frequency analysis

1. Frequency Analysis and Data
Reading: Applied Hydrology Sections 12.3-12.6

2. 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
of
Frequency
1
Magnitude 

3. 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
T
x
X 
T
x
X
T
x
X 
 of
ocurrences
between
Time

)
(
E
p
T
E
1
)
( 


T
x
X
P T
1
)
( 


4. 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.
N
N
T
T
T
T
T
T
p
years
N
in
once
least
at
x
X
P
years
N
all
x
X
P
years
N
in
once
least
at
x
X
P
p
x
X
P
x
X
P
p






















1
1
1
)
1
(
1
)
(
)
(
1
)
(
)
1
(
)
(
)
(

5. Upper Brushy Creek Hydrologic Model
Jeff Irvin, URS

6. Hydrology: the Mindset
Hydrology = Data (Rainfall, Runoff, Land Use)
Data bad = Hydrology bad
Data good = Hydrology good
How do you test data?

7. 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)

8. Choice of Calibration Storms: Storm of 2007
Representative in location and time?
Are there enough data?
• Spatially vs storm shape

9. Choice of Calibration Storms: TS Hermine
Are there enough data?
• Spatially vs storm shape

10. Choice of Calibration Storms
Representative?
• In temporal shape
2007 Storm vs SCS 24 hour hyetograph TS Hermine vs SCS 24 hour hyetograph

11. Antecedent Moisture Condition
p. 149 Applied Hydrology
http://www.wcc.nrcs.usda.gov/ftpref/wntsc/H&H/CNarchive/CNbeyond.doc

12. 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 little 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

13. Results of Rainfall/Runoff Calibration
2007 Event
Tropical
Storm
Hermine
Dam 1 82.52 72.2 43.0
Dam 2 80.19 64.9 *
Dam 3 79.83 66.7 40.0
Dam 5 79.48 60.0 40.0
Dam 6 80 * **
Dam 11 78.2 60.7 51.0
Dam 12 80.25 61.2 40.0
Dam 13A 80 61.6 46.0
Dam 14 80.53 84.8 23.0
Dam 16 80.08 - 47.0
Dam 19 77.58 - 49.0
Average
(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

14. 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?
Rainfall
Land Use
Soil Type
% Impervious
Antecedent Runoff Condition

15. Antecedent Runoff
2007 Rainfall
2010 Rainfall
Are the two storms
homogeneous in terms of
antecedent conditions?

16. Results of Rainfall/Runoff Calibration
2007 Event
Tropical Storm
Hermine
Dam 1 82.52 72.2 63.4
Dam 2 80.19 64.9 *
Dam 3 79.83 66.7 60.3
Dam 5 79.48 60.0 60.1
Dam 6 80 * **
Dam 11 78.2 60.7 70.6
Dam 12 80.25 61.2 59.8
Dam 13A 80 61.6 66.4
Dam 14 80.53 84.8 41.4
Dam 16 80.08 - 66.6
Dam 19 77.58 - 69.3
Average
(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)

17. 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 63.4
Dam 2 80.19 65.19 64.9 *
Dam 3 79.83 64.83 66.7 60.3
Dam 5 79.48 64.48 60.0 60.1
Dam 6 80 65 * **
Dam 11 78.2 63.2 60.7 70.6
Dam 12 80.25 65.25 61.2 59.8
Dam 13A 80 65 61.6 66.4
Dam 14 80.53 65.53 84.8 41.4
Dam 16 80.08 65.08 - 66.6
Dam 19 77.58 62.58 - 69.3
Average
(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