Quantifying the effect of interannual ocean variability on the attribution of extreme climate events to human influence

Abstract

In recent years, the climate change research community has become highly interested in describing the anthropogenic influence on extreme weather events, commonly termed “event attribution.” Limitations in the observational record and in computational resources motivate the use of uncoupled, atmosphere/land-only climate models with prescribed ocean conditions run over a short period, leading up to and including an event of interest. In this approach, large ensembles of high-resolution simulations can be generated under factual observed conditions and counterfactual conditions that might have been observed in the absence of human interference; these can be used to estimate the change in probability of the given event due to anthropogenic influence. However, using a prescribed ocean state ignores the possibility that estimates of attributable risk might be a function of the ocean state. Thus, the uncertainty in attributable risk is likely underestimated, implying an over-confidence in anthropogenic influence. In this work, we estimate the year-to-year variability in calculations of the anthropogenic contribution to extreme weather based on large ensembles of atmospheric model simulations. Our results both quantify the magnitude of year-to-year variability and categorize the degree to which conclusions of attributable risk are qualitatively affected. The methodology is illustrated by exploring extreme temperature and precipitation events for the northwest coast of South America and northern-central Siberia; we also provides results for regions around the globe. While it remains preferable to perform a full multi-year analysis, the results presented here can serve as an indication of where and when attribution researchers should be concerned about the use of atmosphere-only simulations.

Appendices

Appendix 1: Details for the derivation of the confidence interval of $\phi _p$

Recall the setting introduced in Sect. 7, the goal being to make a confidence statement regarding the population distribution of risk from all possible years, using only a risk estimate from a single year.

The sampling distribution of $\widehat{\xi }_t$ conditional on $\mu$ is derived as follows. Again, recall that the sampling distribution of $\widehat{\xi }_t$ conditional on $\xi _t$ is $N(\xi _t, \nu ^2/n):$ also $\xi _t \sim N(\mu , \sigma ^2).$ The sampling distribution of interest is calculated by averaging over $\xi _t:$

$$\begin{aligned} p(\widehat{\xi }_t | \mu ) = \int _{\xi _t} p(\widehat{\xi }_t | \xi _t) p(\xi _t | \mu ) d\xi _t, \end{aligned}$$

where the implicit conditioning on $\nu ^2$ and $\sigma ^2$ is suppressed in the notation. Given that $p(\widehat{\xi }_t | \xi _t) = N(\xi _t, \nu ^2/n)$ and $p(\xi _t | \mu ) = N(\mu , \sigma ^2),$ the closed-form solution is well-known (this setup is identical to the derivation for the marginal distribution of the data in a Normal-Normal Bayesian posterior calculation). The result is that

$$\begin{aligned} p(\widehat{\xi }_t | \mu ) = N(\mu , \nu ^2/n + \sigma ^2). \end{aligned}$$

(12)

Next, to derive a confidence interval for $\phi _p,$ first note that using (12) we can obtain a $100(1-\alpha )\%$ confidence interval for $\mu$ as

$$\begin{aligned} \left( \widehat{\xi }_t - z_{\alpha /2} \sqrt{\nu ^2/n + \sigma ^2}, \widehat{\xi }_t + z_{\alpha /2} \sqrt{\nu ^2/n + \sigma ^2}\right) . \end{aligned}$$

Because $\phi _p = f(\mu ) = \mu + c_p\sqrt{\nu ^2/n + \sigma ^2}$ is a linear function of $\mu$, statistical theory says that $f(\widehat{\xi }_t) \sim N\big (f(\mu ), \text {Var}[f(\widehat{\xi }_t)]\big ),$ so that a $100(1-\alpha )\%$ confidence interval for $\phi _p = f(\mu )$ is

$$\begin{aligned} \left( f(\widehat{\xi }_t) - z_{\alpha /2} \sqrt{\text {Var} [f(\widehat{\xi }_t)]}, f(\widehat{\xi }_t) + z_{\alpha /2}\sqrt{\text {Var}[f(\widehat{\xi }_t)]} \right) . \end{aligned}$$

Since $\text {Var}[f(\widehat{\xi }_t)] = \text {Var}\widehat{\xi }_t = \nu ^2/n + \sigma ^2,$ the confidence interval for $\phi _p$ is

$$\begin{aligned} \left( \left[ \widehat{\xi }_t - c_p\sqrt{\nu ^2/n + \sigma ^2}\right] - z_{\alpha /2}\sqrt{\nu ^2/n + \sigma ^2}, \left[ \widehat{\xi }_t - c_p\sqrt{\nu ^2/n + \sigma ^2}\right] + z_{\alpha /2}\sqrt{\nu ^2/n + \sigma ^2} \right) \end{aligned}$$

or

$$\begin{aligned} \left( \widehat{\xi }_t + (c_p - z_{\alpha /2}) \sqrt{\nu ^2/n + \sigma ^2}, \widehat{\xi }_t + (c_p + z_{\alpha /2}) \sqrt{\nu ^2/n + \sigma ^2} \right) , \end{aligned}$$

which is what is given in (10).

Appendix 2: Supplemental Figures

See Figs. 13, 14 and 15.