Par Keroboto

B Z Ogutu

Fabio D'andrea

Charles Nyandwi

P G O Weke

Fabio D ' Andrea

professeur, examinateur Michael Ghil

Wandera Ogana

Francis Codron

Ganesh Pokhariyal

Prof Michael Ghil

David Williamson

Ruth Wambui

Za ' Ngoti

Alex Ogutu

Valentine Nyangige

Joy Wangari

Lorna Wanjiku

Energy Balance Mathematical model on Climate Change

This thesis is dedicated to GOD, all my teachers who showed me the beauty of knowledge, my mother -Maria Consolata Nyangige BORORO, my family, and

ABSTRACT

The goal of this study is to build a reduced-complexity model of coupled climate-economybiosphere interactions, which uses the minimum number of variables and equations needed to capture the fundamental mechanisms involved and can thus help clarify the role of the different variables and parameters. The Coupled Climate-Economy-Biosphere (CoCEB) model described herein takes an integrated assessment approach to simulating global change. By using an endogenous growth module with physical and human capital accumulation, this study considers the sustainability of economic growth, as economic activity intensifies greenhouse gas emissions that in turn cause economic damage due to climate change. Various climate change mitigation policy measures are considered. While many integrated assessment models treat abatement costs merely as an unproductive loss of income, this study considers abatement activities also as an investment in increase of overall energy efficiency of the economy and decrease of overall carbon intensity of the energy system.

One of the major drawbacks of integrated assessment models is that they mainly focus on mitigation in the energy sector and consider emissions from land-use as exogenous. Since greenhouse gas emissions from deforestation and current terrestrial uptake are significant, it is important to include mitigation of these emissions in the biota sinks within integrated assessment models. Several studies suggest that forest carbon sequestration can help reduce atmospheric carbon concentration significantly and is a cost efficient way to curb the prevailing climate change.

This study also looks at relevant economic aspects of deforestation control and carbon sequestration in forests as well as the efficiency of carbon capture and storage (CCS) technologies as policy measures for climate change mitigation. v Because full realistic coupled climate models are so complex, analyses of the various potential feedbacks between climate, economy, and biosphere have been rather limited. Potentially important mechanisms are better initially described in low or intermediate complexity models.

The CoCEB is a formal framework in which it is possible to represent in a simple way different elements of the coupled system and their interactions. The model developed, being an exercise in simplicity and not a predictive tool for climate change impacts, brings together and summarizes information from diverse literature on climate change mitigation measures and their associated costs, and allows comparing them in a coherent way.

The model is, of course sensitive, to the choice of key parameters and in particular the parameters setting the costs of the different means of climate change mitigation: the parameter values tested span the range of cost values found in literature.

The study shows that: i) investment in low-carbon technologies helps to reduce the volume of industrial carbon emissions, lower temperature deviations, and lead to positive effects in the long term economic growth; ii) low investment in CCS contributes to reducing industrial carbon emissions and to increasing gross domestic product (GDP), but further investment leads to a smaller reduction in emissions, as well as in the incremental GDP growth; iii) enhanced deforestation control contributes to a reduction in both deforestation emissions and atmospheric carbon dioxide concentration, thus reducing the impacts of climate change and contributing to a slight appreciation of GDP growth, an effect that is very small, though, compared to that of lowcarbon technologies or CCS; and iv) the results in i) and ii) remain very sensitive to the formulation of technological improvements costs. To the contrary, the results for deforestation control are less sensitive to the formulation of its cost. A large range of hypotheses on these costs appear in the literature, and our modeling framework permitted to span this range and check the vi sensitivity of results The sensitivity study is not intended to make precise calibrations; rather, it is meant to provide a tool for studying qualitatively how various climate policies affect the economy.

RÉSUMÉ

L'objectif de cet étude est de construire un modèle de complexité réduite qui intègre les interactions et les rétroactions du système climat-économie-biosphère avec le minimum de variables et d'équations nécessaires afin de rendre les interactions dynamiques entre les différentes variables transparents. Le modèle couplé climat-économie-biosphère (CoCEB) décrit une approche d'évaluation intégrée pour simuler les changements planétaires. En utilisant un module de croissance endogène avec accumulation de capital physique et humaine, cette étude adresse le problème de la durabilité de la croissance économique. L'activité économique intensifie les émissions de gaz à effet de serre qui à leur tour causent des dommages économiques en raison du changement de climat. Diverses mesures de politique d'atténuation du changement climatique sont considérées. Alors que beaucoup IAM (Integrated assessment models) traitent les coûts de réduction des émissions (abatement) simplement comme une perte non productive de revenu, cet étude considère également les activités de réduction des émissions comme un investissement dans l'efficacité énergétique globale de l'économie et dans la diminution de l' « intensité carbone » globale du système énergétique.

Un des inconvénients majeurs des IAM est qu'ils se concentrent principalement sur le secteur énergétique pour les mesures d'attenuation, et ne tiennent compte des émissions provenant de l'utilisation des terres que comme un forçage exogène. Cependant, les émissions de gaz à effet de serre due au changement de destination du sol, et l'effet de la séquestration de carbone par la terre a sont importantes, l éffet des puits de biota doit donc être considéré. Plusieurs études suggèrent que le piégeage du carbone forestier peut aider à réduire de façon significative la concentration de carbone atmosphérique et qu'il est un moyen efficace en termes de coût pour freiner le changement climatique. Cette étude se penche donc également sur les aspects économiques de la séquestration de carbone du au contrôle du déboisement dans les forêts, at aussi de l'application généralisée des technologies de capture et stockage du carbone (CCS).

Du moment que les modèles climatiques couplés réalistes sont très complexes, les analyses des diverses rétroactions potentielles entre climat, économie et la biosphère ont été plutôt limitées.

Mécanismes potentiellement importants sont mieux initialement décrites dans des modèles de complexité faible ou intermédiaire.

La CoCEB est un cadre formel dans lequel il est possible de représenter de façon simple les différents éléments du système couplé et leurs interactions. Le modèle mis au point, étant un exercice de simplicité et pas un outil de prédiction des impacts du changement climatique, rassemble et résume les différentes données trouvées dans la littérature sur les mesures de mitigation et les coûts y afférents, et permet de les comparer de façon cohérente.

Le modèle est sensible au choix des paramètres, en particulier au paramètres définissant les coûts des différents moyens d'atténuation de changement climatique: on a testé les valeurs des paramètres couvrant la gamme des valeurs de coût trouvé dans la littérature.

L'étude montre que: i) investissements dans les technologies à faible intensité de carbone contribue à réduire le volume des émissions de carbone industriel, réduire les écarts de température et entraîner des effets positifs de la croissance économique à long terme; ii) un faible investissement dans les CCS contribue à réduire les émissions de carbone industriel et à une augmentation de la croissance du PIB, mais un investissement supplémentaire a un effet inverse et diminue la réduction dans les émissions ainsi que l'incrément de croissance du PIB; iii) augmentation du contrôle de la déforestation contribue à réduire les émissions de la déforestation et concentration de CO 2 atmosphérique, ce qui réduit les impacts du changement climatique. Ces éléments viii contribuent à une légère appréciation de la croissance du PIB, mais cela reste très faible par rapport à l'effet des technologies à faible intensité carbonique ou CCS; iv) les résultats en i) et ii) restent très sensibles à la formulation du coût des améliorations technologiques. Un large éventail d'hypothèses sur ces coûts se trouve dans la littérature, notre modèle permet d'étendre cette gamme et vérifier la sensibilité des résultats. À l'inverse, les résultats pour le contrôle de la déforestation sont moins sensibles à la formulation de son coût. L'étude de sensibilité ne représente pas un calibrage précis ; au contraire, il est destiné à fournir un outil pour étudier qualitativement comment diverses politiques climatiques influent sur l'économie. ……………………………………………………………………....................................56 Table 10 Policy scenario values at year 2100 with 1.8

τ α = , 0 f = , 0 B = , d 0 R = ,

Albedo

Fraction of solar radiation reflected back by a surface or object, often expressed as a percentage.

Biomass

The organic material both above-ground (stem, branches, bark, seeds and foliage) and below-ground (living biomass of life roots), and both living and dead.

Carbon cycle

The flow of carbon in various forms (for example, CO 2 ) through the climate System.

Carbon sequestration

The process through which agricultural and forestry practices remove carbon dioxide (CO 2 ) from the atmosphere.

Climate

The statistical description in terms of the mean and variability of relevant quantities (surface temperature, precipitation, wind, etc.) over a period of time ranging from months to thousands or millions of years.

Climate change

A change of the state of the climate system that can be identified by changes in the mean and/or variability of its properties and that persists for an extended period, typically decades or longer.

Climate system

A complex system consisting of five major components: the atmosphere, the hydrosphere, the cryosphere, the lithosphere, and the biosphere, and the interactions between them.

Climate variability

Variations beyond the mean state and other statistics of the climate on all spatial and temporal scales.

CO 2 fertilization

The enhancement of plant growth as a result of elevated atmospheric CO 2 xv concentration.

Damage function

The relation between changes in the climate and reductions in economic activity relative to the rate that would be possible in an unaltered climate.

Deforestation

Those forestry practices or processes that result in a long-term land-use change from forest to agriculture or human settlements or other non-forest uses.

Differential equation

A mathematical equation for a function of one or more independent variables involving the function and its derivatives.

Energy balance

The difference between the total incoming and the total outgoing energy. If this balance is positive, warming occurs; if it is negative, cooling occurs. Averaged over the globe and over long time periods of at least 30 years, the balance must be zero. A perturbation of this balance, be it human-induced or natural, is called radiative forcing.

Feedback

The phenomenon whereby the output of a system is fed into the input and the output is subsequently affected.

Forcing

The action of an agent outside the climate system (volcanic eruption, solar variation, anthropogenic action, etc.) causing a change in the climate system.

GDP

Gross Domestic Product. The value of all goods and services produced (or consumed) within a nation's borders.

Greenhouse effect

The trapping of heat by greenhouse gases (GHGs) within the surfacetroposphere system. An increase in the concentration of GHGs leads to an increased opacity for infrared radiation of the atmosphere.

Integrated assessment

A method of analysis that combines results and models from the physical, biological, economic and social sciences, and the interactions between these xvi components, in a consistent framework, to project the consequences of climate change and the policy responses to it.

Kyoto Protocol

A United Nations Protocol of the Framework Convention for Climate Change that aims to reduce anthropogenic emissions of CO 2 . It sets limits for anthropogenic CO 2 emissions with a view to reducing overall emissions to 5 per cent below 1990 levels by 2008 to 2012. See http://unfccc.int.

Land-use

The total of arrangements, activities, and inputs undertaken in a certain land cover type (a set of human actions). The social and economic purposes for which land is managed (e.g., grazing, timber extraction, and conservation).

Land-use change

Parameterization

The method of incorporating a process by representation as a simplified function of some other fully resolved variables without explicitly considering the details of the process.

Photosynthesis

The metabolic process by which plants take CO 2 from the air (or water) to build plant material, releasing O 2 in the process.

xvii

Radiative forcing A change in the average net radiation at the tropopause -the region between the troposphere and the stratosphere -brought about by changes in either the incoming solar radiation, or in the outgoing infrared radiation. Radiative forcing therefore disturbs the balance that exists between incoming and outgoing radiation. As the climate system evolves over time, it responds to the perturbation by slowly re-establishing the radiative balance.

Reforestation

Planting of forests on lands that have previously contained forests but that have been converted to some other use.

Sequestration

The process of increasing the carbon content of a carbon reservoir other than the atmosphere. Biological approaches to sequestration include direct removal of carbon dioxide from the atmosphere through land -use change, afforestation, reforestation, and practices that enhance soil carbon in agriculture. Physical approaches include separation and disposal of carbon dioxide from flue gases or from processing fossilfuels to produce hydrogenand carbon dioxide-rich fractions and long-term storage in underground in depleted oil and gas reservoirs, coal seams, and saline aquifers.

Sinks

This is term used here to describe agricultural and forestry land that absorbs CO 2 , the most important global warming gas emitted by human activities.

Solar constant

The amount of radiation from the Sun incident on a surface at the top of the atmosphere perpendicular to the direction of the Sun. Currently taken to be and s is the Stefan-Boltzmann constant.

Surface air temperature

The temperature of the air near the surface of the Earth, usually determined by a thermometer in an instrument shelter about 1.3 m above the ground. (Farmer and Cook 2013, p. 4;[START_REF] Mokhov | Assessments of the relationship of changes of the global surface air temperature with different natural and anthropogenic factors based on observations[END_REF][START_REF] Stern | The economics of climate change[END_REF][START_REF] Stott | Impacts of incentives to reduce emissions from deforestation on global species extinctions[END_REF], have, to date, been highly correlated with economic output [START_REF] Barker | Global warming and energy demand[END_REF]. As a result there is a negative feedback between climate change and economic growth that is mediated by CO 2 emissions: an increase in human wealth causes an increase in emissions and global warming, but the warming damages human wealth, slowing its rise or even making it fall.

ABBREVIATIONS AND ACRONYMS

Although some integrated assessment models (IAMs) do include the climate-economy-biosphere feedback albeit only weakly [START_REF] Nordhaus | A question of balance[END_REF], this feedback is typically neglected in a standard climate change assessment [START_REF] Soden | An assessment of climate feedbacks in coupled ocean atmosphere models[END_REF], which is largely a serial process going from socioeconomic scenarios to emissions to climate change to impacts [START_REF] Cox | Climate change: a changing climate for prediction[END_REF] (see Figure 1). A feasible sensitivity of the economy to the climate results in important emergent processes and feedbacks which need to be better understood inorder to address the climate change challenge.

This study focuses on the feedbacks between the climate, economy, and biosphere systems.

Because full realistic coupled climate models are so complex, analyses of the various potential feedbacks have been rather limited. Thus, potentially important mechanisms are better initially described in low or intermediate complexity models. The use of a reduced scale model in this study is meant to bring out the interplay between the climate, economy, and biosphere. General

Circulation Models (GCMs) by far the most sophisticated tools for performing global climate simulations are ill-suited for the task of policy-oriented global and/or regional climate change assessment, in that the computational costs required in performing long-term simulations are largely prohibitive. Although substantial resources have been devoted to calibrating and building GCMs, there remains substantial uncertainty about many of their integral parts. Concerns about the role of clouds, the generation of precipitation, the role of ice, the interaction with oceans, soils, and the biosphere, and the role of other gases in the atmosphere remain problematic. Further, the models still struggle to reproduce the current regional climates of earth [START_REF] Mendelsohn | Assessing the impacts of climate change on natural resource systems[END_REF]. Global climate models are, in addition, unable to provide the degree of flexibility, ease-of-use, and transparency that policy-oriented modeling requires. Moreover, it is impossible for the moment to incorporate large-scale climate models into decision-analytic frameworks.

A reduced-scale model was selected for its simplicity and transparency. Simple models do not allow us to make a quantitative description of the coupled climate-economy-biosphere system dynamics; conversely, the study of such models makes it possible to understand the qualitative mechanisms of the coupled system processes and to evaluate their possible consequences.

The effort undertaken in this study operated under a critical chain of assumptions (Figure 1):

! human activities will result in greenhouse gas emissions ! atmospheric CO 2 concentrations will increase ! increased atmospheric CO 2 concentrations will cause atmospheric warming ! atmospheric warming will threaten living conditions ! threatened living conditions will require measures to mitigate the threat ! climate change mitigation strategies will affect climate change or its impacts through a variety of additional processes

Statement of the problem and justification

Climate change represents one of the greatest environmental, social, and economic threats facing planet Earth today. The global climate has been changing due to human activities and is projected to keep changing even more rapidly. The consequences of climate change could be devastating, with increased atmospheric greenhouse gas concentrations resulting in large-scale, high-impact, non-linear, and potentially abrupt and/or irreversible changes in physical and biological systems [START_REF] Mitchell | Sea sick: the global ocean in crisis[END_REF].

In developing countries, climate change will have a significant impact on the livelihoods and living conditions of the poor. Increasing temperatures and shifting rain patterns across the Earth's continents reduce access to food and create effects that impact regions, farming systems, households, and individuals in varying ways. Additional global changes, including changed trade patterns and energy policies, have the potential to exacerbate the negative effects of climate change on some of these systems and groups.

Thus, analyses of the biogeophysical, biogeochemical and socioeconomic factors that determine exposure, mitigation and/or adaptation, and the capacity to mitigate and/or adapt to climate change are urgently needed so that policymakers can make more informed decisions.

Objectives of the study

Global climate models offer the best approach to understanding the physical climate system. At various resolutions, they capture the basic behaviour of the physical processes that drive the climate. However, these models focus only on natural systems, and do not represent socioeconomic systems that affect and are affected by natural systems. The most common approach to combining socio-economic and biophysical systems involves applying projected trends (scenarios)

to "drive" the climate model. But such an approach disregards the existing dynamic feedbacks.

To bridge such gaps, the general objective of this research is to study the interactions and feedbacks between the climate, economy, and biosphere systems including the climate change related damages.

The specific objectives of the study are:

i) To develop a reduced-complexity Coupled Climate-Economy-Biosphere (CoCEB) model.

ii) Application of the reduced-scale model to examine the interactions and feedbacks between the climate, economy, and biosphere systems and the sensitivity to the implementation of the various climate change mitigation policy measures with their associated costs.

Significance of the study

The CoCEB is a formal framework in which it is possible to represent in a simple and clear way different elements of the coupled system and their interactions as well as feedbacks, while using the minimum number of variables and equations needed to capture the fundamental mechanisms involved and can thus help clarify the role of the different variables and parameters. The model developed, being an exercise in simplicity and transparency and not a predictive tool for climate change impacts, brings together and summarizes information from diverse fields in the literature on climate change mitigation measures and their associated costs, and allows comparing them in a coherent way.

Research methodology and outline of the study

The model describes the temporal dynamics of six variables: per capita physical capital K , per capita human capital H , the average global surface air temperature T , the CO 2 concentration in the atmosphere C , biomass/vegetation B , and industrial CO 2 emissions Y E .

The study came up with a set of modules, which will be linked and will represent a crucial step in efforts to assess the influence that policy choice is likely to have on future climate. The study considered the nature of the relation between K , H , T , C , B , Y E . Consequently by the use of a set of nonlinear, coupled Ordinary Differential Equations (ODEs), the temporal dynamics of these six variables are described by deriving a reduced-scale climate-economy-biosphere model composed of various modules the climate module, economy module, biosphere module that is used to explore the consequences of various climate change mitigation measures on economic growth.

The simplicity of the model makes it easier to clearly identify the relationships in the complex system. After the relationships are found, the mechanisms for these relationships are discussed and comparisons with observations or other studies, made, to evaluate their reasonability or correctness. The model structure and numerical analysis derives some of its parameters from previous climatic and economic studies (see, e.g., [START_REF] Eriksson | The role of the forest in an integrated assessment model of the climate and the economy[END_REF][START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF][START_REF] Greiner | The global environment, natural resources and economic growth[END_REF]IPCC 2001a;Nordhaus 1994[START_REF] Nordhaus | The challenge of global warming: economic models and environmental policy[END_REF][START_REF] Nordhaus | Integrated economic and climate modeling. Handbook of computable general equilibrium modeling[END_REF][START_REF] Nordhaus | Warming the world: economic models of global warming[END_REF][START_REF] Mcguffie | A climate modelling primer[END_REF][START_REF] Schwartz | Heat capacity, time constant, and sensitivity of Earth's climate system[END_REF][START_REF] Schwartz | Reply to comments by G Foster et al, R Knutti et al and N Scafetta on ''Heat capacity, time constant, and sensitivity of Earth's climate system[END_REF][START_REF] Uzawa | Economic theory and global warming[END_REF][START_REF] Van Wassenhove | Using an optimal control model to simulate carbon dioxidebiomass interactions[END_REF]among others).

The study is outlined in Figure 2 below. It summarizes the various modules of the study.

The next Section, Chapter 2, looks at the literature review. The history of scientific study of climate change is long. More than a century ago, for example, [START_REF] Fourier | Remarques générales sur les températures du globe terrestre et des espaces planétaires[END_REF][START_REF] Fourier | Mémoire sur les températures du globe terrestre et des espaces planétaires[END_REF] was the first to notice that the Earth is a greenhouse, kept warm by an atmosphere that reduces the loss of infrared radiation. The overriding importance of water vapor as a greenhouse gas was recognized even then. In the late 1890s, [START_REF] Arrhenius | On the influence of carbonic acid in the air upon the temperature of the ground[END_REF] was the first to quantitatively relate the concentration of CO 2 in the atmosphere to global surface temperature. Given this long-standing history, one might lament the fact that -perhaps owing, in part, to the politically-charged nature of the topic -many people mistakenly assume that the science that underlies our current understanding of climatic change is, in some way, suspect or unreliable. Of course, the nature of the greenhouse debate is far too complex and multifaceted to lend itself well to simplistic "is it happening or isn't it?" characterizations.

The vast evidence that the climate of the Earth is changing due to the anthropogenic increase in greenhouse gases (GHGs) is compiled in the successive reports of the Intergovernmental Panel on Climate Change (IPCC 1996a(IPCC , 2001a(IPCC , 2007a(IPCC , 2013)), CO 2 being the largest contributor (Farmer and Cook 2013, p. 4;[START_REF] Stern | The economics of climate change[END_REF][START_REF] Stott | Impacts of incentives to reduce emissions from deforestation on global species extinctions[END_REF]. Typically, the effect of global warming on the economic system is modeled using integrated assessment models (IAMs). IAMs are motivated by the need to balance the dynamics of carbon accumulation in the atmosphere and the dynamics of de-carbonization of the economy (Nordhaus 1994a). A specific goal of these studies is to evaluate different abatement scenarios as to economic welfare and their effects on GHG emissions.

Integrated assessment modelling (IAM)

The emergence of IAMs as a science-policy interface

With the immense enhancement in computer technology, integrated modelling surfaced in the mid-1980s as a new paradigm for interfacing science and policy concerning complex environmental issues such as climate change. In the second half of the eighties, it was believed that integrated modelling would be the optimal way to interface science with policy. According to [START_REF] Parson | Searching for integrated assessment: a preliminary investigation of methods and projects in the integrated assessment of global climatic change[END_REF]:

"To make rational, informed social decisions on such complex, long-term, uncertain issues as global climate change, the capacity to integrate, reconcile, organize, and communicate knowledge across domains to do integrated assessment is essential." Therefore, integrated assessment models are believed to produce insights that cannot be easily derived from the individual natural or social science component models that have been developed in the past [START_REF] Weyant | Integrated assessment of climate change: an overview and comparison of modeling approaches[END_REF]; see also, Meyers (2012, pp. 5399 5428) andRasch (2012, Ch. 8) for a further discussion.

According to Beltran et al. (2005, p. 70), Integrated Assessment (IA) can be defined as an interdisciplinary process of combining, interpreting and communicating knowledge from diverse scientific disciplines in such a way that the whole cause-effect chain of a problem can be evaluated from a synoptic perspective with two characteristics: (i) it should have added value compared to single disciplinary assessment; and (ii) it should provide useful information to decision makers.

Classification of IAMs

Nowadays IAMs are capable of reflecting a range of modelling approaches that aim to provide policy--relevant information, and most can be summarized by: (i) policy optimization that seeks optimal policies and (ii) policy evaluation models that assess specific policy measures. The complexity of optimization models is limited, however, because of the requirement of a large number of numerical algorithms in optimization. Therefore these models tend to be based on compact representations of both the socioeconomic and natural science systems. They thus contain a relatively small number of equations, with a limited number of geographic regions. Apart from policy optimization, policy evaluation models tend to be descriptive and can contain much greater modelling detail on bio-geo-physical, economic or social aspects. These models are often referred to as simulation models, and are designed to calculate the consequences of specific climate policy strategies in terms of a suite of environmental, economic, and social performance measures. An early example of this type of model is the Integrated Model to Assess the Global Environment (IMAGE) [START_REF] Rotmans | IMAGE an Integrated Model to Assess the Greenhouse Effect[END_REF]Alcamo et al. 1998).

Other policy evaluation models include Asian-Pacific Integrated Model (AIM), Model for Energy Supply Strategy Alternatives and their General Environmental impacts (MESSAGE) [START_REF] Gusti | Technical description of the IIASA model cluster[END_REF], etc. These models are not subject to the constraints of optimization models, and therefore can incorporate greater complexity in their representations of natural and social processes at the regional scale without losing detail. Thus, they are generally applied to comparisons of the consequences (e.g., regional economic and environmental impacts) of alternative emissions scenarios. But even with these detailed descriptive capabilities, they are not appropriate to optimize the economic activities of the energy-economy sector.

Application of integrated assessment models

Integrated Assessment Modelling is usually comprehensive, but it produces less detailed models than conventional climate-or socio-economic-centred approaches. It is based on an understanding that feedbacks and interconnections in the climate-society-biosphere system drive its evolution over time [START_REF] Davies | An integrated system dynamics model for analyzing behavior of the social-economic-climatic system: model description and model use guide[END_REF]. Rotmans et al. (1997, p. 36) state that integrated assessments "are meant to frame issues and provide a context for debate. They analyze problems from a broad, synoptic perspective."

Integrated assessment modelling is not a new concept; it rather has a long history of being applied to many problems. Over the past decade or so, integrated assessment models (IAMs) have been widely utilized to analyze the interactions between human activities and the global climate [START_REF] Weyant | Integrated assessment of climate change: an overview and comparison of approaches and results[END_REF]. The first IPCC report referenced two IAMs, the Atmospheric Stabilization et al. 2008). Later, MAGICC modelling framework became a foundation for the IPCC process, as it can easily show the climate implications of different emissions scenarios and can be benchmarked to have climate responses that mimics those of any of the GCMs. [START_REF] Rotmans | Perspectives on global change: the TARGETS approach[END_REF], mention that the integrated assessment approach allows for an exploration of the interactions and feedbacks between subsystems and provides flexible and fast simulation tools. It also identifies and ranks major uncertainties, and supplies tools for communication between scientists, the public, and policy makers. [START_REF] Davies | Modelling feedback in the Society-Biosphere-Climate system[END_REF] provides some examples of integrated assessment models including the Integrated Model to Assess the Greenhouse Effect, IMAGE 2.0 [START_REF] Alcamo | Modeling the global societybiosphere-climate system: part 1: model description and testing[END_REF], the Asian Pacific Integrated Model, AIM [START_REF] Matsuoka | Scenario analysis of global warming using the Asian-Pacific Integrated Model (AIM)[END_REF], the Model for Evaluating Regional and Global Effects of GHG reduction policies, MERGE [START_REF] Manne | MERGE a model for evaluating regional and global effects of GHG reduction policies[END_REF], the Tool to Assess Regional and Global Environmental and health Targets for Sustainability, TARGETS [START_REF] Rotmans | Perspectives on global change: the TARGETS approach[END_REF], the Integrated Global System Model, IGSM [START_REF] Prinn | Integrated global system model for climate policy assessment: feedbacks and sensitivity studies[END_REF], Integrated Climate Assessment Model, ICAM [START_REF] Dowlatabadi | Bumping against a gas ceiling[END_REF], the Dynamics Integrated Climate-Economy model, DICE [START_REF] Nordhaus | Warming the world: economic models of global warming[END_REF], the Feedback-Rich Energy-Economy model, FREE [START_REF] Fiddaman | Feedback complexity in integrated climate-economy models[END_REF][START_REF] Fiddaman | Exploring policy options with a behavioral climate-economy model[END_REF], and World3 [START_REF] Meadows | Limits to growth: the thirty year update[END_REF]). The list of IAMs and Computable General Equilibrium (CGE) models used in climate policy analyses is long. The reader can refer to [START_REF] Ortiz | Integrated impact assessment models of climate change: a literature review[END_REF] and [START_REF] Stanton | Inside integrated assessment models: four issues in climate economics[END_REF] for a literature review of some of these models.

Most IAMs consist of (i) an economy module in which the interactions among economic sectors and agents are represented; (ii) a climate module representing the relationships between GHG emissions and concentrations and temperature changes; and (iii) predetermined relationships between both modules; i.e. damage functions representing the impact of temperature changes in the economy, and abatement cost functions summarizing the available climate change mitigation options. The level of details employed in each of these components characterizes and differentiates the existing models [START_REF] Ortiz | DICER-A tool for analyzing climate policies[END_REF].

It has been predicted that global climate change will have significant impacts on society and the economy, and that the adaptation measures to tackle global climate change will be accompanied with very large economic burden. It is estimated that GHG emissions will increase to over one-half of total global emissions by the end of the next century (Akhtar 2011, p. 42). The Integrated Assessment Model (IAM) provides a convenient framework for combining knowledge from a wide range of disciplines; it is one of the most effective tools to increase the interaction among these groups.

Challenges for IAM studies

The foremost challenge for IAM Studies is the integration of the natural and socioeconomic systems in order to better model the relationship between human activities and the global environment. To the present, many integrated assessment models share the same basic framework.

Whether current IAMs have reached a level of development where they can serve as the adequate basis for judgments in formulating actual global environmental measures is debatable. Modellers appear to agree, however, that for the most part the framework itself is acceptable. The integrated assessment of global environmental issues from the perspectives of the natural and social sciences is not a field of learning involving the pursuit of truth. Rather, it is a practical science that aims at providing useful guidance to policy makers seeking to establish rules and policies that help smooth the relationships between natural rule, the global environment and humanity. Conventionally, it is possible to encapsulate the relationships between such practical scientific studies and the real world in a relatively simple framework.

Any attempt to represent fully a complex issue and its numerous interlinkages with other issues in a quantitative modelling framework is doomed to failure [START_REF] Rotmans | Uncertainty management in integrated assessment modeling: towards a pluralistic approach[END_REF].

However, even a simplified integrated assessment model can provide valuable insight into certain aspects of complex issues. Through their intersectoral links and communication facilities, IAMs can provide more accurate representations of such problems as climate change than those studies based on a conventional modelling framework. IAMs thus remain a very useful tool for decision makers, scientists-especially in the field of climate change studies.

In analyzing implications of climate policies, these models often assume that the growth rate of the economy is exogenously given, and feedback effects of lower GHGs concentrations in the atmosphere on economic growth are frequently neglected. For example, in [START_REF] Nordhaus | Warming the world: economic models of global warming[END_REF] different abatement scenarios are analyzed where the growth rate of the economy is assumed to be an exogenous variable and the results are compared with the social optimum. Also, the fundamental alterations in wealth holdings are systematically downplayed by the practices of current integrated assessment modeling [START_REF] Decanio | Economic models of climate change: a critique[END_REF]Kirman 1992, p. 132).

Improvements of IAMs

There are several aspects in which IAMs need to be improved. Besides the need for better data on expected economic damages of climate change, future research on IAMs should consider:

! Economic modeling in developing countries. Most current IAMs do not match the economic and social organization of developing countries well [START_REF] Carraro | Climate change policy: Models, controversies and strategies[END_REF]. This leads to biases in global assessments where climate change mitigation and impacts are evaluated in developing countries as if their economies work like those of developed countries.

! Endogenous Technical Change. Most IAMs models have considered technical change as an exogenous variable, where emission intensity of output is expected to decrease based on historical records [START_REF] Kelly | Integrated assessment models for climate change control[END_REF]. But, technical change might be critically important in GHGs mitigation scenarios. For example, the development of inexpensive electric automobiles or solar power might reduce significantly GHGs emissions at low cost. Further research is needed in order to incorporate endogenous innovation in climate models.

! Specifying Regulation Instruments [START_REF] Kelly | Integrated assessment models for climate change control[END_REF]. Most IAMs calculate optimal carbon taxes for achieving emission reduction targets. But, the impact of recycling such tax revenues needs to be evaluated. Also, regulation instruments have associated monitoring costs and penalties for non-compliance which would reduce the overall efficiency of mitigation strategies.

! Adjustment to Climate Change [START_REF] Kelly | Integrated assessment models for climate change control[END_REF]. Agents within the economy would respond to global warming in order to reduce its impacts. For example, given changes in rainfall and precipitation, farmers could modify crop choice in order to reduce the losses caused by climate change. Also, migration patterns and urbanization in developing countries might be modified in such a way that areas highly vulnerable to climate change would limit their growth.

! Include carbon mitigation in sinks. One of the major drawbacks of IAMs is that they mainly focus on mitigation in the energy sector (van Vuuren et al. 2006b, p. 166). For example, the RICE (Regional Dynamic Integrated model of Climate and the Economy) and DICE (Dynamic Integrated model of Climate and the Economy) [START_REF] Nordhaus | Warming the world: economic models of global warming[END_REF] models consider emissions from land use as exogenous (see also, Tol 2010 p. 97). But, GHGs emissions from land use and current terrestrial uptake are significant, so including GHGs mitigation in sinks is something to be considered within IAMs [START_REF] Wise | Implications of limiting CO 2 concentrations for land use and energy[END_REF]).

This study

This thesis looks at the interaction between global warming and economic growth, along the lines of the Dynamic Integrated model of Climate and the Economy (DICE) of Nordhaus (1994a), with subsequent updates in [START_REF] Nordhaus | Warming the world: economic models of global warming[END_REF], [START_REF] Nordhaus | The challenge of global warming: economic models and environmental policy[END_REF][START_REF] Nordhaus | A question of balance[END_REF][START_REF] Nordhaus | Integrated economic and climate modeling. Handbook of computable general equilibrium modeling[END_REF]Nordhaus ( , and 2013a)). [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF] (see also [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF] extended the DICE framework by including endogenous growth, to account for the fact that environmental policy affects not only the level of economic variables but also the long-run growth rate. Using the extended DICE model, Greiner argues that higher abatement activities reduce GHG emissions and may lead to a rise or decline in growth. The net effect on growth depends on the specification of the function between the economic damage and climate change.

Since anthropogenic GHGs are the result of economic activities, the main shortcoming in [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF] approach is that of treating industrial CO 2 emissions as constant over time.

Another problematic aspect of Greiner's emissions formulation is its inability to allow for zero abatement activities. In fact, his formulation only holds for a minimum level of abatement.

This study addresses these issues by using a novel approach to formulating emissions that depend on economic growth and vary over time; in this approach, abatement equal to zero corresponds to Business As Usual (BAU). To do so, this work uses logistic functions [START_REF] Akaev | Stabilization of the planetary climate in the twenty first century by transition to a new paradigm of energy consumption[END_REF][START_REF] Sahal | Patterns of technological innovations[END_REF]) that yield the global dynamics of carbon intensity, i.e. of energy emissions per unit of energy consumed, and of energy intensity, i.e. of energy use per unit of aggregate gross domestic product (GDP) throughout the whole 21 st century [START_REF] Akaev | Stabilization of the planetary climate in the twenty first century by transition to a new paradigm of energy consumption[END_REF]).

The study further uses the extended DICE modeling framework by considering both human and physical capital accumulation, in addition to the GHG emissions, as well as a ratio of abatement spending to the tax revenue or abatement share (see also [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF][START_REF] Greiner | The global environment, natural resources and economic growth[END_REF]. The methodology utilized can analytically clarify the mutual causality between economic growth and the climate change-related damages and show how to alter this relationship by the use of various mitigation measures geared toward reduction of CO 2 emissions [START_REF] Hannart | Disconcerting learning on climate sensitivity and the uncertain future of uncertainty[END_REF]Metz et al. 2007). The study will use the abatement share to invest in the increase of overall energy efficiency of the economy (Diesendorf 2014, p. 143) and decrease of overall carbon intensity of the energy system. It will be shown below that over the next few decades, up to the mid-21 st century, mitigation costs do hinder economic growth, but that this growth reduction is compensated later on by the having avoided negative impacts of climate change on the economy; see also Kovalevsky and Hasselmann (2014, Figure 2).

The thesis also introduces CO 2 capturing and storing (CCS) technologies and reduction of deforestation, as well as increasing photosynthetic biomass sinks as a method of controlling atmospheric CO 2 and consequently the intensity and frequency of climate change related damages.

This move is necessitated on one part by the fact that most of the scenario studies that aim Examples of studies that focus on the energy sector are the RICE (Regional Dynamic Integrated model of Climate and the Economy) and DICE (Dynamic Integrated model of Climate and the Economy) [START_REF] Nordhaus | Warming the world: economic models of global warming[END_REF] models which consider emissions from land-use as exogenous (see also, Tol 2010 p. 97). Nevertheless, GHG emissions from deforestation and current terrestrial uptake are significant, so including GHG mitigation in the biota sinks has to be considered within integrated assessment models (IAMs), cf. [START_REF] Wise | Implications of limiting CO 2 concentrations for land use and energy[END_REF].

Several studies provide evidence that forest carbon sequestration can reduce atmospheric CO 2 concentration significantly and could be a cost-efficient way for curbing climate change (e.g., [START_REF] Bosetti | Linking reduced deforestation and global carbon market: implications for clean energy technology and policy flexibility[END_REF][START_REF] Gullison | Tropical forests and climate policy[END_REF][START_REF] Tavoni | Forestry and the carbon market response to stabilize climate[END_REF][START_REF] Wise | Implications of limiting CO 2 concentrations for land use and energy[END_REF]). Again, most earlier studies have not considered the more recent mitigation options currently being discussed in the context of ambitious emission reduction, such as hydrogen and carbon capture and storage (CCS); see [START_REF] Edmonds | Modelling greenhouse gas energy technology responses to climate change[END_REF], IEA (2004) and[START_REF] Ipcc | IPCC Special Report on carbon dioxide capture and storage. Prepared by Working Group III of the IPCC[END_REF]. Given current insights into climate risks and the state of the mitigation literature, then, there is a very understandable and explicit need for comprehensive scenarios that explore different long-term strategies to stabilize GHG emissions at low levels [START_REF] Metz | How, and at what costs, can low-level stabilization be achieved? An overview[END_REF][START_REF] Morita | Greenhouse gas emission mitigation scenarios and implications[END_REF]). This study works towards this direction by studying relevant economic aspects of deforestation control and carbon sequestration in forests, as well as the widespread application of CCS technologies as alternative policy measures for climate change mitigation.

The Coupled Climate-Economy-Biosphere (CoCEB) model is not intended to give a detailed quantitative description of all the processes involved, nor to make specific predictions for the latter part of this century. It is a reduced-complexity model that attempts to incorporate the climate-economy-biosphere interactions and feedbacks, while using the smallest number of variables and equations needed to capture the main mechanisms involved in the evolution of the coupled system. We merely wish to trade greater detail for more flexibility in the analysis of the dynamical interactions between the different variables. The modeling framework here brings together and summarizes information from diverse fields in the literature on climate change mitigation measures and their associated costs, and allows comparing them in a coherent way. The need for a hierarchy of models of increasing complexity is an idea that dates back in the climate sciences to the beginnings of numerical modeling (e.g., [START_REF] Schneider | Climate modeling[END_REF], and has been broadly developed and applied since [START_REF] Ghil | Hilbert problems for the geosciences the 21 st century[END_REF], and references therein).

The study seeks to show that:

(i) Investment in low-carbon technologies helps to reduce the volume of industrial CO 2 emissions, lower temperature deviations, and lead to positive effects in economic growth.

(ii) Low investment in CCS contributes to reducing industrial carbon emissions and to increasing GDP growth, but further investment leads to a smaller reduction in emissions, as well as in the incremental GDP growth.

(iii) Enhanced deforestation control contributes to a reduction in both deforestation emissions and atmospheric CO 2 concentration, thus reducing the impacts of climate change and contributing to a slight appreciation of GDP growth, but this effect is very small compared to that of implementing low carbon technologies or CCS.

(iv) The result in (ii) is very sensitive to the formulation of CCS costs. To the contrary, the results for deforestation control are less sensitive to the formulation of its cost.

A large range of hypotheses on CCS costs appears in the literature, and our modeling framework permits to span this range and check the sensitivity of results.

The sensitivity study carried out is not intended to make precise calibrations; rather, the study wants to provide adiagnostic tool for studying qualitatively how various climate policies affect the economy.

The next chapter describes the theoretical model, detailing the additions with respect to Nordhaus (2013a), [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF] and [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF], introduces the biomass equation and the effect on the carbon emissions of CCS and of deforestation control. Chapter 4

presents the numerical simulations and their results. In Chapter 5, we test the sensitivity of the results to key parameters. Chapter 6 summarizes, discusses the results, and formulates our conclusions with caveats and avenues for future research.

CHAPTER 3 MODEL DESCRIPTION

Climate module

The time evolution of the average surface temperature T (SAT) on Earth is modeled via an energy balance equation given by

( ) ( ) T 1 4 T a h h h 1 α Q 6.3β 1 ξ εσ τ d In d 4 T C T t c c c C - - ⎛ ⎞ = - + ⎜ ⎟ ⎝ ⎠ , (1)
see, for instance, Ghil and Childress (1987, Ch. 10), Hans and Hans (2013, Ch. 2) or McGuffie and Henderson-Sellers (2005, p. 81-85;2014). Here the first and second terms on the right-hand side are incoming and outgoing radiative fluxes respectively, while the third term is radiative forcing due to increase in GHGs [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF][START_REF] Kemfert | An integrated assessment model of economy-energy-climate -the model Wiagem[END_REF]; T σ is the Stefan-Boltzmann constant, a τ the infrared (long-wave) transmissivity of the atmosphere, ε the emissivity that gives the ratio of actual emission to blackbody emission, T α the mean planetary albedo, Q is the average solar constant. The specific heat capacity h c of Earth is largely determined by the oceans [START_REF] Levitus | Warming of the World ocean, 1955-2003[END_REF] and it is taken equal to 16.7 Wm -2 K -1 [START_REF] Schwartz | Heat capacity, time constant, and sensitivity of Earth's climate system[END_REF][START_REF] Schwartz | Reply to comments by G Foster et al, R Knutti et al and N Scafetta on ''Heat capacity, time constant, and sensitivity of Earth's climate system[END_REF], which corresponds to an ocean fractional area of 0.71 and a depth of 150 m of the ocean mixed layer.

The current CO 2 concentration C is given in gigatons of carbon (GtC, 1 Gt = 10 15 grams) and Ĉ is the pre-industrial CO 2 concentration. All the feedbacks, are represented in this highly idealized model by the factor 1 β , which is assumed to take values between 1.1 and 3.4 (Greiner and Semmler 2008, p. 62); in this study, it was assumed that 1 β 3.3 = . The parameter ξ 0.23 = captures the fact that part of the warmth generated by the greenhouse effect is absorbed by the oceans and transported from their upper layers to the deep sea [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF]. The other parameters have standard values that are listed in Table 1.

At equilibrium, that is for d d 0 T t = , Equation ( 1) gives an average SAT of 14 0 C for the pre-industrial GHG concentration, i.e. for Ĉ C = . Doubling the CO 2 concentration in Equation (1) yields an increase of about 3.3 0 C in equilibrium temperature, to 17 0 C. This increase lies within the range of IPCC estimates, between 1.5 and 4.5 0 C [START_REF] Charney | Carbon dioxide and climate: a scientific assessment[END_REF]IPCC 2001a, p. 67;IPCC 2013) with a best estimate of about 3.0 0 C (IPCC 2007a, p.12).

The study represents the evolution C of the concentration of CO 2 in the atmosphere, following [START_REF] Uzawa | Economic theory and global warming[END_REF] and [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF], as ( )

2 Y o β µ dC E C C dt = - -, (2)
where Y E is industrial CO 2 emissions. The excess C above pre-industrial level is reduced by the combined effect of land and ocean sinks. The inverse o µ of the atmospheric lifetime of CO 2 is estimated in the literature to lie within an uncertainty range that spans 0.005 0.2 (IPCC 2001a, p.

38);

The study takes it here to equal o µ 1120 0.0083 = = , i.e. closer to the lower end of the range (IPCC 2001a, p. 38;Nordhaus 1994a, p. 21). The fact that a certain part of GHG emissions is taken up by the oceans and does not remain in the atmosphere is reflected in Equation ( 2) by the parameter 2 β .

Economy module

In [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF] and [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF] the per capita GDP, Y , is given by a modified version of a constant-return-to scale Cobb-Douglas production function [START_REF] Cobb | A theory of production[END_REF], ( )

α 1 α Â Y K H D T T - = -. ( 3
)
Here K is the per capita physical capital, H is the per capita human capital, A 0 > the total factor of productivity, 0 α 1 < < is the capital share, ( )

D T T
is the damage, expressed as a function of the temperature difference due to climate change. The damage function is described in Subsection (3.3.3) below.

The economy income identity in per capita variables is given by

E E Y X I M G -= + + , (4)
with τ X Y =
the (per capita) tax revenue, 0 τ 1 < < the per annum tax rate, I investment, E M consumption, and E G abatement activities. This means that national income after tax is used for investment, consumption, and abatement. The study assumes that E G is expressed as a fraction of

X , E b b τ τ τ G X Y = = , (5)
with b 0 τ 1 ≤ < the ratio of per annum abatement share, used as a policy tool. Consumption is also expressed as a fraction of Y after tax, that is,

( ) E 1 τ M c Y = - , (6)
with 0 1 c < < the global annual consumption share.

The accumulation of per capita physical capital K is assumed to obey ( )

E E K d δ d K Y X M G n K t = -- -- + , (7)
the logistic-type human population growth rate 0

1 n < < is given, in turn, by n d 1 1 d 1 δ n n t ⎛ ⎞ = - ⎜ ⎟ - ⎝ ⎠ , (8)
with n δ being the per year decline rate of n , and K δ the per year depreciation rate of physical capital. Substituting the definitions of Y , X , E M , and E G into Equation ( 7) the study gets

( ) ( ) ( ) ( ) α 1 α b K d  1 τ 1 τ 1 τ δ d K K H D T T c n K t - = - - + - - - + ⎡ ⎤ ⎣ ⎦ . ( 9
)
For physical capital to increase, d d 0 K t > , the parameters must satisfy the inequality

( ) ( ) b 0 τ 1 τ 1 τ 1 c < + + - < ⎡ ⎤ ⎣
⎦ . Now, proceeding as above for K , I assume that the per capita human capital H evolves over time as

( ) ( ) ( ) { } ( ) α 1 α b H d φ A 1 τ 1 τ 1 τ δ d H K H D T T c n H t - = - - + - - - + ⎡ ⎤ ⎣ ⎦ , ( 10
)
here φ 0 > is a coefficient that determines how much any unit of investment contributes to the formation of the stock of knowledge and H δ gives the depreciation of knowledge.

Note that the study takes, as a starting point, the Solow-Swan approach [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF][START_REF] Solow | A contribution to the theory of economic growth[END_REF][START_REF] Swan | Economic growth and capital accumulation[END_REF], in which the share of consumption and saving are given.

This is done because the study wants to focus on effects resulting from climate change, which affect production as modeled in Equations ( 3)-( 10) and, therefore, neglect effects resulting from different preferences.

The formulation assumes, furthermore, that government spending, except for abatement, does not affect production possibilities. Emissions of CO 2 are a byproduct of production and hence are a function of per capita output relative to per capita abatement activities. This implies that a higher production goes along with higher emissions for a given level of abatement spending. This assumption is frequently encountered in environmental economics (e.g., [START_REF] Smulders | Entropy, environment, and endogenous growth[END_REF]. It should also be mentioned that the emission of CO 2 affect production indirectly by affecting the climate of the Earth, which leads to a higher SAT and to an increase in the number and intensity of climaterelated disasters (see, e.g., [START_REF] Emanuel | Increasing destructiveness of tropical cyclones over the past 30 years[END_REF][START_REF] Min | Human contribution to more intense precipitation extremes[END_REF]).

Industrial CO 2 emissions

In [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF] and [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF], emissions Y E are formally described, as a function of the production Y , by

γ γ γ E b b τ τ τ τ aY aY a G Y ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ = = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ , (11)
here γ 0 > is a constant and 0 a > a technology index that describes how polluting a given technology is. Note that Equation ( 11) is defined only for b τ different from zero; hence, it does not consider a no-abatement or BAU scenario. Moreover, Equation ( 11) also gives constant emissions over time even when the economic activity is changing, which is unrealistic. Here, the study uses instead a formulation of emissions Y E that vary over time and in which abatement can be let to be zero.

Specifically, the study uses the Kaya-Bauer identity [START_REF] Bauer | Carbon capturing and sequestration an option to buy time[END_REF][START_REF] Kaya | Impact of carbon dioxide emission control on GNP growth: interpretation of proposed scenarios[END_REF]) that breaks down CO 2 emissions Y E (in GtC/y) into a product of five components: emissions per unit of energy consumed (carbon intensity of energy), energy use per unit of aggregate GDP (energy intensity), per capita GDP, human population, and carbon emission intensity, as shown below: The Y E level also depends on abatement activities, as invested in the increase of overall energy efficiency in the economy and decrease of overall carbon intensity of the energy system.

tot Y Y tot c c ccs ccs κ σ κ . E E energy Y E L energy Y L E c e YL YL ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ = Here Y is aggregate GDP, ( ) Y Y L = is per capita GDP, L is the human population,
The case of b τ 0 = in Equation ( 5) corresponds to unabated emissions, i.e. BAU. Emissions are reduced as the abatement share increases. Taking the natural logarithms and differentiating both sides of the Kaya-Bauer identity yields

[ ] Y σ Y c c s Y d d E g g n g E t = + + + , ( 12
)
where σ g is the growth rate of σ , Y g is the growth rate of Y , n is the population growth rate and ccs g is the CCS growth rate. If CCS is applied, then Y t o t E E < . There are many concerns and uncertainties about the CCS approach and it is usually not taken as a real sustainable and environmental friendly mitigation option to reduce emissions over a longer period [START_REF] Tol | Carbon dioxide mitigation[END_REF]).

The study now formulates the technology-dependent carbon intensity σ . The thesis follows the approach of [START_REF] Sahal | Patterns of technological innovations[END_REF], who models the replacement of one technology by another using a logistic law. The energy intensity c e , in tons of reference fuel (TRF)/$1000 of Y , is the share of hydrocarbon-based energy (coal, oil, and natural gas) in the global energy balance (GEB) of the twenty-first century. Its dynamics are described by a descending logistic function [START_REF] Akaev | Stabilization of the planetary climate in the twenty first century by transition to a new paradigm of energy consumption[END_REF],

( ) ( ) ( ) c c exp ψ 1 1 exp ψ 1 r t e f r t ⎛ ⎞ = - ⎜ ⎟ ⎜ ⎟ + - ⎝ ⎠ , ( 13
)
here the study takes 1990 as the time when the use of renewable energy sources (biomass and wastes, hydropower, geothermal energy, wind energy, and solar energy) and biofuels became significant in the GEB. The multiplier c 0.881 f = corresponds to Equation ( 13) using these values indicate that the share of fossil fuels will be significant throughout the whole twenty-first century and, when b τ 0 = , this share decreases to 35 % only by its end [START_REF] Akaev | Stabilization of the planetary climate in the twenty first century by transition to a new paradigm of energy consumption[END_REF].

As different types of fossil fuels produce different volumes of CO 2 in combustion, the dynamics of fossil fuel consumption i.e., the relative shares of coal, oil, and natural gas should be taken into account when calculating the future dynamics of CO 2 emission. Since these shares are not known at this time, the study assumes a logistic function for describing a reduction of the carbon intensity of energy c c , in tons of carbon/tons of reference fuel (tC/TRF), throughout the 21 st century (Akaev 2012), ( )

c c 1 exp ψ a c c r t -∞ = + + - , (14)
with c 0 a > a constant.

Thus the carbon intensity σ , which is technology-dependent and represents the trend in the CO 2 -output ratio, can now be given by the product of the energy intensity c e in Equation ( 13) and the carbon intensity of energy c c in Equation ( 14), thus:

( ) ( ) ( ) ( ) c c exp ψ σ 1 1 exp ψ 1 exp ψ 1 r t a f c r t r t -∞ ⎡ ⎤ ⎡ ⎤ = - + ⎢ ⎥ ⎢ ⎥ + - + - ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ . ( 15
)
The study can now calculate the de-carbonization of the economy, i.e. the declining growth rate of σ , by taking the natural logarithms of Equation ( 15) and getting the derivative with respect to time:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 c c σ 2 2 c c ψ exp ψ 1 exp ψ 1 ψ exp ψ ψ exp ψ 1 1 exp ψ 1 exp ψ 1 r t r t r t a r t f g e c r t r t ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ + -- ⎡ ⎤ - ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎢ ⎥ ⎢ ⎥ = + ⎢ ⎥ ⎢ ⎥ + - ⎡ ⎤ ⎡ ⎤ + - ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ . ( 16
)
In a similar way as Equation ( 16) was derived from [START_REF] Aseev | The Pontryagin maximum principle and economic growth[END_REF], the growth rate Y g of per capita output is obtained from Equation ( 3) as ( )

1 α 1 d α d d 1 d d d d d d d Y K H D T Y t K t H t D T t - = + + ' or, ( ) Y K H 1 d d α 1 α d d D T g g g D T t = + - + , (17)
with K g the per capita physical capital growth and H g the per capita human capital growth.

Human population evolves; cf. [START_REF] Golosovsky | Hyperbolic growth of the human population of the Earth: analysis of existing models[END_REF], as

( ) ( ) { } d 1 exp 1990 d L nL L L t ⎡ ⎤ = - - ⎣ ⎦ , ( 18
)
where n is the population growth rate as given in Equation [START_REF] Sm | Carbon capture and storage: Technologies, policies, economics, and implementation strategies[END_REF]. Equation ( 18) yields L = 9×10 9 people in the year t = 2100. This value is consistent with the 2100 population projections of scenarios in the literature (e.g., van Vuuren et al. 2011, Table 3).

Inclusion of CCS in the industrial CO 2 emissions equation

In order to express the term ccs g in Equation ( 12), the study assumes the leakage of captured carbon to be zero and use [START_REF] Akaev | Stabilization of the planetary climate in the twenty first century by transition to a new paradigm of energy consumption[END_REF] formula to define the reduction of emissions by the CCS as a fraction κ ccs :

( ) ( )

2 exp 1 exp ccs t t ω κ ω - = + - , (19)
In this equation,

( ) { } 0 ω b ω ω 1 1 1 α τ f = - + ⎡ ⎤ ⎣
⎦ , with 0 ω and ω α constant, and the parameter f , as mentioned above, represents the share of investment in CCS; the investment in low-carbon technologies therefore is 1 f and appears in the energy intensity parameter ψ in Equation 13.

Taking the natural logarithms and differentiating both sides of Equation ( 19), we get the growth rate of κ ccs as ( ) ( ) The estimated CO 2 emissions reduction due to CCS for the time interval 2020-2050 is 0.0038-0.7 GtC/year (Bosetti 2010, p. 344;[START_REF] Galiana | Technology-led climate policy[END_REF][START_REF] Ipcc | IPCC Special Report on carbon dioxide capture and storage. Prepared by Working Group III of the IPCC[END_REF]. Metz (2010, p. 216), on the other hand, projected the 2030 CCS reduction potential of CO 2 emissions at 0.0273-0.0545 GtC/y with a possibility of growing to 0.1364-0.409 GtC/y by 2050; also see, [START_REF] Uyterlinde | The contribution of CO 2 capture and storage to a sustainable energy system[END_REF].

ccs ω 1 exp ω g t - = + - ⎡ ⎤ ⎣ ⎦ . ( 20
)

Cost of CCS

Keeping in mind this range of emissions reduction and of prices, we calibrated the parameter ω α in that affects ω in Equation ( 19) above, in order to obtain similar values. For GtC/year by 2050 and 0.17 GtC/year by 2100. This emissions reduction comes at an approximate aggregate cost of $124/tC by 2050 and $558/tC by 2100. The cost is computed as

E b τ τ fG L f YL = ,
i.e. the product of the share of investment in CCS (in this case f = 1.0) and the aggregate abatement costs; see Equation ( 5) and Equation ( 18) above. These costs lie within the range of the CCS costs in the literature, as given above. Given the large incertitude in this range of costs, we conduct in Subsection 5.3 below a sensitivity study to changes in the ω α value.

Damage function

The damage function D gives the decline in Y , the global GDP, which results from an increase of the temperature T above the pre-industrial temperature T . Nordhaus (1994a) formulates it as ( ) ( )

1 χ 1 ˆ1 D T T m T T - ⎡ ⎤ -= + - ⎢ ⎥ ⎣ ⎦ , (21)
with 1 0 m > and χ 0 > , and the damage is defined as ( )

1 Y DY D Y - = -
. The greater T T -, the smaller the value of ( )

D T T
-, and accordingly the smaller the value DY of the remaining GDP, after the damage.

The representation of climate change damages is both a key part and one of the weakest points of IAMs [START_REF] Tol | On the representation of impact in integrated assessment models of climate change[END_REF]. Temperature was used originally by Nordhaus (1994a) as a proxy for overall climate change. This may have taken the research community′s focus off from potentially dangerous changes in climate apart from temperature [START_REF] Toth | Practise and progress in integrated assessments of climate change: a workshop overview[END_REF]. However, without using a detailed climate model, temperature remains the best option available. This study assumes, in choosing this option, that physical and human capitals are distributed across infinitely many areas in the economy, and that the damages by natural disasters are uncorrelated across areas. With such an assumption, some version of the law of large numbers can justify a result like Equation ( 21) above; see [START_REF] Dell | What do we learn from the weather? The new climateeconomy literature[END_REF] for an insightful discussion about the damage function.

Nordhaus (1994a) first estimated the damage from CO 2 doubling which, in his calculations was equivalent to a 3 0 C warming to be 1.33 % of global GDP [START_REF] Nordhaus | An transition path for controlling greenhouse gases[END_REF].

Additionally, he argued that damage would increase sharply as temperature increases; hence he used a quadratic function, in which χ 2 = , and 1 m is chosen to have 1.33 % loss of GDP for a 3 0 C warming.

Roughgarden and Schneider (1999), using the same functional form (Equation 21), derived damage functions for each of the disciplines represented in an expert opinion solicited by a climate change survey. Taking an average of their values, this study gets 1 0.0067 m = ; see, for instance, Table 1 in [START_REF] Labriet | Coupling climate damages and GHG abatement in a linear programming framework[END_REF]. On the other hand, the nonlinearity parameter χ 2.43 = is calibrated in this study, so that the model's BAU emissions of CO 2 per year and concentrations as well as change in global mean SAT from the pre-industrial level by 2100 mimic the Representative Concentration Pathway (RCP) 8.5. In fact, the projected climate change damages before and after abatement, as given by the damage function D in Equation ( 21), are consistent with the damages projected in [START_REF] Stern | The economics of climate change[END_REF]; see also [START_REF] Creedy | Sustainable preferences and damage abatement: value judgments and implications for consumption streams[END_REF] as well as Chen et al. (2012, p. 5).

Inclusion of a

Biosphere module: CO 2 -biomass interactions [START_REF] Uzawa | Global warming initiatives: the Pacific Rim[END_REF][START_REF] Uzawa | Economic theory and global warming[END_REF] extended the analysis of the CO 2 cycle by including forests, represented by a state variable B (biomass). Biomass absorbs CO 2 , so that an additional carbon sink appears in Eq.

1d. Thus, the forest acreage augments the absorption of CO 2 from the atmosphere. The only function of the stock of biomass in Uzawa's work was to sequester CO 2 and its stock could only be increased by net forestation activities, which use constrained resources. We did include here, though, the benefits of CO 2 fertilization, as suggested by [START_REF] Rosenberg | Global warming initiatives: comments[END_REF] in his commentary to [START_REF] Uzawa | Global warming initiatives: the Pacific Rim[END_REF] paper.

In order to include fertilization effects in the Uzawa model, van Wassenhove (2000) proposed a model of the interaction between biomass and CO 2 that is an adaptation of the Lotka Volterra predator-prey model [START_REF] Lotka | Elements of Physical Biology[END_REF][START_REF] Volterra | Leçons sur la Théorie Mathématique de la Lutte pour la Vie[END_REF]. Including fertilization effects and deforestation, our system of equations for this adaptation is:

( ) b b b d 1 γ d d Λ for B B g B B C C t ⎛ ⎞ = - + -- ⎜ ⎟ ⎝ ⎠ , (22)
[ ] ( ) ( )

2 Y B o b d ˆβ µ γ d C E E C C B C C t = + - -- -, (23)
where C is the CO 2 concentration in the atmosphere, B is the terrestrial photosynthetic biomass, b Λ is biomass carrying capacity, b g is the intrinsic colonization rate, b γ is the fertilization parameter. The term for d stands for deforestation efforts and B E denotes emissions from deforestation, both these are defined in the next subsection. Here Y E is industrial emissions as in Equation ( 12), and Ĉ the pre-industrial CO 2 .

Equation ( 23) is not different from Equation ( 2), apart from the addition of the fertilization term. In this case, the "excess" CO 2 is absorbed into the ocean (second term on the right-hand side of Equation 23) but also into the terrestrial biomass (third term on the right-hand side of Equation 23). Biomass change and CO 2 sequestration via photosynthesis is represented by the logistic Equation 22described by [START_REF] Clark | Mathematical Bioeconomics. The optimal management of renewable resources[END_REF] as a population growth model.

Carbon flux from deforestation and deforestation control

This section follows the work of [START_REF] Eriksson | The role of the forest in an integrated assessment model of the climate and the economy[END_REF] who investigated the role of the forest in an IAM of the climate and the economy. In that work, deforestation does not change the growth rate but leads to a smaller stock of biomass -which is subject to that growth -as well as to a smaller carrying capacity, i.e., a smaller area where forest can potentially re-grow.

Deforestation is formulated in terms of forest biomass volume and not in terms of land area. The maximum forest biomass carrying capacity is modeled to decrease with deforestation as follows:

b b dΛ Λ d for d t B = - , (24)
where for d is deforestation effort as in Equation ( 22), while the fraction b Λ B is a rescaling to convert biomass deforestation into biomass carrying capacity.

Deforestation is considered exogenous; we model it in our CoCEB model in agreement with [START_REF] Nordhaus | Warming the world: economic models of global warming[END_REF], who prescribed carbon emissions from deforestation to decrease in time according to:

( ) ( ) B B 0 b d exp δ 1 E E t R = - - ⎡ ⎤ ⎣ ⎦ , ( 25
)
where the parameter B0 E represents carbon emission in the first time period, b δ is the rate of decline of land-use emissions, and d 0 R ≥ is the deforestation control rate. These emissions can be converted into biomass deforestation by means of a global carbon intensity parameter for θ [START_REF] Eriksson | The role of the forest in an integrated assessment model of the climate and the economy[END_REF]; see also FAO 2010). The carbon intensity parameter, in this case, represents the average amount of carbon per volume of growing forest biomass. The total biomass deforestation in GtC at any time period is then given by ( ) ( )

B0 b d exp δ 1 θ for for E d t R ⎡ ⎤ = - - ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ . ( 26
)
When d 0 R = , we have the baseline deforestation. The deforestation control rate can either reduce or increase deforestation. When net deforestation is prevailing, for 0 d > or d 0 1 R ≤ < , and when net afforestation or reforestation is prevailing, for 0

d < or d 1 R > .
The total carbon emissions are hence assumed here to be the sum of industrial fossil fuel use emissions Y E from Equation ( 12) and of deforestation emissions B E from Equation (25).

Cost of the deforestation activity

The rental cost -that is, the rental payment to the landowner to hinder conversion of forested land -of avoiding direct release of carbon in one time period is given by the marginal cost function [START_REF] Eriksson | The role of the forest in an integrated assessment model of the climate and the economy[END_REF][START_REF] Kindermann | Global cost estimates of reducing carbon emissions through avoided deforestation[END_REF]):

( ) ( ) ( )

2 5 e π π mc 1 e 3 4 π π π 1 R V R t ⎡ ⎤ = + + - ⎣ ⎦ , ( 27
)
where the π's are the estimated cost parameters and R e is the reduction of direct carbon emission from deforestation. From Equation [START_REF] Canadell | Managing forests for climate change mitigation[END_REF] this is given by

( ) ( ) e B 0 b d exp δ R E t R = - . ( 28
)
The marginal cost or d R increases with the level of reduction of carbon emission due to deforestation. The land under forest is assumed to carry primarily a low opportunity cost. As more land under forest is targeted for deforestation control, its opportunity cost and hence its marginal cost increases over time. This is due to the fact that as the deforestation level declines, the land under forest that remains carries a high opportunity cost.

The total cost of avoiding deforestation which can be written as

( ) mc d d t V V s ds t = ∫ . ( 29
)
Rental payment occurs each time period and land under forest saved from conversion will not be deforested in future time periods. The study assumes forested land conversion, for example to agricultural land, as an investment in the primary input land, viewing land in the capital stock as a representative for the capital value of land devoted to production of non-forest goods.

The capital stock is hence assumed to grow with investment in land, i.e., conversion of land to agricultural land and urbanization or infrastructure. Deforestation is mainly caused by these two types of conversions, and hence the capital stock increases with deforestation. The accumulated investment in land is here assumed to be implicit in the total capital stock and does not affect the development of the total capital stock when following the baseline deforestation pattern. Reducing the baseline deforestation is here equivalent to a disinvestment of land capital resulting in a smaller net investment in the total capital stock. The per capita cost of avoiding deforestation is thus V V L = .

Through a meta-analysis of published works, [START_REF] Phan | The economic costs of avoided deforestation in the developing world: a meta-analysis[END_REF] Finally, including the biosphere module and deforestation control, the evolution of total per capita capital accumulation K in Eq. 9 can be written as

( ) [ ] ( ) α 1 α b K d  1 τ(1 τ ) (1 τ) δ d K K H D T T c n K V t - = - -+ --- + -. ( 30
)
Given the large incertitude of the estimated cost of deforestation control, a sensitivity analysis to the values of the parameters in Equation ( 27) is performed in Subsection 5.4 below.

Climate change abatement measures

A key part of the mitigation literature concentrates on the feasibility of different climate targets, often defined by GHG concentrations or by radiative forcing levels, and the associated costs; see [START_REF] Van Vuuren | A proposal for a new scenario framework to support research and assessment in different climate research communities[END_REF] and the citations therein. The broad range of options available for mitigating climate change includes the reduction of CO 2 emissions (increasing energy efficiency, increasing non-fossil fuel-based energy production, and the use of CCS), and CO 2 removal [START_REF] Edenhofer | On the economics of de-carbonization in an imperfect world[END_REF][START_REF] Steckel | Development without energy? Assessing future scenarios of energy consumption in developing countries[END_REF]).

Abatement policies

For reasons of political feasibility as well as of efficiency, the focus of climate policy has been on energy intensity and carbon intensity of energy, and not on population and wealth [START_REF] Tol | Carbon dioxide mitigation[END_REF]. All the popular policies point to increased de-carbonization efforts, i.e., to an increase in σ g . The historical record, however, shows quite clearly that global and regional rate of de-carbonization have seen no acceleration during the recent decade and in some cases even show evidence of recarbonization [START_REF] Canadell | Contributions to accelerating atmospheric CO 2 growth from economic activity, carbon intensity, and efficiency of natural sinks[END_REF][START_REF] Prins | How to get climate policy back on course[END_REF]).

Among the various market-based (or economic) instruments adopted to reduce CO 2 emissions, carbon taxes and tradable permits are the most widely discussed cost-efficient policies, both at a national and international level [START_REF] Fiddaman | Feedback complexity in integrated climate-economy models[END_REF][START_REF] Fischer | Instrument choice for environmental protection when technological innovation is endogenous[END_REF]IPCC 2007c;[START_REF] Mankiw | One answer to global warming: a new tax[END_REF][START_REF] Nordhaus | A question of balance[END_REF]Pizer 1997aPizer ,b, 1999a,b;,b;[START_REF] Uzawa | Economic theory and global warming[END_REF][START_REF] Weitzman | Prices vs. quantities[END_REF]. Forestry policies, particularly reduced deforestation, also emerge as additional low cost measures for the reduction of CO 2 emissions. Reduced deforestation would cut CO 2 emissions and increased afforestation would sequester CO 2 from the atmosphere (see, e.g., [START_REF] Bosetti | Linking reduced deforestation and global carbon market: implications for clean energy technology and policy flexibility[END_REF][START_REF] Rose | Land-based mitigation in climate stabilization[END_REF][START_REF] Tavoni | Forestry and the carbon market response to stabilize climate[END_REF][START_REF] Wise | Implications of limiting CO 2 concentrations for land use and energy[END_REF]).

Abatement share

The abatement costs of several IAMs tend to cluster in the range of about 1-2 % of GDP as the cost of cutting carbon emissions from baseline by 50 % in the period 2025-2050, and about 2.5-3.5 % of GDP as the cost of reducing emissions from baseline by about 70 % by 2075-2100 [START_REF] Boero | The macroeconomic consequences of controlling greenhouse gases: a survey[END_REF][START_REF] Boero | Global warming some economic aspects[END_REF][START_REF] Clarke | Controlling greenhouse gases -a survey of global macroeconomic studies[END_REF]Cline 1992, p. 184;Tol 2010, p. 87, Figure 2.2) with an increasing dispersion of results as higher emission reduction targets are set [START_REF] Boero | The macroeconomic consequences of controlling greenhouse gases: a survey[END_REF].

Using the definition of abatement in Equation ( 5) and the GDP evolution in Equation ( 3), the study obtains an abatement share that gives an abatement cost equivalent to 1 % of GDP by

2050 to be E b b τ τ 0.01 τ 0.05 G Y = = ⇒ = . ( 31
)
Similarly, the abatement share giving an abatement cost equivalent to 2 % of GDP by 2050 is b τ 0.1 = . The study takes, as the lower abatement share, the average b τ 0.075 = of the two abatement shares that give an abatement cost equivalent to 1.5 % of GDP by 2050.

Next, the study chooses the low-carbon technologies abatement efficiency parameter IPCC 2013;[START_REF] Fujino | Multi-gas mitigation analysis on stabilization scenarios using AIM global model. Multi-gas mitigation and climate policy[END_REF][START_REF] Hijioka | Global GHG emissions scenarios under GHG concentration stabilization targets[END_REF]. For the other non-BAU scenarios, the study chooses abatement shares of b τ 0.11 = and 0.145, such that an emissions reduction of 50 % or more from baseline by 2050 and beyond gives a reduction in GDP of 2.2 % and 2.9 %, respectively; the scenario given by b τ 0.11 = also mimics RCP4. 5 (IPCC 2013;Clerke et al. 2007;[START_REF] Wise | Implications of limiting CO 2 concentrations for land use and energy[END_REF]. Note that the abatement shares in [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF] and [START_REF] Greiner | The global environment, natural resources and economic growth[END_REF], which use Equation ( 11), are about 10 times lower than the ones chosen here.

Deforestation control and afforestation

Forestry including afforestation (the planting of trees on land where they have not recently existed), reforestation, avoided deforestation [START_REF] Rose | Land-based mitigation in climate stabilization[END_REF][START_REF] Wise | Implications of limiting CO 2 concentrations for land use and energy[END_REF], and forest management can lead to increased sequestration of atmospheric CO 2 and has therefore been proposed as a strategy to mitigate climate change [START_REF] Anderson | Biophysical considerations in forestry for climate protection[END_REF][START_REF] Canadell | Managing forests for climate change mitigation[END_REF]IPCC 2000;[START_REF] Pacala | Stabilization wedges: solving the climate problem for the next 50 years with current technologies[END_REF]. Under the Kyoto Protocol, the so-called flexible mechanisms have been established to combat GHGs cost-effectively. One of these mechanisms, the CDM, allows governments and business organizations from industrialized countries to invest in forestry in developing countries to accrue carbon credits to offset industrialized emissions.

There are parallel negotiations underway on the development of policies for Reducing Emissions from Deforestation and Forest Degradation in Developing Countries (REDD) a voluntary scheme to mitigate land carbon emissions from developing countries. Overall, there is strong interest in the role of forestry in climate mitigation agreements and legislation [START_REF] Schlamadinger | Carbon accounting beyond 2012[END_REF].

To be effective in mitigating climate change, forests need to sequester carbon or allow for reduced fossil fuel burning through bioenergy production, while avoiding biophysical effects that would jeopardize the net climate benefits and long-term sustainability [START_REF] Anderson | Biophysical considerations in forestry for climate protection[END_REF]. This study has incorporated deforestation control into the model framework.

Summary: CoCEB, the Coupled Climate-Economy-Biosphere model

The coupled CoCEB model is described by Equations ( 1), ( 10), ( 12), ( 22), [START_REF] Bosetti | Technology-led climate policy -an alternative perspective[END_REF], and [START_REF]Handbook of climate change mitigation[END_REF]. The model describes the temporal dynamics of six variables: per capita physical capital K , per capita human capital H , the average global surface air temperature T , the CO 2 concentration in the atmosphere C , biomass B , and industrial CO 2 emissions Y E .These six main variables are governed by a set of nonlinear, coupled ordinary differential equations (ODEs); they are complemented by a number of auxiliary variables, which are connected to them by ODEs and algebraic equations.

The equations are grouped for the reader's convenience below:

( ) [ ] ( ) ( ) ( ) [ ] { } ( ) ( ) [ ] ( ) ( ) [ ] ( ) ( ) α 1 α b K α 1 α b H T 1 4 a T h h h 2 Y o b b b b d  1 τ(1 τ ) (1 τ) δ , 32 d d φ A 1 τ(1 τ ) (1 τ) δ , 32 d 1 α Q 6.3β 1 ξ ετ σ d In , 32 d 4 d ˆβ µ γ , 32 d d 1 γ d Λ B K K H D T T c n K V a t H K H D T T c n H b t T C T c t c c c C C E E C C B C C d t B B g B B C C t - - = - - + - - - + - = - - + - - - + - - ⎛ ⎞ = - + ⎜ ⎟ ⎝ ⎠ ⎡ ⎤ = + - - - - ⎣ ⎦ ⎛ ⎞ = - + - ⎜ ⎟ ⎝ ⎠ ( ) [ ] ( ) Y σ Y c c s Y d , 32 d . 32 d for e E g g n g E f t ⎡ ⎤ - ⎣ ⎦ = + + +
The parameter values used in the model are as described in the text above and in Table 1 below.

They have been chosen according to standard tables and previous studies.

CHAPTER 4 NUMERICAL SIMULATIONS AND ABATEMENT RESULTS

Experimental design

In the following, the study confined the investigations to the transition path for the 110 years from the baseline year 1990 to the end of this century. The thesis studied the abatement share and how investment in clean technologies effected industrial carbon emissions. The effect of including biomass and deforestation control as well as CCS technologies into the model was also analyzed.

The goal was to understand how the different mitigation measures compare and which was more effective.

Table 2 The scenarios studied herein Scenario Control The scenarios studied herein are summarized in Table 2. We perform 37 integrations with an aggregate CO 2 concentration larger than or equal to the pre-industrial level:

i) The first is a control or BAU integration, with no abatement activities, i.e., b τ 0 = and no biomass, CCS or deforestation control;

ii) Next, three integrations with abatement measures, corresponding to b τ = 0.075, 0.11 and 0.145, as chosen in Subsection 3.5.2 again with no biomass, CCS or deforestation control;

iii) The third is again a control integration, with biomass evolution included but no CCS and deforestation control. This is equivalent to a BAU simulation in the IPCC terminology, but not the same as the BAU in i) above. The difference lies in the presence of interactive biomass that exchanges carbon with the atmosphere; iv) Then we perform 12 integrations using CCS investments but no deforestation control, d 0 R = .

The 12 runs correspond to a matrix of four values of the share f of investment in CCS, f = 0, 0.3, 0.6, and 1.0, times three values of total abatement share b τ , b τ = 0.075, 0.11, and 0.145; v) Last, 20 integrations with inclusion of deforestation control are performed; they correspond to a matrix of five values each of d R = 0, 0.1, 0.5, 1.0, and 1.2, times four values of b τ = 0, 0.075, 0.11, 0.145, with f = 0.

The CoCEB model is integrated in time starting from the initial values at year 1990, as listed in Table 1. The damage function exponent χ in Equation ( 21) is taken to be super-quadratic, χ 2.43 = ; all other parameter values are as in Table 1. The time step is 1 year and the integrations are stopped at year 2100. The values of CO 2 emissions and concentration, biomass, temperature, damage and GDP growth at the end of the integrations (year 2100) are shown in Tables 3,6, 7, and 8, respectively, for the low-carbon runs, the BAU runs, the CCS runs, and the deforestation control runs.

Integrations without and with investment in low-carbon technologies and with no CCS, biomass or deforestation control

From Table 3, it is clear that, if no action is taken to reduce baseline industrial CO 2 emissions, these will attain 29.3 GtC/y by 2010, leading to an atmospheric CO 2 concentration of 1842 GtC, i.e. about 3.1 times the pre-industrial level at that time. As a consequence, global average SAT will rise by 5.2 0 C from the pre-industrial level with a corresponding damage to the per capita GDP of 26.9 %. This compares well with the IPCC results for their RCP8.5 scenario, cf. Table 5 below.

The year-2100 changes in our three non-BAU scenarios' global mean SAT from the preindustrial level are 3.4 0 C, 2.6 0 C, and 2 0 C. The RCP6.0, RCP4.5, and RCP2.6 give a similar range of change in global SAT of 1.4-3.1 0 C with a mean of 2.2 0 C, 1.1-2.6 0 C with a mean of 1.8 0 C, and 0.3-1.7 0 C with a mean of 1 0 C, respectively (IPCC 2013). We note that our scenarios' change in temperature compare well with the IPCC ones.

The cumulative CO 2 emissions for the 1990-2100 period in this study's non-BAU scenarios are 1231 GtC, 1037 GtC, and 904 GtC. On the other hand, for the 2012-2100 period, RCP6.0 gives cumulative CO 2 emissions in the range of 840-1250 GtC with a mean of 1060 GtC;

RCP4.5 gives a range of 595-1005 GtC with a mean of 780 GtC, while RCP2.6 gives a range of 140-410 GtC with a mean of 270 GtC. The two former RCPs agree rather well with our results, while RCP2.6 is less pessimistic. This physical result reduces the economic damages (panel d) and hence the GDP growth decrease is strongly modified (panel e).

Figure 3e is the key result of this study: it shows that abatement policies do pay off in the long run. From the figure, it is seen that because of mitigation costs per capita GDP growth on the paths with nonzero abatement share, b τ 0 ≠ , lies below growth on the BAU path for the earlier time period, approximately between 1990 and 2060. Later though, as the damages from climate change accumulate on the BAU path (panel d), GDP growth on the BAU slows and falls below the level on the other paths (panel e), i.e., the paths cross.

This crossing of the paths means that mitigation allows GDP growth to continue on its upward path in the long run, while carrying on BAU leads to great long-term losses. As will be shown in Table 3 below, the losses from mitigation in the near future are outweighed by the later gains in averted damage. The cross-over time after which abatement activities pay off occurs around year 2060; its exact timing depends on the definition of damage and on the efficiency of the modeled abatement measures in reducing emissions.

The average annual growth rates (AAGRs) of per capita GDP between 1990 and 2100, are given in our model by ( ) ( )

2100 1990 1 110 = = ∑ t Y t
g t and their values, starting from the BAU scenario, are 2.6 %/y, 2.4 %/y, 2.1 %/y, and 1.8 %/y, respectively. Relative to 1990, these correspond to approximate per capita GDP increase of 5.5-14.5 times, that is 34×10 3 -90×10 3 1990 US dollars in year 2100, up from an approximate of $ 6×10 3 in 1990. Our scenarios' AAGRs and the 2100-to-1990 per capita GDP ratio agree well with scenarios from other studies, which give AAGRs of 0.4-2.7 %/y and a per capita GDP increase of 3-21 fold, corresponding to 15×10 3 -106 ×10 3 1990 US dollars [START_REF] Chakravorty | Endogenous substitution among energy resources and global warming[END_REF][START_REF] Grübler | Dynamics of energy technologies and global change[END_REF][START_REF] Holtz-Eakin | Stoking the fires? CO 2 emissions and economic growth[END_REF][START_REF] Krakauer | Economic growth assumptions in climate and energy policy[END_REF][START_REF] Leggett | Emissions scenarios for IPCC: An update[END_REF]Nakićenović and Swart 2000;[START_REF] Nordhaus | The challenge of global warming: economic models and environmental policy[END_REF][START_REF] Rabl | Discounting of long-term costs: what would future generations prefer us to do?[END_REF]Schrattenholzer et al. 2005, p. 59;[START_REF] Stern | The economics of climate change[END_REF][START_REF] Van Vuuren | A proposal for a new scenario framework to support research and assessment in different climate research communities[END_REF].

It is worth noting here that there has been a raging debate on the choice of either the market exchange rates (MER) or the purchasing power parity (PPP) (see, e.g., [START_REF] Vachris | International price comparisons based on purchasing power parity[END_REF] in expressing GDP growth rates. However, [START_REF] Manne | Market exchange rates or purchasing power parity: does the choice make a difference to the climate debate?[END_REF], on posing the question as to whether, when projecting future temperature, it makes a difference if MER or PPP is used, found the answer to be yes, but with a minor difference. Their results suggested that the debate over the proper conversion factor for potential GDP may be decoupled from that over SAT change due to climate change. Now, According to the United Nations Framework Convention on Climate Change (UNFCCC 1992), the average global SAT should not exceed its pre-industrial level by more than 2 0 C. This SAT target means that global efforts to restrict or reduce CO 2 emissions must aim at an atmospheric CO 2 concentration of no more than 1171.5 GtC. This CO 2 target can be achieved if carbon emissions are reduced to no more than 3.3 GtC/y, or nearly half relative to the 1990 level of 6 GtC/y [START_REF] Akaev | Stabilization of the planetary climate in the twenty first century by transition to a new paradigm of energy consumption[END_REF]). This goal is met, in the highly simplified model, by the path with the highest abatement share of the four, b τ 0.145 = . From Table 3 and Figure 3, it is noticed that this level of investment in the increase of overall energy efficiency of the economy and decrease of overall carbon intensity of the energy system enable emissions to decrease to 2.5 GtC/y by year 2100 (Figure 3a), about a 58 % drop below the 1990 emissions level. This emissions drop enables the deviation from pre-industrial SAT to reach no higher than 2 0 C by year 2100 (Figure 3c). 4 for the year 2100. From the table it is noticed that, generally, the more one invests in abatement, the more emissions are reduced relative to baseline and the less the cost of damages from climate change.

From Tables 3 and4, it is noticed that limiting global average SAT to about 2 0 C over preindustrial levels would require an emissions reduction of 92 % from baseline by 2100, at a per capita cost of $990, which translates to 2.9 % of per capita GDP. Although attaining the 2 0 C goal comes at a price, the damages will be lower all along and the GDP growth better than for BAU starting from the cross-over year 2058.

Recall, moreover, that the benefits of GHG abatement are not limited to the reduction of climate change costs alone. A reduction in CO 2 emissions will often also reduce other environmental problems related to the combustion of fossil fuels. The size of these so-called secondary benefits is site-dependent (IPCC 1996b, p. 183), and it is not taken into consideration as yet in the CoCEB model. emissions per year and the concentrations in the transition path up to year 2100 agree fairly well with those of RCP8.5, RCP6.0 and RCP4.5.

Control integration: run with biomass, no CCS and no deforestation control (new BAU)

In Table 6, a summary of the behavior of the BAU integration with inclusion of the biomass is shown. The results of the BAU integration of Susection contributes to about 92 % of this increment, due to increased per capita GDP growth, while emissions from deforestation, which are declining over time, contribute about 8 %.

Table 6 Variable values for year 2100 for the model with no biomass (B = 0) and no CCS ( f = 0), i.e.

BAU of Table 3, and with no deforestation control but 0 B ≠ (new BAU run) Scenario Emissions Y B There is no contradiction in the fact that these higher CO 2 emissions are accompanied by lower temperature increase. The increase of emissions is due to the appreciation in per capita GDP, in turn due to a decrease in atmospheric CO 2 through its sequestration owing to biomass fertilization and hence a decline in global surface air temperature (SAT) and consequently The inclusion of CCS investment tends to reduce industrial CO 2 emissions from BAU.

E E +

When the share of investment in CCS is increased ( f = 0.3, second row), one notes that for τ 0.075 b = , the 2100 deforestation emissions are 0.4 GtC/y (value in parentheses) while industrial CO 2 emissions slightly decrease. This contributes to a slight decline in SAT and consequently, to a small increment in per capita GDP. Further investment share in CCS, namely f = 0.6 and 1.0, causes CO 2 emissions to increase back slightly. This increase, in turn, contributes to a small increment in SAT and consequently, to a slight decline in per capita GDP.

From the table, we notice that 100 % investment in CCS, i.e. f = 1.0, is slightly less efficient than the combined investment in both low-carbon technologies and CCS technologies. A higher rate of GDP growth is observed when f = 0.3 and τ b = 0.075. This corresponds to total emissions reduction from baseline of approximately 0.19 GtC/y at a total CCS cost of about

τ b f τ 0.075 b =
, leads to CO 2 emissions that are below control by 2100. Further investment in CCS, of 60 % and 100 % respectively, leads to an initial reduction, followed by an increment in CO 2 emissions by 2100. We also note that, with an increased abatement share of τ b = 0.11 (Figure 4b) and 0.145 (Figure 4c), this effect is amplified, i.e., the emissions decrease at the beginning and then increase even more by 2100.

Integrations with inclusion of deforestation control

In Table 8, the CCS investment share is taken to be 0 and we analyze the effect of increasing deforestation control with different values of b τ , in the absence of CCS investments, f = 0. We first consider the b τ = 0.075 column and note that, generally, an increase of d R contributes to an increase of biomass; such an increase, in turn, contributes to the sequestration of atmospheric CO 2 due to photosynthesis, as evidenced by the reduction in the Ĉ C ratio.

For instance, we note that increasing d R from 0 to 1.2 gives a per annum sequestration of atmospheric CO 2 of 0.26 GtC/y between 1990 and 2100. Comparing with other studies on biomass photosynthetic sequestration of atmospheric CO 2 due to afforestation, this particular annual amount of CO 2 fertilization agrees quite well with the average range of 0.16-1.1 GtC/y by 2100 in [START_REF] Canadell | Managing forests for climate change mitigation[END_REF], and with the range of 0.1-0.4 GtC/y obtained by Luo and Moonry (1996); see also [START_REF] Polglase | Potential for forest carbon plantings to offset greenhouse emissions in Australia: economics and constraints to implementation[END_REF]. The reduction in atmospheric CO 2 due to biomass photosynthesis contributes to a decrease in SAT and consequent damages. These actually increase the GDP growth slightly. The improvements due to d R are nevertheless small compared to the effect of low-carbon technologies or CCS. It has to be said, however, that besides reducing carbon emissions, reduced deforestation also delivers other benefits, such as biodiversity conservation and watershed and soil quality protection [START_REF] Chomitz | The domestic benefits of tropical forests: a critical review[END_REF][START_REF] Ebeling | Generating carbon finance through avoided deforestation and its potential to create climatic, conservation and human development benefits[END_REF][START_REF] Eriksson | The role of the forest in an integrated assessment model of the climate and the economy[END_REF][START_REF] Sedjo | The economics of managing carbon via forestry: assessment of existing studies[END_REF] [START_REF] Stickler | The potential ecological costs and co-benefits of REDD: a critical review and case study from the Amazon region[END_REF][START_REF] Stott | Impacts of incentives to reduce emissions from deforestation on global species extinctions[END_REF]World Bank 2011). The latter benefits are not accounted for in the present version of our CoCEB model. In fact, little attention has been paid so far in the literature to the presence of these co-benefits of deforestation control when calculating its cost [START_REF] Phan | The economic costs of avoided deforestation in the developing world: a meta-analysis[END_REF], Table 1).

; d R τ b

A mix of mitigation measures

Even though it is beyond this study's ability to predict a realistic international emissions mitigation regime, CoCEB simulations suggest that best results are obtained by combining the various mitigation measures discussed. This was found in Table 7 and Figure 4, where we noted that 100 % investment in CCS or low-carbon technologies is slightly less efficient than the combined investment in both technologies. For illustration purposes, we chose now a 30 % investment in CCS technologies and a deforestation control of d 0.1 R = , while the other parameter values are as in Table 1. The values of CO 2 emissions and concentration, temperature, damage and GDP growth at year 2100 are shown in Table 9 for the four scenarios corresponding to the abatement share b τ = 0, 0.075, 0.11 and 0.145.

From the table, the scenario corresponding to b τ 0 = attains total emissions of 34.2 GtC/y by 2100. This leads to an atmospheric CO 2 concentration of 1727 GtC, i.e. about 2.9 times the preindustrial level at that time. As a consequence, global average SAT will rise by 4.9 0 C from the pre-industrial level with a corresponding damage to the per capita GDP of 24.4 % and a GDP growth of 1.42 %. This compares well with the IPCC results for their RCP8.5 scenario (IPCC 2013; [START_REF] Riahi | Scenarios of long-term socio-economic and environmental development under climate stabilization[END_REF][START_REF] Rao | The role of non-CO 2 greenhouse gases in climate change mitigation: long-term scenarios for the 21 st century. Multi-gas mitigation and climate policy[END_REF].

For the scenarios corresponding to b τ = 0.075, 0.11 and 0.145, the results obtained are slightly better than those in Table 7 when f = also note that, for b τ = 0.075 and 0.11, the CO 2 emissions per year, as well as the CO 2 concentrations and SAT deviations from preindustrial level in year 2100, agree fairly well with those of RCP6.0 and RCP4. 5a) and for f = 0.3 and d 0.1 R = scenario (Figure 5b). In both panels, we notice that per capita GDP growth on the paths with nonzero abatement share, b 0 ≠ , lies below growth on the BAU path, i.e., when using b τ 0 = , for the earlier time period, approximately between 1990 and 2060 in Figure 5a and approximately between 1990 and 2058 in Figure 5b.

Later though, as the damages from climate change accumulate on the BAU path, GDP growth in the BAU scenario slows down and falls below the level on the other paths, i.e. the paths cross and mitigation strategies pay off in the longer run. We also observe that the growth in Figure 5b -with 30 % investment in CCS technologies and 70 % investment in low-carbon technologies, together with a deforestation control of 10 % -is slightly higher than that in Figure 5a. The sensitivity to the nonlinearity parameter χ is considerably higher. Decreasing it by 50 % reduces the damages to per capita GDP from 26.9 % to about 6.3 %, i.e., a 76.6 % reduction on the BAU path. This contributes to higher economic growth and higher emissions of 99.6 GtC/y.

Conversely, increasing χ by 50 % increases the damages to per capita GDP from 26.9 % to about 41.6 %, i.e., a 54.6 % increase on the BAU path. This contributes to a decrease in economic growth and to lower emissions of 6 GtC/y in the year 2100.

In Figure 6 are plotted the GDP growth curves with time for the experiments summarized in Table 10. It is clear from the figure that the growth rate of per capita GDP is more sensitive to the nonlinearity parameter χ than to 1 m . A decrease of 1 m by 50 % pushes the crossover point further into the future, from year 2058 to 2070 (Figure 6a), while an increase by 50 % pulls the crossover point closer to the present, to about 2053 (Figure 6b). Decreasing χ by 50 %, on the other hand, pushes the crossover point even further away, past the end of the century (Figure 6c), while an increase of χ by 50 % pulls it from year 2058 to about 2040 (Figure 6d).

Robustness to changes in the low-carbon abatement efficiency parameter α τ

Next, the study modifies the value of the parameter τ α by +50 % and -50 % from the standard value of τ α 1.8 = used in Tables 1-10 above, and examine in Table 11 how that affects the model emissions reduction from baseline by the year 2100, as well as the per capita low-carbon abatement costs and the per capita damage costs. There is a substantial decrease in emissions reduction for all three scenarios with b τ 0 > , compared to Table 4, and hence more damages for the same abatement costs. Furthermore, the increased damages increase the depression of the economy and contribute to low economic growth.

On the other hand, a 50 % increase in the abatement efficiency, to τ α 2.7 = , leads to an increase in the emissions reduction from baseline by 2100. This reduces the damages and hence lessens the depression to the economy, enabling economic growth to increase.

Robustness to changes in the CCS abatement efficiency parameter α ω

The study modifies the value of the parameter ω α by -84 % and +84 % from the standard value of ω α 46.1 = used in Tables 1234567891011Table 12 how that affects the model emissions reduction and the GDP growth from baseline by the year 2100. The idea is to check how the results are affected by the hypothesis that the costs of CCS were much higher or much lower than the ones used here, and compared to the cost uncertainties found in the literature. The low value of ω α is equivalent to $615/tC by 2100, while the high value is equivalent to $548/tC; these values agree quite well with those given in the literature. We recall once more that the costs everywhere in this study are expressed in constant 1990 USD. (in parentheses) in the middle, the modified values for the standard +84 % on the modified values for the standard -84 % on the right-hand side. From the observed span of the expected values, we notice that in the case of cheap CCS, at $548/tC, the f = 1.0 case gives more or less the same emissions reduction and GDP growth as f = 0

Comparing the efficiency of CCS and low-carbon technologies, which depend on their cost estimation, we note that given the uncertainties, low-carbon can be either slightly more efficient or equally efficient. The qualitative result that a mix of the two is better than 100 % of the one or 100 % of the other is quite robust.

Robustness to changes in the deforestation control cost parameters

Taking τ b = 0.075, f = 0.3, and with the standard values (given in Table 1) of the d R cost parameters 1 π , 2 π , 3 π , 4 π , and 5 π , we note that by increasing d R from 0 to 0.1, the deforestation emissions are reduced from approximately 0.4 GtC/y to 0.3 GtC/y at a total cost of $164/tC, while the per capita GDP growth would be of 2.40 %/y by 2100.

We now vary, simultaneously, the d R cost parameters from the standard values so so as to span the range of costs given by [START_REF] Phan | The economic costs of avoided deforestation in the developing world: a meta-analysis[END_REF]. A variation of -99 % gives a total cost of $0.9/tC and that of +47 % gives a total cost of $246/tC. Even using these two extreme values, no significant effect is observed on the integration of the CoCEB model. The results in both cases only differ from Table 9 in the third decimal place. This study assumed the hypothesis that the current global warming is caused largely by anthropogenic increase in the CO 2 concentration in the Earth's atmosphere. It also assumed that all nations participate in carbon emissions mitigation activities. But as of 2013, there were no effective international agreements to limit the emissions of CO 2 and other GHGs (Nordhaus 2013b, p. 11) Using this model, the thesis investigated in Chapter 4 the relationship between investing in the increase of overall energy efficiency of the economy and decrease of overall carbon intensity of the energy system through abatement activities, as well as the time evolution, from 1990 to 2100, of the growth rate of the economy under threat from climate change-related damages. This study has also investigated the relationship between the long-run effects of using CCS and deforestation control, and the long-term growth rate of the economy. The framework developed allows one to investigate policy sensitivity to the choice of key parameters. We analyzed in particular the effect of the parameters setting the costs of the different means of climate change mitigation: in the present work, the parameter values tested spanned the range of cost values found in the mitigation literature.

The CoCEB model shows that taking no abatement measures to reduce GHGs leads eventually to a slowdown in economic growth; see also Kovalevsky and Hasselmann (2014, Figure 2).

This slowdown implies that future generations will be less able to invest in emissions control or adapt to the detrimental impacts of climate change [START_REF] Krakauer | Economic growth assumptions in climate and energy policy[END_REF]. Therefore, the possibility of a long-term economic slowdown due to lack of abating climate change [START_REF] Kovalevsky | Assessing the transition to a low-carbon economy using actor-based system-dynamic models[END_REF] heightens the urgency of reducing GHGs by investing in low-carbon technologies, such as electric cars, biofuels, CO 2 capturing and storing (CCS), renewable energy sources [START_REF] Rozenberg | Building SSPs for climate policy analysis: a scenario elicitation methodology to map the space of possible future challenges to mitigation and adaptation[END_REF], and technology for growing crops [START_REF] Wise | Implications of limiting CO 2 concentrations for land use and energy[END_REF]). Even if this incurs short-term economic costs, the transformation to a de-carbonized economy is both feasible and affordable according to [START_REF] Azur | Are the economic costs of stabilizing the atmosphere prohibitive?[END_REF], [START_REF] Schneider | Geoengineering: Could We or Should We Make It Work?[END_REF], [START_REF] Stern | The economics of climate change[END_REF], [START_REF] Weber | A multi-actor dynamic integrated assessment model (MADIAM) of induced technological change and sustainable economic growth[END_REF], and would, in the long term, enhance the quality of life for all [START_REF] Hasselmann | The climate change game[END_REF]. The great flexibility and transparency of the CoCEB model has helped us demonstrate that an increase in the abatement share of investments yields a win-win situation: higher annual economic growth rates, on average, of per capita GDP can go hand-in-hand with a decrease in GHG emissions and, as a consequence, to a decrease in average global SATs and the ensuing damages. These results hold when considering the entire transition path from 1990 to 2100, as a whole.

In the climate modeling literature, the role of a full hierarchy of models, from the simplest to the most detailed ones, is well understood (e.g., [START_REF] Schneider | Climate modeling[END_REF]Ghil 2001, and references therein). There is an even greater need for such a hierarchy to deal with the highercomplexity problems at the interface of the physico-chemical climate sciences and of socioeconomic policy.

The CoCEB model lies toward the highly idealized end of such a hierarchy: it cannot, nor does it claim to, represent the details of the real world, but its simplicity is also a strength. Simple models do not allow one to provide a quantitative description of the fully coupled dynamics of the real climate-economy-biosphere system; on the other hand, though, the study of such models makes it possible to understand the qualitative mechanisms of the coupled-system processes and to evaluate their possible consequences.

More than just a simple model, CoCEB is a formal framework in which it is possible to represent in a simple way several components of the coupled system and their interactions. In this study, we showed as an example how to insert the effects of CCS and deforestation control.

Several choices are possible in modeling these effects.

In this study, formulations taken from the literature have been integrated into the CoCEB framework. Doing so allowed us to treat low-carbon technologies, CCS and deforestation control consistently, and to translate the range of uncertainties on their relative cost into long-term effects on the climatic and economic system. The CoCEB framework also allowed us to evaluate the sensitivity of the results on the cost parameters.

Given the recent scientific evidence on global warming and its consequences, as documented in the numerous IPCC reports, the importance of climate change mitigation policies represents by now a consensus that is widely accepted by the climate community. Delaying action may mean that high temperatures and low growth are approached on a path that becomes irreversible. To prevent human society's engaging on such a path, the IPCC reports (IPCC 1995(IPCC , 2007a(IPCC , 2014) ) propose a significant number of policy measures to prevent further emission of GHGs and a further rise of global temperature.

As measures leading toward a low-carbon economy, the IPCC Fourth Assessment Report emphasizes the role of technology policies to achieve lower CO 2 stabilization levels (IPCC 2007b, pp. 149-153, 218-219), a greater need for more efficient research and development efforts, and higher investment in new technologies over the next few decades, as emphasized further in IPCC (2012, Ch. 11, p. 878). The most recent assessment reports recommend government initiatives for funding or subsidizing alternative energy sources, including solar energy, ocean power, windmills, biomass, and nuclear fusion.

Forestry policies, particularly reduced deforestation, also emerge as additional low-cost measures for the reduction of carbon emissions. Reduced deforestation would cut carbon emissions and increased afforestation would sequester CO 2 from the atmosphere. As noted earlier, besides reducing carbon emissions, reduced deforestation can also deliver other benefits -such as biodiversity conservation and watershed and soil quality protection. It is advisable that future research focuses on the presence of the co-benefits of avoided deforestation, which could not be done in the present study nor in the existing mitigation literature. Overall, the IPCC stresses the fact that there are a number of effective policy measures available now that can reduce GHG emission.

This study considered technological abatement activities, as well as deforestation control to reduce the sources and enhance the sinks of GHGs, thereby lessening the radiative forcing that leads to temperature rise and economic impacts. Our results indicate that a pure CCS policy or a pure low-carbon technologies policy carry their own specific risks of being less efficient in combating climate change, a sentiment echoed by [START_REF] Akashi | Halving global GHG emissions by 2050 without depending on nuclear and CCS[END_REF], [START_REF] Kalkuhl | The role of carbon capture and sequestration policies for climate change mitigation[END_REF]), Riahi et al. 2004a, Riahi et al. 2004b[START_REF] Uyterlinde | The contribution of CO 2 capture and storage to a sustainable energy system[END_REF], among others.

Through our CoCEB framework, we have demonstrated that best results are obtained by combining the various mitigation measures discussed in this study, i.e., high investment in lowcarbon technologies and low investment in CCS technologies, as well as inclusion of deforestation control. While we have also shown that certain results are robust to very substantial variations in parameter values, uncertainties do remain. Further research is, therefore, necessary, to reduce these uncertainties in the cost of the CCS technologies and of deforestation control.

Recent academic work has argued for a greater urgency to implement effective climate policies to combat climate change. Yet, to the best of our knowledge, no study has sufficiently explored the possibility of bringing together all the three mitigation measures under one coherent framework -including their impact on economic growth -as suggested here.

Another essential issue that has not been sufficiently addressed so far is how to reconcile (2014). We hope this study will serve as an illustrative pointer in this direction.

A finite horizon optimal climate change control solution can be gotten by assuming that the government takes per capita consumption and the annual tax rate as given and sets abatement such that welfare is maximized. As to welfare, one can assume that it is given by the discounted stream of per capita utility times the number of individuals over a finite time horizon. The Pontryagin Maximum Principle [START_REF] Hestenes | Calculus of variations and optimal control theory[END_REF][START_REF] Pontryagin | The mathematical theory of optimal processes[END_REF][START_REF] Sethi | Optimal control theory: applications to management science and economics[END_REF] is used to find the necessary optimality conditions for the finite-horizon control problem.

The Maximum Principle for infinite-horizon control problems is presented in [START_REF] Michel | On the transversality conditions in infinite horizon optimal control problems[END_REF], [START_REF] Seierstadt | Optimal control theory with economic applications[END_REF], Aseev andKryazhimskiy (2004, 2007), and [START_REF] Maurer | Optimal control of growth and climate change exploration of scenarios[END_REF].

For a modern theory of infinite-horizon control problems the reader is referred to [START_REF] Lykina | Different interpretations of the improper integral objective in an infinite horizon control problem[END_REF]. The determination of an optimal abatement path along the lines above will be the object of future work.

Concerning the damage function, [START_REF] Stern | The economics of climate change[END_REF] states that "Most existing IAMs also omit other potentially important factors -such as social and political instability and cross-sector impacts. And they have not yet incorporated the newest evidence on damaging warming effects," and he continues "A new generation of models is needed in climate science, impact studies and economics with a stronger focus on lives and livelihoods, including the risks of large-scale migration and conflicts" [START_REF] Stern | The structure of economic modeling of the potential impacts of climate change: grafting gross underestimation of risk onto already narrow science models[END_REF]. Nordhaus (2013a) suggests, more specifically, that the damage function needs to be reexamined carefully and possibly reformulated in cases of higher warming or catastrophic damages. In the CoCEB model, an increase in climate-related damages has the effect of anticipating the crossover time, starting from which the abatement-related costs start paying off in terms of increased per capita GDP growth.

Another possible route toward a low-carbon future would include deployment of largescale nuclear power as a substitute for fossil fuel power generation. The paper by [START_REF] Ahearne | Prospects for nuclear energy[END_REF] discusses the key questions about the future of nuclear energy: Will there be a nuclear renaissance?

Is one already under way? Should there be a nuclear renaissance? What would it look like? If a renaissance is happening or could happen, what are the problems associated with that?

In his discussion of [START_REF] Ahearne | Prospects for nuclear energy[END_REF]) paper, Steinbruner (2011) argues that limitations on alternative options might force an extensive expansion of nuclear power generation, but that such an expansion cannot be undertaken safely on the basis of current reactor designs, current fuel cycle management practices, and current national security relationships. Instead, a strong case can be made for developing the more promising small, passively safe, and sealed reactor designs. On their part, [START_REF] Rabl | External costs of nuclear greater or less than the alternatives[END_REF], who compare the external costs of nuclear with those of the alternatives, argued that it would not be wise to retire nuclear plants precipitously, if the alternatives entail total (private + external) costs that are even higher. However, [START_REF] Rogner | Future nuclear perspectives based on MESSAGE integrated assessment modeling[END_REF] analysis indicates that under a comprehensive and global mitigation effort, the stabilization of GHG concentrations at low levels (261.4 GtC) would be technically achievable even at high energy demand and with a nuclear phase-out. They identified that significant investments in energy efficiency improvements and energy demand reduction offer the most flexibility in energy supply options and may or may not include nuclear power; see also the discussions of Diesendorf (2014, pp. 142 143) on nuclear energy.

Now, the CoCEB model can be extended in several directions:

i)

The next most interesting item on the research agenda is to let the biomass colonization rate and human population growth depend on the availability and quality of water, and to investigate how this will affect model feedbacks. Doing so will require a simple treatment of the water cycle.

ii)

The CoCEB model can be regionalized, while maintaining its essential simplicity. For example, one might want to establish separate energy balance modules for the tropical and extratropical areas, and extend a similar separation to the economic module.

iii) Finally, even though there are several truly coupled IAMs (e.g., [START_REF] Ambrosi | Optimal control models and elicitation of attitudes towards climate change[END_REF][START_REF] Nordhaus | Roll the DICE again: the economics of global warming[END_REF][START_REF] Stern | The economics of climate change[END_REF]), these IAMs disregard variability and represent both climate and the economy as a succession of equilibrium states without endogenous dynamics. This can be overcome by introducing business cycles into the economic module (e.g., [START_REF] Akaev | Derivation of the general macroeconomic dynamics equation describing the joint interaction of long-term growth and business cycles[END_REF]Hallegatte et al. 2008) and by taking them into account in considering

99 Appendix 1 : 99 Appendix 2 :Figure 1 3 Figure 2 7 Figure 3 45 Figure 4 53 Figure 5 57 Figure 6 1

 991992132734545355761 Figure 1 Schematic of climate-economy-biosphere interactions (see also, Kellie-Smith and Cox

  varying 1 m , and χ………………………………………………………………………………………..............60

  A change in the use or management of land by humans, which may lead to a change in land cover. Land cover and land-use change may have an impact on the albedo, evapotranspiration, sources and sinks of greenhouse gases, or other properties of the climate system, and may thus have an impact on climate, locally or globally.MitigationTechnological change and substitution that reduce resource inputs and emissions per unit of output with respect to climate change, mitigation means implementing policies to reduce GHG emissions and enhance sinks.

Fig. 1

 1 Fig. 1 Schematic of climate-economy-biosphere interactions (see also, Kellie-Smith and Cox 2013)

Fig. 2

 2 Fig.2The various modules of the study (see also,Edwards et al. 2005, p. 2, Figure 1.1)

Framework

  from US Environmental Protection Agency (EPA) and the Integrated Model for the Assessment of the Global Environment (IMAGE) model from the Netherlands (van Vuuren et al. 2006a). These were employed to assess the factors controlling the emissions and concentrations of GHGs over the next century. Model for the Assessment of Greenhouse-gas Induced Climate Change (MAGICC) was then developed to account ocean heat transport and a carbon cycle component to respond the land-use change; it is a multi-box energy balance model (Meinshausen

  to identify and evaluate climate change mitigation strategies (see, e.g.,[START_REF] Hourcade | Global, regional and national costs and ancillary benefits of mitigation[END_REF] Morita and Robinson 2001) focus on the energy sector(van Vuuren et al. 2006b, p. 166).

  is the fraction of emissions that is vented to the atmosphere and involves CCS.

10 1.0107 10 ×

 1010 TRF as the share of fossil fuels in the GEB ( 10 1.1472 10 × TRF) in 1990 (Akaev 2012, Table 2). The parameters r and ψ are derived by assuming a level of 95 % fossil fuels used for year 2020 and of 5 efficiency parameter, chosen such that for the path corresponding to b τ 0.075 = , carbon emissions reduction from baseline is about 50 % by year 2050; see Subsection (3.5.1) for details. The parameter f represents the share of investment in CCS (see Equation 19 below); the investment in low-carbon technologies is 1 f -. Calculations based on

  f = 1.0, gives aggregate carbon emissions reduction from baseline of 0.4

  estimated the cost of carbon emissions reduction due to deforestation control to range from $0.11/tC to $246/tC with a mean of $19/tC. Actually, Kindermann et al. (2008) used three economic models of global land use and management -Global Timber Model (GTM), Dynamic Integrated Model of Forestry and Alternative Land Use (DIMA), and Generalized Comprehensive Mitigation Assessment Process Model (GCOMAP) -to analyze the economic potential contribution of deforestation control activities to reduced GHG emissions. The latter authors found out that a 10 % deforestation control could be feasible within the context of current financial flows. Following the latter result, we take d 0.1 R = as the standard value in this study, but will test the robustness of our results by also using other d R -values. In the CoCEB model, with 100 % investment in low-carbon technologies and with b τ = 0.075, the value of d 0.1 R = gives an approximate aggregate cost of deforestation emissions reduced of $164/tC by 2100. We notice that the CoCEB total cost for d 0.1 R = is within the range of deforestation control costs given by Phan et al. (2014).

Fig. 3

 3 Fig. 3 Evolution of several CoCEB model variables in time, for abatement shares b τ that range from 0.0

  for the various emission reduction paths are given in Table

5 respectively(

 5 Clerke et al. 2007;[START_REF] Fujino | Multi-gas mitigation analysis on stabilization scenarios using AIM global model. Multi-gas mitigation and climate policy[END_REF][START_REF] Hijioka | Global GHG emissions scenarios under GHG concentration stabilization targets[END_REF] IPCC 2013;[START_REF] Smith | Multi-gas forcing stabilization with the MiniCAM[END_REF][START_REF] Wise | Implications of limiting CO 2 concentrations for land use and energy[END_REF]).

Fig. 5 Figure 5

 55 Fig. 5 GDP growth over time, with biomass module ( 0 B ≠ ), as a function of abatement share values b τ between 0.0 (no abatement) and 0.145. (a) d 0 R = and 0 f = ; and (b) d 0.1 R = and 0.3 f = ; see legend

Fig. 6

 6 Fig. 6 GDP growth over time as a function of abatement share values b τ between 0.0 and 0.145; see legend for curve identification, while τ α 1.8 = , 0 f = , 0 B = , d 0 R = . Panels (a, b) 1 m is larger or smaller by 50 % than the value in Tables 1-9; (c, d) same for the nonlinearity parameter χ

  This study introduced a simple coupled climate-economy-biosphere (CoCEB) model with the goal of understanding the various feedbacks involved in the system and also for use by policy makers in addressing the climate change challenge. In this study, economic activities are represented through a Cobb-Douglas output function with constant returns to scale of the two factors of production: per capita physical capital and per capita human capital. The income after tax is used for investment, consumption, and abatement. Climate change enters the model through the emission of GHGs arising in proportion to economic activity. These emissions accumulate in the atmosphere and lead to a higher global mean surface air temperature (SAT). This higher temperature then causes damages by reducing output according to a damage function. A biomass equation, representing the biosphere module, was also added and the related exchanges of CO 2 taken into consideration. The CoCEB model, as formulated here, was summarized as Equations[START_REF] Ciais | Europe-wide reduction in primary productivity caused by the heat and drought in 2003[END_REF] in Section 3.6.

  and couple the IPCC's Representative Concentration Pathways (RCPs) and the Shared Socioeconomic Pathways (SSPs) being developed in the framework of more detailed integrated assessment models (IAMs) by the impacts, adaptation, and vulnerability communities; see Ebi et al. (2014); Kriegler et al. (2014); O'Neill et al. (2014); Rozenberg et al. (2014); Vuuren et al.

Table 1

 1 List of variables and parameters and their values used………………………………......39

Table 2

 2 The scenarios studied herein……………….………………………………………..........42

Table 3

 3 Variables values for year 2100 for the model without and with investment in low-carbon technologies: scenarios i) and ii) in Table2, with χ 2.43 = ………………………………….........44

Table 4

 4 Per capita abatement costs and damage costs at year 2100, with χ 2.43 = ………………48

Table 5

 5 Comparison between global results of alternative policies………………………………49

Table 6

 6 Variable values for year 2100 for the model with no biomass (B = 0) and no CCS (f = 0),

i.e. BAU of Table

3

, and with no deforestation control but B ≠ 0 (new BAU run)………………..50

Table 7

 7 Variable values for year 2100 with deforestation emissions in parenthesis, for the runs

with investment in CCS scenario……………………………………………..................................52

Table 8

 8 Variable

values for year 2100, with deforestation emissions in parenthesis, for runs with inclusion of deforestation control scenario………………………………………………………...55

Table 9

 9 Target values of key variables for our policy scenarios at year 2100, with

	f =	0.3	and

Table 11

 11

	Effect of varying τ α by year 2100;	0 f = ,	0 B = ,

d 0 R = , other parameter values as in

Table 1………………………………………………………………………………………..........62

Table 12

 12

	Effect of varying ω α by year 2100;	0 B ≠ , d 0 R = , τ b = 0.075, and all other parameter
	values as in Table 1………………………………………………………………………...........63

Adaptation

Adjustment in natural or human systems to a new or changing environment.

INTRODUCTION 1.1 Background to the problem

	models CHAPTER 1
	GEB	Global energy balance
	GHGs	GreenHouse Gases
	Gt	Gigatonnes
	GtC It is widely accepted that climate change will have major impacts on humankind. Depending on Gigatonnes of Carbon
	IAMs the magnitude of twenty-first century climate change, human societies and ecosystems are Integrated Assessment Models
	IPCC expected to be greatly affected by climate change (IPCC 2007b) and in particular by the frequency The Intergovernmental Panel on Climate Change. Established in 1988 and jointly
	sponsored by United Nations Environmental Programme and World Health and intensity of extreme events (e.g., Changnon et al. 1996; Ciais et al. 2005; IPCC 2012a).
	BAU Negative impacts are expected on water, food, human health and conflict (IPCC 2001b, p. 238; Organization. Note that the IPCC is an assessment, not a research organization Business-as-Usual C KP Kyoto Protocal IPCC 2007b) and ultimately economic growth (Dell et al. 2014 and the citations therein; Nordhaus Carbon CCS NGOs Non-Government Organizations 2008; Stern 2007). Global carbon dioxide (CO 2 ) emissions, which are the largest contributor to Carbon Capture and Sequestration CDM TRF Tons of reference fuel Clean Development Mechanism REDD Reduced Emissions from Deforestation and forest Degradation anthropogenic climate change
	CO 2 UN	Carbon dioxide United Nations
	EBM	An Energy Balance Model. Probably the simplest model of the Earth
		system, based on the energy balance between the solar energy absorbed from the Sun
		and the thermal radiation emitted to space by the Earth
	UNFCCC The UN Framework Convention on Climate Change. Signed at the UN
		Conference on Environment and Development in 1992 and ratified in 1994. The FCCC
		has defined climate change to be only the human-induced effects (i.e. not natural
		variability) for its negotiations
	GCM	A General Circulation Model or Global Climate Model. Initially used with reference to
		three-dimensional models of the atmosphere alone, the term has come to be loosely
		used to encompass three-dimensional models of the ocean (OGCMs) and coupled
		xix

Table 1

 1 List of variables and parameters and their values used

	Symbol	Meaning	Value	Units	Source
	INDEPENDENT VARIABLES
	K			Per capita physical capital	Trillions $
	H			Per capita human capital	Trillions $
	T				Average global surface temperatures	Kelvin (K)
	C				Atmospheric CO 2 concentration	GtC
	B				Biomass	GtC
	E	Y	Industrial CO 2 emissions	GtC/y
	INITIAL (1990) VALUES FOR INDEPENDENT VARIABLES
	k	0			Per capita physical capital-human	8.1	Ratio	Erk et al. (1998)
						capital ratio 0 K H	0
	K	0		0.8344	10 4 $	Nordhaus and Boyer (2000)
	H	0		0.1039	10 4 $	0 K k	0
	0 T				287.77	Kelvin (K)
	C	0		735	GtC	Nordhaus and Boyer (2000)

b τ a τ b Λ d R

Table 3

 3 Variables values for year 2100 for the model without and with investment in low-carbon technologies: scenarios i) and ii) in Table2, with χ 2.43 =

	τ	b	Emissions	CO 2	Deviation from	Damages	GDP
			E	Y	Ĉ C	pre-industrial	(% GDP)	growth Y g (%/y)
			(GtC/y)		T T -( 0 C)
	0	29.3	3.1	5.2	26.9	1.1
	0.075	11.8	2.1	3.4	11.6	2.1
	0.11	5.9	1.7	2.6	6.6	2.2
	0.145	2.5	1.5	2.0	3.5	2.0

Table 4

 4 Per capita abatement costs and damage costs at year 2100, with χ 2.43 =

	Abatement share	% emissions ( Y E ) reduction	Per capita abatement	Per capita damage
	τ	b	from baseline	costs (% Y )	costs (% Y )
	0	0	0	26.9
	0.075	60	1.5	11.6
	0.11	80	2.2	6.6
	0.145	92	2.9	3.5

Table 5

 5 Comparison between global results of alternative policies

	Global industrial CO 2 emissions (GtC/y)
	Policy Scenario				1995	2005	2010	2020	2030	2050	2100
	CoCEB model:	b τ =	0	7.1	10.8	13.2	19.3	27.0	43.4	29.3
	CoCEB model :	b τ =	0.075	6.8	9.2	10.6	13.8	17.0	21.6	11.8
	CoCEB model :	b τ =	0.11	6.7	8.6	9.6	11.7	13.5	14.7	5.9
	RCP8.5 (Rao and Riahi 2006;	-	8	8.9	11.5	13.8	20.2	28.7
	Riahi et al. 2007)
	RCP6.0 (Fujino et al. 2006;	-	8	8.5	9	10	13	13.8
	Hijioka et al. 2008)
	RCP4.5 (Clerke et al. 2007; Smith	-	8	8.6	9.9	11	11	4.2
	and Wigley 2006; Wise et al.
	2009)
	Global atmospheric CO 2 concentration (GtC)
					1995	2010	2020	2030	2050	2075	2100
	CoCEB model:	b τ =	0	743	793	852	939	1206	1612	1842
	CoCEB model :	b τ =	0.075	743	785	826	880	1014	1168	1231
	CoCEB model :	b τ =	0.11	743	781	816	858	948	1027	1037
	RCP8.5 (Riahi et al. 2007)	-	829	886	956	1151	1529	1993
	RCP6.0 (Fujino et al. 2006;	-	829	872	914	1017	1218	1427
	Hijioka et al. 2008)
	RCP4.5 (Clerke et al. 2007; Wise	-	829	875	927	1036	1124	1147
	et al. 2009)

Table 5

 5 gives a comparative summary of the CoCEB model's results and those from other studies that used more detailed IAM models and specific IPCC (2013) RCPs. It is noticed that the CO 2

  4.1 (reported in the 1 st line of the table for comparison) and in the present Subsection's BAU are qualitatively similar, yet the new BAU has CO 2 emissions of 34 GtC/y by year 2100. This is an increase of approximately 4.7 GtC/y from the 29.3 GtC/y of the BAU of Subsection 4.2. From our calculations (not shown) industrial CO 2

Table 7

 7 Variable values for year 2100 with deforestation emissions in parentheses, for the runs with

	investment in CCS scenario
			0	0.075	0.11	0.145
		Y E E B +	34.0 (0.4)	13.3 (0.4)	6.7 (0.4)	3.0 (0.4)
	0	T T Y -g	4.93 1.42	3.12 2.30	2.37 2.32	1.78 2.08
		Y E E B +	34.0 (0.4)	12.7 (0.4)	6.8 (0.4)	3.4 (0.4)
	0.3	T T Y -g	4.93 1.42	2.99 2.39	2.30 2.35	1.78 2.08
		Y E E B +	34.0 (0.4)	13.7 (0.4)	8.1 (0.4)	4.6 (0.4)
	0.6	T T Y -g	4.93 1.42	3.02 2.36	2.40 2.29	1.91 2.02
		Y E E B +	34.0 (0.4)	15.5 (0.4)	10.3 (0.4)	6.6 (0.4)
	1.0	T T Y -g	4.93 1.42	3.12 2.27	2.55 2.19	2.09 1.94

Table 8

 8 Variable values for year 2100, with deforestation emissions in parenthesis, for runs with inclusion of deforestation control scenario

					0	0.075	0.11	0.145
		Y E E B +	34.0 (0.4)	13.3 (0.4)	6.7(0.4)	3.0 (0.4)
	0	Ĉ C T T -	2.90 4.93	1.94 3.12	1.64 2.37	1.44 1.78
		g	Y	1.42	2.30	2.32	2.08
		Y E E B +	34.2 (0.3)	13.3 (0.3)	6.7 (0.3)	2.9 (0.3)
	0.1		Ĉ C	2.90	1.93	1.63	1.43
		-	T T	4.93	3.11	2.36	1.76
		g	Y	1.42	2.31	2.33	2.09
		Y E E B +	34.7 (0.2)	13.4 (0.2)	6.6 (0.2)	2.8 (0.2)
	0.5	Ĉ C T T -	2.88 4.91	1.92 3.08	1.62 2.31	1.42 1.71
		g	Y	1.45	2.34	2.35	2.10
		Y E E B +	35.3 (0)	13.5(0)	6.6 (0)	2.7 (0)
	1.0	Ĉ C T T -	2.87 4.88	1.90 3.03	1.60 2.25	1.40 1.64
		g	Y	1.48	2.37	2.38	2.12
		Y E E B +	35.6 (-0.1) 13.6 (-0.1) 6.6 (-0.1)	2.6 (-0.1)
	1.2	Ĉ C T T -	2.86 4.87	1.89 3.01	1.59 2.23	1.39 1.61
		g	Y	1.49	2.39	2.39	2.13

Table 9

 9 Target values of key variables for our policy scenarios at year 2100, with

	f =	0.3	and d 0.1 R =

Table 10

 10 Policy scenario values at year 2100 with

								1.8 α = , τ	0 f = ,	0 B = , d 0 R , varying 1 m , and χ
				τ	b	Emissions	CO 2 ,	Deviation from pre-	Damages	GDP
						E	Y	Ĉ C	industrial,	-	T T	(% GDP)	growth
						(GtC/y)			( 0 C)	Y g (%/y)
				0		50.8	3.7		5.9	20.3	1.8
	1 =0.0034 m	(-50 %)	χ=2.34	0.075 0.11 0.145 0	16.0 7.3 2.8 20.4	2.2 1.8 1.5 2.8		3.7 2.8 2.1 4.7	7.3 3.8 1.9 30.3	2.5 2.4 2.1 0.7
	m 1 =0.01	(+50 %)		0.0175 0.11	9.3 5.0	2.0 1.7		3.2 2.5	14.4 8.6	1.8 2
				0.145	2.2	1.5		1.9	4.8	1.9
				0		99.6	4.5		6.7	6.3	3.6
	χ=1.215	(-50 %)	1 =0.0067	0.075 0.11 0.145 0	19.1 7.8 2.9 6.0	2.3 1.8 1.5 2.1		3.8 2.8 2.1 3.6	3.3 2.3 1.6 41.6	3.0 2.6 2.2 -0.2
	χ =3.645	(+50 %)	m	0.075 0.11	4.9 3.5	1.8 1.6		2.8 2.4	22.9 13.5	1.0 1.6
				0.145	1.9	1.5		1.9	6.6	1.8

Table 11

 11 Effect of varying τ

				α by year 2100;	0 f = ,	0 B = , d 0 R = , other parameter values as in Table 1
				Abatement	% reduction of	Per capita	Per capita	GDP
				share b τ	emissions ( Y E )	abatement costs	damage costs	growth
					from baseline	(% Y )	(% Y )	Y g (%/y)
	Abatement	efficiency = 0.9	(-50 %)	0 0.075 0.11 0.145	0 48 67 81		0 1.5 2.2 2.9	26.9 13.6 8.8 5.5	1.1 1.8 1.9 1.8
	Abatement	efficiency = 2.7	(+50 %)	0 0.075 0.11 0.145	0 71 90 98		0 1.5 2.2 2.9	26.9 9.4 4.4 1.9	1.1 2.3 2.4 2.1
		A 50 % decrease of the low-carbon abatement efficiency gives τ α 0.9 =	in the upper half
	of the table.

Table 12

 12 Effect of varying ω

	α by year 2100;	0 B ≠ , d 0 R = , τ b = 0.075, and all other parameter values
	as in

Table 1

 1

the impact of both natural, climate related and purely economic shocks (Groth et al. 2014; Hallegatte and Ghil 2008).

Jean Albergel (Representative of the French IRD for East Africa), Dr. Fogel-Verton Séverine and NGUEMA Sarah-Ayito (Cooperation Attaché Embassy of France in Kenya) and the School of Mathematics (University of Nairobi) Board of Postgraduate Committee members for taking their time to serve in their various positions. I would also like to appreciate my colleagues at the Department of Statistics and Actuarial Science (DeSAS)

damages. Atmospheric CO 2 decreases from 1842 GtC to 1729 GtC, i.e., about 113 GtC by 2100, which implies a sequesteration of approximately 1 GtC/y between 1990 and 2100. The model's behavior in response to inclusion of biomass agrees with Mackey et al.'s (2013) claims that the capacity of terrestrial ecosystems to store carbon is finite and that the current sequestration potential primarily reflects depletion due to past land-use. Therefore, avoiding emissions from land carbon stocks and refilling depleted stocks reduces atmospheric CO 2 concentration, but the maximum amount of this reduction is equivalent to only a small fraction of potential fossil fuel emissions.

Using CCS methods but no deforestation control

The effects of including CCS into the model, via a fraction f of the total abatement share b τ , are summarized in Table 7. Deforestation control is not implemented in these runs, R d = 0. Note that the first column of Table 7 repeats for comparison the results of the new BAU run of Table 6; since b τ = 0 in this column, the same results are obviously obtained for all values of f .

On the other hand, when f = 0, i.e for the first row of $149/tC by 2100. This cost is within the range of the cost of CCS as given in the literature, cf. Subsection 3.3.2 and references there. Note that more investment in CCS ( f = 0.6 and 1), along with an increasing abatement share ( τ b = 0.11 and 0.145), also contributes to a decline in per capita GDP growth rate from what is found in the f = 0.3 row and τ b = 0.075 column.

In the f = 1.0 row, we note that inclusion of CCS without abatement in the energy sector also has potential for global change mitigation, although a little less efficiently. 11, and (c) b τ = 0.145; see legend for curves, with f = 0 -dashed, f = 0.3 -solid, f = 0.6 -dash- dotted, and f = 1.0 -dotted In Figure 4, the time-dependent evolution of the reduction in CO 2 emissions from baseline for the different values of f is shown, from 1990 to 2100, keeping the deforestation reduction equal to 0. Figure 4a shows that initial investment in CCS of 30 %, when the abatement share is CHAPTER 5

SENSITIVITY ANALYSIS

The estimates for the cost of CCS and of deforestation control are still very uncertain in the mitigation literature. For this reason, the conducted an analysis to ascertain the robustness of the CoCEB model's results and to clarify the degree to which they depend on five key parameters:

the damage function parameters 1 m and χ, the low-carbon abatement efficiency parameter τ α , CCS abatement efficiency parameter ω α , and the pi's parameters of Equation ( 27). The last two parameters effectively govern the cost of CCS and deforestation control. The values of these parameters are varied below in order to gain insight into the extent to which particular model assumptions affect results in Chapter 4 above.

Damage function parameters m 1 and χ

The study modifies the values of the parameters 1 m and χ by +50 % and -50 % from their respective values 1 0.0067 m = and χ 2.43 = in Tables 123456789above. It examines how that affects model results for year 2100. In Table 10

From the table, it is noticed that reducing 1 m by 50 % lowers the damages to per capita GDP from 26.9 % to 20.3 %, i.e., a 24.5 % decrease on the BAU ( b τ 0 = ) path. This depresses the economy less and contributes to higher CO 2 emissions of 50.8 GtC/y. On the other hand, increasing 1 m by 50 % increases the damages from 26.9 % to 30.3 %, i.e., a 12.6 % increase on the BAU path. This depresses the economy more and lowers CO 2 emissions in 2100 to 20.4 GtC/y.

The study has also shown that: (i) low investment in CCS contributed to a reduction in industrial carbon emissions and to an increase in GDP growth, but a further investment leads to a decrease in the reduction of emissions, as well as in the incremental GDP growth; (ii) enhanced deforestation control contributes to a reduction in both deforestation emissions and atmospheric CO 2 concentration, thus reducing the impacts of climate change; and (iii) the results in (i) remain very sensitive to the formulation of CCS costs. Conversely, the results for deforestation control were found to be less sensitive to the formulation of its cost. A large range of assumptions on these costs is found in the literature and the flexibility of the CoCEB model permitted us to span this range and to check the sensitivity of its results.

We found that per capita GDP growth on the paths with nonzero abatement share lies below growth on the Business as Usual (BAU) path for the earlier time period, approximately for 1990 to 2060, while GDP growth in the BAU scenario slows down and falls below the level on the other paths, i.e. the paths cross and mitigation strategies pay off in the longer run.

Discussion

The CoCEB model builds upon previous work on coupled models of global climate-economy interactions, starting from the pioneering work of Nordhaus (1994a), as extended in [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF] by the inclusion of endogenous growth. [START_REF] Greiner | Anthropogenic climate change in a descriptive growth model[END_REF] treated industrial CO 2 emissions as constant over time, while excluding the particular case of zero abatement activities (BAU); in fact, his model only applied for a minimum level of abatement. The study takes into account, more generally, emissions that depend on economic growth and vary over time, while including the case of abatement equal to zero, i.e. BAU. This was done by using logistic functions [START_REF] Akaev | Stabilization of the planetary climate in the twenty first century by transition to a new paradigm of energy consumption[END_REF][START_REF] Sahal | Patterns of technological innovations[END_REF]) in formulating equations for the evolution of energy intensity and carbon intensity of energy throughout the whole 21 st century [START_REF] Akaev | Stabilization of the planetary climate in the twenty first century by transition to a new paradigm of energy consumption[END_REF].

APPENDICES Appendix 1: Table of conversions

Notes: on units of weight used in this study.

Dealing with global/regional change involves large quantities. Here I use a Gigatonne (Gt) as the base unit of weight. This is related to other quoted weights as follows:

1. Gigatonnes of carbon (1 GtC = 3.667 GtCO 2 )

2. 1 tonne = 10 6 g; 1Mg = 1tC ; 1TgC (teragrams of carbon) = 1MtC (Megatonnes of carbon); 9. Mg ha -1 = t ha -l or 1 Mg ha -1 = 100 g m -2

10. 1g dry matter (DM) ≈ 0.5 g C for woody tissues and slightly less for herbaceous plants.

(The factor 1.9 comes from a combination of changing ppv to mass per volume and then integrating over the atmospheric column on Earth.)

Units for measuring energy

Rate of energy exchange is called power. A Watt (W) is a power Joule per second. Integrating biomass into the CoCEB and applying deforestation control as well as CCS technologies has the following results: (i) low investment in CCS contributes to reducing industrial carbon emissions and to increasing GDP, but further investment leads to a smaller reduction in emissions, as well as in the incremental GDP growth; and (ii) enhanced deforestation control contributes to a reduction in both deforestation emissions and in atmospheric carbon dioxide concentration, thus reducing the impacts of climate change and contributing to a slight appreciation of GDP growth. This effect is however very small compared to that of low-carbon technologies or CCS. We also find that the result in (i) is very sensitive to the formulation of CCS costs, while to the contrary, the results for deforestation control are less sensitive.