Hysteresis in River Discharge Rating Curves Histerésis … 2013... · Hysteresis in River...

Hysteresis in River Discharge Rating Curves

Histerésis en las curvas de

gasto en ríos (caudal/calado)

Marian Muste and Kyutae LeeIIHR‐Hydroscience & EngineeringThe University of Iowa, U.S.A.

Madrid, March 25, 2013

Conventional Discharge Rating Curves

Rating Curves (RC): Practical solutions to continuously provide stream discharge

Option 1: stage‐discharge (most often)

• One rating curve• Requires continuous stage measurement (pressure sensors, radar, ultrasonic, etc)

Option 2: index‐velocity (emerging with the advent of acoustic and image‐based instruments)

• One to three rating curves (Kennedy, 1984)• Requires continuous stage & velocity measurements

Option 3: slope‐area (rarely used for continuous, mostly for RC extrapolation)• No rating curves (synthetic)• Requires cross‐section and free‐surface slope measurements

1. Direct discharge measurements over a wide range of flows 2. Build the RC3. Convert measured stages in discharges using RC

Option 1: Stage‐discharge Rating Curves

h

Underlying assumption: Steady Flow

USGS 05454200 Coralville, Iowa, 7 years of records

• RC‐derived measurements (125,865)

• direct measurements (237)

Step 1 Step 2

Step 3

1. Direct measurements for Vindex, Q, h, and A2. Build stage‐area RC 3. Build velocity‐index RC 4. Compute instantaneous discharges as Q = V*A

Step 2: Stage-Area Rating (h A)

-0.40-0.200.000.200.400.600.801.001.20

-0.50 0.00 0.50 1.00 1.50

Vm

ean

V(index)

Step 3: Index Velocity Rating (Vindex V)

WMO (2011)

Step 4: Q = V*A

Step 1

Option 2: Index‐velocity Rating Curves

Option 3: Slope–area Rating Curves

Step 1

Step 2

Step 3

1. Survey cross section 2. Survey free‐surface slope (HGL) 3. Compute instantaneous discharges using Manning eqn.

1 2 3⁄ 1 2⁄ SI units

Dependence of a system not only of the present state but also of its past(Wikipedia)

What is hysteresis?

Example: Loading and unloading a rubber band

Hysteresis in discharge RCs

Accelerated flow (phase I) Decelerated flow (Phase II)

Steady (normal)

Adapted from Graf & Qu (2004)

Conventional assumption for Options 1, 2, and 3: STEADY FLOW STATIC RCs (one‐to‐one relationship)

Calibration measurements can be randomly acquired over the flow range

However, storm runoff conveyed to streams propagates as UNSTEADY TRANSITORY FLOWS

HYSTERESIS in RC (dynamic, looped curve) Calibration measurements need to be sampled commensurate with the event time scale

Focus:Stage‐discharge (h – Q) RCs

Measurements with appropriate protocols enable to capture hysteresis

Sample Hysteresis in Stage‐Discharge RC

Small streams: Blackwater (UK); Gunawan (2010) Medium streams: Chattahoochee (USA); Faye and Cherry (1980)

Large rivers: Mississippi River (USA); Fread (1973) Large rivers: Yantze (China); Herschy (2009)

0.40 0.55 0.70 0.85 1.00 1.15 1.30 1.45 1.600.4

0.5

0.6

0.7

0.8

Source: Budi Gunawan, 2008

H(m

)

Q(m3/s)

ΔQ=18%

1000 2000 3000 4000 5000 6000 7000881

881.5

882

882.5

883

883.5

884

884.5

885

885.5

886

Discharge (cfs)

Sta

ge (f

t)

ΔQ=27%

ΔQ=41%

Δh= 10% Δh= 26%

Δh= 13%

Δh= 14 %

Hysteresis sensitivity factors

Most important factors in well‐developed hysteresis:•Gage setting•Event intensity and duration

0

2000

4000

6000

8000

10000

12000

0 20 40 60 80 100 120 140

Disc

harg

e Q (f

t3 /t)

Time (hr)

C3 (Tp=24hr,Tb=24hr)C6 (Tp=24hr,Tb=12hr)C7 (Tp=24hr,Tb=72hr)

0

5000

10000

15000

20000

25000

0 20 40 60 80 100 120 140

Disc

harg

e Q (f

t3 /t)

Time (hr)

C3 (peak = 10000)C8 (peak = 20000)

0

5

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 110

Dep

th (f

t)

Discharge Q (ft3/t)

C3 (Tp=24hr,Tb=24hr)C6 (Tp=24hr,Tb=12hr)C7 (Tp=24hr,Tb=72hr)

0

10

20

30

40

50

60

70

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22

Dep

th (f

t)

Dischrage Q (ft3/t)

C3 (peak = 10000)

C8 (peak = 20000)

0 500 1000 1500 2000 2500 3000700

701

702

703

704

705

706

Discharge (cfs)

Sta

ge (f

t)

Bed Slope = 0.0001Bed Slope = 0.001Bed Slope = 0.01

Need for diagnostic protocols(currently under development)

How to capture hysteresis?

A) Direct discharge measurements (using event‐based, high temporal frequency sampling protocols) EXPENSIVE, NO PROTOCOLS, INCREASINGLY TESTED

B) Analytical investigation using simplified approaches (1D)INEXPENSIVE, MANY PROTOCOLS, SCARSELY VALIDATED

C) Numerical modeling using physically‐based modeling (2D, 3D)EXPENSIVE, MANY MOELS, SCARSELY VALIDATED


A) Direct discharge measurements (using event‐based, high temporal frequency sampling protocols)

B) Analytical investigation using simplified approaches

C) Numerical modeling using physically‐based modeling

Our attempts to capture hysteresis (2011‐13)Measurement Site: Clear Creek, Oxford, IA (USGS 05454220)

Hysteresis: Direct measurements


A) Direct discharge measurements

B) Analytical investigation using simplified approaches (1D corrections formulae)

C) Numerical modeling using physically‐based modeling

Abundant choices, few validations or recommendations for implementation

Method Data required Flood Routing

1 Jones Qo, B, So,(∂y/∂t), (∂Qo/∂z) Kinematic approximation

2 Henderson Qo, So,(∂y/∂t), (∂y/∂x) Parabolic approximation

3 Di Silvio Qb, Qp, A, So, Fr, R, Tr, Tf, Ap, Rp, Am, (∂C/∂A)

Triangular approximation

4 Fread So, A, B, ,(∂B/∂y), (∆z/∆t), (∆U/∆t), Qp, Qb, Tr, hp, hb, Am,

Parabolic approximation

5 Marchi Qs, B, So, A, ,(∂B/∂y), (∂A/∂t) Kinematic approximation

6 Faye & Cherry

K, A, y(t±∆t), yt, R, Ut, (∂Qo/∂z), So, U(t±∆t), n

Kinematic approximation

7 Fenton Qs, A, K, U, So, Qo, B, (∂Qo/∂z), (∂y/∂t), (∂2y/∂t2), (∂3y/∂t3)


8 Perumal Qs, B, So, (∂Qo/∂z), (∂y/∂t), Fr, P, (∂R/∂y), (∂A/∂y), (∂2y/∂t2)

Approximate convection diffusion

9 Boyer Plots of Qm vs. z, ∂z/∂t Kinematic approximation

10 Lewis Qm, ∂z/∂t, Plots of Qm vs. z, J Kinematic approximation

11 Wiggins Plots of R vs. Vm, , n, Classification of bed surface, ∂z/∂t, Qm

No convective and local acceleration term

12 Peterson-Overleir

∂z/∂t, BFGS algorithm and its parameters


√ 0 110 0

10

• Qn – normal flow• kinematic wave: term a• diffusion wave: terms a and b• full dynamic wave: terms a, b, and c

Our option: Fread (1975)•full dynamic wave•stage measurements at one station

Hysteresis correction methods

Fread’s formula

Fread (1973 & 1975)

1. Inputs: Hydraulic depth, width, bed slope, Manning’s roughness, rate of changes of depth (dh/dt), initial discharge (randomly selected), time step for output

1. Output: looped rating curve

Fread’s formula

Modified Fread method for small stream channels (iterative solution)

Implementation case studiesCase 1 One event, Clear Creek, USGS 05454220 Oxford, Iowa (USA)

Case 2 One event, Ebro River (Spain)

Case 3 Multiple events, Clear Creek, USGS 05454220 Oxford, Iowa (USA)

Energy slope, Sf

Wave celerity coefficient, K

Fread’s formula implementation case 1: one event

USGS 05454220, Oxford Iowa (processed data)

14-Apr-2012 15-Apr-2012 16-Apr-2012 17-Apr-2012 18-Apr-2012100

200

300

400

500

600

700

Time Series

Dis

char

ge (c

fs)

Evaluation of Saint-Vernant equation

Steady-stateFread (1975)Points

1

2

3

4

5

6

Modified Fread vs. USGS steady RC ‐4% to 10.5%

100 200 300 400 500 600 700700

701

702

703

704

705

706

Discharge (cfs)

Sta

ge (f

t)

Stage-discharge rating curve comparisons

Modified Fread RCUSGS Steady RC

14-Apr-2012 15-Apr-2012 16-Apr-2012 17-Apr-2012 17-Apr-2012 18-Apr-2012-4

-2

0

2

4

6

8

10

12

TimeR

elat

ive

unce

rtain

ty in

pre

dict

ion

of Q

(%)

Evaluation of the uncertainty in Prediction of Q

Fread’s formula implementation case 2: one event

Asco station, Ebro River, Spain (Ferrer, Moreno, Sanchez, 2013)

20-Jun-2012 20-Jun-2012 20-Jun-2012 20-Jun-2012 21-Jun-2012200

300

400

500

600

700

800

900

1000

1100

1200

Time Series

Dis

char

ge (c

ms)

Evaluation of Saint-Vernant equation

Steady-stateModified FreadADCP Artificial flood event for vegetation

removal (June 2012)‐ Not all the needed data available

200 300 400 500 600 700 800 900 1000 1100 12001.5

2

2.5

3

3.5

4

4.5

5

5.5

Discharge (cms)

Sta

ge (m

)


Steady RCModified FreadADCP

Fread’s formula implementation case 3: event series

USGS 05454220, Oxford Iowa (provisional data – similar with the info available during floods)

Series of rainfalls on frozen ground (good cases for hysteresis)(February – March, 2013)

E v e n t 1 E v e n t 2 E v e n t 3

Fread’s formula implementation case 3: event seriesEvent 3: most violent rainfall (March 10, 2013)

696.00

698.00

700.00

702.00

704.00

706.00

708.00

710.00

712.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00

710.67ft (2,340cfs at 11:30am, Mar 10)

709.18ft (1,330cfs at 5:15pm, Mar 10)

700.22ft (66cfs at 10:00am, Mar 12)

705.63ft (667cfs at 10:00am, Mar 11)

Event 3: most violent rainfall of the series(March 10, 2013)

09-Mar-2013 10-Mar-2013 11-Mar-2013 11-Mar-2013 12-Mar-20130

500

1000

1500

2000

2500

3000

3500

Time Series

Dis

char

ge (c

fs)

USGS HydrographModified FreadPoints

1

2

36

4 5

0 200 400 600 800 1000 1200 1400 1600 1800700

701

702

703

704

705

706

707

708

709

710

Discharge (cfs)

Sta

ge (f

t)

USGS Steady RCModified FreadPoints

1

2

3

6

4

5

Overbank flow

Fread’s formula implementation case 3: event seriesUSGS 05454220, Oxford Iowa (provisional data)

0 200 400 600 800 1000 1200 1400 1600 1800698

700

702

704

706

708

710

Discharge (cfs)

Sta

ge (f

t)


USGS Steady RC

Event 1 Event 2 Event 3

0 200 400 600 800 1000 1200 1400 1600 1800698

700

702

704

706

708

710

Discharge (cfs)

Sta

ge (f

t)


Event1 on Feb 7-9, 2013

USGS Steady RC

0 200 400 600 800 1000 1200 1400 1600 1800698

700

702

704

706

708

710

Discharge (cfs)

Sta

ge (f

t)




USGS Steady RC

0 200 400 600 800 1000 1200 1400 1600 1800698

700

702

704

706

708

710

Discharge (cfs)

Sta

ge (f

t)


Event1 on Feb 7-9, 2013Event2 on Feb 10-12, 2013Event3 on Mar 9-12, 2013USGS Steady RC

Uncertainty bounds due to unsteady flows

ΔQ=800cfs±100cfs (12.5%)

ΔH=706.5ft±0.5ft (5%)

USGS 05454220, Oxford Iowa(provisional data)

Fread’s formula implementation case 3: event series


A) Direct discharge measurements

B) Analytical investigation using simplified approaches

C) Numerical modeling using physically based modeling (2D, 3D)

Clear Creek watershed including USGS 05454220 Clear Creek, Oxford, Iowa

Hysteresis: numerical simulations

HEC‐RAS model

Watershed description• Size: approximately 103 mi2

• Land use: farm land combined urban areas (Oxford, Tiffin, Coralville, and Iowa City)• Length of modeled reach: 24.1km (HEC‐RAS) and 4.3km (HEC‐HMS)

HEC‐HMS model


HEC‐HMS – model setup

HEC‐HMS model setup‐6 sub‐basins, 3 sub‐reaches, 4 junctionsHEC‐HMS model components‐Basin model, meteorologic model, control specifications, and time series data

a) peak‐weighted RMS error function

b) percent error volume

Validations for alternative HEC‐HMS simulations


HEC‐RAS – model setupRiver system

Boundary conditions•S1: Discharge hydrographs •S4: Normal depth (friction slope: 0.00075)

Monitoring locations•S2: USGS 05454220 Oxford Clear Creek•S3: USGS 05454500 Coralville Clear Creek

Geometry setup•Reach length: 24.1km•Cross‐sections: 192 (approx 130m interval)•Bridges: 10 •Roughness coefficient: 0.035 (in bank),

LCD (floodplain)•Obstructions (buildings) ‐ included

Hysteresis: numerical simulationsHEC‐RAS results

Scenario 1: large event(June 02, 2008)Qpeak_S1 = 68m3

Max thickness: about 10cm at S2


0 10 20 30 40 50 60214.0

214.5

215.0

215.5

216.0

216.5

217.0Plan: 1 River: Clear_Cr Reach: Clear_Cr RS: 19839.50

Flow(m3/s)

Sta

ge (m

)

Legend

RC

0 10 20 30 40 50 60198.5

199.0

199.5

200.0

200.5


Flow(m3/s)

Sta

ge (m

)

Legend

RC



0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5213.9

214.0

214.1

214.2

214.3

214.4


Flow(m3/s)

Sta

ge (m

)

Legend

RC

0.0 0.5 1.0 1.5 2.0 2.5 3.0198.5

198.6

198.7

198.8

198.9


Flow(m3/s)

Sta

ge (m

)

Legend

RC

b)

Input hydrograph at S1

24000600120018002400060012001800240006001200180003Dec2011 04Dec2011 05Dec2011

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5River: Clear_Cr Reach: Clear_Cr RS: 24131.31

Date

Flow

(m

3/s)

Legend

Flow

a)


2400 0600 1200 1800 2400 0600 1200 180003Jun2008 04Jun2008

0

10

20

30

40

50

60

70River: Clear_Cr Reach: Clear_Cr RS: 24131.31

Date

Flow

(m

3/s)

Legend

FlowScenario 2: typical event December 04, 2011, Qpeak_S2 = 3.2m3

Hysteresis: numerical simulationsHEC RAS: Sensitivity analysis

Peak discharge timing Summary of the results


Simulated RCs at S1

Simulated RCs at S2

S1 (m)% wrt depth

changesS2 (m)

% wrt depth changes

2008 Large event 0.1 4.0% 0.15 6.9%2011 Typical event 0.01 2.2% 0.04 10.3%

Peak discharge(low to high)

0.06 3.8% 0.09 7.1%0.1 4.7% 0.14 8.0%

Duration(high to low)

0.07 3.3% 0.14 8.0%0.18 9.7% 0.18 10.8%

Peak timing(slow to fast)

0.03 1.9% 0.06 4.8%0.13 8.4% 0.15 12.0%

Event duration and peak discharge timing

most important parameters (max error: 12%)

For high, unsteady flows RC uncertainties are considerable increased. The top contributing uncertainties are:

• measurement uncertainty• extrapolation of the rating• change in cross section (overbank flow)• neglecting the hysteresis effect

• Hysteresis‐induced uncertainty is generally small• Important for stream reaches on mild slopes, under channel control, and major

storm events (during floods when RC accuracy is most important)• Selected hysteresis‐induced uncertainty estimates:• 2ft difference from RC in Chatttahooche and Ohio Rivers (Petersen – Overleyer, 2006) • 5 ft difference from RC in Mississippi River (Fread, 1975)• These differences are typically lower then the steady RC reading (occur

on the rising limb) important for flood intervention

Hysteresis practical implications

Stage

Stage

Uncertainty estimator for steady RCs during storms

(based on previous data records )

Predictor for actual discharge during storms using steady RC as basis(based on an initial steady RC data)

How can be hysteresis used in practical applications?

Measurements and models embedded in an integrated system for uncertainty assessment and/or forecasting h‐Q RC Slope‐area RC

Tentative research


Floods

Better planning during floods by predicting more accurate flood stages and their timing!


Questions?

Hysteresis in River Discharge Rating Curves Histerésis … 2013... · Hysteresis in River...

Documents

Transcript of Hysteresis in River Discharge Rating Curves Histerésis … 2013... · Hysteresis in River...