A Hydrological Tool for Analysis of Extreme Floods

Stochastic Event Flood Model (SEFM)

Stochastic Modeling of Extreme Floods

Mel Schaefer Ph.D. P.E.

MGS Engineering Consultants, Inc. 

Olympia, WA 

NRC Workshop – Probabilistic Flood Hazard Assessment (PFHA) Jan 2013
Stochastic Modeling of Extreme Floods ...

PURPOSE

Develop Magnitude-Frequency Relationships 

(Hydrologic Hazard Curves) for:

• Flood Inflow Discharge (Peak, Max 6-hr, 24-hr, 72-hr, etc) 

• Flood Runoff Volume

• Maximum Reservoir Outflow

• Maximum Reservoir Level ( primary interest ) 

• Depth of Overtopping Flows 

• Duration of Spillway Flows exceeding a discharge threshold 
Stochastic Modeling of Extreme Floods ...

APPLICATIONS

• Flood Magnitude-Frequency

Provide Information for Decision Making about:

• Hydrologic Hazard Curves for Risk Analysis

• Assess Conservatism of Proposed PMF

• Seasonality of Floods

• Reservoir Operations for Floods

• Conduct Global Sensitivity Analysis
Advances That Make 

Stochastic Flood Modeling Possible...

• GIS Spatial Mapping Products and Methods 

particularly for Precipitation (PRISM) 

• Increases in Computational Power of PC 

20,000 simulations in 1-hour

• Regional Analysis Methods and L-Moment Statistics 

for developing basin-specific 

precipitation-frequency relationship including extreme events

Long record lengths for precipitation data 

35+ years records in mountains (SNOTEL)
History of SEFM ...

Development started in 1996

Used by USBR for Hydrologic Risk Analyses since 1998

Bumping Lake Dam – Bumping River, WA

Cle Elum Dam – Cle Elum River, WA

Keechelus Dam – Yakima River, WA

Minidoka Dam – Snake River, ID

Whiskeytown Dam – Clear Creek, CA

Trinity Dam – Trinity River, CA

A.R. Bowman Dam – Crooked River, OR

Altus Dam – North Fork Red River, OK
History of SEFM ...

BC Hydro

Mica Dam (787-ft), Upper Columbia River, BC

received International Peer Review - 2001

US Corps of Engineers

Folsom Dam, American River, CA

SEFM Accepted by USCOE 

for Analysis of Extreme Floods and PMF - 2005 

Puget Sound Energy

Baker River Project, Baker River, WA

FERC Licensed Project - 2009

BC Hydro

Campbell River System, Vancouver Island BC

3 Dams in series 1,500-km2 watershed - 2012 
Current Projects 2012 - 2013 - SEFM ...

BC Hydro

Bridge River System, Coastal Mountains, BC

3 dam system - 3,500-km2 watershed

USBR and Southern California Edison

Friant Dam and Mammoth Pool Dam, San Joaquin River, CA

6 SCE Dams in Upper Watershed - 1,600-mi2 watershed 
SEFM – Primary Deliverable ...

Magnitude-Frequency Curve for Maximum Reservoir Level 

(Hydrologic Hazard Curve)

Integrates

Frequency Information

Flood Peak Discharge 

 Runoff Volume

Hydrograph Shape

Initial Reservoir Level 

Reservoir Operations

while

Preserving Seasonality

of Events
SEFM – Other Outputs ...

Magnitude-Frequency Curves for Flood Discharge

0

60

120

180

240

300

360

420

480

540

600

660

720

Thousands

ANNUAL EXCEEDANCE PROBABILITY

72-HOUR DISCHARGE (cfs)

10-6

Extreme Value Type 1 Plotting Paper

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

Model Outputs 

for Reservoir Inflow

Instantaneous Peak

 Max 6-hr Discharge

Max 24-hr Discharge

Max 72-hr Discharge
SEFM Structure ...

SEFM Engine 

conducts stochastic simulations 

and many rainfall-runoff and snowmelt computational tasks 

Watershed Model 

conventional watershed modeling tasks 

that were not conducted by SEFM engine; 

for HEC-1, primarily used as network model 

for routing of streamflow from sub-basins

Post Processor 

processes watershed model output 

to develop flood-frequency relationships, 

stores all simulation inputs and outputs, flood hydrographs, etc
SEFM Operational Modes ...

• Completely Deterministic Mode

• Completely Stochastic Mode

• Mixed Mode - Some Inputs are Set (Fixed) 

Other Inputs Treated as Variables (Stochastic)
Stochastic Approach ...

GOAL

Simulate the hydrologic behavior of the watershed 

in a manner that provides an unbiased measure 

of the magnitude-frequency characteristics of floods 

(looking for reality/truth, not conservative estimates)

SEFM draws heavily on the analysis of historical data 

using regional analysis methods 

Historical data are analyzed 

to obtain a better understanding of the actual behavior 

of the hydrometeorological components 

to assist in the realistic simulation of floods

 
Stochastic Approach ...

1) Use Deterministic Rainfall-Runoff Model 

HEC-1,UBCWM, WATFLOOD, (HEC-HMS in future)

2) Treat Hydrometeorological Inputs as Variables

3) Stochastically Generate Multi-Thousand Years of Storms 

and Dates of Storm Occurrence

4) Select Hydrometeorological Inputs to Accompany Storms 

and Maintain Seasonal Characteristics and Dependencies
Stochastic Approach ...

6) Rank Flood Outputs in Descending Order of Magnitude 

and Assign Exceedance Probabilities 

using a Plotting Position Formula

7) Construct Probability-Plots for Flood Characteristics 

of Interest – No Need to Fit a Probability Distribution, 

Floods Characteristics of Interest Found from Interpolation 

Not Extrapolation

5) Compute Multi-Thousand Flood Annual Maxima 

using Hydrologic Model and Input Datasets – 

Conduct Sufficient Simulations 

to Exceed Flood Magnitudes of Interest
Stochastic Simulation Storm Related Variables ...

Magnitude of Basin-Average 

Precipitation (24-hr, 72-hr)

Spatial Distribution of 

Precipitation over Watershed

Temporal Distribution of 

Precipitation over Watershed

variable storm duration 0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

72 96 120 144 168 192

HOURLY PRECIPITATION (in)

ELAPSED TIME (Hours)

Friant Watershed Basin-Average Dec 18-27, 1955

72-Hour Maxima = 27.0-in

Scaled Storm
Stochastic Simulation 

Hydrometeorological Variables ...

• Antecedent Soil-Moisture 

(spatially distributed by soil type)

• Antecedent Snowpack 

(spatially distributed snow depth and density) 

• Freezing Level and Air Temperature Temporal Pattern

• Initial Streamflow

• Initial Reservoir Level 

• Antecedent Precipitation – Spatially Distributed
Stochastic Simulation 

Rainfall-Runoff Modeling ...

• Surface Runoff Response

• Runoff Modeled on Distributed Basis

• Interflow Runoff Response

• Snowmelt Runoff Computation 

includes Snow Water Accounting within Snowpack 

and Energy-Budget Approach
Watershed Model Calibration ...

• Stochastic Model Calibrated to Historical Flood-Frequency 

Curves at Multiple Durations (24-hr, 72-hr)

• Watershed Model Calibrated to Historical Floods
Stochastic Simulations

Each flood simulation represents an annual maxima flood 

based on historical behavior of the hydrometeorological inputs 

and the observed flood response of the watershed 

Sufficient flood simulations conducted so there is no need 

to fit a probability distribution to the flood outputs 

flood-frequency relationship can be depicted via a probability-plot

Flood simulations reflect flood hazards 

based on current climatic characteristics

effects of climate change can be assessed 

through sensitivity analysis or uncertainty analysis 
SEFM – Output...

Primary Outputs are Magnitude-Frequency Curves 

(Hydrologic Hazard Curves)

Hydrologic loading for extreme floods are of primary interest

400

410

420

430

440

450

460

470

480

490

ANNUAL EXCEEDANCE PROBABILITY

RESERVOIR STAGE (Feet)

10-6

Extreme Value Type 1 Plotting Paper

10-2 10-3 10-5 10-1 .5

American River at Folsom Dam

10-4

 Stochastic Flood Model 

Curve Extension Method

Top of Flood Control Pool

1997 Flood

1986 Flood

Regulated Frequency Curve
SEFM – Example Output...

Safe Channel Capacity within the Levee System 

is a Concern in the Sacramento Valley 

Magnitude-Frequency Relationships for 

Maximum Reservoir Level and Reservoir Discharges 

are Typically Very Non-Linear - Due to Operations 
SEFM – Example Output...

Strathcona Dam - Vancouver Island BC

Various Reservoir Elevations Are Often of Interest 

for Evaluating Potential Failure Modes
Selected Examples of Interest ...

• Watershed Layout for Distributed Rainfall-Runoff Modeling

• Seasonality of Storms

• Precipitation-Frequency Relationships for Watershed

• Diversity of Temporal Patterns for Storms
Distributed Rainfall-Runoff, Snowmelt Modeling

11 Zones of Mean Annual Precipitation

Mean Annual Precipitation 

varies from 

20-inches (zone 1) 

to 72-inches (zone 11)

American River, CA
Distributed Rainfall-Runoff, Snowmelt Modeling

Elevation varies from 

300-feet (zone 1) 

to 12,000-feet (zone 9)

9 Elevation Zones

American River, CA
Distributed Rainfall-Runoff, Snowmelt Modeling

Soil Characterization from NRCS

7 Zones for Describing Soil Characteristics

Merged to produce 7 Soil Zones 

with similar hydrologic characteristics
Distributed Rainfall-Runoff, Snowmelt Modeling

Hydrologic Runoff Units (HRUs) are polygons of land 

formed from the intersection of Zones 

of Mean Annual Precipitation, Elevation and Soil Type 

263 unique HRUs in American River Watershed for:

• Soil moisture accounting

• Snow-water accounting

• Spatial allocation of snowpack

• Rainfall-runoff modeling 

• Snowmelt modeling
Stochastic Hydrometeorological Inputs

Studies in western US and British Columbia 

Show Storm Seasons to be Normally Distributed

Seasonality of Storms

0.00

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG

FREQUENCY

MONTH

WEST FACE SIERRA MOUNTAINS 

Storms exceeding 10-year event

40 Storms 72 Hour Duration

Historical Storms

Normal Distribution
Stochastic Hydrometeorological Inputs

Precipitation-Frequency for American River Watershed 1,862-mi2

Slightly More Positive Skew than Extreme Value Type 1 

Magnitude of 72-Hour Precipitation Annual Maxima
PMP Estimate Revised – Dam Goes from “Safe” to “Unsafe” ?
 Large Storms occur on Campbell River Watershed 

when Moist Inflow Winds are from the East and ESE

Orographic Precipitation occurs from Upslope Winds 

on what is typically the Leeward Mountain Face 

Result: Large Volume Storms/Floods are Rare 

for Campbell River Watershed Relative to Windward Face

Duration of 

Heavy Precipitation 

dependent upon 

sustaining 

moist inflow winds 

from East and ESE 

Duration of Upslope Winds 

is Transient Condition 

During Storm Passage
Stochastic Hydrometeorological Inputs

Each of 33 sub-basins has a separate temporal pattern, 

scalable by the selected 72-hour basin-average precipitation 

Scalable Spatial and Temporal Storm Patterns

72-Hour 

Precipitation 

(inches)

American River Watershed, CA

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192

Hourly Precipitation (in)

TIME (hours)

Dec 28, 1996 - Jan 3, 1997

Total storm duration not limited to 72-hours
Stochastic Hydrometeorological Inputs

24 Prototype Temporal and Spatial Templates 

developed from historical storms observed on the watershed

Scalable Spatial and Temporal Storm Patterns

72-Hour 

Precipitation 

(inches)

American River Watershed, CA

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216

Hourly Precipitation (in)

TIME (hours)

Feb 12-20, 1986
0

4

8

12

16

20

24

28

32

0 24 48 72 96 120 144 168 192 216 240

HOURLY PRECIPITATION (mm)

TIME (Hours)

Strathcona Basin Basin-Average Mar 5-14, 1983

72-Hour = 500-mm

Scaled Storm

 Strathcona Basin 

500-mm 

72-hour precipitation 

1: 50,000 AEP 

 Note Diversity: 

Temporal Patterns 

Multi-Pulse 

Storms 

Max Intensities 

Storm Duration
0

4

8

12

16

20

24

28

32

0 24 48 72 96 120 144 168 192 216 240 264 288

HOURLY PRECIPITATION (mm)

TIME (Hours)

Strathcona Basin Basin-Average Oct 2-12,1984

72-Hour Maxima = 500-mm

Scaled Storm

0

4

8

12

16

20

24

28

32

0 24 48 72 96 120 144 168 192 216 240 264 288

HOURLY PRECIPITATION (mm)

TIME (Hours)

Strathcona Basin Basin-Average Nov 25- Dec 5, 1993

72-Hour Maxima = 500-mm

Scaled Storm

Diversity 

of Storm 

Temporal 

Patterns 

Provides for 

Robust 

Assessment 

of Inflow Flood 

Characteristics 

and Reservoir 

Responses 
Summary ...

SEFM provides a Hydrological Tool 

for Developing Flood-Frequency Relationships 

(Hydrologic Hazard Curves) for Flood Discharges, 

Runoff Volumes and Maximum Reservoir Level 

and for 

Assessing the Annual Exceedance Probability (AEP) 

of Extreme Floods including IDFs and the PMF
End-of-Slides

SEFM Description and Examples...