Hysteresis in River Discharge Rating Curves. Histerésis en las curvas de gasto en ríos (caudal/calado) Madrid, March 25, 2013

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1 Hysteresis in River Discharge Rating Curves Histerésis en las curvas de gasto en ríos (caudal/calado) Madrid, March 25, 2013 Marian Muste and Kyutae Lee IIHR Hydroscience & Engineering The University of Iowa, U.S.A.

2 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

3 Option 1: Stage discharge Rating Curves 1. Direct discharge measurements over a wide range of flows 2. Build the RC 3. Convert measured stages in discharges using RC h Step 1 Step 2 Underlying assumption: Steady Flow Step 3 USGS Coralville, Iowa, 7 years of records RC derived measurements (125,865) direct measurements (237)

4 Option 2: Index velocity Rating Curves 1. Direct measurements for V index, Q, h, and A 2. Build stage area RC 3. Build velocity index RC 4. Compute instantaneous discharges as Q = V*A Step 2: Stage-Area Rating (h A) Step 1 WMO (2011) Step 3: Index Velocity Rating (V index V) Vmean V(index) Step 4: Q = V*A

5 Option 3: Slope area Rating Curves 1. Survey cross section 2. Survey free surface slope (HGL) 3. Compute instantaneous discharges using Manning eqn. Step 2 Step 1 Step SI units

6 What is hysteresis? Dependence of a system not only of the present state but also of its past (Wikipedia) Example: Loading and unloading a rubber band

7 Hysteresis in discharge RCs 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 Accelerated flow (phase I) Decelerated flow (Phase II) Steady (normal) Focus: Stage discharge (h Q) RCs Adapted from Graf & Qu (2004)

8 Sample Hysteresis in Stage Discharge RC Measurements with appropriate protocols enable to capture hysteresis Δh= 10% Δh= 26% H(m) ΔQ=18% Stage (ft) ΔQ=27% Q(m 3 /s) Source: Budi Gunawan, Discharge (cfs) Small streams: Blackwater (UK); Gunawan (2010) Medium streams: Chattahoochee (USA); Faye and Cherry (1980) Δh= 13% ΔQ=41% Δh= 14 % Large rivers: Mississippi River (USA); Fread (1973) Large rivers: Yantze (China); Herschy (2009)

9 Hysteresis sensitivity factors Most important factors in welldeveloped hysteresis: Gage setting Event intensity and duration Stage (ft) Discharge Q (ft 3 /t) C3 (Tp=24hr,Tb=24hr) C6 (Tp=24hr,Tb=12hr) C7 (Tp=24hr,Tb=72hr) Depth (ft) C3 (Tp=24hr,Tb=24hr) C6 (Tp=24hr,Tb=12hr) C7 (Tp=24hr,Tb=72hr) 701 Bed Slope = Bed Slope = Bed Slope = Discharge (cfs) Time (hr) Discharge Q (ft 3 /t) Discharge Q (ft 3 /t) C3 (peak = 10000) C8 (peak = 20000) Depth (ft) C3 (peak = 10000) C8 (peak = 20000) Need for diagnostic protocols (currently under development) Time (hr) Dischrage Q (ft 3 /t)

10 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

11 How to capture hysteresis? 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

12 Hysteresis: Direct measurements Our attempts to capture hysteresis ( ) Measurement Site: Clear Creek, Oxford, IA (USGS )

13 How to capture hysteresis? A) Direct discharge measurements B) Analytical investigation using simplified approaches (1D corrections formulae) C) Numerical modeling using physically based modeling

14 Hysteresis correction methods Abundant choices, few validations or recommendations for implementation Method Data required Flood Routing Jones Q o, B, S o,( y/ t), ( Q o / z) Kinematic approximation 2 Henderson Q o, S o,( y/ t), ( y/ x) Parabolic approximation 3 Di Silvio Q b, Q p, A, S o, F r, R, T r, T f, A p, R p, A m, ( C/ A) 4 Fread S o, A, B,,( B/ y), ( z/ t), ( U/ t), Q p, Q b, T r, h p, h b, A m, Triangular approximation Parabolic approximation Q n normal flow kinematic wave: term a diffusion wave: terms a and b full dynamic wave: terms a, b, and c 5 Marchi Q s, B, S o, A,,( B/ y), ( A/ t) Kinematic approximation 6 Faye & Cherry K, A, y (t± t), y t, R, U t, ( Q o / z), S o, U (t± t), n Kinematic approximation 7 Fenton Q s, A, K, U, S o, Q o, B, ( Q o / z), ( y/ t), ( 2 y/ t 2 ), ( 3 y/ t 3 ) Kinematic approximation Our option: Fread (1975) full dynamic wave stage measurements at one station 8 Perumal Q s, B, S o, ( Q o / z), ( y/ t), F r, P, ( R/ y), ( A/ y), ( 2 y/ t 2 ) Approximate convection diffusion 9 Boyer Plots of Q m vs. z, z/ t Kinematic approximation 10 Lewis Qm, z/ t, Plots of Q m vs. z, J Kinematic approximation 11 Wiggins Plots of R vs. V m,, n, Classification of bed surface, z/ t, Q m 12 Peterson- Overleir z/ t, BFGS algorithm and its parameters No convective and local acceleration term Kinematic approximation

15 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

16 Fread s formula Modified Fread method for small stream channels (iterative solution) Energy slope, S f Wave celerity coefficient, K Implementation case studies Case 1 Case 2 Case 3 One event, Clear Creek, USGS Oxford, Iowa (USA) One event, Ebro River (Spain) Multiple events, Clear Creek, USGS Oxford, Iowa (USA)

17 Fread s formula implementation case 1: one event USGS , Oxford Iowa (processed data) Evaluation of Saint-Vernant equation Steady-state Fread (1975) Points Discharge (cfs) Stage-discharge rating curve comparisons Apr Apr Apr Apr Apr-2012 Time Series Evaluation of the uncertainty in Prediction of Q Stage (ft) Modified Fread RC USGS Steady RC Discharge (cfs) Relative uncertainty in prediction of Q (%) Apr Apr Apr Apr Apr Apr-2012 Time Modified Fread vs. USGS steady RC 4% to 10.5%

18 Fread s formula implementation case 2: one event Asco station, Ebro River, Spain (Ferrer, Moreno, Sanchez, 2013) Discharge (cms) Evaluation of Saint-Vernant equation Steady-state Modified Fread ADCP Artificial flood event for vegetation removal (June 2012) Not all the needed data available Jun Jun Jun Jun Jun-2012 Time Series Stage-discharge rating curve comparisons 4 Stage (m) Steady RC Modified Fread ADCP Discharge (cms)

19 Fread s formula implementation case 3: event series USGS , Oxford Iowa (provisional data similar with the info available during floods) Event 1 Event 2 Event 3 Series of rainfalls on frozen ground (good cases for hysteresis) (February March, 2013)

20 Fread s formula implementation case 3: event series Event 3: most violent rainfall (March 10, 2013) ft (2,340cfs at 11:30am, Mar 10) ft (1,330cfsat 5:15pm, Mar10) ft (667cfs at 10:00am, Mar 11) ft (66cfs at 10:00am, Mar 12)

21 Fread s formula implementation case 3: event series USGS , Oxford Iowa (provisional data) Stage (ft) Event 3: most violent rainfall of the series (March 10, 2013) Discharge (cfs) USGS Hydrograph Modified Fread Points Overbank flow 0 09-Mar Mar Mar Mar Mar-2013 Time Series USGS Steady RC Modified Fread Points Discharge (cfs)

22 Fread s formula implementation case 3: event series Event 1 Event 2 Event 3 USGS , Oxford Iowa (provisional data) Stage-discharge rating curve comparisons ΔH=706.5ft±0.5ft (5%) ΔQ=800cfs±100cfs (12.5%) 706 Uncertainty bounds due to unsteady flows Stage (ft) Event1 on Feb 7-9, 2013 Event1 on Feb 7-9, Event2 on Feb 10-12, 2013 Event2 USGS on Steady Feb 10-12, RC 2013 Event3 on Mar 9-12, 2013 USGS Steady RC USGS Steady RC Discharge (cfs)

23 How to capture hysteresis? A) Direct discharge measurements B) Analytical investigation using simplified approaches C) Numerical modeling using physically based modeling (2D, 3D)

24 Hysteresis: numerical simulations Clear Creek watershed including USGS Clear Creek, Oxford, Iowa HEC HMS model HEC RAS model Watershed description Size: approximately 103 mi 2 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)

25 Hysteresis: numerical simulations HEC HMS model setup Validations for alternative HEC HMS simulations a) peak weighted RMS error function HEC HMS model setup 6 sub basins, 3 sub reaches, 4 junctions HEC HMS model components Basin model, meteorologic model, control specifications, and time series data b) percent error volume

26 Hysteresis: numerical simulations HEC RAS model setup River system Boundary conditions S1: Discharge hydrographs S4: Normal depth (friction slope: ) Monitoring locations S2: USGS Oxford Clear Creek S3: USGS Coralville Clear Creek Geometry setup Reach length: 24.1km Cross sections: 192 (approx 130m interval) Bridges: 10 Roughness coefficient: (in bank), LCD (floodplain) Obstructions (buildings) included

27 Hysteresis: numerical simulations HEC RAS results Scenario 2: typical event December 04, 2011, Q peak_s2 = 3.2m 3 Flow (m3/s) b) River: Clear_Cr Reach: Clear_Cr RS: Dec Dec Dec2011 Date Input hydrograph at S1 Legend Flow Scenario 1: large event (June 02, 2008) Q peak_s1 = 68m 3 Flow (m3/s) a) River: Clear_Cr Reach: Clear_Cr RS: Legend 60 Flow Jun Jun2008 Date Input hydrograph at S1 Stage (m) Stage (m) Plan: 15 River: Clear_Cr Reach: Clear_Cr RS: Legend RC Flow(m3/s) Max thickness: about 1cm at S2 Plan: 15 River: Clear_Cr Reach: Clear_Cr RS: Legend Flow(m3/s) Max thickness: about 4cm at S3 RC Stage (m) Stage (m) Plan: 1 River: Clear_Cr Reach: Clear_Cr RS: Legend RC Flow(m3/s) Max thickness: about 10cm at S2 Plan: 1 River: Clear_Cr Reach: Clear_Cr RS: Legend Flow(m3/s) Max thickness: about 15cm at S3 RC

28 Hysteresis: numerical simulations HEC RAS: Sensitivity analysis Peak discharge timing Summary of the results Input hydrograph at S1 Simulated RCs at S1 S1 (m) % wrt depth changes S2 (m) % wrt depth changes 2008 Large event % % 2011 Typical event % % Peak discharge % % (low to high) % % Duration % % (high to low) % % Peak timing % % (slow to fast) % % Event duration and peak discharge timing most important parameters (max error: 12%) Simulated RCs at S2

29 Hysteresis practical implications 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

30 How can be hysteresis used in practical applications? 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) Stage Stage

31 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

32 How can be hysteresis used in practical applications? Floods Better planning during floods by predicting more accurate flood stages and their timing!

33 Questions?