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appendix6.tex
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\chapter{MONTHLY RAINFALL EXCEEDING THE 75\texorpdfstring{\textsuperscript{th}}{th} PERCENTILE}
This appendix presents the cumulative probability distributions for monthly rainfall exceeding the 75th percentile. The analysis in Chapter 4 Table 4.13 focuses on the Generalized Extreme-Value (GEV) distribution for ten stations and the Gamma distribution for one station in El Salvador. These additional results are provided for further exploration and comparison.
\section{Cumulative Probability Distribution}
This section illustrates the cumulative probability distribution (CDF) of monthly rainfall exceeding 75\textsuperscript{th} percentile for the five (5) distributions fitted in the study.
\subsection{Generalized Pareto Distribution}
\begin{figure}[H]
\centering
\subfloat[Butuan]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Butuan_GPD_CDF_monthly_0.75.png}}\\
\subfloat[Cotabato]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Cotabato_GPD_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Butuan, and Cotabato}
\label{fig:monthly_0.75_appendix_gpd_pt1}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Davao]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Davao_GPD_CDF_monthly_0.75.png}}\\
\subfloat[Dipolog]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Dipolog_GPD_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Davao, and Dipolog}
\label{fig:monthly_0.75_appendix_gpd_pt2}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[El Salvador]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/El_Salvador_GPD_CDF_monthly_0.75.png}}\\
\subfloat[General Santos]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/GenSan_GPD_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for El Salvador, and General Santos}
\label{fig:monthly_0.75_appendix_gpd_pt3}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Hinatuan]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Hinatuan_GPD_CDF_monthly_0.75.png}}\\
\subfloat[Lumbia]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Lumbia_GPD_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Hinatuan, and Lumbia}
\label{fig:monthly_0.75_appendix_gpd_pt4}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Malaybalay]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Malaybalay_GPD_CDF_monthly_0.75.png}}\\
\subfloat[Surigao]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Surigao_GPD_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Malaybalay, and Surigao}
\label{fig:monthly_0.75_appendix_gpd_pt5}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Zamboanga]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Zamboanga_GPD_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Zamboanga}
\label{fig:monthly_0.75_appendix_gpd_pt6}
\end{figure}
\subsection{Generalized Extreme-Value}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth, height=15cm, keepaspectratio]{APPENDIX CDF MONTHLY (0.75)/El_Salvador_GEV_CDF_monthly_0.75.png}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for El Salvador}
\label{fig:CDF_ElSal_GEV}
\end{figure}
\subsection{Gumbel Distribution}
\begin{figure}[H]
\centering
\subfloat[Butuan]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Butuan_GB_CDF_monthly_0.75.png}}\\
\subfloat[Cotabato]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Cotabato_GB_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Butuan, and Cotabato}
\label{fig:monthly_0.75_appendix_gb_pt1}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Davao]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Davao_GB_CDF_monthly_0.75.png}}\\
\subfloat[Dipolog]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Dipolog_GB_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Davao, and Dipolog}
\label{fig:monthly_0.75_appendix_gb_pt2}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[El Salvador]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/El_Salvador_GB_CDF_monthly_0.75.png}}\\
\subfloat[General Santos]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/GenSan_GB_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for El Salvador, and General Santos}
\label{fig:monthly_0.75_appendix_gb_pt3}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Hinatuan]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Hinatuan_GB_CDF_monthly_0.75.png}}\\
\subfloat[Lumbia]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Lumbia_GB_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Hinatuan, and Lumbia}
\label{fig:monthly_0.75_appendix_gb_pt4}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Malaybalay]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Malaybalay_GB_CDF_monthly_0.75.png}}\\
\subfloat[Surigao]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Surigao_GB_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Malaybalay, and Surigao}
\label{fig:monthly_0.75_appendix_gb_pt5}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Zamboanga]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Zamboanga_GB_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Zamboanga}
\label{fig:monthly_0.75_appendix_gb_pt6}
\end{figure}
\subsection{Gamma Distribution}
\begin{figure}[H]
\centering
\subfloat[Butuan]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Butuan_Gamma_CDF_monthly_0.75.png}}\\
\subfloat[Cotabato]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Cotabato_Gamma_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile Butuan, and Cotabato}
\label{fig:monthly_0.75_appendix_gamma_pt1}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Davao]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Davao_Gamma_CDF_monthly_0.75.png}}\\
\subfloat[Dipolog]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Dipolog_Gamma_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Davao, and Dipolog}
\label{fig:monthly_0.75_appendix_gamma_pt2}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[General Santos]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/GenSan_Gamma_CDF_monthly_0.75.png}}\\
\subfloat[Hinatuan]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Hinatuan_Gamma_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for General Santos, and Hinatuan}
\label{fig:monthly_0.75_appendix_gamma_pt3}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Lumbia]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Lumbia_Gamma_CDF_monthly_0.75.png}}\\
\subfloat[Malaybalay]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Malaybalay_Gamma_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Lumbia, and Malaybalay}
\label{fig:monthly_0.75_appendix_gamma_pt4}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Surigao]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Surigao_Gamma_CDF_monthly_0.75.png}}\\
\subfloat[Zamboanga]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Zamboanga_Gamma_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Surigao, and Zamboanga}
\label{fig:monthly_0.75_appendix_gamma_pt5}
\end{figure}
\subsection{Weibull Distribution}
\begin{figure}[H]
\centering
\subfloat[Butuan]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Butuan_Weibull_CDF_monthly_0.75.png}}\\
\subfloat[Cotabato]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Cotabato_Weibull_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Butuan, and Cotabato}
\label{fig:monthly_0.75_appendix_wb_pt1}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Davao]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Davao_Weibull_CDF_monthly_0.75.png}}\\
\subfloat[Dipolog]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Dipolog_Weibull_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Davao, and Dipolog}
\label{fig:monthly_0.75_appendix_wb_pt2}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[El Salvador]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/El_Salvador_Weibull_CDF_monthly_0.75.png}}\\
\subfloat[General Santos]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/GenSan_Weibull_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for El Salvador, and General Santos}
\label{fig:monthly_0.75_appendix_wb_pt3}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Hinatuan]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Hinatuan_Weibull_CDF_monthly_0.75.png}}\\
\subfloat[Lumbia]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Lumbia_Weibull_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Hinatuan, and Lumbia}
\label{fig:monthly_0.75_appendix_wb_pt4}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Malaybalay]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Malaybalay_Weibull_CDF_monthly_0.75.png}}\\
\subfloat[Surigao]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Surigao_Weibull_CDF_monthly_0.75.png}}\\
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Malaybalay, and Surigao}
\label{fig:monthly_0.75_appendix_wb_pt5}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[Zamboanga]{\includegraphics[width=0.8\linewidth]{APPENDIX CDF MONTHLY (0.75)/Zamboanga_Weibull_CDF_monthly_0.75.png}}
\caption{CDF of Monthly Rainfall Exceeding the 75\textsuperscript{th} Percentile for Zamboanga}
\label{fig:monthly_0.75_appendix_wb_pt6}
\end{figure}