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