Big and small, fast and slow: our random yet predictable atmosphere Table of Contents

Big and small, fast and slow: our random yet predictable atmosphere
Table of Contents

Preface

Zooming through scales by the billion What is weather? What is climate? Why do we need more categories? From milliseconds to the age of the earth: a voyage through scales in time Box: Paleotemperatures Box: removing annual, daily cycles From millimeters to the size of the planet Box: Leonardo da Vinci Complexity, emergent laws, scale invariance and the unfinished nonlinear revolution Box: Complexity or scale invariant simplicity? Box: A metric for geo and cosmic complexity Overview of the book

2. New worlds to scale invariance: van Leeuwenhoek to Mandelbrot and beyond 2.1 A new world in a drop of water: scale bound thinking Box: Antoni van Leeuwenhoek 2.2 Scale invariance: Big whirls have little whirls and little whirls have lesser whirls Box: Jean Perrin: the coast of Brittany Box: Lewis Fry Richardson: cascades Box: Benoit Mandelbrot: fractals Box: Edwin Hurst: long range memory 2.3 Scaling and the phenomenological fallacy 2.4 Scaling versus scale bound classifications Box: Henry Stommel: space-time diagrammes

3. Testing scaling: fluctuations as a microscope 3.1 Fluctuations 3.2 The fluctuation exponent H and the H model Box: Spectra and the missing quadrillion

4. Scaling regimes: weather, macroweather, climate, macroclimate and megaclimate 4.1 Scaling and atmospheric dynamics Box: Stochastic versus deterministic chaos Box: Statistics versus deterministic mechanism Box: “Fractals: where’s the physics?” 4.2 The weather is a scaling, turbulent cascade Box: Andrei Kolmogorov: turbulent laws Box: World record wind Box: How wet is the coast of Brittany? Box: Numerical weather and climate models are scaling 4.3 Expect Macroweather: fluctuations decreasing with scale Box: A Martian family goes for a picnic 4.4 The climate: fluctuations (again) increasing with scale Box: Solar, volcanic climate forcings are scaling Box: How accurately do we know the temperature of the Earth? 4.5 Macroclimate and the ice ages: scaling or cycles? Box: Svante Arrhenius: doubling CO2 Box: Milutin Milankovitch, orbital forcing 4.6 Megaclimate: long term temperature instability and the end of Gaia Box: James Lovelock

5. What is scale? 5.1: Scale as an emergent turbulent property: Generalized Scale Invariance Box: Distance as a emergent property in General Relativity Box: Is isotropic turbulence relevant in the atmosphere? 5.2 What is the dimension of atmospheric motions? Box: Numerical Weather models: 23/9 dimensional? 5.3 Aircraft measurements are not what they seem

6. Scaling, e Invariance and extremes and tipping points 6.1 White, Grey and Black Swan events 6.2 The multifractal butterfly effect Box: Per Bak: Sandpiles, Self-organized Criticality

7. Scaling and giant natural fluctuations: climate closure 7.1 Why the warming can’t be natural Box: “A mephitic ectoplasmic emanation of the forces of darkness” 7.2 The $100,000 Giant Natural climate Fluctuation and Anthropogenic warming

8. Using scaling for prediction: exploiting long range memory 8.1 Weather forecasting and the butterfly effect: deterministic predictability limits Box: Edward Lorenz: Texas tornadoes and Brazilian butterflies 8.2 Macroweather forecasting and stochastic predictability limits: The Stochastic Seasonal and Interannual Prediction System (StocSIPS) 8.3 The future of weather and climate forecasting

9. Earth, water, fire, air 9.1 Scale invariance in the hydrosphere 9.2 Scale invariance in volcanoes 9.3 Scale invariance in the solid earth

What the reader will learn:

1. 
   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”).
   
2. 
   What is scaling including the main scaling objects: fractal sets and multifractal fields.
   
3. 
   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”.
   
4. 
   Readers will learn what is weather, what is the climate and why we need more categories.
   
5. 
   How weather and climate forecasting are done today, how scaling can improve it.
   
6. 
   How scaling can help to show that the industrial epoch warming can’t be natural.
   
7. 
   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 weather is 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 17^th century – is not adequate for understanding the atmosphere’s astonishing variability. In its place, the book describes the new paradigm of scaling associated 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” whereby the 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 have quite 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, the book 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.

Scaling is needed in order to properly classify atmospheric dynamics into different regimes, each characterized by the way that they change under “zooming”; thus yielding the 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 the probabilities 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 scaling paradigm, 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 19^th 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 scaling to 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.