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

QQ

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