Frequency Analysis and Data
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Transcript of Frequency Analysis and Data
Frequency Analysis and Data
Reading: Applied Hydrology Sections 12.3-12.6
2
Hydrologic extremes
• Extreme events• Floods • Droughts
• Magnitude of extreme events is related to their frequency of occurrence
• The objective of frequency analysis is to relate the magnitude of events to their frequency of occurrence through probability distribution• It is assumed the events (data) are independent and
come from identical distribution
occurence ofFrequency 1Magnitude
3
Return Period• Random variable:• Threshold level:• Extreme event occurs if: • Recurrence interval: • Return Period:
Average recurrence interval between events equalling or exceeding a threshold
• If p is the probability of occurrence of an extreme event, then
or
TxX
TxX
TxX of ocurrencesbetween Time
)(E
pTE 1)(
TxXP T
1)(
4
More on return period• If p is probability of success, then (1-p) is the
probability of failure• Find probability that (X ≥ xT) at least once in N years.
NN
T
TT
T
T
TpyearsNinonceleastatxXP
yearsNallxXPyearsNinonceleastatxXPpxXP
xXPp
111)1(1)(
)(1)()1()(
)(
Upper Brushy Creek Hydrologic Model
Jeff Irvin, URS
Hydrology: the Mindset Hydrology = Data (Rainfall, Runoff, Land Use)Data bad = Hydrology badData good = Hydrology good
How do you test data?
Choice of Calibration storms The runoff hydrograph has two main parameters that define shape:• A parameter that defines
how much rain runs off (runoff volume)• A parameter that defines
time of peak (runoff temporal shape)
Choice of Calibration Storms: Storm of 2007Representative in location and time?
Are there enough data?• Spatially vs storm shape
Choice of Calibration Storms: TS Hermine
Are there enough data?• Spatially vs storm shape
Choice of Calibration StormsRepresentative?
• In temporal shape
2007 Storm vs SCS 24 hour hyetograph TS Hermine vs SCS 24 hour hyetograph
Antecedent Moisture Condition
p. 149 Applied Hydrology
http://www.wcc.nrcs.usda.gov/ftpref/wntsc/H&H/CNarchive/CNbeyond.doc
Choice of Calibration Storms
Point of Comparison June 2007 Storm TS Hermine Comment
Spatial Variation High intensity rainfall in northern County and Leander
Extreme rainfall throughout west and central watershed, to include Leander, Cedar park, and Austin
Both storms much less intense in eastern watershed
Antecedent Runoff Condition
Moderate: substantial rains within two weeks of main event
Very dry: very l ittle rain over previous two months
Should expect a calibrated CN for 2007 to be on our about a ARCII condition, and for 2010 on or about a ARCI condition
Return Period, Rainfalll durations <= 1 hour
On the order of 20-50 year return period storm in main area of storm
On the order of 2-5 year storm in main area of storm
A storm similar to the 2007 storm would be expected to stress small to medium watershed (approx 1 hour lag time) local drainage: storm drains, road conveyance. The 2010 storm would have less sever effect.
Return Period, Rainfall durations 2 hour
On the order of 20-50 year return period storm in main area of storm
varies within main storm area: part has 5 to ten year return period, part has 20-175 year return period Both storms similar for this duration
Return Period, Rainfall durations 3 hour to 24-hour
Return period diminishing with increase in duration
Return period increasinging with increase in duration, up to 300+ years for 24-hours
Downstream main stem (with large watershed with longer lag time) expected to have much worse flooding in 2010 than 2007
Return Period, Rainfall durations 24-hour
5 to ten year return period, much less than design storm for flood pools of dams
90 to 320 year return period, equal to to much greater than design storm for flood pools of dams
District dams provided designed flood protection in 2007, capacity (to contain regulatory flood) exceeded in 2010
Results of Rainfall/Runoff Calibration
2007 Event
Tropical Storm
HermineDam 1 82.52 72.2 43.0Dam 2 80.19 64.9 *Dam 3 79.83 66.7 40.0Dam 5 79.48 60.0 40.0Dam 6 80 * **Dam 11 78.2 60.7 51.0Dam 12 80.25 61.2 40.0Dam 13A 80 61.6 46.0Dam 14 80.53 84.8 23.0Dam 16 80.08 - 47.0Dam 19 77.58 - 49.0Average(exluding dam 14) 79.88 63.9 44.5
- Gage not installed* Bad stage data from gage
** Bad precip data from gage
Curve Numbers Derived Per Calibration Using District Gage Precip
Watershed
Computed Values Per
TM2
Why are results inconsistent?Can we compare 2007 storm runoff results to 2012 storm runoff results?
Are the conditions that affect runoff homogeneous between the two storms?
RainfallLand UseSoil Type% ImperviousAntecedent Runoff Condition
Antecedent Runoff
2007 Rainfall
2010 Rainfall
Are the two storms homogeneous in terms of antecedent conditions?
Results of Rainfall/Runoff Calibration 2007 Event
Tropical Storm Hermine
Dam 1 82.52 72.2 63.4Dam 2 80.19 64.9 *Dam 3 79.83 66.7 60.3Dam 5 79.48 60.0 60.1Dam 6 80 * **Dam 11 78.2 60.7 70.6Dam 12 80.25 61.2 59.8Dam 13A 80 61.6 66.4Dam 14 80.53 84.8 41.4Dam 16 80.08 - 66.6Dam 19 77.58 - 69.3Average(exluding dam 14) 79.88 63.9 64.6
- Gage not installed* Bad stage data from gage
** Bad precip data from gage
Watershed
Curve Numbers Derived Per Calibration Using District Gage Precip Computed
Values Per TM2 Antecedent Runoff Condition 1
(Dry)
Antecedent Runoff Condition 2(Normal)
Results of Rainfall/Runoff Calibration
No Adjust- ment
Adjusted Per TXDOT, 2011 2007 Event
Tropical Storm Hermine
Dam 1 82.52 67.52 72.2 63.4Dam 2 80.19 65.19 64.9 *Dam 3 79.83 64.83 66.7 60.3Dam 5 79.48 64.48 60.0 60.1Dam 6 80 65 * **Dam 11 78.2 63.2 60.7 70.6Dam 12 80.25 65.25 61.2 59.8Dam 13A 80 65 61.6 66.4Dam 14 80.53 65.53 84.8 41.4Dam 16 80.08 65.08 - 66.6Dam 19 77.58 62.58 - 69.3Average(exluding dam 14) 79.88 64.88 63.9 64.6
- Gage not installed* Bad stage data from gage
** Bad precip data from gage
Watershed
Computed Values Per TM2
Curve Numbers Derived Per Calibration Using District Gage Precip