Island City On a Wedge

Paper Discussion

Dr. James Doss-Gollin

Wednesday, February 4, 2026

Galveston, 1900

Target: 1:00. Open with the deadliest natural disaster in US history. Don’t linger—move to the problem they faced.

Source: Galveston Historical Foundation

September 8, 1900: Category 4 hurricane, 8,000+ deaths

The response:

• 17-foot seawall (still standing)
• Raised the entire city by up to 17 feet
• Moved thousands of buildings

The question: Build a wall? Raise the land? Retreat? All three?

ICOW: The Middle Path

Target: 1:03. Introduce ICOW as the solution.

ICOW = Island City On a Wedge (Ceres et al., 2019)

• Fast: evaluate millions of strategy combinations
• Rich: graduated damage (not binary)
• Flexible: portfolios of defenses (wall + retreat + elevate)

Key insight: You don’t need every street corner—just the right abstraction.

How ICOW Works

Target: 1:07. High-level overview of inputs and outputs. We’ll unpack each piece over the next slides.

ICOW takes city geometry + defense choices → computes expected damages. Source: Ceres et al. (2019)

The Wedge Geometry

Today

1. The Wedge Geometry

2. The Economics

3. Activity: Map Your City

Picture a Coastal City

Target: 1:08. Build intuition for why the wedge is a good abstraction. The ICOW paper uses Lower Manhattan as its case study.

The ICOW paper was modeled after Lower Manhattan. Source: Ceres et al. (2019)

What do coastal cities share?

• Waterfront at low elevation
• Terrain rises inland
• Density highest near water

The Wedge Abstraction

Target: 1:10. Explain the geometry. These are the parameters students will estimate in the activity.

The wedge geometry captures essential features. Source: Ceres et al. (2019)

What Gets Flooded?

Target: 1:12. Use the wedge figure to build intuition about zone-based damage. Pause after each question to let students think before revealing answer.

Source: Ceres et al. (2019)

If water reaches Zone 4—what’s the damage?

→ Three zones underwater (large fraction of city value)

If water reaches Zone 3?

→ Zero… unless the dike fails

What happens when dikes fail?

Key Parameters

Target: 1:14. These are the parameters you’ll estimate in the activity. Values are from the ICOW paper—ask students if they seem reasonable.

Parameter	Symbol	Meaning
Maximum elevation	\(H_{\text{city}}\)	How high does the city rise?
City depth	\(D_{\text{city}}\)	How far inland does the city extend?
Coastline length	\(W_{\text{city}}\)	How long is the waterfront?
Seawall height	\(H_{\text{seawall}}\)	Existing protection height

From the paper (Manhattan): \(H_{\text{city}} \approx 17\) m, \(D_{\text{city}} \approx 2\) km, \(W_{\text{city}} \approx 43\) km

Do these seem reasonable? (We’ll check in the activity.)

The Five Defense Levers

Target: 1:15. Key vocabulary. Students don’t need to memorize—just recognize.

Lever	What it does	Real-world example
Withdrawal (\(W\))	Vacate low-lying land	Managed retreat, buyouts
Dike Base (\(B\))	Where the wall starts	Seawall location
Dike Height (\(D\))	How tall the wall is	Seawall height
Resistance Height (\(R\))	Flood-proof buildings	Elevating structures
Resistance Fraction (\(P\))	What % of buildings	Retrofit programs

The key constraint: \(W + B + D \leq H_{\text{city}}\)

You can’t withdraw past the city limits, and you can’t build a dike taller than the land behind it.

The Economics

Today

1. The Wedge Geometry

2. The Economics

3. Activity: Map Your City

Damage Isn’t Binary

Target: 1:17. Contrast with simple models. Key insight: damage depends on what’s underwater and how deep.

Simple models say: flood = total loss, no flood = zero.

Reality: A 1-foot flood ruins your carpet. A 10-foot flood destroys the structure.

ICOW computes damage based on volume flooded:

\[\text{Damage} = \text{Zone Value} \times \frac{\text{Volume Flooded}}{\text{Total Volume}} \times 0.39\]

The 0.39 is an empirically-derived depth-damage parameter: the fraction of zone value destroyed at full inundation (from flood damage curves).

This connects to Monday’s EAD formula (Week 4 lecture)—but now we can compute damage for any surge height.

Dikes Aren’t Perfect

Target: 1:19. The fragility curve is intuitive. This creates interesting risk trade-offs.

A dike doesn’t magically hold until overtopped, then fail.

Fragility curve: Failure probability ramps up as water approaches the crest

• Water below 95% of crest: very low failure probability
• Water at 95%+: failure probability ramps linearly
• At 100%: certain overtopping

The levee effect: People behind dikes often don’t evacuate. If the dike fails, they’re caught off guard. ICOW models this: damage behind a failed dike is 1.3× worse than open flooding.

Activity: Map Your City

Today

1. The Wedge Geometry

2. The Economics

3. Activity: Map Your City

The Task

Target: 1:21. Clear instructions. Make sure everyone has Google Maps open.

Work in pairs. Use Google Maps to estimate ICOW geometry parameters for a real coastal city.

You’ll need:

• Google Maps with terrain view
• ICOW.jl documentation: https://dossgollin-lab.github.io/ICOW.jl/equations.html#parameters

Make a Prediction

Target: 1:23. Quick prediction to create cognitive investment before the activity. Have students write down a guess before seeing any data.

Before we look anything up—take 30 seconds:

Which city do you think has the steepest geometry? (highest \(H_{\text{city}}/D_{\text{city}}\) ratio)

• Miami Beach
• Galveston
• New Orleans

• Rotterdam
• Mumbai
• Venice

Write down your guess. We’ll check later.

Pick a City

Target: 1:25. Assign cities if students hesitate: “Table 1 takes Miami, Table 2 takes Rotterdam…”

• Galveston, TX
• Miami Beach, FL
• New Orleans, LA
• Boston, MA

• Mumbai, India
• Jakarta, Indonesia
• Lagos, Nigeria
• Shanghai, China

• Rotterdam, Netherlands
• Venice, Italy
• Ho Chi Minh City
• Your hometown?

Estimate These Parameters

Target: 1:27. Give 6 minutes for estimation. Students need ALL four parameters for Friday’s lab.

Circulate and address common issues: - “Where does the city end?” → Focus on the flood-prone coastal zone, not the whole metro area - “I can’t find elevation” → Try Google Earth, or search “[city] topography” - “What’s a seawall?” → Any hard barrier at the water’s edge - “My city has no seawall” → Use 0m. The model handles this—it just means no existing protection. - “The terrain isn’t really a wedge” → Focus on the flood-prone coastal zone, not the whole metropolitan area. Most waterfronts approximate a wedge locally.

Parameter	How to Estimate
\(H_{\text{city}}\)	Elevation change: waterfront → highest urban point
\(D_{\text{city}}\)	Horizontal distance: waterfront → highest point
\(W_{\text{city}}\)	Length of exposed coastline
\(H_{\text{seawall}}\)	Existing protection height (search online)

Tools: Google Maps terrain view, Google Earth elevation, Wikipedia

You’ll need all four parameters for Friday’s lab!

Share Out

Target: 1:33. Call time. Facilitate cross-table comparisons. Look for interesting contrasts (e.g., Miami vs. Rotterdam, steep vs. flat cities).

Pair up with a table that studied a different city:

1. Compare your \(H_{\text{city}}/D_{\text{city}}\) ratios
2. Which city is steeper? Which is flatter?
3. What does that imply for dike strategy?

Class discussion: A steep city vs. a flat city—who benefits more from a 3m dike?

Key Takeaways

Target: 1:41. Debrief: “Notice how different geometries suggest different strategies.”

1. ICOW abstracts complex cities into a few key parameters
2. The wedge geometry captures essential physics: higher surges flood more area
3. Different cities → different optimal strategies
4. Friday’s lab: You’ll use ICOW.jl to compute EAD for a single year

Preview: Friday’s Lab

Target: 1:44. Brief preview.

Friday we’ll implement single-year EAD analysis:

• Use the same parameters you estimated today
• Add a storm surge distribution
• Compute expected annual damage
• Explore how the five levers change EAD

One More Thing…

Target: 1:47. Hook for Friday—leave them thinking.

Rotterdam is 6 meters below sea level.

How does ICOW even work there?

(We’ll find out Friday.)

References

Ceres, R. L., Forest, C. E., & Keller, K. (2019). Optimization of multiple storm surge risk mitigation strategies for an island City On a Wedge. Environmental Modelling & Software, 119, 341–353. https://doi.org/10.1016/j.envsoft.2019.06.011