## Abstract

How much is better information about climate change worth? Here, I use PAGE09, a probabilistic integrated assessment model, to find the optimal paths of CO_{2} emissions over time and to calculate the value of better information about one aspect of climate change, the transient climate response (TCR). Approximately halving the uncertainty range for TCR has a net present value of about $10.3 trillion (year 2005 US$) if accomplished in time for emissions to be adjusted in 2020, falling to $9.7 trillion if accomplished by 2030. Probabilistic integrated assessment modelling is the only method we have for making estimates like these for the value of better information about the science and impacts of climate change.

## 1. Introduction

Much effort has been devoted to improving our understanding of climate, and how it might change with increasing concentrations of greenhouse gases in the atmosphere. Some critics have suggested that this effort might not represent good value for money [1]. Here, I use PAGE09, a probabilistic integrated assessment model, to calculate the value of better information about one aspect of climate, the transient climate response (TCR). This parameter describes the rise in global mean temperature that would be caused at the end of 70 years by a 1% per year increase in the concentration of CO_{2} in the atmosphere, at the time the concentration doubled. It has been shown in earlier work with the PAGE09 model to be the physical parameter that has the most influence in determining our uncertainty about the impacts of climate change [2]. The traditional range for this parameter is between 1°C and 2.8°C [3]. Systematic biases and errors in climate models have been only modestly reduced in the past 10 years, and estimates of the TCR have barely changed in that time [4]. It has been proposed that we can expect to see a 50% reduction in its uncertainty range by 2030 [5], or earlier if international supercomputing centres dedicated to climate prediction are set up to build high-resolution global climate models [4]. Here, I show that approximately halving the uncertainty range for TCR has a net present value of about $10.3 trillion (year 2005 US$) if accomplished in time for emissions to be adjusted in 2020, falling to $9.7 trillion if accomplished in time for emissions to be adjusted by 2030.

## 2. The PAGE09 integrated assessment model

The method used here is close to what has been called an ideal uncertainty analysis, including probability-weighted values of the output variables, optimal decisions in the light of imperfect knowledge, a measure of risk or dispersion about the outcome and the value of information for a key variable, the TCR [6].

PAGE09 is an integrated assessment model that values the impacts of climate change and the costs of policies to abate and adapt to it. PAGE09 is designed to help policy makers understand the costs and benefits of action or inaction. All results reported here are from 100 000 or 400 000 runs of the model. The probabilistic structure of the model enables consideration of the full spectrum of risks from climate change.

PAGE09 is an updated version of the PAGE2002 integrated assessment model [7] that has been used to value the impacts and calculate the social cost of CO_{2} [8,9], and value the impacts and costs of deforestation [10]. PAGE09 accounts for recent scientific and economic information, primarily in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) [11].

PAGE09 uses simple equations to simulate the results from more complex specialized scientific and economic models, accounting for the profound uncertainty that exists around the impacts of climate change. Calculations are made for eight world regions, 10 time periods to the year 2200 and four impact sectors (sea level, economic, non-economic and discontinuities). All calculations are performed probabilistically, using Latin hypercube sampling to build up probability distributions of the results. The results for two policies and the difference between them are calculated in a single run of the model, so that the incremental costs and benefits of different emission paths can be found. A summary description of the model is given in appendix A of this paper, and a complete set of default input values are given in appendix B. More detail can be found in the supplementary material to [12].

The PAGE09 model uses relatively simple equations to capture complex climatic and economic phenomena. This is justified because the results approximate those of the most complex climate simulations, as shown in [7], and because all aspects of climate change are subject to profound uncertainty. To express the model results in terms of a single ‘best guess’ could be dangerously misleading. Instead, a range of possible outcomes should inform policy. PAGE09 builds up probability distributions of results by representing over 100 key inputs to the calculations by probability distributions, making the characterization of uncertainty the central focus, as recommended by Morgan & Dowlatabadi [13].

## 3. Finding optimal emission paths

In this application, 14 decision variables (emissions of CO_{2} in annexe 1 regions and non-annexe 1 regions in 2020, 2030, 2040, 2050, 2075, 2100 and 2150) are chosen to minimize the mean net present value of the sum of climate change impacts and abatement costs. Emissions of non-CO_{2} greenhouse gases and sulfates continue along the IPCC A1B business-as-usual scenario path [14].

The optimization is performed under uncertainty with the genetic algorithm-based RiskOptimizer from [15]. The optimal combination of emissions is found from 1000 simulations, each of 1000 iterations. A simulation of 400 000 iterations is then performed to reduce the standard error of the estimate of the mean net present value from this optimal emission path.

## 4. Results

Figure 1 shows the optimal global emissions of CO_{2} from PAGE09 if no new information is received about the TCR, and if the new information is received at a later date, in this case in time to re-optimize emissions by 2020. If no new information about the TCR is received, our knowledge is assumed to be represented throughout by a triangular probability distribution, with a minimum of 1.0°C, a most likely value of 1.3°C and a maximum value of 2.8°C. With no new information, the optimal emissions initially fall, as negative cost emission reduction possibilities are taken up, then rise slightly, but then fall to 9% of their year 2010 levels by 2100. These emissions give a mean CO_{2} concentration in 2100 of 516 ppm, with a 5–95% range of 481–557 ppm, and a mean global mean temperature in 2100 of 2.9°C above pre-industrial levels, with a 5–95% range of 1.8–4.6°C.

With new information, the optimal emissions initially follow the optimal path with no new information, from the base year in the model, 2008, until 2010, but then diverge once the new information is received. In other words, the emissions up to 2010 are calculated assuming that we do not know that new information will be obtained, described as an open-loop strategy by Hanemann [16]. The next analysis year in the model is 2020, and emissions are allowed to diverge from the optimal path with no new information at that date. The model effectively interpolates emissions between 2010 and 2020, so that is how they are shown in figure 1. If the new information is that the TCR is in the lower part of the range (giving a triangular distribution with minimum 1.0°C, most likely 1.15°C, maximum 1.3°C), the optimal emissions rise more sharply to 2050, and by 2100 are still at 62% of their year 2010 levels. If the TCR is in the middle of the range (minimum 1.15°C, most likely 1.3°C, maximum 2.05°C), the optimal emissions lie slightly above the optimal path with no new information. If the TCR is high (minimum 1.3°C, most likely 2.05°C, maximum 2.8°C), the optimal emissions fall more rapidly, and are below zero by 2100. The three posterior triangular probability distributions for the TCR with new information have to be of this form so that, when appropriately weighted, they coincide with the prior triangular probability distribution, as required for prior-posterior consistency.

Figure 2 shows the corresponding emission paths if the new information about the TCR is received later, in time to re-optimize emissions by 2030. All the emission paths follow the ‘no new information’ path out to 2020, in an open-loop strategy, and diverge thereafter. The next analysis year in the model is 2030, and emissions are allowed to diverge from the optimal path with no new information at that date. The model effectively interpolates emissions between 2020 and 2030, so that is how they are shown in figure 2.

Table 1 shows the mean net present value of the sum of climate change impacts (including the costs of adaptation) and abatement costs for the optimal emission paths if no new information is received, if the new information is received in time to re-optimize emissions by 2020 (as in figure 1), and if it is received in time to re-optimize emissions by 2030 (as in figure 2). If no new information is received, the mean sum of costs and impacts is $169.53 trillion (year 2005 US$). This is a substantial sum, but well below the mean sum of costs and impacts for the business-as-usual scenario of about $400 trillion [2].

If the new information about the TCR is received in time to re-optimize emissions by 2020, and the TCR turns out to be high, the mean sum of costs and impacts is $236.31 trillion; if medium, $112.84 trillion; and if low, $52.73 trillion. The sum of costs and impacts is higher with a high sensitivity because impacts will be higher, with much greater possibilities of discontinuities such as the melting of the Greenland and Antarctic ice sheets [17] even with optimized emissions, and vice versa. Of course, this does not mean that the value of better information is negative, as we do not know before getting the better information whether it will say that the TCR is high, medium or low.

If the new information about the TCR is received in time to re-optimize emissions by 2030, emission paths can only start to be re-optimized in that analysis year, as shown in figure 2. This delay means that, if the climate sensitivity turns out to be high, the mean sum of costs and impacts is $237.93 trillion; if medium, $112.53 trillion; and if low, $53.50 trillion. Logically, all of these should be slightly higher than if the new information is received in time to re-optimize emissions by 2020, as an extra constraint has been imposed. This is seen if the TCR turns out to be high or low, rather than medium, as a high or a low TCR would prompt larger adjustments in optimal emission paths. If the TCR turns out to be medium, the mean sum of the impacts and costs is the same whether the new information is received in time to re-optimize by 2020 or 2030, to within the resolution of the model.

The weighted average of the mean costs and impacts is $159.27 trillion if the new information is received in time for 2020, and $159.86 trillion if the new information is received in time for 2030. The weights are 0.083, 0.5 and 0.42 on the high, medium and low TCR, respectively; these weights make the sum of the posterior probability distributions of TCR identical to the prior distribution, as required for consistency.

Subtracting these values from the mean costs and impacts with no new information gives the mean value of the better information about TCR as $10.26 trillion if received in time for 2020, and $9.67 trillion if received in time for 2030. The mean value decreases with time as expected. The mean extra value of receiving the better information about TCR in time to re-optimize emissions in 2020 rather than 2030 is $0.59 trillion or $590 billion.

## 5. Precision of the results

A simulation of 400 000 iterations gives a standard error of the estimate of the mean net present value with no new information of $0.35 trillion. The standard error of the estimate of the mean net present value with new information is $0.19 trillion, giving a standard deviation for the value of better information of $0.40 trillion. The standard deviation of the drop in the value of better information if it is received in time for 2030 rather than 2020 is $0.57 trillion.

It is impossible to be sure that the genetic algorithm finds the globally optimal set of emissions, but even if this combination is not exactly optimal, it will have a net present value very close to the optimal combination. The 10 best emission combinations have mean net present values within $0.04 trillion of the combination that the genetic algorithm finds to be optimal. Any further uncertainty introduced by the genetic algorithm can safely be assumed to be negligible compared with the uncertainties described above.

## 6. Discussion

These estimates of the value of better (but not perfect) information are about three orders of magnitude greater than earlier estimates of $10 billion (in 1990 US$) obtained using a variation of the dynamic integrated climate—economy (DICE) model for the value of perfect information about the climate sensitivity [18]. The difference is due to the higher mean discount rate used in the DICE model, the better representation of discontinuities in the PAGE09 model, and the general agreement that the impacts of climate change may have been underestimated in previous work [19].

The value of better information will only be realized if appropriate action is taken to re-optimize emissions when it is received. There must of course be some doubt that this will occur. If in general people and governments do not act optimally in conditions of great uncertainty, better information might still have some value. If better information makes it 10% more likely, say, that people will move from the highly sub-optimal business-as-usual emissions path to the optimal path, the information would now be worth $23 trillion (10% of the difference between the mean sum of costs and impacts of $400 trillion for the business-as-usual path, and $170 trillion for the optimal path).

Stern [20] makes some important suggestions for improving the next generation of integrated assessment models. The results reported here show why such an effort is worthwhile and should be supported. Probabilistic integrated assessment modelling is the only method we have for estimating the value of better information about the science and impacts of climate change. Making the estimates reported here pushes the PAGE09 model as far as it can be pushed. The standard deviation of the drop in the value of better information if it is received in time for 2030 rather than 2020 is almost as large as the mean estimate of the drop in the value. But as John Maynard Keynes noted, it is better to be roughly right than precisely wrong—or not to make any estimate at all (*Economist* 2013).

Supporting data can be found in appendices A and B.

## Competing interests

I have no competing financial interests.

## Funding

The study was funded by the Met Office and formed part of its 2014 Business Case for a replacement supercomputer. The Case was approved by Government Ministers in October 2014 (https://www.gov.uk/government/news/97-million-supercomputer-makes-uk-world-leader-in-weather-and-climate-science). The development of PAGE09 was funded by DECC and the EU ClimateCost Programme. An earlier version of this calculation using the PAGE2002 model was made with Dr Stephane Alberth in 2006.

## Appendix A. More detailed structure of the PAGE09 model

A full description of the updated treatment of the science, impact, abatement and adaptation costs in the latest default version of the model, PAGE09 v. 1.7, and the full set of model equations and default inputs to the model are given in the supplementary material to Hope [12].

In summary, PAGE09 contains equations that model:

*Emissions of the primary greenhouse gases, CO _{2}, methane, nitrous oxide including changes in natural emissions stimulated by the changing climate.* PAGE09 allows the explicit modelling of a fourth set of gases whose forcing is linear in concentration, and models other greenhouse gases, such as black carbon, as a time-varying addition to background radiative forcing.

*The greenhouse effect*. PAGE09 keeps track of the accumulation of anthropogenic emissions of greenhouse gases in the atmosphere, and the increased radiative forcing that results, using a logarithmic relationship between concentration and forcing for CO_{2}, a square root form for methane and nitrous oxide and a linear form for the fourth set of gases.

*Cooling from sulfate aerosols*. The direct and indirect reductions in radiative forcing are separately modelled.

*Regional temperature effects*. For the eight world regions in PAGE09, the equilibrium and realized temperature changes are computed from the difference between greenhouse warming and regional sulfate aerosol cooling, and the slow response as excess heat is transferred from the atmosphere to land and ocean. Sulfate cooling is greatest in the more industrialized regions, and tends to decrease over time due to sulfur controls to prevent acid rain and negative health effects.

*Sea-level rise*. In PAGE09, sea-level rise is modelled explicitly as a lagged linear function of global mean temperature, with a long characteristic response time.

*Nonlinearity and transience in the damage caused by global warming*. Climatic change impacts in each analysis year are modelled as a polynomial function of the sea-level rise and the regional temperature increase in that year. Adaptation can give a time-varying tolerable level of temperature change, which gives impacts of the form (*T*−*T*_{tol})^{n}, where *n* is an uncertain input parameter.

Expected utility and discounting. PAGE09 converts changes in consumption to utility, which amounts to multiplying the changes in consumption by
where *G*( *fr*,0) is today’s gross domestic product (GDP) *per capita* in some focus region (which could be the world as a whole, but in PAGE09 is normally the European Union), and EMUC is the negative of the elasticity of the marginal utility of consumption. This equity-weighted damage is then discounted at the utility rate of interest, which is the pure time preference rate. As EMUC is always greater than zero, the effect is to increase the valuation of impacts in regions that are poorer than the focus region in the base year and decrease the valuation of impacts in regions that are richer.

*Regional economic growth*. Impacts are evaluated in terms of an annual percentage loss of GDP in each region, for a maximum of two sectors; defined in this application as economic impacts and non-economic (environmental and social) impacts.

*Adaptation to climate change*. Investment in adaptive measures (e.g. the development of drought-resistant crops) can increase the tolerable level of temperature change (*T*_{tol}) before economic losses occur and also reduce the intensity of both non-economic and economic impacts.

*The possibility of a future large-scale discontinuity*. This is modelled as a linearly increasing probability of a discontinuity that substantially reduces gross world product being triggered as the global mean temperature rises above a threshold. The losses associated with a discontinuity do not all occur immediately, but instead develop with a characteristic lifetime after the discontinuity is triggered.

*Abatement of greenhouse gas emissions*. In PAGE09, marginal abatement costs (MACs) for each gas in each region are represented by a continuous curve, with an optional possibility of negative costs for small cutbacks, with marginal costs becoming positive for larger cutbacks. The curve is specified by three points, and by two parameters describing the curvature of the MAC curve below and above zero cost, respectively.

## Appendix B. Full set of default inputs for the calculations

Table 2 shows the default Base data, Library data and Policy A files from the PAGE09 model used in this paper. They are sufficient for any researcher with access to the PAGE09 model to replicate the results obtained in this paper.

## Footnotes

One contribution of 12 to a discussion meeting issue ‘Feedbacks on climate in the Earth system’.

- Accepted August 12, 2015.

- © 2015 The Author(s)

Published by the Royal Society. All rights reserved.