FLOOD ROUTING

Siti Kamariah Md Sa’atSchool of Bioprocess Engineering, UniMAP

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 Calculate 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 types1. 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 Flood Routing

Basic Equation

tO

tI

dtt

dS

Hydrologic river routing (Muskingum Method)

Wedge storage in reach

IQ

QQ

QI

AdvancingFloodWaveI > Q

II

IQ

I QRecedingFloodWaveQ > 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

Continuity Equation in Difference Form

Referring to figure, the continuity equation in difference form can be expressed as

2

)2O1(O

2

)2I1(I

_O

_I

1t2t1S2S

tS

Routing

Derivation of Muskingum Routing Equation• By Muskingum Model,

at t = t2, S2 = K [X I2 + (1 - X)O2]

at t = t1, S1 = K [X I1 + (1 - X)O1]

• Substituting S1, S2 into the continuity equation and after some

algebraic manipulations, one has

O2 = Co I2 + C1 I1 + C2 O1

• Replacing subscript 2 by t +1 and 1 by t, the Muskingum routing equation is

Ot+1 = Co It+1 + C1 It + C2 Ot, for t = 1, 2, …

 

where ; ; C2 = 1 – Co – C1

Note: K and t must have the same unit.

t0.5KXK

t0.5KXo

C

t0.5KXK

t0.5KX1

C

Muskingum Routing Equation

where C’s are functions of x, K, t and sum to 1.0

tttt QCICICQ

QCICICQ

21101

1211202

Muskingum Equations

where

C0 = (– Kx + 0.5t) / D

C1 = (Kx + 0.5t) / D

C2 = (K – Kx – 0.5t) / D

D = (K – Kx + 0.5t)

Repeat for Q3, Q4, Q5 and so on.

Estimating Muskingum Parameters, K and x

Graphical Method: Referring to the Muskingum Model, find

X such that the plot of XIt+ (1-X)Ot (m3/s) vs St (m

3/s.h) behaves almost nearly as a single value curve. The assume value of x lies between 0 and 0.3.

The corresponding slope is K.

Example 8.4: Estimating the value of x and K.

Try and error to get the nearly straight line graph.

Muskingum Routing Procedure

Given (knowns): O1; I1, I2, …; t; K; X

Find (unknowns): O2, O3, O4, …

Procedure: (a) Calculate Co, C1, and C2

(b) Apply Ot+1 = Co It+1 + C1 It + C2 Ot

starting from t=1, 2, … recursively.

Example 8.5

Given K and x. Initial outflow, Q also given.

Solution:Calculate Co, C1, and C2

C0 = (– Kx + 0.5Dt)/ DC1 = (Kx + 0.5Dt)/ DC2 = (K – Kx – 0.5Dt)/ DD = (K – Kx + 0.5Dt)

Solution: 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

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

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

Flood Control

Structural Measures Non-structural Methods

Structural Measures

Storage and detention reservoir Flood ways (new channel) Levees (flood embankment) Channel Improvement

Reservoirs Reservoirs reduce flooding by temporarily

storing flood waters behind dams or in storage or detention basins.

Reservoirs lower flood heights by holding back, or detaining, runoff before it can flow downstream.

Flood waters are detained until the flood has subsided, then the water in the reservoir or detention basin is released or pumped out slowly at a rate that the river can accommodate downstream.

Timah Tasoh Dam

Reservoirs

Flood control reservoirs are most commonly built for one of two purposes. Large reservoirs are constructed to protect property from existing flood problems.

Smaller reservoirs, or detention basins are built to protect property from the impacts of new development (i.e., more runoff).

Many dams have a function for flood management, but in some cases

dams actually make floods worse!

Think!

Flood way diversion A diversion is a new channel that sends

floodwaters to a different location, thereby reducing flooding along an existing watercourse.

Diversions can be surface channels, overflow weirs, or tunnels.

During normal flows, the water stays in the old channel.

During flood flows, the floodwaters spill over to the diversion channel or tunnel, which carries the excess water to a receiving lake or river.

Flood levees Also known as dikes or flood embankments. Probably the best known flood control

measure is a barrier of earth (levee) or concrete (floodwall) erected between the watercourse and the property to be protected.

Levees and floodwalls confine water to the stream channel by raising its banks.

They must be well designed to account for large floods, underground seepage, pumping of internal drainage, and erosion and scour.

Flood levees

Channel/Drainage Improvement

There are three types of drainage improvements that are usually pursued to reduce storm water flooding: Channelization- straightening, deepening

and/or widening a ditch or drainage way to remedy local drainage or flooding problems.

removing obstructions caused by stream crossings, such as culverts and bridges with small openings - constricts flows and causes localized backwater flooding.

Drainage system maintenance to clean out blockages caused by debris, sediment or vegetation and repair stream bank erosion

Clearing the drainage/channel

Non-structural measures Flood plain zoning

Normal level, alert level and danger level Flood forecast/warning

Flood forecasting system by DID and MMD, Malaysia. Flood warning is meaningful if given in sufficient

time. Evacuation and relocation

Evacuation of communities along their livestocks and other valuables in the flood affected areas and relocate them to the safer locations.

Flood insurance Provide a mechanism for spreading the loss over

large numbers of individuals and modifies the impact of loss burden.

Flood control in Malaysia.

In 5 month interval, 2 flood event happen at Perlis in 2011. From your opinion, how to control the flood from happen again.

Write your proposal. Submit next week