# A Comprehensive Methodology for the Statistical Characterization of Solar Irradiation: Application to the Case of Morocco

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## Abstract

**:**

## Featured Application

**Determination and validation of solar irradiation data for the techno-economic valuation of solar projects.**

## Abstract

## 1. Introduction

#### 1.1. State of the Art

#### 1.2. Justification and Objectives

## 2. Materials and Methods

#### 2.1. Methodology

#### 2.2. Case Study Definition and Data Collection and Validation

**Figure 5.**Monthly irradiation values within the analyzed time intervals comparing pairs of databases and linear regression for the validation of data. Source: own elaboration.

**Figure 6.**Categorization of the DNI and GHI data according to the month and considered city. Source: own elaboration.

#### 2.3. Probability Distribution Function Fitting

## 3. Results and Discussion

#### 3.1. Obtained Results

**Table 6.**PDFs for the DNI case for each city and month (normal = Nor, logarithmic = Log, extreme value = ExV, gamma = Gmm, Weibull = Web, kernel = Krn). Source: own elaboration.

Zone | City | Month | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sept. | Oct. | Nov. | Dec. | ||

1 | Agadir | Log | ExV | ExV | ExV | Nor | Nor | ExV | Log | ExV | Nor | Log | Web |

Casablanca | ExV | Web | ExV | ExV | Log | Nor | ExV | Web | ExV | Nor | Krn | ExV | |

Essaouira | Krn | ExV | Nor | Nor | ExV | ExV | Nor | ExV | ExV | ExV | ExV | Log | |

Kenitra | ExV | Web | ExV | Log | Nor | Nor | ExV | Nor | ExV | Web | Gmm | Nor | |

Laayoune | ExV | Nor | Log | ExV | ExV | Log | Nor | Web | ExV | Web | Log | Log | |

Rabat | ExV | Web | Krn | Nor | Nor | Nor | Nor | Nor | Nor | ExV | Log | Nor | |

Safi | Log | Web | ExV | Nor | ExV | Nor | Nor | ExV | ExV | Log | Nor | Log | |

Sidi Ifni | Log | Log | ExV | Nor | ExV | Nor | Nor | ExV | ExV | ExV | ExV | Log | |

2 | Al Hoceima | ExV | Nor | Nor | Nor | ExV | Log | Log | Log | Log | Web | Log | ExV |

Larache | Log | Log | ExV | ExV | Log | Nor | Nor | Nor | Log | Nor | ExV | ExV | |

Nador | ExV | ExV | Nor | Krn | ExV | ExV | Log | ExV | Nor | ExV | Nor | Nor | |

Tanger | ExV | ExV | ExV | Log | Nor | Nor | Nor | Krn | Web | ExV | Log | ExV | |

Tetouan | ExV | Nor | Krn | Nor | ExV | Web | Log | Log | Nor | Nor | Log | Nor | |

3 | Beni Mellal | Krn | ExV | ExV | Nor | ExV | Log | Log | ExV | Nor | Log | Nor | ExV |

Fes | Nor | ExV | ExV | Web | Log | Log | Log | ExV | Nor | ExV | Log | ExV | |

Meknes | Nor | Web | ExV | ExV | Log | Krn | Nor | ExV | Web | Nor | Log | ExV | |

Oujda | ExV | ExV | Nor | ExV | ExV | Web | Web | ExV | ExV | Nor | Nor | Log | |

Taza | Nor | Log | ExV | ExV | ExV | Log | Web | Web | ExV | Web | Log | Log | |

4 | Ifrane | ExV | ExV | ExV | Nor | Nor | Log | Web | Log | ExV | Nor | Log | Nor |

Midelt | Log | ExV | Log | ExV | ExV | Log | Nor | ExV | Log | Log | ExV | Log | |

5 | Marrakech | Nor | Krn | ExV | Nor | ExV | ExV | Log | Log | Log | Log | Krn | Log |

6 | Er-Rachidia | Log | ExV | Log | ExV | ExV | ExV | Log | ExV | Log | Log | ExV | Log |

Ouarzazate | Nor | ExV | Log | Web | ExV | ExV | Web | Nor | Krn | Nor | Web | Log |

**Table 7.**PDFs for the GHI case for each city and month (normal = Nor, Logarithmic = log, extreme value = ExV, gamma = Gmm, Weibull = Web, kernel = Krn). Source: own elaboration.

Zone | City | Month | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sept. | Oct. | Nov. | Dec. | ||

1 | Agadir | ExV | Web | Web | Nor | Web | Web | Krn | Log | ExV | Web | Web | Log |

Casablanca | Nor | Gmm | Web | Nor | Nor | Web | ExV | Nor | Web | ExV | Nor | Web | |

Essaouira | Log | Gmm | ExV | Log | ExV | Log | ExV | ExV | Web | ExV | Log | Log | |

Kenitra | Nor | Log | Web | Log | Log | Web | ExV | ExV | Nor | Nor | Nor | Krn | |

Laayoune | ExV | Web | Nor | ExV | ExV | Log | ExV | Web | Web | Log | Log | Krn | |

Rabat | Log | Log | Web | Log | Nor | Log | ExV | Krn | Log | Nor | Log | Krn | |

Safi | Log | Log | ExV | Krn | ExV | Log | ExV | ExV | Nor | Nor | Log | Log | |

Sidi Ifni | Nor | Log | Log | Log | Nor | Nor | ExV | ExV | Nor | ExV | Web | Log | |

2 | Al Hoceima | Log | Log | Krn | Nor | ExV | Nor | Nor | Log | Log | Web | Log | Web |

Larache | Log | Log | Web | Log | Nor | Nor | Nor | Web | Nor | Nor | Log | ExV | |

Nador | Nor | Krn | Krn | Nor | ExV | Nor | Log | Nor | Log | Web | Web | Nor | |

Tanger | Log | Gmm | Web | Log | Web | Krn | Log | ExV | Nor | Web | Log | ExV | |

Tetouan | Log | Web | Web | ExV | ExV | ExV | Krn | Log | Log | ExV | Nor | ExV | |

3 | Beni Mellal | Nor | ExV | Log | Web | ExV | Web | Web | ExV | Web | Log | Nor | ExV |

Fes | Log | Nor | ExV | Log | Log | Web | Nor | Nor | ExV | Nor | Nor | ExV | |

Meknes | Log | Nor | ExV | Log | Log | ExV | Nor | ExV | ExV | Krn | Nor | ExV | |

Oujda | Nor | ExV | Log | ExV | ExV | Log | Web | Web | Nor | Web | Web | Log | |

Taza | Log | Log | Log | ExV | Krn | Log | Web | Nor | ExV | Web | Log | ExV | |

4 | Ifrane | ExV | ExV | ExV | ExV | Log | Log | Nor | Log | ExV | Nor | Nor | ExV |

Midelt | ExV | Nor | Log | Krn | ExV | Log | ExV | Nor | ExV | Log | Log | ExV | |

5 | Marrakech | Nor | Nor | Log | ExV | ExV | ExV | Log | Web | Web | Gmm | Log | Nor |

6 | Er-Rachidia | Gmm | Log | Log | Nor | Nor | Web | Nor | ExV | Log | Krn | Web | ExV |

Ouarzazate | Nor | Log | Nor | Web | ExV | ExV | ExV | Nor | Nor | Web | ExV | ExV |

**Figure 11.**Bar chart with the rate of appearance of the PDFs in each month per climatic zone (GHI case). Source: own elaboration.

#### 3.2. Analysis and Discussion of Results

^{2}. Next, from the PDF obtained for the city of Rabat in the month of October depicted at Figure 12, a Monte Carlo simulation was run.

^{2}. This figure also shows the evolution of the average of all the simulated values as the number of samples grows. The obtained mean of 137.01 kWh/m

^{2}represents a relative difference of 1.5% regarding the 2020 benchmark data of 139.12 kWh/m

^{2}. The interpretation of this result is that the PDF in Figure 12 can provide a set of Nsamples feasible values of accumulated monthly GHI for the benchmark city and month, whose behaviour properly reflects the implied stochastic pattern of the irradiation.

**Figure 13.**Basic structure of the Monte Carlo simulation algorithm for testing the PDFs. Source: own elaboration.

**Figure 14.**Evolution of the GHI average for October in Rabat according to the number of samples obtained in the Monte Carlo simulation. Source: own elaboration.

## 4. Conclusions

^{2}. This value was then confronted to the most recent satellite data corresponding to the same city and month, i.e., the year 2020. A relative difference of 1.5% was obtained, thus evincing the goodness of the method for representing the stochastic pattern of the irradiation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**CSP capacity installed in the MENA region. Source: own elaboration based on [3].

**Figure 2.**Characterization of solar irradiation in the scientific literature, dealing with either daily (H), average daily ($\overline{\mathrm{H}}$), hourly (I) or average hourly ($\overline{\mathrm{I}}$) global, beam (

_{b}) and diffuse (

_{d}) values. Source: own elaboration.

**Figure 4.**Climatic zones of Morocco. Source: own elaboration based on [57].

**Figure 9.**Bar chart with the rate of appearance of the PDFs in each month per climatic zone (DNI case). Source: own elaboration.

**Figure 10.**Example of the extreme value, normal and kernel PDFs’ fitting test results for the month of October at Nador, December at Kenitra and March at Tetouan (DNI case). Source: own elaboration.

**Figure 12.**Examples of the extreme value, normal and kernel PDFs’ fitting test results for the month of February in Ifrane, the month of October in Nador and the month of March in Tetouan (GHI case). Source: own elaboration.

Term of Solar Irradiance Forecasting | |
---|---|

Short-term irradiance forecasting[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35] | [9] Intra-hour GHI cloud retrieval technique to develop a physics-based smart persistence model |

[10] Intra-day GHI and DNI algorithm using cloud physical properties | |

[11] A 15 min GHI forecasting model | |

[12] Hourly-averaged GHI forecasts | |

[13] Hourly GHI and DNI clear-sky irradiance vs. RRTMG physical radiative transfer model | |

[14] Hourly and daily GHI from mesoscale atmospheric weather research forecasting model | |

[15] Hourly GHI with a three-dimensional meteorology–chemistry model including a treatment of aerosols | |

[16] Hourly GHI exponential smoothing model with decomposition methods | |

[17] A 1 min DNI under a probabilistic approach | |

[18] Short-term GHI with hybrid convolutional ANN model with spatiotemporal correlations | |

[19] Short-term GHI and DNI forecasts of a global numerical weather model | |

[20,21] A 5–30 min GHI and DNI with machine learning techniques | |

[22] A 15 min GHI and DNI with machine learning techniques | |

[23] Intra-day GHI with machine learning techniques | |

[24] A 30 min GHI with ANN algorithm | |

[25,26] Hourly GHI ANN models | |

[27] Mean daily GHI with ANN models | |

[28] A 500 ms–5 min GHI based on k-means algorithm | |

[29] A 5–30 min GHI and DNI based on the k-nearest neighbours algorithm | |

[30] A 30 min–5 h GHI Gaussian process regression method | |

[31] Daily GHI with ANN models for for 25 Moroccan cities | |

[32] Daily GHI with empirical and machine learning models for 5 Moroccan cities | |

[33] Monthly mean daily GHI using time series models | |

[34] Daily GHI with hybrid ARIMA–ANN model for 3 cities in Morocco | |

[35] Daily GHI with ANN models for 35 Moroccan, Algerian, Spanish and Mauritian cities | |

Monthly irradiance forecasting [36,37,38,39,40,41] | [36] Best Practices Handbook for the Collection and Use of Solar Resource Data, selection of potential sites |

[37] Steps for solar resource assessment, selection of potential sites | |

[38] Solar resource assessment, selection of potential sites | |

[39] Monthly data, ANN models are used to estimate it in Saudi Arabia | |

[40] ANN models are used to estimate it in Saudi Arabia | |

[41] ANN models are used to estimate it in Uganda | |

Use of satellite-based data for solar resource assessment | |

Use of satellite-based data for solar resource assessment [42,43,44,45,46,47,48,49,50,51,52,53,54] | [42] Satellite data comparison with ground measurements in Morocco |

[43] Satellite data comparison with ground measurements in North Africa | |

[44] Satellite data comparison with ground measurements in the Canary Islands | |

[45] Satellite data comparison with ground measurements for sites in Europe | |

[46] Satellite data validation through statistical methods in Algeria | |

[47] Satellite data validation through statistical methods in Spain | |

[48] Satellite data comparison with ground measurements for European and Mediterranean sites | |

[49,50,51] SARAH satellite database validation for several sites, especially for Africa | |

[52] PVGIS satellite database validation for both Europe and Africa | |

[53,54] Variability of irradiance values in areas with variable landforms |

Zone | City | Latitude [Degrees] | Longitude [Degrees] |
---|---|---|---|

1 | Agadir | 30.383 | −9.567 |

Casablanca | 33.567 | −7.667 | |

Essaouira | 31.517 | −9.783 | |

Kénitra | 34.300 | −6.600 | |

Laâyoune | 27.160 | −13.210 | |

Rabat | 34.050 | −6.767 | |

Safi | 32.283 | −9.233 | |

Sidi Ifni | 29.360 | −10.180 | |

2 | Al Hoceima | 35.180 | −3.850 |

Larache | 35.180 | −6.130 | |

Nador | 35.150 | −2.910 | |

Tànger | 35.733 | −5.900 | |

Tétouan | 35.580 | −5.330 | |

3 | Beni Mellal | 32.360 | −6.400 |

Fes | 33.933 | −4.983 | |

Meknes | 33.883 | −5.533 | |

Oujda | 34.793 | −1.933 | |

Taza | 34.217 | −4.000 | |

4 | Ifrane | 33.500 | −5.167 |

Midelt | 32.683 | −4.733 | |

5 | Marrakech | 31.617 | −8.033 |

6 | Er-Rachidia | 31.930 | −4.400 |

Ouarzazate | 30.933 | −6.900 |

CM-SAF and ERA5 | SARAH and ERA5 | SARAH and CM-SAF | |||||||
---|---|---|---|---|---|---|---|---|---|

City | MAD | MBD | RMSD | MAD | MBD | RMSD | MAD | MBD | RMSD |

Agadir | 17.57 | −11.62 | 23.53 | 23.18 | −19.75 | 29.28 | 12.91 | −5.01 | 16.09 |

Al Hoceima | 13.02 | 4.45 | 16.70 | 27.26 | −24.88 | 31.79 | 29.03 | −27.39 | 33.59 |

Beni Mellal | 20.98 | −20.33 | 24.05 | 20.52 | −19.43 | 24.26 | 13.14 | 1.78 | 16.24 |

Casablanca | 14.23 | −0.18 | 17.09 | 21.63 | −17.89 | 25.49 | 20.96 | −12.96 | 25.34 |

Er−Rachidia | 39.11 | −39.11 | 41.09 | 19.48 | −15.24 | 21.83 | 26.33 | 25.13 | 30.61 |

Essaouira | 17.98 | 17.71 | 21.04 | 18.80 | −17.32 | 22.90 | 33.18 | −32.71 | 36.88 |

Fes | 23.23 | −21.11 | 27.88 | 17.14 | −11.45 | 20.28 | 24.40 | 11.62 | 30.82 |

Ifrane | 23.82 | −23.01 | 26.82 | 26.35 | −25.51 | 29.89 | 13.02 | −1.68 | 16.97 |

Kenitra | 15.15 | 11.13 | 18.76 | 19.15 | −16.30 | 22.22 | 24.58 | −23.50 | 29.05 |

Laayoune | 14.55 | −12.71 | 17.80 | 11.92 | −8.08 | 15.02 | 12.38 | 6.21 | 15.81 |

Larache | 13.17 | −5.86 | 16.85 | 19.19 | −16.93 | 21.95 | 16.74 | −14.04 | 20.66 |

Marrakech | 10.61 | −7.06 | 13.47 | 14.30 | −8.06 | 16.70 | 12.88 | 0.02 | 15.75 |

Meknes | 12.61 | −7.89 | 15.56 | 16.73 | −13.23 | 19.22 | 13.46 | −3.79 | 16.84 |

Midelt | 24.60 | −24.36 | 27.14 | 25.74 | −23.79 | 30.58 | 15.78 | 1.58 | 19.79 |

Nador | 16.93 | 4.57 | 21.47 | 25.88 | −24.26 | 30.56 | 27.78 | −25.55 | 33.88 |

Ouarzazate | 21.79 | −21.71 | 24.18 | 15.92 | −9.87 | 21.35 | 19.81 | 14.58 | 24.82 |

Oujda | 14.81 | −2.52 | 17.49 | 19.23 | −18.68 | 22.31 | 19.54 | −13.91 | 24.61 |

Rabat | 15.24 | 8.14 | 17.83 | 21.76 | −19.38 | 24.95 | 25.31 | −22.44 | 29.88 |

Safi | 14.83 | 12.33 | 17.52 | 15.50 | −11.98 | 19.71 | 24.73 | −22.82 | 29.06 |

Sidi Ifni | 26.04 | −13.87 | 33.89 | 25.83 | −25.29 | 32.75 | 25.82 | −16.33 | 29.85 |

Tanger | 14.23 | −3.23 | 17.78 | 17.67 | −15.10 | 21.62 | 18.20 | −10.85 | 21.76 |

Taza | 10.98 | 0.43 | 13.66 | 15.42 | −10.35 | 18.40 | 15.78 | −8.96 | 19.57 |

Tetouan | 36.69 | −36.10 | 44.23 | 38.43 | −37.95 | 46.31 | 13.97 | −1.22 | 18.15 |

CM-SAF and ERA5 | SARAH and ERA5 | SARAH and CM-SAF | |||||||
---|---|---|---|---|---|---|---|---|---|

City | MAD | MBD | RMSD | MAD | MBD | RMSD | MAD | MBD | RMSD |

Agadir | 6.51 | 1.30 | 8.30 | 6.06 | 0.89 | 7.53 | 3.87 | 0.55 | 5.35 |

Al Hoceima | 7.54 | 4.80 | 8.93 | 6.05 | −2.51 | 8.96 | 6.55 | −6.20 | 8.20 |

Beni Mellal | 4.65 | −1.93 | 6.24 | 5.07 | −1.93 | 6.98 | 3.73 | 0.46 | 4.64 |

Casablanca | 7.23 | 5.53 | 8.51 | 5.70 | 2.44 | 6.88 | 5.29 | −1.27 | 6.99 |

Er-Rachidia | 11.00 | −11.00 | 12.24 | 4.38 | 1.77 | 6.05 | 14.16 | 13.81 | 15.11 |

Essaouira | 12.07 | 12.07 | 13.07 | 5.19 | 2.61 | 6.60 | 8.19 | −8.10 | 10.05 |

Fes | 4.97 | −1.24 | 6.23 | 5.62 | 3.88 | 6.86 | 6.91 | 5.90 | 8.40 |

Ifrane | 7.36 | −6.10 | 8.77 | 6.15 | −3.61 | 7.97 | 5.10 | 3.05 | 6.44 |

Kenitra | 10.45 | 10.34 | 11.96 | 5.49 | 3.73 | 6.57 | 5.54 | −4.89 | 7.55 |

Laayoune | 4.89 | 2.75 | 6.29 | 7.00 | 5.36 | 8.03 | 6.33 | 3.79 | 7.76 |

Larache | 3.95 | −0.55 | 5.17 | 4.59 | 2.38 | 5.51 | 3.30 | 2.33 | 4.21 |

Marrakech | 4.86 | 3.03 | 5.73 | 5.36 | 3.76 | 6.52 | 3.31 | 1.14 | 4.22 |

Meknes | 4.70 | 2.71 | 6.17 | 4.82 | 2.78 | 5.85 | 3.27 | 0.71 | 4.07 |

Midelt | 8.79 | −8.62 | 10.60 | 7.50 | −5.91 | 10.34 | 6.95 | 3.59 | 8.93 |

Nador | 7.50 | 2.81 | 9.61 | 5.75 | −1.49 | 8.63 | 5.12 | −2.92 | 6.61 |

Ouarzazate | 3.88 | −2.00 | 4.82 | 6.85 | 2.23 | 9.33 | 8.53 | 5.77 | 10.05 |

Oujda | 4.69 | 1.20 | 6.04 | 4.21 | 0.24 | 5.50 | 4.04 | 0.15 | 5.13 |

Rabat | 9.91 | 9.56 | 11.46 | 4.98 | 1.80 | 6.02 | 6.67 | −5.50 | 8.94 |

Safi | 9.06 | 8.88 | 10.20 | 5.09 | 3.03 | 6.38 | 5.75 | −4.79 | 7.78 |

Sidi Ifni | 12.48 | 0.31 | 15.45 | 8.17 | −2.60 | 11.66 | 11.22 | −4.97 | 13.01 |

Tanger | 5.61 | 3.63 | 6.86 | 5.26 | 3.00 | 6.31 | 3.89 | −0.30 | 4.68 |

Taza | 6.70 | 5.77 | 8.36 | 5.97 | 4.04 | 7.26 | 4.13 | −0.55 | 5.85 |

Tetouan | 13.08 | −12.41 | 18.69 | 10.75 | −7.97 | 16.04 | 5.42 | 4.87 | 7.87 |

Distribution Name | PDF [f(x)] | CDF [F(x)] |
---|---|---|

Beta | $\frac{{x}^{\alpha -1}{\left(1-x\right)}^{\beta -1}}{B\left(p,q\right)}$ | $\frac{{{\displaystyle \int}}_{0}^{z}\left({t}^{p-1}{\left(1-t\right)}^{q-1}dt\right)}{B\left(p,q\right)}$ |

Chi-square | $\frac{\mathrm{exp}\left(-x/2\right){x}^{\frac{v}{2}-1}}{{2}^{v/2}\text{}\mathsf{\Gamma}\left(v/2\right)}$ | $\frac{\gamma \left(\frac{v}{2},\frac{x}{2}\right)}{\mathsf{\Gamma}\left(\frac{v}{2}\right)}$ |

Exponential | $\frac{1}{\beta}\mathrm{exp}\left(-\frac{x-\mu}{\beta}\right)$ | $1-\mathrm{exp}\left(-x/\beta \right)$ |

Extreme value | $\frac{1}{\beta}\mathrm{exp}\left(\frac{x-\mu}{\beta}\right)\mathrm{exp}\left(-\mathrm{exp}\left(\frac{x-\mu}{\beta}\right)\right)$ | $1-{e}^{-{e}^{x}}$ |

Gamma | $\frac{{x}^{\left(\gamma -1\right)}\mathrm{exp}\left(-x\right)}{\mathsf{\Gamma}\left(\gamma \right)}$ | $\frac{{{\displaystyle \int}}_{0}^{x}\left({t}^{\alpha -1}\mathrm{exp}\left(-t\right)dt\right)}{\mathsf{\Gamma}\left(\gamma \right)}$ |

Lognormal | $\frac{\mathrm{exp}\left(-\left(\frac{{\left(ln\left(\frac{x-\theta}{m}\right)\right)}^{2}}{2{\sigma}^{2}}\right)\right)}{\left(x-\theta \right)\sigma \sqrt{2\pi}}$ | $\mathsf{\Phi}\left(\frac{\mathrm{ln}\left(x\right)}{\sigma}\right)$ |

Normal | $\frac{\mathrm{exp}\left(-\frac{{\left(x-\mu \right)}^{2}}{2{\sigma}^{2}}\right)}{\sigma \sqrt{2\pi}}$ | ${{\displaystyle \int}}_{-\infty}^{x}\frac{\mathrm{exp}\left(-{x}^{2}/2\right)}{\sqrt{2\pi}}$ |

Rayleigh | $\frac{x}{{\sigma}^{2}}\mathrm{exp}\left(-\frac{{x}^{2}}{2{\sigma}^{2}}\right)$ | $1-\mathrm{exp}\left(-\frac{{x}^{2}}{2{\sigma}^{2}}\right)$ |

T-distribution | $\frac{{\left(1+\left(\frac{{x}^{2}}{v}\right)\right)}^{-\frac{v+1}{2}}}{B\left(0.5,0.5v\right)\sqrt{v}}$ | $\frac{1}{2}+\frac{1}{2}\left[I\left(1;\frac{1}{2}r,\frac{1}{2}\right)-I\left(\frac{r}{r+{t}^{2}},\frac{1}{2}r,\frac{1}{2}\right)\right]sgn\left(t\right)$ |

Weibull | $\frac{\gamma}{\alpha}{\left(\frac{x-\mu}{\alpha}\right)}^{\gamma -1}\mathrm{exp}\left(-{\left(\frac{x-\mu}{\alpha}\right)}^{\gamma}\right)$ | $1-\mathrm{exp}\left(-\left({x}^{\gamma}\right)\right)$ |

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## Share and Cite

**MDPI and ACS Style**

Bouhorma, N.; Martín, H.; de la Hoz, J.; Coronas, S.
A Comprehensive Methodology for the Statistical Characterization of Solar Irradiation: Application to the Case of Morocco. *Appl. Sci.* **2023**, *13*, 3365.
https://doi.org/10.3390/app13053365

**AMA Style**

Bouhorma N, Martín H, de la Hoz J, Coronas S.
A Comprehensive Methodology for the Statistical Characterization of Solar Irradiation: Application to the Case of Morocco. *Applied Sciences*. 2023; 13(5):3365.
https://doi.org/10.3390/app13053365

**Chicago/Turabian Style**

Bouhorma, Naoufal, Helena Martín, Jordi de la Hoz, and Sergio Coronas.
2023. "A Comprehensive Methodology for the Statistical Characterization of Solar Irradiation: Application to the Case of Morocco" *Applied Sciences* 13, no. 5: 3365.
https://doi.org/10.3390/app13053365