## 4 Evaluation and Discussion
### Evaluation Index of the Quality of the Generated Data
#### 4.1.1 Standard Deviation (STD)  
The STD, denoted by the Greek letter (\(\sigma\)), is a statistical metric that measures data value dispersion or difference [58]. A lower STD score means that the data points are close to the median (also known as the anticipated values) of the collection, whereas a higher STD score shows that data points are distributed throughout a broader scope of real values. Equation (10) describes the computation of STD. \[\sigma_{\text{t}}=\sqrt{\frac{1}{\text{N}}\sum_{\text{i=i}}^{\text{N}_{\text{ t}}}(y_{\text{ti}}-\mu_{\text{t}})^{2}}(\text{t}=1,2,\ldots,60) \tag{10}\]  
where \(\mu_{\text{t}}\) and \(\sigma_{\text{t}}\) are the anticipated value and the STD of a collection of solar radiation data \(y_{\text{ti}}\) at a given period t, and \(\text{N}_{\text{t}}\) is the overall specimen volume of that set. This statistical measure examines in practice the statistical similarity between the original and augmented solar radiation data curves based on the distribution of the solar radiation data curve to assess the patterns and variety of produced specimens, such as vectors consisting of 60 medium values for solar radiation data that are identical at specific time points (n = 60), based on [1]. Regarding a collection of solar radiation data produced at a specific period, a higher STD could refer to the larger dispersion grade of the collection, which validates the solar radiation data variety at the same time point. However, a low STD score means that the generative model can only remember the training data and not provide diversity. Figure 4 compares the produced and actual curves for all three locations (i.e., the dataset that was created depending on GAN-CSVR and the original solar radiation dataset). The blue curves match the orange curves closely in most, but there is a little difference overall. Moreover, the visualization curves of other meteorological data are illustrated in the Supplementary File. The samples generated by the GAN-CSVR model can sometimes cover a broader range of values than the actual samples. This fact shows that the GAN-CSVR model can retain the maximum pattern diversity for the original dataset samples. Thus, the GAN-CSVR model can generate new specimens not included in the original training data but that adhere to a similar statistical distribution as the authentic specimens. To summarize, the GAN-CSVR model aims to create distinctive new specimens that extract the inherent properties of the pristine data. The GAN-CSVR model offered high pattern diversity where the generated solar radiation data curves were similar to the original but not identical. This event further confirms the two critical properties of the GAN-CSVR model: statistical similarity and pattern diversity for the new augmented datasets. The STD values of solar radiation data between the original and augmented datasets by the GAN-CSVR model are 0.0208, 0.1603, and 0.9393 for San Francisco, San Diego, and Los Angeles, respectively. The error value of the STD in Los Angeles is slightly higher than in San Francisco and San Diego. The varied geography of the area, in addition to the rapid climatic fluctuations and the periodic cloudiness cycle, may be responsible for the high value for error of the STD in Los Angeles. This study utilizes standard datasets for three major zones of California, which are San Diego, San Francisco, and Los Angeles; these regions cover a variety of climates and experience a variety of weather conditions. Using three different datasets from distinct locations is a robust validation strategy and evaluates how well the GAN-CSVR model  
Figure 4: The STD curve of GHI data for the original and augmented dataset. generalizes across diverse data distributions. The normalization techniques help in the success of the GAN-CSVR model to adapt to different data types, making it versatile enough to generate realistic samples across various scenarios.