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Climate: Past, Present & Future

climate change

God does not play DICE – but Bill Nordhaus does! What can models tell us about the economics of climate change?

Climate change has been described as “the biggest market failure in human history”[1]. Although fuel is costly, emitting the by-product CO2 is for free; yet it causes damages to society. In other words, those who benefit, by using the atmosphere as waste dump, do not pay the full costs, i.e. the adverse effects climate change has on societies on a global scale. Can this market failure be cured? Should humankind sacrifice some of its present welfare to prevent future climate damages? William Nordhaus was jointly awarded the Nobel Prize for economy for providing a framework to answer these questions.

DICE– the Dynamic Integrated model of Climate and the Economy [2] – combines a simple economic model with a simple climate model. The aim is not to fully cover all details of economic and climate processes, but rather to provide a model that is sufficiently simple to be used by non-specialists, including policy makers. Figure 1 shows a simplified structure of the DICE model.

Figure. 1: Schematic illustration of the DICE model. The dark blue arrows correspond to the purely economic component of the model. The yellow and green arrows indicate how the economy impacts climate and vice versa. The light blue arrows illustrate the effect of climate policy.

The economy of the DICE model

The heart of DICE is an economic growth model (dark blue arrows in fig. 1). Economic production occurs when labour and capital is available. Labour is proportional to the world population, which is homogenous and grows according to externally prescribed data. Part of the economic production is invested to create capital for the next time step, while the remaining part is consumed. It is assumed that the “happiness” (called utility in the jargon) of the population depends exclusively on consumption, in a sublinear fashion: The more you consume, the happier you are. However, if you are already rich, then one extra Euro will not increase your happiness as much as when you are poor.

In this purely economic model, the only decision the world population has to take is to determine the saving rate – the fraction of economic production to invest for the next period. If we invest too much, we reduce our current happiness; if we invest too little, we have too little to consume next period. Therefore, the aim is to find an optimal pathway to be reasonably happy now and in the future. However, there is a twist: observations suggest that we, humans, value the present more than the future. E.g. if we are offered 1 Euro either now or next year, we would prefer to be paid now, even in absence of inflation or increasing income. However, if offered 1 Euro now or 1.03 Euro next year, we might begin to prefer the delayed, but larger payment. The extra amount needed to make later payment acceptable is called “Rate of Pure Time Preference”; in our example, it is 3% [3, p.28]. A high Rate of Pure Time Preference basically means that we care much less about future welfare than about the present one. If there is an economic growth (which is the case in DICE), there is an additional reason to prefer being paid now rather than later: In the future, you will be richer, so one additional Euro will mean less to you than now while you are still relatively poor. This effect means that the total “discount rate”, defined as the extra payment needed to make delayed payment attractive, is even higher than the rate of pure time preference [3, chapter 1] .

 

The impact of climate change

To bring climate change into play, Nordhaus assumed that apart from labour and capital, economic production also requires energy. However, energy production causes CO2 emissions. Part of the CO2 ends up in the biosphere or in the ocean, but another part remains in the atmosphere, leading to global warming.

Practically, everyone agrees that substantial warming will have damaging effects on the economy. Although there may not be “good” or “bad” temperatures a priori, ecosystems and human societies are adapted to the current climate conditions, and any (rapid) change away from what we are accustomed to will cause severe stress. For example, there may not be an “ideal” sea level, but strong sea level rise – or fall – will cause severe strain on coastal communities who are adapted to the current level[4].

These damages are extremely hard to quantify. First, we obviously have no reliable empirical data – we simply have not yet experienced the economic damages associated with rapid warming by several degrees. Second, there could be “low chance, high impact” events [5], e.g. events that even under climate change are deemed unlikely to our current knowledge, but would have dramatic consequences if they occur – for example, a collapse of large parts of the Antarctic ice sheet. Third, there are damages, like the loss of a beautiful glacial landscape or the human suffering inflicted by famine, which cannot be quantified in terms of money.

When formulating his Nobel prize-winning DICE model, William Nordhaus tried to solve the first problem by performing an extensive review of the (scarce) existing studies on climate-induced damages and greatly extrapolating the results. E.g. if data was available on reduced wheat production in the Eastern US during a heat wave, Nordhaus might assume that damage for all food crops in Africa is, say, twice as big (as Africa is more dependent on agriculture than the US). This may still be quite ad-hoc, but one might argue that even rough data is better than no data at all. The second and third of the above points where largely circumvented with the “willingness-to-pay” approach [2]: people were asked how much they would pay to prevent the extinction of polar bears or the collapse of the Antarctic ice sheet, for example, and the price they names was used as substitute for damages associated to these events.

Finally, Nordhaus came up with an estimate for climate damage:

D=k1T + k2T2

where D is the damage in % of the GDP, T is the global mean temperature change, and k are constants (k1 = -0.0035 K-1 and k2=+0.0045 K-1) [2, p. 207]. Note that the k1<0 implies that for small T, global warming is actually beneficial. 2.5 degree and 5 degree warming yield damages of 1.1% and 6.5% of the GDP, respectively. Later versions of DICE have k1=0.

 

To reduce global warming, humanity can reduce their carbon emissions. In other words, part of the global economic production is sacrificed to pay for greener energy. This will leave less money to spend on consumption and/or investment in capital, but it also diminishes future climate damages. Therefore, in order to maximise the “happiness”, two control variables must now be chosen at each time step: the saving rate and the emission reduction fraction. We want to reduce carbon emissions enough to avoid very dangerous climate change, but also avoid unnecessary costs.

 

 

Figure. 2 Results of the DICE model. The optimal policy (i.e. maximising “happiness”) in the 2013 version of DICE. The blue lines indicate the optimal policy, while yellow lines indicate no climate policy (i.e. zero emission reduction). The first plot shows the emission reduction fraction or “abatement”, i.e. the fraction of carbon emissions that are prevented. 1 means that no CO2 is emitted. The second plot shows the atmospheric CO2 concentrations in ppmv. For the optimal policy, CO2 concentrations peak at 770ppmv, whereas in absence of a policy, they rise beyond 2000ppmv. The pre-industrial value is 280ppmv. The third plot shows the global mean temperature change. For the optimal policy, it peaks at about 3.2K, i.e. above the limit of 2K or even 1.5K agreed by the Paris agreement.

 

Results and Criticism

The results in fig. 2 show that under the “optimal” policy, i.e. the policy which maximises “happiness”, the Paris agreement will not be met. This result suggests that the costs required for keeping global warming below 1.5 or 2ºC warming are too high compared to the benefit, namely strong reduction in climate damages. However, some researchers
criticise that DICE severely underestimates the risks of climate change. For example, the damage function might be too low and does not explicitly take into account the risk of “low chance, high impact events”. Including such events, occurring at low probability but causing high damages if they occur, will lead to more stringent climate action [6].

The rate of pure time preference has given rise to even fiercer discussions [7,8,9]. As explained above, a society’s discount rate can be estimated from market interest rates [3]. Knowing the economic growth, we can infer the rate of pure time preference used in market decisions. Many economists argue that the rate of pure time preference in models like DICE should be chosen consistent with observations[8]. Nordhaus followed this approach. However, one can argue that even if individuals care less for the future than the present, this does not mean that such an approach is ethically defendable in the context of climate change. Individuals are mortal and may choose to consume their own savings before they die. But climate change is a global and intergenerational problem, and it has been argued [7,9] that we should care for future generations as much as for ourselves. Therefore the rate of pure time preference must be (nearly) zero. Note that this still allows for some discounting, arguing that if future generations are richer, they might be able to deal better with climate change.

Another reason for the relatively weak carbon emission reduction in DICE’s optimal policy may be that it is too pessimistic concerning future costs of emission reduction. For example, DICE does not include the learning-by-doing effect: The more we reduce emissions, the more efficient technologies we discover, and the cheaper it gets. In addition, the costs for green energy are partly one-time investments, e.g. restructuring the energy distribution grids, which are now adapted for few, central energy providers, to a more decentralised structure with smaller providers (e.g. households with solar panels). Once these (large) efforts have been made, the costs for green energy will decrease. But if DICE overestimates the costs of carbon emission reduction, it will be biased towards recommending low reductions.

Due to the above, and many more, issues some researchers criticise that models like DICE are “close to useless”, and even harmful, as they pretend to give precise instructions to policy makers while in fact they struggle with huge uncertainties [10]. In my opinion, models like DICE should not be used for precise policy recommendations like fixing the carbon tax, but are still useful for a somewhat qualitative scenario exploration. For example, it can be fruitful to add “low chance, high impact events” or the learning-by-doing effect and investigate the qualitative effect on the optimal abatement.

Many more economy-climate models have been written in the last decades, some of which are much more sophisticated than DICE. Moreover, there are many models focussing only on specific aspects of the problem, for example, the details of the energy sector. This is still a very active field of research. So, however limited DICE may be, it has laid the foundations for a highly relevant scientific and societal discussion. And even if one should take its precise output with a lump of salt, it is a valuable tool to help policy makers to qualitatively grasp the essence of climate economy.

This post has been edited by the editorial board.

REFERENCES

[1] Nicholas Stern: “The Economics of Climate Change” ( RICHARD T. ELY LECTURE ) http://darp.lse.ac.uk/papersdb/Stern_(AER08).pdf

[2] A thorough description of the model is given by William Nordhaus and Jospeh Boyer, “Warming the World. Economic Models of global warming” (https://eml.berkeley.edu//~saez/course131/Warm-World00.pdf). There are newer model versions available, but the underlying concepts remain the same.

[3] A thorough introduction to discounting is given in this book: Christian Gollier, “Pricing the Future: The economics of discounting and sustainable development” (http://idei.fr/sites/default/files/medias/doc/by/gollier/pricing_future.pdf), especially chapter 1.

[4] see e.g. Wong, P.P., I.J. Losada, J.-P. Gattuso, J. Hinkel, A. Khattabi, K.L. McInnes, Y. Saito, and A. Sallenger, 2014: Coastal systems and low-lying areas. In: Climate Change 2014: Impacts, Adaptation, and Vulnerability. Part A:
Global and Sectoral Aspects. Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change https://www.ipcc.ch/pdf/assessment-report/ar5/wg2/WGIIAR5-Chap5_FINAL.pdf

[5] e.g. Lenton et al. “Tipping elements in the Earth’s climate system”, http://www.pnas.org/content/pnas/105/6/1786.full.pdf

[6] Cai et al., “Risk of multiple interacting tipping points should encourage rapid CO2 emission reduction”, https://www.nature.com/articles/nclimate2964.pdf?origin=ppub
[7] The Stern Review on the Economics of Climate Change (http://webarchive.nationalarchives.gov.uk/20100407172811/http://www.hm-treasury.gov.uk/stern_review_report.htm)

[8] Peter Lilley: “What’s wrong with Stern?” (http://www.thegwpf.org/content/uploads/2012/10/Lilley-Stern_Rebuttal3.pdf)

[9] Frank Ackermann: “Debating Climate Economics: The Stern Review vs. Its Critics” (http://www.ase.tufts.edu/gdae/Pubs/rp/SternDebateReport.pdf)

[10] Robert Pindyck, “The Use and Misuse of Models for Climate Policy”, https://academic.oup.com/reep/article/11/1/100/3066301

 

Of butterflies and climate: how mathematics helps us to better understand the atmosphere

Applied mathematics is often seen as an obscure field, which the general public has no hope of ever understanding. In the context of climate science, this is far from the truth. In fact, many mathematical concepts and ideas applied to the study of the climate system stem from intuitive arguments. While their implementation can be very complex, understanding the basic ideas behind them does not require a PhD in Science.

The Lorenz 1963 attractor, often known as the “Lorenz Butterfly”. Author: Paul Bourke (http://paulbourke.net/fractals/lorenz/)

For example, this is the case of some recent developments in the field of dynamical systems analysis applied to atmospheric data. The atmosphere changes continuously and in many ways: for example, winds become stronger or die down, temperatures rise or fall and rain comes and goes. Understanding this evolution is important in many domains, from weather forecasting to air traffic management to catastrophe response services. The basic idea of the dynamical systems approach is to visualize the evolution of the atmosphere as a series of points connected with a line, which form a trajectory. The figure above shows a well-known example of such a trajectory: the so-called “Lorenz butterfly” (Lorenz, 1963). Now imagine focusing on a specific variable – for example daily surface temperature – and a specific region – let’s say Europe. We can build a trajectory, similar to the one shown above, describing the day-by-day properties of this two-dimensional (latitude by longitude, just as in a geographical map) temperature field. From day to day, the temperature varies therefore each day corresponds to a different point along the trajectory. In the case where two days are very similar to each other, they will correspond to two points very close together. On the contrary, if they show very different temperatures, the points will be further apart. If the similar days are well separated in time, for example occurring during different years, the trajectory representing surface temperature over our chosen region will therefore return close to a point it had previously visited, meaning that the closeness of the points and their distance in time do not always correlate. In the figure below, for example, the three turquoise dots are close to each other and also correspond to successive days along the atmospheric trajectory. The two red dots correspond to temperature configurations similar to those of the turquoise dots, but are separated from the latter by several days.

The continuous black line represents an idealized trajectory, while the circles correspond to successive days along the trajectory. The arrows indicate the direction the time goes.

This way of visualizing the atmosphere might seem bizarre, but it can give us some very powerful insights on how the climate system works. Consider, for example, summer heatwaves in Europe. The most severe ones can persist for several days and can have major impacts on human health, the environment and the economy. As can be intuitively understood, their persistence is due to the fact that the large-scale atmospheric conditions causing them are also persistent. If we return to our atmospheric trajectory, this will mean that we have a large number of points which are close to each other and successive in time – such as is the case for the three turquoise dots in the figure above. Namely, the trajectory moves very slowly and for several days the large-scale circulation only changes very slightly. In mathematical terms, this is a “sticky” state, and again the name is very intuitive! Analyzing the stickiness of the atmospheric states help us to predict how long a given circulation configuration is likely to last, thus providing useful information for weather forecasts.

The next natural step is to try to predict what the atmosphere will do once it has left a sticky state. Dynamical systems theory can again help us. It is in fact possible to define another quantity called “local dimension”, which tells us how complex the state of the atmosphere is. Once again the word “complex” here means exactly what you imagine: a complex temperature state will be one with lots of small, complicated spatial patterns. A simple state will be one with only a small number of large-scale features: for example, a day with high temperatures across the Mediterranean region and cold temperatures over most of Continental and Eastern Europe. Returning to our trajectory, these complex (or high-dimensional) and simple (or low-dimensional) states can be interpreted as follows. In the simple case, it is easy to predict the direction the trajectory will take in the future. This is the same as saying that all similar states evolve in a similar way. So if we want to forecast tomorrow’s temperature and we know that today is a “simple” state, we can look for states similar to today in the past years and we know the evolution of today’s state will be similar to that of these past states. In the complex case, on the contrary, it is very difficult to predict what the trajectory will do in the future. This means that similar atmospheric states will evolve in very different ways, and looking at past days with similar temperatures to today will not help us to forecast tomorrow’s temperature. A complex, high-dimensional state will therefore be more challenging for weather forecasters than a simple, low-dimensional one.

Now imagine looking at a very long climate dataset, for example covering the last century. If the climate system is always the same, one would expect the trajectories for the first and second half of the century to be indistinguishable. If, however, the climate is changing, then one would expect the trajectories representing it to also change. To make an analogy, imagine taking your heart rate. If you measure it on two different days while you are at rest, the number of heart beats per minute will probably be equal. In this case the system – which is here your body – is always in the same state. However, if one day you take your heart rate at rest and the following day you take it while you are running, the results will be very different. In this case something in the system has changed. In just the same way, if the climate system is changing, its “pulse” – namely the trajectory – will change with it. The trajectories of the two half-centuries in the dataset will therefore look different, and their local dimensions and stickiness will display different properties – for example a different mean value. The same two indicators that can help us improve weather predictions at daily to weekly timescales can therefore also help us to understand how climate varies across the centuries.

The dynamical systems approach can be applied to a wide range of scientific problems beyond the examples discussed above. These range from turbulence in fluids to the analysis of financial datasets. Picturing such a complex system as the atmosphere as a “spaghetti plot” is therefore an excellent example of an intuitive mathematical approach that can help us advance our knowledge of the world around us.

Edited by Célia J. Sapart.

Reference: Lorenz, E. N. (1963). Deterministic nonperiodic flow. J. Atmos. Sci., 20(2), 130-141.

A Climate Modeling Workshop in the South of France!

Climate and its effects on the past, present and future of the human race is a heated, topic of debate these days. There are many competing interests at stake from governments and politicians to the big oil and energy companies of the world to the scientists trying to work on climate change problems to the people of the world most acutely affected by these changes on the Earth we live. Thus, I think it is extremely important that everyone works together in this day and age to bring together what each individual party excels at to the table and to combine these things into a powerful plan to help mitigate the effects of climate change for future generations that will call Earth home. This is why a group of young and senior scientists gathered in Aix-en-Provence, France the last week of January: to pave the way forward for future generations to investigate, reflect upon and solve climatic problems that plague our civilization.

It was quite a diverse group with PhD students, Post-Docs and professors from all over the world including France, Germany, the U.K., Spain, The Netherlands, the U.S., Canada, Italy and many others. It was not only diverse culturally, but also in the geologic disciplines we come from with all of the big fields in representation such as isotope geochemistry, climate modelers, organic geochemists, geochronologists and thermochronologists, sedimentologists, structural geologists and of course many others.

The climate workshop was sponsored by the Marie Curie Initial Training Network (ITN) called iTECC, which stands for Integrating Tectonic Erosion Climate Couplings (www.itecc-eu.eu). We are a group of 15 PhD students, 4 Post-Docs, all of our respective advisors and a number of other organizations and institutions involved in various ways with the project. Of course, each student and post-doctorate has his or her respective project within the frame work of the iTECC ITN, but as a whole group we are generally concerned about Himalayan geology in all forms. But more specifically we have these goals and aims:

  • Training of scientists with the ability to contribute to multi-disciplinary research ranging from solid Earth processes to climate dynamics, and application of these skills in academia and industry;
  • Integration of research on present-day deformation with information from the geological record to understand how the lithosphere deforms;
  • Significant improvement in the recovery and exploitation of tectonic, erosive, weathering and climatic records from sedimentary sequences;
  • Evaluation of the impact of elevation and exhumation of the Himalayas on climate;
  • Evaluation of the impact of climate, through erosion, on the tectonic evolution of the Himalayan orogeny;
  • Validation of climate models and applying them to verify the interconnections between tectonics and climate;
  • Building a bridge between science and the local community through outreach.

It is quite an extensive and connected project and I feel very grateful for the opportunity to be involved in something so expansive and important. Anyway, part of our training is to attend these “mini-workshops” as a group every few months. iTECC has organized an Earth Observation Workshop, an Isotope Geochemistry workshop, a so-called “Research in Progress” workshop as well as a Thermochronology workshop, among others. These workshops serve as opportunities to expand our knowledge base and make connections between our specific projects/fields and new geo-disciplines that maybe we would have not made otherwise.

The climate workshop that we are now talking about in Aix brought together, of course iTECC, but a number of professors, scientists and PhD and Post-Docs outside of iTECC. For example, the University of Chicago, University of Bristol, University of Paris Saclay, the University of Bergen, GFZ Potsdam and others.

Here is a list of the speakers that presented at this conference and their topics:

  • Didier Paillard (U Paris-Saclay): On the diversity of “climate” models
  • Matt Huber: Eocene Warm climates and the transition into our icehouse world
  • Dan Lunt (U. Bristol): The role of palaeogeography in controlling Cretacous and Paleogene climate and climate variability
  • Jérémy Jacob (ISTO): Should representativness of sedimentary lipid and their dD values be discussed with palaeoclimatologists?
  • Ray Pierrehumbert (U. Chicago): Approaches to idealized modeling of the climate system
  • Zhongshi Zhang (U. Bergen): Tethys shrinkage and monsoon evolution in Asia and Africa
  • Francis Codron (U. Paris 6): Middle latitudes atmospheric circulation
  • Dorian Abbott (U. Chicago): Dealing with cloud uncertainty when modeling paleoclimate
  • Dirk Sachse (GFZ Potsdam): Compound-specific C and H isotopes from lipid biomarkers as molecular rain gauges
  • Bodo Bookhagen (U. Bergen): Extreme Events and Intensified Monsoon Periods in the Himalayan Field
The goal is to model these complex systems at the present time but also into the recent and geologic past and into the future. This gets complicated quickly with all of the factors involved.

The goal is to model these complex systems at the present time but also into the recent and geologic past and into the future. This gets complicated quickly with all of the factors involved.

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Of course, all of the students and post-doc’s were able to take away some amazing new information about unfamiliar analytical techniques or maybe remote sensing or even new knowledge about these popular(?) and infamous(?) Global Climate Models (GCMs). But I think what I took away from this workshop the most was first pointed out by Didier Paillard in the first lecture and then confirmed by many of the other modelers present, especially since I come from a modeling background. Didier really wanted us to understand that it is ok for our models to be wrong, or that is, not represent the data or findings that we want to compare the model too. And, in fact, he expressed to us that we should want our models to be wrong!

One type of GCM displaying the sea surface temperature and the sea ice concentration.

One type of GCM displaying the sea surface temperature and the sea ice concentration.

Now you are saying, “Hold on there for just one minute! Don’t we need models to be right to be able to understand what happened in the past and also what might happen in the future?” Well, yes this is obviously true. But, to be wrong means that we know how to analyze the output of a model and then adjust the input so that model is more accurate for the next time. Also, being wrong can lead to an amazing new discovery that would have never happened if the model(s) were always right. Some of the most famous discoveries in science (and other fields) happened not because the scientists did the right things, but because they made a mistake and were subsequently smart about it! As Didier called them, “smart mistakes.” What, smart mistakes? Yes, well obviously you can make mistakes while doing anything, but the point is that you can learn from that mistake and not make it again or can continually make the same mistake. Hence, the former is considered a “smart mistake.”

And I think these lessons that we learned in this climate workshop and in general in our studies our especially important as young scientists in crucial fields such as climate change, where I tend to think that some (but not all) of the older generation, especially those outside the technical fields, have not learned these lessons and experienced them at work. Thus, we are trying so very hard to find the perfect solution to the world’s climate problems in one try, that, unfortunately, we do not learn from our mistakes and many times perpetuate them over and over again. But maybe there is hope with our generation that can take these lessons and knowledge about climate change and how it works and use it find sustainable solutions for the future. Who knows! But I do know I am very much looking forward to the next iTECC workshop! Stay up to date with iTECC and what we are doing via our website’s blog and social media pages!