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Habits in numerical model construction

Habits in numerical model construction

 

Numerical models are omnipresent in climate research. Constructed to understand the past, to forecast future climate and to gain new knowledge on natural processes and interactions, they enable the simulation of experiments at otherwise unreachable time and spatial scales. These instruments have long been considered to be fed – let even determined – by either theories or observations alone. But are they really? Sociological factors are at play too. It is precisely these influences that the present blog entry attempts at presenting through the review of cornerstone sociological studies and new anthropological insights on decision-making of model builders.

 

What we here define as numerical models are computer simulations of processes occurring within a system. Global Circulation Models (GCMs), the climate models used to simulate the Earth’s climate and its response to changes of greenhouse gas concentrations in the atmosphere, are certainly the most widely known representatives of this category of scientific instruments. However, numerical models of all types abound in research fields associated to the study of climate change. Some require to be run on national supercomputing centres, while others run on a laptop. Some might be the product of entire research teams, while others result from individual endeavour. Some simulate climate processes at a global scale, while others focus on gas bubbles in a cubic meter of peat. The term “numerical model” employed hereafter embraces this diversity.

Models have long been considered by philosophers to be logically deduced from theory and observations alone. In the late 1990s, Morgan and Morrison (1999) initiated a new turn by insisting on the partial autonomy of models from theory and observations, arising from the diversity of their ingredients. It is this partial autonomy, the authors claim, which enables us to gain knowledge through models about theories and the world. Simultaneously, several studies of the domain of Science and Technology Studies (STS) attempted to address the actual activity of modelling through immersion within climate research institutes, hereby unveiling complex interactions between actors, institutions and stake-holders.

 

Why does it matter?

Model outputs are widely used as a basis for decision-making, at local up to international level. In a context of political and public defiance, much attention has been devoted to increasing the credibility of numerical models. Model intercomparison projects, uncertainty assessments and “best practice” guidelines have flourished. Yet improving modelling activity also necessarily goes through understanding and analysing current practices. Empirical studies addressing actual practices are a requisite to improve reflexivity – and thereby control – over implicit mechanisms likely to impact model outputs. The question ought hence to be how models are actually constructed, before addressing how they should be.

 

What we already know…

Current practices can be analysed at different levels, from individual to institutional. Most empirical sociological studies have so far investigated the interface between decision-making spheres and modelling, as well as institutional and disciplinary cultures of modelling. Shackley (1999) notably identified different “epistemic lifestyles” within global circulation modelling, which appeared to be influenced among others by the role, location, objectives and funding of the organisation within which the modelling project was conducted. He further highlighted with fellow researchers the influence of the modeller’s own perception of the policy process on his or her modelling practices (Shackley et al., 1999). Similar assertions have been made in neighbouring fields (such as hydrology, land use change and integrative assessment modelling), but rarely based on empirical material.

 

 … and what we know less

 The majority of existing studies considered the epistemic stance of modellers – their perception of the modelling activity, of its objectives and of the modellers’ own roles, as well as the modellers’ positioning with respect to particular issues encountered in climate modelling. However, how modellers really make choices during the construction of their model – and which factors influence these – has barely been examined. This is exactly what we aimed to scrutinize through our study presented at the EGU General assembly 2018.

 

Decisions in model construction

Studying decision-making within the process of model construction implies to assume that choices have to be made. As straightforward as this claim might seem, the very existence of choices has been largely absent from philosophical reflexion upon modelling during the 20th century and remains yet to be granted appropriate attention. Modellers however make, sometimes in an iterative manner, a plethora of choices during the model building activity. The temporal and spatial scales need to be selected and along with them the natural processes at play, their interactions, their representation through physical equations or parameterization, their numerical implementation, the source of data, the hardware and software at use, etc. (Babel et al., 2019).

The following video summarizes the rationale behind our research and the approach we used.

Choosing how to represent a natural process

We decided to focus on one particular type of choice: the representation of natural processes through equations (time transfer functions) and their numerical implementation. Even when modellers have selected to simulate a particular natural process (evapotranspiration, for example), several representations of one and the same process can generally be contemplated (Guillemot, 2010). We then asked ourselves on which basis modellers choose one representation and not another. We expected mostly technical aspects to come forefront, such as the required data or software and hardware limitations. These indeed take a prominent place in specialized literature.

 

Interviewing modellers

We adopted a well-established methodology from social sciences based on semi-directed interviews, which were conducted with researchers who developed a model from its earliest stage on. The interviewees were not aware of the exact subject of the interview. Prior to the interviews, we identified in the literature accompanying the presentation of the models one or several processes for which no justification was given on the reasons leading to the choice of the employed representation. After introductive, general questions on the modelling project, the researchers were invited to explain the use of this particular representation.

All interviews were recorded and transcribed. The interviewees came from five universities or research institutes located in four different countries in Europe and Northern America. All but one were senior scientists. A diversity was sought among the types of models (from highly complex ones to models openly described as simplistic) and scientific disciplines, ranging from ecology to geochemistry. With the exception of astrophysics, which we included in order to test a hypothesis not detailed in the present blog entry, all models were devoted to research questions associated to climate change. A total of 14 interviews were conducted.

 

The role of actors – or what we did not expect

As stated above, we expected the modellers to justify the choice of representations with mostly technical constraints. They did not. Rather, the narratives granted particular emphasis to actors – colleagues, professors, PhD directors – who belonged to the modeller’s network during the construction of his or her model. Many of the interviewees had started building their model (which they nowadays continue developing) as doctorate students. The use of a certain process representation was often explained as having been transferred by the (PhD) research director or colleagues. Two decades later, the representation was still part of the model – and modelling practices of these actors played a paramount role in the modellers’ justification of its use, even in competitive and controversy-laden contexts (Babel et al., 2019).

 

From transfer to habit

Many of the interviewees were surprised to be asked about an equation or a numerical scheme they did not perceive to be a distinctive, novel feature of their model. Even if other alternatives to the process representation existed in all the analysed cases, they did not necessarily consider to have made a choice. The choice had often been made by others at the very beginning of their career and transferred to them by their PhD directors or colleagues. They incorporated it in their own practices, a process one of the interviewees described as a “natural evolution”.

(…) during my PhD, my PhD director was only working with [this process representation]. And so I was educated with it. And so I couldn’t imagine doing something else (…) And so after my thesis, I naturally evolved with this approach because it was what I knew. It was a natural evolution, it is as… yes, when we can speak a language, we evolve with this language. So here it is a bit the same, I knew how to speak [this process representation] and so I naturally kept on evolving with this approach. But it is true that… yes, it is the main reason, I believe “  (interview quoted in Babel et al., 2019).

The natural evolution this interviewee referred to can be equated to a path dependence. The modeller developed skills and expertise through the repeated use of the representation, which rendered its implementation increasingly evident in the course of his career. We employed the sociological concept of habit, notably analysed by Latour (2013) to describe the progressive incorporation of choices becoming self-evident practices.

Figure 1. Illustration of the transfer of natural processes representations and incorporation within modelling practices.

 

Habits are required – but self-reflexivity over them too

While the term has often a negative overtone in everyday language, habits can be considered as deeply necessary. As stated by Latour (2013), these smooth out the course of actions: a modeller who would constantly re-consider, on a daily basis, the use of a programming language, a database or a certain variable would lose herself in perpetual decision-making requiring both attention and time. By repeating actions without engaging on new paths – by evolving with the same language, as the interviewee quoted above put it – we gain in efficiency and expertise. Yet, a danger is looming: that of falling into automatisms, losing sight and control over the initial crossroad and hence the ability to reverse, whenever necessary, our paths of actions. Questioning modelling habits and tracking them back to their roots – both on an individual and a collective basis – appears an unavoidable step to gain a better understanding over existing modelling practices.

 

Collectives may reinforce path dependence

The modellers interviewed during our study displayed striking consciousness of their process representation being often particular to a certain collective (a “school” or “field”) they nowadays identified with. By transferring them with a process representation, their director or colleague had also anchored them within a network: that of scientists using the same representation. This anchoring, which was often unconscious at the beginning of their career, could act as reinforcing the path dependence. Changing of process representation would not only often necessitate considerable effort and time to reach the same level of efficiency and expertise gained over the years, but also imply to turn away from a collective within which the modellers had established themselves (Babel et al., 2019).

 

A word of caution

Our study does not describe modellers as being determined as habits. Rather, we aimed at shedding light on inter-individual and collective influences within the modelling process often disregarded in field-specific literature. We assume habits to play a role among other factors. The fact that these other (computational, cost-related) factors were rarely mentioned by the modeller during the interviews could be explained by them being perceived as evident or self-speaking; additional studies would be required to explore the intertwinement of other triggers of model decision with inter-individual and collective influences.

Finally, this study was based on a limited number of interviews: we did not seek for exhaustivity or generalizations, but for case studies enabling a first glance on rarely studied processes.

This post has been edited by Janina Bösken and Carole Nehme.

REFERENCES
Babel, L., Vinck, D., Karssenberg, D. (2019). Decision-making in model construction: unveiling habits. Environmental Modelling and Software, 120, in press. DOI: https://doi.org/10.1016/j.envsoft.2019.07.015

Guillemot, H. (2010). Connections between simulations and observation in climate computer modeling. Scientist’s practices and “bottom-up epistemology” lessons. Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys., Special Issue: Modelling and Simulation in the Atmospheric and Climate Sciences 41, 242–252.

Latour, B. (2013). An Inquiry into Modes of Existence. An Anthropology of the Moderns. Harvard University Press, Cambridge, Massachusetts.

Morgan, M.S., Morrison, M. (1999). Models as Mediators: Perspective On Natural and Social Science. Cambridge University Press, Cambridge.

Shackley, S. (2001). Epistemic Lifestyles in Climate Change Modelling, in: Edwards, P.N. (Ed.), Changing the Atmosphere: Expert Knowledge and Environmental Governance. MIT Press, Cambridge, Massachusetts.

Shackley, S., Risbey, J., Stone, P., Wynne, B. (1999). Adjusting to Policy Expectations in Climate Change Modeling. Clim. Change 43, 413–454.

 



			

		

Magnetic minerals: storytellers of environmental and climatic conditions

Magnetic minerals: storytellers of environmental and climatic conditions
Name of proxy

Environmental Magnetism (also known as enviromagnetics)

Type of record

Environment and climate proxy

Paleoenvironment

Sedimentary environments (for the most part)

Period of time investigated

Present times to millions of years (depending on the preservation conditions)

How does it work?

Magnetism is a physical property that results from the behaviour of elementary particles in any substance. Depending on the chemical composition and distribution of elements within the material, different kinds of magnetism may result. In environmental magnetism mainly the strong magnetic iron minerals in samples are analyses to gain information on environmental processes and climatic conditions. These samples frequently originate from hard or soft rocks from land, caves, lakes, rivers, or oceans. However, the method can be used to monitor environmental pollution in dust, water, or sediments as well [1]. 

Figure 1. Simplified representation of the methodological approach.

The presence or absence of certain minerals in a sample and its properties (e.g. their physical appearance) are typical of specific environmental and climatic conditions (Fig. 1). This is the basic assumption of environmental magnetism. The minerals can be detected by modern equipment even when they are only present in trace amounts. The identification of the minerals is performed by a number of experimental procedures, which all focus on monitoring changes in magnetic properties while subjecting the sample material to different magnetic fields or temperatures. The resulting measurement signal always shows the behaviour of all magnetic components in the sample material. This signal can already be used as proxy for environmental changes and climate conditions. However, only successively performed data analyses allow to distinguish different kinds of magnetic particles by varying magnetic properties. To fully understand the palaeoclimatic and palaeoenvironmental information of the collected data, one needs the information on the components and must understand the processes that form, transform, or break down magnetic minerals. If magnetic minerals are extracted from sample material, they can be subjected to optical or chemical analysis. Thereby, information on the physical appearance of individual grains and their exact chemical composition can supplement the magnetic data.

What are the key findings that have been done using this proxy?

Magnetic analyses were used to unveil environmental conditions in numerous studies. A famous example is the analysis of air-blown sediments (loess) from China [2]. The study of a thick sequence of more than a 100 m shows an alternation of high and low magnetisation values, which correspond to colour changes from brownish to yellowish, respectively (Fig. 2). The brownish sediments were formed during moist and warm conditions, whereas the yellowish loess deposits were accumulated during cold and dry periods. The variation in magnetic properties results from the different processes associated to the formation of minerals in soils, which only take place in warm and moist climates. The occurrence of these newly formed minerals can be monitored by the magnetic susceptibility, which is a measure of a material’s ability to be magnetized. Thereby, the magnetic susceptibility of the Chinese loess is a palaeoclimatic proxy for variations in temperature and rainfall. This information was used for the reconstructions of the past atmospheric circulation pattern and the evolution of the Asian monsoon.

Figure 2: Illustration of the change of a bulk sediment property, using the example of susceptibility. No real data is shown.

In another example, environmental magnetism was applied to sediment cores from the Heidelberg Basin in Germany [3]. Because of the complex genesis of these fluvial deposits, the sediments are composed of a number of different magnetic minerals, which are all telling parts of the story of this region. To identify the different minerals, their individual magnetic signals were extracted from the overall magnetic signal by different very specific and time consuming analytical methods. Additionally, the physical conditions of the magnetic minerals were determined (e.g. grain shape). The combination of all results revealed the lower half of the investigated sediment cores to be deposited under Mediterranean climate conditions in which the groundwater table fluctuated, while the upper part was formed under cooler climates and stable groundwater conditions. Geological archives of the evolution of the Rhine River are rare and most methods fail to disclose details on the past climate conditions.  Here, environmental magnetism provides valuable information on the hydrological regime and the climatic conditions.

Taken together, environmental magnetism is a non-destructive method that is applicable in a number of geological settings. The strengths of the method are manifold. In some settings well constraint information can be gained by fast and non-destructive measurements (example one). In other geological settings information on climatic and environmental conditions is unveiled, when other methods fail to contribute any result (example two).

This post has been reviewed by the editorial board

References

[1] EVANS, M. E. & HELLER, F. (2003) Environmental Magnetism - Principles and Applications of Enviromagnetics, San Diego, Academic Press.

[2] HELLER, F. & TUNG‐SHENG, L. (1986) Palaeoclimatic and sedimentary history from magnetic susceptibility of loess in China. Geophysical Research Letters, 13, 1169-1172.

[3] SCHEIDT, S., EGLI, R., FREDERICHS, T., HAMBACH, U. & ROLF, C. (2017) A mineral magnetic characterization of the Plio-Pleistocene fluvial infill of the Heidelberg Basin (Germany). Geophysical Journal International, 210, 743-764.

How earthworms can help us understand past climates?

How earthworms can help us understand past climates?
Name of proxy

Earthworm calcite granules (ECG)

Type of record

Paleotemperature and paleoprecipitation reconstruction; radiocarbon dating

Paleoenvironment

Continental environments – loess/paleosol sequences

Period of time investigated

Mostly Last full Glacial cycle – from 112,000-15,000 years Before Present (BP) (or older depending on the preservation of the granules).

How does it work?

Earthworms are commonly found living in soil and feeding on organic matter at the soil surface. In carbonate soil, some of them secrete small granules (0.1 to 2 mm) within 20 cm of the soil surface (Fig. 1). These granules, composed of crystalline calcite, are formed in the calciferous glands of the common earthworm species Lumbricus (Fig. 1).

Figure 1. Formation and structure of earthworm calcite granules: A) Schema of the calciferous glands of Lumbricus terrestris (Canti, 1998; Darwin, 1881), B) Scanning Electron Microscopy of a fossil granule, modified from CoDEM/BATLAB C) Distribution of granules through present day experimental soil (Canti and Piearce, 2003), D) Thin section of a fossil granule (photo P. Antoine).

Fossil earthworm calcite granules (ECG) are common in various carbonate-rich Quaternary deposits and have been identified in loess-paleosol sequences in western Europe. Aeolian loess (i.e. accumulation of silt size sediment formed by the deposition of wind-blown dust) preserves evidence for climatic fluctuations in the past: generally, primary loess representing periglacial conditions coeval with expanded ice sheets alternates with tundra permafrost horizons and arctic soils representing milder climates.

Over the last glacial cycle (between 112-15 ky BP), the climate of the Earth varied on millennial timescales between cold (stadial) and temperate (interstadial) periods. This climate variability is reflected in the character of the loess sediment. These short-term climatic changes had a strong influence on landscapes, ecosystems, including human beings. However, loess sediment analysis only give us information on the relative changes of climates. We lack quantitative temperature and precipitation data to precisely reconstruct past conditions.

The granules of earthworms living in past loess environments provide a quantitative tool. The granule concentrations correlate with the nature of the loess sediment; paleosols preserve the highest concentrations while primary loess the lowest. These observations highlight a rapid response of the earthworm population to climatic variations suggesting milder climatic conditions during the formation of paleosol. ECG can be considered as a new paleoenvironmental proxy, capable of detecting rapid climatic events within the Last Glacial loess sequence. Furthermore, the chemistry of these ancient earthworms’ diets can be calibrated to the temperature and precipitation of the climate prevailing at the time.

What are the key findings that have been done using this proxy?

We developed a new method to calculate past temperatures and precipitations based on oxygen and carbon stable isotope compositions of earthworm granules from loess at the Nussloch site in the Rhine Valley, Germany. Our results provide the first quantitative past climate data from loess sediments.

Figure 2: First quantification of paleoclimate data in a loess sequence: Comparison between radiocarbon dating (Moine et al., 2017), granule concentration (Prud’homme et al., 2018b) and quantitative paleoclimate parameters (Tair and MAP, Prud’homme et al., 2016, 2018a) of the Nussloch loess sequence (Antoine et al., 2009) with the δ18O of Greenland ice core (NGRIP, Rasmussen et al., 2014).

Figure 2 shows the results stable isotope geochemistry of earthworm granules from selected strata within the loess sequence at Nussloch. Temperatures for the warmest months were estimated between 10 to 12°C and the mean annual precipitation was estimated between 250 and 400 mm during the formation of palaeosols. Our results suggest that the climate at Nussloch during the temperate periods (interstadials) were most likely subarctic with cool summers and very cold winters.

Earthworm granules can also be directly dated by radiocarbon methods (Moine et al., 2017). Since the nature of loess sediments reflects climatic variations over short (millennial) timescales, the lack of precise chronologies in loess can be a problem when trying to correlate with global climatic events. Our new approach, combining precise radiocarbon dating with quantitative climate reconstruction, represents a major advance for understanding climate in terrestrial regions.

Moreover, the radiocarbon chronology facilitates precise correlation between terrestrial sequences and ice core records. This is fundamental for understanding teleconnections between mid- and high-latitude climate changes, as well as the spatial and temporal impact on prehistoric populations in Europe.

This post has been reviewed by the editor.

References

Antoine, P., Rousseau, D.D., Moine, O., Kunesch, S., Hatté, C., Lang, A., Tissoux, H. & Zöller, L. (2009) Rapid and cyclic aeolian deposition during the Last Glacial in European loess: a high-resolution record from Nussloch, Germany. Quaternary Science Reviews 28, 2955–2973.

Canti, M.G. (1998) Origin of calcium carbonate granules found in buried soils and Quaternary deposits. Boreas 27, 275–288.

Canti, M.G. & Piearce, T.G. (2003) Morphology and dynamics of calcium carbonate granules produced by different earthworm species. Pedobiologia 47, 511–521.

Darwin, C. (1881) The Formation of Vegetable Mould through the action of Worms, with Observations on their Habits. Murray, London.

Moine, O., Antoine, P., Hatté, C., Landais, A., Mathieu, J., Prud’homme, C. & Rousseau, D.D. (2017) The impact of Last Glacial climate variability in west-European loess revealed by radiocarbon dating of fossil earthworm granules. Proceedings of the National Academy of Sciences of the United States of America, 1–6.

Prud’homme, C., Lécuyer, C., Antoine, P., Moine, O., Hatté, C., Fourel, F., Martineau, F. & Rousseau, D.D. (2016) Palaeotemperature reconstruction during the Last Glacial from δ18O of earthworm calcite granules from Nussloch loess sequence, Germany. Earth and Planetary Science Letters 442, 13–20.

Prud’homme, C., Lécuyer, C., Antoine, P., Moine, O., Hatté, C., Fourel, F., Amiot, R., Martineau, F. & Rousseau, D.D. (2018) δ13C signal of earthworm calcite granules: a new proxy for palaeoprecipitation reconstructions during the Last Glacial in Western Europe. Quaternary Science Reviews 179, 158–166.

Prud’homme, C., Moine, O., Mathieu, J., Saulnier-Copard, S. & Antoine, P. High-resolution quantification of earthworm calcite granules from western European loess sequences reveals stadial–interstadial climatic variability during the Last Glacial. Boreas. Accepted 1st October 2018

Rasmussen, S.O., Bigler, M., Blockley, S.P., Blunier, T., Buchardt, S.L., Clausen, H.B., Cvijanovic, I., Dahl-Jensen, D., Johnsen, S.J., Fischer, H., Gkinis, V., Guillevic, M., Hoek, W.Z., Lowe, J.J., Pedro, J.B., et al. (2014) A stratigraphic framework for abrupt climatic changes during the Last Glacial period based on three synchronized Greenland ice-core records: Refining and extending the INTIMATE event stratigraphy. Quaternary Science Reviews 106, 14–28.

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