Aviation and the Global Atmosphere

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6.6.2. Uncertainties and Confidence Intervals

Throughout this report, we focus on "best estimates" for each component of atmospheric perturbations caused by aircraft and then of subsequent climate forcing or ultraviolet change. We also try to understand the confidence that we have in these estimates using uncertainty ranges deduced in Chapters 2, 3, and 4 and those from the modeling and combining of RF in this chapter.

Uncertainties in estimating aviation's RF values are addressed with a confidence interval (indicated by error bars or whiskers about each best value) and a description ("good," "fair," "poor," "very poor") of the level of scientific understanding of the physical processes, models, and data on which the calculation is based. The confidence intervals shown in Figures 6-14b and 6-15b define a likelihood range such that the probability that the true value falls within the interval is 2/3. The interval and the quality-of-the-science descriptions are, to a large extent, independent measures covering different aspects of uncertainty.

The likelihood range is defined consistently within this report as the 2/3 or 67% probability range. These probability ranges are meant to be symmetric about the best value; hence, the best value is not always the mean of the upper and lower values. In this case, the probability that the value is less than the lower value is 16%, and the probability that it is less than the upper value is 84%. The range between the low and high values is equivalent to the "1-sigma" range of a normal (i.e., Gaussian) probability distribution. Unfortunately, derivation of these confidence intervals lies with the expert judgment of the scientists contributing to each chapter and may include a combination of objective statistical models and subjective expertise. Thus, the 67% confidence intervals do not imply a specific statistical model and, for example, cannot be used to infer the probability of extreme events beyond the stated confidence interval.

The confidence interval in RF stated here combines uncertainty in calculating atmospheric perturbation to greenhouse gases and aerosols with that of calculating radiative forcing. It includes, but is not based solely on, the range of best values from different research groups. For example, the interval for the HSCT(1000) impact on O3 was derived from high- and low-end calculations using different combinations of atmospheric models and chemical assumptions. The range in RF from these stratospheric O3 perturbations was expanded further in this chapter to account for the difficulty in calculating RF for stratospheric perturbations. The tropospheric O3 perturbation from the subsonic fleet (scenario Fa1) was presented with the 67% confidence interval as a factor of 2 higher and lower than the best value. In this case, the RF calculation did not significantly add to the uncertainty because tropospheric perturbations can be more accurately calculated. The confidence interval for aviation-induced CH4 changes is believed to be about 1.5 times larger (log-scale) than that for tropospheric O3, but potential errors in both are highly correlated. The confidence interval for contrails is taken directly from Chapter 3; the RF from additional cirrus clouds is highly uncertain and no probability range is given.

The RF uncertainties from different perturbations have been determined by different methods; potential errors in individual components may not be independent of one another, and the error bars may not represent Gaussian statistics. The uncertainty ranges for the totals in Figures 6-14b and 6-15b do represent a 2/3 probability range as for the individual components. The uncertainty estimate for the total radiative forcing (without additional cirrus) is calculated directly from the individual components as the square root of the sums of the squares of the upper and lower ranges. There is a further issue on confidence levels that is not quantified here-namely, the accuracy of representing the climate perturbation by the sum of RF values that are global means.

Overall, addition of the best values for RF provides a single best estimate for the total. The uncertainty ranges for individual impacts can be used to assess whether they are potentially major or trivial components and to make a subjective judgment of confidence in the summed RF.

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