Emergence of a Multiplicity of Time Scales in the Modelling of Climate, Matter, Life, and Economy

Abstract

This topic review communicates working experiences regarding the interaction of a multiplicity of processes. We draw on examples of climate change modelling, materials science, cell physiology, public health, and macroeconomic modelling. Recent years have witnessed astonishing advances not only in broadband temporal frequency sampling, multiscale modelling, and fast large-scale numerical simulation of complex systems, but also in the continual uncertainty of many science-based results. In accordance with the aims of this collection, in this chapter we describe and analyze properties that depend on the time scale of the measurement, structural instability, tip** points, thresholds, hysteresis, and feedback mechanisms with runaways, stabilization or delays. While paying tribute to the advances in data collection and interpretation, we point to grave disorientation in statistical sampling, the interpretation of observations, and the design of control when neglecting the presence or emergence of multiple characteristic times. To us, environmental research is the preferred field of application to demonstrate the meaning of these working experiences, mostly gained in materials science, public health, and macroeconomics.

This work was supported by CIRCLES—Roskilde University’s Centre for Interdisciplinary Research and Education in Circular Economy and Sustainability.

Appendix A: Communicating the Emergence of Multiple Time Scales

1.1 The Public Disregard

Regarding multiscale problems, we register a wide gap between

• (A) The mathematical proficiency in modelling and simulation of multiscale systems

• (B) The public disregard even of the most elementary multiscale aspects, like the emergence of multiple time scales

Claim (A) is evident from

• The enormous literature, both

  • Learned journals

  • Specialized textbooks as E [2011], Engquist et al. [2005, 2009], Horstemeyer [2012], Majda [2016, 2019] and 120 other textbooks and scientific monographs with the entry multiscale in the title, according to zbMATH https://zbmath.org/?q=ti%3Amultiscale+%26+dt%3Ab&p=1

  • A variety of survey articles like E and Engquist [2003], König [2016]

• The new paradigm of modelling (often required by the intricacies of the numerical simulation of multiscale problems), namely doing the mathematical modelling, i.e., the choice of the relevant equations on the different scales, in parallel with designing the numerical algorithms as elaborated by E and Engquist in [2003, Outlook, p. 1069]:

  …in much of computational mathematics, we are used to taking for granted that the models are given, they are the ultimate truth, and our task is to provide methods to analyze and solve them. This shields us from the frontiers of science where phenomena are analyzed and models are formulated.

  Multiscale, multiphysics modelling brings in a new paradigm. Here the problems are given, and a variety of mathematical models at different levels of detail can be considered. The right equation is selected during the process of computation according to the accuracy needs. This brings mathematical analysis and computation closer to the actual scientific and engineering problems. It may no longer be necessary to wait for scientists to develop simplified equations before computational modelling can be done. This is an exciting new opportunity for computational science and for applied mathematics. It will bring applied mathematics closer to other fields of mathematics, as, for example, mathematical physics and probability theory. It will also bring these fields closer to the frontiers of science.

• The multiscale modelling and simulation for design verification and validation purposes of nuclear weapons that permitted the Treaty on the Limitation of Underground Nuclear Weapon Tests, also known as the Threshold Test Ban Treaty (TTBT) to enter into force in 1990, see what Mark Horstemeyer recalls in Horstemeyer [2012, Section 1.3, pp. 4f] about that side of the history and reliability of multiscale modelling and simulation.

Claim (B) is evident from a large study [Santos et al. 2016] of 2016. Assessing student perceptions and comprehension of climate change in Portuguese higher education institutions and surveying studies from other countries, the authors found

• 1. A lack of interrelation between the common attention to Climate Change (CC) in general terms and the personal or political attitudes of the respondents

• 2. A different, but mostly low level of physical understanding

• 3. Absence of any feeling for dynamics and characteristic time scales, e.g., when the respondents were mixing the presence, the near future, and further developments

So much for the academic youth. For quite another cohort, investors on the financial markets, we can derive a similar disregard of the multiple time scales of climate change and transforming for sustainability. In Allen [2018], the author, a capital markets correspondent for the Financial Times, reports:

Sales of green bonds are stuttering after several years of rapid growth. In the three months to the end of September 2018, issuers around the world sold $31.6bn of green-labelled debt, according to research by credit rating agency Moody’s. That is 30 per cent lower than the tally for the second quarter, and 18 per cent down on the $38.5bn sold in the same quarter of 2017.

Moody’s had originally forecast that green bond sales in 2018 would hit $250bn, a considerable increase from the last year’s record $163bn.

In the annual BP Statistical Review of World Energy, S. Dale, British Petrol’s chief economist, gives a related picture of the growth of world coal consumption in 2017 by 1% after annual decrease since 2013, a corresponding increase by 1.5% of CO${}_2$ emissions from energy consumption, and the lack of almost any improvement in the power sector fuel mix over the past 20 years. “The share of coal in the power sector in 1998 was 38% — exactly the same as in 2017,” states Dale [2018], and the price per ton of CO${}_2$ is on the order of 1$, while it should be 25$ per ton of CO${}_2$ now to keep the temperature increase below $2{\frac{1}{2}}^{\circ}\mathrm{C}$ in 2050 according to Nordhaus [2013, p. 316].

In Wolf [2018], the Financial Times’ chief economics commentator M. Wolf searched for an explanation of that “shameful” behaviour of investors. Not surprisingly, he too found a disregard of the multiple time scales at the heart of the problem:

In all, we need to shift the world on to a different investment and growth path right now. This is more technically possible than we used to think. But it is politically highly challenging. Above all, climate change involves huge distributional issues – between rich countries and poor ones, between countries that caused the problem and those that did not, between countries that matter for the solution and those that do not and, not least, between people today, who make the decisions, and people tomorrow, who suffer the results (emphasized by the authors). The natural tendencies are either to do nothing, while insisting there is no problem, or to agree there is a problem, while merely pretending to act. It is not clear which form of obfuscation is worse.

This is not the place to discuss whether this is a clash between economic rationality (more precisely, capitalists’ profit orientation) and environmental, science-based arguments¹, as proponents of the Climate Justice Movement may argue, see, e.g., Bek-Thomsen et al. [2017], Bullard and Müller [2012], Jacobsen [2018] — or just, as, e.g., M. Porter, a Harvard authority on competitive strategy, or W. Nordhaus, the 2017 Nobel laureate in economic theory, may claim with Wolf, a common disregard of shared values in multiple time scales, see Porter and Kramer [2011] and Nordhaus [2013, Ch. 26, “Prisoners of the present”].

1.2 Can Scientists Reach the Public

To communicate the emergence of multiple time scales, we may draw on experts in science communication. The British study [Bowater & Yeoman 2012] distinguishes between three phases associated with the development of science communication (with somewhat unlucky acronyms):

SL:

scientific literacy

PUS:

public understanding of science

PEST:

public engagement with science and technology (the current challenge)

Similarly the recent Illingworth and Allen [2016a, Introduction, p. 1-4].

Another study Hartomo and Cribb [2002, pp. 106f] of 2002 recalls the continuous flow of firm recommendations for public consultation to become an integral part of doing science — not an optional add-on. They comment in rather sharp wording: “This may seem a bit heretical in lands where science policy is still in the hands of the science mafia, and the game is how to limit and exclude rather than to engage, listen and learn. But there is more than a grain of commonsense in it.” They quote from the British Council’s useful report on the democratization of science a list of essential preconditions, among them: independent advice and research; and initiatives to forecast, recognize, and resolve conflict. Surely, that are valuable guidelines for communicating the emergence of multiple time scales in climate change and transforming for sustainability, combined with the advice of Illingworth and Allen [2016b]: there is an obligation for scientists to communicate their research to the rest of society, to inform people about scientific advances, and to ultimately engage them in a two-way dialog so that the general public does not just understand what science is doing, but that they also have a say in what is being done.

1.2.1 Urgent Tasks for the IPCC

Clearly, one has to be grateful to the IPCC that it opts in The IPCC Special Report on 1.5 ${}^{\circ }$C [Masson-Delmotte et al. 2018] for a rigorous interpretation of the 1.5 ${}^{\circ }$C limit on global warming. We deplore though, that the report solely describes the means to reach that goal and the necessary adaptations but underplays the alarming fact that global warming is accelerating and that there are no signs for a decrease in global carbon emissions (see Le Quéré et al. [2018]). Based on our insight into the emergence of multiple time scales, we fully agree with the comment Xu et al. [2018] in Nature that

Policymakers should ask the IPCC for another special report, this time on the rates of climate change over the next 25 years… Researchers should improve climate models to describe the next 25 years in more detail, including the latest data on the state of the oceans and atmosphere, as well as natural cycles. They should do more to quantify the odds and impacts of extreme events. The evidence will be hard to muster, but it will be more useful in assessing real climate dangers and responses.

In multiscale modelling and simulation, the general wisdom (quoted occasionally by W. E) is

For most of the problems we are facing in science and engineering, the theoretical challenges lie in mathematics and algorithms.

Regarding the emergence of multiple time scales in climate change, an even better advice might be to recall (1) what we have learned as children, namely to take care of our resources and not to throw our garbage in the environment, visible or invisible and (2) what we have learned as adults, namely to overcome social and political border that hinder to exercise responsibility — and to follow that teaching rigorously.