[Vision2020] Moscow, Russia July 2010 Heat Wave: "On record-breaking extremes" & Food Prices/Arab Spring

[Ted Moffett]

Interesting analysis below, "On record-breaking extremes," from
Realclimate.org, implying that the Moscow, Russia heat wave of July 2010,
that hit a large area in Russia, and internationally raised some food
prices due to negative agricultural impacts, that some have linked to the
so called "Arab Spring" uprisings (reference below), is part of a trend of
increasing record events, that might be of interest to computer code
wizards (not I), from Stefan Rahmstorf, author of the following 2009
Proceedings of the National Academy of Sciences article on sea level rise
projections to 2100.  I found it coincidentally surprising that this
afternoon I relocated a thermometer out of the path of sun light, to avoid
this direct exposure causing a false air temperature reading, then I just
read the following comment from the "On record-breaking extremes" article
below:
"Apart from the urban adjustment problems discussed in our previous
post<http://www.realclimate.org/index.php/archives/2011/10/the-moscow-warming-hole/>,
there is the possibility for a large warm bias during warm sunny summers in
the earlier part, because thermometers were then not shaded from reflected
sunlight – a problem that has been well-documented for pre-1950 instruments
in France (Etien et al., Climatic Change
2009<http://www.springerlink.com/content/j1324173k4843207/>).
"

I also found the following comment from the same article amusing:

"Next, pretend you are one of those alarmist politicized scientists who
allegedly abound in climate science (surely one day I’ll meet one). "  You
think of a cunning trick: how about hyping up the number of records by
ignoring the first, cooling half of the data? Only use the second half of
the data in the analysis, this will get you a strong linear warming trend
instead of zero trend! "
-------------------------
 Global sea level linked to global temperature

   1. Martin Vermeer<http://www.pnas.org/search?author1=Martin+Vermeer&sortspec=date&submit=Submit>
   a <http://www.pnas.org/content/106/51/21527#aff-1>,1<http://www.pnas.org/content/106/51/21527#corresp-1>and
   2. Stefan Rahmstorf<http://www.pnas.org/search?author1=Stefan+Rahmstorf&sortspec=date&submit=Submit>
   b <http://www.pnas.org/content/106/51/21527#aff-2>

http://www.pnas.org/content/106/51/21527
"...projects a sea-level rise ranging from 75 to 190 cm for the period
1990–2100."
----------------------------------------
 July 2010 becomes hottest month in Moscow
history<http://en.rian.ru/Environment/20100723/159925062.html>
http://en.rian.ru/Environment/20100723/159925062.html

---------------------------------------
Climate Case Studies – The 2010 Russian Heat Wave

http://www.wunderground.com/blog/RickyRood/article.html?entrynum=208

"Let’s continue: The winter of 2010 and the spring of 2011 were
characterized by very high food prices. An essay by Sarah Johnstone and
Jeffrey Mazo entitled, Global Warming and Arab
Spring<http://www.collide-a-scape.com/wp-content/uploads/2011/04/recent-essay.pdf>,
draws a convincing line that the pressure on food prices was a contributor
to the start of the revolutions of the Arab Spring – the tumultuous
uprising against many Arab governments.  (also
here<http://www.iiss.org/publications/survival/survival-2011/year-2011-issue-2/global-warming-and-the-arab-spring/>)
To diffuse the arguments that are sure to follow – this was a contributor,
along with many other factors that came together to fuel a movement. This
is the idea of climate extremes as a threat multiplier. "
---------------------------------------

Graphs are omitted from the pasted in text below:

On record-breaking extremes
http://www.realclimate.org/index.php/archives/2011/11/on-record-breaking-extremes/#more-9643

Filed under:

   - Climate Science<http://www.realclimate.org/index.php/archives/category/climate-science/>
   - Instrumental
Record<http://www.realclimate.org/index.php/archives/category/climate-science/instrumental-record/>

— stefan @ 6 November 2011

It is a good tradition in science to gain insights and build intuition with
the help of thought-experiments. Let’s perform a couple of
thought-experiments that shed light on some basic properties of the
statistics of record-breaking events, like unprecedented heat waves. I
promise it won’t be complicated, but I can’t promise you won’t be surprised.

Assume there is a climate change over time that is U-shaped, like the blue
temperature curve shown in Fig. 1. Perhaps a solar cycle might have driven
that initial cooling and then warming again – or we might just be looking
at part of a seasonal cycle around winter. (In fact what is shown is the
lower half of a sinusoidal cycle.) For comparison, the red curve shows a
stationary climate. The linear trend in both cases is the same: zero.

*Fig. 1.*Two idealized climate evolutions.

These climates are both very boring and look nothing like real data,
because they lack variability. So let’s add some random noise – stuff that
is ubiquitous in the climate system and usually called ‘weather’. Our
U-shaped climate then looks like the curve below.

*Fig. 2.* “Climate is what you expect, weather is what you get.” One
realisation of the U-shaped climate with added white noise.

So here comes the question: how many heat records (those are simply data
points warmer than any previous data point) do we expect on average in this
climate at each point in time? As compared to how many do we expect in the
stationary climate? Don’t look at the solution below – first try to guess
what the answer might look like, shown as the ratio of records in the
changing vs. the stationary climate.

When I say “expected on average” this is like asking how many sixes one
expects on average when rolling a dice a thousand times. An easy way to
answer this is to just try it out, and that is what the simple computer
code appended below does: it takes the climate curve, adds random noise,
and then counts the number of records. It repeats that a hundred thousand
times (which just takes a few seconds on my old laptop) to get a reliable
average.

For the stationary climate, you don’t even have to try it out. If your
series is *n* points long, then the probability that the last point is the
hottest (and thus a record) is simply *1/n*. (Because in a stationary
climate each of those *n* points must have the same chance of being the
hottest.) So the expected number of records declines as *1/n* along the
time series.

Ready to look at the result? See next graph. The expected record ratio
starts off at 1, i.e., initially the number of records is the same in both
the U-shaped and the stationary climate. Subsequently, the number of heat
records in the U-climate drops down to about a third of what it would be in
a stationary climate, which is understandable because there is initial
cooling. But near the bottom of the U the number of records starts to
increase again as climate starts to warm up, and at the end it is more than
three times higher than in a stationary climate.

*Fig. 3.* The ratio of records for the U-shaped climate to that in a
stationary climate, as it changes over time. The U-shaped climate has fewer
records than a stationary climate in the middle, but more near the end.

So here is one interesting result: even though the linear trend is zero,
the U-shaped climate change has greatly increased the number of records
near the end of the period! Zero linear trend does not mean there is no
climate change. About two thirds of the records in the final decade are due
to this climate change, only one third would also have occurred in a
stationary climate. (The numbers of course depend on the amplitude of the U
as compared to the amplitude of the noise – in this example we use a sine
curve with amplitude 1 and noise with standard deviation 1.)

*A second thought-experiment*

Next, pretend you are one of those alarmist politicized scientists who
allegedly abound in climate science (surely one day I’ll meet one). You
think of a cunning trick: how about hyping up the number of records by
ignoring the first, cooling half of the data? Only use the second half of
the data in the analysis, this will get you a strong linear warming trend
instead of zero trend!

Here is the result shown in green:

*Fig. 4.* The record ratio for the U-shaped climate (blue) as compared to
that for a climate with an accelerating warming trend, i.e. just the second
half of the U (green).

Oops. You didn’t think this through properly. The record ratio – and thus
the percentage of records due to the climatic change – near the end is
almost the same as for the full U!

The explanation is quite simple. Given the symmetry of the U-curve, the
expected number of records near the end has doubled. (The last point has to
beat only half as many previous points in order to be a record, and in the
full U each climatic temperature value occurs twice.) But for the same
reason, the expected number of records in a stationary climate has also
doubled. So the ratio has remained the same.

If you try to go to even steeper linear warming trends, by confining the
analysis to ever shorter sections of data near the end, the record ratio
just drops, because the effect of the shorter series (which makes records
less ‘special’ – a 20-year heat record simply is not as unusual as a
100-year heat record) overwhelms the effect of the steeper warming trend.
(That is why using the full data period rather than just 100 years gives a
stronger conclusion about the Moscow heat record despite a lesser linear
warming trend, as we found in our PNAS
paper<http://www.pik-potsdam.de/~stefan/Publications/Nature/rahmstorf_coumou_2011.pdf>
.)

So now we have seen examples of the same trend (zero) leading to very
different record ratios; we have seen examples of very different trends
(zero and non-zero) leading to the same record ratio, and we have even seen
examples of the record ratio going down for steeper trends. That should
make it clear that in a situation of non-linear climate change, the linear
trend value is not very relevant for the statistics of records, and one
needs to look at the full time evolution.

*Back to Moscow in July*

That insight brings us back to a more real-world example. In our recent
PNAS paper<http://www.pik-potsdam.de/~stefan/Publications/Nature/rahmstorf_coumou_2011.pdf>we
looked at global annual-mean temperature series and at the July
temperatures in Moscow. In both cases we find the data are not well
described by a linear trend over the past 130 years, and we fitted smoothed
curves to describe the gradual climate changes over time. In fact both
climate evolutions show some qualitative similarities, i.e. a warming up to
~1940, a slight subsequent cooling up to ~ 1980 followed by a warming trend
until the present. For Moscow the amplitude of this pattern is just larger,
as one might expect (based on physical considerations and climate models)
for a northern-hemisphere continental location.

NOAA has in a recent analysis of linear
trends<http://www.esrl.noaa.gov/psd/people/brant.liebmann/russia/plot-trend_1880-2010_GISS.gif>confirmed
this non-linear nature of the climatic change in the Moscow data:
for different time periods, their graph shows intervals of significant
warming trends as well as cooling trends. There can thus be no doubt that
the Moscow data do not show a simple linear warming trend since 1880, but a
more complex time evolution. Our analysis based on the non-linear trend
line strongly suggests that the key feature that has increased the expected
number of recent records to about five times the stationary value is in
fact the warming which occurred after 1980 (see Fig. 4 of our paper, which
shows the absolute number of expected records over time). Up until then,
the expected number of records is similar to that of a stationary climate,
except for an earlier temporary peak due to the warming up to ~1940.

This fact is fortunate, since there are question marks about the data
homogeneity of these time series. Apart from the urban adjustment problems
discussed in our previous
post<http://www.realclimate.org/index.php/archives/2011/10/the-moscow-warming-hole/>,
there is the possibility for a large warm bias during warm sunny summers in
the earlier part, because thermometers were then not shaded from reflected
sunlight – a problem that has been well-documented for pre-1950 instruments
in France (Etien et al., Climatic Change
2009<http://www.springerlink.com/content/j1324173k4843207/>).
Such data issues don’t play a major role for our record statistics if that
is determined mostly by the post-1980 warming. This post-1980 warming is
well-documented by satellite data (shown in Fig. 5 of our paper).

*It ain’t attribution*

Our statistical approach nevertheless is not in itself an attribution
study. This term usually applies to attempts to attribute some event to a
physical cause (e.g., greenhouse gases or solar variability). As Martin
Vermeer rightly said in a
comment<http://www.realclimate.org/index.php/archives/2011/10/the-moscow-warming-hole/comment-page-1/#comment-217665>to
our previous
post<http://www.realclimate.org/index.php/archives/2011/10/the-moscow-warming-hole/>,
such attribution is impossible by only analysing temperature data. We only
do time series analysis: we merely split the data series into a ‘trend
process’ (a systematic smooth climate change) and a random ‘noise process’
as described in time-series text books (e.g. Mudelsee 2010), and then
analyse what portion of record events is related to either of these. This
method does not say anything about the physical cause of the trend process
– e.g., whether the post-1980 Moscow warming is due to solar cycles, an
urban heat island or greenhouse gases. Other evidence – beyond our simple
time-series analysis – has to be consulted to resolve such questions. Given
that it coincides with the bulk of global warming (three quarters of which
occurred from 1980 onwards) and is also predicted by models in response to
rising greenhouse gases, this post-1980 warming in Russia is, in our view,
very unlikely just due to natural variability.

*A simple code*

You don’t need a 1,000-page computer model code to find out some pretty
interesting things about extreme events. The few lines of matlab code below
are enough to perform the Monte Carlo simulations leading to our main
conclusion regarding the Moscow heat wave – plus allowing you to play with
the idealised U-shaped climate discussed above. The code takes a climate
curve of 129 data points – either half a sinusoidal curve or the smoothed
July temperature in Moscow 1881-2009 as used in our paper – and adds random
white noise. It then counts the number of records in the last ten points of
the series (i.e. in the last decade of the Moscow data). It does that
100,000 times to get the average number of records (i.e the expected
number). For the Moscow series, this code reproduces the calculations of
our recent PNAS paper. In a hundred tries we find on average 41 heat
records in the final decade, while in a stationary climate it would just be
8. Thus, the observed gradual climatic change has increased the expected
number of records about 5-fold. This is just like using a loaded dice that
rolls five times as many sixes as an unbiased dice. If you roll one six,
there is then an 80% chance that it occurred because the dice is loaded,
while there is a 20% chance that this six would have occurred anyway.

To run this code for the Moscow case, first download the file
moscow_smooth.dat here <http://www.pik-potsdam.de/~stefan/moscow.html>.

----------------------
load moscow_smooth.dat
sernumber = 100000;
trendline = (moscow_smooth(:,2))/1.55; % trendline normalised by std dev of
variability
%trendline = -sin([0:128]'/128*pi); % an alternative, U-shaped trendline
with zero trend
excount=0; % initialise extreme counter
for i=1:sernumber % loop through individual realisations of Monte Carlo
series
  t = trendline + randn(129,1); % make a Monte Carlo series of trendline +
noise
  tmax=-99;
  for j = 1:129
    if t(j) > tmax; tmax=t(j); if j >= 120; excount=excount+1; end; end %
count records
  end
end
expected_records = excount/sernumber % expected number of records in last
decade
probability_due_to_trend = 100*(expected_records-0.079)/expected_records
----------------------

*Reference*

Mudelsee M (2010) Climate Time Series Analysis. Springer, 474 pp.

------------------------------------------

Vision2020 Post: Ted Moffett
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