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Reservoir Routing with the Level Pool Method Solution Procedure Level pool routing consists of two main components: 1. Develop the storage-outflow function, Q vs. 2S/Δt + Q 2. Route the inflow hydrograph through the reservoir using the discrete form of the continuity equation

 2S j 1   2S j    Q j 1   I j  I j 1     Q j   t   t 

Steps to develop storage-outflow function 1. Determine the Q-H relation. This relation will be given based on measured outflow or calculated using the features of the outflow structure(s), e.g. orifice and/or weir equations. 2. Determine the S-H relation using the reservoir geometry. 3. Find 2S/Δt + Q using the results of the first two steps (note: Δt is determined by the inflow hydrograph). Comments:  Watch units for Δt! Q is usually in cfs; therefore S must be in ft3 and Δt in s.  If Q increases faster than 2S/Δt, the solution will become unstable. In this situation, reduce Δt.

Steps to route hydrograph (computations occur at the j+1 step) 1. Calculate I j  I j 1

 2S j   Q j  , i.e. for the previous step (if the basin is empty and there 2. If j+1 = 2, calculate   t  is no outflow, the value will be zero). After j+1 = 2, this step is not necessary.

 2S j 1   2S j   Q j 1   I j  I j 1     Q j  3. Calculate   t   t 

CE 460/560

Level Pool Routing

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4. Linearly interpolate the value for Qj+1 using the value from the previous step and storageoutflow function. Once Qj+1 is found, the depth in the reservoir H can be found by interpolating the Q-H relation or direct calculation, if an equation is available.

 2S j 1   2S j 1   Q j 1     Q j 1   2Q j 1 . This value is needed for the next time 5. Calculate   t   t  step, (j+2), and replaces step 2.

Review of Linear Interpolation Given pairs of known values (x1, y1) and (x2, y2), the interpolated value for y corresponding to a given value of x where x1 ≤ x ≤ x2 is

y  y1 

 y 2  y1   x  x1  x2  x1 

y2

y1

x1 CE 460/560

x2 Level Pool Routing

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