Millennium Post

Gearing up for nature's wrath

The perspectives of Chaos Theory and Random Walk may have unprecedented impact on studies of climate and finance, elucidate Auroop R. Ganguly and Udit Bhatia.

Gearing up for natures wrath
A 2013 news article in the Science magazine by Richard Kerr was titled 'Forecasting regional climate change flunks its first test', while a 2010 article in the journal Nature by Quirin Schiermeier titled 'The real holes in climate science' mentioned that, "The sad truth of climate science is that the most crucial information is the least reliable." On the other hand, in a recent paper in the journal Theoretical and Applied Climatology, Rasmus Benestad and his colleagues (including the well-known climate scientist and communicator Katharine Hayhoe), found that even the very small fraction of scientific papers that deny climate change are mostly faulty. How can we make sense of all this and still inform decision makers and stakeholders? Can climate models, which convey useful information but are not perfect, especially at higher space-time resolutions and decadal time horizon, still convey meaningful information to stakeholders such as engineers, resource managers, and planners? Two new papers from our Lab, as well as one older paper, suggest that this may be possible. While one of the papers attempts to lay an empirical foundation for dealing with the change and uncertainty, the other two develop insights into the context of climate-induced water stress on the power production at risk, in the United States. The underlying challenges and methodologies are often conceptually similar across disparate fields, such as climate and finance.

Here is a quote attributed to Theodore von Karman, the father of supersonic flight and one of the founders of the Jet Propulsion Laboratory jointly run by NASA and Caltech: "Scientists discover the world that exists; engineers create the world that never was." From climate and water to insurance and finance, the statement remains true now more than ever. Somewhere in the continuum, where scientific knowledge is translated to engineering principles and discoveries are transformed to design, complicated uncertainties must be characterised and managed along with fundamental systemic changes. An analogy can be drawn to gravity, which is relatively well understood, versus friction, which is uncertain but must be characterised for precise predictions. Fundamental changes include human population growth and massive extinctions, climate change and urbanisation, as well as the growing interconnectedness of built and human systems or institutions, along with increasing stresses on the carrying capacity and on food, energy, water, and ecosystem resources. Uncertainties can result from our lack of knowledge (of friction, or of a hurricane and severe storm mechanisms, or of spreading financial perturbations across markets) or owing to the intrinsic natural variability of systems (oscillations in climate or business cycles in finance). What is important to realise is that these uncertainties and variability typically do not eclipse the trends or fundamental change, rather, one is superimposed on the other. Thus, just as one example, there have been speculations that the lack of major US hurricane landfalls over several years followed by the very active 2017 season (Harvey and Irma) may have been at least partly driven by the Atlantic Multidecadal Oscillation (AMO) and/or by sulfate aerosol pollution, superposed on the trend of global warming. The same AMO, incidentally, has been shown to influence the multi-decadal cyclicity in the Indian monsoons.
The ability to develop credible decadal climate projections at scales of relevance to stakeholders is known to be a challenging problem owing to two reasons. First, at these time horizons (suppose, 0-30 years in the future), the variability is comparable to the global warming trend. Second, over these horizons, the variability itself, is at least, partly dominated by the intrinsic variability of the system. Decadal to century scale climate change assessment rely on models developed by research groups around the world. The models, in turn, are evaluated by comparison with observations in the past (to account for lack of knowledge of physics) and with each other in the future (to account for situations where history may not be the sole indicator of future conditions). However, intrinsic variability needs to be considered as well in decadal assessments, which is typically assessed by considering multiple model runs with slightly (statistically indistinguishable) different initial conditions. Multiple model runs are sometimes treated through rigorous statistical approaches while multiple initial condition runs have not been too well handled in the literature, even though some methods exist based on information theory. The uncertainties discussed previously have simple yet profound archetypes: chaos theory for intrinsic natural variability and random walk for statistical uncertainty.
Our Sustainability and Data Sciences Laboratory (SDS Lab) at Northeastern University, has been recently involved in two research and educational efforts where such trends and uncertainties needed to be considered, the first related to coastal weather hazards and impacts on port authorities, infrastructure owners and operators given projections of sea level rise as well as atmospheric and oceanic warming, and the second related to investment priorities for energy agencies in the context of water resilient power production, given future projections of scarcer and warmer waters. Incidentally, both the stakeholders, one pertaining to infrastructures and another to resources, were interested in relatively high-resolution space-time projections at time horizons of a few decades.
Tom Conrad in his Op-Ed article (August 30, 2011) in Forbes Tech wrote: "My study of chaos theory led to my conviction that knowing the limits of our ability to predict is much more important than the predictions themselves, a lesson I apply to both climate science and the financial markets." Chaos theory is observed in differential equation-based models. Such models are deterministic, meaning that once the model is known and the initial conditions are prescribed, the future can be exactly and precisely simulated. Yet, chaotic systems have limits to predictability, because of an important property: extreme sensitivity to initial conditions. If the measurements or prescriptions of initial conditions are even slightly different (so slight as to be undetectable with the very best sensors), the simulations will over time produce very different futures, such as fair weather versus thunderstorms. Even in chaotic systems, only a certain set of model parameters may exhibit chaotic behaviour. The second property of many chaotic systems is positive feedback, where certain patterns of behaviour are reinforced. Yet another property is deceptively predictive behaviour, alternating with sudden bursts of unpredictability, often manifested via what are called strange attractors. Ed Lorenz, the MIT meteorologist who re-discovered chaos in the 1960s in the context of meteorology, came up with a simple differential equation system named after him. This chaotic Lorenz system has a strange attractor shaped like the wings of a butterfly. Lorenz used this imagery to somewhat dramatically describe the effects of initial conditions on weather, by claiming that a flap of a butterfly's wings in Brazil may cause hurricanes in the US. Here are a couple of quotes from a paper by Michele Ca' Zorzi and colleagues dated February 13, 2015: "A long-standing result of academic literature is that the exchange rates are not predictable as macroeconomic models cannot generally beat the random walk. The vast exchange rate literature provides, however, at least two reasons for being cautiously optimistic. The preferred forecasting model for real exchange rates resembles the random walk in the short-run while it gradually approaches PPP [purchasing power parity] over long-term horizons." The random walk was originally discussed in a 1905 paper in the journal Nature by Karl Pearson, who also founded the world's first statistics department at a university. Pictured as a drunkard's walk by the physicist George Gamow, the concept in its simplest form just randomly selects the next step from the current position. Thus, a random walk time series could start randomly, and then sample randomly from a statistical distribution to get to the next point in time and carry on in this manner. If the position of any specific random walk trajectory at any given time is considered a person's wealth, and the random selections at any point in time as outcomes of a gambling process, then two persons following identical strategies may end up being extremely rich or miserably poor and anything in between. In statistical model based simulations such as random walk, deterministic predictions are not possible, but statistical attributes such as mean behaviour or variability can be predicted. Chaos theory and random walk are archetypical examples of intrinsic natural variability and statistical behaviour, which in turn may be used to capture our lack of understanding of the underlying processes.
The complex variability and uncertainties in the sciences, as described above, must be harnessed for engineering plans and designs. Civil engineers build bridges and buildings despite large uncertainties in traffic, wind, earthquake and other loads while giving due consideration to any known trends. The range of plausible behaviour of loadings during the design life (30 or 50 years) of the structures is important since it is the relative highs of these loading combinations that determine the design loads. However, the probabilistic maximum values may be too large for an economically feasible design. Thus, economic and financial considerations almost invariably come into play. Safety factors are used in design to mitigate what may be considered as unprecedented or unknown. In the context of hydraulic infrastructures or stresses on agricultural systems or infrastructures, larger values of both highs (heat waves and floods) and lows (cold snaps and droughts) may need to be considered. The same analogy extends onto climate and insurance.
Scientists studying the physics and biogeochemistry of climate change and water sustainability, as well as social scientists and economists working on financial or economic principles, attempt to understand and discover new insights on the natural, built, and the human world. Engineers design built natural and human systems to prepare for extremes and to adapt to change, whether in the context of globalisation and climate change, or urbanisation, land use change and irrigation. Engineered systems of interest to civil, mechanical, electrical and computer engineers range from road, rail, air and maritime networks, water and wastewater distribution systems, power grids and energy transmission lines, as well as communication networks and cyber infrastructures; besides buildings, bridges, dams, levees, seawalls and power plants. Environmental, water resources, civil and agricultural engineers are concerned with farmlands and crops, natural and managed water systems, and ecosystems including riverine, coastal and marine systems. Financial and data engineers, together with economists and behavioural scientists, deal with human systems and institutions, such as stock markets and housing prices to supply chains and insurance sectors. Risk modellers for the insurance and reinsurance sectors may need to consider, for example, climate hazards and stresses, impacts on infrastructures and exposed human lives and assets, as well as regulatory principles and policies. Insurance sectors determine incentive structures and financial instruments, such as catastrophe or resilience bonds, which determine funding priorities for disaster preparedness and recovery as well as adaptation and mitigation strategies. The science of climate and economics tells us that weather hazards and stresses related to water or energy are likely to exacerbate in parts of the world, and their consequences are likely to become worse. With economic assets and people congregating in cities and along coastlines; with urban and regional lifeline infrastructure networks (such as transport, communication, power and water) getting more and more interconnected; with water, energy and food increasingly being sourced from locations further apart; and with power plants and energy infrastructures often regionally co-located; the consequences of extreme events and stresses are getting worse. Financial instruments are needed to drive incentive structures for investments in preparedness and recovery, while risk models drive insurance premiums and regulatory principles. The crucial question that animates these challenges is the ability to tame the uncertainties to inform decisions.
A set of research papers from our research group at the SDS Lab has taken one of the first few steps toward addressing these complex societal challenges, specifically in the context of water stress on thermoelectric power production in the United States. Electricity use in the US is expected to grow by an average of 0.8 per cent per year from 2013 to 2040, 91 per cent of the total electricity in the US is generated by nuclear or fossil fuel-based thermoelectric power plants, which in turn accounts for 45 per cent of total US water withdrawals, 90 per cent of which is used for cooling. Scarcer and warmer water makes power production and cooling processes less efficient while increasing the effluent water temperature which runs in danger of falling afoul to regulatory standards. The first paper in the series, published in 2015 in the journal Computing in Science and Engineering by Auroop Ganguly, considers changes in climate, population and multi-sector water use, and develops proof-of-principle risk profiles by considering how warmer or scarcer water endangers thermoelectric power production. A paper just accepted in the journal Climate Dynamics by Devashish Kumar and Auroop Ganguly, attempts to lay an empirical foundation to comparatively assess the different types of variability, specifically, multiple models and multiple initial conditions, based on a relatively straightforward design of experiments and strategy which yield new climate science and impacts-relevant insights. The third paper, just published in Nature's Scientific Reports, suggest that developing impacts assessment and informing adaptation decisions is possible despite the uncertainties. This paper considers a multivariate standardised water stress index based on the scarcity and warming of water and is expected to be available to power plants across the US. It suggests that 27 per cent of the power production may be severely impacted by the 2030s. What is really new and exciting about these set of papers is the empirical grounding of the different types of uncertainty and the change with a view to informing stakeholders. Climate impact studies, such as the 2017 paper in Science magazine by Eva Sinha and colleagues at Stanford and Princeton which examine climate impacts on water quality, and our own 2015 paper in the journal Nature by Daiwei Wang and colleagues which investigate climate impacts on coastal upwelling, have typically not performed a comprehensive treatment of uncertainties. We believe it is time for uncertainties and change to be fully embraced in science, engineering and finance, partly because no prediction is fully accurate and partly because some of the plausible futures simulated by different models may be highly consequential.
We only need to consider how hurricane tracks may suddenly follow a dangerous path most model runs did not predict but a few may have, or how even local financial market crashes may lead to cascading global crashes which most models may not have predicted. A principled approach to complexity and uncertainty may enable stakeholders and policy-makers to consider unprecedented yet unsurprising events.
(Auroop R Ganguly is Professor and Udit Bhatia is a PhD scholar at Northeastern University in Boston, Massachusetts, USA. The views expressed are strictly personal.)

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