | 210.0 | 0.051 | 0.041 | 0.053 |
| Calabar | 5.0 | 8.3 | 9.9 | 5 | 8.3 | 8.0 | 12.0 | 10.6 | 12.4 | 175.4 | 182.4 | 180.5 | 185.4 | 186.0 | 0.040 | 0.040 | 0.044 |
| Yenagoa | 4.9 | 6.3 | 9.9 | 5 | 8.9 | 8.0 | 12.0 | 10.6 | 12.4 | 169.5 | 175.9 | 174.2 | 177.5 | 177.4 | 0.038 | 0.040 | 0.040 |
| Benin Cty | 6.3 | 5.6 | 11.1 | 6.5 | 9.9 | 9.2 | 13.2 | 11.5 | 13.3 | 191.2 | 200.4 | 198.9 | 201.0 | 202.9 | 0.049 | 0.041 | 0.051 |
| Umuahia | 5.5 | 7.5 | 11.1 | 5.5 | 9.3 | 8.5 | 12.5 | 11.0 | 12.8 | 193.4 | 202.3 | 198.8 | 182.7 | 185.1 | 0.046 | 0.041 | 0.055 |
| Awka | 6.2 | 7.7 | 10.9 | 6.5 | 10.0 | 9.1 | 13.1 | 11.4 | 13.3 | 202.2 | 212.5 | 209.7 | 212.0 | 215.1 | 0.051 | 0.041 | 0.056 |
| Abakaliki | 6.4 | 8.1 | 11.2 | 6.5 | 10.5 | 9.2 | 13.2 | 11.5 | 13.4 | 207.4 | 218.3 | 214.9 | 216.7 | 220.3 | 0.053 | 0.041 | 0.058 |
| Enugu | 6.5 | 7.5 | 11.4 | 6.5 | 10.0 | 9.3 | 13.3 | 11.6 | 13.5 | 202.2 | 212.6 | 209.7 | 212.0 | 215.1 | 0.052 | 0.041 | 0.056 |
| Oweri | 5.5 | 7.0 | 11.0 | 5.5 | 9.5 | 8.4 | 12.4 | 10.9 | 12.8 | 193.4 | 202.3 | 197.2 | 200.0 | 202.0 | 0.046 | 0.041 | 0.051 |
| Lagos | 6.6 | 3.6 | 11.5 | 7 | 9.6 | 9.4 | 13.4 | 11.7 | 13.5 | 195.0 | 204.2 | 201.7 | 204.7 | 206.4 | 0.047 | 0.041 | 0.049 |
| Ado-Ekiti | 7.6 | 5.2 | 13.3 | 8 | 10.4 | 10.3 | 14.3 | 12.4 | 14.2 | 202.7 | 214.3 | 211.9 | 214.7 | 225.2 | 0.057 | 0.040 | 0.092 |
| Abeokuta | 7.2 | 3.3 | 12.5 | 7.5 | 9.8 | 9.9 | 13.9 | 12.1 | 13.9 | 201.5 | 212.2 | 208.0 | 211.0 | 214.8 | 0.053 | 0.041 | 0.060 |
| Akure | 7.3 | 5.2 | 12.7 | 7.5 | 10.7 | 10.0 | 14.0 | 12.1 | 14.0 | 202.7 | 214.0 | 212.1 | 214.7 | 220.4 | 0.056 | 0.041 | 0.068 |
| Osogbo | 7.8 | 4.6 | 13.6 | 8 | 10.1 | 10.4 | 14.4 | 12.5 | 14.3 | 200.8 | 211.9 | 208.2 | 210.7 | 218.0 | 0.055 | 0.040 | 0.077 |
| Ibadan | 7.4 | 3.9 | 11.1 | 7.5 | 10.5 | 10.1 | 14.1 | 12.2 | 14.0 | 201.5 | 212.3 | 209.0 | 211.0 | 215.1 | 0.054 | 0.041 | 0.061 |
| Makurdi | 7.7 | 8.5 | 11.6 | 8 | 11.3 | 10.4 | 14.4 | 12.5 | 14.3 | 213.2 | 226.0 | 223.8 | 223.8 | 227.2 | 0.060 | 0.041 | 0.057 |
| Lokoja | 7.8 | 6.8 | 13.6 | 8 | 11.6 | 10.4 | 14.4 | 12.5 | 14.3 | 209.3 | 221.4 | 219.9 | 219.5 | 224.0 | 0.058 | 0.041 | 0.062 |
| Ilorin | 8.5 | 4.6 | 14.9 | 8.5 | 12.0 | 11.0 | 15.0 | 13.0 | 14.8 | 211.6 | 224.5 | 224.4 | 224.2 | 231.0 | 0.061 | 0.041 | 0.072 |
| Lafia | 8.5 | 8.5 | 14.8 | 9 | 12.3 | 11.0 | 15.0 | 13.0 | 14.8 | 220.4 | 235.0 | 230.8 | 231.3 | 235.5 | 0.066 | 0.041 | 0.060 |
| Minna | 9.6 | 6.6 | 14.4 | 10 | 12.3 | 12.0 | 16.0 | 13.8 | 15.5 | 225.4 | 240.9 | 236.1 | 235.8 | 243.2 | 0.069 | 0.041 | 0.073 |
| Jos | 9.9 | 8.9 | 14.9 | 10.5 | 12.7 | 12.3 | 16.2 | 14.0 | 15.7 | 224.7 | 241.6 | 236.2 | 235.9 | 252.6 | 0.075 | 0.041 | 0.114 |
| Abuja | 9.1 | 7.5 | 13.6 | 9.5 | 12.7 | 11.5 | 15.5 | 13.4 | 15.2 | 224.0 | 239.5 | 401.9 | 234.4 | 242.9 | 0.069 | 0.040 | 0.078 |
| Kaduna | 10.5 | 7.4 | 15.8 | 11 | 13.3 | 12.8 | 16.8 | 14.4 | 16.2 | 231.9 | 249.5 | 246.9 | 246.1 | 257.9 | 0.076 | 0.041 | 0.090 |
| Yola | 9.9 | 11.9 | 14.9 | 10 | 12.7 | 12.2 | 16.2 | 14.0 | 15.7 | 239.7 | 257.9 | 245.8 | 246.2 | 253.0 | 0.076 | 0.041 | 0.069 |
| Bauchi | 10.3 | 9.8 | 15.5 | 10.5 | 13.5 | 12.6 | 16.6 | 14.2 | 16.0 | 236.9 | 254.4 | 252.3 | 253.0 | 264.9 | 0.074 | 0.041 | 0.090 |
| Gombe | 10.3 | 11.2 | 15.4 | 10.5 | 13.5 | 12.6 | 16.6 | 14.2 | 16.0 | 236.9 | 253.7 | 252.5 | 252.8 | 261.5 | 0.071 | 0.041 | 0.076 |
| Jalingo | 8.9 | 11.4 | 15.6 | 9.5 | 12.3 | 11.4 | 15.4 | 13.3 | 15.1 | 228.8 | 245.0 | 238.8 | 235.4 | 241.4 | 0.071 | 0.041 | 0.067 |
| Damaturu | 11.7 | 12.0 | 17.6 | 12 | 14.7 | 13.8 | 17.8 | 15.2 | 17.0 | 244.8 | 263.4 | 261.8 | 259.6 | 269.1 | 0.076 | 0.041 | 0.079 |
| Kano | 11.5 | 8.5 | 17.3 | 12 | 14.3 | 13.6 | 17.6 | 15.0 | 16.8 | 240.7 | 259.0 | 258.6 | 257.0 | 267.7 | 0.076 | 0.041 | 0.084 |
| Kastina | 13.0 | 7.6 | 16.2 | 13.5 | 18.0 | 14.9 | 18.9 | 16.0 | 17.8 | 257.8 | 279.8 | 270.0 | 260.8 | 272.5 | 0.086 | 0.041 | 0.087 |
| Bini Kebbi | 12.5 | 4.2 | 15.6 | 13 | 18.2 | 14.4 | 18.4 | 15.7 | 17.4 | 245.3 | 264.9 | 268.8 | 257.5 | 265.6 | 0.080 | 0.041 | 0.074 |
| Dutse | 11.7 | 9.3 | 17.6 | 12 | 16.5 | 13.8 | 17.8 | 15.2 | 17.0 | 242.1 | 260.4 | 266.2 | 257.9 | 268.1 | 0.076 | 0.041 | 0.082 |
| Maidugiri | 11.8 | 13.2 | 17.8 | 12 | 18.3 | 13.9 | 17.9 | 15.3 | 17.0 | 242.2 | 261.0 | 267.7 | 258.3 | 266.6 | 0.078 | 0.041 | 0.074 |
| Gusau | 12.2 | 6.7 | 15.2 | 12.5 | 18.0 | 14.2 | 18.2 | 15.5 | 17.3 | 246.6 | 266.1 | 270.5 | 261.5 | 272.4 | 0.079 | 0.041 | 0.085 |
| Sokoto | 13.1 | 5.2 | 16.3 | 13.5 | 17.3 | 15.0 | 19.0 | 16.1 | 17.9 | 256.2 | 278.1 | 276.6 | 267.1 | 276.8 | 0.085 | 0.041 | 0.078 |
| Average | 8.5 | 7.4 | 8.78 | 215.7 | 229.4 | 231.5 | 225.4 | 231.7 | 0.063 | 0.041 | 0.070 |
Here β is the optimum tilt angle, ϕ is the latitude of the location and theoretical optimum tilt angle model employed as the observed data were generated using equation (12) – (16), H represents yearly global solar radiation in 37 metropolitan towns in Nigeria, L & J [50] model represents Liu and Jordan model for estimating maximum incident solar radiation, GRI stands for the value of global radiation index obtained using datasets such as global solar radiation with associated values of maximum incident radiation obtained from Liu and Jordan model, model 39 represents maximum incident solar radiation evaluated using model 37, model 22 represents the best performing model for sets of computing models for evaluating HT in 37 metropolitan towns in Nigeria. Ho stands for the yearly extraterrestrial solar radiation in 37 metropolitan towns in Nigeria.