## 2 Characterization of Wind-Solar Power Generation for Earth Regions
### The Renewable Resources  
In prospective net-zero emissions energy systems, solar and wind resources will assume a predominant role; the potential emergence of spatial and temporal misalignments between the availability of these resources and the temporal patterns of electricity demand poses a substantial challenge to the overall reliability of the energy system. Historical data from a specific year are often used to reflect or estimate annual solar and wind power production. However, relying on data from just one year does not capture all the various aspects and characteristics of an energy system [32]. Initially, a deterministic model or scenario creates a mathematical representation where identical inputs or initial conditions invariably yield consistent outputs, disregarding randomness or uncertainty in the modeled process. However, different reference years can lead to differing probabilistic outcomes, with a standard year being more likely to occur than extreme years. Employing a probabilistic, stochastic, or non-deterministic model in a second phase seeks to quantify the uncertainty associated with the variable(s) under investigation. The uncertainty associated with renewable energy sources has been extensively analyzed using Monte Carlo analysis (MCA). The MCA entails conducting numerous simulations with random variations in uncertain input. Typically, PDFs are used for this propagation since not all possible values are feasible or realistic (for example, negative wind speeds, negative solar irradiance, or freezing temperatures in typically warm regions might not be adequate). Each assigned PDF is executed multiple times using a single set of inputs for each run. The number of runs can vary from hundreds to several hundred, but it can also be determined statistically. According to [PERSON] formula [33; 34] and [PERSON]'s extended expression of applicability to multivariate distributions [35], 93 runs that ensure a 95% probability of falling within a two-sided 95% confidence interval have to be run. Although this approach originates within the safety margins of the nuclear sector [36], it has found its application in the uncertainty analysis of energy sources [37; 38; 39]. Leveraging the POWER Data Access Viewer database from NASA [30], this study analyzes the solar and wind resource capacities of nine sites relevant to Earth's climate classification. These nine scenarios have been selected to include a comprehensive range of solar and wind resource magnitudes, effectively characterizing the primary terrestrial regions. Within each of these scenarios, solar and wind generation composition has been systematically estimated to ascertain the generation at each location and at any time over the whole Earth. Consequently, each scenario determines the generation at each geographical location over the year. The probabilistic nature of this time series is used to create synthetic datasets for a robust analysis. The statistical properties of solar irradiance, wind speed, and ambient temperature are determined using historical data from the NASA POWER Access Viewer [30] and other sources such as PVGIS [40]. Figure 2 illustrates steps to create the synthetic wind, solar, and temperature hourly data. The approach employed follows the steps of [PERSON] et al. [39] and [PERSON] et al. [38]. Having in mind the considered confidence and coverage and the availability of climatic data, firstly, the PDFs that best fit the observed data are identified using hourly values recorded from 2001 to 2023. The historical data are normalized against the weekly maximum values to obtain an auxiliary parameter, \(k_{i}\), used to generate synthetic data. This normalization removes seasonal effects and ensures the data fit within a common range for better comparison and analysis. Each week has a specific PDF associated with it. The auxiliary parameter being defined as:  
\[k_{i}=\frac{x_{i}}{\max(x_{week,i})} \tag{1}\]  
From the literature, solar irradiance data are best represented with a beta distribution [41], wind speed by Weibull [42].