2.7 Has Climate Variability, or have Climate Extremes,
Changed?
2.7.1 Background
Figure 2.32: Schematic showing the effect on extreme temperatures when
(a) the mean temperature increases, (b) the variance increases, and (c)
when both the mean and variance increase for a normal distribution of temperature. 
Changes in climate variability and extremes of weather
and climate events have received increased attention in the last few years.
Understanding changes in climate variability and climate extremes is made difficult
by interactions between the changes in the mean and variability (Meehl et al.,
2000). Such interactions vary from variable to variable depending on their statistical
distribution. For example, the distribution of temperatures often resembles
a normal distribution where nonstationarity of the distribution implies changes
in the mean or variance. In such a distribution, an increase in the mean leads
to new record high temperatures (Figure 2.32a),
but a change in the mean does not imply any change in variability. For example,
in Figure 2.32a, the range between the hottest
and coldest temperatures does not change. An increase in variability without
a change in the mean implies an increase in the probability of both hot and
cold extremes as well as the absolute value of the extremes (Figure
2.32b). Increases in both the mean and the variability are also possible
(Figure 2.32c), which affects (in this example)
the probability of hot and cold extremes, with more frequent hot events with
more extreme high temperatures and fewer cold events. Other combinations of
changes in both mean and variability would lead to different results.
Consequently, even when changes in extremes can be documented, unless a specific
analysis has been completed, it is often uncertain whether the changes are caused
by a change in the mean, variance, or both. In addition, uncertainties in the
rate of change of the mean confound interpretation of changes in variance since
all variance statistics are dependent on a reference level, i.e., the mean.
For variables that are not well approximated by normal distributions, like
precipitation, the situation is even more complex, especially for dry climates.
For precipitation, for example, changes in the mean total precipitation can
be accompanied by other changes like the frequency of precipitation or the shape
of the distribution including its variability. All these changes can affect
the various aspects of precipitation extremes including the intensity of precipitation
(amount per unit time).
This section considers the changes in variability and extremes simultaneously
for two variables, temperature and precipitation. We include new analyses and
additional data compiled since the SAR which provide new insights. We also assess
new information related to changes in extreme weather and climate phenomena,
e.g., tropical cyclones, tornadoes, etc. In these analyses, the primary focus
is on assessing the stationarity (e.g., the null hypothesis of no change) of
these events, given numerous inhomogeneities in monitoring.
