Equation 1 · Attribution: Tying One Event to a Changing Climate
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol p_1
is one of the signed contributions combined to compute the quantity on the left.
Symbol p_0
is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Denominator: PR
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
The standard output is a probability ratio, also called a risk ratio, comparing the annual probability of the event in the factual climate with its probability in the counterfactual one [ 3 ] . Writing those probabilities as the factual and counterfactual annual exceedance probabilities, . The fraction of attributable risk is a monotone transform of the ratio and contains no additional information. Its name invites a misreading that the field has warned about for two decades: it is not the probability that this event was caused by forcing, and it does not license the statement that a given fraction of the damage was anthropogenic in any individual case. It is a…
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The standard output is a probability ratio, also called a risk ratio, comparing the annual probability of the event in the factual climate with its probability in the counterfactual one [ 3 ] . Writing those probabilities as the factual and counterfactual annual exceedance probabilities, . The fraction of attributable risk is a monotone transform of the ratio and contains no additional information. Its name invites a misreading that the field has warned about for two decades: it is not the probability that this event was caused by forcing, and it does not license the statement that a given fraction of the damage was anthropogenic in any individual case. It is a population-level quantity, and Lloyd and Shepherd’s central methodological point is that population-level attributions do not transfer to singular events without further argument [ 6 ] .
Sources cited in the surrounding passage
- [3] A protocol for probabilistic extreme event attribution analyses ↗
- [6] Foundations of attribution in climate-change science ↗
These citations give research context. Read each source to check which claims it supports.
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