benefit-cost analysis of mitigation of damages due to progressive

ASFPM Conference, June 9 -14, 2013, Hartford, Connecticut.

Benefit-Cost Analysis of Mitigation of Damages due to Progressive River Bank Erosion

Kaveh Zomorodi, Ph.D., P.E., CFM, Dewberry, 8401 Arlington Blvd., Fairfax, VA 22031. email: [email protected]

Risk projection to future is different

Stationary vs. Non-Stationary Hazards

Non-stationary hazard: the relationship between hazard probability and severity may be different from year to year; Example: a gradual sea level rise.

Stationary hazard: the relationship between hazard probability and severity remains constant from year to year; Example: Riverine Flood under a stable stream and hydrologic condition.

2 Benefit-Cost Analysis of Mitigation of Damages due to Progressive River Bank Erosion

• Is based on stationary probability to project future avoided losses and compute project benefits.

The current FEMA BCA software

3 | Benefit-Cost Analysis of Mitigation of Damages due to Progressive River Bank Erosion

• Well-known cases include BCA of land-slide (one-time loss)

• Newer cases requested through BCA Helpline :

• Post-fire flood mitigation, Zomorodi, K., 2012, “Benefit Cost Analysis of Mitigation Projects Subject to Non-stationary Hazards: Case of Post-fire Flood”, presented at 2012 Floodplain Management Conference, September 4-7, Sacramento, California, Annual Conference by Floodplain Management Association, http://www.floodplain.org/

• Progressive stream erosion causing the river getting closer to structures after each flood event (This presentation)

Need for non-stationary analysis


http://www.floodplain.org/

Types of Non-stationary cases each requiring a different approach:


1.A non-recurring hazard: includes special hazards that are not expected to reoccur such as a landslide; if it happens would result in a one-time total loss of a house.

2.A Step-change hazard: This category includes wildfire causing a sudden increase in flood levels in post-fire conditions or stream bank erosion events shifting the hazard level. Other examples include levee failure and ice dam formation.

3.A gradual change hazard: This category includes gradual urbanization of a watershed and sea level rise gradually impacting the coastal flood levels.

Problem Description & Examples (BC Helpline Inquiries) • City of Lompoc, CA:

as river meanders through floodplain it encroaches on bank near City causing bank erosion. They have not had damage yet but it is coming close to hitting utilities and houses. Detailed erosion study and historical progression of erosion indicates that a series of 5 and 10 year storms or a 50-100 year storm would begin to cause damages. The issue is that currently, it is showing $0 damages for 5 or 10 year; and begins to show damages at 50 and 100 years.

• Vermont Case: a river is eroding the road embankment. When considering the expected road damages and closure, is there a way to take into consideration the cumulative nature of erosion? For example, the same amount of erosion (damage) is caused by one 100-year storm or two 25-year storms. How to account for the two 25-year storm’s cumulative damage?.

Proposed Solution Approach

• Needs to be a work-around solution to allow using the current FEMA BCA Software

• Needs to be flexible to consider different hazard-damage scenarios

• Step 1- Select

Hazard- Damages

for each site:

Three Step Solution

Scenario# Scenario

Damage Level

Damage ($)

1 five 5-yr floods 1 3139002 two 10-yr floods 1 3139003 One 50-yr flood 2 5818125

Scenario# Scenario

Damage Level

Damage ($)

1 four 5-yr floods 1 70258372 three 10-yr floods 1 70258373 two 50-yr flood 1 70258374 one 100-yr flood 2 9398462

Riverbank Damage Scenarios

Riverside Damage Scenarios

• Approximate the likelihood that each scenario consisting of one or more occurrence of a certain flood level would result in a given level of damage during the project useful life (50-years).

• Negative Binomial Distribution was used to evaluate the probability of reaching the given number of occurrence of floods in each scenario by each year in the 50-year time series of project useful life.

• This probability varies in time depending on the annual probability of exceedance of the flood and the number of occurrences required causing damage in future.

Step 2- Statistical Analysis of Multiple occurrence of a Given Flood Level


• For example, if three 10-year floods are needed to cause a level 1 damage the probability of this varies annually in future as shown in the following graph (X-axis is the year in future and y-axis is the annual probability):


• Annual probability increases and peaks around the year 20 and then declines after that. Probability of having three 10-year floods by each year can be evaluated by summing all the previous probabilities. The cumulative probability of this scenario happening within the next 50-years is 0.8883. Note that this probability includes the probability of having three or less smaller events including the 5-year flood.

0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

P of

reac

hing

# e

vent

s in

give

n ye

ar

Year

Three 10-yr Series

BCA Software needs a constant Annual Probability of Exceedance and Recurrence Interval for each Level of Damage


• A weighted average scheme based on the discount factor (using FEMA default discount rate of 7%) was used to evaluate the Average Annual Probability Weighted by Discount Factor. This scheme ensures that the impact of each annual probably is considered in proportion to its potential impact on the present value of damages. This is also analogous to finding the average annual damage value that would lead to the same present value of damages over the next fifty years.

• The R.I. for each scenario can then be estimated by the reciprocal of the probability calculated in this manner. This procedure leads to equivalent R.I. that in some cases are smaller and in other cases larger than the reciprocal of the average value of the annual probabilities. For the three 10-year scenario, algebraic average of annual probabilities gives an R.I. of 55.7 years but this scheme gives an R.I. of 68.5 years:

Variable P

Average P

AAPWDF

0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Three 10-yr Series

Results Table for both scenarios:

12 | | Benefit-Cost Analysis of Mitigation of Damages due to Progressive River Bank Erosion

• For Riverbank Level 1 damage Scenario 1 is more likely to happen within the next 50-years than Scenario 2 (0.9815 vs. 0.9662). However, since both scenarios are assumed to cause the same level of damage the scenario with a smaller R.I. (40 years) should be used in the BCA to avoid underestimating the benefits. The Selected R.I.-Damage pairs are used in FEMA BCA as Before-Mitigation Damages.

Scenario# ScenarioDamage

LevelDamage

($)

P Damage due to

this Scenario

Average Annualprobability

weighted by discount factor

Equiv. R.I.

Selected R.I.

1 five 5-yr floods 1 313900 0.9815 0.0161 62.0 N/A2 two 10-yr floods 1 313900 0.9662 0.0250 40.0 40.03 One 50-yr flood 2 5818125 0.6358 0.0159 62.9 50.0

Scenario# ScenarioDamage

LevelDamage

($)

P Damage due to

this Scenario

Average Annualprobability

weighted by discount factor

Equiv. R.I.

Selected R.I.

1 four 5-yr floods 1 7025837 0.9943 0.0218 45.9 46.02 three 10-yr floods 1 7025837 0.8883 0.0146 68.5 N/A3 two 50-yr flood 1 7025837 0.2642 0.0033 300.2 N/A4 one 100-yr flood 2 9398462 0.3950 0.0089 112.7 100.0

Riverbank R.I. - Damage Results

Riverside R.I. - Damage Results

Spreadsheet to Calculate and Select R.I.


Flood RI (Yeasr)

# events tocause damage

finishing year before reaching#events to casue damage

P of reaching # events to casue damage before given year

discountfactor

Flood RI (Yeasr)


finishing year before reaching#events

P of reaching # events to casue damage

discountfactor

Flood RI (Yeasr)


finishing year before reaching#events

P of reaching # events to casue damage

discountfactor

5 5 1 0.0000 0.93458 10 2 1 0.0000 0.93458 50 1 1 0.0200 0.934582 0.0000 0.87344 2 0.0100 0.87344 2 0.0196 0.873443 0.0000 0.81630 3 0.0180 0.81630 3 0.0192 0.816304 0.0000 0.76290 4 0.0243 0.76290 4 0.0188 0.762905 0.0003 0.71299 5 0.0292 0.71299 5 0.0184 0.712996 0.0013 0.66634 6 0.0328 0.66634 6 0.0181 0.666347 0.0031 0.62275 7 0.0354 0.62275 7 0.0177 0.622758 0.0057 0.58201 8 0.0372 0.58201 8 0.0174 0.582019 0.0092 0.54393 9 0.0383 0.54393 9 0.0170 0.54393

10 0.0132 0.50835 10 0.0387 0.50835 10 0.0167 0.5083511 0.0176 0.47509 11 0.0387 0.47509 11 0.0163 0.4750912 0.0221 0.44401 12 0.0384 0.44401 12 0.0160 0.4440113 0.0266 0.41496 13 0.0377 0.41496 13 0.0157 0.4149614 0.0307 0.38782 14 0.0367 0.38782 14 0.0154 0.3878215 0.0344 0.36245 15 0.0356 0.36245 15 0.0151 0.3624516 0.0375 0.33873 16 0.0343 0.33873 16 0.0148 0.3387317 0.0400 0.31657 17 0.0329 0.31657 17 0.0145 0.3165718 0.0419 0.29586 18 0.0315 0.29586 18 0.0142 0.2958619 0.0431 0.27651 19 0.0300 0.27651 19 0.0139 0.2765120 0.0436 0.25842 20 0.0285 0.25842 20 0.0136 0.2584221 0.0436 0.24151 21 0.0270 0.24151 21 0.0134 0.2415122 0.0431 0.22571 22 0.0255 0.22571 22 0.0131 0.2257123 0.0422 0.21095 23 0.0241 0.21095 23 0.0128 0.2109524 0.0408 0.19715 24 0.0226 0.19715 24 0.0126 0.1971525 0.0392 0.18425 25 0.0213 0.18425 25 0.0123 0.18425

0.0000

0.0100

0.0200

0.0300

0.0400

0.0500

1 4 7 1013161922252831343740434649

two 10-yr series

0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

1 5 9 13 17 21 25 29 33 37 41 45 49

one 50-yr series

0.0000

0.0100

0.0200

0.0300

0.0400

0.0500

1 4 7 1013161922252831343740434649

five 5-yr series

Step 3- Input to FEMA BCA Software


• The Selected R.I.-Damage pairs are used in FEMA BCA as Before-Mitigation Damages.

• Set After-Mitigation Damages based on Level of Protection.

• Alex Ubaldo, P.E. and Craig Dierling, P.E., Engineering Division, City of Lompoc, California.

• Craig Steward, P.E., CFM, Penfield & Smith, Santa Barbara, California.

• Andrew Rush, California Emergency Management Agency, Hazard Mitigation Grants Branch.

Acknowledgement


• Flood Calculation Methodology Report, FEMA Benefit-Cost Analysis Re-engineering (BCAR), Version 4.5, May 2009, FEMA 2009.

• RIVERSIDE DRIVE BANK EROSION EVALUATION, Lompoc, California, January 20, 2011, Prepared by Penfield & Smith, Santa Barbara, California.

• SANTA YNEZ RIVER BANK PROTECTION EVALUATION, Lompoc, California, January 20, 2011, Prepared by Penfield & Smith, Santa Barbara,

California. • Zomorodi, K., 2012, “Benefit Cost Analysis of Mitigation Projects Subject to

Non-stationary Hazards: Case of Post-fire Flood”, presented at 2012 Floodplain Management Conference, September 4-7, Sacramento, California, Annual Conference by Floodplain Management Association, http://www.floodplain.org/

References


http://www.floodplain.org/

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