pmp/pmf – stochastic flood · pdf filepmp/pmf – stochastic flood analysis...

PMP/PMF – Stochastic Flood Analysis

Comparison of Methodologies

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Applegate Dam and Reservoir

Outflow Flood

Inflow Flood

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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

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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

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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 …


Month yielding largest flood from PMP

Storm/Flood Dates for full range observed in historical record

American River Watershed

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NON-EXCEEDANCE PROBABILITY

NU

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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

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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

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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

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TIME (hours)

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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


“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


Synthetic pattern

Separate temporal pattern for each prototype storm

based on historical storms

Dec 28, 1996 Start

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0 24 48 72 96 120 144 168 192Elapsed Time (Hours)

Free

zing

Lev

el (F

eet)

Thousand Feet

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Air T

empe

ratu

re (o F

)


Dec 28, 1996 Start1000-mb

Compare Air Temperature Temporal Pattern…

High Freezing Levels for Extreme Storms

Dec 28, 1996 Start

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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


Dependent on air temperature lapse rate

set by analyst

Freezing level is stochastic variable based on radiosonde data

for historical storms

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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


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

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NON-EXCEEDANCE PROBABILITY

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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


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


Commonly “surface” response is modeled

Surface Runoff (quickflow) and Interflow Runoff Responses

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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


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


Watershed Model and rainfall-runoff modeling

Watershed Model and rainfall-runoff modeling

Compare Calibration of Watershed Model…


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


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


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

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1997 Flood

1986 Flood

10-410-2 10-3 10-610-50.5 10-1

End of Slides

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