1. Frequency Analysis Problems
Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

2. Problems 1. Extrapolation 2. Short Records 3. Extreme Data
4. Non-extreme Data
5. Stationarity of Data
6. Data Accuracy
7. Peak Instantaneous Data
8. Gauge Coverage
9. No Routing
10. No Correct Distribution
11. Variation In Results
12. No Verification Of Results
13. Mathematistry
Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

3. 1. Extrapolation
Danger in fitting to known set of data and extrapolating to the unknown, without understanding physics
Example of US population growth chart :
Tight fit with existing data
Application of “accepted” distribution
No understanding of underlying factors
Results totally wrong

4. 1. Extrapolation US Population Extrapolation Thompson (1942)
reported in Klemes (1986)

5. 2. Short Records
Ideally require record length several times greater than desired return period
Alberta has over 1000 gauges with records, but very few are long
Frequency analysis results can be very sensitive to addition of one or two data points
Subsampling larger records indicates sensitivity

6. 2. Short Records Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

7. 2. Short Records Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

8. 2. Short Records Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

9. 3. Extreme Data
The years recorded at a gauge may or may not have included extreme events
Large floods known to have occurred at gauge sites but not recorded
Some gauges may have missed extreme events only by chance e.g flood - originally predicted for Red Deer basin, but ended up on the Oldman basin. The Red Deer and Bow River basins have not seen extreme floods in 50 to 70 years
Presence of several extreme events could cause frequency analysis to over-predict
Presence of no extreme events could cause frequency analysis to under-predict
Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

10. 3. Extreme Data
Gauge 05BH004
Bow River At Calgary

11. 3. Extreme Data
Gauge 05BH004
Bow River At Calgary

12. 4. Non-extreme Data
All data points are used by statistical methods to fit a distribution. Most of these points are for non-extreme events, that have very different physical responses than extreme events e.g. :
magnitude, duration, and location of storm
snowmelt vs. rainfall
amount of contributing drainage area
initial moisture
impact of routing at lower volumes of runoff
Fitting to smaller events may cause poor fit and extrapolation for larger events
Impact of change in values at left tail impact the extrapolation on the right - makes no physical sense
Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

13. 4. Non-extreme Data
Gauge 05BH004
Bow River At Calgary

14. East Humber River, Ontario
4. Non-extreme Data
A - Original Fit
B - 3 lowest points slightly reduced
C - 3 lowest points slightly increased
East Humber River, Ontario
Klemes (1986)

15. 4. Non-extreme Data

16. 5. Stationarity Of Data
Changes may have occurred in basin that affect runoff response during the flow record e.g.
man-made structures - dams, levees, diversions
land use changes - agriculture, forestation, irrigation
In order to keep the equivalent length of record, hydrologic modelling would be required to convert the data so that it would be consistent.
This modelling would be very difficult as it it would cover a wide range of events over a number of years
Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

17. 6. Data Accuracy Extreme data often not gauged
Extrapolated using rating curves
Channel changes during large floods - geometry, roughness, sediment transport,
Problems with operation of stage recording gauges e.g. damage, ice effects
Problems with data reporting e.g. Fish Ck, 1915
Hydrograph examination can ID problems

18. 6. Data Accuracy

19. 6. Data Accuracy Gauge 05AA004 Pincher Ck - 1995
Highest Recorded Water Level
Highest Gauge Measurement
Gauge 05AA004
Pincher Ck

20. 6. Data Accuracy Gauge 05BK001 Fish Ck - 1915 Qi reported as 200 m3/s
Does not fit mean daily flows
Gauge 05BK001
Fish Ck

21. 7. Peak Instantaneous Data
Design discharge is based on peak instantaneous values, but sometimes this data is not available
Conversion of mean daily data to instantaneous requires consideration of the hydrograph timing e.g. peaks near midnight vs. peaks near noon
Different storm durations can result in very different peak to mean daily ratios for the same basin
Applying a multiplier to the results of a frequency analysis based on mean daily values can lead to misleading results
Statistical methods require that all data points be consistent, even though many are irrelevant to extrapolation

22. 7. Peak Instantaneous Data
Gauge 05AA023
Oldman R
Qi/Qmd - Peak At Noon /740 = 1.77
Qi/Qmd - Peak At Midnight /599 = 2.19

23. 7. Peak Instantaneous Data
Oldman R Dam
mm runoff - Qi/Qmd = 1.25
1: mm runoff - Qi/Qmd = 1.25 (based on 1975 hydrograph)
mm runoff - Qi/Qmd ~2.0
Rebuilt 1923 hydrographs from tributaries suggest higher ratio likely

24. 8. Gauge Coverage
Limited number of gauges in province with significant record lengths
Difficult to transfer peak flow number to other sites without consideration of hydrographs and routing
Area exponent method very sensitive to assumed number

25. 8. Gauge Coverage
All Gauges
(1085)
Gauges >30 Years
(212)

26. 8. Gauge Coverage

27. 8. Gauge Coverage

28. 9. No Routing
Peak instantaneous flow value is only applicable at the gauge site
Need hydrograph to rout flows, not just peak discharges
Major Routing Factors include :
Basin configuration
Lakes and reservoirs
Floodplain storage
inter-basin transfers e.g. Highwood - Little Bow River

29. 9. No Routing Discharge (m3/s) Time (hrs) 15 5 10 20 40 60 80 Inflow5 10 20 40 60 80
Inflow
Outflow
Discharge (m3/s)
Hydrograph Generation - Basin parameters are used to determine runoff hydrographs for each distinct area of the basin. Techniques range from detailed tracking of water using overland and in-channel velocities to published unit hydrographs scaled to match the runoff volume and estimated time to peak. Empirical equations are available that relate the time to peak to basin characteristics such as slope and shape.
Hydrograph Routing - The hydrographs from each sub-area are routed through channels and storage elements, with flows being combined at junctions. Channel routing tracks the attenuation in the flood peak and the time of travel as the flood wave moves downstream. Storage routing determines the outflow hydrograph based on the inflow hydrograph, the stage-storage relationship for the storage element, and the stage-discharge curve for the outlet. The outflow will be dependent on the elevation of water in the storage element. Therefore, the degree of attenuation will be highly dependent on the inflow peak, the inflow volume, and the amount of storage available.
Time (hrs)

30. 10. No Correct Distribution
Application of theoretical probability distributions and fitting techniques originated with Hazen (1914) in order to make straight line extrapolations from data
There is no reason why they should be applicable to hydrologic observations
None of them can account for the physics of the site during extrapolation
discharge limits due to floodplain storage
addition of flow from inter-basin transfer at extreme events
changes in contributing drainage area at extreme events
Hydrology - How much water
Hydraulics - How deep, fast
Channels - Dynamic characteristics of streams
Scour - Streambed lowering associated with bridge components
Protection Works - Protecting bridges from stream attack

31. 11. Variation in Results
Different distributions and fitting techniques can yield vastly different results
Many distributions in use - LN2, LN3, LP3, GEV, P3
Many fitting techniques - Moments, Maximum Likelihood, Least Squares Fit, PWM
No way to distinguish between which one is the most appropriate for extrapolation
Extrapolated values can be physically unrealistic

32. Waterton River Near Waterton
11. Variation in Results
Gauge 05AD003
Waterton River Near Waterton
74 Years of Record

33. 11. Variation in Results Gauge 05BL027 Trap Ck Near Longview
20 Years of Record

34. 12. No Verification Of Results
Due to the separation of frequency analysis from physical modelling, the process cannot be tested.
1:100 year flood predictions cannot be actually tested for 100's or 1000's of years.
There is therefore little opportunity to refine an analysis or to improve confidence in its applicability

35. 13. Mathematistry
Gain artificial confidence in accuracy due to mathematical precision
statistics - means, standard deviations, skews, kurtosis, outliers, confidence limits
curve fitting - moments, max likelihood, least squares, probability weighted moments
probability distributions - LN3, LP3, GEV, Wakeby
Loose sight of physics with focus on numbers

36. Conclusions
Statistical frequency analysis has many problems in application to design discharge estimation for bridges.
If frequency analysis is to be employed, extrapolation should be based on extreme events. This can be accomplished using graphical techniques if appropriate data exists.
Alternative approaches to design discharge estimation should be investigated. These should :
be based on all relevant extreme flood observations for the area, minimizing extrapolations
account for physical hydrologic characteristics for the area and the basin

37. Conclusions Recommended articles by Klemes :
“Common Sense And Other Heresies” - Compilation of selected papers into a book, published by CWRA
“Dilettantism in Hydrology: Transition or Destiny?” (1986)
“Hydrologic And Engineering Relevance of Flood Frequency Analysis” (1987)
“Tall Tales About Tails Of Hydrological Distributions” - paper published in ASCE Journal Of Hydrologic Engineering, July 2000