CLIMATE cannot be accurately predicted more than a few weeks ahead with
any respectable degree of reliability. The unpredictability even of a
simple mathematical object whose initial state is not known in sufficiently fine detail has long been proven.Climate is a complex,non-linear object (IPCC, 2001) and is, therefore, aortiori, impossible to predict long-term.
Precisely because it has been proven that long-run climate prediction
is not possible, it is inappropriate to attempt to state that there is
a “consensus” that “global warming” caused by increased greenhouse-gas
concentrations will be dangerous if it continues. Scientific dissent on
the question of climate is and will always be legitimate, because it is
settled, proven science that long-run prediction of the behavior of
mathematical objects such as climate is not possible unless the initial
climatic state at any chosen moment is known to a fineness of detail
that is in practice impossible to attain, and unless the processes for
the subsequent evolution of the object are also known in detail, which
they are not.
It
is the proven characteristic of mathematically-chaotic objects such as
climate that neither the magnitude nor the timing of their
phase-transitions (in environmentalist jargon, “tipping points”) can be
predicted (Lorenz, 1963; IPCC, 2001), because there is simply too
little information about the state of the climate in the present to
allow us to look as far as 100 years into the future and say with any
degree of confidence how little or how much the world will warm.
As Lorenz (1963) put it in the landmark paper with which he founded chaos theory -
“When our results concerning the instability of non-periodic flow are
applied to the atmosphere, which is ostensibly non-periodic, they
indicate that prediction of the sufficiently distant future is
impossible by any method, unless the present conditions are known
exactly. In view of the inevitable inaccuracy and incompleteness of
weather observations, precise, very-long-range weather forecasting
would seem to be non-existent.”
And
climate, of course, is very-long-range weather. Recently another
scientist has considered the limitations upon climatic prediction with
some care. Giorgi (2005) defines two types of prediction:
“In
the late 1960s and mid 1970s the chaotic nature of the climate system
was first recognized. Lorenz defined two types of predictability
problems:
1)
Predictability of the first kind, which is essentially the prediction
of the evolution of the atmosphere, or more generally the climate
system, given some knowledge of its initial state. Predictability of
the first kind is therefore primarily an initial-value problem, and numerical weather prediction is a typical example of it.
2) Predictability of the second kind, in which the objective is to
predict the evolution of the statistical properties of the climate
system in response to changes in external forcings. Predictability of
the second kind is thus essentially a boundary-value problem.”
Giorgi explains:
“… Because of the long time scales involved in ocean, cryosphere and
biosphere processes a first-kind predictability component also arises.
The slower components of the climate system (e.g. the ocean and
biosphere) affect the statistics of climate variables (e.g.
precipitation) and since they may feel the influence of their initial
state at multi-decadal time scales, it is possible that climate changes
also depend on the initial state of the climate system … For example,
the evolution of the thermohaline circulation in response to
greenhouse-gas forcing can depend on the initial state of the
thermohaline circulation, and this evolution will in general affect the
full climate system. As a result, the climate change prediction problem
has components of both first and second kind which are deeply
intertwined. … The relevance of the first-kind predictability aspect of
climate change is that we do not know what the initial conditions of
the climate system were at the beginning of the `industrialization
experiment' and this adds an element of uncertainty to the climate
prediction.”
Giorgi also points out that the predictability of a mathematical object such as climate is adversely affected by non-linearity:
“A
system that responds linearly to forcings is highly predictable, i.e.
doubling of the forcing results in a doubling of the response.
Non-linear behaviors are much less predictable and several factors
increase the non-linearity of the climate system as a whole, thereby
decreasing its predictability.”
Climatic
prediction is, as Lorenz said it was, an initial-state problem. It is
also a boundary-value problem, whose degrees of freedom - the quantity
of independent variables that define it - are approximately equal to
the molecular density of air at room temperature, an intractably large
number. It is also a non-linearity problem. It is also a problem whose
evolutionary processes are insufficiently understood. When studying the
climate we are in the same predicament as Christopher Columbus. When he
set out for the Americas, he did not know where he was going; on the
way there, he did not know what route he was following; when he got
there he did not know where he was; when he returned he did not know
where he had been; and, like very nearly every climate scientist
worldwide, he did the whole thing on taxpayers' money.
A thought-experiment
To
illustrate the difficulty further, let us conduct a thought-experiment,
examining the proven mathematical impossibility of predicting the
future state of a complex, non-linear object. For our little experiment
we shall use the Mandelbrot fractal, which is defined using the simple,
iterative function f(z)= z2 + c. Compare
the extreme simplicity of this function with the complications inherent
in the million-variable computer models upon which the UN so heavily
relies in attempting to predict the future evolution of the climate.
In the function that generates the Mandelbrot fractal, the real part a of the complex number c = a + bi lies on the x axis of the Argand plane; the imaginary part b lies on the y axis. Let z = 0.
Compare this certainty and clarity with the uncertainty and confusion
of the climate object, where, as Lorenz proved, accurate long-term
projection into the future cannot be made unless an exceptionally
precise knowledge of the initial state of every one of the million-plus
variables at any chosen starting point is known to a very great degree
of precision. The UN presumes to make predictions a millennium into the
future. This, as our thought-experiment will convincingly demonstrate,
it cannot possibly do.
With
the Mandelbrot fractal, then, there is no initial-state problem, for we
can specify the initial state to any chosen level of precision.
However, with the climate object, there is a formidable and in practice
unsolvable initial-state problem. Likewise, we know the process by
which the Mandelbrot fractal will evolve, namely the simple iterative
function f(z)= z2 + c. However,
our understanding of evolutionary processes of the climate object,
though growing, is insufficient, and the computer models which try to
project future climatic states continue to be caught by surprise as
events unfold. The computers did not predict the severity of the El
Nino event in 1998; they did not predict the cooling of the oceans from
2003 onwards; and the operators of one of the UN's leading computer
models have recently admitted that the model makes errors that are
orders of magnitude greater than the rather small phenomena which they
are trying to predict.
In
the Mandelbrot fractal, therefore, we have consciously chosen for our
thought experiment an object which is like the climate in that it is
chaotic and non-linear, but which is unlike the climate in that it has
initial conditions which we can specify precisely, and processes for
future evolution that are entirely prescribed.
So to the experiment itself. The game is to take a region of the Argand
plane within the field of the Mandelbrot object, and to try to predict
- at least in rough outline - the picture that will appear as the
specified region of the object is generated. We shall choose values of c, to 16 significant figures, as follows: top left c = 0.2500739507702906 + 0.0000010137903618 i; bottom right c = 0.2500739507703702 + 0.0000010137903127 i. We shall set the color of each point in our picture by counting the iterations before |z|
reaches infinity (or here, for convenience, 1 000). Up to 250 000
iterations will be performed to calculate each individual point.
You have been told the initial state of z, and the range of initial values for c.
You have been told the processes for proceeding up to a defined future
point. Now, before looking at Figure 1 overleaf, make your prediction.
What will the picture of our chosen part of the Mandelbrot fractal look
like? In trying to draw the picture, you are in a far better position
than the IPCC is in trying to predict future states of the climate. But
can you do it? Do you have any idea what the picture might look like?
When you have sketched your predicted picture on a piece of paper,
compare your prediction with what the specified portion of the
Mandelbrot fractal actually looks like (see Figure 1 overleaf). If your
picture looked anything like the picture overleaf, apply at once to the
IPCC - they need you. If you were unable to predict what the picture
would look like, even though our thought-experiment has been made as
easy for you as possible, in that the fundamental initial-state and
subsequent-process problems that prevent the IPCC or anyone from
predicting the climate accurately have been carefully engineered out of
our thought experiment, you will begin to appreciate why Lorenz was
right to state that long-term prediction of climate is impossible.
Lorenz's
paper - one of the most elegant in the history of mathematics - also
used a thought-experiment: an artificial climate object with just five
variables. He demonstrated that a near-vanishingly small alteration in
the initial state of just one of the variables could produce major
phase-transitions (or “tipping-points”) at a later state of the model.
This is often called the “butterfly effect” - a butterfly flaps its
wings in the Himalayas and a consequent hurricane devastates Florida.
Of course, the computer - on being given the precise co-ordinates we
have specified to a precision of 16 decimal places - can model the
Mandelbrot object accurately. However, even a very small variation in
the initial state of the object, as defined by the co-ordinates
expressing the range of values of the complex variable c,leads
to an entirely different picture - or even to no picture at all. This
is an appropriate illustration of the reason why, even with the aid of
the world's most sophisticated computers, climate cannot be predicted
for the long term: we do not know the initial state of the millions of
relevant variables at any chosen moment with sufficient precision to
make reliable projections of the long-term future state of the climate.
This
simple mathematical heuristic is a way of demonstrating that anyone who
says, “The Debate Is Over,” or “The Science Is Certain,” or “Now We
Must Act,” must be wrong. Climate science cannot, by its very nature,
be certain. We conclude, and are compelled to conclude, that long-run
prediction of future climatic states is not possible, and that
accordingly any output from the climate models - however large the
models - should be treated with appropriate caution rather than naïve
credulity.
Four examples of the unwisdom of assuming that we know all we need to know about the climate:
He should have stuck to movies: Early in 2007, Arnold
Schwarzenegger, a B-movie actor turned Governor of California,
declared, “The Debate Is Over. The Science Is Certain. Now We Must
Act.” A few weeks later, three-quarters of the citrus crop that is the
prime agricultural product of the State of California was destroyed,
but not by global warming. The fruit was destroyed by a long, hard
frost.
The unit of cant is the Miliband: A few weeks later, David
Miliband, the UK Environment Minister, said, “The Debate Is Well And
Truly Over.” Within days, the heaviest snowstorm for 10 years fell and
brought the UK to a standstill, preventing a million children from
getting to school.
The “long, hot summer of 2007” predicted by the UK Meteorological Office:
In the spring of 2007, the Meteorological Office in the UK confidently
predicted that, because of “global warming”, the summer would be
unprecedentedly long and hot, with widespread drought. Within six weeks
of this prediction, the UK had undergone the coldest, wettest June
since records began.
The Murdoch diktat: Rupert Murdoch, who owns or controls much of
the world's media of communication, issued an edict to all his editors
in the early summer of 2007 to the effect that they were in future to
reflect his opinion that “global warming” was the worst threat faced by
humankind. Murdoch cited the long drought in Australia as evidence for
“global warming” - an instance of the post hoc ergo propter hoc fallacy. Within two weeks of the Murdoch diktat, much of Australia had been inundated by unprecedented floods.
Given the proven unpredictability of the climate, anyone who says, “The
Debate Is Over” is merely displaying scientific ignorance of a
long-established result in elementary chaos theory as applied to the
climate.
FIGURE 1
Result of a thought-experiment using the Mandelbrot fractal
Result of a thought-experiment:Surprisingly, this decorative, ribbon-festooned Maltese Cross is not man-made: it is the image resulting from the iterative calculations on the values of c specified in our elementary heuristic. If you predicted anything like this, congratulations! If not, imagine the difficulty of predicting the climate, where, unlike the fractal object of which the above picture is a tiny region, its initial state and its subsequent evolutionary processes are insufficiently known.
LORENZ, Edward N. 1963. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20: 130-141.
5
The mathematical reason why long-run
climatic prediction is impossible
Christopher
Walter, Third Viscount Monckton of Brenchley, is a former policy
advisor to Margaret Thatcher during her years as Prime Minister of the
United Kingdom. He may reached through SPPI, or directly at ( +44 1882 632341) (monckton@mail.com).
