Lecture

2023-08-23

Today

What questions will we answer?

Case study: storm surge

Wrapping up

- Rainfall-runoff model
- e.g., peak flow from rational method: \(Q = CiA\)
- \(i\) is rainfall intensity, \(A\) is area, and \(C\) is runoff coefficient

- Design rainfall based on
*return period*\(T\)- \(p(i > i^*) = 1/T\)

- Size your culvert to handle \(Q^* = Ci^*A\)
- Requires knowing \(p(i)\)!

- Analyze historical streamflow data at a gauge
- Take the 99th percentile (100 year
*return level*) of*annual maximum*streamflows - Use a hydraulic model to model where the water goes

- Consider \(N\) years of inflows (and releases, evaporation, etc)
- Count number of times reservoir is empty (“failure”)
- Repeat experiment many different times with different inflows
**If**you are sampling this from \(p(\text{inflow})\), you can estimate the reliability*Monte Carlo*method- Why not just use observed inflows?

- Index insurance: if some index \(I\) is above a threshold \(I^*\), pay out \(X\)
- Total rainfall in a season, area flooded, etc

- Let \(p^* = p(I > I^*)\) is the probability of a payout
- Naive pricing: \(R = p^* X\)
- Risk premium: \(R = X \left( \mathbb{E}[p^*] + \lambda \mathbb{V}^{1/2}[p^*] \right)\)

- Seasonal electricity resource adequacy (Doss-Gollin et al., 2021)
- Levee design (Garner & Keller, 2018)
- Water supply planning (Fletcher et al., 2019)
- Multihazard design (Bruneau et al., 2017)
- etc…

All of these workflows are slightly simplified, but communicate the main idea. For each of these motivating problems, we need to know the probability distribution of some hazard – \(p(\bf{s})\) to use our notation from last class

Today

What questions will we answer?

Case study: storm surge

Wrapping up

You are designing a storm surge barrier on Galveston Bay. What is the probability distribution of storm surge at your location?

This knowledge will help you trade off the cost of the barrier against the residual risk of flooding.

Take a moment, write, and then share

Can we use models to create a longer “synthetic” record?

If we’re going to generate *synthetic storms*, we need to model the wind and rainfall fields (and other boundary conditions) in order to model the storm surge (using Adcirc, GeoClaw, SFINCS, etc)

What separates the scenarios? To first order:

- How much \(CO_2\) we emit
- How much the climate system warms in response to \(CO_2\) (
*climate sensitivity*) - Ice sheet response to temperatures

Sobel et al. (2023):

Models are incorrectly simulating the equatorial Pacific response to greenhouse gas warming. This implies that projections of regional tropical cyclone activity may be incorrect as well

- Historical data
- Measures what we care about
- Sampling uncertainty
- Doesn’t account for future conditions

- Model simulations
- Can account for future conditions
- May be biased or inaccurate
- Model structure uncertainty

Today

What questions will we answer?

Case study: storm surge

Wrapping up

- Return period
- Return level
- Monte Carlo
- Synthetic record
- Climate sensitivity

You should also be able to reason about the merits and limitations of different *methodologies* for estimating the probability distribution of a hazard (more practice incoming!)

Friday:

- Bring your laptop, if you have one.
- Create an account at https://github.com/

I will be absent on Friday (visiting Harris County Flood Control District). Yuchen will lead lab 01.

Bloemendaal, N., Haigh, I. D., de Moel, H., Muis, S., Haarsma, R. J., & Aerts, J. C. J. H. (2020). Generation of a global synthetic tropical cyclone hazard dataset using STORM. *Scientific Data*, *7*(1, 1), 40. https://doi.org/10.1038/s41597-020-0381-2

Bruneau, M., Barbato, M., Padgett, J. E., Zaghi, A. E., Mitrani-Reiser, J., & Li, Y. (2017). State of the art of multihazard design. *Journal of Structural Engineering*, *143*(10), 03117002. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001893

Doss-Gollin, J., Farnham, D. J., Lall, U., & Modi, V. (2021). How unprecedented was the February 2021 Texas cold snap? *Environmental Research Letters*. https://doi.org/10.1088/1748-9326/ac0278

Fletcher, S., Lickley, M., & Strzepek, K. (2019). Learning about climate change uncertainty enables flexible water infrastructure planning. *Nature Communications*, *10*(1), 1782. https://doi.org/10.1038/s41467-019-09677-x

Garner, G. G., & Keller, K. (2018). Using direct policy search to identify robust strategies in adapting to uncertain sea-level rise and storm surge. *Environmental Modelling & Software*, *107*, 96–104. https://doi.org/10.1016/j.envsoft.2018.05.006

Kleiber, W., Sain, S., Madaus, L., & Harr, P. (2023). Stochastic tropical cyclone precipitation field generation. *Environmetrics*, *34*(1), e2766. https://doi.org/10.1002/env.2766

Sobel, A. H., Lee, C.-Y., Bowen, S. G., Camargo, S. J., Cane, M. A., Clement, A., et al. (2023). Near-term tropical cyclone risk and coupled Earth system model biases. *Proceedings of the National Academy of Sciences*, *120*(33), e2209631120. https://doi.org/10.1073/pnas.2209631120