Review of Flood Routing Philip B. Bedient Rice University

Lake Travis and Mansfield Dam

Mansfield Dam, built in 1937 Lake Travis

Brays Bayou High Flow 6 to 7 inches of Rainfall

T.S. Allison June 2001

Hurricane Rita Landed on Sabine, TX On Sep 24, 2006 Houston Galveston Bay Hurricane Rita Landed on Sabine, TX On Sep 24, 2006

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.

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

Inflow and Outflow I1 + I2 – Q1 + Q2 S2 – S1 = 2 2 Dt

Inflow & Outflow Day 3 = change in storage / time Re Repeat for each day in progression

Determining Storage Evaluate surface area at several different depths Use available topographic maps or GIS based DEM sources (digital elevation map) Outflow Q can be computed as function of depth for either pipes, orifices, or weirs or combinations

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 Combined 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 Pond Routing 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 84006 ft3

Example Pond Routing Develop Q (orifice) vs h Develop Q (weir) vs h Develop A and Vol vs h Storage - Indication 2S/dt + Q vs Q where Q is sum of weir and orifice flow rates.

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

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

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

River Routing River Reaches

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

Looped Rating Curves Due to complex hydraulics Higher peak Qp on inflow Lower peak Qp on outflow Due to prism and wedge Red River results shown

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

Muskingum Equations S = K [xI + (1-x)Q] Continuity Equation I - Q = dS / dt S = K [xI + (1-x)Q] Parameters are x = weighting and K = travel time - x ranges from 0.2 to about 0.5 where C’s are functions of x, K, Dt and sum to 1.0

Muskingum Equations C0 = (– Kx + 0.5Dt) / D C1 = (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

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

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 - Qn 2S/dt +Qn Qn 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 3 - Note that 65.6 - 2(17.6) = 30.4 and is repeated for each one