02 FCL 2011 Lecture

IfU Institut fürUmweltingenieurwissenschaften

F&C Lab 1

Environment and Computer Laboratory HS 2011Water Resources Management

Flood Routing – Methods and ModelsExercise – Hydraulic Modelling of Open Channel Flows


F&C Lab 2

Outline

Organisational Issues

Flood Routing – Methods and Models

Introduction of the Exercise

Getting to know HEC-GeoRAS

Getting to know HEC-RAS


F&C Lab 3

Organisational IssuesSupervisor: Verena Maleska, Christina Schornberg, Ellen CerwinkaContact: [email protected] table

C 29…Friday, 16. Dec



C 29…Friday, 25. Nov

C 29Individual work on ExerciseOffice hours: 12.45-16.30, HIL D 21.3Friday, 18. Nov

C 29Open Channel Flow – hydrologic flood routing Introduction Exercise 1 – HEC-RAS Paper assignments

Friday, 11. Nov

Room Topic Date


F&C Lab 4

Organisational Issues1 Exercise + Paper Assignments

- Building up the hydraulic model with HEC-GeoRAS in ArcGIS- Hydraulic Modelling of Open Channel Flows using HEC-RAS- Transferring the results of HEC-RAS into ArcGIS

Exercises carried out in groups of 2 studentsHand in one report for the exercise and the paper assignments

- Report around 15 pagesGrading of WRM1

- HEC-RAS: 80%- Paper Assignments: 20%

Deadline for submission: 19th of December 2011


F&C Lab 5

Organisational Issues

Literature

Lecture notes „Hydraulik 1“ Prof. KinzelbachBollrich: Technische Hydromechanik Band 1Manual HEC-RASwww.sciencedirect.com for paper


F&C Lab 6

Flood Routing – methods and models

Lecture Outline

1 What is Flood Routing? motivationexamples

2 Flood Routinghydraulic flood routing - approximations to the St. Venant equations


F&C Lab 7

Flood Routing – methods and models

1) What is flood routing?

Flood (Flow) routing isa mathematical procedure for predicting the changing in magnitude, speed and shape of a flood wave as a function of time at one or more points along a river

(Handbook of Hydrology, Fread, 1993)


F&C Lab 8

• runoff production

• runoff routing


F&C Lab 9

1) floodspredict flood propagationprotectionwarning

2) designwater conveyance systemsprotective measureshydrosystem operation

3) water dynamicsungauged riverspeak flow estimationriver-aquifer interaction


F&C Lab 10

Risk analysis

1 [1 ( )]ntR P X x= − − ≥R = hydrologic risk of failure is given by the probability that the annual flood event x larger than xtwill occur at least once in n yearse.g. a weir with a life period of n=50 years, P(HQT=100)=1/T=1/100

5050

10011 [1 ( )] 1 1 0.4100

R P X x ⎡ ⎤= − − ≥ = − − ≈⎢ ⎥⎣ ⎦


F&C Lab 11

2) Flood Routing

Flow (Flood) Routing Analysis


F&C Lab 12


F&C Lab 13

Steady Uniform Flow

dv/dt=0 dv/dx=0


F&C Lab 14

Gradually Varied Flow dv/dt=0 dv/dx=0


F&C Lab 15


F&C Lab 16

Unsteady Flow: Physically Based = Hydraulic Routing


F&C Lab 17

St. Venant Equations


F&C Lab 18


F&C Lab 19


F&C Lab 20


F&C Lab 21


F&C Lab 22

Exercise: Hydraulic Modelling of Open Channel Flows

Objectives

Get to know- a numerical hydraulic model for flood routing- the general methodology, possibilities and limitations of numerical

flood routing- the role of different parameters and their influence on the

simulationsand not

- to reproduce a flood event as accurate as possible → no tuning exercise


F&C Lab 23

Tasks

1 Steady State Simulations (d/dt = 0)1.1 Rating curve (Q-H function)1.2 Influence of roughness coefficient

2 Unsteady Flow Simulations2.1 Influence of initial conditions (=> “warm up” time)2.2 Investigation of the temporal discretization2.3 Rating curve for unsteady flow2.4 Numerical damping (influence of weighting factor Θ)2.5 Influence of downstream boundary condition

Answer questions on papers dealing with roughness in open channel flow


F&C Lab 24

River Reach & Flood Events

River Reach:Thur length of about 3 km

Flood Events:Each group chooses and signs in for a flood eventFlood hydrograph: hourly mean flow for the Thur in m3/s with a duration of 30 to 50 hoursToo flashy to be realistic - but suitable for this exerciseTo be used for unsteady flow simulations

Bern

Thun


F&C Lab 25

Available Data

On the webpage:Tasks Flood eventsOrthophotoElevation dataPaper and questionsLecture notes, etc.

Bern

Thun


F&C Lab 26

Building up the Model for HEC-RAS Using ARGIS-Extension HEC-GeoRAS


F&C Lab 27

Flood routing model: HEC-RASHEC-RAS -> Hydrologic Engineering Centers River Analysis System

developed by the US Department of Defense, Army Corps of Engineers in order to manage the rivers, harbors, and other public works

1D - hydraulic flow modela) Steady & Unsteady Flowb) Sediment Transportc) Water Temperature &

Water Quality

http://www.hec.usace.army.mil/software/hec- ras/


F&C Lab 28

Flood routing model: HEC-RASHEC-RAS -> Hydrologic Engineering Centers River Analysis System

http://www.hec.usace.army.mil/software/hec- ras/


F&C Lab 29

Flood routing model: HEC-RASSteady Flow

based on the solution of the one-dimensional energy equationEnergy losses evaluated by friction and contraction / expansionmomentum equation may be used in situations where water surface profile is rapidly varied (hydraulics of bridges )

Unsteady Flowfull, dynamic Saint-Venant equationsusing an implicit, finite difference method


F&C Lab 30

Solutions of the Saint Venant Equations

Partial Differential Equation

Analytically for 1-Dimensional CaseClosed Integration e.g. Laplace/Fourier Transformation

Numerically for Common Caseuse partial difference approximation Solutions: finite differences

finite elementsfinite volume

Nonlinear equation system: iteration!


F&C Lab 31

HEC-RAS: Implicit scheme to solve discretized equationsExplicit Schemes:

- explicit scheme: Xt+1 = F(Xt)- explicit schemes can be solved for Xt+1

- straightforward computation- stability issues for large Δt (CFL-criterion)- e.g Forward step

Implicit Schemes:- implicit scheme: Xt+1 = F(Xt and Xt+1)- generally, implicit schemes can’t be solved

explicitly for Xt+1 (Xt+1 = ….) (depending on F)→ solvable e.g. with matrix inversion

- high computational demand- less strict stability criteria

→ larger time steps possible- e.g. Trapezoidal rule

-> Exc 2.2 & 2.4

tttttt

XtXFXXFtXX

dtdX

+Δ⋅=→=Δ−

≈ ++

)()( 11

[ ])()(21 1

1tt

tt

XFXFtXX

dtdX

+=Δ−

≈ ++


F&C Lab 32

Courant Friedrich Levy (CFL) - Stability Criterion

To choose Δt for a given ΔxStability Criterion for a large class of explicit advection schemes:

Time step Δt shouldn't be longer than the time a water particle needs to get from one computational node to the next (Δx)Or: The distance which a water particle moves in one time step (u*Δt) shouldn’t be larger than Δx

If Δt too long or u too high: Interpolation errors and instabilityWithin limits of stability: trade off between computation time and accuracy

-> Exc 2.2: temporal discretization

1≤ΔΔ⋅xtu

u: highest velocity in the system (⇒ flood wave speed)Δt: computational time stepΔx: spatial discretization (⇒ distance between cross sections)

uxt Δ

≤ΔtxuΔΔ

≤

Δx

tu Δ⋅

x


F&C Lab 33

HEC-RAS: Preissmann-Cunge scheme

weighting factor Θ

-> Exc 2.4: weighting factor Θ

variables:

temporal derivative:

spatial derivative

how to weight “present” (t=n+1) variable / spatial derivative compared to “past” (t=n) variable / spatial derivative?numerically stable for 0.5 ≤ Θ ≤ 1 (in practice: 0.6 ≤ Θ≤ 1)


F&C Lab 34

Deriving Inundation Maps Using HEC-GeoRAS


F&C Lab 35

Form groups and choose a flood eventGet to know HEC-RASstart working on the paper assignmentsBathurst: What are the main elements governing flow resistance in

natural channels?Is the river roughness constant in space and time?

Wohl: How can you estimate the roughness coefficient? Whichparameters influence the roughness in a channel? How dothey influence the roughness?What is the influence of a varying roughness coefficient onthe river flow? Can you make a general statement?

Next week: working on the exercise Deadline 19th December 2011

And now…

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02 FCL 2011 Lecture