## 4 Results and Discussion
### Comparative Study of Probability-Distribution-Function-Based WSP Models  
First, Weibull and Rayleigh parameters were calculated as shown in Table 1. It is clearly seen in the table that the probability distribution for both Weibull and Rayleigh distribution functions were almost the same as the shape parameters of all three sites, close to two. We then investigated the forecasting accuracy using both Weibull- and Rayleigh-distribution-based models. The results from the analysis of the probability-density-based wind prediction model are presented in Tables 2-5. The performance of the models was assessed through various performance metrics such as RMSE, MAE, and RMSE. This analysis was performed for short-term forecast horizons. While evaluating the performance of the next seven hours of time step, each hour of the time step was also evaluated to know about the detail of the forecasting model. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Location**} & \multicolumn{2}{c}{**Weibull Parameter**} & \multicolumn{2}{c}{**Rayleigh Parameter**} \\ \cline{2-4}  & **k** & **c** & **c** \\ \hline South Plains TX & 2.4 & 10.2 & 10.16 \\ Southern Offshore TX & 2.45 & 10 & 10.05 \\ Hills region WV & 2.19 & 8.22 & 8.23 \\ Hills region AR & 1.84 & 7.39 & 7.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Scale and shape parameters for four locations for the year 2010. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**RMSE**} \\ \hline
**Model** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **t = 7** & **Average** \\ \hline WEB & 1.02 & 1.1 & 0.61 & 2.18 & 3.48 & 1.1 & 1.07 & 1.51 \\ WEBS & 0.33 & 4.15 & 0.22 & 4.48 & 1.89 & 3.008 & 0.4 & 2.07 \\ WEBSEC & 1.77 & 1.28 & 0.19 & 3.82 & 0.62 & 2.81 & 0.02 & 1.50 \\ RYM & 1.02 & 1.1 & 0.61 & 2.19 & 3.48 & 3.16 & 1.1 & 1.81 \\ RYMS & 5.62 & 4.54 & 2.4 & 4.69 & 1.99 & 6.39 & 1.24 & 3.84 \\ RYMSEC & 1.3 & 0.52 & 0.4 & 4.67 & 5.36 & 1.02 & 5.26 & 2.65 \\ \hline \multicolumn{6}{c}{**MAE**} \\ \hline
**Model** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **t = 7** & **Average** \\ \hline WEB & 1.02 & 1.1 & 0.61 & 2.18 & 3.48 & 3.16 & 1.1 & 1.81 \\ WEBS & 0.32 & 4.17 & 0.22 & 4.48 & 1.89 & 3.008 & 0.4 & 2.07 \\ WEBSEC & 1.77 & 1.28 & 0.19 & 3.82 & 0.62 & 2.81 & 0.01 & 1.50 \\ RYM & 1.02 & 0.107 & 0.61 & 2.19 & 3.48 & 3.16 & 1.1 & 1.67 \\ RYMS & 5.62 & 4.54 & 2.4 & 4.69 & 1.99 & 6.39 & 1.24 & 3.84 \\ RYMSEC & 1.36 & 0.52 & 0.4 & 4.67 & 5.36 & 1.02 & 5.26 & 2.66 \\ \hline \multicolumn{6}{c}{**MAPE**} \\ \hline
**Model** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **t = 7** & **Average** \\ \hline WEB & 0.12 & 0.14 & 0.064 & 0.19 & 0.27 & 0.25 & 0.1 & 0.16 \\ WEBS & 0.04 & 0.52 & 0.023 & 0.4 & 0.15 & 0.24 & 0.04 & 0.20 \\ WEBSEC & 0.22 & 0.16 & 0.02 & 0.34 & 0.05 & 0.23 & 0.001 & 0.15 \\ RYM & 0.12 & 0.14 & 0.06 & 0.19 & 0.27 & 0.26 & 0.1 & 0.16 \\ RYMS & 0.7 & 0.57 & 0.25 & 0.41 & 0.16 & 0.52 & 0.12 & 0.39 \\ RYMSEC & 0.17 & 0.06 & 0.04 & 0.41 & 0.42 & 0.08 & 0.52 & 0.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance results of different WSP models for the South Plains TX region.