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text that follows is a PREPRINT.

Please cite as:

Fearnside,
P.M., D.A. Lashof and P. Moura-Costa. 2000.  Accounting for time in mitigating global
warming through land-use change and forestry. Mitigation and Adaptation
Strategies for Global Change 5(3): 239-270.

ISSN:
1381-2386

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Springer

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ACCOUNTING FOR TIME IN
MITIGATING GLOBAL WARMING THROUGH LAND-USE CHANGE AND FORESTRY

PHILIP
M. FEARNSIDE1, DANIEL A. LASHOF2 and PEDRO MOURA-COSTA3

1 National Institute for Research in the Amazon (INPA), Av. André Araújo, 2936, C.P. 478, 69011-970 Manaus, Amazonas, Brazil

2
Natural Resources Defense Council (NRDC), 1200 New York Ave., NW,
Suite 400, Washington, DC 20005, U.S.A.

3
EcoSecurities, Ltd., 45 Raleigh Park Road, Oxford OX2 9AZ, U.K.

21 Feb. 2000

17 Apr. 2000

Abstract. Many of the
proposed activities for mitigating global warming in the land-use and forestry
(LUCF) sector differ from measures to avoid fossil fuel emissions because
carbon (C) may be held out of the atmosphere only temporarily.  In addition, the timing of the effects
is usually different.  Many LUCF
activities alter C fluxes to and from the atmosphere several decades into the
future, whereas fossil-fuel emissions avoidance has immediate effects.  Non-CO2 greenhouse gases
(GHGs), which are an important part of emissions from deforestation in
low-latitude regions, also pose complications for comparisons between fossil
fuel and LUCF, since the mechanism generally used to compare these gases
(global warming potentials) assumes simultaneous emissions.  A common numeraire is needed to express
global warming mitigation benefits of different kinds of projects, such as
fossil fuel emissions reduction, C sequestration in forest plantations, avoided
deforestation by creating protected areas and through policy changes to slow
rates of land-use changes such as clearing.  Megagram (Mg)-year (also known as
“ton-year”) accounting provides a mechanism for expressing the
benefits of activities such as these on a consistent basis.  One can calculate the atmospheric load
of each GHG that will be present in each year, expressed as C in the form of CO2
and its instantaneous impact equivalent contributed by other gases.  The atmospheric load of CO2-equivalent
C present over a time horizon is a possible indicator of the climatic impact of
the emission that placed this load in the atmosphere.  Conversely, this index also provides a
measure of the benefit of not producing the emission.  One accounting method compares
sequestered CO2 in trees with the CO2 that would be in
the atmosphere had the sequestration project not been undertaken, while another
method (used in this paper) compares the atmospheric load of C (or equivalent
in non-CO2 GHGs) in both project and no-project scenarios.

Time preference,
expressed by means of a discount rate on C, can be applied to Mg-year
equivalence calculations to allow societal decisions regarding the value of
time to be integrated into the system for calculating global warming impacts
and benefits.  Giving a high value
to time, either by raising the discount rate or by shortening the time horizon,
increases the value attributed to temporary sequestration (such as many forest
plantation projects).  A high value
for time also favors mitigation measures that have rapid effects (such as
slowing deforestation rates) as compared to measures that only affect emissions
years in the future (such as creating protected areas in countries with large
areas of remaining forest).  Decisions
on temporal issues will guide mitigation efforts towards options that may or
may not be desirable on the basis of social and environmental effects in
spheres other than global warming.
How sustainable development criteria are incorporated into the approval
and crediting systems for activities under the Kyoto Protocol will determine
the overall environmental and social impacts of pending decisions on temporal
issues.

Key words: carbon dioxide, discount rate, global warming,
greenhouse effect, land-use change, mitigation, time preference, deforestation.

1. Introduction

Temporal issues are among
the most fundamental questions governing the amount of credit that will be
given to different kinds of global warming mitigation measures.  These issues include establishing both a
time horizon and a discount rate (zero or otherwise) for carbon (C).  Temporal issues will be key factors in
determining whether efforts to mitigate global warming will include CO2
sinks in the land-use change and forestry (LUCF) sector, and within the LUCF
sector whether priority is given to plantation forestry or to avoiding
deforestation.

Questions that are still
undecided include whether megagram (Mg)-year (also known as
“ton-year”) accounting will be applied to calculating the benefit
of mitigation activities under the Kyoto Protocol, what time horizon will be
used, and whether a non-zero discount rate will be applied.  For the first commitment period
(2008-2012), these decisions will probably be made at the Sixth Conference of
the Parties (COP-6) in November 2000, after taking into consideration the
Intergovernmental Panel on Climate Change (IPCC) Special Report on Land-Use
Change and Forestry (SR-LUCF), to be completed in May 2000 (Watson and Verardo,
2000).  The question of whether any
LUCF activities, especially forest conservation, will be included under the
Clean Development Mechanism (CDM) established in Article 12 of the Kyoto
Protocol (UN-FCCC, 1997a) will also be decided at that time.  The Clean Development Mechanism provides
a mechanism by which Annex B countries (countries that have commitments to
limiting their national emission totals under the Kyoto Protocol) can finance
activities in non-Annex B countries to offset the financing country’s
fossil fuel C emissions.  Clean
Development Mechanism projects must demonstrate that C benefits are additional
to what would have occurred in the absence of the project.

Carbon dioxide (CO2)
sinks in general have been criticized as temporary and therefore inherently
less beneficial than avoiding fossil fuel emissions (e.g., Matoon, 1998).  Confusion has often resulted from
lumping all LUCF activities in a single category as biotic sinks.  Lashof and Hare (1999), for example,
have argued that credits from biotic sinks under the Protocol carry a risk of
having perverse effects on atmospheric CO2 concentrations.  However, Fearnside (1999a) has argued
that this reasoning applies only to forest plantations, and that within the
category of plantations it applies only to their role in CO2
sequestration (as distinct from fossil fuel substitution).  Lashof and Hare's argument is that, by
allowing countries to emit more C from fossil stocks into the active C pool
(biosphere + atmosphere), the increases in biotic C stocks that have been
encouraged under the Kyoto Protocol as carbon offsets (1) have a risk of
subsequent release into the atmosphere, and (2) reduce the options available
for future responses in the forest sector because the capacity of these options
to absorb C will have been saturated.
However, Fearnside (1999a) has argued that, in the case of avoiding
deforestation in low-latitude regions, the result is more like reducing fossil
fuel C emissions than it is like carbon sequestration in plantations.  C stocks in areas of high-biomass low-latitude
rain forests are very unlikely to be allowed to regenerate to their present
levels if these forests are cut down.
Most of the C released from deforesting these areas is, therefore, an
addition to what might be called the most active C pool (i.e., atmospheric C +
C in rapidly cycling stocks such as plantation biomass) that is as permanent as
is release of fossil C.  Clean
Development Mechanism or other activities that help low-latitude (tropical)
forest countries avoid deforestation keep C out of the “most active
pool” in the same way that avoiding fossil C emissions would.  The C releases avoided are, for
practical purposes, as irreversible as fossil fuel combustion (Fearnside,
1999a.

If cMg-year
accounting (Chomitz, 1998; Fearnside, 1995a, 1997a; Tipper and de Jong, 1998; Moura-Costa and Wilson, 2000) is needed useful for
comparing avoided fossil fuel emissions with plantations and other mitigation
options in the forest sector.  Under
a Mg-year system, credit would be given for the number of tons of C held out of
the atmosphere each year.  Discounting,
zero or otherwise, would apply to the C value calculated for each year over the
time horizon when the expectations for different proposed mitigation projects
are compared (“not discounting” is really only a special case of
discounting, where the discount rate is equal to zero).  Discounting can be applied in
conjunction with Mg-year accounting, although use of a non-zero discount rate
is not required.  It is also
possible to apply discounting to net stock changes (i.e., to fluxes), rather
than to the atmospheric load of C as in Mg-year accounting (e.g., Hourcade et al., 1996; Schlamadinger and Marland,
1999).

Mg-year accounting recognizes that keeping a
unit of C out of the atmosphere during any given year has the same value,
whether the C atoms are cycled through successive short-lived products or
whether they are held in a mahogany wood desk that lasts a century.  Under a Mg-year accounting system,
delaying deforestation merits credit irrespective of the long-term fate of the
forest, although the cumulative credit that can be earned from a given forest
stand is obviously greater the longer the
forest remains intact.  Comparisons
can be made between forest reserve creation and policies to slow deforestation
by using C Mg-year accounting.
Policies affecting the motives for deforestation will have rapid effect
on GHG emissions, whereas the effect of reserve creation can only reduce
emissions years in the future when available forests outside of the reserve
have been exhausted.

The discounting applied
here does not take into account threshold effects that may exist in the damage
function relating climatic impacts to atmospheric changes.  Our knowledge of such thresholds is
currently insufficient to incorporate them in calculations of this kind, although
this could be done when our understanding of the climate system improves.  As of now, decisions must be based on
the best available information, such as that in the IPCC’s Second Assessment Report (SAR).

2. Duration of Sequestration

Carbon sequestration in
forest and other types of land cover is inherently reversible, unlike avoided
emissions of fossil fuel C (which is generally considered a permanent
gain).  Carbon dioxide sequestration
must be distinguished from fossil fuel substitution, which can also be achieved
by some LUCF options, such as charcoal substitution for mineral coal.  Fossil fuel substitution through
forestry is just as permanent as avoided emissions through measures such as
enhancing energy efficiency (Hall et al.,
1993; Marland and Schlamadinger, 1997).

It has been argued that
postponing deforestation is a valid mitigation measure even if the forests in
question are later cut for harvesting or other purposes, including cutting up
to the theoretical maximum of clearing all forests in a country (Fearnside,
1999b).  The credit for such a delay
depends on two key parameters: time horizon and discount rate (or other
alternative time-preference scheme).
From a CO2 perspective, under some conditions postponing a
given number of hectares of clearing for one year is equivalent to avoided
emissions by reduced combustion of fossil fuels.  In the fossil fuel case, avoided
emissions are counted as a permanent
gain, even though the same barrels of oil not burned in a given year will be
burned just one year later.  The
fossil fuel displacement is assumed to cascade forward, either (1) indefinitely
(i.e., assuming that fossil fuel stocks are infinite for practical purposes),
(2) until after the end of the time horizon, or (3) until fossil fuel burning
ceases at some fixed point in time due either to development of technological
alternatives or to social changes.
In the case of fossil fuels, the total stock of approximately 5000 Pg
(petagrams = gigatons) C (Bolin et al.,
1979) is far beyond the capacity of human society to burn and to mitigate to
acceptable levels of environmental impact, and can be considered infinite for
practical purposes.  While some
categories of fossil fuels, such as natural gas, may be exhausted within a
100-year time horizon, one can assume that switching will then occur to other
forms of fossil fuel energy.

In the case of
deforestation, the assumption of an effectively infinite cascading effect can
break down if the area of remaining forest is small enough that it could be
exhausted within the time horizon under consideration.  If a country runs out of forest (or of
accessible or unprotected forest) within the time horizon, then no carbon
advantage would accrue from postponing deforestation if the discount rate is
zero (except for credit for delay generated by the time horizon, to be
explained later).

It is important to
understand that the logic behind considering either fossil fuel or forest as
permanent is not based on the
assumption that specific atoms of C will remain in the ground or in the forest
forever.  Instead, the effect of
delaying for one year a given amount of fossil fuel burning or a given amount
of deforestation will be delaying for one year the time that C is released from
each barrel of oil or hectare of forest that would be burned or deforested in
subsequent years.  The emission
displacement cascades forward either forever or until the end of the time
horizon, resulting in a permanent savings.
In Figure 1, Mg number 1 (Mg1) is burned in year 1 in the
baseline scenario, but in year 2 in the mitigation scenario.  By the end of the time horizon (year n),
n Mg have been burned in the baseline scenario, but only n-1 Mg in the
mitigation scenario.  In the case of
forest, this example does not include the effect of degradation (or
aggradation).

[Figure
1 here]

The cascading effect
of displaced emissions depends heavily on the assumption that the C reserve
(either forest or fossil) will last beyond the end of the time horizon.  If this is not the case, as in Figure 2
where only two Mg of C exist and the forest that contains them is destroyed
within the time horizon in both the baseline and mitigation scenarios, no
credit is gained by delaying deforestation in an accounting that considers only
the total emission (i.e., where no removal of C from the atmosphere is
considered).  As will be shown
later, even in a case such as this where forest runs out within the time
horizon, delaying deforestation should receive some credit if a more complete
accounting is made of the stocks in the atmosphere using a Mg-year
approach.  In this simplified
example, the effect of degradation (or aggradation) is also not considered.

[Figure 2 here]

3. Time
Horizons and Emissions Impacts

Establishing a finite
time horizon, as in Figures 1 and 2, implies a value for time independent of
any additional value for time preference that may be added through a mechanism
such as a discount rate.  The global
warming potentials (GWPs) from the SAR (Schimel et al., 1996) have been adopted by the Kyoto Protocol (Article 5.3)
for establishing the equivalence among different GHGs, and a 100-year time
horizon has been specified for this purpose (UN-FCCC, 1997b).  We assume that this time horizon will
apply to other aspects of GHG accounting.
Whether intended or not, choice of a time horizon has created a value
for time under the Protocol.  The
100-year zero-discount formulation used for GWPs adopted from the SAR is
equivalent to an annual discount rate of approximately 10.9%
if with a very
long (1000-year) time horizon (Fig. 3)the tail of the
curve representing impacts is truncated at some sufficiently distant time, such
as 1000 years (Fig. 3).
A variety of arguments point to 100 years as a reasonable choice for
policy-making with a minimum of perverse distortions (Fearnside, 2000a).

[Figure
3 here]

In the context of the present calculation, the
impact of a GHG on global warming is represented by the amount of heat that it
has blocked from escaping into space over the 100-year time horizon.  In other words, it is proportional to
the instantaneous radiative forcing of one Mg of the GHG multiplied by the
number of Mg present in each year, summed over the years in the time horizon.

The parameters used in the SAR can be used to calculate
the fraction of the atmospheric load from an emission that remains in any given
year.  C emitted to the atmosphere
as CO2 declines in a non-linear fashion in accord with the Revised
Bern Model, which will be described shortly.  Methane (CH4) and nitrous
oxide (N2O) decline exponentially with half lives of 12.2 years and
120 years, respectively (Schimel et al.,
1996).  While these gases remain in
the atmosphere, their instantaneous radiative forcings (not to be confused with
GWPs, which are integrated over a time horizon) per Mg of gas are 58 for CH4
and 206 for N2O, relative to a value of 1 for CO2 (Shine et al., 1995).  For each year of the calculation, the
atmospheric load of the non-CO2 GHGs can be converted to CO2
gas equivalents in terms of instantaneous radiative forcing, and then converted
to C by multiplying by the ratio of the atomic weight of C to the molecular
weight of CO2 (12/44).
An example is given in Table 1 for emissions from 1 ha of deforestation,
using average per-hectare emissions from deforestation in Brazilian Amazonia in
1990 and treating all emissions as net committed emissions (i.e., treating all
delayed emissions and CO2 uptakes as occurring in the year of
deforestation).  The ability of
Mg-year accounting to deal fairly with non-CO2 GHGs is important,
especially for quantifying the benefits of avoiding deforestation, which is a
major source of these gases through biomass burning.

[Table
1 here]

Discounting can be used to express the impact
of emissions of different gases occurring at different times in terms of
immediate C emission equivalents.
This can be thought of as a net present value, but we prefer the term
immediate C emission equivalent to make clear that the adjustment includes both
the effect of time and translating the effects of non-CO2 GHGs into
C (i.e., CO2 C) equivalents.

The difference between the integrals of the C
load in the atmosphere (and its radiative equivalent from the atmospheric loads
of other gases) is not the only possible index of the benefit of delaying
emissions.  For example, one might
choose the reduction in the atmospheric load of C at some fixed point in time,
such as at the time the 2 ´ CO2 milestone is passed in
approximately 2070 (A in Fig. 4), rather than the difference in the integrals
adopted here.  The area under the curve in the
delayed-emission case is smaller than that in the immediate-emission case by an
amount that has been pushed beyond the end of the time horizon (B in
Fig. 4).  The difference between the
integrals results in greater credit for delaying emissions than does the
fixed-year approach.  For example, a
one-year delay results in a decrease of 0.71% in the integral but only a 0.46%
decrease in the height of the curve (the instantaneous atmospheric load) in
2070.

[Figure
4 here]

When an
emission of CO2 enters the
atmosphere, the atmospheric load of the GHG will begin
to decay following a path that has the same integral over the first 100 years
as an exponential decay with a time constant of 55 years.  However, the precise path followed is
more complex than this, so that over 500 years the integral is the same as an
exponential decay with a time constant of 150 years. The actual decay will
depend on the future composition of the atmosphere and feedbacks from climate
change.

In the
present paper the path assumed for C decline is that calculated by the version of the
Bern Model used in the SAR (Schimel et al., 1996).  Lack of published output from the
revised model has resulted
in virtually all previous discussions of Mg-year
accounting being based on the earlier model used in the 1990 and 1992 IPCC reports.
The revised version incorporates greater uptake by the biosphere,
described by the IPCC as a change that is “believed to be an important
improvement” (Albritton et al.,
1995).  The resulting more rapid
decline in atmospheric C in the early
years indicated by the revised model significantly increases the value of
temporary sequestration of CO2.

Output from the version
of the Bern Model used in the SAR was illustrated graphically in the
IPCC’s 1994 special report (Albritton
et al., 1995), but the only
quantitative parameters published were for an approximation of the earlier
version used in the IPCC’s 1990 and 1992 reports (Albritton et al., 1995):

F[CO2(t)] = 0.3003 exp(-t/6.993) +
0.034278 exp(-t/71.109) + 0.35686 exp(-t/815.727)

where “F” is the fraction of CO2 remaining in the atmosphere and “t”
is the time after emission in years.

The approximation of the
output of the revised model is given by:

F[CO2(t)] = 0.175602 + 0.137467
exp(-t/421.093) + 0.185762 exp(-t/70.5965) + 0.242302 exp(-t/21.42165) +
0.258868 exp(-t/3.41537).

When a Mg of C in the
atmosphere decays as shown in Figure 4, the area under the curve over a 100-year
time horizon is equal to 46% of the area of the rectangle that would represent
the Mg of C remaining
unchanged in the atmosphere over the same period.  Keeping a Mg of C out of the
atmosphere for a full 100 years therefore represents 46 Mg-year equivalents, rather than the 100 Mg-years that would be earned if the CO2
entering the atmosphere had no movement to the ocean or other sinks.  This is 16% lower than the corresponding
number obtained using the older version of the Bern Model (55 Mg-years).

The number of
Mg-year equivalents represents the global warming
impact caused by the emission in question.
If, rather than the Bern Model, the ratio of global CO2 sinks to sources in the 1980s is used for
estimating Mg-year
equivalents, the value of 1 MgC of immediate
emission is 42 Mg-year
equivalents (Tipper and de Jong, 1998).
Because both terrestrial and ocean CO2 sinks could become saturated over the next century
(Cao and Woodward, 1998; Sarmiento et al.,
1998), use of a higher value would be wise in order to avoid risk of
under-compensating current GHG emissions
(Tipper and de Jong, 1998).

If release of
the Mg of C were delayed
for ten years, then the curve (Fig. 4) would be shifted to the right, and part of
it would pass beyond the time horizon (only 90 years would be considered).  The difference between the integrals of
the two curves would represent the gain earned from having delayed the
emission.  As the year of emission
is delayed successively further into the future, the impact of a one-Mg emission declines from 46 Mg-years in the first year to zero in year 100.  Emitting one Mg in year 50 has 60% of the
impact of emitting one Mg in the first
year.  Conversely, a mitigation
project that results in a temporary delay of a C emission will gain progressively more credit the
longer the emission is postponed.
It will gain 100% of the credit of a permanent displacement if the delay
lasts for 100 years, and 40% of the
credit if the delay lasts for 50 years.

The above calculations
consider the difference between the mitigation and baseline scenarios by
comparing the integrals of the atmospheric load of C over the time
horizon.  Somewhat different results
are obtained in computing the benefits of LUCF mitigation projects such as
forest (silvicultural) plantations
if attention is focused on the C in the trees (e.g., Moura-Costa and Wilson,
2000).  The distinction between C in
trees and C in the atmosphere is important because atmospheric C is subject to
removal through natural processes that transfer it to CO2 sinks such
as oceans and the biosphere, whereas C present in the trees is assumed to
remain fixed.  In the Moura-Costa
method (Fig. 5 A), an equivalence time is calculated as the point at which the
area of the rectangle representing biomass C is equal to the area under the
atmospheric C decay curve over the 100-year time horizon.  A different approach (the Lashof method:
Fig. 5 B) reasons that, if C release is delayed because it is held in trees (as
in Figure 1), the benefit will be represented by the difference in the
integrals of the two curves within the time horizon, which is equal to the area
of the tail of the second curve that is pushed beyond the end of the time
horizon as a result of the delay.
The second method is used in the present paper.

[Figure
5 here]

In the case of
evaluating the C benefits of avoided deforestation, the size of the remaining
forest relative to prevailing rates of deforestation is critical (Fig. 6).  The difference in the cascading effect
between countries with forest at risk of being cleared completely within the
time horizon and those that have sufficient forest to exclude this possibility
can be illustrated by a hypothetical example.  Consider a hypothetical country with
only 3 ha of remaining forest and deforestation proceeding at a rate of 1
ha/year (Fig. 6).  This is similar
to the example in Figure 2, but includes the effect of forest degradation.  Areas of forest that have been saved
from deforestation in a mitigation scenario may still lose C through
degradation or destruction by such forces as extreme weather events under
current climate regimes or under regimes altered by climate change, outbreaks
of insects or diseases, and invasion by loggers or deforesters.  Concern with permanence is one of the
main concerns
about the use of biotic sinks as climate change mitigation projectsdoubts that
has led some critics to oppose inclusion of biotic sinks among mitigation
measures under the Kyoto Protocol (e.g., Lashof and Hare, 1999;
Mattoon, 1998, but see Fearnside, 1999c).

[Figure
6 here]

In the hypothetical
example (Fig. 6) the forest is assumed to be rapidly degrading: 20 MgC/ha is
lost to degradation between the first and the second year, 30 MgC/ha is lost
between the second and the third year, and 10 MgC/ha is lost between the third
and the fourth year.  The emission
from 1 ha of deforestation would be 100 MgC if it were cut in year 1, 100
– 20 = 80 MgC if it were cut in year 2, 80 - 30 = 50 MgC in year 3 and 50
- 10 = 40 MgC in year 4.  In the
baseline scenario, the emission from degradation in the second year of 20
MgC/ha will apply over the two remaining hectares of forest (the third hectare
is already cut), making the degradation emissions 20 ´ 2 = 40 MgC and the
total in that year 80 + 40 = 120 MgC.
In the third year the degradation of 30 MgC/ha will apply only to the
one remaining hectare of forest, making the total emission in the third year 50
+ 30 = 80 MgC.  In the fourth year
both deforestation and degradation C emissions are zero because all forest has
already been cleared.  The total
emission over the four years is 300 MgC.

In the mitigation
scenario, deforestation is postponed by one year.  In this case the degradation in the
second year will apply to 3 ha rather than 2 ha, and will decrease in the two
subsequent years as successively less standing forest is present to
degrade.  At the end of four years
the total (cumulative) emission will also be 300 MgC.  Here no net gain in C has been achieved except for that which comes from credit
for having delayed the emission, the credit being based on the effect of
atmospheric C stocks decaying over time (i.e., Fig. 4), plus any additional
credit that may be awarded using a discount rate with a value greater than zero
to represent time preference.

The effect of
correction for decay in atmospheric C stocks is shown by the last row of
numbers in both the baseline and the mitigation scenario sections in Figure 6.  Here, the total emission in each year is
multiplied by the corresponding proportion of the (full) impact of an immediate
emission of a Mg of C, to obtain the immediate emission equivalent in Mg of C.  The total in the baseline scenario is
279.1 MgC, while that in the mitigation scenario is 263.6 MgC, resulting in a
gain of 15.4 MgC.  Although such a
gain is not insignificant, it is substantially lower than what can be gained if
the forest lasts beyond the end of the time horizon.  It should be noted that the values would
be approximately double those in this example if a more realistic net emission
per hectare of deforestation of 200 MgC/ha were used; within the bounds of
uncertainty this represents the per-hectare net committed emission (i.e.,
adjusting for CO2 uptake in secondary forests after deforestation)
of clearing in 1990 in Brazilian Amazonia, which averaged 194 MgC/ha
(Fearnside, 1997b).

If the forest lasts
beyond the end of the time horizon, then the credit that can be gained from
delaying deforestation increases substantially (Fig. 7).  In this hypothetical example, the time
horizon is set at the end of year four.
As in the previous example (Fig. 6), deforestation proceeds at 1 ha/year
and the forest degrades at the same rapid rate.  An important difference is that, because
not all of the forest will be cleared before the end of the time horizon in the
mitigation scenario, one must follow the fate of an additional hectare of
forest that would have been cleared in the baseline scenario.  This displaced area degrades from 100
MgC/ha in year 1 to 40 MgC/ha at the end of the time horizon in year 4.  These 40 MgC/ha represent a net gain in
the total emission, being equal to the 400 MgC total emission in the baseline
scenario minus the 360 MgC total emission in the mitigation scenario.  With a Mg-year equivalence accounting of
the immediate emission equivalent, the net gain is 363.6 – 315.8 = 47.8
MgC, which is much greater than the 15.4 MgC gain in the case where the forest
runs out before the end of the time horizon.

[Figure
7 here]

Possible
effects of forest degradation (or aggradation) in forest areas saved from
deforestation could be corrected by appropriate adjustments in the crediting
system (e.g., as in Figs. 6 and 7).
Whether actions changing forest degradation and/or aggradation will be
included among the additional activities under Article 3.4 of the Kyoto
Protocol is still undecided (Schlamadinger and Marland, 1998).  This will be critical for determining
the baseline for emissions trading under Article 17 for any tropical countries
that join Annex B of the Protocol.
For non-Annex B countries, credit under the Clean Development Mechanism
(Article 12) will be based on additional C effects in a project scenario as
compared to a baseline or no-project scenario.  Assuming that deforestation avoidance is
included under the Clean Development Mechanism, it remains undecided whether
effects such as degradation would be included in the accounting.  Nothing prevents degradation (or
aggradation) effects from being estimated and the corresponding adjustments
made to C credit earned.  Forest
aggradation, the opposite of degradation, could also be adjusted for in the
areas that are saved from deforestation.
The principle is relevant that changes that result in damage to the
atmosphere (i.e., forest degradation) should have obligatory adjustments, while
changes that result in atmospheric benefits (i.e., forest aggradation) should
be optional (Sathaye, et al., 1997).

It is important to
note that the examples given in Figures 6 and 7 do not include a discount rate
on C benefits to reflect society’s time preference (to be discussed in
the next section).  Over a 100-year
time horizon, applying a discount rate, even if no greater than 1-2%/year,
would add substantially to the attractiveness of delaying deforestation as
compared to other mitigation options, because delaying deforestation results in
substantial reduction in annual emissions in the short term.  All C accounting implies a discount
rate, whether it is zero or otherwise.
A decision to use a zero discount rate is just as much a decision as
choosing any other rate.  There is
no escape from facing the choice of specifying a value for time.  Sound reasons exist for adopting a
discount rate for C greater than the zero value currently used in most
discussions of C accounting.

4. Time Preferences and Discounting

4.1. RATIONALE FOR
DISCOUNTING

Applying to C either
discounting or some alternative form of time preference can be justified for reasons
other than the selfish interests of the current generation weighting
(Fearnside, 2000c, Richards, 1997).
Global warming impacts need to be separated into two categories that are
calculated and reported separately: impacts that can be expressed in terms of
money, and those that cannot, especially human life impacts (Fearnside,
1998).  Discounting is the mechanism
by which a value for time is normally translated into economic decision-making.

Value for time, or the
social rate of time preference, is a combined result of the pure rate of time
preference (time preference based solely on an event’s position in time,
independent of how wealthy we expect to be at that time) and the utility (the
utility per unit of wealth multiplied by the expected wealth per capita).  Two approaches exist for deriving these
values: a prescriptionist approach based on ethical principles, usually
assigning a low or zero value to the pure rate of time preference (e.g., Cline,
1992), and a descriptionist approach based on observed economic behavior (e.g.,
Nordhaus, 1991).  Annual discount
rates (social rates of time preference) over the long term are usually in the
0.5-3% range for prescriptionists and in the 3-6% range for descriptionists
(Arrow et al., 1996).  The result is that prescriptionists
recommend greater spending on mitigation and adaptation than do descriptionists
because long-term impacts of climate change have a greater net present value at
low discount rates (Arrow et al.,
1996).  It is important to note,
however, that the effect of discount rate on the overall level of spending
justified by climatic change is not the same as the effect on how the money
would be allocated among different mitigation response options: higher discount
rates will increase the relative attractiveness of options with rapid effects
on atmospheric GHG levels, such as slowing deforestation.

Derivation of the social rate of time
preference requires values for three factors, all of which are subjects of
controversy: the pure rate of time preference, which is often described as the
result of “impatience” or “myopia” is greater than zero
if based on the observed behavior of individuals (whose behavior is influenced
by awareness of their own mortality), but which can be argued to be zero from
the perspective of whole societies.
Sensitivity tests of discounting in the Dynamic Integrated Model of Climate and the Economy (DICE) by Nordhaus (1997) indicate that optimal
allocation to combating global warming is most sensitive to the pure rate of
time preference.  The other
parameters are the expected level of wealth in the future and the marginal
utility per unit of additional wealth, which is expected to range from 1.5 to
0.8 (Scott, 1989; Pearce and Ulph, 1995; see Arrow et al., 1996).

Many people will die as
impacts begin to appear from global warming.  Using Fankhauser's (1995) estimates for
a jump to double the pre-industrial CO2 concentration with the world
(including its population size) as it was in 1990, the result would be loss of
US$ 221 billion (in 1990 prices) annually, exclusive of human life losses, that
would total 138,000 lives per year (115,000 of which would be in non-OECD
countries) (see Pearce et al.,
1996).  The above reasoning assumes
that global warming initiates a step-function change in death rates, rather
than an increase that lasts for a finite period of time.

All such estimates are
subject to great uncertainty, especially on the high side due to its unbounded
nature.

It is important to
understand that avoiding mortality, even by delaying global warming by a single
year, represents a permanent gain.
This is true even though the individuals so saved may die the next year
from this or some other cause.  The
avoided mortality benefits cascade forward in the same way as avoided C
emissions in Figure 1.  Based on
global emissions from fossil fuel and tropical forest land-use change (Table
2), one can calculate the human life value of avoided C emissions (including
immediate emission equivalents gained from delaying emissions or temporary
sequestration of C).  This
calculation does not consider the CO2 sink of 0.5 PgC/year in
temperate and boreal forest growth.
Note that the value of 2.4 PgC/year for emission from tropical forest
land-use change (Fearnside, 2000d) used in Table 2 is 50% higher than the 1.6
PgC/year value used by the SAR, and that the additional size of the missing
sink implied by this difference results in the impact per Mg of current
emission being reduced in proportion to the change in the total anthropogenic emission.  It is 26% higher than the value of 1.9
PgC estimated by Houghton (1999).
Each million Mg of avoided emission results in the saving of 16.4 lives
(Table 2).  The obviously
unrealistic assumption of fixed global population size over the 1990-2070 period
makes this value conservative by a factor of two or more (Fankhauser and Tol,
1997).  The human-life value of
delaying global warming gives time a value that is independent of arguments
based on money, and provides a rationale for applying some form of time
preference, as by discounting, to C.

[Table
2 here]

The human-life benefit of
delaying global warming is illustrated schematically in Figure 8.  Here it is arbitrarily assumed that
global warming-induced mortality simply ramps up in a linear fashion from zero
in 2000 to the SAR figure of 138,000 deaths/year in 2070 (the approximate year
of 2 × CO2), and remains constant thereafter.  Delaying global warming by one year
shifts the curve to the right, creating a gain of 138,000 lives regardless of
what time horizon is adopted (so long as it is after 2070).  It should be emphasized that this gain
is not reduced by discounting C, and that human life is not discounted.

[Figure
8 here]

Various other arguments
for discounting have been put forward by different authors, although none of
these controversial arguments is necessary to justify the use of discounting
(or of some alternative means of expressing time preference) in global warming
calculations.  One argument is that
expected increases in the wealth of the population suffering global warming
impacts will reduce the perceived loss of utility from the monetary impacts of
global warming because wealthier people attribute less value to a given amount
of monetary loss (Azar and Sterner, 1996).
The opposite relationship between wealth and value has been suggested
for human life losses (Fankhauser and Tol, 1997), and strongly contested
(Fearnside, 1998).  Yet another
argument for discounting is that it favors temporary carbon sequestration
activities that buy time for expected technological improvements reducing the
future cost of mitigation per Mg of C (Chomitz, 1998).  Another line of argument would even
indicate negative discount rates: greater movement of C to ocean and
terrestrial sinks as a result of CO2 fertilization and other effects
of future increases in atmospheric CO2 levels, as well as greater
time that atmospheric loads of C could be present to decay while still below
dangerous levels, led Wigley et al.
(1996) to suggest that C emissions are better now than later.  Schneider
(1997) counters the argument of Wigley et
al. (1996) by noting that greater loads of carbon in the atmosphere might
trigger non-linearities, sometimes referred to as “climatic
surprises.”  In addition,
immediate policy responses can restore efficiency that is hampered by
pre-existing market failures, such as spillovers in research and development
markets (Schneider and Goulder, 1997).

Exponential discount
rates greater than zero can have perverse effects on economic decision making
because even catastrophic events in the long-term future are reduced to
insignificance (Cline, 1992; Costanza, 1991; Fearnside, 1989; Pearce, 1991;
Price, 1993).  Rejection of
discounting in these contexts must be tempered with recognition of its
appropriateness in the context of carbon accounting.  Pretending that time has no value also
has potential perverse effects.

The effect of discounting
reducing long-term costs and benefits to insignificance is a characteristic of
the exponential discounting most commonly employed in economic analyses.  A variety of alternative time-weighting
mechanisms has been  proposed to
avoid this consequence, including hyperbolic discounting where the annual
discount rate decreases as time progresses (Schneider et al., 2000), Heal discounting (Heal, 1997) where the discount
rate falls in steps, for example using a market rate (the opportunity cost of
capital) for the first 30 years and thereafter using a discount rate derived
from a zero rate of pure time preference and conservative assumptions about
long-term economic growth, a generation-weighting system that results in a
thicker tail of the distribution than does traditional discounting (but only
within a limited time horizon) (Fearnside, 2000c), and an alternative to pass a
fixed percentage of decision-making weight beyond the end of the time horizon
(Fearnside, 2000a).

Agreement on a discount
rate or other time-preference weighting arrangement for C is fundamental to comparing
forest-sector options with fossil fuel substitution (Fearnside, 1995a,
1999c).  Interpretation would be
greatly simplified if the discount rate chosen is consistent with choices for
global warming potentials (Lashof and Ahuja, 1990).  Discounting C need not be the same as
money, although some advocate that the same rate should be applied (e.g., van
Kooten et al., 1997).  The implications of discount rates as
high as those for money are substantial for the relative impacts of different
activities (Fearnside, 1997a).  The
choice of discount rates for other purposes, such as private investment
decisions, public expenditures, and public regulation of renewable natural
resources management, all have independent rationales.  Since decisions are so sensitive to
discount rate choices (for example, the difference between a 3% and 6% annual
discount rate is a factor of 20 over the course of a century), the consequences
of allowing choices on global warming decisions to be determined by discount
rates derived in other spheres could be severe.

4.2. CONSEQUENCES OF
DISCOUNTING

The impact of one Mg of C
emission at different discount rates is shown in Figure 9, indicating the
percent of full impact recognized depending on the year that an emission occurs
(considering a discrete
approximation using one-year increments).  For example, for the zero-discount case,
the impact of a one-Mg emission is 46 Mg-years if emitted in year 0 (i.e., the
area under the baseline curves in Figure 5), and declines to 46 – 17 = 29
Mg-years if emitted in year 46 (i.e., the mitigation case in Figure 5 B).  The impact of emitting one Mg in year 46
is therefore 29/46 = 63% of the immediate emission impact (Fig. 9).  From the zero-discount line,
progressively larger discount rates cause impact to decrease rapidly in the
first years after emission (Fig. 9).
The converse of Figure 9, for purposes of calculating credit for
delaying emissions through sequestration, is given in Figure 10.

[Figures
9 and 10 here]

Discounting can radically
alter choices of energy sources and mitigation options (Fearnside, 1995a,
1997a; Marland et al., 1997; Price
and Willis, 1993).  The length of
the time horizon has a strong effect on the importance of discounting.  As time horizons become longer, the
distortions become greater if no discounting is applied.  In the case of forest sector options
that can transfer C to very long-term pools, these pools can dominate the
results if very long horizons are considered without discounting.  In the case of an infinite or very long
time horizon, equilibrium conditions will apply.  Slow buildup of C in very-slow-turnover
classes of wood products dominates the results at equilibrium, but occurs at
such remote times that it has little bearing on present decisions when
discounting is applied.  These
problems also apply to calculations made under the assumption that the shadow
price of C increases at the same rate as the discount rate for money, thereby
allowing analysis without discounting C (Fearnside, 1995a).

In the energy sector,
higher discount rates for C will progressively reduce the attractiveness of
building hydroelectric dams to substitute for fossil fuel-based thermal
generation.  This is because dams
produce substantial emissions from concrete, steel and energy use during the
construction phase years before any power is generated, followed soon after
filling the reservoir by a large peak of additional emissions of CO2
from above-water decay of flooded trees (if the dam is in a tropical forest
area) as well as emissions of CH4 (Fearnside, 1995b, 1997a).  Thermal power, in contrast, produces
little emission during power plant construction, followed by emissions at a
constant rate over many decades, emissions impacts and energy benefits coming
in direct proportion and at the same time.
Consequently, the cost of carbon benefits earned by switching from
thermal to hydroelectric power will increase with higher discount rates for C,
approaching infinity at the breakeven point between the two energy
sources.  Similarly, higher discount
rates will tend to reduce the benefits attributed to wind, solar and energy-efficiency
projects compared to fossil fuel power plants to the
extent that they involve larger emissions
related to building the capital equipment (with no emissions during
operation).  Higher
financial discount rates also make these projects less economically
attractive.

In forest-sector options,
higher discount rates for C would favor deforestation avoidance (by slowing
rates of forest loss) over plantation silviculture because deforestation
produces large and immediate releases of GHGs, while plantations accumulate C
slowly.  As discount rates for C
increase, the cost per Mg of C can be expected to climb for forest plantation
mitigation options, but would remain relatively flat for avoided
deforestation.  Policy measures with
immediate effects on reducing deforestation rates will be favored over creation
of protected areas which can only be expected to result in reduced
deforestation rates years later when the remainder of the available forest has
been exhausted.  This can be seen by
considering a hypothetical case to illustrate the implications of Mg-year
accounting and discounting for the two major categories of deforestation
avoidance efforts: creation of protected areas and policy changes to slow rates
of clearing.

Consider a country (Fig.
11 A) that is clearing its remaining forest at a constant rate and will run out
of forest in nine years.  If a park
is created from 1/18 (5.5%) of the remaining forest (Fig. 11 B), the available
forest will be exhausted in 8.5 years, after which there will be no more
clearing.  Note that this implies
some simplifying assumptions as compared to real cases: deforestation activity
shifts completely from the reserve area to other sites (i.e., there is 100%
leakage), and deforestation proceeds linearly until the last tree is cut.  The alternative strategy—policy
measures to reduce clearing rates—is illustrated in Figure 11 C, where
clearing rate is reduced by 50% and proceeds to destroy the entire forest in 18
years.

[Figure
11 here]

The effect of discount
rate on the choice between park creation and policy measures to slow
deforestation is shown in Figure 12, using as an example the same scenario as
Figure 11 with a baseline deforestation time of nine years.  If the park option is to be as
attractive as the slowing deforestation option, the area of park that would
need to be created, expressed as a percent of the remaining forest area,
increases steadily with increasing discount rates; examples for 50% and 40%
reduction in deforestation rate are shown from the family of curves that would
describe this relationship.

[Figure
12 here]

Another means of
visualizing the choice between parks and slowing deforestation is illustrated
in a second example (Fig. 13).  A
ratio of the atmospheric impact the under slowing deforestation scenario and
under the park creation scenario greater than one indicates that park creation
would be preferable.  Here a
baseline time to deforestation of 45 years is assumed, and a fixed park area of
1/9 (11%) of the remaining forest.
The annual discount rates needed to cause a switchover in deforestation
avoidance strategy are substantially lower in this example than in the previous
one: for a 25% reduction in deforestation rate, parks are favored if the annual
discount rate is less than 1.45%, whereas for a 50% reduction in deforestation
rate slowing deforestation is the favored option at all discount rates.

[Figure
13 here]

Results such as those in
Figure 11 are highly dependent on all of the emissions in all of the scenarios
compared occurring within the time horizon.  If, for example, the time to complete
deforestation under the baseline scenario extends beyond the time horizon, then
park creation will receive no credit (or partial credit in the case of
deforestation ending soon after the time horizon).  If slowing deforestation results in the
demise of the forest being pushed beyond the end of the time horizon, then
policy changes to slow clearing rates get substantially more credit.  These discontinuities may be seen as
either benefits or distortions, depending on the point-of-view.  Choice of the time horizon is the
critical factor in determining when they come into play.  The shorter the time horizon, the more
countries will be affected by this factor.
At 100 years, Brazil would only escape the time horizon effect after
about 200 years, given (extremely optimistic) linear extrapolation of recent
deforestation rates as the baseline.

5. Sustainable
Development Implications of Mitigation

The above consequences of
discounting C have a variety of implications for other environmental and social
costs and benefits.  Generation of
electrical power from fossil fuels has significant health consequences through
air pollution (Rosa and
Schechtman, 1996).  On the other hand, hydroelectric power
can have tremendous impacts on biodiversity, indigenous peoples and
resettlement, as well as impacts on health, fisheries and a long list of other
concerns.  Two of the most notorious
dams in the world in terms of these associated impacts are the Belo
Monte/Altamira (formerly Babaquara) complex in Brazil and the Three Gorges Dam
in China (Barber and Ryder, 1993; Dai
Qing, 1994; Fearnside, 1988, 1994, 1996a; Santos and de Andrade, 1990).
Both of these have been put forward in recent debates over the Clean
Development Mechanism as possibly meriting C credit!  The almost total lack of connection
between discussions in the carbon sphere and those in other spheres of
environmental and social impact assessment is evident.

In the forestry sector,
the effect of discounting C in favoring deforestation avoidance over forest
plantations is highly beneficial from the biodiversity standpoint.  On the other hand, the effect in
favoring policy initiatives over establishing protected areas is perhaps not
the best result for long-term maintenance of biodiversity (Fearnside,
1999d).  Natural forests provide
critical environmental services, including maintenance of biodiversity and
watershed functions (e.g., Daily, 1997; Schneider, 1998).

The associated
environmental and social impacts of energy and forestry choices that are
influenced by decisions regarding time preference for C make clear the need for
explicit consideration of these impacts in decision making on global-warming
abatement.  They cannot be addressed
indirectly by fiddling with the discount rate in order to achieve progress on
an alternative environmental and social agenda through global-warming
mitigation efforts.  Neither can
these concerns be compartmentalized as beyond the ken of mitigation decisions
and left up to each country to decide as it sees fit through whatever system of
environmental impact assessment, if any, it may have.  Such a solution would both favor the
implantation of mitigation projects in countries with little or no
environmental and social impact regulation and would result in projects being
funded that grossly violate standards in the funding countries (the two
hydroelectric dam examples mentioned earlier provide glaring examples).  How sustainable development criteria are
applied in carrying out global-warming mitigation measures under the Kyoto
Protocol will be crucial in determining the associated impacts and benefits of
the projects (e.g., Fearnside, 1996b, 1999e).  Sustainable development criteria and
procedures represent another undecided area in Kyoto Protocol implementation.

Countries often have very different views as to
what constitutes sustainable development.
The United Nations Framework Convention on Climate Change (UN-FCCC)
clearly recognizes the sovereignty of each country in deciding how to mitigate
global warming within its borders.
LUCF activities funded internationally for carbon credit under the Kyoto
Protocol will inevitably have to meet the sustainable development criteria of both the countries receiving and those
providing the funds (Fearnside, 1999a).
Specifying the criteria to be used in this winnowing process and the
institutional mechanism for carrying it out are tasks that can only be done by
the Parties.  As a hypothetical
example, a country might propose to cut a tropical forest containing endangered
species and tribal peoples in order to implant a Eucalyptus plantation with C benefits.  The criteria used to define sustainable
development will determine whether such a project would receive funding and/or
carbon credit, and thereby determine the environmental and social implications
of the mitigation effort.  In
addition to screening out unacceptable projects, sustainable development
criteria could also play a role through a reward system to encourage more
desirable projects.  Premiums for
benefits in such areas as biodiversity and social parameters could be
incorporated into the carbon crediting structure adopted by the Parties (e.g.,
Schneider, 1998; Schneider et al.,
2000).  The extent that such a
system is implemented will determine the extent to which the effects of
discount rate choices for C will guide development in desirable or perverse
directions, or a mixture of both.

6. Conclusions

1.) Mg-year equivalence
provides a needed mechanism for comparing the global warming impacts of
different activities and the benefits of different mitigation projects.  It allows temporary sequestration of CO2
to be compared on a equitable and consistent basis with permanent C
sequestration or fossil fuel emission avoidance.

2.) Time preference,
expressed by means of a discount rate on C, can be applied to Mg-year
equivalence calculations to allow societal decisions regarding the value of
time to be integrated into the system for calculating global warming impacts
and benefits.  The moral choice of
specifying a value for time, zero or otherwise, cannot be avoided.

3.) Time-preference
choices for C through discount rate (or alternative mechanisms) can strongly
influence economic decisions and the social and environmental impacts and/or
benefits of the favored mitigation options.  For example, the choice between creating
protected areas and instituting policy measures to slow deforestation rates is
heavily depending on time preference.
Pending decisions on sustainable development criteria under the Kyoto
Protocol could be critical in determining the consequences that C
time-preference choices have in spheres other than global warming.

Acknowledgments

An earlier version of this discussion was
presented at the 8th Meeting of the F-7 research network on tropical
forests and climate change, 27-28 August 1999, Wageningen, the
Netherlands.  Brazil's National
Council of Scientific and Technological Development (CNPq AIs 350230/97-98
& 523980/96-5) and the National Institute for Research in the Amazon (INPA
PPIs 5-3150 & 1-3160) provided financial support.  We thank F. Joos for the
revised Bern model.  S.V.
Wilson P.M.L.A. Graça, R. Dixon and three reviewers provided helpful
comments.

References

Albritton, D.L., Derwent, R.G., Isaksen,
I.S.A., Lal, M. and Wuebbles, D.J.: 1995, ‘Trace gas radiative forcing
indices’, in Houghton, J.T., Meira Filho, L.G., Bruce, J., Lee, H,
Callander, B.A., Haites, E., Harris, N. and Maskell, K. (eds.), Climate
Change 1994: Radiative Forcing of Climate Change and An Evaluation of the IPCC
IS92 Emission Scenarios, Cambridge, Cambridge University Press, pp.
205-231.

Arrow, K.J., Cline, W.R., Maler, K-G., Munasinghe,
M., Squitieri, R. and Stiglitz, J.E.: 1996, ‘Intertemporal equity,
discounting, and economic efficiency,’ in Bruce, J.P., Lee, H. and Haites, E.F. (eds.), Climate Change 1995:
Economic and Social Dimensions--Contributions of Working Group III to the
Second Assessment Report of the Intergovernmental Panel on Climate Change,
Cambridge, Cambridge University Press, pp. 125-144.

Azar, C. and Sterner, T.:
1996, ‘Discounting and distributional consideration in the context of
global warming,’ Ecological Economics 19, 169-184.

Barber, M. and Ryder, G. (eds.): 1993, Damming
the Three Gorges, Second Edition, Toronto, Probe International/Earthscan,
183 pp.

Bolin, B., Degens, E.T., Duvigneaud, P. and Kempe, S.:
1979, ‘The global biogeochemical carbon cycle,’ in Bolin, B.,
Degens, E.T., Kempe, S. and Ketner, P. (eds.) The Global Carbon Cycle.
Scientific Committee on Problems of the Environment (SCOPE) Report No. 13.
New York, John Wiley & Sons, pp. 1-56.

Cao, M. and Woodward, F.I.: 1998,
‘Dynamic responses of terrestrial ecosystem cycling to global climate
change,’ Nature 393,
249-252.

Chomitz, K.M.: 1998, The
permanence and duration issue in carbon offsets based on sequestration, World
Bank Working Paper, Washington, DC, Development Research Group, 20 pp.

Cline, W.R.: 1992, ‘The Economics of
Global Warming,’ Washington, DC, Institute of International Economics,
399 pp.

Costanza, R. (ed.): 1991,
Ecological Economics: The Science and Management of Sustainability, New
York, Columbia University Press, 525 pp.

Dai Qing (ed.): 1994, Yangtze!
Yangtze! Toronto, Probe International and Earthscan, 295 pp.

Daily, G.C. (ed.): 1997, Nature’s
Services: Societal Dependence on Natural Ecosystems. Covelo, California,
Island Press. 392 pp.

Fankhauser, S.: 1995, Valuing
Climate Change--The Economics of the Greenhouse, London, EarthScan, 180 pp.

Fankhauser, S. and Tol,
R.S.J.: 1997, ‘The social costs of climate change: The IPCC Second
Assessment Report and beyond,’ Mitigation and Adaptation Strategies
for Global Change 1(4), 385-403.

Fearnside, P.M.: 1988, ‘China's Three
Gorges Dam: "Fatal" project or step toward modernization?’ World
Development 16(5), 615-630.

Fearnside, P.M.: 1994, ‘The Canadian
feasibility study of the Three Gorges Dam proposed for China's Yangtze River: A
grave embarassment to the impact assessment profession,’ Impact
Assessment 12(1), 21-57.

Fearnside, P.M.: 1995a,
‘Global warming response options in Brazil's forest sector: Comparison of
project-level costs and benefits,’ Biomass and Bioenergy 8(5), 309-322.

Fearnside, P.M.: 1995b, ‘Hydroelectric
dams in the Brazilian Amazonia as sources of 'greenhouse' gases,’ Environmental
Conservation 22(1), 7-19.

Fearnside, P.M.: 1996a, ‘Hydroelectric
dams in Brazilian Amazonia: response to Rosa, Schaeffer & dos
Santos,’ Environmental Conservation 23(2), 105-108.

Fearnside, P.M.: 1996b, ‘Socio-economic
factors in the management of tropical forests for carbon,’ in Apps, M.J.
and Price, D.T. (eds.) Forest Ecosystems, Forest Management and the Global
Carbon Cycle, NATO ASI Series, Subseries I, Vol. 40, Heidelberg,
Springer-Verlag, pp. 349-361.

Fearnside, P.M.: 1997a,
‘Greenhouse-gas emissions from Amazonian hydroelectric reservoirs: The
example of Brazil's Tucuruí Dam as compared to fossil fuel
alternatives,’ Environmental Conservation 24(1), 64-75.

Fearnside, P.M.: 1997b, ‘Greenhouse gases
from deforestation in Brazilian Amazonia: Net committed emissions,’ Climatic
Change 35(3), 321-360.

Fearnside, P.M.: 1998,
‘The value of human life in global warming impacts,’ Mitigation
and Adaptation Strategies for Global Change 3(1), 83-85.

Fearnside, P.M.: 1999a, ‘The potential of
Brazil's forest sector for mitigating global warming under the Kyoto Protocol's
"Clean Development Mechanism,"’ in Kinsman, J.D., Mathai, C.V.,
Baer, M., Holt, E. and Trexler, M. (eds.) Global Climate Change: Science,
Policy, and Mitigation/Adaptation Strategies. Proceedings of the Second
International Specialty Conference, Washington, DC, 13-15 October 1998.
Sewickley, Pennsylvania, Air & Waste Management Association (AWMA), pp.
634-646.

Fearnside, P.M.: 1999b,
‘Forests and global warming mitigation in Brazil: Opportunities in the
Brazilian forest sector for responses to global warming under the "Clean
Development Mechanism",’ Biomass and Bioenergy 16(3), 171-189.

Fearnside, P.M.: 1999c, ‘Bogging down in
the sinks,’ World Watch 12(3),
6-7.

Fearnside,
P.M.: 1999d, ‘Biodiversity as an environmental service in Brazil's
Amazonian forests: Risks, value and conservation,’ Environmental
Conservation 26(4), 305-321.

Fearnside, P.M.: 1999e, ‘Environmental and social
impacts of wood charcoal in Brazil,’. in Prado, M. (ed.) Os
Carvoeiros: The Charcoal People of Brazil.  Rio de Janeiro, Wild Images Ltda., pp. 177-182.

Fearnside, P.M.:
2000a, ‘Why a 100-year time horizon should be used for global warming
mitigation calculations,’ (manuscript).

Fearnside, P.M.: 2000b. ‘Greenhouse gas
emissions from land use change in Brazil's Amazon region,’ in Lal, R.,
Kimble, J.M. and Stewart, B.A. (eds). Global Climate Change and Tropical
Ecosystems, Boca Raton, Florida, CRC Press, pp. 231-249.

Fearnside, P.M.: 2000c, ‘Time preference in global warming calculations: A
proposal for a unified index,’ (manuscript).

Fearnside, P.M.: 2000d,
‘Global warming and tropical land-use change: greenhouse gas emissions
from biomass burning, decomposition and soils in forest conversion, shifting
cultivation and secondary vegetation,’ Climatic Change (in press).

Hall, D.O.,
Rosillo-Calle, F., Williams, R.H. and Woods, J.: 1993, ‘Biomass for
energy: Supply prospects,’ in Johanssen, T.B., Kelly, H., Reddy, A.K.N.
and Williams, R.H. (eds.) Renewable Energy: Sources for Fuels and
Electricity. Covelo, California, Island Press, pp. 593-652.

Heal, G.: 1997, ‘Discounting and climate
change,’ Climatic Change 37(2),
335-343.

Houghton, R.A.: 1999, ‘The annual net
flux of carbon to the atmosphere from changes in land use 1850-1990,’ Tellus
51B, 298-313.

Hourcade, J.C. and 22 others: 1996,
‘Estimating the costs of mitigating greenhouse gases,’ in Bruce, J.P., Lee, H. and Haites, E.F. (eds.),
Climate Change 1995: Economic and Social Dimensions--Contributions of
Working Group III to the Second Assessment Report of the Intergovernmental
Panel on Climate Change, Cambridge, Cambridge University Press, pp.
263-296.

Lashof, D.A. and Ahuja,
D.R.: 1990, ‘Relative global warming potentials of greenhouse gas
emissions,’ Nature 344,
529-531.

Lashof,
D.A. and Hare, B.: 1999, ‘The role of biotic carbon stocks in stabilizing
greenhouse gas concentrations at safe levels,’ Environmental Science
and Policy 2(2), 101-109.

Marland, G. and Schlamadinger, B.: 1997,
‘Forests for carbon sequestration or fossil fuel substitution? A
sensitivity analysis, Biomass and Bioenergy 13, 387-397.

Marland, G.,
Schlamadinger, B. and Leiby, P.: 1997, ‘Forest/biomass based mitigation
strategies: Does the timing of carbon reductions matter?’ Critical
Reviews in Environmental Science and Technology 27, S213-S226.

Mattoon, A.T.: 1998,
‘Bogging down in the sinks: Escapist accounting and tree planting,’ World Watch 11(6), 28-36.

Moura-Costa, P. and
Wilson, C.: 2000, ‘An equivalence factor between CO2 avoided
emissions and sequestration—description and applications in
forestry’ Mitigation and Adaptation Strategies for Global Change 5(1),
51-60.

Nordhaus, W.D.: 1991, ‘To slow or not to
slow: The economics of the greenhouse effect,’ Economic Journal 101(407), 920-937.

Nordhaus, W.D.: 1997, ‘Discounting and
economics in climate change,’ Climatic Change 37(2), 315-328.

Pearce, D.W.: 1991,
‘Internalising long-term costs: Global warming and intergenerational
fairness’, in Hanisch, T. (ed.), A Comprehensive Approach to Climate
Change, Oslo, Norway, CICERO, pp. 19-31.

Pearce, D.W., Cline,
W.R., Achanta, A.N., Fankhauser, S., Pachauri, R.K., Tol, R.S.J. and Velinga,
P.: 1996, ‘The social costs of climate change: Greenhouse damage and the
benefits of control,’ in J.P. Bruce, H. Lee and E.F. Haites (eds.), Climate
Change 1995: Economic and Social Dimensions--Contributions of Working Group III
to the Second Assessment Report of the Intergovernmental Panel on Climate
Change, Cambridge, Cambridge University Press, pp. 179-224.

Pearce, D.W. and Ulph, D:
1995, ‘A social discount rate for the United Kingdom,’ London,
Centre for Social and Economic Research on the Global Environment, University
College, London and University of East Anglia, 21 pp.

Price, C.: 1993, Time,
Discounting and Value, Oxford, Blackwell, 393 pp.

Price, C. and Willis, R.:
1993, ‘Time, discounting and the valuation of forestry's carbon
fluxes,’ Commonwealth Forestry Review 72(4), 265-271.

Richards, K.R.: 1997, ‘The time value of
carbon in bottom-up studies,’ Critical Reviews in Science and
Technology 27, S279-S292.

Rosa, L.P. and Schechtman, R.: 1996, Avaliação de
Custos Ambientais de Geração Termelétrica:
Inserção de Variáveis Ambientais no Planejamento da
Expansão do Setor Elétrico, Cadernos de Energia, No. 9, Vol.
II, Rio de Janeiro, Brazil, Centro de Estudos de Energia Elétrica
(ENERGE), pp. 159-256.

Santos, L.A.O. and de Andrade, L.M.M. (eds.):
1990, Hydroelectric Dams on Brazil's Xingu River and Indigenous Peoples,
Cultural Survival Report 30, Cambridge, Massachusetts, Cultural Survival, l92
pp.

Sarmiento, J.L., Hughes, T.M.C., Stouffer, R.J.
and Manabe, S.: 1998, ‘Simulated response of the ocean carbon cycle to
anthropogenic climate warming,’ Nature 393, 345-249.

Sathaye, J., Makundi, W.,
Goldberg, B., Jepma, C. and Pinard, M. (eds.): 1997, ‘International
workshop on sustainable forestry management: Monitoring and verification of
greenhouse gases: Summary statement,’ Mitigation and Adaptation
Strategies for Global Change 2(2-3),
91-99.

Schimel, D. and 75
others: 1996, ‘Radiative forcing of climate change,’ in Houghton,
J.T., Meira Filho, L.G., Callander, B.A., Harris, N., Kattenberg, A. and
Maskell, K. (eds.), Climate Change 1995: The Science of Climate Change,
Cambridge, Cambridge University Press, pp. 65-131.

Schlamadinger, B. and
Marland, G.: 1998, ‘The Kyoto Protocol: Provisions and unresolved issues
relevant to land-use change and forestry,’ Environmental Science and
Policy 1, 313-327.

Schlamadinger, B. and
Marland, G.: 1999, ‘Net effect of forest harvest on CO2
emissions on the atmosphere: A sensitivity analysis on the influence of
time,’ Tellus 51B,
314-325.

Schneider, S.H.: 1997,
‘Integrated assessment modeling of global climate change: Transparent
rational tool for policy making or opaque screen hiding value-laden
assumptions?,’ Environmental Modeling and Assessment 2(4), 229-248.

Schneider, S.H.: 1998,
‘Kyoto Protocol: The unfinished agenda,’ Climatic Change 39, 1-21.

Schneider, S.H. and
Goulder, L.H.: 1997, ‘Achieving low-cost emissions targets,’ Nature
389, 13-14.

Schneider, S.H.,
Kuntz-Duriseti, K., and Azar, C.: 2000, ‘Costing nonlinearities,
surprises and irreversible events,’(manuscript).

Scott, M.F.: 1989, A
New View of Economic Growth, Oxford, Clarendon Press. 592 pp.

Shine, K.P. and 45 others:
1995, ‘Radiative forcing,’ in Houghton, J.T., Meira Filho, L.G.,
Bruce, J, Hoesung Lee, Callander, B.A., Haites, E., Harris, N. and Maskell, K.
(eds.) Climate Change 1994: Radiative Forcing of Climate Change and an
Evaluation of the IPCC IS92 Emission Scenarios. Cambridge, Cambridge
University Press, pp. 163-203.

Tipper, R. and de Jong,
B.H.: 1998, ‘Quantification and regulation of carbon offsets from
forestry: Comparison of alternative methodologies, with special reference to
Chiapas, Mexico,’ Commonwealth Forestry Review 77(3), 219-228.

UN-FCCC
(United Nations Framework Convention on Climate Change): 1997a, ‘Kyoto
Protocol to the United Nations Framework Convention on Climate Change,’
Document FCCC/CP/1997;7/Add1 (available at http://www.unfccc.de).

UN-FCCC
(United Nations Framework Convention on Climate Change): 1997b, ‘Addendum to the Protocol, Decision
2/CP.3, para. 3,’ (available
at http://www.unfccc.de).

van Kooten, G.C.,
Grainger, A., Ley, E., Marland, G. and Solberg, B.: 1997, ‘Conceptual
issues related to carbon sequestration: Uncertainty and time,’ Critical
Reviews in Environmental Science and Technology 27, S65-S82.

Warrick, R.A. and 23 others:
1996, ‘Changes in sea level,’ in Houghton, J.T., Meira Filho, L.G.,
Callander, B.A., Harris, N., Kattenberg, A. and Maskell, K. (eds.), Climate
Change 1995: The Science of Climate Change, Cambridge, Cambridge University
Press, pp. 359-405.

Watson, R.T., Meira Filho, L.G., Sanhueza, E.
and Janetos, A.: 1992, ‘Greenhouse gases: Sources and sinks,’ in
Houghton, J.T., Callander, B.A. and Varney, S.K. (eds.), Climate Change
1992: The Supplementary Report to the IPCC Scientific Assessment,
Cambridge, Cambridge University Press, pp. 25-46.

Watson, R.T. and Verardo, D. (eds.): 2000, Intergovernmental
Panel on Climate Change Special Report on Land Use, Land-Use Change and
Forestry. Cambridge, Cambridge University Press. (in preparation).

Wigley, T.M.L., Richels,
R. and Edmonds, J.A.: 1996, ‘Economic and environmental choices in the
stabilization of atmospheric CO2 emissions,’ Nature 379, 240-243.

FIGURE LEGENDS

Figure 1.  Cascading effect of displaced emissions:
case where C reserve (forest or fossil) lasts beyond the end of the time
horizon.  In this example no account
is taken of movement of carbon from atmosphere to other pools over the time
horizon.  A net gain is achieved.

Figure 2.  Cascading effect of displaced emissions:
case where C reserve (forest) runs out within the time horizon.  In this example no account is taken of
movement of CO2 from atmosphere to other pools over the time
horizon.  No net gain is achieved.

Figure 3.  Discount rate equivalent of a time
horizon.  The area under a negative
exponential curve at approximately 1% annual discount (assuming truncation at
year 1000) is equal to that under the 100-year time horizon zero discount
system adopted for global warming potentials.

Figure 4.  Alternative indices of the value of
delaying emissions.  Benefit in a
fixed year, such as 2070 (option A) is one measure.  The difference between the integrals
within the time horizon, which is equal to the area pushed beyond the time
horizon in the curve for the delayed emission (option B) is the index used in
the present paper.

Figure 5.  Alternative methods of crediting CO2
sequestration.  Method (A) follows C
in planted trees, results in a greater calculated benefit for delaying an
emission (through sequestration) than does Method (B), which follows
atmospheric pools of carbon.

Figure 6.  Effect of forest degradation on
mitigation through avoided deforestation: case where forest is destroyed before
the end of the time horizon.

Figure 7.  Effect of forest degradation on
mitigation through avoided deforestation: case where forest lasts beyond the
end of the time horizon.

Figure 8.  Human-life benefit of delaying global
warming.  This provides a rationale
for discounting independent of arguments based on money.

Figure 9.  Discount rate effects on the impact of C
emissions in different years.

Figure 10.  Discount rate effects on C credit earned
by delaying emissions for different periods.

Figure 11.  Comparison of
park creation versus policy changes to slow deforestation in a hypothetical
country where continuation of the current rate of deforestation would eliminate
the remaining forest in nine years (A.).
Here, creation of a park from 1/18 (5.5%) of the remaining forest (B.)
is compared with a policy change slowing deforestation by 50% (i.e., doubling
the time to the expected demise of the forest to 18 years) (C.).  In the park creation case, deforestation
is assumed to continue unchanged outside of the park (i.e., there is 100%
leakage).  The graphs at the right
include effects of CO2, CH4 and N2O.  A 100-year time horizon is assumed.

Figure 12.  Effect of
discount rate on the area of park that would need to be created to be
equivalent to deforestation rate reductions of 50% and 40%.  If park area is 5.5% of remaining forest
and the deforestation rate reduction is 50% (as in Fig. 11), the switchover
from parks to slowing deforestation as the preferred strategy occurs at an
annual discount rate of 0.73%, assuming a time horizon of 100 years.

Figure 13.  Relation of the
relative impact on the atmosphere of park creation versus slowing deforestation
at different discount rates.  In
this example, a 25% reduction in deforestation rate would be preferable to
creating a park from 11% of the remaining forest if the annual discount rate is
less than 1.45%, but the 25% deforestation rate reduction would be preferable
at discount rates above this value; a 50% deforestation rate reduction would be
preferable to a park of the same size at all discount rates.  A 45-year baseline time to deforestation
and a 100-year time horizon are assumed.

Table 1:

Climatic impact
per hectare of tropical deforestation, including effects of non-CO2
GHGs and discounting

Year

Atmospheric load
(t gas)(a)

CO2-C
equivalent (t)(b)

Total CO2-C
equivalent (t)

CO2

CH4

N2O

CO2

CH4

N2O

Discount

Discount

Discount

0 %/year

1 %/year

2 %/year

1

677

0.97

0.09

185

15.42

5.09

205

205

205

2

623

0.92

0.09

170

14.57

5.06

190

188

186

3

581

0.87

0.09

158

13.76

5.03

177

175

174

4

540

0.82

0.09

149

13.00

5.00

167

166

164

5

520

0.78

0.09

142

12.28

4.97

159

156

156

:

:

:

:

:

:

:

:

:

:

10

441

0.58

0.09

120

9.25

4.83

134

133

132

:

:

:

:

:

:

:

:

:

:

25

350

0.25

0.08

95

3.94

4.43

104

103

102

:

:

:

:

:

:

:

:

:

:

50

281

0.06

0.07

77

0.95

3.83

81

81

80

:

:

:

:

:

:

:

:

:

:

75

246

0.01

0.06

67

0.23

3.32

71

70

69

:

:

:

:

:

:

:

:

:

:

100

225

0.00

0.05

61

0.06

2.87

64

64

63

Total

8,509

278.18

387.68

9,175

9,085

8,995

(a) Per-hectare
emissions are average net committed emissions for 1990 deforestation in
Brazilian Amazonia (Fearnside, 2000b).
Atmospheric loads of all gases decline as in the IPCC’s Second
Assessment Report (SAR) (Schimel et al.,
1996): CO2 declines non-linearly in accord with the Revised Bern
Model while CH4 and N2O decline exponentially with half
lives of 12.2 and 120 years, respectively.

(b) Instantaneous
radiative forcings per ton of gas are taken from the SAR (Shine et al., 1995): 1 for CO2, 58
for CH4 and 206 for N2O.

Table 2:

Human life value of delaying global warming

Item
Value
Units
Source

Mortality at 2 X CO2, with constant
population

138,000

lives/year

(Fankhauser, 1995;

Pearce et al.,
1996)

Fossil fuel annual emission 1981-1990

6

PgC/year

(Watson et al.,
1992: 29)

Tropical forest land-use change

annual emission 1981-1990

2.4

PgC/year

(Fearnside, 2000d).

Total annual anthropogenic emission

1981-1990

8.4

PgC/year

Calculated as fossil fuel + tropical land-use change
annual emissions

Value of avoided emission

60,870

MgC immediate emission equivalent/life

Calculated as total annual anthropogenic emission /
mortality at 2 X CO2

Value of avoided emission

16.4

lives/million MgC immediate emission equivalent

Calculated as mortality at 2 X CO2 / total annual
anthropogenic emission

Fig 1

Cascading effect of displaced emissions: large forest case

Time
Total

Horizon
emission

¯
(tC)

Year                         1          2          3  . . .  n

Baseline               ton1    ton2    ton3 . .tonn     n

Scenario

Mitigation                        ton1    ton2 . .tonn-1    n-1

Scenario

Benefit                                              1

Fig. 2

Cascading effect of displaced emissions:

small forest case

Time        Total

Horizon
emission

¯
(tC)

Year                         1          2          3   . . .   n

Baseline               ton1    ton2                               2

Scenario

Mitigation                        ton1    ton2                   2

Scenario

Benefit                                              0

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13