November	2014	 	 B‐1	

Appendix	B:	Temporal	Scale	

Table of Contents

1. Introduction	.................................................................................................................................................................	B‐2

2. Key	Temporal	Scale	Considerations	...................................................................................................................	B‐3

2.1. Emissions	Horizon,	Assessment	Horizon,	and	Time	of	Reporting	...............................................	B‐3

2.2. Temporal	Differences	between	Feedstocks	..........................................................................................	B‐3

2.3. Interactions	Between	Spatial	and	Temporal	Scales	...........................................................................	B‐4

2.4. Temporal	Differences	between	Baselines	..............................................................................................	B‐4

3. Illustration	of	General	Temporal	Dynamics	Using	Decay	Rates	.............................................................	B‐5

4. Potential	Methods	for	Assessing	Multiyear	Fluxes	......................................................................................	B‐7

4.1. Front‐Loading	....................................................................................................................................................	B‐8

4.2. Year‐to‐Year	Carryover	..............................................................................................................................	B‐10

4.3. Annualized	Carryover	.................................................................................................................................	B‐11

4.4. Temporal	Scale	of	the	Illustrative	Future	Anticipated	Baseline	Approach	in	the	Technical	

Appendices	..........................................................................................................................................................	B‐13

5. Discounting	and	Its	Relevance	to	the	Framework	....................................................................................	B‐14

5.1. Time	Preference	in	CO2	Emissions	.........................................................................................................	B‐16

5.2. Discounting	Summary	.................................................................................................................................	B‐19

6. References..................................................................................................................................................................	B‐20

List of Tables

Table	B‐1.	Theoretical	Illustration	of	How	the	Impact	of	Time	Depends	on	the	Natural	Decay	Rate	

and	Time	Period	...................................................................................................................................................	B‐6

Table	B‐2.	100‐Year	Emissions	Annualized	over	20‐,	30‐,	and	100‐Year	Assessment	Horizons.	...	B‐12

Table	B‐3.	20‐Year,	30‐Year,	and	100‐Year	Emissions	Annualized	over	20‐,	30‐,	100‐Year	Time	

Periods,	Respectively.	.....................................................................................................................................	B‐13

List of Figures

Figure	B‐1.	Annual	Fraction	of	Carbon	Emitted	(FCE),	Cumulative	Fraction	of	Carbon	Emitted	(FCE),	

and	Fraction	of	Carbon	Remaining	(FCR),	Dependent	on	the	Decay	Rate	and	Time	Period.B‐7

Figure	B‐2.	Cumulative	FCE	and	Front‐loaded	FCE	with	a	5%	Loss	per	Year	Assumption	over	100	

Years.	.........................................................................................................................................................................	B‐9

Figure	B‐3.	Year‐to‐Year	Annual	Fraction	of	Carbon	Emitted	(FCEt)	Depends	on	the	Decay	Rate.	B‐11
November	2014	 	 B‐2	

1. Introduction

The	purpose	of	this	appendix	is	to	discuss	considerations	related	to	the	treatment	of	time	in	

possible	applications	of	the	framework.	It	is	important	to	consider	possible	treatments	of	time	and	

the	implications	of	these	treatments	in	developing	strategies	for	long‐term	and	short‐term	

emissions	accounting,	because	the	choice	of	treatment	may	have	significant	impacts	on	the	outcome	

of	an	assessment	framework	application.	While	there	is	no	single,	scientifically	correct	method	for	

the	treatment	of	time	when	assessing	biogenic	emissions,	there	are	a	number	of	options	for	

incorporating	temporal	dynamics	into	an	assessment	of	biogenic	carbon	fluxes.	The	choice	of	

temporal	assessment	method	could	ultimately	depend	on	the	context	of	a	specific	framework	

application.		

This	appendix	discusses	various	aspects	related	to	assessing	time‐dependent	effects	in	the	

production,	processing,	and	consumption	of	biogenic	feedstocks.	Considerations	related	to	time	can	

include	a	variety	of	issues	such	as:	

 Emissions	horizons	and	reporting	periods	(i.e.,	fluxes	related	to	feedstock	production	may	

occur	over	many	years,	whereas	reporting	may	be	the	current	year);		

 Interplay	with	spatial	scale	(i.e.,	implications	of	larger	scales	and	shorter	time	frames	

versus	smaller	scales	and	longer	time	frames);		

 Baseline	perspective	(i.e.,	is	the	analysis	forward‐	or	backward‐looking,	or	both?);	and		

 Differences	in	temporal	characteristics	of	different	feedstocks	(i.e.,	annual	crops,	short	

rotation	energy	crops,	and	longer	rotation	forestry	systems).		

In	general,	accounting	for	temporal	effects	will	be	most	significant	when	considering	future	

potential	fluxes	related	to	long	rotation	feedstocks	(e.g.,	roundwood),	activities	that	affect	the	

equilibrium	storage	in	soil	carbon	pools,	decay	rates,	or	in	cases	of	significant	land	use	change,	

where	biogenic	feedstock	production	has	implications	for	long‐term	emissions	changes	in	

terrestrial	carbon	stocks.	

Given	that	different	temporal	perspectives	could	be	used	by	the	framework,	two	different	baseline	

approaches	are	evaluated	in	this	framework	report:	retrospective	reference	point	and	future	

anticipated	baseline.	These	baseline	approaches	use	aspects	of	time.	The	retrospective	reference	

point	baseline	does	not	take	into	account	future	potential	biogenic	emissions	fluxes	related	to	

biogenic	feedstock	production,	processing,	and	use.	The	future	anticipated	baseline,	due	to	its	

prospective	nature,	can	take	into	account	such	future	potential	fluxes.	As	such,	most	of	the	

discussion	in	this	appendix	focuses	on	potential	methods	for	considering	time	in	terms	of	a	

prospective	analysis.	

This	appendix	provides	various	illustrative	treatments	of	temporal	dynamics	when	activities	and	

related	emissions	fluxes	do	not	fit	neatly	into	single	assessment	time	periods.	As	presented	in	

Section	4,	illustrative	treatments	for	prospective	applications	of	the	framework	in	this	appendix	

include	a	frontloading	approach,	a	year‐to‐year	carryover	approach,	and	an	annualized	carryover	

approach.	A	discussion	of	discounting	time	is	provided	in	Section	5.	
November	2014	 	 B‐3	

2. Key Temporal Scale Considerations

The	production,	processing,	and	use	of	biogenic	feedstocks	for	energy	can,	in	some	circumstances,	

have	emission	effects	extending	into	the	future	and	there	are	different	methods	to	and	perspectives	

about	how	to	assess	future	emissions	trajectories	(Dornburg	and	Marland,	2008;	Fargione,	2008;	

Kendall	et	al.,	2009;	Levasseur	et	al.,	2010;	Walker	et	al.,	2010;	Cherubini	et	al,	2011;	Mitchell	et	al.,	

2012;	Helin	et	al.,	2013;	Walker	et	al.,	2013;	Miner	et	al.,	2014).	Accounting	for	these	emissions	

appropriately	in	different	policy	contexts	may	necessitate	various	decisions	that	reflect	the	goals	

and	parameters	of	the	policy.	An	application	of	the	framework	presented	in	this	report	that	

includes	assessment	over	time	may	need	to	identify	emissions	and	assessment	horizons,	reporting	

periods,	the	appropriate	baseline	method,	the	appropriate	spatial	scale,	and	the	temporal	

characteristics.	These	considerations	are	discussed	below	in	more	detail.		

2.1. Emissions Horizon, Assessment Horizon, and Time of Reporting

An	application	of	the	framework	that	includes	assessment	over	time	may	need	to	articulate	how	

biogenic	CO2	emissions	fluxes	over	time	from	biogenic	feedstock	production,	processing,	and	use	

relate	to	stationary	source	biogenic	CO2	emissions	in	a	single	period	(e.g.,	time	of	biogenic	feedstock

use	or	reporting).	It	is	not	only	a	question	of	how	far	into	the	future	must	an	analysis	look,	but	also	

how	these	emissions	are	accounted	for	and	valued	over	time,	and	when	are	they	accounted	for	or	

reported.	Thus,	it	may	be	necessary	to	distinguish	between	the	“emissions	horizon”	and	the	

“assessment	horizon.”	The	emissions	horizon	is	the	period	of	time	during	which	the	carbon	fluxes	

resulting	from	actions	taking	place	today	actually	occur,	while	the	assessment	horizon	is	a	period	of	

time	selected	for	the	analysis	of	the	carbon	fluxes.	In	effect,	these	time	horizons	can	differ	

significantly.		

For	example,	the	emissions	horizon	reflects	all	future	estimated	net	carbon	fluxes	associated	with	

the	production	and	harvest	or	removal	of	a	feedstock	today.	Therefore,	the	emissions	horizon	may	

need	to	span	a	year	to	several	decades,	depending	on	the	feedstock	and	production	site	conditions,	

to	account	for	all	these	effects.	The	assessment	horizon,	however,	may	be	a	specified	time	frame	

over	which	estimated	future	effects	may	be	taken	into	account.	For	example,	a	specific	policy	may	

allow	the	inclusion	of	future	potential	effects	over	20	years,	whereas	the	estimated	emissions	

horizon	is	50	years.	The	time	of	reporting	may	be	a	one‐time	event	or	an	annual	event	at	the	time	or	

in	the	year	in	which	the	harvest/removed	feedstock	is	consumed	at	the	stationary	source.	When	

making	determinations	about	time	frame	per	policy	or	program	needs,	one	should	consider	how	to	

address	these	different	time	horizons.	Illustrative	general	methods	for	reconciling	these	different	

horizons	are	discussed	in	Section	4.		

2.2. Temporal Differences between Feedstocks

Biogenic	carbon	fluxes	related	to	biogenic	feedstock	growth,	harvest,	and/or	collection,	feedstock	

production	site	soil	carbon	levels,	and	land	use	and/or	management	change	do	in	many	cases	occur	

over	a	period	greater	than	one	year.	The	consideration	of	multiyear	time	dynamics	for	biogenic	

feedstock	growth	is	particularly	relevant	for	long	rotation	feedstocks	or	feedstocks	where	carbon	

stored	in	biomass	accumulates	over	time	subject	to	biological	growth	functions	and	where	
November	2014	 	 B‐4	

feedstock	production	and/or	collection	affect	landscape	soil	carbon	dynamics	or	other	land	use	

changes.	For	long	rotation	feedstocks,	the	amount	of	biogenic	CO2	emissions	from	harvest	and	

combustion	may	take	years	to	be	sequestered	on	the	same	site	from	which	it	was	harvested.	For	

logging	residues,	analysts	may	need	to	consider	decay	and	associated	landscape	biogenic	CO2

emissions.	For	example,	the	collection	and	combustion	of	logging	residues	result	in	an	immediate	

release	of	biogenic	CO2	emissions	that	otherwise	might	have	instead	occurred	in	the	form	of	CO2	

and	CH4	over	a	series	of	years	through	natural	decomposition	on	the	forest	floor.	Concurrently,	

removal	of	the	logging	residues	can	cause	increased	emissions	through	loss	of	soil	carbon	over	

time,	while	also	altering	rates	of	forest	growth	and	carbon	sequestration.	Changing	management	

practices	can	also	potentially	affect	mineral	soil	carbon	pools	(Buchholz	et	al.,	2013).	

Time	dynamics	may	also	be	a	relevant	consideration	for	some	agricultural	feedstocks.	For	example,	

land	use	change	such	as	the	removal	of	forests	for	agricultural	feedstock	production	could	result	in	

an	initial	release	of	carbon	that	is	not	fully	recaptured	in	subsequent	use	of	the	land	for	agriculture.	

Furthermore,	cultivation	of	perennial	bioenergy	feedstocks	such	as	switchgrass	can	lead	to	long‐

term	increases	in	soil	organic	carbon	relative	to	annual	crops	due	to	extensive	root	systems	

(belowground	biomass)	and	reduction	of	tillage	disturbances.	Also,	changing	management	

practices,	such	as	removing	agricultural	residues	like	corn	stover,	may	reduce	decay‐related	

emissions	but	also	reduce	soil	carbon	inputs	and	thus	long‐term	soil	organic	carbon	stocks.		

2.3. Interactions between Spatial and Temporal Scales

Temporal	aspects	of	biogenic	carbon	fluxes	can	also	depend	on	the	choice	of	spatial	scale.	In	some	

circumstances,	assessing	biogenic	carbon	fluxes	at	a	small	spatial	scale	for	a	long	period	of	time	can	

result	in	similar	outcomes	to	those	from	considering	a	large	spatial	scale	over	a	short	period	of	

time.	For	example,	the	harvest	of	a	long‐rotation	feedstock,	such	as	roundwood,	on	a	significantly	

small	spatial	scale	(e.g.,	plot	or	stand)	will	initially	result	in	biogenic	carbon	emissions,	but	over	

enough	time,	replanted	trees	(e.g.,	assuming	similar	species,	conditions)	will	sequester	

approximately	the	same	amount	of	carbon	that	was	released	by	the	previous	harvest.	However,	if	

that	same	amount	of	harvest	is	considered	over	a	larger	spatial	scale	(e.g.,	a	stand	within	a	region),	

the	biogenic	carbon	emitted	from	the	harvested	stand	will	be	balanced	out	by	sequestration	in	that	

region	from	the	continued	growth	of	unharvested	roundwood	and	any	reforestation	activities	in	the	

region	over	a	relatively	short	time	frame	(likely	shorter	than	regrowth	of	the	stand	itself).	

2.4. Temporal Differences between Baselines

The	retrospective	reference	point	baseline	and	future	anticipated	baseline	approaches	both	include	

treatments	of	time.	However,	the	way	in	which	these	two	baseline	approaches	consider	time	is	

markedly	different.	The	retrospective	reference	point	baseline	approach	is	inherently	backward‐

looking	(because	it	evaluates	measured	or	modeled	emissions	fluxes	over	a	specific	time	frame	in	

the	past),	while	the	future	anticipated	baseline	approach	is	inherently	forward‐looking	(because	it	

evaluates	points	in	time	along	different	future	simulations).		

When	the	reference	point	baseline	approach	is	applied	retrospectively,	it	takes	into	account	net	

atmospheric	biogenic	CO2	contributions	associated	with	biogenic	feedstock	production	on	the	
November	2014	 	 B‐5	

landscape	by	assessing	differences	in	biogenic	stocks	and	flows	between	two	points	in	time	in	the	

past.	Under	this	baseline	approach,	one	must	decide	which	specific	reference	points	in	time	to	use,	

including	the	length	of	time	between	reference	points	(e.g.,	5,	10,	15	years,	or	other?)	and	the	

location	of	the	points	in	the	chosen	time	horizon	(e.g.,	at	what	point	in	time	was	data	first	collected,	

when	were	the	most	recent	data	produced?).	Integration	of	future	multiyear	fluxes	(e.g.,	from	

potential	decay,	soil	carbon	equilibrium	changes)	is	not	necessary	when	values	for	framework	

terms	are	derived	through	a	backward‐looking	approach	(i.e.,	the	retrospective	reference	point	

baseline).	Appendices	H	and	I	show	illustrative	equation	term	calculations	and	case	study	

applications	for	forest‐	and	agriculture‐derived	feedstocks	using	the	retrospective	reference	point	

baseline	approach.		

The	future	anticipated	baseline	approach	assesses	the	estimated	net	change	in	carbon	stocks	

between	two	projected	future	scenarios	at	the	same	specified	point	in	time,	that	is,	between	a	

business‐as‐usual	(BAU)	scenario	and	an	alternative	scenario	with	changes	in	estimated	

environmental,	economic,	and/or	policy	conditions	(e.g.,	Searchinger	et	al.,	2009).	Because	this	

baseline	approach	can	be	used	to	project	future	biogenic	carbon‐based	fluxes	associated	with	

biogenic	feedstock	production,	processing,	and	use,	there	are	more	considerations	about	how	to	

represent	and	incorporate	elements	of	time	into	such	an	analysis	than	in	the	retrospective	

reference	point	approach.	Integration	of	future	multiyear	fluxes	(e.g.,	from	potential	decay,	soil	

carbon	equilibrium	changes,	other	land	use	and/or	management	change	effects)	may	be	necessary	

for	framework	terms	representing	biogenic	landscape	attribute	values	(GROW, AVOIDEMIT,

SITETNC,	and	LEAK,	if	included)	and	possibly	process	attributes	(depending	on	treatment	of	

biogenic	carbon	losses	through	the	supply	chain,	including	storage	losses	or	carbon	stored	in	final	

products,	as	captured	by	the L and	P	terms).	Appendices	J,	K,	and	L,	respectively,	discuss	future	

anticipated	baseline	considerations,	possible	baseline	construction	methods,	and	illustrative	forest‐	

and	agriculture‐derived	feedstock	case	study	applications	using	this	baseline.	Waste‐derived	

feedstocks,	as	discussed	in	detail	in	Appendix	N,	are	assessed	in	this	report	by	using	potential	

alternative	pathways	and	related	GHG	pathways	for	those	materials,	which	in	many	cases	include	

consideration	of	future	potential	methane	emissions	from	decomposition	if	not	used	for	energy.		

3. Illustration of General Temporal Dynamics Using Decay

Rates

The	magnitude	of	an	emissions	pulse	(meaning,	in	this	context,	the	cumulative	biogenic	carbon‐

based	emissions	over	a	time	period)	may	depend	on	how	far	into	the	future	an	analysis	is	extended.	

In	theory,	one	could	look	as	far	into	the	future	as	required	to	physically	account	for	a	multiyear	

carbon	flux	(i.e.,	the	entire	emissions	horizon	over	which	the	flux	occurs).	In	practice,	however,	a	

shorter	time	frame	may	be	warranted	in	specific	accounting	circumstances,	especially	if	the	fluxes	

toward	the	tail	end	of	a	multiyear	flux	pattern	are	very	small	or	a	specific	program	or	policy	

application	necessitates	a	specific,	shorter	time	frame.	

To	simply	explain	the	general	dynamics	of	time,	this	appendix	uses	concepts	called	the	“Fraction	of	

Carbon	Remaining”	(FCRt)	and	“Fraction	of	Carbon	Emitted”	(FCEt)	to	illustrate	the	implications	of	

different	choices	of	time	frame	when	assessing	emissions	flux	dynamics	over	time	(t).	Using	the	
November	2014	 	 B‐6	

specific	context	of	natural	decay	from	logging	residue	feedstock	as	an	example,	FCRt is	the	amount	

of	carbon	that	remains	(in	terms	of	mtCO2e)	on	the	site	(CRt)	after	a	particular	time	frame	divided	

by	the	magnitude	of	the	original	carbon	pool	(CR0),	assuming	a	particular	decay	rate:	

࢚ࡾ࡯ ൌ ࢚ࡾ࡯ࡲ

૙ࡾ࡯

(EQ. B.1)

Where:	

࢚ࡾ࡯ ൌ ࡾ࡯	 ૙ൈ ሺ૚ െ ࢟ࢇࢉࢋࢊ	ࢋ࢚ࢇ࢘ሻ࢚) EQ. B.2)

FCEt	is	calculated	as:	

࢚ࡱ࡯ࡲ ൌ ૚ െ ࢚ࡾ࡯ࡲ) EQ. B.3)

FCRt	and	FCEt	are	unit‐free	(i.e.,	dimensionless)	values	by	their	definitions.	Table	B‐1	provides	

examples	of	the	impact	of	different	accounting	time	frames	on	the	emissions	pulse	accounting	(i.e.,	

FCEt	over	the	defined	time	period)	from	the	natural	decay	of	1	mtCO2e	woody	residue	feedstock	left	

onsite.	Note	that	these	are	not	emissions	due	to	biogenic	feedstock	harvest	or	consumption,	but	

emissions	related	to	decay	of	the	logging	residue	if	left	onsite.	The	representative	values	presented	

in	Table	B‐1	and	depicted	in	Figure	B‐1	illustrate	the	fraction	of	carbon	emissions	over	three	time	

frames:	20	years,	30	years,	and	100	years.	

Table	B‐1	shows	that	for	a	low	decay	rate	of	5%	loss	per	year,	64%	of	the	biogenic	CO2	is	emitted	

over	20	years,	whereas	99%	of	the	biogenic	CO2	is	emitted	over	100	years.	However,	for	a	high	

decay	rate	of	25%	loss	per	year,	nearly	all	biogenic	CO2	is	emitted	within	the	first	20	years.	

Table B-1. Theoretical Illustration of How the Impact of Time Depends on the Natural Decay Rate 

and Time Period 

Loss/Year

(decay rate)

Cumulative FCE

Time Period (t)

20 years 30 years 100 years

5% 0.64	 0.79 0.99

10% 0.88	 0.96 1.00

25% 1.00	 1.00 1.00

Figure	B‐1	illustrates	the	annual	and	cumulative	FCE,	as	well	as	the	FCR,	over	a	100‐year	time	frame	

using	a	5%	annual	decay	rate	assumption.	
November	2014	 	 B‐7	

Figure B-1. Annual Fraction of Carbon Emitted (FCE), Cumulative Fraction of Carbon Emitted 

(FCE), and Fraction of Carbon Remaining (FCR), Dependent on the Decay Rate and Time Period. 

4. Potential Methods for Assessing Multiyear Fluxes

In	terms	of	the	BAF	equation,	the	assessment	treatment	of	multiyear	carbon	fluxes	within	a	

prospective	analysis	allows	for	the	estimation	of	biogenic	CO2	emissions	associated	with	certain	

feedstocks	(i.e.,	woody	biomass)	with	slow	rates	of	natural	decay	(in	the	case	of	residues	or	fallen	

trees)	and/or	long	growth	periods	(referred	to	generally	as	“long‐rotation”	feedstocks).	However,	

accurately	capturing	these	multiyear	landscape	effects	related	to	feedstock	production,	processing,	

and	use	can	be	challenging	in	the	context	of	an	assessment	framework	application	that	may	need	to	

estimate	and	report	annual	biogenic	CO2	emissions	from	a	stationary	source.		

Various	terms	in	the	BAF	equation	(AVOIDEMIT, GROW, SITETNC, LEAK,	if	included,	and	possible	

losses	within	the	L	term)	can	represent	biogenic	CO2	fluxes	that	have	a	temporal	dimension	longer	

than	an	annual	cycle	for	certain	feedstocks	and,	thus,	may	require	application	of	an	accounting	

method	for	these	temporal	effects.	The	GROW	term,	for	example,	represents	the	projected	change	in	

biogenic	carbon	fluxes	from	feedstock	growth	in	a	given	area	over	a	given	time	period.1	The	

SITETNC	term	reflects	estimated	site‐induced	changes	in	above‐	and	belowground	carbon	that	

typically	occur	over	a	multiyear	period	due	to	a	direct	land	use	or	land	use	management	change	

that	triggers	changes	in	carbon	stocks.	Similarly,	the	AVOIDEMIT	term	accounts	for	the	avoidance	of	

estimated	biogenic	emissions	that	could	have	occurred	on	the	feedstock	landscape	without	biogenic	

																																																													

1

 Note that under the retrospective reference point baseline approach in a regional application, GROW is calculated 

as recent growth in the region where the feedstock is produced and not in terms of future regrowth over time. 
November	2014	 	 B‐8	

feedstock	removal	(e.g.,	avoided	decomposition,	which	also	may	occur	over	a	year,	multiple	years,	

or	decades	depending	on	the	feedstock)	or	per	an	alternative	management	strategy	(e.g.,	waste‐

derived	feedstocks).	LEAK	represents	leakage	effects	that	can	occur	from	feedstock	production,	

including	indirect	land	use	changes	that	could	affect	landscape	CO2	fluxes	for	years	into	the	future.	

Feedstock	losses	captured	in	the	L	term	may	be	used	to	reflect	decomposition	of	feedstocks	in	

storage	or	other	processing	along	the	supply	chain.		

Each	approach	to	time	discussed	below	integrates	future	multiyear	carbon	flux	values	(i.e.,	carbon	

emissions	and/or	sequestration	that	occur	over	multiple	years)	into	an	annual	accounting	

framework	(meaning	net	emissions	are	reported/calculated	annually)	for	illustrative	purposes.	

Note	that	the	need	to	integrate	future	multiyear	fluxes	is	necessary	only	when	a	specific	application	

of	the	framework	allows	for	or	requires	consideration	of	counterfactual	or	future	emissions	fluxes	

related	to	biogenic	feedstock	production	activities.	Again,	it	is	not	necessary	to	integrate	these	

forward‐looking	temporal	elements	when	values	for	accounting	terms	are	derived	through	a	

retrospective	reference	point	baseline	approach.	

The	three	potential	approaches	for	incorporating	multiyear	carbon	fluxes	into	the	framework	are	

presented	in	this	section.	These	concepts	are	for	illustrative	purposes	and	do	not	present	an	

exhaustive	list	of	how	temporal	aspects	could	be	treated	in	a	framework	application.	These	

illustrative	temporal	accounting	approaches	are	(1)	front	loading;	(2)	year‐to‐year	carryover;	and	

(3)	annualized	carryover.	Another	approach,	discounting,	is	discussed	in	a	separate	section	below.	

The	frontloading	approach	sums	all	future	estimated	net	emissions	associated	with	biogenic	

feedstock	production	and	accounts	for	them	in	the	time	period	the	biogenic	feedstock	is	used.	

Under	the	year‐to‐year	carryover	approach,	emissions	are	tracked	over	time	and	recorded	as	a	

cumulative	amount	as	they	occur	over	time.	Under	the	annualized	carryover	option,	estimated	

cumulative	emissions	fluxes	are	annualized	over	a	specific	time	period	(which	can	be	the	time	

frame	in	which	the	emissions	impacts	are	expected	to	occur	or	some	other	determined	time	frame).		

The	basic	advantages	and	disadvantages	associated	with	each	of	these	options	are	discussed	below.	

It	is	important	to	note	that	none	of	these	three	approaches	involve	discounting	as	presented	here.	

This	means	that	net	biogenic	CO2	fluxes	that	occur	many	years	in	the	future	are	treated	identically	

as	net	emissions	that	occur	in	the	present	in	all	methods	discussed	below.	However,	discounting	

could	be	utilized	in	conjunction	with	any	of	the	three	approaches	outlined	below	(the	last	section	of	

this	appendix	discusses	discounting).	Lastly,	the	methods	below	include	some	estimation	of	future	

conditions	and	related	emissions	fluxes,	which	may	over‐	or	underestimate	future	emissions	fluxes	

relative	to	actual	emission	fluxes	trajectories	that	come	to	pass.		

4.1. Front‐Loading

With	the	front‐loading	approach,	consideration	is	given	to	all	the	biogenic	carbon	fluxes	that	will	

occur	over	some	period	of	time	(which	could	be	the	estimated	emissions	horizon	or	some	other	

specified	period	such	as,	for	example,	20	years,	30	years,	or	100	years)	as	a	result	of	a	particular	

biogenic	feedstock	production	activity	in	the	current	time	period	(for	example,	a	land	use	change	or	

residue	removal).	Then,	these	emissions	fluxes	can	be	summed	over	time	for	a	cumulative	estimate.	

These	fluxes	are	then	accounted	for	in	the	current	period,	or	period	when	the	feedstock	is	used	(or	
November	2014	 	 B‐9	

reported),	in	units	of	CO2e	per	ton	of	feedstock.	In	this	way,	the	total	carbon	fluxes	associated	with	a	

particular	unit	of	feedstock	production	are	accounted	for	up	front,	before	the	estimated	future	

emissions/sequestration	associated	with	that	unit	of	feedstock	actually	occur.	

Under	the	front‐loading	approach,	multiyear	net	biogenic	carbon	fluxes	are	accounted	for	over	a	

specific	time	frame	but	attributed	to	a	single	(annual	or	other	defined	reporting)	time	period.	The	

approach	captures	all	of	the	present	and	future	estimated	net	emissions	associated	with	growth,	

harvest,	decay,	and/or	land	use	changes	related	to	the	biogenic	feedstock	production,	processing,	

and	use.	Also,	economic	discounting	could	be	incorporated	into	the	front‐loading	approach	if	it	is	

determined	that	future	carbon	fluxes	should	not	be	treated	the	same	as	current	fluxes,	or	if	

discounting	is	appropriate	in	a	specific	policy	or	program	application	of	the	framework.		

Figure	B‐2	illustrates	the	calculations	of	FCEt	under	the	front‐loading	approach	in	the	context	of	

logging	residues.	For	a	100‐year	accounting	period,	the	front‐loaded	FCEt	is	the	sum	of	annual	FCEt

values	over	100	years.	In	this	case,	the	front‐loaded	FCEt	equals	0.99.	

Figure B-2. Cumulative FCE and Front-loaded FCE with a 5% Loss per Year Assumption over 100 

Years2

. 

There	may	be	policy	applications	or	other	framework	applications	in	which	the	assessment	horizon	

is	shorter	than	the	emissions	horizon.	For	instance,	the	emissions	horizon	for	certain	feedstock	

production	effects	is	75	years,	but	the	time	frame	for	analysis	is	only	50	years.	In	such	a	

circumstance,	all	the	estimated	future	net	effects	may	not	be	included	in	an	analysis	using	this	

approach.		

This	basic	method	for	incorporating	temporal	dynamics	is	relatively	straightforward	in	that	all	or	a	

portion	of	the	estimated	future	net	biogenic	CO2	emissions	fluxes	are	accounted	for	in	a	single	time	

																																																													

2

 The sum of the annual FCE values over 100 Years is the front-loaded FCE over a 100-year accounting period. 
November	2014	 	 B‐10	

step.	However,	there	are	inherent	uncertainties	related	to	future	socioeconomic	and	biophysical	

projections	and	related	trajectories	of	estimated	net	emissions	fluxes	related	to	the	biogenic	

feedstock	production	and	use.	Also,	if	all	estimated	future	emissions	effects	are	captured	in	the	

current	time	period	or	when	the	biogenic	feedstock	is	utilized,	for	some	feedstocks	this	could	be	a	

relatively	large	assessment	factor,	which	could	discourage	use	of	that	biogenic	feedstock.		

4.2. Year‐to‐Year Carryover

In	the	year‐to‐year	carryover	accounting	method	presented	here,	the	biogenic	CO2	fluxes	associated	

with	a	unit	of	feedstock	production	in	the	current	period	are	accounted	for	in	the	year	in	which	the	

fluxes	actually	occur.	For	example,	land	use	change	that	occurs	during	the	production	of	this	year’s	

biogenic	feedstock	might	generate	a	small	increase	in	soil	carbon	sequestration	each	year	for	the	

subsequent	20	or	30	years.	In	this	accounting	approach,	the	accounting	for	the	subsequent	annual	

increment	of	change	in	emissions	occurs	in	the	year	of	the	emissions	change.		

In	the	year‐to‐year	carryover	accounting	approach,	net	emissions	from	feedstock	production	for	a	

given	year	are	reported	in	the	same	year	that	those	emissions	occur.	Any	net	carbon	fluxes	carried	

over	from	feedstock	utilization	in	previous	years	are	also	included.	For	example,	if	a	feedstock	

removed	from	a	site	in	year	t	triggers	fluxes	of	emissions	to	and	from	the	atmosphere	over	

subsequent	n	years,	the	magnitude	of	the	fluxes	is	projected	n	years	into	the	future.	The	fluxes	

would	then	be	accounted	for	in	the	future,	in	the	year	(t	+	1	year,	t	+	2	years,	t	+	3	years	...	up	to	t	+	n

years)	in	which	they	actually	occur.	Under	the	year‐to‐year	carryover	accounting	approach,	the	

emissions	horizon	is	the	same	as	the	assessment	horizon.	Thus,	an	entity	may	be	accounting	in	a	

given	year	for	carbon	fluxes	associated	with	biogenic	feedstocks	used	over	multiple	prior	years	(the	

number	of	years	depends	on	the	time	frame	chosen).	

The	carryover	approach	may	increase	the	complexity	of	accounting	requirements	that	would	need	

to	be	implemented	by	stationary	sources	and	program	administrators.	Under	the	year‐to‐year	

carryover	approach,	multiple	terms	in	the	framework	may	change	from	one	year	to	the	next,	

thereby	complicating	the	calculations.	Also,	economic	discounting	could	be	incorporated	into	year‐

to‐year	carryover	if	future	carbon	fluxes	should	not	be	treated	the	same	as	current	fluxes	or	if	

discounting	is	appropriate	in	a	specific	policy	or	program	application	of	the	framework.		

Figure	B‐3	illustrates	the	annual	FCEt	year	to	year	over	a	100‐year	time	frame	using	assumptions	of	

5,	10,	and	25%	emissions	per	year	in	the	case	of	logging	residues.	The	annual	FCE	is	calculated	by	

subtracting	each	year’s	FCRt	value	from	the	previous	year’s	FCRt	value.	As	an	example	using	a	5%	

loss	per	year,	in	Year	1,	95%	of	the	carbon	is	remaining	and	is	subtracted	from	the	prior	year	

(100%),	which	gives	0.05	as	the	annual	FCEt	in	Year	1.	The	representative	values	depicted	in	Figure	

B‐3	illustrate	that	the	annual	FCEt	in	a	particular	year	depends	on	the	actual	time	profile	(i.e.,	decay	

rate)	of	the	emission	pulse.	
November	2014	 	 B‐11	

Figure B-3. Year-to-Year Annual Fraction of Carbon Emitted (FCEt) Depends on the Decay Rate. 

This	method	could	allow	for	future	estimated	biogenic	CO2	fluxes	related	to	the	use	of	a	feedstock	to	

be	reflected	in	the	values	for	framework	equation	terms	as	they	occur	on	the	landscape	rather	than	

during	the	year	of	feedstock	use.	Also,	this	method	permits	updates	to	future	trajectories	of	

estimated	emissions	fluxes	related	to	the	biogenic	feedstock	production	and	use	in	case	initial	

estimated	trajectories	prove	to	differ	from	actual	emissions	flux	trajectories.	However,	the	values	of	

framework	equation	terms	for	a	given	year’s	feedstock	use	may	change	over	subsequent	years,	

which	may	cause	market	and	investment	uncertainty	(the	BAF	can	be	applied	only	to	the	annual	

emissions	from	a	stationary	source	in	a	given	year,	which	can	vary).3	As	a	result,	adjustment	of	

future‐year	stationary	source	biogenic	CO2	emissions	may	not	capture	and	represent	the	actual	net	

emissions	impact	(on	a	tonnage	basis)	of	future‐year	carbon	fluxes	related	to	previous‐year	

feedstock	consumption.	

4.3. Annualized Carryover

The	annualized	carryover	approach	accounts	for	cumulative	emissions	over	the	emissions	horizon	

and	then	divides	those	emissions	equally	over	the	assessment	horizon.	Thus,	values	for	future	

estimated	annual	net	emissions	are	equal	across	the	assessment	horizon	and	are	determined	by	the	

annualized	value.	Depending	on	the	dynamics	of	the	biogenic	CO2	processes	on	the	landscape,	

annualized	carryover	may	over‐	or	underestimate	the	fluxes	at	the	start	of	the	accounting	period	

compared	with	year‐to‐year	carryover	accounting. The	illustrative	examples	of	annualized	

carryover	in	this	appendix	do	not	include	economic	discounting.	However,	economic	discounting	

could	be	incorporated	into	this	approach	in	applications	of	the	framework	where	future	biogenic	

CO2	fluxes	were	not	be	treated	the	same	as	current	fluxes.	It	is	possible	that	a	specific	policy	or	

																																																													

3

 If both the BAF and emissions varied each year, then these two factors introduce uncertainty into the annual 

emissions estimate, making it difficult for a stationary source to have stability for investments. 
November	2014	 	 B‐12	

program	application	of	the	framework	would	discount	future	biogenic	CO2	fluxes	(discussed	in	

Section	5).	

Under	the	annualized	carryover	approach,	the	values	of	future	estimated	annual	net	emissions	for	

each	year’s	feedstock	production	are	the	same.	The	time‐related	values	for	relevant	BAF	equation	

terms	would	remain	the	same	over	time	(or	until	recalculated	based	on	new	reference	data)	and	

provide	simplicity	for	application	of	the	BAF	equation.	However,	because	future	net	emissions	

effects	related	to	a	current	year’s	consumption	of	feedstock	are	accounted	for	in	future	years,	

applied	accounting	complications	could	arise.	For	example,	as	with	year‐to‐year	carryover	

accounting,	future	fluxes	related	to	previous	years’	feedstock	consumption	would	need	to	be	

applied	in	each	year	when	calculating	a	stationary	source’s	BAF	related	to	the	use	of	a	feedstock.	If	

the	stationary	source	changes	ownership	or	operating	status,	properly	transferring	the	accrued	

future	emissions	accounting	values	related	to	past	feedstock	consumption	may	prove	complex.	

To	illustrate	these	dynamics,	Table	B‐2	presents	the	annualized FCEt	over	a	100‐year	emissions	

horizon	for	a	representative	multiyear	carbon	flux	related	to	forest	residue	decay,	with	different	

percentage	carbon	loss	assumptions	and	different	assessment	horizons.	To	calculate	annualized	

FCEt	for	a	100‐year	emissions	pulse,	cumulative	emissions	up	to	100	years	were	divided	by	20‐,	30‐,	

and	100‐year	time	periods,	respectively	(e.g.,	annualized	FCEt	for	a	5%	decay	rate	over	a	20‐year	

assessment	horizon	is	0.99	divided	by	20,	which	equals	0.05).	

Table B-2. 100-Year Emissions Annualized over 20-, 30-, and 100-Year Assessment Horizons. 

Loss/Year

(decay rate)

Annualized FCE (100‐year emissions)

Time Period (t)

20 Years 30 Years 100 Years

5% 0.05 0.03 0.01	

10% 0.05 0.03 0.01	

25% 0.05 0.03 0.01	

Table	B‐3	presents	a	truncated	annualizing	approach	where	the	emissions	horizon	is	truncated	at	

20,	30,	and	100	years.	The	cumulative	emissions	after	20,	30,	and	100	years	are	then	divided	

equally	over	the	same	time	periods.	Under	the	truncated	approach,	not	all	of	the	estimated	

emissions	are	captured,	and	the	assessment	horizon	is	the	same	as	the	truncated	emissions	horizon	

(20,	30,	and	100	years	in	this	case).	These	time	periods	were	chosen	to	represent	different	

assessment	horizons	(e.g.,	facility	lifetimes)	that	could	be	applied	in	practice.	For	example,	the	

annualized	FCEt	for	truncated	emissions	at	20	years	for	a	2%	carbon	decay	rate	is	0.33	divided	by	

20,	which	equals	0.02.	
November	2014	 	 B‐13	

Table B-3. 20-Year, 30-Year, and 100-Year Emissions Annualized over 20-, 30-, 100-Year Time 

Periods, Respectively. 

Loss/Year

Annualized FCE [truncated emissions]

Time Period

20 Years 30 Years 100 Years

5% 0.03 0.03 0.01	

10% 0.04 0.03 0.01	

25% 0.05 0.03 0.01	

The	representative	values	in	Table	B‐2	illustrate	that	in	determining	appropriate	emission	

annualized	values,	it	is	important	to	consider	both	the	emissions	horizon	for	the	feedstock	effects	as	

well	as	the	assessment	horizon	for	the	reporting	of	those	emissions.	Specifically,	annualized	

emissions	increase	as	the	emissions	horizon	increases;	for	example,	under	a	5%	decay	rate	the	non‐

truncated	annualized	FCEt	for	a	100‐year	emissions	horizon	and	20‐year	assessment	horizon	(0.05)	

is	greater	than	the	truncated	annualized	FCEt	for	a	20‐year	emissions	horizon	and	20‐year	

assessment	horizon	(0.03).	However,	as	the	assessment	horizon	increases,	annualized	emissions	

decrease:	for	example,	under	a	5%	decay	rate	the	non‐truncated	annualized	FCEt	for	a	100‐year	

emissions	horizon	and	100‐year	assessment	horizon	(0.01)	is	less	than	the	non‐truncated	

annualized	FCEt	for	a	100‐year	emissions	horizon	and	20‐year	assessment	horizon	(0.05).	

This	method	for	accounting	for	time	allows	for	inclusion	of	all	emissions	fluxes	over	the	emissions	

horizon	within	the	assessment	horizon.	Also,	similar	to	the	year‐to‐year	carryover	approach,	this	

method	can	allow	updates	to	future	trajectories	of	estimated	emissions	fluxes	related	to	biogenic	

feedstock	production	activities	and	use	in	case	initial	trajectories	prove	to	differ	from	actual	

emissions	flux	trajectories.	However,	similar	to	the	year‐to‐year	approach,	framework	equation	

term	values	for	a	given	year’s	feedstock	use	may	change	over	subsequent	years,	which	may	cause	

market	and	investment	uncertainty.	The	BAF	can	be	applied	to	the	annual	emissions	from	a	

stationary	source	in	a	given	year,	which	can	vary.4	As	a	result,	adjustment	of	future‐year	stationary	

source	CO2	emissions	may	not	capture	and	represent	the	actual	net	emissions	impact	(on	a	tonnage	

basis)	of	future‐year	carbon	fluxes	related	to	previous‐year	feedstock	consumption.	

4.4. Temporal Scale of the Illustrative Future Anticipated Baseline

Approach in the Technical Appendices		

When	using	a	future	anticipated	baseline,	integrating	time	into	the	assessment	of	forward‐looking	

phenomena	is	inherent	in	the	approach,	and	decisions	about	temporal	dynamics	may	affect	the	

outcomes	(as	discussed	in	the	previous	subsection).	The	future	anticipated	baseline	approach	as	

generally	discussed	in	this	report	could	conceptually	apply	whatever	future	time	horizon	is	

necessary	for	the	specific	program	or	policy	analysis	at	hand.	This	report	does	not	apply	the	

framework	to	specific	policies	or	programs	and	thus	has	no	specific	temporal	parameters	such	as	

																																																													

4

 If both the BAF and emissions varied each year, then these two factors introduce uncertainty into the annual 

emissions estimate, making it difficult for a stationary source to have stability for investments. 
November	2014	 	 B‐14	

an	assessment	horizon	or	time	of	reporting.	For	illustrative	purposes	in	the	technical	future	

anticipated	baseline	appendices	of	this	report	(Appendices	J,	K,	and	L),	the	year‐to‐year	carryover	is	

applied	using	a	50‐year	simulation	horizon.	This	assessment	time	scale	is	long	enough	to	capture	

significant	carbon	dynamics	of	longer	rotation	feedstock	species,	land	use	and	land	use	

management	changes,	and	soil	carbon	pools.	Conversely,	it	is	short	enough	to	detect	significant	

biogenic	CO2	fluxes	related	to	biogenic	feedstock	production	and	harvest.	The	year‐to‐year	

carryover	approach	is	used	to	show	how	estimated	future	net	biogenic	CO2	emissions	fluxes	could	

change	over	time	and	to	provide	insights	about	the	potential	future	impacts	of	biogenic	feedstock	

production,	processing,	and	use.	In	addition	to	annual	accounting	using	the	year‐to‐year	carryover	

approach,	one	can	also	use	this	approach	to	evaluate	cumulative	emissions	for	a	specific	time	

horizon.	Additional	discussion	of	periodic	(flux	based)	and	cumulative	landscape	emissions	

projections	using	the	year‐to‐year	carryover	approach	can	be	found	in	Appendices	K	and	L.		

5. Discounting and Its Relevance to the Framework

Broadly	speaking,	there	is	a	value	to	time.	For	example,	benefits	and	costs	are	typically	valued	

higher	if	they	are	experienced	sooner	(OMB	Cir	A‐94).	This	value	of	time	is	usually	discussed	as	a	

“discount”	of	what	the	future	holds.	Discounting	is	regularly	applied	in	finance	and	economics,	

where	it	represents	the	time	value	of	money,	and	quantitative	values	can	generally	be	assigned.	

Discounting	allows	for	assessment	of	the	future	value	in	today’s	terms	(i.e.,	the	net present value).	

To	compute	net	present	value,	it	is	necessary	to	discount	future	benefits	and	costs.	The	discount	

rate	is	the	interest	rate	used	in	calculating	the	present	value	of	expected	yearly	benefits	and	costs	

(OMB	Cir	A‐94).	

For	example,	money	invested	today	will	accrue	interest,	and	the	quantity	of	money	will	grow	over	

time	according	to	the	interest	rate.	Similarly,	a	debt	will	increase	over	time	according	to	the	interest	

rate.	Money	received	today	has	more	value	than	the	same	amount	of	money	received	in	the	future.	

If	the	interest	rate	is	known,	the	net	present	value	of	future	costs	(e.g.,	the	monetary	value	of	

building	and	maintaining	seawalls)	can	be	calculated,	as	can	the	future	value	of	benefits	(e.g.,	the	

monetary	value	of	homes	and	tourism	on	the	seashore).	In	other	words,	the	net	present	value	of	

future	costs	and	benefits	can	be	calculated	by	multiplying	the	costs	and	benefits	in	each	future	year	

by	a	discount	factor,	then	summing	all	values	over	the	lifetime	of	an	investment,	policy,	or	decision.	

Discounting	the	value	of	damages	associated	with	GHG	emissions,	which	span	multiple	generations,	

is	particularly	complex	and	raises	difficult	and	controversial	questions	of	science,	economics,	

philosophy,	and	law.	The	U.S.	federal	government	reviewed	the	literature	on	intergenerational	

discounting	several	years	ago	when	developing	estimates	of	the	social	cost	of	carbon,	i.e.,	the	

monetized	value	of	damages	associated	with	a	marginal	change	in	CO2	emissions.	The	federal	

government	found	that	although	it	is	well	understood	that	the	discount	rate	has	a	large	influence	on	

the	current	value	of	future	damages	from	GHG	emissions,	there	is	no	consensus	about	what	rates	to	

use	in	this	context.	

Recognizing	the	lack	of	consensus	about	an	appropriate	intergenerational	discount	rate	and	

uncertainty	regarding	how	interest	rates	might	change	over	time,	the	federal	government	selected	

three	rates	to	span	a	plausible	range	of	certainty‐equivalent	constant	discount	rates:	2.5,	3,	and	5%	
November	2014	 	 B‐15	

per	year.	In	sum,	average	returns	on	longer‐term	investments	were	used	to	inform	selection	of	

certainty‐equivalent	discount	rates.	The	federal	government	viewed	this	approach	as	defensible	

and	transparent	given	its	consistency	with	current	benefit‐cost	analysis	principles	as	well	as	OMB’s	

guidelines	for	such	analysis	as	embodied	in	OMB	Circular	A‐4.	The	Technical	Support	Document,	

Social Cost of Carbon for Regulatory Impact Analysis Under Executive Order 12866,	discusses	this	

analysis	in	detail	(Interagency	Working	Group,	2010).	

The	federal	government	has	continued	to	research	alternative	approaches	for	intergenerational	

discounting.	In	particular,	a	group	of	world‐recognized	experts	convened	at	an	EPA‐funded	

workshop	in	20115	to	explore	what	principles	should	be	used	to	determine	the	rates	at	which	to	

discount	the	costs	and	benefits	of	regulatory	programs	when	costs	and	benefits	extend	over	very	

long	horizons.	The	charge	questions	that	were	the	subject	of	the	workshop	discussion	focused	on	

three	main	areas:	(1)	whether	and	in	what	context	it	is	appropriate	to	apply	a	Ramsey	discounting	

framework	in	an	intergenerational	setting;	(2)	whether	and	how	to	directly	estimate	discount	rates	

over	long	time	horizons;	and	(3)	how	to	apply	discounting	in	a	regulation	where	some	costs	and	

benefits	accrue	intra‐generationally	while	others	accrue	inter‐generationally.	Notably,	the	group	

reached	consensus	that	there	are	compelling	arguments	for	using	a	declining	discount	rate	

schedule,	though	determined	that	practical	questions	remain	regarding	how	to	establish	and	

implement	such	a	schedule	(Arrow	et	al.,	2013).	

Discounting	is	more	challenging	when	applied	to	nonmonetary	quantities	where	there	is	not	a	clear	

interest	rate,	thereby	making	it	difficult	to	quantitatively	equate	present	and	future	events.	If	the	

discount	rate	is	known	in	the	context	of	avoiding	future	climate	change	impacts,	the	net	present	

value	of	future	costs	(e.g.,	the	monetary	value	of	damages	associated	with	climate	change	impacts)	

can	be	calculated,	as	can	the	future	value	of	benefits	(e.g.,	the	monetary	value	of	avoided	damages	

or	avoided	GHG	emissions.)	Also,	if	carbon	emissions	have	monetary	value	as	determined	through	a	

carbon	tax,	a	cap‐and‐trade	system,	an	emissions	limit	or	permit	system,	or	through	the	structure	of	

the	damages	caused,	then	quantitatively	discounting	the	value	of	emissions	is	more	

straightforward.	However,	discounting	becomes	more	challenging	when	the	quantitative	links	

between	physical	emissions	and	costs	or	benefits	are	less	clear.	

The	traditional	role	of	discounting	is	to	compare	the	costs	and	benefits	of	quantities	(such	as	money	

or	the	monetary	value	of	CO2	emissions)	that	occur	at	different	periods	in	time.	The	higher	the	

discount	rate,	the	lower	the	present	value	of	the	future	unit	(money,	carbon	etc.)	in	the	future.	This	

means	that	a	high	discount	rate	implies	a	strong	time	preference,	such	that	events	in	the	future,	for	

example,	are	given	far	less	value	than	those	occurring	today.	Failure	to	discount	future	events	

assumes	a	discount	rate	of	0	and	implies	no	time	preference;	that	is,	a	0	discount	rate	assumes	that	

future	events	have	the	same	value	as	current	events.	For	carbon	accounting,	the	fundamental	issue	

is	whether	carbon	emissions	(or	sequestration	today)	are	valued	the	same	as	carbon	emissions	(or	

sequestration	in	the	future),	and	how	the	valuation	of	time	is	factored	into	carbon	accounting.	For	

example,	if	one	ton	of	CO2	is	emitted	this	year	and	one	ton	of	carbon	is	sequestered	20	or	100	years	

from	now,	the	treatment	or	valuation	of	time	will	determine	if	these	events	are	of	equal	and	

																																																													

5

 Link to workshop summary: http://rff.org/Events/Pages/Intergenerational-Discounting-Workshop.aspx 
November	2014	 	 B‐16	

opposite	value	so	that	the	net	effect	is	0	or	not.	It	is	clear	that	time	is	important,	but	the	challenge	

lies	in	how	to	deal	with	this	preference	quantitatively.	

5.1. Time Preference in CO2 Emissions		

As	mentioned	above,	one	of	the	current	challenges	in	carbon	accounting	is	the	time	value	of	carbon	

emissions	(or	sequestration).	Do	emissions	at	some	time	in	the	future	have	the	same	value	as	

emissions	now?	Does	the	time	path	of	emissions	and	sequestration	matter?	Is	there	value	in	

delaying	emissions?	Is	there	value	in	temporary	storage	of	emissions	if	they	will	be	released	later?	

The	importance	of	the	time	value	of	carbon	has	been	recognized	for	many	years	(e.g.,	Richards,	

1997),	but	there	continues	to	be	much	debate	on	how	to	deal	quantitatively	with	time	and	what	the	

“appropriate”	discount	factor	is	in	the	context	of	monetizing	future	GHG	emissions.	A	recent	

advisory	group	to	the	California	Air	Resources	Board	struggled	with	this	topic	without	reaching	

consensus	but	did	provide	the	consensus	statement	that	“the	timing	of	emissions	[is]	important	

and,	as	a	general	goal,	policy	should	differentiate	based	on	timing	where	possible”	(Martin,	

Kloverpris,	Kline,	Mueller,	&	O’Hare,	2011,	p.48).	The	group	also	concluded	that	there	is	“no	

intellectually	supportable	escape	from	the	universally	demonstrated	judgment	of	society	that	

consequences	occurring	at	different	times	must	be	valued	with	reference	to	the	time	of	occurrence,”	

but	the	group	acknowledged	the	difficulty	of	determining	appropriate	discount	rates	(Martin	et	al.,	

2011,	p.27).	Similarly,	an	EPA	(2010a)	publication	on	economic	analyses	discusses	approaches	for	

dealing	with	time	without	ending	up	with	a	quantitative	conclusion	but	recommends	that	analyses	

“display	the	time	paths	of	benefits	and	costs	as	they	are	projected	to	occur	over	the	time	horizon	of	

the	policy...”	

The	prevailing	view	is	that	physical	carbon	flows	should	not	be	discounted	as	a	function	of	time	but	

that—where	carbon	flows	have	economic	value—the	monetary	value	of	the	flows	should	be	

discounted.	As	O’Hare	et	al.	(2009)	wrote	in	a	paper	on	their	view	of	the	proper	accounting	for	time	

in	biofuels	analyses,	“the	discounting	model	applies	to	costs	and	benefits,	not	to	physical	

phenomena	that	generate	them,	unless	their	economic	value	is	otherwise	stable	over	time”	(p.	3)	

and	“before	such	economic	analysis	can	be	meaningfully	pursued	the	relationship	between	the	

physical	and	economic	quantities	must	be	established”	(p.	4).	If	carbon	emissions	were	currently	

subject	to	taxation,	for	example,	the	tax	rate	would	be	the	economic	value	of	reducing	(or	avoiding)	

emissions	and	possibly	used	as	a	discount	rate	in	net	present	value	calculations.	The	concept	of	

applying	a	discount	to	a	physical	measure,	however,	is	difficult	to	rationalize:	a	ton	of	carbon	is	a	

ton	of	carbon,	and	differences	arise	only	from	its	equated	economic	value.		

Any	program	or	policy	that	considers	effects	of	carbon	emissions	over	time	will	need	to	decide	on	

the	applicability	of	valuing	these	emissions	and,	if	done	monetarily,	how	to	discount	them.	One	

recent	example	of	this	decision‐making	process	can	be	found	in	the	Renewable	Fuel	Standard	

Program	(RFS2)	Regulatory	Impact	Analysis	(EPA,	2010b).	When	considering	how	to	measure	the	

lifecycle	GHG	emissions	from	a	given	type	of	renewable	fuel	relative	to	a	2005	petroleum	baseline,	

two	important	elements	were	considered	in	terms	of	how	to	estimate	the	stream	of	emissions	and	

benefits	over	time:	(1)	the	time	period	considered	and	(2)	the	discount	rate	applied	to	future	

emissions.	Although	a	range	of	options	was	considered	in	the	proposed	rule,	for	the	final	rule	EPA	

chose	a	30‐year	time	period	and	a	0%	discount	rate.	Although	a	relatively	short	time	period	of	30	
November	2014	 	 B‐17	

years	was	chosen	because	it	was	similar	to	the	life	span	of	a	biofuels‐producing	facility,	a	discount	

rate	of	0%	was	chosen	“due	to	the	many	issues	associated	with	applying	an	economic	concept	to	a	

physical	parameter”	(p.	423).	This	is	primarily	because	the	Energy	Independence	and	Security	Act	

(EISA)	of	2007	did	not	establish	any	monetary	valuation	of	carbon	emissions	for	the	RFS2	program,	

as	well	as	the	“lack	of	consensus	as	to	the	appropriate	discount	rate	to	apply	to	GHG	lifecycle	

emissions	streams	through	time”	(EPA,	2010b,	p.	423).	

The	peer	review	report	Methods and Approaches to Account for Lifecycle Greenhouse Gas Emissions

from Biofuels Production over Time	(EPA,	2009)	is	particularly	direct	in	its	opposition	to	discounting	

physical	emissions,	stating	that	“all	reviewers	noted	in	some	way	that	a	discount	rate	should	only	

be	applied	to	a	monetary	unit,	rather	than	a	physical	unit	such	as	a	carbon	emission.”	Similarly,	

“proper	discounting	...	can	only	be	conducted	on	value	(i.e.,	damages,	not	physical	quantities	such	as	

emissions)”	(p.	B‐2)	and	“discount	rates	are	only	justifiable	when	applied	to	monetary	impacts,	not	

physical	impacts”	(p.	13).	Further,	“economic	discounting	cannot	logically	be	applied	to	physical	

quantities	such	as	GHG	emissions,	only	to	economic	quantities	such	as	climate	change	damages”	(p.	

B‐4).	Similarly,	Martin	et	al.	(2011)	wrote	that	“in	the	absence	of	agreement	on...values,	discount	

rates	become	meaningless”	(p.	27)	and	that	when	considering	discounting,	“a	prerequisite	is	to	

begin	with	a	monetized	value	to	discount”	(p.	26).	Other	sources,	such	as	the	Interagency	Review	on	

Social	Cost	of	Carbon	(Interagency	Working	Group,	2010)	and	Johnson	and	Hope	(2012),	do	not	

address	the	concept	of	discounting	physical	emissions	and	focus	on	damages,	costs	and	benefits,	or	

other	concepts	of	monetized	value.	

Although	the	literature	is	generally	opposed	to	the	concept	of	discounting	physical	emissions,	some	

sources	do	discuss	related	instances	where	the	strategy	may	be	applicable.	First,	as	noted	by	a	few	

respondents	in	the	peer	review	report	mentioned	above	(EPA,	2009),	discounting	physical	

emissions	may	be	appropriate	if	these	emissions	are	used	as	a	direct	proxy	for	damages.	

Discounting	is	“justifiable	if	physical	emissions	were	being	used	as	a	proxy	for	economic	damages	

associated	with	warming”	(p.	15)	and	only	in	this	case	are	discount	rates	used	for	physical	carbon	

units	“analogous	to	monetary	discount	rates”	(p.	22).	

A	number	of	recent	efforts	have	attempted	to	describe	a	time‐dependent	damage	function	for	

emissions,	that	is,	efforts	to	link	emissions	to	atmospheric	concentrations	and	subsequently	to	the	

climatic	effects	(damages)	of	increasing	concentrations.	This	approach	encompasses	more	than	a	

time	preference,	because	it	can	include	recognition	of	the	dynamics	of	changing	marginal	damages	

over	time	(i.e.,	the	notion	that	the	climate	impact	of	one	ton	of	CO2	emissions	today	is	not	equal	to	

the	impact	of	one	ton	of	emissions	in	the	future	because	of	factors	such	as	the	persistence	of	GHGs	

in	the	atmosphere,	options	for	mitigation,	or	damages	that	are	a	function	of	the	total	level	of	

atmospheric	CO2	at	the	time).	Whereas	traditional	time	preference	should	result	in	a	decreasing	

importance	of	future	emissions,	equating	emissions	with	damages	could	result	in	increasing	

importance	of	future	emissions	if	the	damage	function	is	increasing	faster	than	the	rate	of	time	

preference	(see,	for	example,	Richards,	1997).	As	characterized	by	Marshall	(2009),	“Ideally,	a	GHG	

accounting	method	...	should	explicitly	analyze	the	expected	damage	associated	with	flows	over	

time.	The	corresponding	monetary	units	associated	with	this	damage	can	then	be	discounted	to	

determine	how	the	impacts	of	future	flows	compare	to	those	of	the	present.”	Fargione	wrote	that	“if	
November	2014	 	 B‐18	

EPA	is	not	willing	to	make	assumptions	about	the	relationship	between	emissions	and	damages,	

then	they	should	not	use	any	discounting”	(EPA,	2009,	p.	B‐4).	

Papers	by	O’Hare	et	al.	(2009)	and	Cherubini	et	al.	(2011),	for	example,	calculate	cumulative	

radiative	forcing	(described	by	O’Hare	et	al.	as	“a	physically	plausible	proxy	for	the	total	damage	to	

the	planet	from	the	CO2	emissions”)	or	GWPbio	(defined	by	Cherubini	et	al.	as	“the	effective	climate	

impact”)	in	efforts	to	describe	a	damage	cost	that	reflects	the	time	path	of	CO2	emissions.	Similarly,	

Kendall	et	al.	(2009)	propose	a	“time	correction	factor”	to	“properly	account	for	the	timing	of	...	

greenhouse	gas	emissions	in	the	biofuels	life	cycle”	(see	also	Alissa	Kendall	&	Price,	2012).	

Levasseur	et	al.	(2010)	describe	a	dynamic	life‐cycle	analysis	that	considers	the	time	value	of	

emissions.	Conceptually,	discounting	marginal	damages	is	related	to	traditional	discounting	in	that	

it	makes	assumptions	about	changing	values	over	time,	but	in	this	case,	the	“value”	is	expressed	in	

terms	of	the	impact	on	climate.	

Ultimately	at	least	three	factors	enter	into	considering	the	time	dependence	of	the	value	of	carbon	

flows:	(1)	the	monetary	values	potentially	captured	in	cost‐benefit	analyses	(as	discussed	above);	

(2)	the	existence	of	irreversibilities	or	tipping	points	(see,	for	example,	Kolstad,	1994);	and	(3)	the	

role	of	learning	(see,	for	example,	Kolstad,	1993).	On	tipping	points,	Marshall	(2009,	p.9)	wrote,	

“the	potential	for	irreversible	change	is	one	of	the	significant	determinants	of	the	expected	damage	

function	for	GHG	emissions	that	must	be	considered	in	determining	how	to	compare	current	to	

future	emissions,	and	is	one	of	the	most	convincing	arguments	for	the	need	to	make	some	sort	of	

distinction	between	current	and	future	...	emissions.”	Kolstad	(1994)	includes	the	investment	

capital	of	mitigation	measures	as	an	irreversibility.	On	the	role	of	learning,	Kolstad	(1993)	notes	the	

role	of	uncertainty	in	the	relative	value	of	current	and	future	emissions	and	concludes	that	

“accelerated	learning	tends	to	reduce	current	period	optimal	emissions.”	That	is,	rapid	reductions	

in	uncertainty	tend	to	reduce,	but	not	eliminate,	expenditures	to	reduce	current	emissions	as	

uncertainty	is	being	resolved.	Dornburg	and	Marland	(2008)	raise	many	of	these	issues	in	the	

context	of	the	value	of	temporary	carbon	sequestration	or	of	delaying	emissions.	

Uncertainty	becomes	a	dominant	factor	in	attempting	to	discount	future	emissions	(or	

sequestration)	when	significant	time	intervals	are	involved	in	lifecycle	analyses	or	the	impacts	of	

land	use	change.	Despite	recognition	of	the	importance	of	dealing	with	the	time	value	of	CO2

emissions,	there	is	great	uncertainty	in	the	appropriate	value	of	a	discount	rate.	This	uncertainty	is	

due	to	uncertainty	about	the	future,	uncertainty	about	the	correct	relationship	between	emissions	

and	damages,	and	the	potentially	long	times	involved	in	consideration	of	climate	change	impacts.	It	

is	clear	that	application	of	constant	discount	rates	is	not	appropriate	over	long	time	periods	(e.g.,	

intergenerational	times)	(see,	for	example,	EPA,	2009;	Schelling,	1995).	There	is	the	suggestion	that	

for	consideration	of	long	time	periods	it	may	be	appropriate	to	use	discount	rates	that	decrease	

with	time	(see,	for	example,	Guo,	Hepburn,	Tol,	&	Anthoff,	2006).	Note	that	the	imposition	of	any	

time	horizons	(as	done	with	traditional	measures	of	global	warming	potential)	to	limit	

consideration	of	effects	after	a	specific	period	of	time	implicitly	assumes	that	the	discount	rate	

increases	to	100%	and	that	impacts	after	that	time	are	not	counted	at	all.	

Ultimately,	O’Hare	writes	(personal	communication,	2012),	“at	least	in	the	short	and	medium	term,	

something	like	compound	discounting	at	a	rate	in	the	3–7%	range	is	necessary	to	rational	decision	
November	2014	 	 B‐19	

making	about	any	actions	with	consequences	that	occur	in	the	future.	This	discounting	must	be	

applied	to	something	like	the	social	cost	and	not	mere	quantities	of	discharge.”	Richards	(1997)	

suggested	that	“at	a	minimum,	carbon	discount	rates	should	be	tested	for	values	equal	to	the	social	

discount	rate	and	zero.”	In	2009,	Richards	(in	EPA,	2009)	suggested	discount	rates	of	2%,	3%,	and	

5%.	The	specific	discount	rate	chosen	depends	on	the	circumstances.	Although	nearly	all	

individuals	possess	a	time	preference,	the	strength	of	this	preference	can	vary	greatly	and	with	it	

the	corresponding	discount	rate.	In	the	realm	of	policy	making	and	finance,	the	selected	discount	

rate	is	often	simply	the	market	interest	rate,	which	generally	fluctuates	between	2%	and	7%.	

Considering	the	long	time	horizons	associated	with	climate	change	and	climate	change	policy,	small	

changes	to	the	discount	rate	can	have	very	large	consequences.	A	widely	cited	report	on	the	costs	

and	benefits	of	climate	mitigation	strategies	and	published	responses	that	criticize	its	use	of	very	

low	discount	rates	illustrate	the	large	impact	of	discount	rates	over	long	time	periods	(see	

Nordhaus,	2007;	Stern,	2006).	

Note	that	the	decision	to	ignore	time	is	in	effect	a	decision	to	assume	that	the	value	of	emissions	is	

not	affected	by	the	time	path	of	emissions	and	that	the	appropriate	discount	rate	is	0.	Marland	et	al.	

(2010),	in	the	context	of	the	carbon	stored	in	durable	wood	products,	showed	that	where	

discounting	of	carbon	flows	is	implemented,	it	is	very	important	to	represent	the	time	path	of	CO2

emissions	as	accurately	as	possible.	

There	is	much	discussion	and	uncertainty	about	appropriate	rates	for	compounded	discounting,	but	

at	the	same	time	there	is	a	widespread	consensus	that	the	time	value	of	carbon	emissions	is	

important.	Specifically,	as	Richards	wrote	in	1997,	“the	time	value	of	carbon	is	an	important	issue	

that	requires	an	explicit	decision.”	Writing	in	2009,	Richards	added	“if	it	doesn’t	matter	when	it	is	

done,	it	doesn’t	matter	whether	it	is	done”	(EPA,	2009,	p.	F‐2).		

5.2. Discounting Summary

The	production	and	use	of	biogenic	feedstocks	for	energy	can	in	some	circumstances	have	emission	

implications	extending	well	into	the	future.	Questions	then	arise	about	whether	and	how	to	value	

emissions	fluxes	that	occur	over	time	in	present	terms.	Although	there	is	no	single,	scientifically	

correct	treatment	of	time,	the	choice	of	treatment	may	have	significant	impacts	on	the	results	of	an	

accounting	framework	application.	It	is	important	to	consider	possible	treatments	of	time	and	the	

implications	of	different	treatments	in	terms	of	the	respective	strategies	chosen	for	long‐term	and	

short‐term	emission	accounting.		

The	prevailing	view	in	the	technical	literature	is	that	there	is	a	value	of	time	that	can	have	

important	ramifications	for	prospective	accounting	and	analysis,	that	it	ought	to	be	considered	

explicitly,	and	that	time	preference	is	traditionally	viewed	as	related	only	to	monetary	or	other	

values	and	is	not	inherent	in	physical	measures	of	carbon	emissions.	Aside	from	certain	financial	

transactions	where	there	is	an	explicit	discount	rate	(the	interest	rate),	it	can	be	difficult	to	

determine	an	appropriate	discount	rate	for	any	given	circumstance,	including	accounting	for	GHG	

emissions	over	time.	The	debate	continues	about	how	to	value	(i.e.,	what	discount	rates	to	choose)	

when	evaluating	the	future	value	of	biogenic	CO2	emissions,	where	the	impacts	on	the	global	carbon	

cycle	may	occur	over	very	long	periods	of	time	and	the	impact	of	small	changes	in	discount	rate	can	
November	2014	 	 B‐20	

be	very	large.	The	scientific	literature	does	not	provide	guidance	on	selecting	one	appropriate	

discount	rate	but	does	suggest	using	multiple	values	to	illustrate	the	great	importance	of	time.	

The	decision	on	how	to	treat	the	time	value	of	biogenic	CO2	emissions	(or	sequestration)	will	likely	

fall	to	policies	or	programs	like	a	carbon	tax,	a	cap‐and‐trade	system,	or	other	legal	decisions	that	

deal	with	society’s	willingness	to	consider	the	inherent	risks	of	a	changing	climate.	The	decision	to	

not	discount	the	value	of	emissions	over	time	is	an	effective	decision	to	select	a	discount	rate	of	0.	

For	the	purposes	of	accounting	for	biogenic	CO2	emissions	from	stationary	sources,	the	framework	

application	in	this	report	focuses	primarily	on	the	physical	flows	of	biogenic	CO2	and,	in	the	

forward‐looking	context,	the	comparison	of	different	potential	flows	across	alternative	future	

scenarios.	Applications	of	the	framework	could	incorporate	discount	rates	into	calculations	of	the	

biogenic	assessment	factor	as	appropriate	for	that	specific	application.		

6. References

Arrow	et	al.,	2013.	Determining	Benefits	and	Costs	for	Future	Generations.	Science	26	July	2013:	

341	(6144),	349‐350.	[DOI:10.1126/science.1235665]	

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