PMP/PMF – Stochastic Flood Analysis
Comparison of Methodologies
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
220000
240000
0 24 48 72 96 120 144 168
Dis
char
ge (c
fs)
Elapsed Time (Hours)
Applegate Dam and Reservoir
Outflow Flood
Inflow Flood
400
410
420
430
440
450
460
470
480
490R
ESER
VOIR
STA
GE
(Fee
t)
ANNUAL EXCEEDANCE PROBABILITY
Extreme Value Type 1 Plotting Paper
Top of Flood Control Pool
1997 Flood
1986 Flood
10-410-2 10-3 10-610-50.5 10-1
Western Hydropower Dam Owners
Workshop July, 2011
Deterministic PMF…
A single flood hydrograph is developed
for assessing the hydrologic and hydraulic adequacy
of a dam and reservoir project
PMF Inflow
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
220000
240000
0 24 48 72 96 120 144 168
Dis
char
ge (c
fs)
Elapsed Time (Hours)
Applegate Dam and Reservoir
Outflow Flood
Inflow Flood PMF Sensitivity Analyses
sometimes used
to further assess
project adequacy
Stochastic Flood Analysis…
Multi-thousand flood hydrographs computed to develop
flood-frequency relationships for peak inflow, runoff volume,
maximum reservoir level and maximum spillway releases
based on diversity of storms/floods representative of basin
Robust examination
of reservoir response
to wide range of
flood characteristics 400
410
420
430
440
450
460
470
480
490R
ESER
VOIR
STA
GE
(Fee
t)
ANNUAL EXCEEDANCE PROBABILITY
Extreme Value Type 1 Plotting Paper
Top of Flood Control Pool
1997 Flood
1986 Flood
10-410-2 10-3 10-610-50.5 10-1
Hydrologic Hazard Curve for Max Reservoir Level is Primary Deliverable
Stochastic Flood Analysis… Flood-frequency relationships developed
for any flood characteristics of interest
using flood hydrographs generated from stochastic simulations
Other flood-frequency characteristics can be computed such as:
duration of spillway operation or dam overtopping at certain thresholds
Compare Storm Magnitudes …
PMP can be viewed
as one extreme
storm among
a range of extreme
storms
PMP/PMF Stochastic Flood Analysis
72-Hour PMP
Full Range of Storm Magnitudes Basin-Average 72-hr
Precipitation-Frequency Curve
Compare Storm Seasonality …
PMP/PMF Stochastic Flood Analysis
Month yielding largest flood from PMP
Storm/Flood Dates for full range observed in historical record
American River Watershed
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
NON-EXCEEDANCE PROBABILITY
NU
ME
RIC
AL S
TO
RM
DAT
E
.5 .98.7 .9 .999.99.95
Normal Plotting Paper
.02 .05 .8.6.4.2.1 .3.001 .01
Normal Distribution
72-Hour Extreme 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
FREQ
UEN
CY
MONTH
WEST FACE SIERRA MOUNTAINS
Storms exceeding 10-year event
40 Storms 72 Hour Duration
Historical Storms
Normal Distribution
Compare Storm Temporal Patterns …
Suite of Historical Storms (Commonly 12-24 storms)
Each prototype storm has separate temporal pattern
PMP/PMF Stochastic Flood Analysis 1 Synthetic
temporal pattern Suite of temporal patterns based on historical storms
0.00.10.20.30.40.50.60.70.80.91.0
0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216
TIME (hours)
Hou
rly P
reci
pita
tion
(in)
Feb 12-20, 1986
Note: storm duration not limited to 72-hours
0.00.10.20.30.40.50.60.70.80.91.0
0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192
TIME (hours)
Hour
ly P
reci
pita
tion
(in)
Dec 28-Jan 3, 1997 Storms scaled by selected
72-hour precipitation from precipitation-frequency
relationship
Compare Storm Spatial Distributions …
Suite of Historical Storms
Each prototype storm has unique spatial
and temporal pattern
PMP/PMF Stochastic Flood Analysis
“Critical Centering”
Suite of spatial patterns based on historical storms
Compare Air Temperature Temporal Pattern…
1000-mb Temperature and Freezing Level
are variables
Patterns are scaled by values of
1000-mb Temperature and Freezing Level
chosen by Monte Carlo methods
PMP/PMF Stochastic Flood Analysis
Synthetic pattern
Separate temporal pattern for each prototype storm
based on historical storms
Dec 28, 1996 Start
2468
1012141618
0 24 48 72 96 120 144 168 192Elapsed Time (Hours)
Free
zing
Lev
el (F
eet)
Thousand Feet
122028364452606876
0 24 48 72 96 120 144 168 192
Air T
empe
ratu
re (o F
)
Elapsed Time (Hours)
Dec 28, 1996 Start1000-mb
Compare Air Temperature Temporal Pattern…
High Freezing Levels for Extreme Storms
Dec 28, 1996 Start
2468
1012141618
0 24 48 72 96 120 144 168 192Elapsed Time (Hours)
Free
zing
Leve
l (Fe
et)
Thousand Feet
Compare Freezing Level …
Freezing level is correlated
with storm magnitude
and 1000-mb dewpoint
PMP/PMF Stochastic Flood Analysis
Dependent on air temperature lapse rate
set by analyst
Freezing level is stochastic variable based on radiosonde data
for historical storms
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Max 24-Hour Basin-Average Precipitation (in)
Free
zing
Lev
el (1
000
Feet
) Freezing Level for Day of Max 24-Hour Precipitation
Example of 500-simulations – Sierra Mountains CA
Compare Antecedent Soil Moisture …
Antecedent precipitation
used for soil moisture
accounting and setting
antecedent snowpack
PMP/PMF Stochastic Flood Analysis
Wet antecedent conditions
Full range of soil moisture conditions observed in historical record
varies by date (month)
Example: End-of-February storm date in semi-arid climate, Oregon
Barnes Oregon
0
2
4
6
8
10
12
14
NON-EXCEEDANCE PROBABILITY
PREC
IPIT
ATIO
N (i
n)
.5 .98.7 .9 .999.99.95
Normal Plotting Paper
.02 .05 .8.6.4.2.1 .3.001 .01
Gamma Distribution
October - February Precipitation
Compare Antecedent Snowpack… PMP/PMF Stochastic Flood Analysis
Conservative Snowpack
Full range of snowpack conditions observed in historical record
Snowpack depth and density varies spatially
by date, elevation and antecedent precipitation
Example: End-of-February storm date in semi-arid climate, Oregon
Compare Soil - Runoff Characteristics…
Soil moisture conditions dependent upon soil moisture
accounting based on storm date, antecedent
precipitation and evapo-transpiration
PMP/PMF Stochastic Flood Analysis
Soil Moisture Deficit = 0 Minimum loss rates
Soil moisture deficit and soil loss rates
dependent on soil moisture conditions
Compare Runoff Response…
Slower interflow response common in forested mountain watersheds with some quickflow response for extreme storms
PMP/PMF Stochastic Flood Analysis
Commonly “surface” response is modeled
Surface Runoff (quickflow) and Interflow Runoff Responses
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480
DISC
HARG
E (cf
s)
ELAPSED TIME (Hours)
Characteristic Streamflow Responses to Runoff Generation
235-mi2 - Mountain Watershed
Quickflow Runoff Response
Interflow Runoff ResponseDelayed Groundwater Response
Compare Initial Reservoir Level …
Historical reservoir level data inherently reflects reservoir
operations in addition to seasonal climatic variables
PMP/PMF Stochastic Flood Analysis
Conservative reservoir level
Based on historical reservoir levels for chosen storm date
Stochastic simulations will mimic seasonal variability
in reservoir level exhibited in historical record
Compare Flood Computations…
Distributed rainfall-runoff modeling
preferred for stochastic method
where runoff computed on
land segments
smaller than sub-basin level
PMP/PMF Stochastic Flood Analysis
Watershed Model and rainfall-runoff modeling
Watershed Model and rainfall-runoff modeling
Compare Calibration of Watershed Model…
PMP/PMF Stochastic Flood Analysis
Calibrated to large historical floods
Calibrated to large historical floods and other storm/flood events
to assess model parameters over wide range of climatic conditions
Also Calibrated to historical flood-frequency relationship
for project inflows
2 Additional Levels of Calibration for
Watershed Model and SEFM
Compare Sensitivity Analysis …
Global sensitivity analysis
can account for interaction
and dependencies between
inputs/model parameters
PMP/PMF Stochastic Flood Analysis
One-at-a-Time approach
Global Sensitivity Analysis is standard output
from stochastic simulations
Scatter due to numerous other
hydrometeorological inputs
affect maximum reservoir level
Compare Uncertainty Analysis …
Uncertainty analyses can be conducted
and uncertainty bounds can be developed
for flood-frequency relationships
PMP/PMF Stochastic Flood Analysis
Not Done – Feasibility?
Optional
Summary …
Deterministic PMP/PMF uses a single flood hydrograph (PMF)
and sensitivity analyses to assess hydrologic and hydraulic adequacy
of a dam and reservoir project
based on
conservative selections
of hydrometeorological inputs
and watershed parameters
(policies and guidelines)
Summary …
Stochastic Flood Analysis
Produces flood-frequency relationships
based on simulation of multi-thousand flood hydrographs
produced by combinations of hydrometeorological conditions
consistent with the historical record
Hydrometeorological inputs are simulated by Monte Carlo methods
which preserves the seasonal characteristics
and dependencies between parameters
exhibited in the historical record
Summary …
Stochastic Flood Analysis Robust examination of reservoir response
to diversity of flood characteristics
The focus is on assessing the magnitude and frequency of extreme floods
and providing information for Risk-Informed Decision-Making
400
410
420
430
440
450
460
470
480
490
RES
ERVO
IR S
TAG
E (F
eet)
ANNUAL EXCEEDANCE PROBABILITY
Extreme Value Type 1 Plotting Paper
Top of Flood Control Pool
1997 Flood
1986 Flood
10-410-2 10-3 10-610-50.5 10-1
End of Slides