Synthetic detection-and-attribution explorer

This page shows a simplified zero-dimensional attribution problem. The observed time series could be something like annual maximum 1-day rainfall averaged over a region. The model asks whether that observed record contains the greenhouse-gas fingerprint, the aerosol fingerprint, the volcano fingerprint, or some combination of them.

y(t) = βGHGG(t) + βAERA(t) + βVOLCV(t) + ε(t)

This version uses one synthetic observed time series: GHG + aerosol + volcano. Move the sliders. Your goal is to make the green line, which is the fitted sum of the fingerprints, best approximate the black line, which is the synthetic observation. The best visual fit also minimizes the RMS error.

The best you can do is an RMS error of --. The box below shows the potential improvement: the current RMS error minus the best possible RMS error. Your goal is to get this value as close to zero as possible.

The left panel shows the individual scaled fingerprints: βGHGG(t), βAERA(t), and βVOLCV(t). These curves change as you move the sliders. The right panel shows the synthetic observation in black and the fitted sum, βGHGG(t) + βAERA(t) + βVOLCV(t), in green.

Observed time series

GHG + aerosol + volcano attributed signal

GHG coefficient, βGHG
Value 0.00
Aerosol coefficient, βAER
Value 0.00
Volcano coefficient, βVOLC
Value 0.00
Potential improvement
0.00
Current RMS error minus best possible RMS error
βGHGG(t) βAERA(t) βVOLCV(t) Observed time series Sum of fitted fingerprints

The fingerprints and observations are synthetic. The aerosol fingerprint is designed to increase until 1970 and decrease after 1970. The volcano fingerprint has three short pulses, beginning in 1963, 1982, and 1992, and each lasts three years. The left panel shows the fingerprints after multiplying by the selected coefficients. In a real study, the fingerprints would come from climate-model ensembles.