# Systematic Analysis of Wind Resources for Eolic Potential in Bangladesh
## 3 Materials and Methods
For the physical model, \(\rho\) is the air density, i.e., 1.225 (Kg/m\({}^{3}\)), and \(A\) is the area for the rotor blades. In the present study, unit area (m\({}^{2}\)) is approximated for a wind turbine. Of note, area is another key variable for power estimations as power output doubles by increasing swept areas on the blades for turbines [15]. Model parameters for nonlinear regressions are calculated based on data sensitivity tests and least square methods. The least square method characterizes minimization of loss functions (shown in Equation (4)), which is also well-known as the sum of square error (SSE). For diverse datasets, consistency in determination of coefficients is established for SPPM to generalize fitting curves for all divisions in Bangladesh. Table 2 summarizes sensitivity tests and concludes for SPPM with sample size (N) of 1100. When the determination of coefficients, residual standard error (RSE), and SSE are found consistent and relatively small, SPPM model parameters are concluded for applications. To justify model accuracy, the mean absolute percentage error (MAPE) is calculated by Equation (5) \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data** & **ECMWF Reanalysis 5 th (ERA5) Generation at Pressure Levels** & **Global Wind Atlas (GWA) Simulation v3.0** \\ \hline Horizontal & & Global (30 km), Mesoscale (3 km), \\ Resolution & & \& Microscale (250 m) \\ \hline Vertical & & \\ Resolution & 37 levels (with 25 hPa) & 5 layers (10, 50 to 200 m) \\ \hline Temporal & & \\ Resolution & & Static (averaged from 2008 to 2017) \\ \hline Atmospheric & & \begin{tabular}{c} Wind (U, V) in (m/s) at 10 m; \\ 1000, 975, 950, 925, and 900 hPa \\ \end{tabular} & \begin{tabular}{c} Mean Wind Intensity (m/s) \\ \end{tabular} \\ \cline{2-3} and Power & & Mean Power density (W/m\({}^{2}\)) \\ \cline{2-3} Density & & Mean Boundary Layer Height (m) & 10, 50, 100, 150, and 200 m \\ \hline \
\begin{tabular}{c} Website: \\ Open Access \\ \end{tabular} & [[https://climate.copernicus.eu/climate-reanalysis](https://climate.copernicus.eu/climate-reanalysis)]([https://climate.copernicus.eu/climate-reanalysis](https://climate.copernicus.eu/climate-reanalysis)) & [[https://globalwindatlas.info/](https://globalwindatlas.info/)]([https://globalwindatlas.info/](https://globalwindatlas.info/)) \\ \hline
\begin{tabular}{c} Accessed \\ Date \\ \end{tabular} & 10 December 2020 & 5 December 2020 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of experimental data in the present study. based on [25]. Table 3 summarizes the finalized SPPM and model coefficients and the model predictability for power estimations. To obtain annual energy production (AEP), Equation (6) is incorporated, similar to [23; 24; 25]. Finally, pressure levels are approximated to meter by Equation (7) for comparing SPPM forecasts to observed wind speed, particularly for ERA5 data. Equation (7) is a general formula to convert atmospheric heights from pressure levels to meters [27]. The conversions might affect coarse representation in meters because atmospheric pressure changes depending upon weather systems. Equations (4)-(6) are presented below:  
\[SSE=\sum_{i=1}^{n}(P_{O}-P_{M})^{2} \tag{4}\]  
\[MAPE=\frac{1}{N}\ \sum_{i=1}^{N}\frac{|P_{O}-P_{M}|}{P_{O}}\times 100 \tag{5}\]  
\[AEP=8760\int_{V_{0}}^{V_{m}}P_{M} \tag{6}\]  
Here, \(P_{O}\) and \(P_{M}\) illustrate observed and modelled power, respectively, at each \(i\) wind speed for total datasets, i.e., \(N\). \(P_{M}\) is power for SPPM to be calculated within a range of \(V_{0}\) (minimum) and \(V_{m}\) (maximum) wind speeds, and 8760 is a constant value equal number of hours in a year [23; 24; 25]. As SPPM developed from GWA datasets, these models must forecast in the given range of 1.68 to 11.88, respectively, for \(V_{0}\) and \(V_{m}\). Moreover, Equation (7) is as follows:  
\[P=P_{o}\ e^{-z/H} \tag{7}\]  
Here, \(P\) represents pressure at any expected level where \(P_{o}\) is a reference level, i.e., 1000 hPa.