Políticas comerciales en la provincia del Carchi

Cloud motion identification is the next important step to compute the irradiance forecast. Most of the literature compares two consecutive images to identify pixel correlations and cloud velocity fields. Then, assuming spatial homogeneity, a unique motion vector, here called global motion vector, is obtained. Finally, assuming a persistent cloud motion for the following time interval, the cloud map is advected at the speed and direction of the global motion vector to obtain the predicted cloud map. Several methods have been proposed in the literature

for cloud motion identification. Chow et Al., [14], use the cross-correlation method (CCM), applied to two consecutive images, to search the vector with the largest cross-correlation coefficient. Another technique for cloud tracking is the optical flow, [119], which consists of a collection of apparent velocities of objects in an image. It is applied for predicting sun occlusions in [120], using consecutive frames shot at 5 seconds distance. To stabilize the tracking process, the Kalman Filter is applied as a predictor-corrector algorithm. Authors of [121] propose to use the particle image velocimetry (PIV) and by then applying the k-means clustering on the obtained velocity vectors in order to obtain a representative velocity vector. Quesada-Ruiz et al. in [122] propose a method for cloud tracking applied to intra-hour direct normal irradiance forecast. A sector-based method is used to detect the direction of motion of potentially sun-blocking clouds, and an adjustable-ladder method focuses on sky regions that potentially affects DNI values. Finally, Bernecker et al. in [123] introduced non-rigid registration for detecting cloud motion. A sun occlusion probability is filtered by a Kalman filter to obtain continuous GHI forecasts for up to 10 min.

In our analysis three methods are considered to compute the motion fields:

1. Particle Image Velocimetry (PIV). In brief, PIV consists in comparing two consecutive pictures by evaluating the cross-correlation between portions of the images, called interrogation areas. This allows inferring the most likely particle displacement and to compute the motion vectors. We use the "MPIV" library in [124] and using an inter- rogation window of 32x32 pixels, the velocity vectors are calculated by the minimum quadratic difference algorithm, and with 0 overlapping between consecutive windows.

2. The optical flow (OF). OF is performed by implementing the Lucas-Kanade method is its Matlab formulation, [125]. It assumes that the flow is constant in a local neighbourhood of the pixel under consideration, and solves the basic optical flow equations for all the pixels in that neighbourhood, using the least squares criterion.

3. The persistent method. This method assumes that the clouds are persistent in a short- term horizon, and therefore the global cloud motion vector is zero.

Once the cloud fields are obtained from the PIV and OF, the global motion vector is obtained by spatially averaging the obtained vectors.

4.6.1 Local Cloud Cover Computation

The last step of our chain aims at predicting the local cloud cover at the following time step. It consists in translating the current cloud map according to the global motion vector, which is scaled in magnitude according to the forecasting horizon. This leads to the so-called forecasted cloud map.

Figure 4.5 – Example of the forecasted cloud map procedure.

the undistorted view of the sky with the sun location (blue circle) and motion vectors (green arrows). The global motion vector, obtained by spatially averaging the vectors, is used to translate the cloud map obtained by segmenting the original image. The translated cloud map is shown in Fig. 4.5b, where the white color denotes cloudy pixels, blue the clear-sky, and yellow the circumsolar region. Fig. 4.5c shows the 1 min ahead realization. Fig. 4.5d compares the forecasted cloud map (purple color) against the future ground truth cloud map from Fig. 4.5c (green color). The white color denotes those pixels which are correctly classified as cloudy.

The forecasted local cloud cover is computed as the percentage of cloudy pixels in the fore- casted cloud map in a region around the sun. The considered region is a disk centered at the sun position. We consider a circumsolar area rather than the whole picture since this is the region with the largest interest when considering short-term sun occlusions by clouds.

4.6.2 Results on Cloud Motion

In order to evaluate the performance of the cloud motion, we select 20 consecutive pictures during a partly cloudy period and we manually segment them such that the segmentation error is negligible in this analysis. Then, the three cloud motion methods (PIV, OF and Persistent) are applied to obtain the forecasted local cloud cover (which is computed on an area of 100 pixels around the sun position). We define the cloud motion error as the relative error between the forecasted local cloud cover and the ground truth one.

Table 4.3 – Comparison on cloud motion. PIV OF Persistent Cloud Motion Error [%] 2.0 1.2 2.5

following analysis.