1998-2013:
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Er worden 4 hypothese besproken, getoetst en vervolgens weerlegd:
3.1 Hypothesis I: hiatus in temperature trend during 1998–2013
A basic assertion regarding the hiatus is that the steady increase in global surface temperature
around a linear positive trend has stopped, or “paused” (Guemas et al. 2013).
This sentiment is reflected in statements that “Despite a sustained production of anthropogenic
greenhouse gases, the Earth’s mean near-surface temperature paused its rise
during the 2000–2010 period” (Guemas et al. 2013), and that “climate skeptics have
seized on the temperature trends as evidence that global warming has ground to a halt”
(Tollefson 2014). These scientific claims can be turned into a precise statistical null hypothesis:
the slope in the regression line of global temperature on time is zero during the hiatus
period
3.2 Hypothesis II: difference in temperature trends
Otto et al. (2013) state that: “the rate of mean global warming has been lower over the
past decade than previously.” This statement encompasses a second interpretation of the
purported hiatus: that the hiatus represents a “slowdown” of global warming (Chen and
Tung 2014), in which the rate of warming is less during the hiatus compared with the
warming prior to the hiatus (Chen and Tung 2014; Otto et al. 2013; Smith 2013). This
claim can be formulated as a testable statistical hypothesis, where the null hypothesis is
that the regression slope before the hiatus period minus the regression slope during the
hiatus period is zero or negative, versus the alternative hypothesis that this difference
is positive.
We employ three different methods with increasing levels of statistical sophistication
to test this hypothesis. Specific details of the methodology are provided in Supplementary
Section 3.2. First, a standard regression of global temperature on time is fitted to both
the 1998–2013 hiatus period and the period 1950–1997, with errors assumed to be independently
and identically distributed (see Fig. 2 top left panel). The first method yields a
p-value of 0.210. Thus, there is no evidence of a difference in warming trends even at the
10 % significance level. The second method accounts for the temporal dependency in the
global temperature record by using a block bootstrap approach, yielding a p-value of 0.323.
The evidence for a difference in trends is further weakened when temporal dependency
is accounted for. The third approach uses the method of subsampling (Politis et al. 1999;
Rajaratnam et al. 2014) to determine how the current 16-year trend during 1998–2013 compares
against all the previous 16-year trends observed between 1950 and 1997. A p-value of
0.3939 is obtained and evidence for the hiatus is further weakened. From the plots in Fig. 2
(bottom panel), observe that during the 1950–1997 period, there are several 16-year periods
with both higher and lower linear trends. Therefore the observed trend during 1998–2013
does not appear to be anomalous in a historical context.
See Fig. 2 (top right panel) for a summary of results of hypothesis II. Varying the
cut-off year from 1998 to either 1999 or 2000 yields p-values of 0.214 and 0.348, respectively,
for the bootstrap method. Even after properly accounting for temporal dependence,
and undertaking a sensitivity analysis, there is no compelling evidence to suggest that the
slopes are significantly different. We therefore conclude that the rate of warming over the
past ? 15 years is not appreciably different from the rate of warming prior to the recent
period.
3.3 Hypothesis III: hiatus in the mean global temperature
Some claims have simply asserted that the annual mean global temperature has remained
constant since 1998 (versus slowing of the trend in global warming). For example, Kosaka
and Xie (2013) state that “Despite the continued increase in atmospheric greenhouse gas
concentrations, the annual-mean global temperature has not risen in the twenty-first century”,
while Tollefson (2014) states that “Average global temperatures hit a record high in
1998 – and then the warming stalled.” This claim can also be precisely formulated as a
testable statistical hypothesis. The statistical model can be written as xt = ?t + ?t, where t
denotes time (in years), xt is the 1998–2013 global mean temperature anomalies series, ?t
is the mean parameter and ?t is the random noise component(with E(?t ) = 0,Var(?t ) =?2). The corresponding null hypothesis and alternative are given as H0 : E(x1998) =
E(x1998+t ) for t = 1, 2, · · · , 15 versus HA : E(x1998) = E(x1998+t ).
Specific details of the methodology are provided in Supplementary Section 3.3. Hypothesis
III is tested in four different ways. There are two options for determining the value of
E[x1998] = ?1998 : to directly use the observed 1998 temperature record x1998 as a substitute
for ?1998, or to alternatively estimate ?1998 from the regression line from the period
1950–1997. Figure 3 (top panel) illustrates this concept. As the two approaches for specifying
?1998 yield fixed values, the inherent variability therein can be explicitly accounted for
by using the bootstrap. Doing so propagates the variability in a rigorous manner. The table
in Fig. 3 (bottom panel) summarizes the results of testing hypothesis III.
For Method A, when x1998 is used as a substitute for ?1998, the statistical test concludes
that the mean has decreased during the hiatus, and thus strongly favors the hiatus
claim. However, since this one single observed value is not a consistent estimate of ?1998,
the conclusion is not reliable. In Method B when ?1998 is estimated from the 1950–1997
regression line, the null hypothesis is rejected in the opposite direction, suggesting that the
mean temperature has actually increased during the hiatus period. Thus, the selection effect
from choosing 1998 as the reference cut-off year has a tremendous impact on the statistical
conclusion. Method C, which specifically incorporates the variability inherent in estimating
?1998 as x1998 leads to a different conclusion than in Method A. In particular, as soon as the
variability in estimating ?1998 to be x1998 is incorporated, one can no longer reject the null
hypothesis that the mean has remained constant - even when the high value x1998 is used.
Method D uses a value for ?1998 which is estimated from the 1950–1997 regression and Fig. 3 Top panel figure
illustrating how the mean ?1998
can be estimated. Bottom panel
summary table of results for
Hypothesis III with 1998 as start
of hiatus period
1950 1970 1990 2010
-0.2
0.0
0.2
0.4
0.6
0.8
Temperature Anomaly (°C)
x1998
?^
1998
1950-1998
OLS Line
Hypothesis 3
Raw Data
E(x1998) Variability of x1998 Result Remark
Assume fixed
Assume fixed
Simulate by bootstrap
Simulate by bootstrap
Reject H0
Reject H0
Retain H0
Reject H0
decrease in mean
increase in mean
increase in mean
no change in mean
x1998
x1998
^?
1998
^?
1998
Hypothesis 3 with 1998 as start of “hiatus” period:
also incorporates the variability of this estimate. Here the assertion that the mean is either
zero, or has decreased, is rejected.
Given the results of this nuanced analysis, we conclude that claims that the global mean
temperature has not changed in recent decades are not supported by evidence. In addition,
our nuanced analysis gives much needed rigor to the claim that using 1998 as a reference
year amounts to “cherry picking” (Leber 2014; Stover 2014), see also Supplemental Section
for detailed discussions). The results are further validated when the analysis is repeated
with 1999 and 2000 as the starts of the hiatus period (see Supplemental Section 3.3). Note
furthermore that since 2014 was the warmest year on record Karl et al. (2015), ignoring
2014 in our analysis can be viewed as being even more conservative, similar to using 1998
as the starting point.
Fig. 3 Top panel figure
illustrating how the mean ?1998
can be estimated. Bottom panel
summary table of results for
Hypothesis III with 1998 as start
of hiatus period
1950 1970 1990 2010
-0.2
0.0
0.2
0.4
0.6
0.8
Temperature Anomaly (°C)
x1998
?^
1998
1950-1998
OLS Line
Hypothesis 3
Raw Data
E(x1998) Variability of x1998 Result Remark
Assume fixed
Assume fixed
Simulate by bootstrap
Simulate by bootstrap
Reject H0
Reject H0
Retain H0
Reject H0
decrease in mean
increase in mean
increase in mean
no change in mean
x1998
x1998
^?
1998
^?
1998
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