1
What is climate?
Big and small, fast and slow: our random yet predictable atmosphere
Table of Contents
Preface / Idescribe how the book came to be written. It includes some personal details about how - during my PhD research - of Mandelbrot’s book on fractals, and the subsequent pursuit of scale invariant ideas throughout my career, on to the (2014) statistical testing (and rejecting) of the Giant natural fluctuation hypothesis for explaining global warming.- Zooming through scales by the billion
- What is weather? What is climate? Why they are not enough
- From milliseconds to the age of the earth: a voyage through scales in time
Box: removing annual, daily cycles
1.3From millimeters to the size of the planet
Topic:Zooming in space: structures within structures
1.4Complexity, emergent laws, scales, scalingand the unfinished nonlinear revolution
Topic: Complexity or scale invariant simplicity?
Box: A common metric for geo andcosmic complexity
1.5Overview of the book / This is the section 1.1,Idiscuss the popular saying “the climate is what you expect, the weather is what you get”, asking what is the climate and why it can’t be just averaged weather? Later - ch. 3 - I explain why the saying is wrong: don’t expect the climate. The same understanding answers the question “what is the weather”. Considerations of scale allow us to define a new intermediate “macroweather” regime and allows us to distinguish natural and human induced variations. It explains why there are limits to the predictability for both weather and macroweather and how they depend on time and space scales. It turns out that the scale issue is fundamental and it explains why we frequently observe extreme “outlier” weather events and potentially also, climate “tipping points”.
In sections 1.2, 1.3, the reader will get an immediate and intuitive idea of why things are not as simple as he/she imagined. She is taken through a sequence of plots of temperature and proxy temperature series spanning time scales from milliseconds to hundreds of millions of years. Similarly, satellite and other images visually demonstratethe same idea in space: structures within structures within structures. This gives a visual idea of the incredible range of time and space scales over which the atmosphere is variable from ratios big/small of billions (space) to ratios of long/short of billions of billions (time). How can we possibly understand, theorize and model such behaviour?
Section 1.4 is a general discussion (with much historical flavour) of the nonlinear revolution, complexity, emergent (high level) laws: scalingmanifested by fractal structures, multifractal fields (these are described in more detail later).
This is followed by an overview of the book and its structure.
2.New worlds versus scaling: from van Leeuwenhoek to Mandelbrot and beyond
2.1 A new world in a drop of water: scale bound thinking
Topic: Antoni van Leeuwenhoek, and the modern “powers of ten” paradigm
2.2 Scaling: Big whirls have little whirls and little whirls have lesser whirls
Topic: Perrin and Steinhaus: thewigglinessand length of the coast of Brittany
Topic: Lewis Fry Richardson: cascades
Topic: Benoit Mandelbrot: fractals
Topic: Edwin Hurst: long range memory
2.3: Scale as an emergent property: and the phenomenological fallacy
Topic: What is the dimension of atmospheric motions?
Topic: Atmospheric stratification and rotation.
Box: Distance as a emergent property in General Relativity
Box: Is isotropic turbulence relevant in the atmosphere?
Box: Numerical Weather models: 23/9 dimensional?
2.4Fluctuations as a microscope
Topic: Understanding the fluctuation exponent H: the H model
Topic: An empirical overview in time: fluctuation analysis from milliseconds to hundreds of millions of years
Topic: an empirical overview in space from millimeters to the size of the planet
Box: Spectra and the missing quadrillion
2.5Space and time: scalingor scale bound dynamics?
Topic: Henry Stommel and space-time diagrammes / The two extreme opposite approaches for dealing with systems with structures over huge ranges of scale are the “scale bound” and the “self-similar scaling” approaches associated with van Leuwenhoek (17th C)and Mandelbrot.
In the former, (section 2.1)every factor of ten or so of “zooming” leads to something totally different, in the latter(section 2.2), on average, zooming changes nothing. To understand this, in we give the basic scaling equation:
(Size)= (scale)D
whereD is a scale invariant exponent, here a fractal dimension.
Then (section 2.3), we generalize Mandelbrot’s self-similar scaling to include processes that are the same from big to small, as long as wealso squash and/or rotate structures. The result is that structures are different at different scales even though they are produced by the same scalingmechanism. This demonstrates the common “phenomenological fallacy” whereby differences in structure/appearance from one scale to another are used to hypothesize the dominance of qualitatively different processes at different scales. Scale invariant systems generally have structures with different appearances even though the underlying mechanisms are the same at all scales.
In section 2.4 we describe fluctuation analysis that allows us to quantitatively distinguish and characterize scale bound and scale invariant approaches. To do this we need to define fluctuations that are then evaluated at large and small scales and then compared statistically. In a scaling system, we have:
(Fluctuation) = (Scale)H
This expressesthe scaling of the fluctuations and the scale invariance of the exponent H. We demonstrate this with some simple geometric fractal constructions (the “H model”).
It turns out that we must treat the notion of scale not as something pre-ordained by the observer, but as an emergent property that is determined by the complex nonlinear dynamics themselves: “Generalized Scale Invariance”. This generalization of the notion of scale is necessary to account for the stratification and rotation of structures as we zoom into the atmosphere.
This allows us to account for vertical stratification and space-space relations. We can understand convection and other processes classically explained by scale bound models as being on the contrary manifestations of scaling process.
Having discussed fluctuation analysis, we apply it to the time domain to the data and proxy data discussed and displayed in ch. 1.
3. Weather, macroweather, climate, macroclimate and megaclimate
3.1Scaling and atmospheric dynamics
Topic: Stochastic versus deterministic chaos
Topic: Statistics versus deterministic mechanisms
Topic: “Fractals: where’s the physics?”
3.2The weather is a scaling, turbulent cascade
Topic: Andrei Kolmogorov: turbulent laws
Topic: lifetime-size relations
Topic: How wet is the coast of Brittany?
Topic: Numerical weather and climate models are scaling
3.3Expect Macroweather: fluctuations decreasing with scale
Topic: The atmosphere versus the ocean
Topic: Mars versus Earth
Box: A Martian family goes for a picnic
3.4 The climate: fluctuations increasing (again) with scale
Topic: Solar, volcanic climate forcings are scaling
Box: How accurately do we know the temperature of the Earth?
3.5Macroclimate and the ice ages: scaling or cycles?
Topic: Svante Arrhenius: doubling CO2
Topic: MilutinMilankovitch, orbital forcing
3.6Megaclimate: long term temperature instability and the end of Gaia
Box: James Lovelock / The analysis of the previous section shows that between milliseconds and hundreds of millions of years, that are five different regimes, each defined by the way fluctuations change as we zoom from long to short time intervals.
In this chapter we consider each scale invariant regime separately, discussing topics such as turbulence and cascades, including the pedagogical additive-multiplicative H- model, the existence of stable atmospheric layers,the dimension of atmospheric motions, the difference between earth and mars,ice ages, and the Gaia hypothesis.
4.Extremes: Black Swans or tipping points?
4.1White, Grey and Black Swan events, The multifractal butterfly effect
Topic: Black swans versus Outliers and tipping points
Topic: Per Bak: Sandpiles, Self-organized Criticality
4.2Examples:
Topic: Weather: Extreme precipitation and flooding
Topic: World record winds
Topic: Extreme precipitation and flooding
Topic: Dansgaard-Oeschgerevents: tipping points from past climates? / Scalingprocesses have dynamics that repeat scale after scale from large to small. It turns out that this builds up stronger and stronger variability as we move to from large to small scales so that atmospheric variability has extreme fluctuations (corresponding to extreme storms, winds, heat waves etc.). These extremes are so much stronger than the conventional weak “bell curve” type extremes that they have been termed “grey” or “black swan” type events. We discuss the scaling of extremes and how they are generated by a multifractal (scale invariant) version of the “butterfly effect” and its relation of black swans toepistemological uncertainty. This shows that “tipping points” may not necessarily “outliers”: that they may occur in a continuum of more and more extreme events or transitions.
5. What about us?
5.1Why the warming can’t be natural
Topic: Anthropogenic warming and climate closure
Topic: “A mephitic ectoplasmic emanation of the forces of darkness”
5.2The $100,000 Giant Natural climate Fluctuation and Anthropogenic warming / Scaling in time was used to define the macroweather regime; in the pre-industrial epoch it rangesover time scales from weeks to centuries. In the previous chapter we also discussed the link between scalingand extremes. In this chapter, we bring the two together to explain how we can statistically test the hypothesis that the industrial epoch warming is simply a giant natural fluctuation. We give various anecdotes about the author’s dealings with climate sceptics including the ongoing $100,000 climate contest.
6. Why it’s hard to predict… and how scaling can help
6.1Hours, days, a week: Weather forecasting
Topic: Texas tornadoes and Brazilian butterflies: deterministic predictability limits
Topic: How random numbers already make better forecasts
6.2Next month, season, year, decade: Macroweather forecasting
Topic:Stochastic predictability limits
Topic: Exploiting the long range memory
Topic: The Stochastic Seasonal and Interannual Prediction System (StocSIPS)
Topic: The future of weather and climate forecasting
6.3 What will it be like in 2050?
Topic: Projecting the climateGCM’s versus historical projections / Scalingimplies long range (in space and in time) interactions and correlations. It turns out that this can be used for macroweather forecasting (months to decades). In future it may be also useful for weather forecasting.
How accurately can we forecast? In the weather regime, usual(deterministic) forecasts are limited to about 10 days by the butterfly effect (“sensitive dependence on initial conditions”). In the macroweather regime, we make statistical forecasts and these are instead limited by “stochastic” (statistical) limits to predictability. We discuss the new scaling based StocSIPSprediction systemfor macroweather forecasting (months to decades) and compare it to the standard numerical model (Global Circulation Model, GCM) approach, showing why and by how much the new StocSIPSmethod is better while simultaneously being both simpler and about a million times faster.
In a final section we discuss how future climate projections are currently made with large scale Global Circulation Models (GCM’s) and how scaling can help sidestep these to directly use the historical data.
7. Earth, water, fire, air
7.1Scale invariance in the hydrosphere
7.2Scale invariance in volcanoes
7.3Scale invariance in the solid earth / Having explained scalingin space and in time,and the link to the extremes, in this final chapter we give numerous examples showing how the same ideas can be applied in the hydrosphere (precipitation, river flows, floods) and to volcanoes and volcanic processes and phenomena more to the traditional solid-earth geophysics including topography, mantle convection, geogravity, geomagnetism. This brings out a new aspect of the unity of the geosciences: the fact thatgeofields generally exhibit wide range scaling, including the scaling of their extremes.
What the reader will learn:
a)That science is an interlocking hierarchy of theories and how while both low high level theories can be correct, the high level theories are usually more useful. The high level theories – here based on scaling – are “emergent”with respect to the low level theories - here those of continuum mechanics and thermodynamics. Whereas the latter are deterministic, the former are statistical (“stochastic”).
b)What is scaling including the main scaling objects: fractal sets and multifractal fields.
c)That structures such as clouds, “weather systems”, eddies can be of very different scale yet still be produced by fundamentally the same scaling mechanism. Classifying, analyzing and modelling the atmosphere on the basis of appearance “phenomenology” is not justified: the “phenomenological fallacy”.
d)Readers will learn what is weather, what is the climate and why we need more categories.
e)How weather and climate forecasting are done today, how scaling can improve it.
f)How scaling can help to show that the industrial epoch warming can’t be natural.
g)How scale invariance can help understand other areas of geoscience including the hydrosphere, the lithosphere, volcanoes.
Synopsis
This book describes in layman’s terms a new paradigm for understanding the atmosphere from millimeters to the size of the planet and from milliseconds to the age of the earth. Whereas the popular expression states that “the climate is what you expect, the weatheris what you get”, in this book, we take the reader by the hand and explain that there is a third regime –macroweather–in between the weather and climate so that on the contrary, the climate is not what you expect: expect macroweather.
In order to understand this new view, the book takes the reader on a journey through scales in both space and in time. It describes why the traditional “scale bound” (“powers of 10”) approach - inherited from van Leeowenhoek in the 17th century – is not adequate for understanding the atmosphere’s astonishing variability. In its place, the book describes the new paradigm of scalingassociated with fractal structures and multifractal processes. In its simplest form championed by Mandelbrot – “self-similarity” - it describes systems that are the opposite of scale bound:under “zooming” they just reveal just more of the same: they are “scale invariant”.
As the book progresses, more nuanced ideas of scaling and scale invariance are described wherein one must zoom and possibly squash and/or rotate in order to obtain the same. This is the more general case needed to deal with stratification and rotation both in the atmosphere and in many other geosystems including the rocks (lithosphere). It reveals the “phenomenological fallacy” wherebythe quite different appearances of small and large structures are used to justify the elaboration of separate theories and models: in scale invariant processes, a unique mechanism repeats scale after scale yet the large and small may easily havequite different appearances. The scale invariance paradigm emerged in the 1970’s and 80’s as part of the nonlinear “revolution”; the book gives some of this history. Indeed, thebook will have many roughly one page “boxes” that are intended to be asides on key historical characters and concepts. In addition, there will be footnotes for readers who want to dig deeper.
Scalingis needed in order to properly classify atmospheric dynamics into different regimes, each characterized by the way that they change under “zooming”; thusyieldingthe weather, macroweather, climate, macroclimate, megaclimate regimes. It turns out that scaling in time and in space are connected to extreme events that are much more extreme than are usually assumed.Recall that when theprobabilities follow the conventional “bell curve”, extreme events are exceedingly rare. However, on the contrary, scale invariant processes generates “black swan” events that are totally outside the realm of the standard theories. Rather than being “outliers” – as in the usual scale bound approaches - they are simply extreme manifestations of the same mechanism that generates the “usual” non-extreme events.
Having described the contours of the scalingparadigm, the book goes on to describe some significant applications. For example, the chapter on “Climate Closure” describes how the new understanding of atmospheric space-time variability as a function of scale can be exploited for testing the hypothesis that the warming since the 19th century is simply a giant fluctuation of natural origin. Just as in medical testing where – in spite of the complexity of biological systems – ineffective medications and treatments can confidently be rejected, so here we can reject the natural variability hypothesis. This chapter also gives some colourful descriptions of interactions that the author had with the climate sceptic community.
In the chapter on prediction, we explain how to use the long range memory implicit in scalingto predict the atmosphere over scales of months to decades. Finally, in the last chapter, we give examples of how the new framework is needed to better understand other geosystems including the hydrosphere and lithosphere.
The book will have numerous illustrations – including many of beautiful fractals and multifractals as well as many graphs. However, it will be nearly devoid of mathematics – the only exception is that there will be a single very simple equation – a power law – that will occur in several places. The audience is therefore nonspecialist with high school level mathematics and with an interest in the climate and the atmosphere. Many professional colleagues will find it an easy overview of the emerging scaling approach.