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\title{Estimated Ecological Flow of the Preto River by the Wetted Perimeter Method}
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\begin{document}

             \author[1]{Prof. MAnica De Aquino Galeano Massera Da  Hora}

             \author[2]{Rodrigo Sanguedo  Baptista}

             \affil[1]{  Fluminense Federal University}

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\date{\small \em Received: 6 December 2012 Accepted: 5 January 2013 Published: 15 January 2013}

\maketitle


\begin{abstract}
        


The ecological flow is the minimum flow of a river necessary to maintain its aquatic fauna. In the present study, this flow was estimated for the Preto River, which belongs to the Piabanha River Basin, located in the state of Rio de Janeiro, Brazil. Because the Preto River?s entire length is within the state, its management is under the responsibility of the Rio de Janeiro State Environmental Institute (INEA). The INEA adopts the value of 50% of Q7,10 as the minimum ecological flow for rivers in the state. Hydrological data were obtained from a stage gauge located on the river, allowing estimation of the ecological flow. The results were satisfactory, because the two ecological flow values calculated were lower than the lowest flow observed during the historic discharge series of the river. 

\end{abstract}


\keywords{ecological flow, wetted perimeter method, preto river.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
as the minimum ecological flow for rivers in the state. Hydrological data were obtained from a stage gauge located on the river, allowing estimation of the ecological flow. The results were satisfactory, because the two ecological flow values calculated were lower than the lowest flow observed during the historic discharge series of the river. Keywords: ecological flow, wetted perimeter method, preto river. he rational use and preservation of water resources are vital elements of public policy. In Brazil, Law 9,433/1997 established the National Water Resource Policy, which includes a series of measures regarding the use of water resources for various purposes and preservation of the quantity and quality of water. In rivers, a minimum flow, called the ecological flow, is necessary to maintain the aquatic fauna. Although there is no consensus on the method to calculate this metric, it can be estimated by hydraulic methods that relate characteristics of the current and channel, considering reference flow values and including holistic methods based on economic values and habitat classification techniques to identify physical and environmental traits of the water course in question [1]. This article presents the ecological flow, estimated by two equations, to be considered for the Preto River, located in the Piabanha River Basin. 
\section[{II.}]{II.} 
\section[{Piabanha River Basin}]{Piabanha River Basin}\par
The Piabanha River Basin is located in the state of Rio de Janeiro (Figure \hyperref[fig_0]{1}). It covers approximately 4,484 km² and contains about 700 thousand inhabitants, in ten municipalities, of which six lie totally within the basin. The Piabanha River extends 80 km and passes through the municipalities of Petrópolis, Areal and Três Rios. The Preto River, with extension of 54 km, is its main tributary [2].  
\section[{Water Availability, Maximum Surface Water Withdrawal and Ecological Flow}]{Water Availability, Maximum Surface Water Withdrawal and Ecological Flow}\par
The Preto River lies completely within the state of Rio de Janeiro, so according to Federal Law 9,433/1997, it is under state domain, with the Rio de Janeiro State Environmental Institute (INEA) having responsibility for its management. To grant water use rights, it is necessary to evaluate the water availability. This evaluation considers, among other factors, the maximum surface water withdrawal (MSW), which represents the maximum flow that can be taken from the river, or granted for use. The water availability is calculated by equation (1).eco granted Q Q MSW WA ? ? ? = (\textbf{1})\par
Where WA is the water availability; MSW is the maximum surface water withdrawal; ? granted Q is the sum of the flows granted for use upstream of the point studied and eco Q is the ecological flow, defined as 50\% of Q 7,10 . Q 7,10 T is defined as the smallest average flow occurring during a period of 7 consecutive days in a period of 10 years of recurrence. IV. 
\section[{Wetted Perimeter Method and Premises Adopted}]{Wetted Perimeter Method and Premises Adopted}\par
The wetted perimeter method is based on the existence of a direct relation between the wetted perimeter and the availability of habitats for ichthyofauna [1]. This method assumes there is a relation between the wetted perimeter and the habitat availability \hyperref[b0]{[3]}.\par
To apply this method, we relied on data from the Fazenda Sobradinho stage gauge (code 58420000), located on the Preto River. These data are stored in the HidroWeb database \hyperref[b1]{[4]}. Table \hyperref[tab_0]{1} presents the descriptive information on this post. Source : ANA (2013)\par
The lowest flow value measured at the Fazenda Sobradinho stage gauge occurred on September 23, 1955. This flow and the associated hydraulic variables are reported in Table \hyperref[tab_1]{2}. However, the cross-section data available in the HidroWeb database do not include data for 1955, making it necessary to identify a cross section corresponding to the lowest flow in the historic series, which was September 9, 1997. It is important to stress that the use of the minimum flow values measured is based on the premise that the ecological flow must be present in all natural flows of the river, i.e., it is expected to be lower than or equal to the lowest flow measured/ observed in the river. The information regarding this cross section, measured on September 9, 1997, is shown in Table \hyperref[tab_2]{3}. We superimposed the cross sections to note any relevant modification over the years for which data were available. This analysis is important, because if the cross section has undergone a considerable change, it means the cross section used as the baseline will not be an accurate representation to allow correlation with information for previous years. Figure \hyperref[fig_2]{2} presents the overlapped cross sections avaialable in the database.  ? Definition of the critical point based on the maximum curvature \hyperref[b0]{[3]}. Table  {\ref 4} shows the flow results obtained by multiplying the wetted area by the current speed selected. 
\section[{Table 4 : Flows obtained for each wetted area}]{Table 4 : Flows obtained for each wetted area}\par
From the data in Table  {\ref 4}, we plotted a graph relating the flows and the corresponding wetted perimeters. According to \hyperref[b0]{[3]}, the ecological flow is the flow value corresponding to the highest slope present in this curve. To determine this point, \hyperref[b0]{[3]} suggest using the maximum curvature method, for which purpose it is necessary to define the function that best fits the points on the graph. For this, as in \hyperref[b0]{[3]} we used Manning's formula:2 1 3 2 S R A n 1 Q ? ? ? = (\textbf{2})\par
Where Q is the flow; n is the Manning's roughness coefficient; A is the wetted area of the water course's cross section; R is the hydraulic radius and S is the water surface slope.\par
The geometry of river cross sections normally varies between roughly rectangular and triangular \hyperref[b4]{[6]}.\par
According to \hyperref[b0]{[3]}, from equation (1), for channels with rectangular and trapezoidal cross sections, the best approximation of the relation between the wetted perimeter and flow is given by a logarithmic function, represented by equation ( \hyperref[formula_4]{3}).( ) 1 Q ln a PM + ? =\textbf{(3)}\par
According to \hyperref[b0]{[3]}, for channels with triangular cross sections, the best approximation of this relation is given by a power function represented by: bQ PM = (4)\par
From observation of Figure \hyperref[fig_2]{2}, it can be perceived that the cross section used to calculate the ecological flow is rectangular, so we used the logarithmic function to approximately fit the points on the graph. However, in Brazil the usual practice is to use a power function to relate the hydraulic characteristics of a cross section with flow, as recommended by \hyperref[b4]{[6]}. Therefore, we employed both logarithmic and exponential equations to represent the relation between the flow versus wetted perimeter values, allowing comparison of the ecological flow results.\par
V. 
\section[{Results}]{Results}\par
We first plotted a graph of flow versus wetted perimeter by fitting a logarithmic trend line (Figure \hyperref[fig_4]{4}).  \hyperref[formula_4]{3}) we used a scale factor to normalize the two axes of the graph, so that both ranged from zero to one, as shown in Figure \hyperref[fig_5]{5}.  The curvature (k) is the rate at which a curve's slope changes. It is a function of the angle formed by the tangent line to the curve with the x-axis and the arc length \hyperref[b0]{[3]}, expressed by equation (  {\ref 5}). To find the curvature of a logarithmic function, equation ( \hyperref[formula_6]{6}) is used, while to find the curvature of a power function, equation (  {\ref 7}) is used.2 3 2 2 Q a 1 Q a k ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? =\textbf{(6)}\par
( )2 3 2 1 b 2 b Q b 1 Q b k ? ? ? ? ? ? ? + ? = ? ? (7)\par
Where |k| is the absolute value of the curvature; Q is the flow; b is the exponent of equation (  {\ref 4}) and a is the number that multiplies ln(Q) in equation \hyperref[b0]{(3)}.\par
By applying these two equations, we identified the points of greatest curvature, resulting in a flow equal to 0.206 m³/s for the logarithmic approximation and of 0.034 m³/s for the exponential approximation.\par
To help compare the order of magnitude of the ecological flow values resulting from application of the hydraulic method, we calculated the ecological flow adopted as a criterion by the INEA, namely 50\%Q 7,10  
\section[{Conclusion}]{Conclusion}\par
Based on the ecological flow results calculated by the wetted perimeter method, it can be seen that these are lower than the ecological flow value adopted by INEA (50\%Q ). Therefore, the results can be classified as satisfactory. One of the difficulties encountered during this study was the shortage of data on cross sections, since the results would have more closely reflected the real situation of the cross section for September 23, 1955 had been available, when the lowest flow was recorded in the historic series.\par
In closing, as mentioned earlier, there is still no consensus on the best method to calculate a river's ecological flow, so further research is necessary, given the importance of this subject for environmental studies and water resource management policies.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_2}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-4.png}
\caption{\label{fig_3}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-5.png}
\caption{\label{fig_4}Figure 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-6.png}
\caption{\label{fig_5}Figure 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-7.png}
\caption{\label{fig_6}Figure 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_7}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.425\textwidth}P{0.425\textwidth}}
\multicolumn{2}{l}{Sobradinho stage gauge}\\
Code\tabcellsep 58420000\\
Name\tabcellsep FAZENDA SOBRADINHO\\
Sub-basin\tabcellsep PARAÍBA DO SUL RIVER (58)\\
River\tabcellsep PRETO RIVER\\
State\tabcellsep RIO DE JANEIRO\\
Municipality\tabcellsep TERESÃ?"POLIS\\
Latitude\tabcellsep -22:12:1\\
Longitude\tabcellsep -42:54:4\\
Altitude (m)\tabcellsep 700\\
Drainage Area (km 2 )\tabcellsep 719\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.85\textwidth}}
1955\\
Source: ANA (2013)\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.22521367521367522\textwidth}P{0.12350427350427351\textwidth}P{0.18888888888888888\textwidth}P{0.07991452991452991\textwidth}P{0.23247863247863249\textwidth}}
\tabcellsep \tabcellsep 1997\tabcellsep \tabcellsep \\
Depth (cm)\tabcellsep Flow (m 3 /s)\tabcellsep Wetted area (m 2 )\tabcellsep Width (m)\tabcellsep Average current speed (m/s)\\
53\tabcellsep 6.12\tabcellsep 18.8\tabcellsep 23\tabcellsep 0.326\\
\multicolumn{3}{l}{Source : ANA (2013)}\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_2}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.11333333333333333\textwidth}P{0.068\textwidth}P{0.136\textwidth}P{0.04533333333333334\textwidth}P{0.374\textwidth}P{0.056666666666666664\textwidth}P{0.056666666666666664\textwidth}}
Q 7,10\tabcellsep (m³/s)\tabcellsep 50\%Q\tabcellsep 7,10\tabcellsep \multicolumn{2}{l}{Function (m³/s) Logarithmic Power}\\
\multicolumn{2}{l}{3.75}\tabcellsep \multicolumn{3}{l}{1.88}\tabcellsep 0.206\tabcellsep 0.034\\
\tabcellsep \tabcellsep VI.\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_3}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_4}}\end{figure}
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