Question 1

What kind of model actually runs behind this simulation?

Accepted Answer

Each of the N ensemble members is an independent Ornstein-Uhlenbeck process: a mean-reverting stochastic differential equation, discretized to annual steps, of the form X(t+1) = X(t) + theta*(mu(t) - X(t)) + sigma*Z, where Z is a fresh standard-normal random draw for every member at every year. The equilibrium mu(t) rises linearly over time according to the warming-drift slider, representing the deterministic forced-warming component of a climate scenario, while theta (mean reversion) and sigma (volatility) control how strongly and how noisily each path tracks that moving target. This is a genuine multi-path Monte Carlo simulation computed live in JavaScript, not a pre-rendered animation.

Question 2

How is the shaded percentile band computed?

Accepted Answer

At every simulated year, the current temperature-anomaly value of all N ensemble members is collected, sorted numerically, and the 10th and 90th percentile values are read directly out of that sorted array -- exactly the same empirical-percentile method used in real ensemble climate projections (e.g. CMIP-style spread plots). The band is therefore recomputed from the live ensemble at every year of the projection, not interpolated from a fixed formula, so changing the ensemble size, drift, or volatility sliders and resampling immediately reshapes the band you see.

Question 3

What does the extreme-risk exceedance probability represent?

Accepted Answer

The histogram panel bins the anomaly values of every ensemble member at the current projection year, then counts what fraction of members currently sit above your chosen extreme-risk threshold. That fraction, expressed as a percentage, is a direct empirical estimate of the probability that the region's climate risk exceeds the extreme threshold in that year -- the same logic climate-risk models use to translate an ensemble spread into an exceedance probability for insurers, planners, or infrastructure engineers.

Question 4

Why do individual paths look noisy while the band narrows and widens?

Accepted Answer

Each path is subject to independent random annual shocks (the volatility parameter), so no single path is a reliable forecast on its own -- that is precisely why ensembles are used. The percentile band's width reflects the ensemble's collective uncertainty: higher volatility or weaker mean reversion widens it, since paths diverge more from the shared equilibrium trend, while a large ensemble size gives a more stable, less noisy estimate of where those percentiles actually sit.

Question 5

How do the drift, volatility, and mean-reversion sliders interact?

Accepted Answer

Drift sets how fast the shared equilibrium anomaly rises per decade, representing the forced warming signal from greenhouse-gas scenarios. Volatility sets the size of each year's random shock, representing natural climate variability (ENSO-like swings, volcanic aerosols, weather noise). Mean reversion sets how strongly each path is pulled back toward the equilibrium after a shock -- a higher value keeps paths tightly clustered around the trend, while a lower value lets shocks persist and paths wander further before correcting, producing a much wider ensemble spread over time.

Question 6

Is this the same approach used by real climate-risk models?

Accepted Answer

The core methodology -- running many stochastic realizations forward and reading empirical percentiles and exceedance probabilities off the live ensemble -- mirrors how real climate-risk and financial-risk models quantify uncertainty (CMIP multi-model ensembles, catastrophe models, and Monte Carlo risk simulations all work this way). The specific process here (a single-variable Ornstein-Uhlenbeck anomaly with linear drift) is a simplified teaching model rather than a full coupled climate model with multiple physical variables, regional grids, and calibrated forcing scenarios, so treat it as a faithful illustration of ensemble-projection mechanics rather than an operational forecast.

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