Incorporating the Costs and Benefits of Adaptation Measures in Preparation for Extreme Weather Events and Climate Change—Guidebook (2020)

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141 The following presents a worksheet for Level 2 analysis. Level 2: Climate-Adapted Benefit-Cost Analysis Level 2 analysis builds on Level 1 analysis. A Level 2 analysis uses existing conditions without climate change only to calculate the new return period for future conditions with climate change, that is, the maximum return period under climate change conditions for which no damages will occur, Tf. A Level 2 analysis then calculates future damages under climate change conditions without and with resilience/mitigation measures in place. Step 1. Summarize results of Study Level 1 in the table that follows. A P P E N D I X H Worksheet for Level 2 Analysis

Current pre-mitigation conditions Future (climate change) pre-resilience Return period Future discharge Interpolated damages Base case future damage increment Return period Damages (in current $) Damage increment Current discharge Tfnd=33 Qfnd= 9,000 Dfnd Dafnd Max return period resulting in no damages Tcnd =50 Dcnd=0 Dacnd=0 Qcnd=9,000 T’fnd= 50 Q’fnd=9,979 D’fnd=1,060,312 D’afnd=5,270 Next level return period resulting in some damages Tcmod=100 Dcmod=1,630,000 Dacmod=8,150 Qcmod=10,505 Tfmod= 100 Qfmod=11,665 Dfmod=2,162,793 Dafmod=16,116 Return period resulting in maximum damages Tcmax=500 Dcmax=3,227,000 Dacmax=19,428 Qcmax=13,982 Tfmax= 500 Qfmax=15,562 Dfmax=3,591,659 Dafmax=23,018 =0 =0

Worksheet for Level 2 Analysis 143 Step 2. Add points to Future Discharges and Damage curves. Adding more points for the discharge versus return period and damages versus discharge graphs will correct for discrepancies between existing conditions and future climate conditions. Use the following equations to calculate climate-adjusted return periods ( ) for based on Step 1. = Log − − * − − = Log (100 ) − (100 ) − ( 50) * 11,665 − 10,505 11,665 − 9,979 = 2 − (2 − 1.699 ) * 0.688 = 2 − 0.207 = 1.793 = 62 years Step 3. Add points to Future Discharges and Damages. Adding more points for the discharge versus return period and damages versus discharge graphs will correct for discrepancies between existing conditions and future adapted conditions. Use the following equations to calculate climate-adapted return periods ( ) for based on Step 1. = log − − * − − = log (500 ) − (500 ) − (100 ) * 15,562 − 13,982 15,562 − 11,665 = 2.699 − (2.699 − 2 ) * 0.405 = 2.699 − (2.699 − 2 ) * 0.405 = 2.699 − 0.283 = 2.416 = 260 years Step 4. Summarize the results in the table below. The results in step 2 and 3 assume that under climate change conditions Tfint1 will have the same flow as Qcmod and Tfint2 will have the same flow as Qcmax. The damages for these newly calculated return periods in Tfint1 and Tfint2 will have the same value as the original periods of Tcmod and Tcmax (i.e., Dcmod and Dcmax).

Current pre-mitigation conditions Future (climate change) pre-resilience Return period Future discharge Interpolated damages Base case future damage increment Return period Damages (in current $) Damage increment Current discharge Tfnd=33 Qfnd= 9,000 Dfnd=0 Dafnd Max return period resulting in no damages Tcnd =50 Dcnd=0 Dacnd=0 Qcnd=9,000 T’fnd= 50 Q’fnd=9,979 D’fnd=1,060,312 D’afnd=5,270 Next level return period resulting in some damages Tcmod=100 Dcmod=1,630,000 Dacmod=8,150 Qcmod=10,505 Tfint1 = 62 Qfint1=10,505 Dfint1= 1,630,000 Dafint1= 8,150 Return period resulting in maximum damages Tcmax=500 Dcmax=3,227,000 Dacmax=19,428 Qcmax=13,982 Tfmod= 100 Qfmod=11,665 Dfmod=2,162,793 Dafmod=16,116 Tfint2 = 260 Qfint2=13,982 Dfint2= 3,227,000 Dafint2=19,428 Tfmax= 500 Qfmax=15,562 Dfmax=3,591,659 Dafmax=23,018 =0

Worksheet for Level 2 Analysis 145 Step 5. Based on Step 4, plot the additional flows and return periods on the log graph (Return Period versus Discharge curve) and the damages and discharges on the second plot (Discharge versus Damages curve) from Level 1 for future conditions for the two additional points. (Graph paper provided on next pages.) Step 6. Next, the analysis adds the impacts that a resilience/adaptation action could have on damages to the asset after the resilience action has been implemented to accommodate the modeled climate change conditions. The analysis assumes that resilience action will eliminate future damages under climate change conditions for the future T’fnd (i.e., same as current level without climate change), and the damages for the post-resilience future Tfmod and Tfmax events (i.e., without climate change). It is assumed that the resilience action taken will restore the climate-adjusted conditions to mirror existing conditions, meaning the post-resilience values of damages for the climate-adjusted 100- and 500-year return periods are assumed to be equal to the level of damages under current conditions. Summarize the assumptions in the table that follows the graph paper.

Current pre-mitigation conditions Future (climate change) pre-resilience Future post-resilience Return period Future discharge Interpolate d damages Base case future damage increment Return period Future discharge Damages (in current $) Base case future damage increment Return period Damages (in current $) Damage increment Current discharge Tfnd=33 Qfnd= 9,000 Dfnd=0 Dafnd= 0 Trnd=33 Qrnd=0 Drnd=0 Darnd=0 Max return period resulting in no damages Tcnd =50 Dcnd=0 Dacnd=0 Qcnd=9,000 T’fnd= 50 Q’fnd=9,979 D’fnd= 1,060,312 D’afnd=5,270 T’rnd=50 Q’rnd= 9,979 D’rnd=0 D’arnd=0 Next level return period resulting in some damages Tcmod= 100 Dcmod= 1,630,000 Dacmod= 8,150 Qcmod= 10,505 Tfint1 = 62 Qfint1=10,505 Dfint1= 1,630,000 Dafint1= 8,150 Trint1=62 Qrmod=10,505 Return period resulting in maximum damages Tcmax= 500 Dcmax= 3,227,000 Dacmax= 19,428 Qcmax= 13,982 Tfmod= 100 Qfmod=11,665 Dfmod= 2,162,793 Dafmod=16,116 Trmod=100 Qrmod=11,665 Drmod= 1,630,000 Tfint2 = 260 Qfint2=13,982 Dfint2= 3,227,000 Dafint2=19,428 Trint2=260 Qrint2=13,982 Tfmax= 500 Qfmax=15,562 Dfmax= 3,591,659 Dafmax=23,018 Trmax=500 Qrmax=15,562 Drmax= 3,227,000

Worksheet for Level 2 Analysis 149 Step 7. Determine the damages for Trint1 using the assumption in Step 6. = + ( − ) * ( − ) − = 0 + (10,505 − 9,979 ) * (1,630,000 − 0 ) 11,665 − 9,979 = 0 + 526 * 1,630,000 1,686 = 0 + 526 * 1,630,000 1,686 = 0 + 508,529 = $508,529 Step 8. Determine the damages for Trint2 using the assumption in Step 6. = + ( − ) * ( − ) − = 1,630,000 + (13,982 − 11,665 ) * (3,227,000 − 1,630,000 ) 15,562 − 11,665 = 1,630,000 + 2,317 * 1,597,000 3,897 = 1,630,000 + 949,512 = $2,579,512 Step 9. Determine the annualized damages for Trint1 using the assumption in Step 6. = + 2 * 1 − 1 = 0 + 508,529 2 * 1 50 − 1 62 = 254,265 * 0.0039 = $984

150 Incorporating the Costs and Benefits of Adaptation Measures in Preparation for Extreme Weather Events and Climate Change—Guidebook Step 11. Determine the annualized damages for Trint2 using the assumption in Step 6. = + 2 * 1 − 1 = 1,630,000 + 2,579,512 2 * 1 100 − 1 260 = 2,104,756 * 0.00615 = $12,952 Step 12. Determine the annualized damages for Trmax using the assumption in Step 6. = + 2 * 1 − 1 = 2,579,512 + 3,227,000 2 * 1 260 − 1 500 = 2,903,256 * 0.00185 = $5,360 Step 10. Determine the annualized damages for Trmod using the assumption in Step 6. = + 2 * 1 − 1 = 508,529 + 1,630,000 2 * 1 62 − 1 100 = 1,069,265 * 0.0061 = $6,554 Step 13. Summarize the results in the table below.

Current pre-mitigation conditions Future (climate change) pre-resilience Future post-resilience Return period Future discharge Interpolated damages Base case future damage increment Future discharge Return period Damages (in current $) Base case future damage increment Return period Damages (in current $) Damage increment Current discharge Tfnd=33 Qfnd= 9,000 Dfnd=0 Dafnd =0 Trnd=33 Qrnd=0 Drnd=0 Darnd=0 Max return period resulting in no damages Tcnd =50 Dcnd=0 Dacnd=0 Qcnd=9,000 T’fnd= 50 Q’fnd=9,979 D’fnd= 1,060,312 D’afnd=5,270 T’rnd=50 Q’rnd= 9,979 D’rnd=0 D’arnd=0 Next level return period resulting in some damages Tcmod= 100 Dcmod= 1,630,000 Dacmod= 8,150 Qcmod= 10,505 Tfint1 = 62 Qfint1=10,505 Dfint1= 1,630,000 Dafint1= 8,150 Trint1=62 Qrmod=10,505 Drint1= 508,529 Darint1=984 Return period resulting in maximum damages Tcmax= 500 Dcmax= 3,227,000 Dacmax= 19,428 Qcmax= 13,982 Tfmod= 100 Qfmod=11,665 Dfmod= 2,162,793 Dafmod=16,116 Trmod=100 Qrmod=11,665 Drmod= 1,630,000 Darmod=6,554 Tfint2 = 260 Qfint2=13,982 Dfint2= 3,227,000 Dafint2=19,428 Trint2=260 Qrint2=13,982 Drint2= 2,579,512 Darint2=12,952 Tfmax= 500 Qfmax=15,562 Dfmax= 3,591,659 Dafmax=23,018 Trmax=500 Qrmax= 5,562 Drmax= 3,227,000 Darmax=5,360

152 Incorporating the Costs and Benefits of Adaptation Measures in Preparation for Extreme Weather Events and Climate Change—Guidebook Step 14. Calculate the total annualized future damages for the post-resilience action by adding the annualized incremental damages for the different return period. = + + + + + = 0 + 0 + 984 + 6,554 + 12,952 + 5,360 = $25,850 Step 15. Multiply the total annualized future damages after resilience measures that have been implemented (Step 14) by the present value factor. = * = 25,850 * 13.801 = $356,756 Step 16. Subtract the post-resilience total damages (Step 15) from the pre-resilience total damages under climate change conditions (Step 22 from Level 1 analysis) to yield the present value of the benefits associated with implementing the resilience measure. = − = 612,820 − 356,756 = $256,064 For the resilience measure to be cost-effective, the net present value of the benefits minus the costs must be greater than 0. So, a resilience measure with an overall cost less than the calculated benefits (Step 16) would be considered cost-effective. Another way of evaluating the results is to use a benefit-cost ratio. If the ratio of the benefits to the costs is greater than 1, the measure is considered to be cost-effective.