Finiteelements computer simulations
This mixing of climate with weather is dubious. Moreover, letting
meteorologists study the climate will lead nowhere. Why?
Think about it. The meteorologists use supercomputers to predict the
weather. The atmosphere is an extremely difficult system, but for the
meteorologists this is not a hindrance, because they just divide the
atmosphere in 'tiny' cells in socalled finiteelements calculations.
With some basic knowledge of atmospheric processes, they put everything
in parameters.
http://www.simundo.org/science/simulationgrids/
The values of the parameters are then found in an iterative way:
 Predict the weather.
 See what the actual weather will be.
 Go back to the simulation and determine what values of parameters
would have predicted the weather.
 Use these values for the next prediction iteration. Etc.
After thousands of iterations, a 'model' (simulation package) with
reasonable predictive power (35 days) was achieved. The first
predictions were abominable, but they kept on increasing the quality in
the past 30 years.
An iteration takes about the same time span as the prediction (3 days;
weather). It took about 4000 iterations to get it (reasonably) right.
If we use the same technique for the climate, we can expect the same
convergence speed of getting the prediction right. The first
predictions completely failed, as was to be expected (see IPCC
predictions
) and we
can only hope to get a reasonable predictive quality after some
thousands of iterations. With each iteration taking about the time span
as the prediction (30 years; climate), we will have to wait hundreds of
centuries before we can predict the climate!
Another approach the meteorologists might have is to assume climate
prediction is just longterm weather prediction. If we want to extend
our weather prediction (days) to climate prediction (years), we are in
for a long haul. Imagine, every day added to the weather prediction
increases the difficulty by a factor of, say, 2 (which is an
underestimation). Extending from 3 days to 30 years will increase the
complexity by a factor 2
^{10000}, which is approximately a
factor 10
^{3000}. Hold your horses building the new
supercomputer!
The conclusion is that the meteorological approach, treating climate
with weather tools, leads nowhere.
Statistics of weather extremes
Although it is generally accepted that climate is not weather and no
weather event can be used as an indication for climate changes (be they
manmade or not), lately, 'scientists', respond to the cry of the
public to say something about the extreme weather events. "Are they, or
are they not caused by climate changes?!" The response of these
'scientists' is to redefine science itself:
A citation from Peterson, et al. [1], which finishes with a
miscitation of a Nature article [2]. Actually, the referred article of
Nature does not mention that "attribution statements ... are possible
...", but only that the public would like to
hear such statements from
scientists. There is a market for them (and this gives Peterson and
coworkers a
raison d'être).
Let's
analyze
their
reasoning
which is representative for the modern
culture in climate research.
Peterson and coworkers jump to the occasion in this paper "Explaining
extreme events of 2011 from a climate perspective". They come with
statements such as: "It cannot be excluded that the severe event X is
caused by Global Warming" (quote is fictitious, just an example of what
they might say). Meaning that, with 0.0000006%, it is likely to be
caused and explained only by Global Warming. For Peterson and coworkers
this is good enough. They can make statements about the cause of
extreme weather events, as long as they provide a probability to the
hypotheses, even if the probabilities calculated are insanely
meaningless. The public happily ignores the probabilities and remain
with the idea that "Extreme event X probably caused by Global Warming".
And if, by this method, even for most of the weather extremes still
nothing at all can be concluded(*), that doesn't matter; as long as
there is sporadically one that escapes  which is completely natural
in any randomdriven statistics; Statistically, no individual has any
chance of winning the lottery, yet it happens every week  these ones
will make it to the headlines. Nobody will make it to the headlines
saying
"A spell of extremely normal
weather hits Western Europe!!"
while scientifically it is just as interesting as the weather extremes.
(*) actually, if they did their work well, all could have been
used, as shown later
Statistics, a tricky tool
Statistics are a very nice but dangerously complicated and tricky
instrument. Let me give you an example:
We roll a 6face
die. Imagine we roll it 1000 times and find the statistics. They are
moreorless as expected, with maybe a couple of times more a '3'
compared to a '5', etc. Lets assume that actually the die was
completely normal and had normal statistics with 1/6 probability for
each number.
Now we roll it again, 3 times, and find '1', '6' and '4'. Have the
probabilities of the die changed?!
Absolutely!
If we only look at the last rolls, '6' and '4', we can say that the
probabilities for these rolls have changed from (average)
1/6, 1/6, 1/6, 1/6, 1/6, 1/6
to (the last single rolls)
0, 0, 0, 0, 0, 1
and
0, 0, 0, 1, 0, 0
as proven by the statistics. Well, it happened, duh! Whatever the laws
of nature underlying it, the final outcome was '4', so the best model
is the one that predicts (retroactively) a '4'. The real model, had we
had knowledge of all underlying physics, would have predicted the above
outcome. Continuing with 1/6forall probabilities just shows our
ignorance of the physical laws of the system. But, without knowing why the outcome was '4', the
probabilities must have been
100% for a '4', because that is what happened.
The same with the weather. In other words, the weather events, like dieroll events, are
completely deterministic. We are only blinded by our own
ignorance into thinking there are some kind of probabilities involved.
Like this, we are doomed to make wrong statements about the statistics.
We can also reason the other way around (as modern climatologists do).
While for the past the probabilities are 0% and 100%, and we know them
now, what about the future?
While for future events the probabilities are also 0% and 100%, the
difference is we do not know them (yet). But we can use 'human'
probabilities and predictions. That is, not probabilities, but a distribution of frequency of occurrence
(which is for instance the climate or the bias of a die) whose
distribution function we can estimate on basis of samples. (The term
'human probabilities' is used because humans see them as
probabilities). Did this distribution function  these 'human
probabilities' for future events  change? We can test the
nullhypothesis 'nothing has changed' by asking "Not knowing anything
about the system, what is the probability that
the frequencyofoccurrence distribution is unaltered (for future die
rolls), given the fact that the last roll was a '4'?" The answer might
be 99.97%. The climatealarmisttype scientists will then say
"Probabilities have changed  the die has changed  with 0.03%
probability". These statements are allowed "provided proper account is
taken of the probabilistic nature of attribution", or in other words,
as long as we supply an error margin with the statements. The media
then pick it up "Die has changed!" and omit the ridiculous percentages
which actually say that it is likely that nothing has changed.

(Now apply this reasoning to the extreme weather events). Actually, any
weather event is a sign/proof of climate changes!
Take this simplified imaginary situation: The only information we have
is this: There was never a flooding in Pakistan. For the last 99 years
(all measurements). Thus, the probability  our bestestimator for the
risk  of flooding in Pakistan was 0%.
Then Pakistan gets hit by flooding. What is now our bestestimator of
probability of flooding in the next year? 1%. Namely once every 100
years.
Conclusions:
1) The probability of flooding was 0% and the
occurrence of flooding was 0% until last
year.
2) The probability of flooding (and
occurrence
of flooding) last year was 100%.
3) The probability of flooding for the coming years is 1%.
Climate has changed! Sure it did. Our bestestimator has changed. And
the more we start digging into the subject and the more we understand
the physical laws governing the weather in Pakistan, the more we stop
talking about probabilities and start talking about certainties: "It
flooded because of X, Y and Z. These things were absent in the years
before, and last year they were there. So, the system  the climate 
has changed, namely in the aspects X, Y and Z"
Climate Alarmists would only be convinced of there not being climate
changes if every year everywhere at every moment the weather is exactly
the average. And, right they are; any deviation from average is
considered (and in fact
is)
climate change.
The funny truth is that, if the weather has changed, so has the
climate! It seems counterintuitive, against what we learn at school,
but it isn't. Climate is by definition the average weather of 30 years.
If the weather is not exactly equal to the average of the last 30
years, this average, i.e. 'the climate', has changed, albeit it not
with the same magnitude as the weather, since variations are amortized
by a factor 30.
(More precisely, in a 30yearwindow movingaveraging definition of
climate, the latest weather  the weather that moves into the window
 should be equal to the weather exactly 30 years ago  the weather
that moved out of the window , to result in unchanged climate). In
other words, we can mix statements of weather and climate at will.
Weather changes are climate changes, the difference between them is
only an amortization factor of 30.
The question can now be answered: Was weather extreme X caused by
climate changes? Absolutely!
Any
weather event (not only extremes) that did not happen before (at the
same place and time of the year) is the result of climate changes,
because the weather is completely deterministic, even if we,
ignorami, cannot determine the underlying laws: There
must have been changes in
circumstances in the atmosphere (the climate) that caused a change of
probability of occurrence of the weather event from 0% to 100% (Note
that other probabilities do not exist in a deterministic world).
And if next year the event X does not occur, it means the
weather/climate has changed again, from 100% back to 0% probability.
And if we average the weather event occurrences over 30 years, we can
say that the climate has changed if not exactly the same things happen
at the same time.
And if we study more, namely the
underlying physical processes, we can even determine what it is exactly that has changed in the
climate. But that the climate has changed is irrefutable.
Moreover, since the climate from a human point of view is described as
bestestimators of weather/climate
parameters (temperature, precipitation, etc.) and they are the averages
of those parameters in our averaging
window, any weather event that has a value for a particular parameter
that is not exactly equal to the average value will change the average
and thus our bestestimator for that parameter and thus our estimation
of the climate. "Did the climate change?" is thus converted into
nothing more than "Has the average value changed?" The
only discussion we can now have is about the direction and magnitude of
changes and
eventually about the permanent state of these changes, where the latter
cannot be decided on statistics alone.
Conclusion: If we want to attribute a weather event to climate changes,
we can fully justifiably do so. There is no problem with limitations of
statistics. Any event can be used. For higher (emotional) impact, it is
best to use weather catastrophes, though. Peterson et al. use these
weather extremes and determine which ones had damages caused by the
extremity of the weather itself (and thus undeniably the result of
climate changes, i.e., Global Warming) and which ones occurred in
'normal' weather, but where the large catastrophic damages were caused
by changes in society (removal of forests, excessive building in
dangerous zones, etc.). Nothing more. Yet, the message to the public is
"some weather extremes (that were catastrophic) were caused by Global
Warming".
Weather events (extremes)
What
most modern climatologists often hint at is something like "The
(extreme) event X this year falls outside the statistics distribution
of all the other years (and this should be seen as a sign of climate
changes)". Imagine every year it rained between 1000 and 1100 mm and
suddenly there is 1200 mm of rainfall. These are obviously climate
changes, but, once again, it would also be climate changes if it had
rained 'abnormally' 1037 mm, since this has also never happened before.
Once again: any weather event is a sign of climate changes.
Moreover, either there is a trend (slowly rising from 1000 mm to 1100
mm to 1200 mm), or the 1200 mm is incidental, a onetime occurrence.
While, trend or no trend they are climate changes, the attention is
given only because of the surprising sudden step. Actually, the common
opinion among scientists is that climate changes are more associated to
gradual changes, things that
are changing slowly and statistically proven by a large number of
events. That makes isolated weather events useless for proving climate
changes. So what that there is suddenly a flood in Thailand? The
biggest ever? Big deal!
Climate
changes are changing trends and not incidents. Atypical events are
normally considered 'outliers' and removed from the statistics.
This is common practice. Only trends count. Of course they are signs of
climate changes, but so is everything.
These outliers have only recently been included into the story, because
of the public demand and the ease of selling the messages. This is easy
money. (Catastrophe + climate change = money). Peterson and coworkers
jump to the occasion.
The idea is that some weather parameter (like temperature or rainfall)
is normallydistributed in a Gaussian probability function, exp((xμ)
^{2}/σ
^{2}).
If
an
event
then
lies more than 2σ away from the median μ, it is
considered abnormal and thus a sign of climate changes. This is a
misconception.
This
particular reasoning is false (although any event is a sign of climate
changes, also outliers, as discussed above).
The reasoning normally followed is this:
1) Assume the events are normally distributed with a Gaussian function
exp((xμ)
^{2}/σ
^{2})
2) Find the parameters μ and σ of the real data
3) Determine by a Student'st test if a new event lies within 2σ or not
and if it supports the nullhypothesis or is an extreme event
The reasoning goes wrong with the basic assumption, the distribution is
namely not Gaussian. Upon arrival of a new datapoint that is falling
outside the expected range of the normal distribution, it is then
concluded that the parameter μ has changed (climate changes), but it
might as well be that the conclusion should be that your assumption of
normal distribution is wrong.
Most events (like earthquakes and volcano eruptions, etc.) follow a
power law, meaning that an event with magnitude
x has
x^{α} frequency of occurrence,
with
α a constant. See the
work of Newman for an excellent summary of these powerlaw
functions[3]. Powerlaw functions can mimic Gaussian functions,
especially for small numbers of samples, but they lack the parameter σ
and drawing conclusions on basis of this parameter can thus not be
done. Actually, these functions are horrendously difficult to work
with. It is as good as impossible to draw conclusions with these
functions, as anybody working with them knows. In some cases also
stretchedexponential functions are found, exp(x
^{β}), equally
messy. And even if it is not a powerlaw or stretchedexponential
distribution function, that does not mean that the distribution is as
simple as normal Gaussian. Just because you cannot come up with
something better does not make your choice valid. The outliers prove
you wrong.
Larger events, outliers, have tiny probability, but they
will happen every now and then.
Imagine that a Pakistanscale flooding has a yearly probability of 0.1%
of occurring in Pakistan. (Once every 1000 years on average).
Negligible! Has never happened, obviously. Can be ignored. But every
now and then it
will happen,
against all odds. And since there are many 'Pakistans' in the world,
the probability that it happens
somewhere
in the world is very large.
This is again similar to the probability of winning the lottery.
Winning it has so immensely tiny probability that we can safely neglect
the possibility this ever happening to us. Yet, it happens every week
to someone, because there are many people playing the lottery. (The
winner normally attributes it to divine intervention because of its low
probability).
It would be very very unlikely indeed if nowhere in the world some
exceptionally unlikely weatherevent would happen. Looking backwards,
afterwards we can then say "This event was
extremely improbable and is (thus)
a sign of climate changes". The word 'thus' is imagined by the public
or inserted by journalists somewhere in the process (no selfrespecting
scientist will say it). The second part  'climate changes'  is an
empty statement, since, as discussed above, anything is a sign of
climate changes. What remains is "The event had small occurrence
before" (but occurred now, it is an outlier).
The conclusion is that no extreme
event ('outlier') can be considered a proof of climate
changes as such (even though any event is a sign of climate changes)
regardless of the fact that it lies far outside the normal distribution.
This is the reason why normally outliers are thrown away. They
are messing up everything. Yet, they come in handy for the panichungry
Climate Alarmists. They are easily sold as 'something out of the
ordinary' (thus the public opinion is that they
must be global warming), something
destructive and easily statistically proved to be caused by climate
changes.
[1] T.C. Peterson, et al., Am. Meteo. Soc. July 2012, p.1041 (2012).
[2] Nature v.477, p.131 (2011).
[3] M.E.J. Newman, Contemp. Phys. v.46, p.323 (2005).
For more information, contact me at The University of The Algarve,
Prof. Peter Stallinga
http://w3.ualg.pt/~pjotr