 # Review of Flood Routing

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Review of Flood Routing
Philip B. Bedient Rice University

Lake Travis and Mansfield Dam

LAKE LIVINGSTON

LAKE CONROE

Storage Reservoirs - The Woodlands

Detention Ponds These ponds store and treat urban runoff and also provide flood control for the overall development. Ponds constructed as amenities for the golf course and other community centers that were built up around them.

DETENTION POND, AUSTIN, TX

LAKE CONROE WEIR

Comparisons: River vs. Reservoir Routing
Level pool reservoir River Reach

Reservoir Routing Reservoir acts to store      water and release through      control structure later. Inflow hydrograph Outflow hydrograph S - Q Relationship Outflow peaks are reduced Outflow timing is delayed Max Storage

Inflow and Outflow

Numerical Equivalent I1 + I2 – Q1 + Q2 S2 – S1
Assume I1 = Q1 initially I1 + I2 – Q1 + Q S2 – S1 = 2 2 Dt

Numerical Progression
I1 + I2 – Q1 + Q S2 – S1 1. = DAY 1 2 2 Dt I2 + I3 – Q2 + Q S3 – S2 2. DAY 2 2 2 Dt I3 + I4 – Q3 + Q S4 – S3 3. DAY 3 2 2 Dt

Determining Storage Evaluate surface area at several different depths
Use available topographic maps or GIS based DEM sources (digital elevation map) Storage and area vary directly with depth of pond Elev Volume Dam

Determining Outflow Evaluate area & storage at several different depths Outflow Q can be computed as function of depth for Pipes - Manning’s Eqn Orifices - Orifice Eqn Weirs or combination outflow structures - Weir Eqn Weir Flow Orifice/pipe

Determining Outflow Weir H Orifice H measured above
Center of the orifice/pipe

Typical Storage -Outflow
Plot of Storage in acre-ft vs. Outflow in cfs Storage is largely a function of topography Outflows can be computed as function of elevation for either pipes or weirs Pipe/Weir S Pipe Q

Reservoir Routing LHS of Eqn is known Know S as fcn of Q
Solve Eqn for RHS Solve for Q2 from S2 Repeat each time step

Example Reservoir Routing Storage Indication

Storage Indication Method
STEPS Storage - Indication Develop Q (orifice) vs h Develop Q (weir) vs h Develop A and Vol vs h 2S/dt + Q vs Q where Q is sum of weir and orifice flow rates. Note that outlet consists of weir and orifice. Weir crest at h = 5.0 ft Orifice at h = 0 ft Area (6000 to 17,416 ft2) Volume ranges from 6772 to ft3

Storage Indication Curve
Relates Q and storage indication, (2S / dt + Q) Developed from topography and outlet data Pipe flow + weir flow combine to produce Q (out) Only Pipe Flow Weir Flow Begins

Storage Indication Inputs
height h - ft Area 102 ft Cum Vol 103 ft Q total cfs 2S/dt +Qn 6 1 7.5 6.8 13 35 2 9.2 15.1 18 69 3 11.0 25.3 22 106 4 13.0 37.4 26 150 5 51.5 29 200 7 17.4 84.0 159 473 Storage-Indication

Storage Indication Tabulation
Time In In + In+1 (2S/dt - Q)n (2S/dt +Q)n+1 Qn+1 10 20 7.2 40 60 5.6 65.6 17.6 30 100 30.4 130.4 24.0 50 110 82.4 192.4 28.1 90 136.3 226.3 40.4 70 145.5 215.5 35.5 Time Note that (7.2) = 5.6 and is repeated for each one

S-I Routing Results See Excel Spreadsheet on the course web site
I > Q Q > I See Excel Spreadsheet on the course web site

S-I Routing Results I > Q Q > I Increased S

RIVER FLOOD ROUTING

CALIFORNIA FLASH FLOOD

River Routing Manning’s Eqn River Reaches

River Rating Curves Inflow and outflow are complex
Wedge and prism storage occurs Peak flow Qp greater on rise limb    than on the falling limb Peak storage occurs later than Qp

Wedge and Prism Storage
Positive wedge I > Q Maximum S when I = Q Negative wedge I < Q

Actual Looped Rating Curves

Muskingum Method - 1938 Storage Eqn S = K {x I + (1-x)Q}
Continuity Equation I - Q = dS / dt Storage Eqn S = K {x I + (1-x)Q} Parameters are x = weighting Coeff K = travel time or time between peaks x = ranges from 0.2 to about 0.5 (pure trans) and assume that initial outflow = initial inflow

Muskingum Method - 1938 Storage Eqn S = K {x I + (1-x)Q}
Continuity Equation I - Q = dS / dt Storage Eqn S = K {x I + (1-x)Q} Combine 2 eqns using finite differences for I, Q, S S2 - S1 = K [x(I2 - I1) + (1 - x)(Q2 - Q1)] Solve for Q2 as fcn of all other parameters

Muskingum Equations Where C0 = (– Kx + 0.5Dt) / D
C2 = (K – Kx – 0.5Dt) / D Where D = (K – Kx + 0.5Dt) Repeat for Q3, Q4, Q5 and so on.

Muskingum River X Select X from most linear plot Obtain K from
line slope

Manning’s Equation Qp = 1.49 A (R2/3) S1/2 n
Manning’s Equation used to estimate flow rates Qp = 1.49 A (R2/3) S1/2 Where Qp = flow rate n = roughness A = cross sect A R = A / P S = Bed Slope n

Hydraulic Shapes Circular pipe diameter D Rectangular culvert
Trapezoidal channel Triangular channel