Kaveh Zomorodi, Ph.D., P.E., CFM

Sea Level Rise Integration in

Coastal Structures Safe Design

NOAA Coastal Flood Exposure Mapper,SLR Map for Delaware City, DE

http://www.csc.noaa.gov/floodexposure/#/start

This map shows sea level rise scenarios of 0 to 6 feet, which represent a rise in

water above the average of the highest high tides (called mean higher high

water, or MHHW) for hydrologically connected areas. Areas that are lower in

elevation will be exposed to flooding from sea level rise first and are

represented by the darkest red.

From SLR in feet to change in

Design Elevation in feet

From SLR in feet to change in

Design Elevation in feetIf SLR is estimated to be 1.0 foot :

NOAA: Tide stations measure Local • NOAA: Tide stations measure Local Sea Level, which refers to the height of the water as measured along the coast relative to a specific point on land. Water level measurements at tide stations are referenced to stable vertical points (or bench marks) on the land and a known relationship is established. However, the measurements at any given tide station include both global sea level rise and vertical land motion, such as subsidence, glacial rebound, or large-scale tectonic motion.

• SLR trends project Local Sea Level into future.

How much should the 100-year flood elevation be raised?

Engineering design and planning • Engineering design and planning is based on probabilistic conceptual flood levels, not just Local Sea Level.

• How do you incorporate projected SLR into a design flood level?

Background to This StudyApril, 2013

April, 2013

FTA-HMCE Tool Version: 1.0Build Date: 1/16/2014

This tool may be used for benefit-cost analysis (BCA) of resilience projects submitted to FTA for consideration

for funding under the Public Transportation Emergency Relief Program and the Disaster Relief Appropriations

Act of 2013 (Pub. L 113-2) for States, local governmental authorities, tribal governments and other FTA

recipients impacted by Hurricane Sandy, which affected mid-Atlantic and northeastern states in October 2012.

Resilience projects are those hazard mitigation projects designed and built to address vulnerabilities to a public

transportation facility or system due to future recurrence of emergencies or major disasters that are likely to

occur in the geographic area in which the public transportation system is located; or projected changes in

development patterns, demographics, or extreme weather or other climate patterns. All proposed projects for

funding are required to provide a cost-effectiveness evaluation leading to a benefit-cost ratio (BCR) for the

proposed project. This information will be used by FTA to evaluate the cost-effectiveness of the proposed

project in reducing an asset’s and the public transportation system’s vulnerabilities to future disasters.

Consistent with Executive Order 12893, selection of projects for funding will be based in part on a systematic

analysis of benefits and costs. In general, a BCR of one or greater indicates a project is cost-effective.

However, there are additional considerations that may lead to some projects with a BCR of less than one to be

considered cost-effective.

Applicants should provide information about the qualitative benefits of the proposed project under Tab 5 of this

tool.

The tool provides a framework for applicants to submit quantitative information about the project and its cost-

effectiveness, including the estimated damage and losses from specifically identified hazards (recorded

historical and/or expected theoretical events) and the reduction in the anticipated losses after such an event as

a result of the proposed project. Quantitative information that applicants must submit includes the estimated

damage and losses from specifically identified hazards (recorded historical or expected theoretical events) and

the reduction in the anticipated damages and losses after such an event as a result of the proposed project.

FTA will review the explanations and justifications provided to determine the reasonableness of the submitted

information, as well as the source of the information.

TAB 2 - Project Information & Cost Estimate

TAB 3 - Pre-Resilience Damages

TAB 4 - Post-Resilience Damages

TAB 5 - Analysis Results & Qualitative Benefits

TAB 1 - Tool Information

Click on a tab title to go directly to it:

Disclaimer:

The results produced by this tool are not

conclusive evidence that a project proposal is or is

not cost-effective. Use of this tool does not

guarantee that a project is eligible for funding

under the FTA Public Transportation Emergency

Relief Program. The analysis conducted is

dependent upon the quality of the information

provided, and will be evaluated in the context of

both analysis results and sufficiency of

Relative Sea Level Change Curves (meters)T(t) = (E+M)t+bt2

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

19

92

19

95

20

00

20

05

20

10

20

15

20

20

20

25

20

30

20

35

20

40

20

45

20

50

20

55

20

60

20

65

20

70

20

75

20

80

20

85

20

90

20

95

21

00

21

05

21

10

21

15

21

20

21

25

21

30

21

35

21

40

21

45

21

50

21

55

21

60

21

65

Re

lati

ve

Se

a L

ev

el

Ch

an

ge

(M

ete

rs)

Year

8638610 - Sewells Point, VA: 4.31 (mm/yr)

USACE High Rate

USACE Intermediate Rate

USACE Low Rate (Current Rate)

Curves are computed using the global rate in cell [I4]/yr + the local

land movement rate in cell [K4], with the start date in cell [J4]

Start by Selecting

Project Location

Select Applicable NOAA Tidal Gage

from USACE Climate Change Adaption

Seal Level Change Curves

Select SLR Trend

Set Project Useful Life (SLR projection

duration) and starting Year

Obtain Parameters

from Coastal Study

Estimate from

FEMA FIS Data

Set baseline flood to which SLR applies

directly

Estimate Moving Average Linear Slope

of the Baseline Flood Elevation + SLR

Estimate Gumbel Revised Location

Revised Scale by multiplying with

Slope up to each year in future

Estimate Equiv. Elevation, Rise and

Year for required profiles: (10, 50, 100

(BFE), 500-years and BFE+1 ft)

Are Gumbel Distribution

Parameters (Location, Scale)

for coastal flood elevations

(including wave) available ?

Yes No

SLR Equivalent Coastal Flood Elevation

considering all of the modified flood levels for the future years an SLR

equivalent coastal flood elevation is calculated that would give the same

probability of failure for the duration of the Project Useful Life as provided

by the current design standards.

For example, a structure designed for the current 100-year flood elevation

has a probability of failure of 39.5% during the next 50 years. The Equiv.

100-year flood depth is found by trial&error that would make the sum of

the failure probability over the next 50 years the same. Failure probability

for each year is calculated by Gumbel Distribution with shifting Locatin

and Scale for each year.

Computational Flow ChartComputational Flow Chart

Method explained through a

Hypothetical Example of a Coastal

Levee at Hampton Roads, VA

currently designed with top-of-

levee elevation set at BFE+1 foot

Select nearby

NOAA Gauge:Select SLR Trend:

The magnitude of SLR is estimated following the USACE Climate Change Adaption Seal Level Change Curves:

http://corpsclimate.us/ccaceslcurves.cfm

select the closest NOAA coastal gauge to resilience project site from drop down list. To see a map of gauge locations visit the link

below and select East Coast and Zoom in to your project location: http://tidesandcurrents.noaa.gov/sltrends/sltrends.shtml

Estimated for Year 2064 based on Accelerated (Intermediate) trend

projection for NOAA Gauge: Sewells Point, VA.

Sewells Point, VAAccelerated (Intermediate)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

2010 2020 2030 2040 2050 2060 2070

SLR

(ft

)

Year

Gumbel Distribution (EV Type I) fit to flood Elevation (including waveheight) Input (Green Cells)Current Design

Freeborad over BFE = 1.0 ft, FB input is optional

Tr

(Year)

Flood

Elev(including

waveheight)(ft) This method is used only when flood elev. data not available to estimate distribution parameters directly.

10 8.76 FIS data for flood including wave from Table 3, Transect 5, City of Norfolk, VA August 5, 2012

50 10.99

100 12.10

500 14.17

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.1 0.02 0.01 0.002

Gumbel fit

by equation

standard P

Location 5.600 Scale 1.401 Shape

P

Gumbel fit

by equation flood elev (ft) using NTGumbel Constant weight diff^2

0.1 0.0998 8.76 0.0998 10 0.00000030

0.02 0.0212 10.99 0.0212 20 0.00002923

0.01 0.0096 12.10 0.0096 100 0.00001357

0.002 0.0022 14.17 0.0022 20 0.00000086

sum sq= 0.000044

Define Baseline flood as the flood elevation to which SLR may be directly added. After trying several variations (i.e., 1.1-yr, etc.) the Mode was selected.

baseline flood elev (ft)

5.60 for Gumbel distribution Mode= Location

Updating each year’s parametersUpdating each year’s parameters

n Year rise

baseline flood

+SLR (ft) slope, m= constant, b=

revised

location revised scale

Revised 100-yr

flood El Simple BFE+SLR

Rise in theoretical

BFE Current BFE's P

0 2014 0.00 5.60 1.0000 0 5.60 1.4015 12.0471 12.10 0.00 0.9904

1 2015 0.02 5.62 1.0032 0 5.62 1.4060 12.0862 12.12 0.04 0.9901

2 2016 0.04 5.64 1.0065 0 5.64 1.4106 12.1256 12.14 0.08 0.9898

3 2017 0.05 5.66 1.0098 0 5.66 1.4152 12.1654 12.15 0.12 0.9895

4 2018 0.07 5.67 1.0131 0 5.67 1.4199 12.2055 12.17 0.16 0.9892

5 2019 0.09 5.69 1.0165 0 5.69 1.4246 12.2461 12.19 0.20 0.9889

6 2020 0.11 5.71 1.0199 0 5.71 1.4294 12.2870 12.21 0.24 0.9886

7 2021 0.13 5.73 1.0233 0 5.73 1.4342 12.3284 12.23 0.28 0.9883

8 2022 0.15 5.75 1.0268 0 5.75 1.4390 12.3701 12.25 0.32 0.9879

9 2023 0.17 5.77 1.0303 0 5.77 1.4439 12.4121 12.27 0.37 0.9876

10 2024 0.19 5.79 1.0338 0 5.79 1.4489 12.4546 12.29 0.41 0.9872

11 2025 0.21 5.81 1.0374 0 5.81 1.4538 12.4975 12.31 0.45 0.9869

12 2026 0.23 5.83 1.0410 0 5.83 1.4589 12.5407 12.33 0.49 0.9865

13 2027 0.25 5.85 1.0446 0 5.85 1.4639 12.5843 12.35 0.54 0.9861

14 2028 0.27 5.87 1.0482 0 5.87 1.4691 12.6283 12.37 0.58 0.9857

15 2029 0.29 5.89 1.0519 0 5.89 1.4742 12.6727 12.39 0.63 0.9853

Calculations carried out for number of years = PUL

Evaluating Equivalent Flood ElevationsEvaluating Equivalent Flood Elevations

change Equiv El to make Equiv Balance zero

need to optimize these values RI of BFE+FB

Tr: 10 50 100 500 211

current values: 8.76 10.99 12.10 14.17 13.10

Equiv EL 9.65 12.23 13.32 15.86 14.50Equiv Balance 0.000000000 0.000000003 0.000000002 0.000000001 0.000000000

Current BFE's P 10-yr 50-yr 100-yr 500-yr BFE+FB

0.9904 P (NF) equiv El P (NF) equiv El P (NF) equiv El P (NF) equiv El P (NF) equiv El

0.9901 0.9448 0.9910 0.9958 0.9993 0.9982

0.9898 0.9435 0.9907 0.9957 0.9993 0.9981

0.9895 0.9423 0.9904 0.9956 0.9993 0.9981

0.9892 0.9410 0.9902 0.9954 0.9992 0.9980

0.9889 0.9397 0.9899 0.9953 0.9992 0.9979

0.9886 0.9384 0.9896 0.9951 0.9992 0.9979

0.9883 0.9370 0.9893 0.9950 0.9991 0.9978

0.9879 0.9356 0.9890 0.9948 0.9991 0.9977

0.9876 0.9342 0.9887 0.9947 0.9991 0.9976

0.9872 0.9327 0.9883 0.9945 0.9990 0.9976

0.9869 0.9312 0.9880 0.9943 0.9990 0.9975

Simple Addition vs. Statistical ApproachSimple Addition vs. Statistical Approach

Recurrence

Interval

(yr)

Percent

Annual

Chance

(%)

Year 0 (2014)

flood Elevation

(including

Wavehight)

FIS Data

Year end (2054)

flood Elevation

(including

Wavehight)

Simple addition

of SLR

Year end (2054)

flood Elevation

(including

Wavehight)

Statistical Method

Equiv Year

flood Elevation

(including

Wavehight)

Data

Equiv

Year

Equiv

Rise

(fT)

10 10.00% 8.76 9.88 10.51 9.65 27 0.89

50 2.00% 10.99 12.11 13.29 12.23 28 1.24100 1.00% 12.10 13.22 14.47 13.32 28 1.22

500 0.20% 14.17 15.29 17.18 15.86 29 1.69

BFE+FB 0.47% 13.10 14.22 15.73 14.50 29 1.40

baseline flood N/A 5.60 6.73 N/A N/A 50 N/A

BFE Increase in Future YearsBFE Increase in Future Years

12.0

12.5

13.0

13.5

14.0

14.5

15.0

2010 2020 2030 2040 2050 2060 2070

10

0-y

r F

loo

d E

lev

., in

clu

din

g w

av

eh

eig

ht

(ft)

Year

Revised (Statistical) BFE Trend

SLR+ BFE

Equiv. BFE

0.0

50.0

100.0

150.0

200.0

250.0

2010 2020 2030 2040 2050 2060 2070

Re

cu

rre

nce

In

terv

al (Y

ea

rs)

Year

Tr current BFE

w/current parameters or revised BFE

w/ moving paramters

Tr current BFE

w/ moving parameters

Tr BFE+SLR

w/current parameters

Tr BFE+SLR

w/ moving parameters

Tr Equiv. BFE

w/ moving parameters

Tr at Equiv. Year

Changes in Recurrence Interval of Current BFEChanges in Recurrence Interval of Current BFE

Method Applied to Six East Coast Locations

Location

NOAA Station

for SLR Sea

Gumbel

Location

Gumbel

Scale

BFE

(ft)

50-yr

SLR

(ft)

BFE Rise

Statistical

(ft)

BFE Rise

Equiv.

(ft)

(BFE Rise

Equiv.) / (50-yr

SLR)

BFE Rise

Equiv. - 50-

yr SLR

(ft)

Equiv.

Year

Transect 177, Woods

Hole,

Barnstable County,

Massachusetts

Woods Hole, MA Buzzards Bay 2.797 2.870 16.00 0.86 4.90 2.48 2.90 1.62 28

Transect 30, City of

Norwalk,

Fairfield County,

Connecticut

Bridgeport, CT Long Island Sound 8.531 1.407 15.00 0.82 1.45 0.73 0.89 -0.09 28

Transect NY-14,

New York, NYThe Battery, NY East River 3.533 2.273 14.00 0.90 3.54 1.80 2.01 0.90 28

Transect 22, Atlantic

County, NJ,Atlantic City, NJ Atlantic Ocean 5.375 1.871 14.00 1.05 2.72 1.39 1.32 0.34 28

Elk River,

Transect 29

Cecil County

Maryland

Chesapeake

CityChesapeake Bay 4.083 1.285 10.00 0.91 2.23 1.15 1.26 0.24 28

Transect 5,

City of Norfolk, VirginiaSewells Point, VA Chesapeake Bay 5.600 1.401 12.10 1.12 2.37 1.22 1.08 0.10 28

Results for Six East Coast LocationsResults for Six East Coast Locations

Regression Equation for Six East Coast LocationsRegression Equation for Six East Coast Locations

MA

CT

NY

NJ

MDVA

y = 0.0281e2.6576x

R² = 0.9931

0.70

1.20

1.70

2.20

2.70

3.20

3.70

4.20

1.25 1.35 1.45 1.55 1.65 1.75

(BF

E R

ise

Eq

uiv

.) /

(5

0-y

r S

LR)

BFE/10yr WSE

Evaluated Points Expon. (Evaluated Points)

50-yr BFE Rise Equiv. = (0.0281 e(2.6576 (BFE/100yr WSE))

) (50-yr SLR)

Regression fit for Six East Coast LocationsRegression fit for Six East Coast Locations

MA

CT

NY

NJ

MDVA

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

2.60

0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60

Re

gre

ssio

n E

va

lua

ted

BFE

Ris

e E

qu

iv.

Evaluated BFE Rise Equiv.

perfect fit line

Ratio Exponential Fit

Application Example

Problem: A coastal structure near Norfolk, VA is considered for mitigation against

coastal floods by elevating it to BFE+1 (considering SLR during the next 30-years which

is FEMA’s default mitigation PUL for elevation projects). How much does the structure

need to be elevated to? What is the equivalent flood elevation for each R.I. that can

be used in a BCA analysis? Accelerated (Intermediate) non-linear 30-year SLR at this

location is 0.62 ft.

Solution: As seen in results table BFE+FB (12.1’+1’) increases from 13.10 ft to 13.72 ft

(simple additions) or 14.55 ft (statistical method). The equivalent value is 13.87 ft

which shows a rise of 0.77’ (0.15’ more than simple 30-year SLR). The equiv. rise for

each R.I. is different and is not the same as the rise by the equiv. year (16 years).

Recurrence

Interval

(yr)

Percent

Annual

Chance

(%)

Year 0 (2014)

flood

Elevation

(including

Wavehight)

FIS Data

Year end (2034)

flood Elevation

(including

Wavehight)

Simple addition

of SLR

Year end (2034)

flood Elevation

(including

Wavehight)

Statistical Method

Equiv Year

flood

Elevation

(including

Wavehight)

Data

Equiv

Year

Equiv

Rise

(fT)

Rise

by

Equiv

Year

(ft)

Added

to

Current

Value

(ft)

10 10.00% 8.76 9.38 9.73 9.25 16 0.50 0.31 9.07

50 2.00% 10.99 11.61 12.30 11.71 16 0.72 0.31 11.30100 1.00% 12.10 12.72 13.38 12.75 16 0.65 0.31 12.41500 0.20% 14.17 14.79 15.90 15.15 16 0.98 0.31 14.48

BFE+FB 0.47% 13.10 13.72 14.55 13.87 16 0.77 0.31 13.41

Questions?

• Kaveh Zomorodi, Ph.D., P.E., CFM

Sea Level Rise Integration in Coastal Structures Safe Design