# Estimation of Hourly, Daily and Monthly Global Solar Radiation on Inclined Surfaces: Models Re-Visited

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Basic Solar Components

**Declination Angle (δ)**

**Hour Angle (ω)**

**Solar Azimuth Angle (γ)**

**Latitude (φ)**

**Hourly Extraterrestrial Radiation (Io)**

^{2}); ${E}_{0}$ is the eccentricity correction factor [10]; $\delta $ is the declination angle; $\phi $ is the latitude of location; ${\omega}_{1}$ and ${\omega}_{2}$ are the hour angle at the beginning and end of the time interval, where all angles are given in degrees. The eccentricity correction factor ${E}_{0}$ can be calculated according to Spencer [7]. The following series gives the equation for time (in minutes).

## 3. Hourly Global Solar Radiation on Horizontal Surfaces (I_{H})

- Diffuse solar radiation (${I}_{b}$)
- Direct beam solar radiation (${I}_{d}$)

#### 3.1. Hourly Diffuse Radiation on Horizontal Surface (I_{d})

- Parametric models
- Decomposition models

#### 3.1.1. Parametric Models

**ASHRAE Model**

**Machler and Iqbal’s Model**

**Parishwad’s Model**

**Nijegorodov’s Model**

#### 3.1.2. Decomposition Models

**Chandrasekaran and Kumar’s Model**

**Erbs’ Model**

**Hawlader’s Model**

**Jacovides’ Model**

**Karatasou’s Model**

**Lam and Li’s Model**

**Louche’s Model**

**Miguel’s Model**

**Orgill and Hollands’ Model**

**Boland’s Model**

**Liu and Jordan’s Model**

**Spencer’s Model**

**Reindl’s Model**

**Oliveira’s Model**

**Soares’ Model**

**Muneer’s Model**

#### 3.2. Hourly Direct Radiation on Horizontal Surface (I_{b})

_{bN}) can be measured by an instrument called a pyrheliometer. Moreover, the direct normal radiation (I

_{bN}) can be estimated by the number of models such as: the Bird model [36], METSTAT [37], the Yang model [38], REST2 [39], and the Ineichen model [40].

#### 3.3. Recognizing Accurate Models to Estimate Diffuse Radiation on Horizontal Surfaces

## 4. Hourly Global Solar Radiation on an Inclined Surface (I_{β})

#### 4.1. Isotropic Models

**Badescu’s Model**

**Koronakis’ Model**

**Liu and Jordan’s Model**

**Tian’s Model**

#### 4.2. Anisotropic Models

**Bugler’s Model**

**Temps and Coulson’s Model**

**Hay’s Model**

**Reindl’s Model**

**Klucher’s Model**

**Klucher’s Model Is Described by the Following Equation:**

**The HDKR Model (the Klucher and Reindl, and Hay and Davies’ Model)**

**Skartveit and Olseth’s Model**

**Steven and Unsworth’s Model**

**Wilmott’s Model**

**Perez’ Model**

_{d}is the hourly diffuse radiation on a horizontal surface and I

_{o}is the extraterrestrial radiation at normal incidence (W/m

^{2}). The ε is a function of hourly diffuse radiation ${I}_{d}$ which is given in Table 4 and direct beam radiation${I}_{b}$ [60]. The required coefficients ${F}_{i,j}$ are obtained from Perez et al., as seen in Table 5.

#### 4.3. Recognizing Accurate Models for Estimation of Diffuse Radiation on Angled Surfaces

#### 4.4. Estimating Direct Beam Radiation of an Angled Surface (I_{bβ})

#### 4.5. Estimating Ground-Reflected Radiation on an Angled Surface (Ir)

#### 4.6. Combination of Diffuse Estimation Models for Horizontal and Inclined Surfaces

## 5. Estimation of Daily Global Solar Radiation on a Horizontal Surface (H_{H})

#### 5.1. Daily Radiation on an Inclined Surface (H_{β})

#### 5.2. Estimation of the Monthly Average Daily Global Radiation on an Inclined Surface

#### 5.3. Optimum Tilt Angle (β)

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

ST | Local solar time |

LT | Local standard time |

${L}_{s}$ | Standard meridian for a local zone |

${L}_{L}$ | Longitude of the location under study in degrees |

ET | Equation of time |

${I}_{o}$ | Hourly extraterrestrial solar radiation on horizontal surface |

${I}_{sc}$ | Solar constant |

${E}_{0}$ | Eccentricity correction factor |

$I$_{H} | Hourly global solar radiation on horizontal surface |

${I}_{b}$ | Hourly direct beam solar radiation on horizontal surface |

${I}_{bN}$ | Hourly direct normal beam radiation on horizontal surface |

${I}_{d}$ | Hourly diffuse solar radiation on horizontal surface |

${M}_{t}$ | Hourly clearness index |

${I}_{\beta}$ | Hourly global solar radiation on inclined surface |

${I}_{d\beta}$ | Hourly diffuse solar radiation on inclined surface |

${P}_{1}$ | Vicinity of the sun’s disc |

${P}_{2}$ | Sky radiation from the region near the horizon |

Z | Correcting factor |

m | Air mass |

${I}_{b\beta}$ | Hourly direct beam solar radiation on inclined surface |

${I}_{r}$ | Hourly ground reflected radiation on inclined surface |

${H}_{H}$ | Daily global radiation on a horizontal surface |

${H}_{b}$ | Beam radiation on a horizontal surface |

${H}_{d}$ | Diffuse radiation on a horizontal surface |

${K}_{t}$ | Daily clearness index |

${w}_{s}$ | Sunrise hour angle |

${H}_{\beta}$ | Daily global radiation on an inclined surface |

${H}_{b\beta}$ | Daily beam radiation on an inclined surface |

${H}_{d\beta}$ | Daily diffuse radiation on an inclined surface |

${H}_{r}$ | Daily reflected radiation on an inclined surface |

${w}_{s}^{\prime}$ | Sunset hour angle |

$n$ | The number of the day in the year |

Greek Symbols | |

$\beta $ | Tilt angle |

$\theta $ | Angle of incidence for a surface facing the equator in degrees |

${\theta}_{z}$ | Zenith angle |

δ | Declination angle |

Г | The day angle in radians |

ω | Hour angle |

γ | Solar azimuth angle |

φ | Latitude |

ε | Function of hourly diffuse radiation |

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**Figure 4.**Diagram of the equality of angles $\theta $ and ${\theta}_{z}$, adapted with permission from Liu and Jordan [50].

January | February | March | April | May | June | July | August | September | October | November | December | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

ASHARE | ||||||||||||

A | 1230 | 1215 | 1186 | 1136 | 1104 | 1088 | 1085 | 1107 | 1152 | 1193 | 1221 | 1234 |

B | 0.142 | 0.144 | 0.156 | 0.180 | 0.196 | 0.205 | 0.207 | 0.201 | 0.177 | 0.160 | 0.149 | 0.142 |

C | 0.058 | 0.060 | 0.071 | 0.097 | 0.121 | 0.134 | 0.136 | 0.122 | 0.092 | 0.073 | 0.063 | 0.057 |

Machler and Iqbal | ||||||||||||

A | 1202 | 1187 | 1164 | 1130 | 1106 | 1092 | 1093 | 1107 | 1136 | 1166 | 1190 | 1204 |

B | 0.141 | 0.142 | 0.149 | 0.164 | 0.177 | 0.185 | 0.186 | 0.182 | 0.165 | 0.152 | 0.144 | 0.141 |

C | 0.103 | 0.104 | 0.109 | 0.120 | 0.130 | 0.137 | 0.138 | 0.134 | 0.121 | 0.111 | 0.106 | 0.103 |

Parishwad et al. | ||||||||||||

A | 610.00 | 652.20 | 667.86 | 613.35 | 558.39 | 340.71 | 232.87 | 240.80 | 426.21 | 584.73 | 616.60 | 622.52 |

B | 0.000 | 0.010 | 0.036 | 0.121 | 0.200 | 0.428 | 0.171 | 0.148 | 0.074 | 0.020 | 0.008 | 0.000 |

C | 0.242 | 0.249 | 0.299 | 0.395 | 0.495 | 1.058 | 1.611 | 1.624 | 0.688 | 0.366 | 0.253 | 0.243 |

Nijegorodov | ||||||||||||

A | 1163 | 1151 | 1142 | 1146 | 1152 | 1157 | 1158 | 1152 | 1150 | 1156 | 1167 | 1169 |

B | 0.177 | 0.174 | 0.170 | 0.165 | 0.162 | 0.160 | 0.159 | 0.164 | 0.167 | 0.172 | 0.174 | 0.177 |

C | 0.114 | 0.112 | 0.110 | 0.105 | 0.101 | 0.098 | 0.100 | 0.103 | 0.107 | 0.111 | 0.113 | 0.115 |

Models | Constraints | Diffuse Fraction $\left({\mathit{r}}_{\mathit{d}}\right)$ |
---|---|---|

Chandrasekaran and Kumar | $0<{M}_{t}\le 0.24$ | $1.0086-0.178{M}_{t}$ |

$0.24<{M}_{t}\le 0.8$ | $0.9686+0.1325{M}_{t}+1.4183{M}_{t}{}^{2}-10.1862{M}_{t}{}^{3}+8.3733{M}_{t}{}^{4}$ | |

$0.8<{M}_{t}\le 1$ | $1.0086-0.178{M}_{t}$ | |

Erbs | $0<{M}_{t}\le 0.22$ | $1-0.09{M}_{t}$ |

$0.22<{M}_{t}\le 0.8$ | $0.9511-0.1604{M}_{t}+4.388{M}_{t}{}^{2}-16.638{M}_{t}{}^{3}+12.336{M}_{t}{}^{4}$ | |

$0.8<{M}_{t}\le 1$ | $0.165$ | |

Hawlader | $0<{M}_{t}\le 0.225$ | $0.915{M}_{t}$ |

$0.225<{M}_{t}<0.775$ | $1.135-0.9422{M}_{t}-0.3878{M}_{t}{}^{2}$ | |

$0.775\le {M}_{t}\le 1$ | $0.215$ | |

Jacovides | $0<{M}_{t}\le 0.1$ | $0.987$ |

$0.1<{M}_{t}\le 0.8$ | $0.94+0.937{M}_{t}-5.01{M}_{t}{}^{2}+3.32{M}_{t}{}^{3}$ | |

$0.8<{M}_{t}\le 1$ | $0.177$ | |

Karatasou | $0<{M}_{t}\le 0.78$ | $0.9995-0.05{M}_{t}-2.4156{M}_{t}{}^{2}+1.4926{M}_{t}{}^{3}$ |

$0.78<{M}_{t}\le 1$ | $0.2$ | |

Lam and Li | $0<{M}_{t}\le 0.15$ | $0.977$ |

$0.15<{M}_{t}\le 0.17$ | $1.237-1.361{M}_{t}$ | |

$0.17<{M}_{t}\le 1$ | $0.273$ | |

Louche | $0<{M}_{t}\le 1$ | ${I}_{b}=\left(-10.676{M}_{t}{}^{5}+15.307{M}_{t}{}^{4}-5.205{M}_{t}{}^{3}+0.99{M}_{t}{}^{2}-0.059{M}_{t}+0.02\right)$ |

Miguel | $0<{M}_{t}\le 0.21$ | $0.995-0.081{M}_{t}$ |

$0.21<{M}_{t}\le 0.76$ | $0.724+2.738{M}_{t}-8.32{M}_{t}{}^{2}+4.967{M}_{t}{}^{3}$ | |

$0.76<{M}_{t}\le 1$ | $0.18$ | |

Orgill and Hollands | $0<{M}_{t}<0.35$ | $1-0.249{M}_{t}$ |

$0.35\le {M}_{t}\le 0.75$ | $1.577-1.84{M}_{t}$ | |

$0.75<{M}_{t}\le 1$ | $0.177$ | |

Boland | For any value of ${M}_{t}$ | $\frac{1}{1+{e}^{7.997\left({M}_{t}-0.586\right)}}$ |

Liu and Jordan | $0.75<{M}_{t}\le 1$ | $0.384-0.416{M}_{t}$ |

Spencer | $0.35<{M}_{t}\le 0.75$ | ${a}_{3}-{b}_{3}{M}_{t}$ |

Reindl-1 | $0<{M}_{t}\le 0.3$ | $1.02-0.248{M}_{t}$ |

$0.3{M}_{t}0.78$ | $1.45-1.67{M}_{t}$ | |

$0.78\le {M}_{t}\le 1$ | $0.147$ | |

Reindl-2 | $0<{M}_{t}\le 0.3$ | $1.02-0.254{M}_{t}+0.0123\mathrm{sin}\alpha $ |

$0.3{M}_{t}0.78$ | $1.4-1.749{M}_{t}+0.177\mathrm{sin}\alpha $ | |

$0.78\le {M}_{t}\le 1$ | $0.486{M}_{t}-0.182\mathrm{sin}\alpha $ | |

Oliveira | $0<{M}_{t}\le 0.17$ | $1$ |

$0.17{M}_{t}0.75$ | $0.97+0.8{M}_{t}-3{M}_{t}^{2}-3.1{M}_{t}^{3}+5.2{M}_{t}^{4}$ | |

$0.75<{M}_{t}\le 1$ | $0.17$ | |

Soares | $0<{M}_{t}\le 0.17$ | $1$ |

$0.17{M}_{t}0.75$ | $0.9+1.1{M}_{t}-4.5{M}_{t}^{2}-0.01{M}_{t}^{3}+3.14{M}_{t}^{4}$ | |

$0.75<{M}_{t}\le 1$ | $0.17$ | |

Muneer | $0<{M}_{t}<0.175$ | $0.95$ |

$0.175{M}_{t}0.755$ | $0.9698+0.4353{M}_{t}-3.4499{M}_{t}^{2}+2.1888{M}_{t}^{3}$ | |

$0.775<{M}_{t}<1$ | $0.26$ |

**Table 3.**Summary of studies on identifying the most accurate diffuse models for horizontal surfaces.

Authors | Location | Most Accurate Models |
---|---|---|

N. A. Engerer | Southeast Australia | Perez |

Wanxiang Yao et al. | China | Gueymard |

Kuo | Taiwan | Erbs, Chandrasekaran and Kumar, and Boland |

Chikh et al. | Algeria | KTCOR |

Dervishi et al. | Vienna, Austria | Erbs, Reindl, and Orgill and Hollands |

**Table 4.**Discrete sky clearness categories [60].

$\mathit{\epsilon}$ | Lower Range | Upper Range |
---|---|---|

1 Overcast | 1 | 1.065 |

2 | 1.065 | 1.230 |

3 | 1.230 | 1.500 |

4 | 1.500 | 1.950 |

5 | 1.950 | 2.800 |

6 | 2.800 | 4.500 |

7 | 4.500 | 6.200 |

8 Clear | 6.200 | ∞` |

**Table 5.**Brightness coefficients for the Perez Anisotropic Sky [60].

$\mathit{\epsilon}$ Bin | F_{11} | F_{12} | F_{13} | F_{21} | F_{22} | F_{23} |
---|---|---|---|---|---|---|

1.000 | −0.008 | 0.588 | −0.062 | −0.060 | 0.072 | −0.022 |

1.065 | 0.130 | 0.683 | −0.151 | −0.019 | 0.066 | −0.029 |

1.230 | 0.330 | 0.487 | −0.221 | 0.055 | −0.064 | −0.026 |

1.500 | 0.568 | 0.187 | −0.295 | 0.109 | −0.152 | 0.014 |

1.950 | 0.873 | −0.392 | −0.362 | 0.226 | −0.462 | 0.001 |

2.800 | 1.132 | −1.237 | −0.412 | 0.288 | −0.823 | 0.056 |

4.500 | 1.060 | −1.600 | −0.359 | 0.264 | −1.127 | 0.131 |

6.200 | 0.678 | −0.327 | −0.250 | 0.159 | −1.377 | 0.251 |

Models | Diffuse Radiation on Inclined Surfaces $\left({\mathit{I}}_{\mathit{d}\mathit{\beta}}\right)$ |
---|---|

Badescu | $\left(\frac{3+\mathrm{cos}\left(2\beta \right)}{4}\right){I}_{d}$ |

Koronakis | $\frac{1}{3}\left(\frac{1}{2+\mathrm{cos}\beta}\right){I}_{d}$ |

Liu and Jordan | $\left(\frac{1+\mathrm{cos}\beta}{2}\right){I}_{d}$ |

Tian | $(1-\frac{\beta}{180}){I}_{d}$ |

Bugler | $\left(\frac{1+\mathrm{cos}\beta}{2}\left({I}_{d}-0.05\frac{{I}_{b\beta}}{\mathrm{cos}{\theta}_{z}}\right)\right)+0.05{I}_{b\beta}\mathrm{cos}\theta $ |

Temps and Coulson | $\frac{1}{2}{I}_{d}\left(1+\mathrm{cos}\beta \right){P}_{1}{P}_{2}$ |

Hay | ${I}_{d}\left[{f}_{Hay}\left(\frac{\mathrm{cos}\theta}{\mathrm{cos}{\theta}_{z}}\right)+\left(\frac{1+\mathrm{cos}\beta}{2}\right)\left(1-{f}_{Hay}\right)\right]$ |

Reindl | ${I}_{d}\left[{f}_{Hay}\left(\frac{\mathrm{cos}\theta}{\mathrm{cos}{\theta}_{z}}\right)+\left(\frac{1+\mathrm{cos}\beta}{2}\right)\left(1-{f}_{Hay}\right)\left(1+{f}_{R}{\mathrm{sin}}^{3}\left(\frac{\beta}{2}\right)\right)\right]$ |

Klucher | ${I}_{d}\left[\frac{1}{2}\left(1+\mathrm{cos}\left(\frac{\beta}{2}\right)\right)\right]\left[1+{f}_{k}{\mathrm{cos}}^{2}\theta \left({\mathrm{sin}}^{3}{\theta}_{z}\right)\right]\left[1+{f}_{k}{\mathrm{sin}}^{3}\left(\frac{\beta}{2}\right)\right]$ |

HDKR | ${I}_{d}\left[\left(\frac{1+\mathrm{cos}\beta}{2}\right)\left(1-{f}_{Hay}\right)\left(1+{f}_{R}{\mathrm{sin}}^{3}\left(\frac{\beta}{2}\right)\right)\right]$ |

Skartveit and Olseth | ${I}_{d}\left[\left({f}_{Hay}\left(\frac{\mathrm{cos}\theta}{\mathrm{cos}{\theta}_{z}}\right)\right)+\left(1-{f}_{Hay}-Z\right)\left(\frac{1+\mathrm{cos}\beta}{2}\right)-S\left(\omega ,{\Omega}_{i}\right)\right]$ |

Steven and Unsworth | ${I}_{d}\left[\left(0.51\left(\frac{\mathrm{cos}\theta}{\mathrm{cos}{\theta}_{z}}\right)\right)+\left(\frac{1+\mathrm{cos}\beta}{2}\right)-\frac{1.74}{1.26\pi}\left\{\mathrm{sin}\beta -\beta \frac{\pi}{180}\mathrm{cos}\beta -\pi {\mathrm{sin}}^{2}\frac{\beta}{2}\right\}\right]$ |

Wilmott | ${I}_{d}\left[\frac{{I}_{bN}{R}_{b}}{{I}_{sc}}+{C}_{\beta}\left(1-\frac{{I}_{bN}}{{I}_{sc}}\right)\right]$ |

Perez | ${I}_{d}\left[\frac{1+\mathrm{cos}\beta}{2}\left(1-{F}_{1}\right)+{F}_{1}\frac{{a}_{1}}{{a}_{2}}+{F}_{2}\mathrm{sin}\beta \right]$ |

Authors | Location | Most Accurate Models |
---|---|---|

Dal Pai.et al. | Brazil | Isotropic and anisotropic models |

Khoo.et al. | Singapore | Perez |

Demain et al. | Belgium | Willmott, Perez |

Gulin et al. | Croatia | 3 different neural network models |

Souza and Escobedo | Brazil | Iqbal, Hay, Reindl, Willmott, Badescu and Koronakis |

Frydrychowicz-Jastrzębska and Bugała | Poland | Hay, Steven and Unsworth |

Włodarczyk and Nowak | Poland | Reindl, Gueymard, Perez, Koronakis and Muneer [70] |

Elminir et al. | Egypt | Perez |

Diez-Mediavilla et al. | Spain | Hay, Muneer and Willmott |

Mehleri et al. | Athens | RBF model |

**Table 8.**Summary of studies on finding the most accurate diffuse models for horizontal and inclined surfaces.

Authors | Location | Most Accurate Models for Horizontal and Inclined Surfaces |
---|---|---|

Shukla et al. | India | Decomposition model + Badescu |

Farhan et al. | Pakistan | Sunshine fraction model + Liu and Jordan’s model |

Lee et al. | South Korea | CIBSE Guide J [85] + Isotropic |

Noorian et al. | Iran | Skartveit and Olseth, Hay, Reindl and Perez |

Notton et al. | French | Maxwell + Klucher |

Padovan and Col | Italy | Erbs+ Perez, Erbs + HDKR |

**Table 9.**Average day for each month as recommended by Klein [68].

Month | Date | Day of the Year |
---|---|---|

January | 17 January | 17 |

January | 16 January | 47 |

January | 16 January | 75 |

April | 15 April | 105 |

May | 15 May | 135 |

June | 11 June | 162 |

July | 17 July | 198 |

August | 16 August | 228 |

September | 15 September | 258 |

October | 15 October | 288 |

November | 14 November | 318 |

December | 10 December | 344 |

Author | Location (Latitude Longitude) | Monthly Tilt Angle (Degree) | Annual Tilt Angle (Degree) | Orientation | Estimation Diffuse Model for Horizontal and Inclined Surface |
---|---|---|---|---|---|

Sinha [88] | Hamirpur, India (31°59′ N, 76°52′ E) | 0 and 60 | 29.25 | south-facing | Erbs model |

Farhan et al. [80] | Sindh, Pakistan (25°12′ N, 67°64′ E) | spring: 21, summer: 0, autumn: 18, winter: 46 | 23 | south-facing | Sunshine fraction model |

Liu and Jordan model | |||||

Khorasanizadeh et al. [89] | Tabass, Iran (33°36′ N, 51°2175′ E) | 62, 53, 38 | 32 | south-facing | Reindl model |

19, 2, 0 | |||||

0, 12, 32 | |||||

49, 60, 64 | |||||

Jafarkazemi and Saadabadi [90] | Abu Dhabi, UAE (24°45′ N, 54°37′ E) | 50, 39, 25 | 2 | south-facing | Klein and Theilacker (KT model) [91] |

10, 3, 9 | |||||

6, 5, 20 | |||||

36, 48, 52 | |||||

Bakirci [92] | Turkey (8 provinces) | optimum tilt angle changed between 0 and 65 | south-facing | Liu and Jordan | |

Ankara | Ankara: 31.21 | ||||

Diyarbakir | Diyarbakir: 32.71 | ||||

Erzurum | Erzurum: 32.61 | ||||

Istanbul | Istanbul: 34.31 | ||||

Izmir | Izmir: 32.61 | ||||

Samsun | Samsun: 32.81 | ||||

Trabzon | Trabzon: 33.21 | ||||

Ertekin et al. [93] | Antalya | For autumn: φ − 3.41 For winter: φ + 8.14 For spring: φ − 23.92 For summer: φ − 35.17 | For throughout the Turkey: φ−17.31 | south-facing | Liu and Jordan |

Edirne | |||||

Hakkari | |||||

Izmir | |||||

Sanliufa | |||||

Trabzonf | |||||

Zhao [94] | Singapore (1.3667 N, 103.8 E) | 27.1, 18.1, 3.4 | - | southwest facing | ARMA model [95] |

0.1, 0.1, 0.1 | |||||

0.1, 0.1, 0.1 | |||||

12.5, 23.3, 28.7 | |||||

Maru [96] | Jodhpur, India | 49.8, 40.20, 27, 9, 0, 0 | 31.80 | south-facing | Liu and Jordan |

0, 3.60, 21.6 | |||||

39, 50.40, 52.80 | |||||

Khatib [5] | Malaysia, 5 cities | - | - | Liu and Jordan | |

Kuala Lumpur, | 29, 19, 5, 0, 0, 0, 0, 0, 0, 14, 24, 24 | ||||

Johor Bharu, | 24, 17, 3, 0, 0, 0, 0, 0, 0, 11, 22, 23 | ||||

Ipoh, | 28, 19, 6, 0, 0, 0, 0, 0, 2, 13, 22, 25 | ||||

Kuching | 19, 16, 3, 0, 0, 0, 0, 0, 0, 11, 21, 22 | ||||

Alor Setar | 32, 22, 8, 0, 0, 0, 0, 0, 2, 15, 26, 31 | ||||

Kazem [97] | Sohar, Oman (24°20′ N,56°40′ E) | 57, 48, 32 | - | - | Liu and Jordan |

10, 0, 0 | |||||

0, 3, 25 | |||||

44, 55, 60 | |||||

Ismail [98] | Ramallah, Palestinian (31.8 N, 35.45 E) | Change between 6.5 and 62.6 from June to December | 32.8 | - | Jain model [99] |

Despotovic [100] | Belgrade, Serbia (44.8 N, 20.46 E) | Average of optimum monthly tilt angle is 43.55 | 39.9 | south-facing | Liu and Jordan |

© 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mousavi Maleki, S.A.; Hizam, H.; Gomes, C.
Estimation of Hourly, Daily and Monthly Global Solar Radiation on Inclined Surfaces: Models Re-Visited. *Energies* **2017**, *10*, 134.
https://doi.org/10.3390/en10010134

**AMA Style**

Mousavi Maleki SA, Hizam H, Gomes C.
Estimation of Hourly, Daily and Monthly Global Solar Radiation on Inclined Surfaces: Models Re-Visited. *Energies*. 2017; 10(1):134.
https://doi.org/10.3390/en10010134

**Chicago/Turabian Style**

Mousavi Maleki, Seyed Abbas, H. Hizam, and Chandima Gomes.
2017. "Estimation of Hourly, Daily and Monthly Global Solar Radiation on Inclined Surfaces: Models Re-Visited" *Energies* 10, no. 1: 134.
https://doi.org/10.3390/en10010134