The outcome is in the assumptions: analyzing the effects

on atmospheric CO2 levels of increased use of bioenergy

from forest biomass

BJART HOLTSMARK

Statistics Norway, PO Box 8131 Dep, Oslo, N-0033, Norway

Abstract

Recently, several studies have quantified the effects on atmospheric CO2 concentration of an increased harvest

level in forests. Although these studies agreed in their estimates of forest productivity, their conclusions were

contradictory. This study tested the effect of four assumptions by which those papers differed. These assumptions regard (1) whether a single or a set of repeated harvests were considered, (2) at what stage in stand growth

harvest takes place, (3) how the baseline is constructed, and (4) whether a carbon-cycle model is applied. A main

finding was that current and future increase in the use of bioenergy should be studied considering a series of

repeated harvests. Moreover, the time of harvest should be determined based on economical principles, thus

taking place before stand growth culminates, which has implications for the design of the baseline scenario.

When the most realistic assumptions are used and a carbon-cycle model is applied, an increased harvest level in

forests leads to a permanent increase in atmospheric CO2 concentration.

Keywords: atmosphere, bioenergy, carbon, climate change, Faustmann, impulse response functions

Received 2 May 2012; revised version received 9 August 2012 and accepted 31 August 2012

Introduction

The literature draws attention to the fact that the conversion of natural habitats to cropland leads to release

of carbon, thus creating a biofuel carbon debt with a

potential payback period of several decades or even

centuries (see, for example, Gurgel et al., 2007; Fargione

et al., 2008; Searchinger et al., 2008; Melillo et al., 2009;

Gibbs et al., 2010; Lapola et al., 2010).

The articles mentioned, however, studied biofuels

based on fast-growing crops, in which the biomass harvested within 1 year is replaced by a new crop. In that

case, the CO2 released by combustion of the biomass

could, for practical purposes, be ignored because the

growth of the new crop requires the capture of the same

amount of CO2 within 1 year.

The issue becomes more complex if the source of bioenergy is a forest. The rotation period of a boreal forest

stand is usually 70–120 years. Hence, a century might

be required for the regrowth of a harvested boreal forest

stand and recapture of the amount of CO2 released originally. Despite this considerable time lag, recent studies

have considered wood fuels from boreal forests as being

carbon neutral, thus ignoring the amount of CO2

released by the combustion of that wood (see, for example, Bright & Strømman, 2009; Sjølie et al., 2010).

Keeping in mind that the carbon intensity of wood

fuels is approximately at the level of coal, it is obvious

that, from a methodological perspective, ignoring these

emissions is not satisfactory. A body of literature has

thus emerged that accounts for the amount of CO2

released from combustion of biomass from forests and

other slow-growing sources of biomass (see, for example, Manomet Center for Conservation Sciences,

2010; Cherubini et al., 2011a,b; McKechnie et al., 2011;

Holtsmark, 2012).1

The conclusions of the articles mentioned vary significantly. For example, Holtsmark (2012) found that

increasing the harvest of a forest permanently lowered

the carbon stock of the forest and, consequently, permanently heightened the amount of CO2 in the atmosphere. In contrast, Cherubini et al. (2011a,b) found that

the CO2 concentration in the atmosphere was lower 60–

70 years after harvesting a relatively slow-growing forest than if the forest had not been harvested. Figure 1

illustrates these differences. The dashed line (left axis)

depicts the atmospheric CO2 that remains after harvest

and combustion of a stock of biomass containing one

metric ton of carbon, as found by Cherubini et al.

(2011a). The solid line (right axis) shows the corresponding result in the work of Holtsmark (2012), in

which increased harvest levels were predicted to

Correspondence: Bjart Holtsmark, tel. + 47 21 09 48 68,

fax + 47 21 09 49 63, e-mail: bjart.holtsmark@ssb.no

1

Haberl et al. (2012a,b) and Schulze et al. (2012) include further

references and discuss the implications of this literature.

© 2012 Blackwell Publishing Ltd 1

GCB Bioenergy (2012), doi: 10.1111/gcbb.12015
increase the amount of CO2 in the atmosphere in the

long term.2

The different conclusions reached in these papers are

explained by different methodological choices or

assumptions. Therefore, an analysis of the importance

of different simplifications and methodological choices

is needed. Here, I will focus on four methodological

choices.

1 Some studies consider a single harvest event occurring at the present time, with no biomass to be harvested in the future. However, a single harvest event

performed at the present time will not produce any

biomass in the future and is, therefore, not satisfactory if one wants to gather knowledge related to the

consequences of the increased use of biomass presently and in the future. A single harvest event performed at the present time will not produce the

required biomass if one aims to replace fossil fuels

with biomass on a permanent basis. I will, therefore,

demonstrate the effects of the replacement of a single

harvest approach with a permanently increased harvest approach.

2 In some studies, it is assumed that a rotation period

ends when the growth of the trees has culminated.

Other studies take into account that, since the publication of the work of Faustmann (1849), and even

earlier,3

, forest economists have known that a

commercial forester will not postpone harvest until

the growth of the trees has culminated, but will

usually harvest at an earlier stage, following the socalled Faustmann rule. I will demonstrate the effects

of the application of a rotation-period length that is in

accordance with this rule.

3 Taking into account that harvest usually takes place

in stands that are still growing, the baseline scenario

becomes important. Not all studies take into account

that the harvest scenario should be measured against

a baseline scenario (with no harvest) in which the

trees are still growing, thus capturing CO2 from

the atmosphere. I will demonstrate the importance of

the use of a realistic baseline scenario along these lines.

4 In some studies, it is assumed, for simplicity, that the

CO2 released from the combustion of biomass

accumulates and remains in the atmosphere forever.

In other studies, an impulse response function is

applied that models the ability of the ocean and

of the terrestrial biosphere to absorb CO2 from the

atmosphere.

Table 1 provides an overview of how the five studies

on the bioenergy from forests mentioned deal with

these methodological choices. The approach of Cherubini et al. (2011a,b) was the inclusion of an impulse

response function in the analysis, whereas the other

studies listed applied a simple accumulation of CO2.

However, Cherubini et al. (2011a,b) and Manomet

Center for Conservation Sciences (2010) considered a

single harvest event exclusively. The methodology used

for the construction of the baseline scenarios also

varied.

To demonstrate quantitatively how the methodological choices influence the conclusions of this type of

study, I will use the articles of Cherubini et al. (2011a)

and Holtsmark (2012) as the starting point, adjust their

methodological choices, and demonstrate the consequences of these adjustments. In contrast with the

approach of Cherubini et al. (2011a), Holtsmark (2012)

considered the consequences of permanently increasing

harvest levels by studying a series of harvests.

Moreover, Holtsmark (2012) took into account that the

harvest usually takes place before the growth of the

stand culminates and how the baseline scenario then

should be designed. Holtsmark (2012), however,

ignored the decay functions of atmospheric CO2 and

considered, for simplicity, accumulated emissions

exclusively.

–10

0

10

20

30

40

50

–0.2

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200

Million tonnes carbon

Tonnes carbon

Time (years)

Cherubini et al. 2011a (left axis)

Holtsmark, 2012 (right axis)

Fig. 1 The dashed line (left axis) shows the atmospheric carbon that remains at time t after a single harvest event at time

t = 0, according to Cherubini et al. (2011a). The solid line (right

axis) shows the atmospheric carbon that remains after a series

of subsequent harvest events as a result of the application of an

impulse response function to the results of Holtsmark (2012).

2

See the red curve in Fig. 4, page 423, in Holtsmark (2012). To

achieve the somewhat different solid line in Fig. 1 here, the

impulse response function of the Bern 2.5CC carbon-cycle

model was applied; see Eqn (1).

3

See the discussion of early contributions to this issue in Samuelson (1976) and Scorgie & Kennedy (1996).

© 2012 Blackwell Publishing Ltd, GCB Bioenergy, doi: 10.1111/gcbb.12015

2 B. HOLTSMARK
This study builds a bridge between the approaches of

these two studies by taking atmospheric decay functions into account, as in Cherubini et al. (2011a), and

including the realistic baseline scenario and the multiple

harvest approach of Holtsmark (2012) in the analysis.

This paper is organized as follows. The model and

the basic methodological choices are presented in the

next section, the results are presented in the third section, and the results are discussed in the fourth section,

which also includes the conclusions of the study.

Materials and methods

Based on Forster et al. (2007) and the Bern 2.5CC carbon-cycle

model, which those authors recommend, Cherubini et al.

(2011a) applied the following atmospheric CO2 decay function:

yðtÞ 1⁄4 D0 þX3

i1⁄41

Dieðt=aiÞ; ð1Þ

where y(t) represents the fraction of an initial pulse of CO2 at

time t = 0 that remains in the atmosphere at time t and where

a and Di are parameters (Table 2). The time unit is 1 year. The

decay is caused by the uptake of CO2 by the ocean and by the

terrestrial biosphere. Cherubini et al. (2011a) considered two

cases. In the first case, those authors did not take into account

the oceanic absorption of anthropogenic CO2 from the atmosphere, although they considered this effect in the second case.

For the purpose of this study, only the latter case is considered,

as it is the most realistic and, therefore, the most interesting

case.

It is assumed that the harvesting of biomass from forests is

followed by replanting and the growth of new biomass. Regrowth implies carbon capture from the atmosphere. Cherubini

et al. (2011a) assumed that the growth and carbon capture of

the stand after a harvest follow the analytic form:

gðsÞ 1⁄4 2pr2 1=2

eðslÞ

2

=2r2

; ð2Þ

where r and l are parameters and τ is the age of the stand. It

can be deduced that a parcel with a stand age τ has the following carbon stock.4

CðsÞ 1⁄4 2pr2 1=2Xs

s0

1⁄40

e

ðs0lÞ

2

=2r2

: ð3Þ

The carbon captured by biomass regrowth should be considered in terms of negative emissions. Negative emissions should

be treated symmetrically regarding positive emissions. Thus, the

decay function presented in (1) should be applied to these negative emissions exactly as it is applied to the positive emissions.

Consider, for example, a parcel replanted at time t = 0. The

carbon captured at time t1 would be g(t1), and at time t2, i.e.,

t2t1 periods later, a fraction y(t2t1) of these negative emissions, i.e., g(t1)y(t2t1), is remaining in the atmosphere.

Assume now that, at time t = 0, the age of the stand is τm

and that harvesting proceeds at this time. Combustion of the

extracted biomass causes a CO2 emission pulse C(τm), which,

for simplicity, is labeled as C in the following equation. Taking

the regrowth function described in (2) into account, the amount

of CO2 in the atmosphere AH (t) at time t, will be as follows:

Table 2 Parameter values

Cherubini et al.

(their case with

r = 100) Present case

D0 0.217 r 25 37.5

D1 0.259 l 50 75

D2 0.338

D3 0.186

a1 172.9

a2 18.51

a3 1.186

Table 1 Methodological differences in five recent papers dealing with bioenergy from forest biomass

Cherubini

et al. (2011a)

Cherubini

et al. (2011b)

Manomet Center

for Conservation

Sciences (2010)

McKechnie

et al. (2011)

Holtsmark

(2012)

Single harvest event or

permanently higher

harvest level?

Single Single Single Permanent Permanent

Does the no harvest baseline

take growth and carbon

capture in mature

stands into account?

No No Yes Yes Yes

Is the time of harvest in

accordance with the

Faustmann rule?

No Some of the scenarios Yes Yes Yes

Impulse response function (IRF) or

simple accumulation of CO2?

IRF IRF Simple

accumulation

Simple

accumulation

Simple

accumulation

4

To show exactly how the numerical examples in the next section are constructed, I used discrete time in the theoretical

model description as well.

© 2012 Blackwell Publishing Ltd, GCB Bioenergy, doi: 10.1111/gcbb.12015

BIOENERGY AND ITS EFFECTS ON ATMOSPHERIC CO2 3
AHðtÞ 1⁄4 C  yðtÞ Xt

t0

1⁄40

gðt

0

Þyðt t

0

Þ; ð4Þ

where the first term on the right-hand side represents what is

left of the pulse in the atmosphere at t periods after harvesting,

whereas the second term represents the effect of regrowth.

Thus far, I have followed the example of Cherubini et al.

(2011a). However, the alternative to harvesting and combustion of

biomass is to not harvest: i.e., letting the stand grow and capture

more CO2. In this case, the amount of CO2 in the atmosphere

would evolve as follows.

ANHðtÞ1⁄4Xt

t01⁄40

gðsm þ t

0

Þyðt t

0

Þ: ð5Þ

Note the assumption of Cherubini et al. (2011a) that harvesting always takes place when the growth of the stand has culminated [see (c) in Fig. 2], which is the reason why those authors

disregarded this effect. If we take this effect into account, the

net effect of harvesting on the atmospheric carbon content will

be as follows:

ASðtÞ 1⁄4 AHðtÞ ANHðtÞ: ð6Þ

The time at which harvesting takes place is a pertinent point.

If we assume that the stock of trunks in the stand is proportional to the amount of biomass C(t) and that the market interest rate is r, then, according to the Faustmann rule, a forest

owner will harvest when the stand age τ satisfies the following

equation. C0

ðsÞ

CðsÞ 1⁄4 r1 ers : ð7Þ

As the interest rate approaches zero, (7) is reduced to

C0ðsÞ

CðsÞ 1⁄4 1s

: ð8Þ

Harvesting at a time at which τ satisfies (8) implies a maximum sustained yield (MSY) and harvesting at point (d) in

Fig. 2. To the extent that the forest owner discounts future

income, the rotation period will be shorter.

The intuition behind the Faustmann rule is as follows. The

forest owner takes into consideration his opportunity to invest

the harvest profit, creating postharvest periodic revenue of

rC(τ). Postponing the harvest has an alternative cost corresponding to this revenue. This could easily be interpreted as

that harvest should take place when τ satisfies the equation

C(τ) = rC′(τ). However, the Faustmann rule (7) also takes into

account that, if the first harvest is postponed, all future harvests must also be postponed. This leads to Eqn (7), which

implies an even earlier harvest than is indicated by the more

simple equation C(τ) = rC′(τ).

The application of the limiting case of the Faustmann rule

described in (8) to the slower growing forest studied by Cherubini et al. (2011a), i.e., a forest with a rotation span of 100 years,

implies that harvesting occurs when the stand is 70 years old.

In other words, the slower growing forest considered by Cherubini et al. (2011a) is actually a relatively rapidly growing boreal forest. The rotation period for MSY in most Scandinavian

forests is reportedly 70–120 years.

I shall, therefore, adjust the parametric assumptions to allow

for a MSY rotation period of 100 years for the stand in question. I will accomplish this using the parameters r = 37.5 and

l = 75 (Table 2). Given these assumptions, the growth and carbon capture of the stand will culminate at a stand age of

approximately 150 years. In other words, the stand will continue to grow and capture CO2 from the atmosphere, as specified in Eqn (5), if it is not harvested after reaching maturity.

The two compared (re)growth scenarios are shown in Fig. 3.

The solid line traces the carbon stock of the stand if it is harvested at time t = 0, whereas the dashed line traces the carbon

stock of the stand if its age is 100 years at time t = 0 and if it is

not harvested.

Results

Single harvest event

First, consider the case studied by Cherubini et al.

(2011a), with a rotation period of 100 years. The harvest gives rise to a pulse emission of one metric ton of

carbon at time 0, which is recaptured completely by

the regrowth of the stand over the next 100 years.

After these 100 years, there is no further growth on the

stand. The dashed line in Fig. 4 shows the atmospheric

carbon remaining from this pulse, according to the calculations of those authors. Note that, after ca. 65 years,

a lower carbon concentration in the atmosphere is estimated in the presence of a harvest event compared

with the case without harvest. This is so because

increased atmospheric CO2 levels lead to an increase in

the accumulation of carbon in the terrestrial

ecosystems, as well as to an increase in oceanic CO2

absorption.

(d) (b) (c)

(a)

Rotation period, r

Time (years)

Aboveground carbon stock

Fig. 2 This diagram is identical to Fig. 1 in Cherubini et al.

(2011a), with the exception of the addition of the dashed lines.

Cherubini et al. (2011a) assumed that harvest takes place at (c),

whereas the Faustmann rule says that harvest usually will take

place somewhere between (b) and (d).

© 2012 Blackwell Publishing Ltd, GCB Bioenergy, doi: 10.1111/gcbb.12015

4 B. HOLTSMARK
As argued in the previous section, when dealing with

a boreal forest, it would be appropriate to consider a

MSY rotation period of 100 years and culmination of

growth after approximately 150 years, which would be

consistent both with the Faustmann rule and with a typical boreal forest stand. The harvest of this forest stand

at time 0 is assumed to lead to a pulse of emission of

one ton of carbon. The gray, solid line in Fig. 4 shows

the level of atmospheric carbon from the pulse that

remains in this case; cf. Eqn (4).

The question of the use of an appropriate baseline arises

at this point. As Cherubini et al. (2011a) assumed that there

is no further growth on the stand in the no-harvest case,

there is no change in atmospheric carbon in their baseline

scenario. The scenario is different if it is assumed that

there is continued growth in the no-harvest case. The dotted curve in Fig. 4 traces the effect on atmospheric CO2

levels in the no-harvest case and corresponds to Eqn (5).

This curve dips below zero because there is no emission

pulse at time t = 0, although carbon is still captured by

continued growth after this time point.

Our interest is related to the net effect of harvesting on

atmospheric CO2 levels. This can be computed by subtracting the amount of atmospheric carbon in the no-harvest case from the amount of atmospheric carbon in the

case with harvest; cf. Eqn (6). The result is the doubleline curve in Fig. 4. Compared with the case studied by

Cherubini et al. (2011a), this case gives a somewhat

longer period of enhanced levels of atmospheric CO2.

Multiple harvest events

The numerical examples presented in the previous section measure the effect of a single harvest event. However, IPCC documents, such as Chum et al. (2012),

envisage a permanent increase in the use of bioenergy

and, accordingly, a higher harvest rate. Therefore, in the

following paragraphs, I will consider a case in which

the harvest events described in the previous section take

place every year on a permanent basis.

Consider now a forest with an age structure such that

every year one parcel, each with a growth function

described by Eqns (1) and (2), reaches the stand age τm

and is, therefore, considered mature and ready for harvest.

The net effect on atmospheric carbon of harvesting a stand

every year compared with the case where the parcels are

left unharvested, is given by the following equation.

AðtÞ 1⁄4 Xt

t0

1⁄40

ASðt

0

Þ: ð9Þ

The function AS(t) is defined in Eqn (6). Given the

numerical assumptions, the expression is shown by the

solid line depicted in Fig. 5. Other than the difference in

scale (million tons and tons of carbon), the solid line

shown in Fig. 5 is not far off the corresponding result

that is obtained when the impulse response function is

applied to the data of Holtsmark (2012), which is indicated by the dotted curve shown in Fig. 5.

To have intuition to the above described results,

study the dashed curve shown in Fig. 5, which is identical to the double lined curve depicted in Fig. 4. These

curves show that the effect of a single harvest on atmospheric CO2 levels is a two-stage process. During the

first stage, the level of atmospheric CO2 is higher than

it would have been in the absence of harvest, whereas

the reverse is true in the second stage. The observation

Fig. 3 Development of the carbon stock of a stand that is

mature at time 0. The solid line represents the harvest case.

The dashed line represents the no-harvest case.

Fig. 4 The dashed line depicts the remaining atmospheric carbon for the methodology applied by Cherubini et al. (2011a),

with a rotation period of 100 years. The gray, solid line represents the atmospheric carbon remaining with a slower growing

stand with harvesting occurring at a stand age of 100 years. In

both cases, harvesting of this stand at time 0 is assumed to

cause an emission pulse of one ton of carbon. The dotted curve

traces the effect on atmospheric carbon levels in the no-harvest

case, whereas the double-line curve shows the net effect of harvest compared with no harvest.

© 2012 Blackwell Publishing Ltd, GCB Bioenergy, doi: 10.1111/gcbb.12015

BIOENERGY AND ITS EFFECTS ON ATMOSPHERIC CO2 5
that the negative effect in the second stage is smaller than

the positive effect during the first stage is important to

predict the outcome of a series of harvest events.

Next, consider the case in which harvest takes place

annually. Every year, there is a pulse of emissions of 1

ton of carbon with subsequent regrowth on the stand.

The set of thin curves shown in Fig. 5 represent the

effects of these subsequent annual harvest events. The

net effect on atmospheric CO2 of this series of harvest

events is calculated via vertical summation of this set of

curves and the dashed curve. This gives the solid line

depicted in Fig. 5, which is measured on the right axis.

Note that the dashed curve converges toward zero,

whereas the solid line converges toward 19 tons of carbon (result not shown here). Hence, a single harvest

event has no long-term effect on atmospheric carbon,

whereas a permanently increased harvest level will

increase atmospheric CO2 permanently. It follows that

an increased harvest level is not a carbon-neutral activity not even in the long term, whereas a single harvest

event is a carbon-neutral activity in the long term.

Discussion

The realization that wood fuels are not carbon neutral

gives rise to a number of methodological questions

or assumptions regarding the manner via which CO2

emissions from wood fuels should be modeled. In this

study, I have focused on four methodological choices.

First, I analyzed whether the consideration of a single

harvest event is sufficient when the consequences of the

increased use of biomass presently and in the future are

to be analyzed. Second, I analyzed whether the assumption that the rotation period ends when the growth of

the trees has culminated is satisfactory. Third, I analyzed the manner via which the baseline no-harvest

scenario should be constructed. Finally, I studied the

importance of including impulse response functions in

the analyses.

The work of Cherubini et al. (2011a) was used as a

starting point to evaluate the importance of these methodological choices. The approach of those authors of

using an impulse response function was adopted. However, their model was adjusted taking into account that

harvest usually takes place before the growth of the

trees has culminated. The baseline (no harvest) scenario

was adjusted accordingly. Finally, a single harvest

approach was supplemented with a multiharvest

approach, which reflects the fact that the policy proposal to be analyzed addresses the question of whether

biomass should be harvested at the current time and in

the future.

The numerical simulations provided information on

the importance of these methodological choices. First,

they showed that the results change fundamentally

when a single harvest approach is replaced with a

multiharvest approach reflecting a permanently

increased harvest level. A single harvest approach could

lead to the conclusion that wood fuels are carbon neutral in the long term, but not in the short term, whereas

a multiharvest approach leads to the conclusion that

wood fuels are not carbon neutral, neither in the long

term nor in the short term. The multiharvest approach

revealed that a permanently increased harvest level

leads to a permanent increase in atmospheric carbon

also when a realistic carbon-cycle model is taken into

account.

Second, it was found that the consideration that harvest usually takes place before growth of the trees has

culminated and the consequent adjustment of the baseline have a significant effect on the results, although

they are not changed fundamentally.

Third, the results of Holtsmark (2012) were adjusted

by incorporating an impulse response function in the

analyses. This approach did not change the results fundamentally. Using simple accumulation of CO2 in the

atmosphere in this type of study is an approximation

that is acceptable.

Another question, which was not discussed here, concerns the extent to which the increased harvest of a forest

may reduce atmospheric carbon if the extracted biomass

Effect of a single harvest event taking place to day on

atmospheric CO2

 (left axis)

Effect on atmospheric CO2 of an increased harvest level

(right axis)

IRF applied to the result in Holtmark, 2012 (right axis)

–6

0

6

12

18

24

30

36

–0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250

(Million) tonnes carbon

Tonnes carbon

Time (years)

Fig. 5 The dashed curve (left axis) shows the net effect on

atmospheric carbon of a single harvest event taking place today

compared with the no-harvest case. The set of thin curves

depicts similar net effects of subsequent annual harvest events.

The thick solid line (right axis) shows the total net atmospheric

carbon that remains after this series of identical annual harvest

events. The dotted curve (right axis) represents the effect of an

increased harvest level, as described in Holtsmark (2012).

© 2012 Blackwell Publishing Ltd, GCB Bioenergy, doi: 10.1111/gcbb.12015

6 B. HOLTSMARK
replaces fossil energy sources. For a discussion of this question, see Holtsmark (2012) and McKechnie et al. (2011).

Acknowledgments

The author gratefully acknowledges valuable comments and

suggestions from Helmut Haberl as well as two referees. While

carrying out this research the author has been associated with

CREE – Oslo Centre for Research on Environmentally friendly

Energy. CREE is supported by the Research Council of Norway. The work has also been supported by the Norwegian

Research Council through the project “Biodiversity and Nature

Index: Understanding, adaptive planning, and economic policy

means for management of open lowlands and forests” (Project

number 204348).

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