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\title{A Flood Forecasting Model for the River Padma}
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\begin{document}

             \author[1]{Md. Abdur Rakib  Hasan}

             \author[2]{Md. AbdurRakib  Hasan}

             \author[3]{Sharid  Shahnewaz}

             \affil[1]{  Rajshahi University of Engineering and Technology}

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\date{\small \em Received: 11 December 2013 Accepted: 3 January 2014 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


Flood constitute one of the critical problems faced by Bangladesh. Due to the unique graphical situation of Bangladesh in the delta of three great rivers, namely the Brahmaputra, the Padma and the Meghna, which drains a vast catchment, flood in this country is usually complex. The problem is gigantic and becomes more complicated with the passage of time. The flood in 1998 sever flood is the highest record. Analysis of water level data of two stations shows that the forecasting model is a linear equation of the type Y= a+bX. Data of the nine hydrologic years have been analyzed in this paper. In most cases values of co-efficient ?a? varies from 0.3112 to 1.558 and ?b? from 1.047 to 11.91. The general equation for the flood forecasting for the GoalundoTransi station has been established as Y = 1.283X - 8.351 in this paper. The value of travel time of flood wave from base station to forecasting station according to historical method andMutreja?s method is 2days for both.

\end{abstract}


\keywords{flood, forecasting model, statistical method, travel time.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
lood affected many of the engineering structures such as bridge, embankment, barrage, levees, reservoirs, etc. while designing the proper safeguards must be made for the safe passage of the maximum expected flood. The structure must be sound not only for its own safety but also for the life and property which might be in danger by its failure. The valley then becomes ''flooded". A flood is commonly considered to be an unusually high stage of a river. It is often the stage at which the stream channel becomes filled and starts overflowing its banks. In Webster's new international dictionary, a ''flood" is "a great flow of water especially, a body of water, rising, swelling and overflowing and not usually thus covered a deluge, a freshet, an inundation". A flood problem in Bangladesh is gigantic and becomes more complicated with the passage of time. Every year a large area of this country is more or less affected by the flood. For the unique geographical situation of Bangladesh flood cannot be protected. But damages caused by the flood are lowered by the proper and timely forecasting about flood. Most of the flood studies are made for the flood controlling. Here flood forecasting system is very poor. So attempts have been taken to develop appropriate flood forecasting model. Flood is a serious problem in our country. Every year a large number of hydraulic structures, crops and properties are damaged by the flood.\par
Author ? ? ?: Department of Civil Engineering, Rajshahi University of Engineering \& Technology, Rajshahi, Bangladesh. e-mails: mnz\textunderscore ruet@yahoo.com, nirjhor.ruet.ce@gmail.com, sharid.shahnewaz@gmail.com\par
The necessity of the study is given below: 1. To ensure the safety of the hydraulic structure (like-Barrage, levees etc.).\par
2. To take measure for the safety of the crops and properties of the adjacent land. Where, Y is a dependent variable and is the water level at the forecasting station at time, t(MSL), X is a independent variable and is the water level at the base station at time (t-T) with T as the travel time between this station and the forecasting station, a, b are multiple correlations co-efficient.\par
It should be noted that the advanced time for the forecast at the forecasting station is the least of the travel times. The procedures involved in the development of the model are:\par
? Identifying flood forecasting stations;\par
? Identifying potential base stations;\par
? Preparation of data base;\par
? Estimation of travel time; and In this method the travel time is considered as the time difference between the peak water level of the base station and forecasting station.?\par
ii. Mutreja's Method This method consists in collecting the water level data of flood at base station for the Nth hour and at the forecasting station for the (N+T)-th hour in a tabular form. By taking different values of T different data tables are prepared such that each data table corresponding to one of assumed T. To compute the cross correlation of the water level data of these two stations at different legs the cross correlation of the data on each table is computed. The value of T corresponding to the data table the maximum correlation is travel time of the reach. 
\section[{c) Necessary Data}]{c) Necessary Data}\par
In this study the following three types of data have been collected:\par
? Daily water level data ? Daily discharge data 
\section[{? Danger level data}]{? Danger level data}\par
All these data used in this study were collected from the surface water hydrology -II of Bangladesh Water Development Board (BWDB). 
\section[{i. Discharge Level Data}]{i. Discharge Level Data}\par
The BWDB in this the primary source of discharge data. The mean daily discharge data during a water year is published by hydrology directorate of the BWDB. Data sheet for daily discharge also contains the annual maximum and minimum discharge. Daily discharge data of Hardinge Bridge and GoalundoTransi station of the river Padma are collected for the purpose of this study. 
\section[{ii. Water Level Data}]{ii. Water Level Data}\par
The BWDB is also the primary source of water level data. The water level of the river is measured 5 times a day, at 6.00, 9.00, 12.00, 15.00 and 18.00 hour on stuff gauges. The mean of the 5 measurements is published as mean daily water level by the hydrology directorate of BWDB of Dhaka. Data sheets containing the mean daily water level at Hardinge Bridge and Goalundo Transi station of the river Padma during a water year (July to October) are given in Appendix-A. The data sheet also contains the annual maximum water level data of the monsoon period has been used for this study.\par
iii. Danger Level Danger level data for two stations Hardinge Bridge and GoalundoTransi has been collected from the BWDB, Dhaka. The danger level of Padma at the selected river at the selected stations is given below:  
\section[{Results and Discussion}]{Results and Discussion} 
\section[{a) Travel Time From Base to Forecasting Station}]{a) Travel Time From Base to Forecasting Station}\par
The travel time from the base station to the forecasting station is given in the following table calculated by two separate methods. The following graphs show the correlation of Nth hour stage of base station with (N+T)-th hour stage of forecasting station. Putting the value of daily water level data at X axis (base station) and daily water level data at Y axis (forecasting station) after the travel time T and finally get a linear equation.  
\section[{Conclusions}]{Conclusions}\par
The following conclusions can be drawn from the above analysis:\par
? The accepted value of travel time from Hardinge Bridge to Goalundo Transi is 2 days. \begin{figure}[htbp]
\noindent\textbf{3123}\includegraphics[]{image-2.png}
\caption{\label{fig_0}3 . 1 . 2 . 3 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{12::8:10}\includegraphics[]{image-4.png}
\caption{\label{fig_2}1 2 Figure : Figure : 8 9Figure : Figure 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.09279475982532752\textwidth}P{0.38973799126637554\textwidth}P{0.259825327510917\textwidth}P{0.1076419213973799\textwidth}}
River\tabcellsep \tabcellsep Stations\tabcellsep Danger\\
\tabcellsep \tabcellsep \tabcellsep level (m)\\
Padma\tabcellsep \multicolumn{2}{l}{Hardinge Bridge(Base Station)}\tabcellsep 14.25\\
\tabcellsep \multicolumn{3}{l}{GoalundoTransi(Forecasting Station) 8.65}\\
\multicolumn{2}{l}{Hydrologic year}\tabcellsep \multicolumn{2}{l}{Travel time (day) Historical method Mutreja's methods}\\
\tabcellsep 2004\tabcellsep 1\tabcellsep 2\\
\tabcellsep 2005\tabcellsep 1\tabcellsep 2\\
\tabcellsep 2006\tabcellsep 2\tabcellsep 2\\
\tabcellsep 2007\tabcellsep 1\tabcellsep 2\\
\tabcellsep 2008\tabcellsep 2\tabcellsep 2\\
\tabcellsep 2009\tabcellsep 1\tabcellsep 2\\
\tabcellsep 2010\tabcellsep 2\tabcellsep 2\\
\tabcellsep 2011\tabcellsep 1\tabcellsep 2\\
\tabcellsep 2012\tabcellsep 1\tabcellsep 2\end{longtable} \par
  {\small\itshape [Note: b) Correlations Between Nth hour stage of Base Station and (N+T)th hour Stage of Forecasting Station]} 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.14166666666666666\textwidth}P{0.05343567251461988\textwidth}P{0.004970760233918128\textwidth}P{0.3007309941520468\textwidth}P{0.20255847953216374\textwidth}P{0.1466374269005848\textwidth}}
\tabcellsep 10\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep Y = 1.283X -8.351\tabcellsep \\
\multicolumn{2}{l}{7.5 8 8.5 9 9.5 HOUR GAUGE OF FORECASTING STATION (m)}\tabcellsep \tabcellsep \tabcellsep \\
(N+T)-TH\tabcellsep 7\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 12.6\tabcellsep 12.8\tabcellsep \multicolumn{2}{l}{13 N-TH HOUR GAUGE OF BASE STATION (m) 13.2 13.4 13.6 13.8}\tabcellsep 14\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep E\\
Hydrological year\tabcellsep Flood Period (day)\tabcellsep \tabcellsep Forecasting model Y= a+bX\tabcellsep Nature of the curve\tabcellsep Remarks\\
2004\tabcellsep 23\tabcellsep \tabcellsep Y = 1.262X-7.450\tabcellsep Linear Variation\tabcellsep Flood Occurred\\
2005\tabcellsep 22\tabcellsep \tabcellsep Y = 0.827X-2.340\tabcellsep Linear Variation\tabcellsep Flood Occurred\\
2006\tabcellsep 19\tabcellsep \tabcellsep Y = 0.850X-3.164\tabcellsep Linear Variation\tabcellsep No Flood\\
2007\tabcellsep 20\tabcellsep \tabcellsep Y = 1.558X-11.91\tabcellsep Linear Variation\tabcellsep Flood Occurred\\
2008\tabcellsep 16\tabcellsep \tabcellsep Y = 0.952X+1.131\tabcellsep Linear Variation\tabcellsep Flood Occurred\\
2009\tabcellsep 19\tabcellsep \tabcellsep Y = 0.736X-1.047\tabcellsep Linear Variation\tabcellsep No Flood\\
2010\tabcellsep 28\tabcellsep \tabcellsep Y = 0.452X+1.529\tabcellsep Linear Variation\tabcellsep Flood Occurred\\
2011\tabcellsep 22\tabcellsep \tabcellsep Y = 0.311X+3.52\tabcellsep Linear Variation\tabcellsep No Flood\\
2012\tabcellsep 24\tabcellsep \tabcellsep Y = 0.99X-4.732\tabcellsep Linear Variation\tabcellsep Flood Occurred\end{longtable} \par
  {\small\itshape [Note: ? Combined co-relation of N-th hour stage of base station with (N+T)th hour stage of forecasting station has been established as a linear equation. ? The general equation for the flood forecasting for the GoalundoTransi station is Y = 1.283X -8.351.]} 
\caption{\label{tab_2}}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US)} 			\footnote{Year 2014} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Reddy ()]{b4}\label{b4} 	 		\textit{A Textbook of Hydrology},  		 			P J R Reddy 		.  		2005. Laxmi Publications.  	 
\bibitem[Mutreja ()]{b3}\label{b3} 	 		\textit{Applied Hydrology},  		 			K N Mutreja 		.  		1986. Tata McGra-Hill Publishing Company Limited.  	 
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\bibitem[Rahman et al. ()]{b0}\label{b0} 	 		‘Development of the Jamuneswari Flood Forecasting System: Case Study in Bangladesh’.  		 			M M Rahman 		,  		 			N K Goel 		,  		 			D S Arya 		.  	 	 		\textit{Journal of Hydrologic Engineering}  		2012. 17  (10)  p. .  	 
\bibitem[Chowdhury and Ward ()]{b1}\label{b1} 	 		‘Hydrometeorological variabilty in the greater Ganges-Brahmaputra-Meghna basins’.  		 			M R Chowdhury 		,  		 			N Ward 		.  	 	 		\textit{International Journal of Climatology}  		2004. 24  (12)  p. .  	 
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