Regional Precipitation-Frequency Analysis 

And Extreme Storms Including PMP 

Current State of Understanding/Practice

Mel Schaefer Ph.D. P.E.

MGS Engineering Consultants, Inc.

Olympia, WA

NRC Workshop - Probabilistic Flood Hazard Assessment Jan 2013
What’s the Status 

of Regional Precipitation-Frequency Analysis 

for Use with Extreme Storms ? 

Precipitation-Frequency Relationships Needed 

for Watersheds for Rainfall-Runoff Modeling 

of Extreme Storms and Floods

Precipitation-Frequency Relationships 

Have Been Developed for Watersheds 

using Regional Analysis Methods since 1998

Hydrologic Risk Assessments - 20 Dam Projects 

USBR BChydro USCOE Hydropower Utilities 
Precipitation-Frequency for Watersheds 

What Does End-Product Look Like ? 

Methodologies Have Been Developed for Computation 

of Mean Frequency Curve and Uncertainty Bounds

0

4

8

12

16

20

24

28

32

36

40

44

48

72-HOUR PRECIPITATION (in) 

ANNUAL EXCEEDANCE PROBABILITY

West Coast Mountain Watershed

Extreme Value Type 1 Plotting Paper

0.99 10-3 0.80 0.50 0.10 0.01 10-6 10-5 10-4

72-Hour Basin-Average 1,800-mi2 Precipitation

90% Uncertainty Bounds

72-HR PMP

PMP 

is just 

another 

point 

on the 

curve
Precipitation-Frequency for Watersheds

Largest Contributions to Total Uncertainty are Typically: 

Uncertainties in Regional L-Skewness 

and Relationship for Point to Areal Precipitation 

Regional 

Analysis 

Dramatically 

Reduces 

Uncertainties 

for More 

Common 

0 Events

4

8

12

16

20

24

28

32

36

40

UNCERTAINTY VARIANCE (in

2)

ANNUAL EXCEEDANCE PROBABILITY

Contribution to Uncertainty Variance

Point to Area Regression

Regional Probability Distribution

Regional L-Skewness

Regional L-Cv

At-Site Mean

10-1 10 10-4 -5 10-3 10-2
What Has Made Development 

of Precipitation-Frequency Relationships 

for Watersheds Possible ? 

PRISM Model 

spatial mapping of precipitation and L-moment statistics 

Chris Daly – Oregon State University

L-Moment Statistics 

major advancement in statistical measures 

for small datasets exhibiting marked skewness 

Jon Hosking – IBM Research

Regional Analysis Methodology 

grouping of datasets of like phenomenon to reduce uncertainties, 

improve identification of parent probability distribution 

Jim Wallis – IBM Research
Why This is Possible Now

Building Foundation of Experience 

experienced gained from analyses 

in variety of climatic settings has lead to better understanding 

and improvements in methodologies 

Isopercental Analysis 

spatial interpolation methods for spatial mapping 

of precipitation (storm events) in mountainous areas 

Improvements in NWS Techniques

SPAS Software 

use of radar data and ground-based precipitation 

for spatial mapping of precipitation (storm events) 

Applied Weather Associates and MetStat Software
Regions - Concepts

Datasets for stations (sites) within 

a Homogeneous Region are grouped for analysis 

Heterogeneous 

Super-Regions 

for Oregon

Homogeneous Regions 

are Subsets of 

Heterogeneous 

Super-Regions

Similar Climatic 

and 

Topographic Storm Setting Track
Large Regional Datasets

Numerous stations (datasets) available for conducting 

Regional Precipitation-Frequency Analysis

Oregon State 

700 Stations 

34,000 Station-Years of Record
The Need for Regionalization

At-Site Analysis 

Subject to High Sampling Variability

Regional Analysis 

Reduces Sampling Variability 

Groups datasets of same phenomenon 

from a homogeneous region for analysis 

Greatly improves reliability of identification 

of regional probability distribution and 

estimation of regional magnitude-frequency relationship

Excel Workbook Simulations
Benefits of Regional Analysis 

(Trading Space for Time Sampling)

Large Geographic Regions relative to Storm Areal Coverage 

Results in Independence or Low Correlation 

of Datasets at Distant Stations

Equivalent Independent Record Length (EIRL) 

is a measure of the statistical information 

in the regional dataset 

EIRL is a function of:

• Size of region relative to typical areal coverage of storms 

• Number of storms per storm season

• Density of precipitation measurement stations

• Chronological length of dataset (1966-2011)
Equivalent Independent Record Length (EIRL)

0

10

20

30

40

50

60

70

80

90

100

110

120

1 10 100 1000 10000

NUMBER OF EXCEEDANCES

ESTIMATED 1/AEP (Years)

EIRL

West Face Sierra Mountains 1966-2011

EIRL=300-Years

EIRL=1,000-Years

EIRL=630-Years

Greater EIRL results in greater reliability 

(smaller uncertainty bounds) for estimates of extreme precipitation

130 stations

4,599 station-yrs

EIRL=14% stn-yrs

63 storms 

(distinct dates) 

exceeding 

1:10 AEP
Graphical Example of Regional Analysis

 Comparing Slope and Shape 

of Dimensionless Probability-Plots 

for Sites on West Face of Sierra Mountains

 Physical Interpretation

Dimensionless Probability-Plots 

Reflect Frequency Characteristics 

of Storms Generated by Pacific Ocean 

Measured on Upwind Mountain Faces
0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

3-DAY PRECIPITATION (in)

ANNUAL EXCEEDANCE PROBABILITY

Huntington Lake

1916-2011 Data

3-Day Maxima

Extreme Value Type 1 Plotting Paper

0.99 0.80 0.50 0.33 0.20 0.10 0.05 0.02 0.01 0.005 0.002

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

3-DAY PRECIPITATION (in)

ANNUAL EXCEEDANCE PROBABILITY

Blue Canyon

1906-2011 Data

3-Day Maxima

Extreme Value Type 1 Plotting Paper

0.99 0.80 0.50 0.33 0.20 0.10 0.05 0.02 0.01 0.005 0.002

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

3-DAY PRECIPITATION (in)

ANNUAL EXCEEDANCE PROBABILITY

Hetch Hetchy

1911-2011 Data

3-Day Maxima

Extreme Value Type 1 Plotting Paper

0.99 0.80 0.50 0.33 0.20 0.10 0.05 0.02 0.01 0.005 0.002

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

3-DAY PRECIPITATION (in)

ANNUAL EXCEEDANCE PROBABILITY

Nevada City

1880-2011 Data

3-Day Maxima

Extreme Value Type 1 Plotting Paper

0.99 0.80 0.50 0.33 0.20 0.10 0.05 0.02 0.01 0.005 0.002

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

3-DAY PRECIPITATION (in)

ANNUAL EXCEEDANCE PROBABILITY

Oroville

1893-2011 Data

3-Day Maxima

Extreme Value Type 1 Plotting Paper

0.99 0.80 0.50 0.33 0.20 0.10 0.05 0.02 0.01 0.005 0.002

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

22.0

24.0

3-DAY PRECIPITATION (in)

ANNUAL EXCEEDANCE PROBABILITY

Giant Forest

1893-2011 Data

3-Day Maxima

Extreme Value Type 1 Plotting Paper

0.99 0.80 0.50 0.33 0.20 0.10 0.05 0.02 0.01 0.005 0.002

72-Hr Precipitation West Face Sierra Mountains
Graphical Example of Regional Analysis

 Similarity of Shapes 

of 6 Dimensionless Probability-Plots

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

RATIO TO AT-SITE MEAN

ANNUAL EXCEEDANCE PROBABILITY

3-Day Maxima

Extreme Value Type 1 Plotting Paper

0.99 0.80 0.50 0.33 0.20 0.10 0.05 0.02 0.01 0.005 0.002

 Rescaled by Station Mean (At-Site Mean)
Graphical Example of Regional Analysis

Differences in probability-plots 

attributed primarily to sampling variability

Region Growth Curve 

Dimensionless Regional Frequency Curve

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

RATIO TO AT-SITE MEAN

ANNUAL EXCEEDANCE PROBABILITY

3-Day Maxima

Extreme Value Type 1 Plotting Paper

0.99 0.80 0.50 0.33 0.20 0.10 0.05 0.02 0.01 0.005 0.002
Numerical Solution of Regional Growth Curve

 Regional L-Cv (dimensionless scale) 

Regional L-Skewness (dimensionless shape) 

used to obtain solution of Regional Growth Curve 

for Identified Regional Probability Distribution 
Regional Probability Distribution 

Studies in Western United States and British Columbia 

have shown 1-Day to 7-Day Precipitation Annual Maxima 

to be Described by a Probability Distribution Near 

the Generalized Extreme Value (GEV) Distribution 

Results from Regions 

in Oregon for 24-Hour 

Precipitation 

Annual Maxima 

4-Parameter 

Kappa Distribution 

Used for 

Watersheds

24-Hour Precipitation Maxima

-0.10

0.00

0.10

0.20

0.30

0.40

-0.10 0.00 0.10 0.20 0.30 0.40 0.50

L-SKEWNESS

L-KURTOSIS

Generalized Extreme Value

Pearson 3

Generalized Logistic

Generalized Pareto

Eastern Oregon Study Area
Development of Precipitation-Frequency 

Relationships for Watersheds

Need Relationship between Point Precipitation 

and Areal Precipitation for Major Storms

GIS Storm Analysis

(Spatial Analysis) 

using 

Isopercental Method

or

SPAS Radar Analysis

y = 0.925x0.903

R2 = 0.893

1

10

100

1 10 100

GIS Storm Analysis (in)

Blue Canyon (in)

72-Hour Precipitation

28 Storms
Spatial Mapping of Precipitation 

with Isopercental Method

Convert from Precipitation Domain to Frequency Domain, 

Divide 72-hr Station Precipitation by At-Site Mean

Inverse Distance Weighting (IDW) in Frequency Domain

Over 100 Major 

Storms Analyzed

Well-Behaved Mild 

Isopercental 

Gradients 

in Frequency Domain
Spatial Mapping of Precipitation 

with Isopercental Method

Transform from Frequency Domain (Isopercental) to 

Precipitation Using Spatial Map of At-Site Means

West Face Sierra Mountains 

72-Hour At-Site Mean Precipitation
Characterize Uncertainties for Use in Developing 

Precipitation-Frequency Curve for Watershed

Develop Probability Distributions for Uncertainties 

Point Precipitation At-Site Mean

Regional L-Cv

Regional L-Skewness

Regional Probability Distribution

Relationship of Point to Areal Precipitation
Monte Carlo Simulation Used to Develop 

Mean Precipitation-Frequency Curve 

and Uncertainty Bounds 

Precipitation-Frequency Relationship for the Watershed 

is Often the Dominant Contributor 

to Behavior of Flood-Frequency Relationships

0

4

8

12

16

20

24

28

32

36

40

44

48

72-HOUR PRECIPITATION (in) 

ANNUAL EXCEEDANCE PROBABILITY

West Coast Mountain Watershed

Extreme Value Type 1 Plotting Paper

0.99 10-3 0.80 0.50 0.10 0.01 10-6 10-5 10-4

72-Hour Basin-Average 1,800-mi2 Precipitation

90% Uncertainty Bounds

72-HR PMP

0

4

8

12

16

20

24

28

32

36

40

UNCERTAINTY VARIANCE (in2)

ANNUAL EXCEEDANCE PROBABILITY

Contribution to Uncertainty Variance

Point to Area Regression

Regional Probability Distribution

Regional L-Skewness

Regional L-Cv

At-Site Mean

10-1 10-5 10-4 10-3 10-2

4-Parameter Kappa Distribution
Summary: Precipitation-Frequency

Key Components for Developing 

Precipitation-Frequency Relationships 

for Watershed-Specific Applications

Regional Analysis Methods

L-Moment Statistics

Large Regional Datasets

Spatial Analysis of Storms (Isopercental, SPAS)

GIS Spatial Mapping Tools, PRISM model
Annual Exceedance Probabilities (AEPs) 

of Published PMP Estimates

AEPs of PMP vary from about 10-4 to perhaps 10-10

AEP varies - nearness to sources of atmospheric moisture 

(Coastal versus Inland Areas) 

AEP varies - number of storms in storm season 

(Arid versus Humid Climates)

AEPs for PMP based on Regional Precipitation-Frequency 

and Analyses of Historical Extreme Storms (%PMP)

AEP varies with storm characteristics of interest

 (Short-duration intensities, Long-duration volume)
Uncertainties in PMP Estimates

• Sampling limitations of storm database (storm efficiency)

• Simplifying assumptions, policy versus science decisions

• Effect of analyst’s judgment

• Inflow moisture flux for moisture maximization

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

FREQUENCY

PERCENT OF ORIGINAL 24-HOUR PMP

West Coast Mountain Watershed 24-Hour PMP

80 86 91 97 103 109 115 121 126 132 138 144 150 156 161 167 173 

10th Percentile = 100% PMP 

Mean = 117% PMP 

90th Percentile = 136% PMP

Uncertainty Distribution PMP

Original 

PMP Estimate

Uncertainty 

Analysis 

for PMP

First of its kind

Jan 2013
Summary - PMP

AEPs for PMP Have Much Wider Range 

Than “Assumed” in Engineering Community

Results of Uncertainty Analysis (PMP bias) 

and Magnitude of Uncertainties in PMP Estimation 

Will Likely Surprise Many in Engineering Community
End of Slides