FLOOD ROUTING
Flood Routing Techniques
Siti Kamariah Md Sa’atPPK Bioprocess..2010
Flow Routing
Procedure to determine the flow hydrograph at a point on a watershed from a known hydrograph upstream
As the hydrograph travels, it attenuates gets delayed
Q
t
Q
t
Q
t
Q
t
Why route flows?
Account for changes in flow hydrograph as a flood wave passes downstream
This helps in Accounting for storages Studying the attenuation of flood peaks
Q
t
Types of flow routing Lumped/hydrologic
Flow is calculated as a function of time alone at a particular location
Governed by continuity equation and flow/storage relationship
Distributed/hydraulic Flow is calculated as a function of space and
time throughout the system Governed by continuity and momentum
equations
Lumped flow routing Three types
1. Level pool method (Modified Puls) Storage is nonlinear function of Q
2. Muskingum method Storage is linear function of I and Q
3. Series of reservoir models Storage is linear function of Q and its time
derivatives
S and Q relationships
Level pool routing Procedure for calculating outflow hydrograph
Q(t) from a reservoir with horizontal water surface, given its inflow hydrograph I(t) and storage-outflow relationship
Wedge and Prism Storage
• Positive wedge I > Q
• Maximum S when I = Q
• Negative wedge I < Q
Hydrologic river routing (Muskingum Method)
Wedge storage in reach
IQ
QI
AdvancingFloodWaveI > Q
II
IQ
I Q
RecedingFloodWaveQ > I
KQS Prism
)(Wedge QIKXS
K = travel time of peak through the reachX = weight on inflow versus outflow (0 ≤ X ≤ 0.5)X = 0 Reservoir, storage depends on outflow, no wedgeX = 0.0 - 0.3 Natural stream
)( QIKXKQS
])1([ QXXIKS
Muskingum Equations
• 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, t and sum to 1.0
Q2 C0I2 C1I1 C2Q1
Muskingum Equations
C0 = (– Kx + 0.5t) / D
C1 = (Kx + 0.5t) / D
C2 = (K – Kx – 0.5t) / D
Where D = (K – Kx + 0.5t)
Repeat for Q3, Q4, Q5 and so on.
Q2 C0I2 C1I1 C2Q1
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
I Q dSdt
Inflow and Outflow
I1 + I2 – Q1 + Q2 S2 – S1
2 t2=
= change in storage / time
Re Repeat for each day in progression
Inflow & Outflow Day 3
I2 I3 / 2 Q2 Q3 / 2 S3 S2
dt
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
Q CA 2gH for orifice flow
Q CLH 3/2 for weir flow
Typical Storage -Outflow• Plot of Storage in vs. Outflow in Storage is largely a function of topography
• Outflows can be computed as function of elevation for either pipes or weirs
S
Q
Combined
Pipe
Comparisons:River vs. ReservoirRouting
Level pool reservoir
River Reach
Example 3:Level Pool Routing
Example 4:Resevoir Routing
Example 5:Flow Routing (Muskingum) Route the following flood hydrograph through
a river reach for which K=12.0hr and X=0.20. At the start of the inflow flood, the outflow flood, the outflow discharge is 10 m3/s.
Time (hr)
0 6 12 18 24 30 36 42 48 54
Inflow (m3/s)
10 20 50 60 55 45 35 27 20 15