Estimating 1% Plus
Ferrin Affleck, P.E., CFM
For Simple and Complex Hydrology
Objectives
• Understand uncertainty & why 1% plus
• Estimate 1% plus for basic hydrology
– Regression analysis
– Gage analysis
– Rainfall runoff models
• Case study – Upper Rogue Watershed
– Application, complications, and solutions
2
Understanding Uncertainty
3
How Old is He?
65,000,038 years
4
New Standard # 84
All riverine engineering Flood Risk Projects shall consist of a hydraulic model with multiple frequencies:
0.2- percent, 1-percent, 2-percent, 4-percent, and 10-percent-annual-chance exceedance events. In
addition, the “1-percent plus” flood elevation shall be modeled for all riverine analyses. The 1% plus
flood elevation is defined as a flood elevation derived by using discharges that include the
average predictive error for the regression equation discharge calculation for the Flood Risk
Project. This error is then added to the 1% annual chance discharge to calculate the new 1% plus
discharge. The upper 84-percent confidence limit is calculated for stream gage records
and rainfall-runoff models for the 1% annual chance event.
The “1-percent plus” flood elevation must be shown on the Flood Profile in the FIS Report to
best understand and communicate the uncertainty of the flood elevation.
1% plus communicates
uncertainty in the
estimated discharge
The mapping of the “1-percent plus” floodplain is optional and will only be produced when it is
determined to be appropriate.
5
A Tale of Two Houses
• First flood study completed with 10 years of record
• Restudied 10 years later, new discharges were higher &
resulted in BFE increases of 2.1 feet
100Yr
+ 1’
1%
Plus
1% Plus Elevation (102.5)
New BFE (102.1)
BFE (100)
6
Estimating the 1% Plus
Regional Regression Equations
7
Regional Regression Equations
• Results are best-fit estimates with an
associated “scatter” or variance
• Assumes the explanatory variables for
the gaged sites are representative of all
sites in the same physiographic region
• The average predictive error for the
regression model can be determined by
computing the average standard error of
regression, SER, or average standard
error of prediction, SEP
Used for 1% plus
8
Average Predictive Error
Estimation of Peak Discharges for Rural, Unregulated Streams in Western Oregon, SIR 2005-5116. Region 2B
Example: Q100 =1,650 cfs,
Q100plus = 1,650 x 1.362 = 2,247 cfs
9
National
Stream
Stats
http://water.usgs.gov/
osw/streamstats/
10
Estimating the 1% Plus
At a Gage
11
Stream Gage Record
Series of Annual Peaks
6000
5000
4000
3000
2000
1000
0
1900
1920
1940
1960
1980
2000
2020
Thief River – 101 Year Record Length
12
Log Pearson Type III
(Bulletin 17B)
Based on probability
(i.e. 100-yr) and
record length
Equation:
 
U P X   X  S K P
U
Discharge
Mean
Standard
Deviation
13
Log Pearson Type III
Upper confidence limit (84%)
Lower confidence limit (16%)
Used for 1% plus
14
USGS PeakFQ Program
A value of 0.84 will compute the 68% confidence
interval (i.e. Upper 84% Confidence Limit)
0.84
15
PeakFQ Result
1% plus
16
Estimating the 1% Plus
Rainfall Runoff Model
17
Analytical Approach
(Synthetic Statistics)
Described in WRC Bulletin 17B (Appendix 5 & 9)
•
•
•
•
•
Used for ungaged watersheds when estimating the
discharge-probability function without recorded
events
Discharge not influenced by regulation
Assumed to fit log-Pearson Type III distribution
Mean, standard deviation, and generalized skew
for the adopted function is defined by the
estimated 50-,10-, and 1-percent annual chance
flood events
Value of the discharge-function is expressed as
the equivalent record length
U P  X   X  S K UP 
From the model
Table 4-5 of USACE
EM 1110-2-1619
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1% Plus For Modeled Discharge
Upper confidence limit (84%)
Bulletin 17B
Appendix 5 & 9
Lower confidence limit (16%)
What you need
 50% discharge
 10% discharge
 1% discharge
 Equivalent Record
20
Case Study
Upper Rogue Watershed, OR
21
Concerns
1. Weighting gaged
discharges with
regression
2. Transferring gaged
discharges to ungaged
sites
• Interpolation
between gages
• Drainage Area
Weighting
3. Discharges affected by
regulation
Upper
Rogue
Watershed
Scope
22
Weighting Independent Estimates
• Improve estimate and reduces uncertainty
• Discussed in Bulletin 17B Appendix 8
• SIR 05-5116:
𝑄𝑠 𝑁 + 𝑄𝑅 𝐸
𝑄𝑤 =
𝑁+𝐸
QW - Weighted discharge at gage,
QS - Log Pearson Type III discharge for the gage
N - Years of gage record
QR - Regional Regression discharge at gage
E - Regression equivalent years of record
Equivalent record
for Qw is the sum
of both records
23
Use Analytical Approach
Upper confidence limit (84%)
Lower confidence limit (16%)
What you need
 50% discharge
 10% discharge
 1% discharge
 Equivalent Record
24
Results for Weighted Discharges at
Gages
Annual Chance
Weighted Discharge (cfs)
Drainage
Area
(Square
Miles)
50%
10%
1%
Gage
Regression
Weighted
14337800
78.8
2,780
4,840
7,910
27
11.6
38.6
9,190
14338000
129
4,460
9,321
16,614
67
11.6
78.6
18,975
14341500
138
1,110
3,060
6,830
61
11.6
72.6
8,267
14348000
293
3,485
6,995
11,940
24
11.6
35.6
14,507
Gage
Record Length (yrs)
1% Plus
(cfs)
25
Upper
Rogue
Watershed
Interpolated
Between Gages
26
Interpolating Between Two Gages
North Fork Little Butte Creek
Between 14343000 & 14344500
6000
5000
4000
14344500
14343000
Power (500-year)
Power (1%Plus)
Power (100-year)
Power (50-year)
Power (25-year)
Discharge,cfs
Power (10-year)
3000
Notes:
• 1% plus profile may cross
the 0.2% profile in the FIS
2000
•
1000
0
40
42
44
46
48
Drainage Area, sqmi
50
52
1% plus discharge may
not always increase with
drainage area
54
27
𝑄𝑢 = 𝑄𝑔
𝐴𝑢
𝐴𝑔
𝑏
Upper
Rogue
Watershed
Drainage Area
Weighting
28
29
Use Analytical Approach
Upper confidence limit (84%)
Lower confidence limit (16%)
What you need
 50% discharge
 10% discharge
 1% discharge
 Equivalent Record
30
Upper
Rogue
Watershed
Regulated
31
Gage at
Lost Creek
Dam
32
Regulated Gages
Applied the difference between the unregulated 1%
annual chance and 1% plus to the regulated discharge
Unregulated
Difference
Regulated
Gage
1% Annual
Chance
1% Plus
(1% Plus - 1% Ann. Chance)
1% Annual
Chance
1% Plus
Lost Creek Dam
50,000
60,314
10,314
21,000
31,314
14339000
95,000
115,135
20,135
50,000
70,135
14359000
135,000
156,179
21,179
98,000
119,179
33
Gage at
Lost Creek
Dam
Add 10,314
To get 1% plus
34
Rogue
River City of
Shady Cove
35
Rogue
River City of
Shady Cove
36
Little Butte
Creek City of
Eagle Point
37
Little Butte
Creek City of
Eagle Point
38
Wrap It Up!!
39
Summary
• 1% plus communicates uncertainty in the hydrology.
• Guidance is clear for basic hydrologic approaches.
• Judgment or interpretation may be required for
special/complex cases.
• 1% plus is not a return period and therefore can
have anomalies (inverse relationships with drainage
area, crossing profiles, etc).
40
Thank you
If you’d like to find out more visit:
www.atkinsglobal.com
© Atkins Limited except where stated otherwise.
Ferrin Affleck, P.E., CFM
[email protected]
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Additional Slides
42
Record Length Impacts
1% plus communicates
uncertainty in the
estimated discharge
10 Years
25 Years
50 Years
Upper 84%
Confidence Limit
Upper 84%
Confidence Limit
Upper 84%
Confidence Limit 
3500
5500
7500
9500
11500
13500
Discharge (cfs)
15500
17500
19500
43
Synthetic Sample Statistics
44
Confidence Limit Definition
45