Aching Joint Probability? – Diagnosing
Your Options for Interior Drainage
Behind Levees for Compliance with
65.10 (A Reviewer’s Perspective)
William Zung, PMP, CFM
Anish Pradhananga, PE, CFM
Rick Nusz, PG, PH, CFM
ASFPM 2013 Conference
June 12, 2013
Agenda
Diagnosis
65.10
Overview
Levees in
NFIP
Interior
Drainage
Analysis
Levees in NFIP
• Levee – A man-made structure, usually an earthen embankment,
designed and constructed in accordance with sound engineering
practices to contain, control, or divert the flow of water so as to
provide protection from temporary flooding.
• 44 CFR 65.10 establishes the criteria for levee systems to meet to
be accredited on FIRMs
• Accredited Levee – A levee shown on the FIRM as providing
protection from the 1-percent-annual-chance flood.
Levees in NFIP
• Interior Area – USACE EM 1110-21413 defines as “the area protected
from direct riverine, lake, or tidal
flooding by levees, floodwalls, or
seawalls and low depressions or
natural sinks.”
• Coincident Events – two events
occurring together
• Joint Probability – The probability of
two events occurring together.
Levees in NFIP
Coincident Events
• Exterior needs,
– Variable B : Stream Gage data or Hydraulic Study
• Interior needs,
– Variable A : Stream Gage data or Rainfall Runoff
models with synthetic storms
– Variable C : Hydraulic model with varying outlet
conditions
Source: HEC SSP User’s Manual
Levees in NFIP
Initiation
PAL
Mapping
• Study initiated and identify levees
• Levee ownership and background research
• PAL eligible / Accredit / Not Accredit
• PAL Meeting
• Progress Reports
• 65.10
• Accredit on FIRM
• Not Accredit on FIRM (Levee Analysis and
Mapping Process)
65.10 Overview
65.10 - Structural
65.10 – Non Structural
(b1) Freeboard
(b2) Closures
(a) General
(b3) Embankment Protection
(c) Operation
(b4) Foundation Stability
(b5) Settlement
(d) Maintenance
(b6) Interior Drainage
(b7) Other
(e) Other
65.10 Overview
www.fema.gov/living-levees-its-shared-responsibility/femalevee-resources-library
65.10 Overview
Reviewer’s Perspective
• PM 63
• Completeness Check
– Submittal Includes all
Elements
– Signed by a PE
– Checklist breaking down
each element
• Tab Submittal
• Detailed Review of
Interior Drainage Analysis
65.10 Overview
Reviewer’s Perspective
• The submitting P.E. is responsible
for the technical content
– Old can still be good
• Check submittal for completeness
to comply with all 65.10 criteria
• Friendly coordination with
submitter to resolve questions
• We will check for consistency…but
make it easy to find
65.10 Overview
Reviewer’s Perspective
• Digital submittals are preferred over
volumes of hard copies
• Rely heavily on the summary report
to tell us the answer
65.10 Overview
Reviewer’s Perspective
• 65.10(b)(6) Interior Flooding
– Interior Flooding Analysis submitted?
– Coincidental Peak Analysis done?
– Pump station operation included in the
analysis?
– Data certified by a Professional
Engineer?
65.10 Overview
Reviewer’s Perspective
• 65.10(b)(6) Interior Flooding
– Areas of Interior Flooding
Identified?
– Site map showing areas of
interior flooding mapped?
– Base Flood Elevations
shown on areas with greater
than 1 foot of flooding?
65.10 Overview
Reviewer’s Perspective
• 65.10(c) Operation Plans and Criteria
– Operation Plan submitted?
– Are closure devices addressed in
Operation Plan?
– Is the interior drainage system (including
flood warning system) addressed in
Operation Plan?
– Periodic Inspection and operation
stated?
– Operations Plan formally adopted as
per criteria in 65.10(c)?
65.10 Overview
Reviewer’s Perspective
• Common Errors
– Not using Joint Probability Analysis
– Documentation is inconsistent
• Pumps in model do not have the same parameters as
documented in the Operation Plan.
• Number of closures in Interior Analysis do not match the
number on the As-Builts and do not match the number in the
O&M plans
– Not using the 1% annual chance
• Many times the design event for interior flooding is more
frequent than the 1% (e.g. 4% [25yr])
Interior Drainage Analysis
What are you symptoms?
• Rainfall Runoff analysis of interior drainage area
• Data availability – Interior and Exterior measurements
– Stream gage data
– Precipitation gages
– Existing detailed flood study on exterior or interior
• Multiple uses of this study than just 65.10
– Capital Improvement Planning
• Engineering Judgment
• Risk justify the analysis
Simple
Complex
Interior Drainage Analysis
What are you symptoms?
• Risk justify the analysis
Heavy Industrial with storm water pipe network
Agricultural with open channels
Interior Drainage Analysis
What are my options?
A. USACE EM 1110-2-1413 has two general methods to perform
the hydrologic analysis in interior areas
1.
Continuous Record Analysis Method
a. Period of record
b. Discrete events of historic record
c. Stochastically generated continuous record
2. Coincident Frequency Method: Weighted frequency relationship
developed from probabilities of exterior and coincident interior stage
condition
B. American Association of State Highway and Transportation
Officials (AASHTO)
C. The Worst Case Scenario
Interior Drainage Analysis
A.1.a. Period of record method
• Estimates the interior runoff hydrograph for a
period of historic precipitation.
• Period of record exterior stage hydrograph at
desired location.
• Need stream data as well as interior rainfall
data.
• The process preserves the, seasonality,
persistence and dependence or independence
of exterior and interior events.
Key Features:
 Gages
 Historic Interior
and Exterior
 Lots of Data
 Preserves
Seasonality
Simple
Complex
Interior Drainage Analysis
A.1.b. Multiple Discrete Event method
• Generates composite stage- frequency function
by analyzing two conditions.
– 1. Selected high exterior events that have on
effect on interior flooding with coincident historic
interior rainfall.
– 2. Selected low exterior events associated with
interior flood generated by coincident historic
interior rainfall or hypothetical frequency storms.
The joint probability theorem is applied to
combine these two functions to generate a
composite function.
•
Key Features:
 Gages
 Interior Flooding
with High Exterior
 Interior Flooding
with Low Exterior
 Joint Probability
Theorem
Joint Probability Theorem
P= P(A)+ P(B) For Partial Duration series
P= P(A)+P(B)-P(A)xP(B) For annual Series
Simple
Complex
Interior Drainage Analysis
A.1.c. Stochastic Method
• Generate synthetic sequences from the historic
record
• Accounts for the randomness of events
• Overcome the limitation due to short period of
records.
Key Features:
 Can be analyzed
with synthetic
sequences
 Recorded Data
limitation is
avoided
 Randomness of
events are
represented
Simple
Complex
Interior Drainage Analysis
B: Coincident Frequency Method
• Hydrologic and Hydraulic modeling
– Uses synthetic events
– Frequency event is known
• Applies Total Probability Theorem to generate
stage-frequency function
– P(A) = probability of exceeding a given interior ponding
elevation
– P(Bi) = probability river is at specific stage interval (i)
– P(A/Bi) = probability of exceeding a given pond
elevation if the river stage is at the stage interval (i)
𝑛
P(A)= �
𝑖=1
P
A
Bi
Key Features:
 Can be analyzed
with synthetic
sequences
 Recorded Data
limitation is
avoided
 Randomness of
events are
represented
X P(Bi)
Simple
Complex
Interior Drainage Analysis
Coincident Frequency Method cont.
Interior stages (ft)
P(A/Bi)
Exterior stages (ft)
P(Bi)
HECSSP
1-percentannual-chance
joint probability
water surface
elevation P(A)
Interior Drainage Analysis
A.2. Coincident Frequency Method – HEC SSP
• Coincident Frequency Plot
• HEC SSP will perform the
Coincident frequency
Analysis and generate a
474.44
frequency curve
Interior Drainage Analysis
B. American Association of State Highway and
Transportation Officials (AASHTO)
• Joint probabilities of design
coincident stream flows at
confluences.
• Coincident frequencies based
on watershed Area Ratio
• Alternative approach for interior
areas with very limited data
• Use the higher result of the two
scenarios
Simple
Complex
Interior Drainage Analysis
C. Assume the Worst Case
•
•
•
•
All gates closed
Pump Stations operate per O&M Plan
1-percent-annual-chance rainfall on watershed
Duration of 24 hours
Pros
• Easy to Calculate
Cons
• The event likely will have
less than 1-percent-annualchance in any given year
• The inundation area may
be larger than 1-percentannual-chance event
Simple
Complex
Diagnosis
• Consider your symptoms
– What is at Risk – Agricultural fields, industrial, homes, etc.
– What impacts of the interior flooding extents on the FIRM
– What is your data availability
• Stream gages,
• precipitation gages
• H&H modeling
– What is your PE comfortable with
• Document your assumptions and clearly summarize your analysis
in the report
– Include backup data as needed
– Make sure it is consistent throughout the report
Diagnosis
Prescription:
Perform the Coincident Frequency Method
• The method most applicable in Joint Probability
Analysis for Interior Drainage Analysis for 65.10
certification
• Applicable with limited gage data
• Hydrologic and Hydraulic modeling using FEMA
approved models
• HEC-SSP used to perform the statistical
calculations
• Repeatable and can be modified for future map
revisions
• Detailed analysis for BFE placement on FIRMs
Key Features:
 Can be analyzed
with synthetic
sequences
 Recorded Data
limitation is
avoided
 Randomness of
events are
represented
Simple
Complex
Questions?
William Zung, PMP, CFM
[email protected]
913-498-0500 x 1
Anish Pradhananda, PE, CFM
[email protected]
913-498-0500 x 5
Rick Nusz, RG, PH, CFM
[email protected]
816-283-7907