Flood RoutingApplied Hydrology

Flow Routing

Channel Routing Reservoir Routing

Routing

Routing is the process of predicting temporal and spatial variation of a flood wave as it travels through a river (or channel reach or reservoir.

Two types of routing can be performed:

Hydrologic Routing

Hydraulic Routing

Hydrologic Routing

In hydrologic routing techniques, the equation of continuity and some linear or curvilinear relation between storage and discharge within the river or reservoir is used.

Applications of routing techniques:

Flood predictions

Evaluation of flood control measures

Assessment of effects of urbanization

Flood warning

Spillway design for dams

Hydrologic Routing

Continuity Equation:

Where I = Inflow

O= Outflow

S/t = Rate of change of storage

Problem:

You have a hydrograph at one location (I)

You have river characteristics (S=f(I,O))

Need:

A hydrograph at different location (O)

S

I Ot

Hydrologic Routing

The hydrograph at B is attenuated due to storage characteristics of the stream reach.

Assumption: no seepage, leakage, evaporation, or inflow from the sides.

Hydrograph at point A

Hydrograph at point B

Hydrologic Channel Routing

Muskingum Method: Flow in a channel

Storage in wedge: KX(I-O)

Storage in prism: KO

So, Storage S=KX(I-O)+KO

wedge

prism

prism wedge

prism

Muskingum Method

Storage S=KO+KX(I-O) rewritten as

S=K[XI+(1-X)O]

Where

S = Storage in the river reach

K = Storage time constant (T)

X = A weighting factor that varies between 0 and 0.5 (defines relative importance of inflow and outflow on storage)

If X=0.5 pure translation, if X=0 max attenuation

Muskingum Method

How it works:

Write continuity equation as

Where

I = Average inflow during t

O= Average outflow during t

or

S

I Ot

1 2 1 2 2 1I I O O S S

2 2 t

Muskingum Method

1 2 1 2 2 1I I O O S S

2 2 t

S k[XI (1 X)O]

Combine and rearrange

1 2 1 2

2 1 2 1I I O O K

[X(I I ) (1 X)(O O )]2 2 t

Simplified into the routing equation:

2 02 11 20O C I C I C I

Subscript 1 refers to t1and 2 to t2 = (t+t)

Muskingum Method

0 1 2C C C 1

Need K and t in the same units

Estimation of K, X and t

K=0.6L/vavg

Where

L = Length of river reach

Vavg = Average velocity in reach

Constraint K<tp/5 (divide reach up if needed)

X = 0.2 for most cases

X = 0.4 for steep channels with narrow flood plains

X = 0.1 for mild channels with broad flood plains

2KX<t<2K(1-X) and ideally t<tp/5. Choose t in numbers that divide into 24 (Daily data)

Example 1

Tp = 4 hr, L = 2 mi, vavg = 2.5 ft/s, wide flat floodplain

Solution:

K = 0.6L/vavg = 0.6(2x5280)/2.5=2,534 sec = 0.7 hr

X = 0.1

t:

2KX = 2(0.7)0.1 = 0.14

2K(1-X) = 2(0.7)0.9 = 1.26

0.14<t<1.26 and t<tp/5 or t<0.8 hr,

so t = 0.5 hr is most accurate.

Example 2

Channel Routing in spreadsheet

Reservoir Routing

Storage-Indication Method:

Apply the storage-indication method for reservoirs that have a spillway.

Assume that storage (S)=0 when no overflow occurs (surcharge storage).

Apply this to an ungated spillway like a weir, outlet discharge pipe, or gated spillway with fixed position.

Reservoir Routing

Use a relationship between outflow (O) and elevation head (H). For example, for a broad crested weir:

Q=CLH3/2

Where

O = Discharge at the outlet (cfs)

C = Discharge coefficient of weir (cfs)

L = Length of crest (ft)

H = Depth above spillway (ft)

Reservoir Routing

Two relationships specific for reservoir:

• Storage-Head Relationship

• Outflow-Head Relationship

Need:

• An inflow hydrograph

• A starting elevation above spillway

Reservoir Routing

Use the continuity equation as:

Where

I = Average inflow during t

O = Average outflow during t

Or

Where subscripts denote the time interval

S

I Ot

i i 1 i i 1 i 1 iI I O O S S

2 2 t

Reservoir Routing

i i 1 i i 1 i 1 iI I O O S S

2 2 t

For i=1, we know Ii and Ii+1 (Initially) and Si (Initially)

We do not know Oi+1 and Si+1

So, we rewrite “Knowns = Unknowns”

Reservoir Routing

We can find Oi+1, if we have a relationship between term on RHS and O. This is possible using the so-called Storage-Indication Curve.

Routing Steps

Set i=1, obtain initial head and inflow hydrograph.

Find initial outflow O1 corresponding to initial head above spillway.

Find 2S/t for S(H) relationship.

From the continuity equation, calculate

Enter storage-indication curve to find O2.

Calculate

Change i=2

From continuity equation, calculate

Repeat steps 4-7, and so on…..

22

2SO

t

33

2SO

t

2 22 2 2

2S 2SO [ O ] 2O

t t

Example 3

Reservoir Routing in spreadsheet