Bob Tisdale, author of the awesome book “Who Turned on the
Heat?” presented an interesting problem that turns out to be a
good application of robust statistical tests called empirical
fluctuation processes. Bob notes that sea surface temperature
(SST) in a large region of the globe in the Eastern Pacific does
not appear to have warmed at all in the last 30 years, in
contrast to model simulations (CMIP SST) for that region that
show strong warming. The region in question is shown below. The
question is, what is the statistical significance of the
difference between model simulations and the observations? The
graph comparing the models with observations from Bob’s book
shows two CMIP model projections strongly increasing at 0.15C
per decade for the region (brown and green) and the observations
increasing at 0.006C per decade (magenta). However, there is a
lot of variability in the observations, so the natural question
is whether the difference is statistically significant? A
simple-minded approach would be to c