# Probabilistic Solar Forecasts as a Binary Event Using a Sky Camera

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## Abstract

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## 1. Introduction

## 2. Overall Methodology and Forecasts Evaluation

## 3. Deterministic Forecasts of Cloud Presence with a Sky Camera

- The picture taken with the sky camera is divided into the different sectors given in Figure 4, since the movement of the clouds will depend on the sector covered by the sky camera.
- The cloud motion vector (CMV) is calculated for each sector by applying the maximum cross-correlation method.
- Different quality tests are applied to ensure the correct determination of the cloud motion.

## 4. Post-Processing with Binary Probabilistic Models

#### 4.1. Parametric Approach

#### 4.2. Non-Parametric Approach

#### 4.3. Implementation

- The deterministic forecast of cloud presence ${\widehat{y}}_{t+h}$;
- The current clear sky index $CS{K}_{t}$;
- The mean over the five past clear sky indices $\overline{CSK}$.

## 5. Case Study and Data

## 6. Results and Discussion

#### 6.1. Deterministic Forecasts Quality

#### 6.2. Probabilistic Forecasts Quality

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ASI | All Sky Imager |

BS | Brier Score |

CIESOL | Center of Research of Solar Energ |

CMV | Cloud Motion Vector |

CSP | Concentrated Solar Plant |

DNI | Direct Normal Irradiance |

DT | Decision Trees |

FAR | False Alarm Ratio |

GLM | Generalized Linear Models |

MSG | MeteoSat Second Generation |

NWP | Numerical Weather Prediction |

POD | Probability Of Detection |

POFD | Probability Of False Detection |

PV | Photovolatic |

RF | Random Forest |

RMSE | Root Mean Square Error |

ROC | Relative Operating Characteristic |

SR | Success Rate |

SS | Skill Score |

## Appendix A. Numerical Results of Forecast Evaluation

**Table A1.**Numerical results of the evaluation of deterministic and probabilistic forecasts for the different horizons.

Horizon | Accuracy | BS | SS | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

(Minutes) | ASI | Probit | Logit | RF | Climato | Probit | Logit | RF | Probit | Logit | RF |

1 | 0.817 | 0.893 | 0.915 | 0.934 | 0.198 | 0.074 | 0.072 | 0.053 | 0.626 | 0.636 | 0.732 |

2 | 0.815 | 0.892 | 0.911 | 0.925 | 0.198 | 0.078 | 0.075 | 0.059 | 0.606 | 0.621 | 0.702 |

3 | 0.814 | 0.889 | 0.907 | 0.920 | 0.198 | 0.080 | 0.078 | 0.064 | 0.596 | 0.606 | 0.677 |

4 | 0.814 | 0.884 | 0.902 | 0.916 | 0.198 | 0.082 | 0.081 | 0.067 | 0.586 | 0.591 | 0.662 |

5 | 0.813 | 0.880 | 0.899 | 0.911 | 0.198 | 0.084 | 0.082 | 0.071 | 0.576 | 0.586 | 0.641 |

6 | 0.813 | 0.871 | 0.893 | 0.909 | 0.198 | 0.086 | 0.084 | 0.073 | 0.566 | 0.576 | 0.631 |

7 | 0.814 | 0.870 | 0.892 | 0.908 | 0.197 | 0.087 | 0.085 | 0.074 | 0.558 | 0.569 | 0.624 |

8 | 0.814 | 0.879 | 0.896 | 0.906 | 0.197 | 0.087 | 0.086 | 0.075 | 0.558 | 0.563 | 0.619 |

9 | 0.815 | 0.874 | 0.893 | 0.906 | 0.196 | 0.088 | 0.087 | 0.076 | 0.551 | 0.556 | 0.612 |

10 | 0.816 | 0.875 | 0.893 | 0.905 | 0.196 | 0.089 | 0.087 | 0.077 | 0.546 | 0.556 | 0.607 |

11 | 0.816 | 0.873 | 0.892 | 0.905 | 0.195 | 0.089 | 0.088 | 0.078 | 0.544 | 0.549 | 0.600 |

12 | 0.817 | 0.877 | 0.894 | 0.904 | 0.194 | 0.089 | 0.088 | 0.078 | 0.541 | 0.546 | 0.598 |

13 | 0.818 | 0.876 | 0.894 | 0.905 | 0.194 | 0.090 | 0.088 | 0.078 | 0.536 | 0.546 | 0.598 |

14 | 0.819 | 0.874 | 0.893 | 0.905 | 0.194 | 0.090 | 0.089 | 0.079 | 0.536 | 0.541 | 0.593 |

15 | 0.820 | 0.878 | 0.895 | 0.905 | 0.193 | 0.090 | 0.089 | 0.080 | 0.534 | 0.539 | 0.585 |

16 | 0.821 | 0.874 | 0.894 | 0.905 | 0.193 | 0.091 | 0.089 | 0.081 | 0.529 | 0.539 | 0.580 |

17 | 0.822 | 0.878 | 0.896 | 0.904 | 0.193 | 0.091 | 0.089 | 0.081 | 0.528 | 0.539 | 0.580 |

18 | 0.823 | 0.884 | 0.898 | 0.903 | 0.192 | 0.091 | 0.089 | 0.082 | 0.526 | 0.536 | 0.573 |

19 | 0.824 | 0.884 | 0.898 | 0.904 | 0.192 | 0.091 | 0.089 | 0.082 | 0.526 | 0.536 | 0.573 |

20 | 0.824 | 0.884 | 0.899 | 0.905 | 0.191 | 0.091 | 0.089 | 0.083 | 0.524 | 0.534 | 0.565 |

21 | 0.825 | 0.887 | 0.900 | 0.905 | 0.191 | 0.091 | 0.090 | 0.082 | 0.524 | 0.529 | 0.571 |

22 | 0.826 | 0.891 | 0.901 | 0.905 | 0.191 | 0.091 | 0.090 | 0.083 | 0.524 | 0.529 | 0.565 |

23 | 0.827 | 0.896 | 0.901 | 0.905 | 0.191 | 0.091 | 0.090 | 0.083 | 0.524 | 0.529 | 0.565 |

24 | 0.827 | 0.888 | 0.900 | 0.905 | 0.190 | 0.092 | 0.090 | 0.084 | 0.516 | 0.526 | 0.558 |

25 | 0.828 | 0.894 | 0.901 | 0.905 | 0.190 | 0.092 | 0.090 | 0.084 | 0.516 | 0.526 | 0.558 |

26 | 0.828 | 0.895 | 0.901 | 0.904 | 0.190 | 0.092 | 0.091 | 0.084 | 0.516 | 0.521 | 0.558 |

27 | 0.828 | 0.892 | 0.901 | 0.905 | 0.190 | 0.092 | 0.091 | 0.085 | 0.516 | 0.521 | 0.553 |

28 | 0.828 | 0.890 | 0.901 | 0.904 | 0.189 | 0.093 | 0.092 | 0.085 | 0.508 | 0.513 | 0.550 |

29 | 0.828 | 0.891 | 0.901 | 0.904 | 0.189 | 0.093 | 0.092 | 0.085 | 0.508 | 0.513 | 0.550 |

30 | 0.828 | 0.887 | 0.900 | 0.903 | 0.189 | 0.094 | 0.092 | 0.086 | 0.503 | 0.513 | 0.545 |

Overall | 0.821 | 0.883 | 0.899 | 0.908 | 0.198 | 0.088 | 0.087 | 0.077 | 0.556 | 0.561 | 0.611 |

## Appendix B. Discussion on the Threshold Used to Convert Probability Forecasts to Deterministic Forecasts

**Figure A1.**Evolution of the accuracy for a probability threshold ranging from 0% to 100%. This threshold is used to convert the probabilistic forecasts into deterministic forecasts for the training set (year 2010).

**Figure A2.**Distribution of the probability forecast of three discrete choice models for the training set (year 2010).

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**Figure 1.**Diagram of the implementation of the forecasting models at time t and a horizon of forecast h.

**Figure 3.**A representation of the sky over CIESOL center. (

**A**) image, represents the original sky cam image; (

**B**) image, the processed sky camera image.

**Figure 7.**Number of observation/forecast pairs (blue bars) and ratio of observed cloudless skies (red line) in the test set (2011) for forecast horizons ranging from 1 to 30 min.

**Figure 8.**Accuracy (or fraction correct) of the deterministic forecasts before (sky imager (ASI)) and after the post-processing by the 3 discrete choice models (Logit, Probit, and RF).

**Figure 11.**BS scores of the original ASI forecasts, of the climatology model used as a reference, and of the probabilistic forecasts resulting from post-processing with the 3 discrete-choice models.

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## Share and Cite

**MDPI and ACS Style**

David, M.; Alonso-Montesinos, J.; Le Gal La Salle, J.; Lauret, P.
Probabilistic Solar Forecasts as a Binary Event Using a Sky Camera. *Energies* **2023**, *16*, 7125.
https://doi.org/10.3390/en16207125

**AMA Style**

David M, Alonso-Montesinos J, Le Gal La Salle J, Lauret P.
Probabilistic Solar Forecasts as a Binary Event Using a Sky Camera. *Energies*. 2023; 16(20):7125.
https://doi.org/10.3390/en16207125

**Chicago/Turabian Style**

David, Mathieu, Joaquín Alonso-Montesinos, Josselin Le Gal La Salle, and Philippe Lauret.
2023. "Probabilistic Solar Forecasts as a Binary Event Using a Sky Camera" *Energies* 16, no. 20: 7125.
https://doi.org/10.3390/en16207125