Global warming from attainable fossil fuel emissions

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A parameterised carbon feedback model for the calculation of global warming from attainable fossil fuel emissions Author: Willem P Nel, PhD Author Affiliation: Sustainable Concepts, PO Box 4297, Cresta, Johannesburg, South Africa, 2118, Tel: +27(0)823338518 E-mail: [email protected] Short Title: Global warming from attainable fossil fuel emissions

Abstract: This paper evaluates the IPCC SRES scenarios against fossil fuel depletion models and proposes attainable carbon emissions trajectories. The contemporary carbon feedback cycle is then evaluated in light of recent studies and attainable carbon emissions. In light of deficiencies in the contemporary carbon feedback cycle, a parametric carbon feedback model is constructed that is consistent with empirical evidence. A radiative feedback model, that overestimates transient response when used in conjunction with equilibrium climate sensitivity, is then used in sensitivity studies to calculate the range of plausible global warming responses. The model predicts a maximum atmospheric concentration of CO 2 in the range of 500560ppm and a maximum global mean surface temperature increase of 1.5-2°C relative to year 2000.

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INTRODUCTION

The Intergovernmental Panel on Climate Change (IPCC) concludes in the Fourth Assessment Report (AR4) that the rapid increase in CO2 emissions, following the industrial revolution, is the dominant driver of anthropogenically induced global warming [1]. The degree of future global warming is thus significantly dependent on a number of associated factors including (i) the attainable carbon emissions from the burning of fossil fuel and other sources such as land-use change; and (ii) the ability of terrestrial and oceanic carbon sinks to absorb excess atmospheric CO2, and iii) the ultimate global warming response (including feedbacks) to the trajectory of altered atmospheric CO2. The IPCC scenarios, from the Special Report on Emission Scenarios (SRES), do not explicitly consider constraints on the availability of fossil fuel resources and hence rely on policy and market responses to mitigate carbon emissions with respect to the SRES-A1 and A2 scenarios, which represent a business-as-usual (BAU) case from an economic growth perspective [2]. Later attempts to motivate BAU emissions scenarios follows a similar approach, with due consideration for fossil fuel demand in an assumed economic growth scenario, but no consideration for the physical realities of fossil fuel supply [3]. Although the SRES scenarios served as a sound basis for a scientific enquiry into the potential impact of CO2 emissions, recent studies in fossil fuel depletion [4-7]1 demand a revision of the scenarios to comply with realistically attainable emissions trajectories. Consideration of realistic emissions trajectories is crucial in a multi-disciplinary context and may ultimately alter the rationale for investments in alternative energy systems (and the efficient use of energy) from a reactive incentive (mitigation of global warming) to a socio-economic imperative (preservation of modern society) [7-8]. Further, the computational complexities of high-order oceanic-terrestrial carbon cycle models have resulted in the development of Impulse Response (IR) functions for use in simple climate models [9, 10]. Subsequently, much focus has been given to the development of process based models as an alternative, but it is evident from the large variation in results that these models are incomplete [1]. Despite remaining uncertainties on carbon-feedback cycles, most models converge on one point: a build-up of atmospheric CO2 above some critical level would have an adverse effect on the ability of carbon sinks to absorb carbon [11]. However, the validity of an IR is dependent on the emissions trajectory to which it is calibrated [12]. For this reason, IRs that are in general use may not be valid for the lower emissions trajectory presented by fossil fuel constraints. This paper reports on sensitivity studies with respect to attainable carbon emissions, evaluates the rationale and validity of impulse response models that are in general use and proposes a 1

ASPO [5] is cited as a source of a substantial body of peer reviewed articles and academic theses on the topic.

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parameterised carbon-feedback model that is consistent with empirical evidence on the atmospheric CO2 record for the analysis of global warming. 2.

MODELING CONSIDERATIONS

2.1

Fossil Fuel Emissions

Nel and Cooper [7] derived an energy reference case (ERC) for the attainable production profiles of fossil fuels using a logistics analysis approach. The author uses the same approach in this paper, but with updated data to include production values for 2007, as reported by BP [13]. The production outlook for fossil fuels has historically been under the auspices of global economic planning institutions such as the International Energy Agency (IEA), an OECD affiliate, and was based on exogenous assumptions about price and availability in demand-based economic growth models. In recent years, academic research into the physical realities of fossil fuel resources has emerged –see ASPO [5] for a comprehensive list of peer reviewed articles and academic theses. There is reasonable agreement between the ERC, and hence the derived production trajectories used in this paper, and this body of research. Exploitation of the fossil fuel resource base, which is far greater than reserves, is constrained by well-understood factors such as the energy profit ratio and logistical constraints under energyeconomic considerations [7-8, 14-15]. The assumption that the full resource base should be considered in economic and global warming analysis, is therefore questioned. A mechanistic application of logistics analysis overestimates the proven reserve base (which represents the potion of resources that is deemed producible) by 29%, 47% and 57% for oil, gas and coal, respectively. This scenario is used as a lower limit to the availability of fossil fuel, designated FL. As a sensitivity analysis, a high case, FH, is constructed by considering a doubling of the overestimations from the logistics analysis, yielding reserve overestimations of 58%, 94% and 114% for oil, gas and coal, respectively. In light of growing consensus on Peak Oil theory (covering both oil and gas) as well as recent downward revisions and changes in the categorization of coal reserves [4], the author considers both these scenarios as optimistic with respect to the future availability of fossil fuels. The associated CO2 emissions trajectories for the FL and FH scenarios are not consistent with most of the SRES scenarios (figure 1.a) – also supported by other peer reviewed work [16]. Future land-use emissions in figure 1 are based on the average of the category ―Other CO2‖ in the SRES scenarios. Proven reserves of fossil fuel must be increased by a factor of 8 to meet the emission trajectories of the highest SRES scenarios (figure 1.b).

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Figure 1. Emissions trajectories (CO2 only) from 1900 to 2200 for (a) the FH scenario and (b) an 8-fold increase in official fossil fuel reserves with SRES scenarios superimposed. Cumulative emissions for FH and FL are presented in figure 2. In light of the significant divergence between the SRES emissions scenarios and attainable fossil fuel emissions, it is appropriate to evaluate the validity of contemporary carbon feedback relationships.

Figure 2. Cumulative fossil fuel emissions only for FL and FH for 1900 to 2200. 2.2

Impulse Response Functions

Most carbon feedback models in general use comply with an analytical decay function that expresses the atmospheric residual of a carbon pulse as a function of time – also termed impulse response (IR) function. IR functions were adopted for their computational efficient and hence suitability for sensitivity studies over a range of emissions scenarios. However, the validity of IR functions for general use is challenged by a number of factors including: (i) The convolution

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integral of the IR over the emissions trajectory only applies while the carbon-climate system remains linear. (ii) The response function is dependent on the magnitude of the CO2 pulse i.e. a sufficiently high pulse would immediately introduce non-linearity as a result of time delay effects in carbon sinks (or by carbon chemistry for even higher pulses as processes are saturated). (iii) The response function is dependent on the existing levels of CO2 in the atmosphere when the pulse is introduced [12]. To overcome some of these uncertainties, IRs are calibrated using modeled data from more complex oceanic-land-vegetation carbon cycle models, often with respect to high emissions trajectories such as a doubling of atmospheric CO2 concentration (e.g. [9,10,12,17]). A further complication to the calibration of IRs is that there is still significant disagreement between process-based coupled climate-carbon feedback models with variations between 20ppm and 200ppm for an inter-comparison study on the SRES A2 scenario [11]. Limited studies on linearity of the convolution integral are available in peer-reviewed literature [17,18]. Although Hoos et al. [17] do not explicitly analyze linearity; their results show that pulses of 1% and 100% above preindustrial levels have differences of ~8-10% in the airborne fraction over the 50-100 year timeframe. The oceanic-land-vegetation carbon cycle models, to which IRs are calibrated, are based on process knowledge of the carbon cycle sinks, but the knowledge and models are incomplete and do not conform to empirical evidence, giving rise to the problem of ―missing sinks‖ or residual sink [1]. The IR function used in AR4 (1) is based on the Bern carbon cycle [1].

CO2  t   a0   ai exp  t   i 

(1)

The calculation of atmospheric residence lifetime, based on the calibrated constants ai and i is arbitrary in the absence of logical fitting constraints, and the use of single half-life, T½ 2, (opposed to an e-folding time) as a measure of atmospheric residence time, has been propose as a more meaningful metric [19]. It is evident that fitting constraints are not standardized, because of variations in model calibrations, and are not consistent with physical considerations, because of the inability of the IR functions to predict empirical results [7,20] – also confirming the concern of ―missing sinks‖ [19]. The constant term, a0, in the IR represents an airborne fraction of CO2 that remains in the atmosphere indefinitely at a new equilibrium level i.e. after the effects of the carbon pulse have stabilized, and is referred to as the Atmospheric Retention Factor (ARF) after Hasselmann et al. [9]. The AR4 model (IR-AR4) has an ARF of 21.7%. This value could not be reconciled with the results in Joos et al. [10], referenced by the AR4, which covers mixed layer oceanic uptake only in an IR with a retention factor of 2.3% and uses a dynamic global vegetation model to integrate the land biosphere into the Bern model. Other modeling studies report considerable variation in 2

T½ is the time required for carbon sinks to absorb half of the out-of-equilibrium CO2 in the model atmosphere.

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oceanic mixed-layer retention factors with values of 13-14% for inorganic oceanic model [18], 16-20% for inorganic oceanic model [21], 1-3% for mixed-layer inorganic ocean [12], 7% for oceanic-organic model [9] and 13% for a non-linear low emissions pulse in an oceanic model [17]. The cumulative effects associated with ARF become evident when analyzing a reconstruction of emissions since 1900 with respect to IR-AR4, overestimating current atmospheric concentration of CO2 by ~20ppm [7,20] – the equivalent of 40 billion tons of carbon (GtC). While some argue that carbon feedback cycles in general use perform adequately relative to empirical data [1], the significant divergence over longer timescales [11] illustrates the cumulative effect of this apparent minor deviation. Further, the notion of a significant ARF (regardless of the historical source-sink dynamics), as interpreted by some researchers [22], has counter-intuitive logic for low emissions trajectories. For example, background annual emissions from natural processes, such as wildfires, over geological time should result in cumulative increases in atmospheric CO2 and a runaway greenhouse effect. The ARF is a dominant feature of IR functions and warrants further evaluation – discussed in Section 2.4. 2.3

A Parameterised Carbon Feedback Model

Given the issues discussed in the preceding section, an analytical carbon feedback model should account for all first-order effects including (i) initial atmospheric concentration when the pulse is released (Ci), (ii) equilibrium atmospheric concentration of CO2 as a function of temperature (Ce), (iii) the absolute capacity of the carbon sink (ocean, terrestrial, ground, etc.) as a function of temperature and time (ST), (iv) the emission rate to account for time (buffering) effects (Ė), and (v) cumulative absorption (CA). These parameters are not necessarily independent. A parameterised functional relationship for a carbon response function should thus take a form such as expressed in (2).

CO2,abs  ppm / year   F  Ci , Ce , ST , E, CA,...

(2)

Although significant progress has been made in the understanding of process based knowledge on the carbon feedback cycle, there is still much uncertainty [1]. Since process knowledge is still incomplete, there are no empirical bases or scientifically deterministic theories to fully and accurately describe the variables listed above, hence the significant disagreement in modeling results. However, there is sufficient empirical evidence based on which a parametric relationship, such as (2) can be calibrated. Despite large inter-annual fluctuations, Hansen and Sato [23] demonstrated that ―the earth absorbs CO2 in proportion to the excess atmospheric CO2 [CO2]‖3 – at least with respect to Excess atmospheric CO2 (CO2) is defined relative to the pre-industrial equilibrium level of CO2,eq = 278 ppm (IPCC, 2007) as compensated for Global Mean Surface Temperature (GMST) anomalies at a rate of +18ppm per °C increase. 3

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historical emissions. Using empirical data for carbon emissions and measured atmospheric concentration, Nel and Cooper [7] reconstructed the relationship between CO2 and the amount of CO2 absorbed by sinks (CO2,abs) to derive a Linear Carbon-Feedback Model (LCFM or AH(0.03) in [7]) that successfully predicts the accumulation of atmospheric CO2 to date when used in conjunction with the instantaneous climate sensitivity. Although LCFM is described as linear with respect to the parameters used, it is not linear in the time domain (figure 3). The LCFM does not consider a breakdown in linearity of the airborne fraction of CO2 that would occur either as a result of high emission trajectories or the build-up of excessive atmospheric CO2 [1,23,24]. Since the validity of extrapolating empirical evidence is in question, guidance on future carbon feedback behavior is sought from the substantial modeling studies reported in peerreviewed papers.

Figure 3. Empirical fit for LCFM and NCFM. Model-based experiments demonstrate that cumulative sinks (land and ocean) as a fraction of cumulative emissions remains constant for the SRES-A1B scenario in compliance with historical equilibrium [24]; suggesting that linearity is nominally retained at emissions levels up to the equivalent rate and magnitude of the SRES-A1B scenario. The SRES-A1B-AIM scenario represents fossil reserve increases of ~300% (in excess of FL and FH). The LCFM should thus hold true for the FL and FH (figure 1.a) emission trajectories and for atmospheric CO2 concentrations of up to ~600ppm.

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However, the development of non-linearity in carbon-feedback for increasing emissions scenarios is unclear. The aforementioned modeling experiments [24] accumulated atmospheric concentrations of ~650ppm for the SRES-A1B scenario. Non-linear behavior in the biosphere ensues at atmospheric concentrations of ~450ppm, albeit under high emission rate trajectories [10, 25] – Fung et al. [24] found a similar result for the higher emissions trajectory in SRES-A2. Sea-to-air carbon fluxes stabilize and reverse for atmospheric CO2 concentrations in excess of ~600ppm [10]. In light of the above, an alternative to the LCFM, referred to as Non-linear Carbon Feedback Model (NCFM), is constructed by considering a second order model (3) that matches the slope of LCFM at CO2 = 25ppm, but has a zero slope at CO2 = 320ppm4 (figure 3) to nominally comply with the results of the modeling experiments discussed.

CO2,abs  A2  CO2   A1  CO2  2

(3)

where CO2,abs is the CO2 absorbed by carbon sinks in ppm, A1 and A2 are constants, and CO2 is the excess atmospheric CO2 in ppm2. The constants are A2 = 0, A1 = 0.03 for the LCFM and A2 = -5.08E-5, A1 = 3.25E-2 for the NCFM. As with the LCFM, the NCFM is intended as a best estimation for low emissions trajectories, considering the results of modeling studies and empirical data, but the model validity is questionable for atmospheric CO2 concentrations in excess of 600ppm. A comparison of LCFM and NCFM to the IR-AR4 demonstrates the dependence of NCFM on the initial conditions with T½ ranging from 24 to 72 years as the atmospheric concentration (in parenthesis in figure 4) changes from 400 to 900ppm.

Figure 4. Decay functions for LCFM and NCFM superimposed on IR-AR4. 4

CO2 of 320ppm is approximately equivalent to an atmospheric concentration of 600ppm.

Global warming from attainable fossil fuel emissions 2.4

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Atmospheric Retention Factor

The atmospheric retention factor (ARF) is a dominant feature of IR-AR4 and the process-based carbon feedback models that form its basis, especially in long-term context. The concept of a significant ARF over several millennia is expressed as the sum of exponential decay functions for various process-based sinks, each with its unique e-folding time (1). Following a rigorous statistical-empirical analysis, Knorr [26] concludes that the airborne fraction (AF) of annual emissions is constant for the period 1850 to present i.e. the temporal trend is insignificant. Knorr proposes that the simplest model of atmospheric growth rate is one with an AF of 0.43, emphasizing the necessity for process-based models to replicate empirical data and concluding that CO2 concentration should govern the uptake of atmospheric CO2 and not changes in emissions. The parametric link between uptake of CO2 and atmospheric concentration is consistent with observations by Hansen and Sato [23]. Nel and Cooper [7] proposed a parametric model that has a linear relationship between CO2 uptake and out-of-equilibrium CO2 (AH(0.03) in [7]), referred to as linear carbon feedback model (LCFM) in this paper. A comparison between a constant AF, IR-AR4 and LCFM is presented in figure 5 under the assumption of exponential growth in carbon emissions from 1850 to 2010 (4) - extrapolation to 2010.

E  t   E0e t

(4)

where E(t) represent emissions in year t and E0 is emissions in the base year. Under the assumption of exponentially growing emissions (4), IR-AR4 reduces to the sums of geometric series (5), which can be readily evaluated to calculate a time series (annually) of cumulative atmospheric fraction (CAF) in (5). t 3   1  e t  i CAF  E0 a0    E0  ai e i 1  1  e   i  1 with i 

 1  e i t   i   1  e 

(5)

i

Parameters used are for total emissions of 518GtC (162GtC for 1850 to 1960 [23] plus estimated 361GtC for 1961 to 2010 – see figure2), E0=0.28 GtC and an exponent,  of 0.0238 as an approximation of the average growth rate from 1960 to 2010. The constant atmospheric fraction (figure 5) model is based on an AF of 0.43 (absorption of 0.57) [26]. The following observations are apparent from figure 5:

 

IR-AR4 deviates significantly from the empirical trend of a constant AF. There is good comparison between LCFM and AF.

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Calculating AF for LCFM from the balance between atmospheric concentration and emissions reveals that AF converges to a constant for a given emissions growth rate (figure 6). Knorr’s [26] proposed AF of 0.43 matches the equilibrium AF of LCFM for a rate that approximates the emissions growth between 1960 and 2010.

Figure 5. Comparison of carbon feedback models. Time series reconstructions of atmospheric CO2 from (1) and LCFM in (3) under the assumption of an exponential emissions growth trajectory (4) allow the calculation of apparent annual AF for the different models. The results indicate that the notion of an AF of 43% [26] can be explained by the dynamic equilibrium between CO2 uptake and an exponential growth emissions trajectory for a model in which uptake of CO2 is dependent on atmospheric concentration i.e. LCFM (figure 6). A change in the emissions trajectory would naturally evoke a new dynamic equilibrium. The observations and analysis in this section supports evidence [7,20,26] that the process-based models (to which IR-AR4 is calibrated) are incomplete and inconsistent with empirical evidence while a parameterised model, as proposed in this work, is consistent with empirical evidence.

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Figure 6. Equilibrium AF for various exponential growth rates in emissions. 2.5

Global Warming Response Model

The purpose of this work relates specifically to the interpretation of the implications of plausible emissions trajectories and carbon feedback models on global warming projections. In this context, a simple climate model of zero-order is considered adequate. Despite severe limitations to zeroorder models, there is general consensus that a radiative forcing model produce comparable results to more sophisticated models for globally averaged temperature response when used within certain constraints [1,23]. The atmospheric CO2 concentration and global mean surface temperature (GMST) response in the IPCC AR4 (page 803) can be reproduced with excellent comparison using IR-AR4 in conjunction with a zero-order radiative forcing model and the SRES emissions trajectories. Except where specifically declared otherwise, the radiative forcing model used to produce the results in this paper complies with the model declared in Nel and Cooper [7]. A radiative forcing model falls well within the gambit of simple climate models and adequately fulfils the modeling objectives of this study. Quoting from AR4 (p. 196) [1]: ―Because the climate responses, and in particular the equilibrium climate sensitivities, exhibited by GCMs vary by much more than 25%, Ramaswamy et al. and Jacob et al. concluded that RF is the most simple and straightforward measure for the quantitative assessment of climate change mechanisms, especially for the LLGHGs.‖

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Climate Sensitivity

One of the specific restrictions in zero-order models is that it cannot predict transient behavior with a satisfactory degree of accuracy, as it does not account for a wide range of transient effects such as heat uptake in the oceans, evolution of special and vertical distribution of forcing agents, the evolution of feedback mechanisms and hence climate sensitivity parameters, etc. The more general use of radiative forcing models is in the calculation of equilibrium climate response, calculating or estimating a climate sensitivity parameter that represents equilibrium response. Climate sensitivity is an important parameter in simple climate models, where feedbacks are not explicitly modeled. A simple analytical expression of transient climate sensitivity has been elusive because of the complex processes involved. The approach used in this paper is to perform a sensitivity analysis of climate response by utilizing a range of climate sensitivities. AR4 [1] considers two different climate sensitivity metrics, namely transient climate response (TCR) and equilibrium climate sensitivity (ECS) to compensate for atmospheric feedbacks - both these parameters are derived from models and observed climate changes. TCR is the annual global mean temperature change at the time of CO2 doubling in a climate simulation with a 1% per year increase in atmospheric CO2 concentration - the average increase from 2000 to 2007 was ~0.5% per year and predicted to decline in the emissions trajectories considered in this paper. The 5 to 95% confidence interval for TCR is 1.5°C to 2.8°C [1] for an average of 2.15°C yielding a climate sensitivity parameter, , of ~0.58°C/(Wm-2), used for further analysis. ECS is the equilibrium annual global mean temperature response to a doubling of atmospheric CO2 i.e. when the atmospheric concentration of CO2 is maintained at the doubled level (~560ppm), with respect to pre-industrial concentration, for the duration required to allow atmospheric feedbacks to stabilize. The 5 to 95% confidence interval for ECS, based on the best efforts from the modeling community, is 2.1°C to 4.4°C [1] for an average of 3.25°C yielding a ~0.88°C/(Wm-2). The validity of this probabilistic interpretation of results from various models is questionable since each model is assumed to be equally credible [1]. Since most results are clustered around 3°C, AR4 advises that the most likely value for ECS is around 3°C [1]. A climate sensitivity parameter of ~0.88°C/(Wm-2), based on the average in the confidence interval, will be used for further analysis. It follows logically that an appropriate transient climate sensitivity parameter depends on the trajectory of atmospheric CO2 concentration – supported by the work and conclusions of Fung et al. [24]. A best estimate for the current [instantaneous] transient response parameter is based on AR4 [1] with a GMST increase of 0.76°C for a radiative forcing of 1.84 Wm-2 yielding ~0.41°C/(Wm-2). This value will increase as atmospheric CO2 increases and feedbacks become active. Application of ECS during the transient response, for a scenario of doubled CO2, would overestimate the transient response in temperature and atmospheric CO2, leading to an

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overestimation of other process parameters, an increase in forcing parameters and ultimately in an overestimation of the equilibrium response. Such a model would represent a conservative upper bound (overestimation) of climate response. 3.

RESULTS

The results in Figures 7 and 8 were calculated using the NCFM and IR-AR4 (Bern) carbon feedback models in a radiative forcing climate model to analyze global warming response from the FL and FH scenarios. Model assumptions comply with AR4 and Nel and Cooper [7]. Nonfossil emissions are assumed as 1GtC throughout the assessment period of 1900 to 1990 and as the average of the SRES scenarios to year 2100. The equilibrium concentration of CO2 is temperature dependent so that the modeled response varies as a function of the climate sensitivity parameter [7]. However, neither the LCFM nor the NCFM predicts atmospheric CO2 to reach doubled levels (figure 7), so that both TCR and ECS may overestimate climate sensitivity in a transient scenario such as presented by FL and FH. This overestimation is apparent in the fact that the atmospheric CO2 trajectory exceeds empirical measurements at Mauna Loa when a climate sensitivity of 0.88°C/(Wm-2) is used (figure 7). Both the LCFM and NCFM give a representative prediction of empirical data on atmospheric CO2 concentration if the instantaneous climate sensitivity of 0.41°C/(Wm-2) is used.

Figure 7. Modeled results of atmospheric CO2 for =0.88°C/(Wm-2) for the emissions scenarios in parenthesis (Source data for measured CO2 from ESRL [30]).

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Although the FH-emissions case is not deemed realistically attainable with today’s knowledge on fossil fuel reserves, the author superimposed it for demonstration purposes. Substantial further increases of the emissions trajectory leads to instability of the predicted results for the NCFM with irreversible and rapid exponentially rising atmospheric CO2 setting in when overestimation of fossil fuel reserves i.e. oil, gas and coal, exceeds 350% (nominally equivalent to the SRESA1B scenario). However, NCFM may not be valid for emissions of this magnitude. A summary of model results is provided in table 1 and table 2 for atmospheric CO2 concentration and Global Mean Surface Temperature (GSMT) anomaly respectively (including modeled values IR-AR4). GMST anomalies are reported relative to an anomaly of 0.25°C in year 2000 to match with curves reported on page 803 and elsewhere inn AR4 [1] (figure 8). Only the IR-AR4 model reaches a doubling of atmospheric CO2 compared to pre-industrial levels, but decreases beyond this maximum to year 2200.

Table 1. Modeled results for peak in atmospheric CO2. Scenario LCFM FL NCFM Bern LCFM FH NCFM Bern

=0.41 CO2[ppm] 449 480 603 478 531 671

Year 2069 2082 2154 2084 2103 2169

 =0.58 CO2[ppm] Year 457 2071 488 2083 603 2154 487 2086 540 2104 671 2169

 =0.88 CO2[ppm] Year 473 2074 503 2086 603 2154 505 2090 557 2107 671 2169

Table 2. Modeled results for peak in GMST anomaly. Scenario LCFM FL NCFM Bern* LCFM FH NCFM Bern*

=0.41 ºC 0.45 0.63 1.28 0.65 0.94 1.52

Year 2115 2116 2200 2126 2131 2200

=0.58 ºC 0.68 0.93 1.81 0.97 1.36 2.16

Year 2119 2118 2200 2128 2133 2200

=0.88 ºC 1.13 1.49 2.75 1.58 2.14 3.27

Year 2125 2123 2200 2133 2136 2200

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Figure 8. Modeled results of GMST anomalies for =0.88°C/(Wm-2) for the emissions scenarios in parenthesis. An important consideration with respect to the temperature response in figure 8 is that the time scale is not synchronized to the actual trajectory since the climate sensitivity parameter is based on equilibrium climate sensitivity. This approach is penalizing in two ways namely i) a reduction in CO2 absorption as a result of temperature feedback and ii) equilibrium climate feedback may never be reached because a doubling in CO2 is not reached and sustained. The time scale for the temperature response is thus not synchronized with the actual climate sensitivity for both the increasing and decreasing trends. The results are, however, representative of the plausible range of response and in this context the accuracy of the time scale is not relevant. The climate sensitivity parameter remains a point of uncertainty with some researchers proposing that feedbacks could be negative [27]. Nevertheless, with NCFM predicting a maximum atmospheric concentration within the doubling limit for ECS and decreasing thereafter (figure 7), the ECS is considered as upper bound for climate sensitivity in this transient analysis. The corresponding GMST anomaly predicted by NCFM is ~2°C above year 2000 for FH, compared to ~1.5°C for the more realistic FL scenario where a doubling of CO2 is not reached and  should logically be lower than ECS since the climate feedbacks at the equilibrium level of ECS are irrelevant. Although acceptance limits for global warming is beyond the scope of this paper, Kharecha and Hansen [20] proposes that GMST anomalies should be constrained to 1°C above year 2000 levels while the European Commission [28] proposes 2°C above pre-industrial levels. The enquiry of

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acceptance limits in the maximum increase in GMST also deals with the duration of the increased temperatures [29]. The NCFM predicts a more rapid decline in GMST, compared to IR-AR4, as the atmospheric CO2 concentration reduces with more rapid carbon absorption in sinks. 4.

CONSLUSIONS

A parameterised carbon feedback model, based on a robust interpretation of process knowledge on carbon feedback cycles, is calibrated to empirical data as well as modeling results from peer reviewed work and is then applied to plausible emission trajectories. Utilizing a simple radiative forcing model, that overestimates transient response when used in conjunction with equilibrium climate sensitivity, the calculated projections of atmospheric CO2 concentrations and GSMT anomalies to year 2200 are calculated. Based on the emissions trajectories considered, the model predicts atmospheric concentration of CO2 to increase to the range of 500-560ppm before decreasing to the range of 395-448ppm by 2200 with the lower range representing best estimates based on current knowledge of fossil fuel supply potential (FL) and the upper estimates based on a hypothetical overestimation of reserves (FH). Taking cognizance of uncertainties in the specification and modeling of a climate sensitivity parameter, the model predicts GSMT anomalies in the range of 1.5-2°C relative to year 2000. This highlights the necessity, when undertaking climate change modeling, to not only reflect the impact of the assumed emissions trajectory, but to also to have realistic input data concerning the extent to which fossil fuel reserves will continue to be exploited in the future. The fossil fuel reserves used in this analysis are not static and account indirectly for challenging technological advances that would be required to expand the currently known exploitable reserves to the estimations used in FL and FH. Since fossil fuels underpin economic development in many developing countries, there is the potential for significant socio-economic consequences in a global scenario where the available fossil fuel reserves are not exploited to their full technical potential and hence FL emission are likely to be achieved as a minimum. Note that FL represents significant mitigation strategies in the contemporary global warming debate. Although this work predicts a lower GMST response compared to some of the IPCC scenarios, a response of 1.5-2°C relative to year 2000 should not be trivialized and may lead to widespread socio-economic disruptions, especially on regional scales. This analysis deals with CO2 emissions trajectories only and does not incorporate detailed assessment of other greenhouse gas trajectories (beyond what is described in the base model[7]). Thus, there remain many essential issues that still need to be resolved in the global warming debate such as the study of acceptable limits, regional impacts and the CH4 feedback-cycle.

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The policy implications of the work include: 

The debate over peak oil and fossil resource depletion is most relevant and important to the global warming debate and should receive focused attention on a comparable scale.



It must be acknowledged that the work does not impact negatively on the need for renewable energy systems. While the global warming response from fossil fuel depletion may be acceptable, the associated economic implications of energy scarcity are not. It is important that the rationale for renewable energy be reframed in this context for it to receive the necessary policy attention.



The carbon derivative market does not have a rational basis and could at best serve to tax fossil based energy for the purpose of stimulating growth in alternative energy systems. Since such a strategy would be dysfunctional, it is doubtful that the proceeds would be invested as intended.



The science of global warming should open itself to analysis and debate on realistic emissions trajectories, carbon feedback cycles that are compatible with empirical evidence, and realistic modeling efforts to determine the impact of a limited mean global surface temperature increases such as is predicted in this paper.



Global warming mitigation efforts should not hamper energy security beyond the constraints already imposed by fossil fuel depletion dynamics since the resulting emissions trajectories already comply with many SRES mitigation scenarios. For this reason, carbon capture and storage should not be pursued any further because of the significant energy penalty it imposes on conventional fossil-based energy systems.

5.

REFERENCES

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http://europa.eu/press_room/presspacks/energy/iasec8.pdf/, 2007; (accessed July, 01 2008). [29] Hansen J, Sato M, Kharecha P, Beerling D, Masson-Delmotte V, Pagani M, Raymo M, Royer DL, Zachos, JC, (2008) Target Atmospheric CO2: Where Should Humanity Aim?, The Open Atmospheric Science Journal 2: 217-231. [30] ESRL, Earth System Research Laboratory, National Oceanic & Atmospheric Administration (NOAA), http://www.esrl.noaa.gov/, (accessed May, 22 2008).

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List of Figures Figure 1. Emissions trajectory from 1900 to 2200 for (a) the FH scenario and (b) an 8-fold increase in official fossil fuel reserves with SRES scenarios superimposed. Figure 2. Cumulative fossil fuel emissions for FL and FH. Figure 3. Empirical fit for LCFM and NCFM. Figure 4. Decay functions for LCFM and NCFM superimposed on IR-AR4. Figure 5. Comparison of carbon feedback models. Figure 6. Equilibrium AF for various exponential growth rates in emissions. Figure 7. Modeled results of atmospheric in parenthesis (Source data for measured CO2 from ESRL [30]).

-2) for the emissions scenarios

Figure 8. scenarios in parenthesis.

-2) for the emissions

List of Tables Table 1. Modeled results for peak in atmospheric CO2. Table 2. Modeled results for peak in GMST anomaly.