# Short-Term Forecasting of Large-Scale Clouds Impact on Downwelling Surface Solar Irradiation

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## Abstract

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## 1. Introduction

^{1}) to forecast satellite-derived effective cloud albedo up to 4 h, and using SPECMAGIC NOW, surface irradiances were calculated. In addition, in the context of short-term forecasting of cloud albedo, a comparison of two optical flow methods TV-L

^{1}and Farnebäck, was performed, with the first method performing better than the former one. Teerakawanich et al. [30] used the optical flow algorithm proposed by Farnebäck to track cloud movement on sky images and the calculated vectors used as input in a convolution neural network (CNN) in order to predict cloud cover events 1 to 2 min in advance. The method showed better results during wintertime when the clear sky and thick clouds are the prevailing sky conditions. During those days, the prediction error was as good as 5%, with this error increasing in the presence of thin clouds. Li et al. [31] performed cloud tracking and forecasting to satellite images using Shi–Tomasi’s method to select features to track, image filtering and finally Horn and Schunck (HS) and Lucas–Kanade (LK) optical flow method to track those features. Although the optical flow methods used originally are dense, the segmentation performed by Shi–Tomasi’s method resulted in a sparse vector field, which requires less computational time. They found that LK with a Gaussian filter as a preprocessor was the most accurate and efficient method. However, their main finding was that satellite cloud images could be useful for irradiance predictions, providing predictable features in wide areas with long-time movement. In this study, for the calculation of the dense optical flow, the Farnebäck [32] and TV-L

^{1}[33] algorithms have been implemented using OpenCV open-source library.

## 2. Materials and Methods

^{1}(FRB and TVL hereafter) applied either on COT and on CMF. We select to treat both variables in order to investigate differences in the final product. COT is a satellite-based product that can be directly retrieved in real time without any post-processing. It describes the attenuation of DSSI reaching the surface through a cloud. On the other hand, CMF describes more directly the cloud effect on DSSI (it describes the attenuation as a fraction compared with cloudless sky DSSI) and especially the important variations caused by low COT values. Cloud inputs are then fed to the FRTM to produce the operational forecast.

#### 2.1. Clouds Observation

_{cls},

_{cls}is the irradiance under clear sky conditions as simulated by the FRTM [36].

#### 2.2. Cloud Motion Vector

#### 2.2.1. Optical Flow

_{1}and u

_{2}, so it cannot be solved, and in order to obtain the solution of Equation (3), an additional constrain can provide the other equation needed.

^{1}norm and a regularization term using the total variation of the flow. In the bibliography of the aforementioned methods, both algorithms were evaluated on a widely used test sequence with known velocity filed, the Yosemite sequence of images, and FRB and TVL methods had small average angular error compared to other techniques [32,33].

#### 2.2.2. FRB

**x**= (x,y)

^{T}) are expressed as:

**x**), which is the desirable field; if local polynomial approximations are used instead of global and after a series of approximations and parameterizations, a robust algorithm is provided, described by [32] in detail. One of the basic assumptions of the FRB method is that the displacement field is slowly varying in space in order to implement the method over the wider areas than point-wise, which is too noisy. In addition, the FRB method works well with small displacements, in contrast to large displacements, which introduce errors in the model. Using iterations and a priori displacement field in the first step is one-way to obtain more accurate results, and especially the approach of multiscaled displacement estimation can obtain increasingly more accurate estimates starting from a coarse scale to get the first estimate of the displacement field and propagate this through finer scales.

_{max}− X)/(X

_{max}− X

_{min}), where X represents each parameter value before the normalization, and the X

_{max}and X

_{min}are the maximum and minimum values of the range of the parameter, respectively.

#### 2.2.3. TVL

#### 2.3. Fast Radiative Transfer Model

#### 2.4. Statistical Tools

_{i}= x

_{f}− x

_{0}are the residuals calculated as the difference between the forecasted values (x

_{f}) and the real observed values (x

_{0}), and N is the total number of values. RMSE describes the overall spread of the error distribution, while MBE quantifies the bias and additionally detects overestimations (MBE > 0) or underestimations (MBE < 0). Finally, the mean absolute error (MAE), the correlation coefficient (r), as well as the standard deviation (σ) were used to represent the proportion of the variability between the forecasted and real observed values.

## 3. Results

#### 3.1. Short-Term Forecasting Overview

#### 3.2. FRB vs. TVL

#### 3.3. COT vs. CMF

#### 3.4. CMV vs. PRS

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ACS | Average cloud speed |

CCM | Cross-correlation method |

CDC | Cloud direction change |

CMF | Cloud modification factor |

CMV | Cloud motion vector |

CNN | convolution neural network |

COT | Cloud optical thickness |

CPP-SICCS | Cloud physical properties of the surface insolation under clear and cloudy skies by SEVIRI |

CPU | Central processing unit |

DSSI | Downwelling surface solar irradiation |

EO | Earth observation |

EUMETSAT | European Organisation for the Exploitation of Meteorological Satellites |

FRB | Farnebäck motion flow method |

FRTM | Fast radiative transfer model |

FY-4A | FengYun-4A |

HPC | High-performance computing |

HS | Horn and Schunck |

IEA | International Energy Agency |

LK | Lucas–Kanade |

LUT | Lookup table |

MAE | Mean absolute error |

MBE | Mean bias error |

MSG | Meteosat second generation |

NWP | Numerical weather prediction |

OpenCV | Open-source computer vision library |

PIV | Particle image velocimetry |

PRS | Persistent |

PV | Photovoltaic |

r | Correlation coefficient |

RAM | Random-access memory |

RMSE | Root mean square error |

SAFNWC | Satellite application facilities to support nowcasting and very short range forecasting |

SEVIRI | Spinning enhanced visible and infrared imager |

SPECMAGIC | Spectrally resolved mesoscale atmospheric global irradiance code |

TVL | Total variation of the motion flow method using the L^{1} norm |

TRS | Transition |

UTC | Coordinated universal time |

VOF | Variational optical flow |

σ | Standard deviation |

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**Figure 1.**The cloud modification factor (CMF) for 14, 22 and 30 April 2020 at 12:15 UTC, as calculated by the fast radiative transfer models (FRTM) using as input the Meteosat second generation (MSG) cloud optical thickness (COT).

**Figure 3.**The sensitivity parameters optimization for the CMV COT approach as a function of the normalized score of forecasted pixels for 15 min-ahead time horizon. (

**a**) Downsampling rate, (

**b**) Pyramid layers, (

**c**) Number of search iterations, (

**d**) Window size, (

**e**) Size of pixel neighborhood, (

**f**) Value of Gaussian filter.

**Figure 5.**The real (

**a**) and the FRB forecasted (

**b**) COT map for 30 April 2020 at 12:15 UTC, as well as the corresponding real (

**c**) and FRB forecasted (

**d**) CMF maps for 3 h-ahead (12 time-step forecasts).

**Figure 6.**Contour plot of the FRB forecasted COT mean absolute error (MAE) percentage as a function of COT classes for 3 h ahead at 15 min intervals.

**Figure 7.**The CMF error during the 3 case study days for the PRS, FRB and TVL short-term forecasting approaches as a function of RMSE and MBE (

**a**), and a zoomed plot for the two CMV methods (

**b**) as to highlight the similarities and discrepancies of the same statistics.

**Figure 8.**The cloudy sky to clear sky TRN forecasting error of CMF in terms of RMSE during the 3 case study days for the PRS, COT, and CMF short-term forecasting approaches for 15 min, 1, 2 and 3 h forecast horizon.

**Figure 9.**Absolute difference between the forecast and real CMF for 15 min ahead as a function of the CMF change (

**a**). The RMSE in terms of CMF for the same forecast time horizon for various CMF classes (

**b**).

**Figure 10.**Density scatter plots of 30 April 2020 covering Europe and North Africa (i.e., 1.5 million pixels) for the PRS (upper line) and FRB forecasted COT (lower line) short-term forecast approaches, for the 15 min, 1, 2 and 3 h ahead time horizons.

**Figure 11.**Classification of PRS and forecasted COT in terms of MAE ± 1σ for the 15 min forecast time horizon.

**Figure 12.**Difference between the CMV and the real CMF during 14 April 2020 at 15 min, 1, 2 and 3 h ((

**a**–

**d**), respectively) ahead time horizons, as well as the difference between the PRS and the real CMF for the same time horizons (

**e**–

**h**).

**Figure 13.**Taylor diagram for the overall CMF error for PRS and CMV approaches under all and TRN conditions.

**Table 1.**The cloud motion vector characteristics and statistics of the selected days in terms of average cloud speed (ACS) and cloud direction change (CDC) under all-sky conditions, clear to cloudy and cloudy to clear sky condition transition (TRNs) and cloudy persistence during the studied 3 h time horizon, i.e., from 9:15 to 12:15 UTC.

Cloud Motion Vector Analysis | 14/04/2020 | 22/04/2020 | 30/04/2020 |
---|---|---|---|

Total number of data comparison | 1.45 million/image × 12 forecasts × 3 days = 52.2 million | ||

Cloud coverage (million pixels) | 9.0 (52%) | 5.6 (32%) | 9.9 (57%) |

ACS (km/h) | 37 | 11 | 23 |

CDC (degrees) | 3 | 13 | 7 |

Total number of clear to cloudy TRN | 2.8 (16%) | 1.7 (9.7%) | 2.5 (14.5%) |

ACS (km/h) | 49 | 17 | 36 |

CDC (degrees) | 6 | 21 | 13 |

Total number of cloudy to clear TRN | 1.3 (7.6%) | 1.1 (6.2%) | 1.0 (5.5%) |

ACS (km/h) | 42 | 14 | 27 |

CDC (degrees) | 2 | 15 | 7 |

Total number of cloudy to cloudy | 5.3 (30.3%) | 3.0 (17.2%) | 6.8 (39%) |

ACS (km/h) | 20 | 2 | 6 |

CDC (degrees) | 1 | 3 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Kosmopoulos, P.; Kouroutsidis, D.; Papachristopoulou, K.; Raptis, P.I.; Masoom, A.; Saint-Drenan, Y.-M.; Blanc, P.; Kontoes, C.; Kazadzis, S. Short-Term Forecasting of Large-Scale Clouds Impact on Downwelling Surface Solar Irradiation. *Energies* **2020**, *13*, 6555.
https://doi.org/10.3390/en13246555

**AMA Style**

Kosmopoulos P, Kouroutsidis D, Papachristopoulou K, Raptis PI, Masoom A, Saint-Drenan Y-M, Blanc P, Kontoes C, Kazadzis S. Short-Term Forecasting of Large-Scale Clouds Impact on Downwelling Surface Solar Irradiation. *Energies*. 2020; 13(24):6555.
https://doi.org/10.3390/en13246555

**Chicago/Turabian Style**

Kosmopoulos, Panagiotis, Dimitris Kouroutsidis, Kyriakoula Papachristopoulou, Panagiotis Ioannis Raptis, Akriti Masoom, Yves-Marie Saint-Drenan, Philippe Blanc, Charalampos Kontoes, and Stelios Kazadzis. 2020. "Short-Term Forecasting of Large-Scale Clouds Impact on Downwelling Surface Solar Irradiation" *Energies* 13, no. 24: 6555.
https://doi.org/10.3390/en13246555