# Overview ✏️ {.unnumbered}


## Introduction to climate hazards

Understanding climate hazards requires grappling with their unique characteristics that distinguish them from typical engineering and statistical problems.

### Motivating Examples

#### Paraguay Floods, 2015

The Paraguay River reached extreme flood levels in 2015, inundating large portions of Asunción and displacing thousands of residents.
This event illustrated how hydrologic extremes can have cascading impacts on urban infrastructure and vulnerable populations.

#### Texas Cold Snap, 2021

An unprecedented winter storm brought sub-zero temperatures to Texas in February 2021, causing widespread power outages and infrastructure failures.
The event highlighted vulnerabilities in systems designed for typical climatic conditions but unprepared for extreme deviations.

### Decision-Making Under Climate Uncertainty

**Bayesian Decision Theory** provides a framework for climate risk management.
The expected reward (or loss) for taking decision $a$ is:

$$
\mathbb{E}(R(a)) = \int_{\mathcal{S}} R(a, \mathbf{s}) p(\mathbf{s}) d\mathbf{s}
$$

**Crucial insight**: Jensen's inequality tells us that:
$$
\mathbb{E}(R(a)) \neq R(a, \mathbb{E}(\mathbf{s}))
$$

This means we cannot simply use average climate conditions to assess risks - the full distribution of possible outcomes matters.

### What Makes Climate Data Unique?

Climate hazards exhibit several characteristics that complicate traditional statistical analysis:

#### Fat Tails
Extreme events occur more frequently than normal distributions would suggest.
The tails of climate distributions often follow power-law or heavy-tailed behavior.

#### Quasi-periodic Oscillations
Climate systems exhibit variability on multiple timescales, from seasonal cycles to multi-decadal oscillations like the Atlantic Multidecadal Oscillation (AMO) and Pacific Decadal Oscillation (PDO).

#### Nonstationarity
Climate statistics are changing over time due to anthropogenic forcing, making historical records insufficient for future risk assessment.
The assumption that "the past is prologue" breaks down.

#### Multi-scale Temporal Variations
Climate hazards vary simultaneously on daily, seasonal, interannual, and multidecadal timescales.
This temporal complexity requires sophisticated modeling approaches.

#### Spatial Structure
Climate extremes exhibit complex spatial dependencies and teleconnections.
Events in one region can influence conditions thousands of kilometers away through atmospheric and oceanic circulation patterns.

#### Emphasis on Extremes
For risk assessment, we care most about rare, high-impact events that occur in the tails of distributions.
Traditional statistical methods focused on central tendencies are insufficient.

### Deep Uncertainty

Many aspects of climate risk involve "deep uncertainty" - situations where we don't know the probability distributions, the set of possible outcomes, or even which models are appropriate.
This requires robust decision-making approaches that perform well across multiple plausible futures.

## How to use this Part

- There are LOTS of fantastic stats, optimization, and Earth science resources, but they are often very narrowly tailored
- This section is NOT designed to be comprehensive. Provides an overview of fundamental concepts, then works through a couple of example methods and then points to resources for other methods.
- A course could work through these chapters in order, but it may make more sense to pick and choose, or to refer to them in the context of other chapters.
