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
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.