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	Horiz on,	and	Time	of	Reporting	.. .............................................	B‐3

2.2. Temporal	Differences	b etween	Feedstocks	.......................

............................................................... ....	B‐3

2.3. Interactions	Between	Spati al	and	Temporal	Scales	.............. .............................................................	B ‐4

2.4. Temporal	Differences	b etween	Baselines	........................

............................................................... .......	B‐4

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

4. Potential	Methods	for	Asse ssing	Multiyear	Fluxes	..............

............................................................... .........	B‐7

4.1. Front‐Loading	.................................................

............................................................... ....................................	B‐8

4.2. Year‐to‐Year	C arryover	........................................

............................................................... .......................	B‐10

4.3. Annualized	C arryover	..........................................

............................................................... ........................	B‐11

4.4. Temporal	Scale	of	the	Illustrati ve	Future	Anticipated	Baseline Approach	in	the	Technical Appendices	....................................................

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

5. Discounting	and	Its	Releva nce	to	the	F ramework	................

............................................................... .....	B‐14

5.1. Time	Preference	in	CO 2 Emissions	..................................................... ....................................................	B‐16

5.2. Discounting Summary	...........................................

............................................................... .......................	B‐19

6. References.....................................................

............................................................... ..............................................	B‐20



## List of Tables

Table	B‐1.	Theoretical	Illustrat ion	of	How	the	Impact	of	Time	D epends	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,	Respe ctively.	........................................

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



## List of Figures

Figure	B‐1.	Annual	Fraction	of	Carbon	Emitted	(FCE),	Cumulative Fraction	of	Carbo n	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	( FCE t )	Depends	on	the	Decay	Rate.	B‐11November	2014	 	 B‐2 

## 1. Introduction

The	purpose	of	this	appendix	is to	discuss	considerations	relat ed	to	the	treatment	of	time	in possible	applications	of	the	fram ework.	It	is	important	to	cons ider	possible	treatments	of	time	and the	implications	of	these	treatm ents	in	developing	strategies	f or	long‐term	and	short‐term emissions	accounting,	because	the choice	of	treatment	may	have significant	impacts	on	the	outcome of	an	assessment	framework	applic ation.	While	there	is	no	singl e,	scientifically	correct	method	for
the	treatment	of	time	when	asse ssing	biogenic	emissions,	there are	a	number	of	options	for incorporating	temporal	dynamics into	an	assessmen t	of	biogenic carbon	fluxes.	The	choice	of temporal	assessment	method	could	ultimately	depend	on	the	conte xt	of	a	specific	framework application.

This	appendix	discusses	various aspects	related to	assessing	ti me‐dependent	effects	in	the production,	processing,	and	consum ption	of	biogenic	feedstocks. Considerations	related	to	time	can include	a	variety	of	issues	such	as:

 Emissions	horizons	and	reporting	p eriods	(i.e.,	fluxes	related to	feedstock	production	may occur	over	many	years,	whereas	r eporting	may	be	the	current	yea r);

 Interplay	with	spatial	scale	(i. e.,	implications	of	larger	scal es	and	shorter	time	frames
versus	smaller	scales	and longer	time	frames);

 Baseline	perspective	(i.e.,	is	t he	analysis	forward‐	or	backwar d‐looking,	or	both?);	and

 Differences	in	temporal	characte ristics	of	different	feedstocks (i.e.,	annual	crops,	short rotation	energy	crops,	and	longer rotation	forestry	systems).

In	general,	accounting	for	tempo ral	effects	will	be	most	signif icant	when	considering	future potential	fluxes	related	to	long rotation	feedstocks	(e.g.,	rou ndwood),	activities	that	affect	the equilibrium	storage	in	soil	carb on	pools,	decay	rates,	or	in	ca ses	of	significant	land	use	change, where	biogenic	feedstock	production	has	implications	for	long‐t erm	emissions	changes	in
terrestrial	carbon	stocks.

Given	that	different	temporal	pe rspectives	could	be	used	by	the framework,	two	different	baseline approaches	are	evaluated	in	this framework	report:	retrospectiv e	reference	point	and	future anticipated	baseline.	These	base line	approaches	use	aspects	of time.	The	retrospective	reference point	baseline	does	not	take	into	account	future	potential	biog enic	emissions	fluxes	related	to biogenic	feedstock	production,	p rocessing,	and	use.	The	future anticipated	baseline,	due	to	its prospective	nature,	can	take	int o	account	such	future	potential fluxes.	As	such,	most	of	the discussion	in	this	appendix	focus es	on	potential	methods	for	co nsidering	time	in	terms	of	a prospective	analysis.

This	appendix	provides	various	illustrative	treatments	of	tempo ral	dynamics	when	activities	and
related	emissions	fluxes	do	not	f it	neatly	into	single	assessme nt	time	periods.	As	presented	in Section	4,	illustrative	treatment s	for	prospective	applications of	the	framework	in	this	appendix include	a	frontloading	approach, a	year‐to‐year	carryover	appro ach,	and	an	annual ized	carryover approach.	A	discussion	of	discoun ting	time	is	provided	in	Secti on	5.November	2014	 	 B‐3 

## 2. Key Temporal Scale Considerations

The	production,	processing,	and	us e	of	biogenic	feedstocks	for energy	can,	in	some	circumstances, have	emission	effects	extending	into	the	future	and	there	are	d ifferent	methods	to	and	perspectives
about	how	to	assess	future	emissi ons	trajectories	(Dornburg	and Marland,	2008;	Fargione,	2008; Kendall	et	al.,	2009;	Levasseur et	al.,	2010;	Wa lker	et	al.,	20 10;	Cherubini	et	al,	2 011;	Mitchell	et	al., 2012;	Helin	et	al.,	2013;	Walker	et	al.,	2013;	Miner	et	al.,	20 14).	Accounting	for	these	emissions appropriately	in	different	polic y	contexts	may	n ecessitate	vari ous	decisions	that	reflect	the	goals and	parameters	of	the	policy.	An application	of	the	framework	p resented	in	this	report	that
includes	assessment	ov er	time	may	need	to	identify	emissions	an d	assessment	horizons,	reporting periods,	the	appropriate	baseline method,	the	appropriate	spati al	scale,	and	the	temporal
characteristics.	These	considera tions	are	discussed	below	in	mo re	detail.



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

An	application	of	the	framework	that	includes	assessment	over	t ime	may	need	to	articulate	how biogenic	CO 2 emissions	fluxes	over	time	from	b iogenic	feedstock	production, processing,	and	use relate	to	stationary source	biogenic	CO 2 emissions	in	a	single	period	(e.g.,	time	of	biogenic	feedstock use	or	reporting).	It	is	not	onl y	a	question	of	how	far	into	th e	future	must	an	analy sis	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	necessa ry	to	distinguish	between	the “emissions	horizon”	and	the
“assessment	horizon.”	The	emissi ons	horizon	is	the	period	of	ti me	during	which	the	carbon	fluxes resulting	from	actions	taking	pl ace	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	horizo n	reflects	all	future	estimate d	net	carbon	fluxes	associated	with the	production	and	harvest	or	rem oval	of	a	feedstock	today.	The refore,	the	emissions	horizon	may need	to	span	a	year	to	several	d ecades,	depending	on	the	feedst ock	and	production	site	conditions,
to	account	for	all	thes e	effects.	The	asse ssment	horizon,	howev er,	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	po tential	effects over	20	years, whereas	the	estimated	emissions horizon	is	50	years.	The	time	of	reporting	may	be	a	one‐time	ev ent	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	ne eds,	one	should	consider	how	to address	these	different	time	horizons.	Illustrative	general	met hods	for	reconciling	these	different
horizons	are	discussed	in	Section	4.



### 2.2. Temporal Differences between Feedstocks

Biogenic	carbon	fluxes	related	t o	biogenic	feedstock	growth,	ha rvest,	and/or	collection,	feedstock production	site	soil	carbon	level s,	and	land	use	and/or	managem ent	change	do	in	m any	cases	occur over	a	period	greater	than	one	year.	The	consideration	of	multi year	time	dynamics	for	biogenic feedstock	growth	is	particularly relevant	for	long	rotation	fee dstocks	or	feedstocks	where	carbon
stored	in	biomass	accu mulates	over	time	subj ect	to	biological	g rowth	functions	and	whereNovember	2014	 	 B‐4 feedstock	production	and/or	colle ction	affect	landscape	soil	ca rbon	dynamics	or	other	land	use changes.	For	long	rotation	feedstocks,	the	amount	of	biogenic	C O 2 emissions	from	harvest	and combustion	may	take	years	to	be	sequestered	on	the	same	site	fr om	which	it	was	harvested.	For logging	residues,	analysts	may	n eed	to	consider	decay	and	assoc iated	landscape	biogenic	CO 2 emissions.	For	example,	the	colle ction	and	combustion	of	loggin g	residues	result	in	an	immediate release	of	biogenic	CO 2 emissions	that	otherwise	might	have	instead	occurred	in	the	fo rm	of	CO 2 and	CH 4 over	a	series	of	years	through natural	decomposition	on	the	fo rest	floor.	Concurrently, removal	of	the	logging	residues	can	cause	increased	emissions	t hrough	loss	of	soil	carbon	over time,	while	also	altering	rates of	forest	growth	and	carbon	seq uestration.	Changing	management practices	can	also	potentially	a ffect	mineral	soil	carbon	pools (Buchholz	et	al.,	2013).

Time	dynamics	may	also	be	a	relevant	consideration	for	some	agr icultural	feedstocks.	For	example, land	use	change	such	a s	the	removal	of	forests	for	agricultural feedstock	production	could	result	in an	initial	release	of	carbon	that	is	not	fully	recaptured	in	su bsequent	use	of	the	land	for	agriculture. Furthermore,	cultivation	of	pere nnial	bioenergy	feedstocks	such as	switchgrass	can	lead	to	long‐ term	increases	in	soil	organic	c arbon	relative	to	annual	crops due	to	extensive	root	systems (belowground	biomass)	and	reducti on	of	tillage	disturbances.	Al so,	changing	management practices,	such	as	removing	agri cultural	residues	like	corn	sto ver,	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	car bon	fluxes	can	also	depend	on	t he	choice	of	spatial	scale.	In	some circumstances,	assessing	biogeni c	carbon	fluxes	at	a	small	spat ial	scale	for	a	long period	of	time	can result	in	similar	outcomes	to	those	from	considering	a	large	sp atial	scale	over	a	short	period	of time.	For	example,	the	harvest	of	a	long‐rotation	feedstock,	su ch	as	roundwood,	on	a	significantly small	spatial	scale	(e.g.,	plot	o r	stand)	will	initially	result in	biogenic	carbon	emissions,	but	over enough	time,	replanted	trees	(e. g.,	assuming	similar	species,	c onditions)	will	sequester approximately	the	same	amount	of	carbon	that	was	released	by	th e	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	ba lanced	out	by	sequestration	in	that region	from	the	continued	growth of	unharvested	roundwood	and	a ny	reforestation	a ctivities	in	the region	over	a	relatively	short	t ime	frame	(likely	shorter	than regrowth	of	the	stand	itself).



### 2.4. Temporal Differences between Baselines

The	retrospective	reference	poin t	baseline	and	future	anticipat ed	baseline	approaches	both	include treatments	of	time.	However,	the way	in	which	these	two	baselin e	approaches	consider	time	is markedly	different.	The	retrospe ctive	reference point	baseline approach	is	inherently	backward‐ looking	(because	it	evaluates	measured	or	modeled	emissions	flu xes	over	a	specific	time	frame	in the	past),	while	the	future	anti cipated	baseline	approach	is	in herently	forward‐looking	(because	it evaluates	points	in	time	along	d ifferent	future	simulations).

When	the	reference	point	baseline	approach	is	applied	retrospec tively,	it	takes	i nto	account	net atmospheric	biogenic	CO 2 contributions	associated	with	bi ogenic	feedstock	production	on theNovember	2014	 	 B‐5 landscape	by	assessing	differences in	biogenic	stocks	and	flows between	two	points	in	time	in	the past.	Under	this	baseline	approa ch,	one	must	decide	which	speci fic	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	cho sen	time	horizon	(e.g.,	at	wha t	point	in	time	was	da ta	first	collected, when	were	the	most	recent	data	produced?).	Integration	of	futur e	multiyear	fluxes	(e.g.,	from potential	decay,	soil	carbon	equ ilibrium	changes)	is	not	necess ary	when	values	for	framework terms	are	derived	through	a	back ward‐looking	approach	(i.e.,	th e	retrospective	reference	point baseline).	Appendices H	and	I	show	illustra tive	equation	term	c alculations	and	case	study applications	for	forest‐	and	agr iculture‐derived	feedstocks	usi ng	the	retrospective	reference	point baseline	approach.

The	future	anticipated	baseline	approach	assesses	the	estimated net	change	in	carbon	stocks between	two	projected	future	sce narios	at	the	same	specified	po int	in	time,	that	is,	between	a business‐as‐usual	(BAU)	scenario and	an	alternative	scenario	wi th	changes	in	estimated environmental,	economic,	and/or policy	conditions	(e.g.,	Search inger	et	al.,	2009).	Because	this baseline	approach	can be	used	to	project	future	biogenic	carbon ‐based	fluxes	associated	with biogenic	feedstock	production,	p rocessing,	and	use,	there	are	m ore	considerations	about	how	to represent	and	incorporate	elements	of	time	into	such	an	analysi s	than	in	the	retrospective reference	point	approach.	Integr ation	of	future	multiyear	fluxe s	(e.g.,	from	poten tial	decay,	soil carbon	equilibrium	changes,	othe r	land	use	and/or	management	ch ange	effects)	may	be	necessary for	framework	terms	representing	biogenic	landscape	attribute	v alues	( GROW, AVOIDEMIT,

SITETNC ,	and LEAK ,	if	included)	and	possibly	proc ess	attributes	(depending	on	tr eatment	of biogenic	carbon	losses	through	the	supply	chain,	including	stor age	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	considerat ions,	possible	baseline	construc tion	methods,	and	illustrative	forest‐ and	agriculture‐derived	feedstoc k	case	study	applications	using this	baseline.	Waste‐derived feedstocks,	as	discussed	in	det ail	in	Appendix	N,	are	assessed in	this	report	by using	potential alternative	pathways	and	related	GHG	pathways	for	those	materia ls,	which	in	many	cases	include consideration	of	future	potentia l	methane	emissions	from	decomp osition	if	not	used	for	energy.



## 3. Illustration of General Temporal Dynamics Using Decay
Rates

The	magnitude	of	an	emissions	pul se	(meaning,	in	this	context, the	cumulative	biogenic	carbon‐ based	emissions	over	a	time	period)	may	depend	on	how	far	into the	future	an	anal ysis	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	e missions	horizon	over	which	the flux	occurs).	In	practice,	however,	a shorter	time	frame	may be	warranted	in	specific	accounting	circ umstances,	especially	if	the	fluxes toward	the	tail	end	of	a	multiye ar	flux	pattern	are	very	small or	a	specific	program	or	policy application	necessitates	a	sp ecific,	shorter	time	frame.

To	simply	explain	the	general	dynamics	of	time,	this	appendix	u ses	concepts	called	the	“Fraction	of Carbon	Remaining”	( FCR t )	and	“Fraction	of	Carbon	Emitted”	( FCE t )	to	illustrate	the	implications	of different	choices	of	time	frame	when	assessing	emissions	flux	d ynamics	over	time	( t ).	Using	theNovember	2014	 	 B‐6 specific	context	of	natural	dec ay	from	logging	residue	feedstoc k	as	an	example, FCR t is	the	amount of	carbon	that	remains	(in	terms	of	mtCO 2 e)	on	the	site	( CR t )	after	a	particular time	frame	divided by	the	magnitude	of	the	original	carbon	pool	( CR 0 ),	assuming	a	parti cular	decay	rate:

ࡾ࡯ࡲ ࢚ ൌ ࡾ࡯ ࢚ ࡾ࡯ ૙ (EQ. B.1)

Where:

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

FCE t is	calculated	as:

ࡱ࡯ࡲ ࢚ ൌ ૚ െ ࡾ࡯ࡲ ࢚ ) EQ. B.3)

FCR t and FCE t are	unit‐free	(i.e.,	dimensionl ess)	values	by	their	definition s.	Table	B‐1	provides examples	of	the	impact	of	different	accounting	time	frames	on	t he	emissions	pulse	accounting	(i.e.,

FCE t over	the	defined	time period)	from	the	natu ral	decay	of	1	mtCO 2 e	woody	residue	feedstock	left
onsite.	Note	that	these	are	not emissions	due	to	biogenic	feeds tock	harvest	or	consumption,	but emissions	related	to	decay	of	the logging	residue	if	left	onsit e.	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	CO 2 is	emitted over	20	years,	whereas	99%	of	the	biogenic	CO 2 is	emitted	over	100	years.	However,	for	a	high decay	rate	of	25%	loss	per	ye ar,	nearly	all	biogenic	CO 2 is	emitted	within	the	first	20	years.

Table B-1. Theoretical Illustration of How the Im pact 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	a s	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	CO 2 emissions	associated	with	certain feedstocks	(i.e.,	woody	biomass) with	slow	rates	of	natural	dec ay	(in	the	case	of	residues	or	fallen trees)	and/or	long	growth	periods (referred	to	generally	as	“lo ng‐rotation”	feedstocks).	However, accurately	capturing	these	multi year	landscape	effects	related to	feedstock	production,	processing, and	use	can	be	challenging	in	the	context	of	an	assessment	fram ework	application	that	may	need	to estimate	and	report	annual	biogenic	CO 2 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	CO 2 fluxes	that	have	a	temporal	dimension	longer than	an	annual	cycle	for	certain	feedstocks	and,	thus,	may	requ ire	application	of	an	accounting method	for	these	temporal	effects.	The GROW term,	for	example,	represents	the	projected	change	in biogenic	carbon	fluxes	from	feed stock	growth	in	a	given	area	ov er	a	given	time	period. 1 The

SITETNC term	reflects	estimated	site‐induced	changes	in	above‐	and	bel owground	carbon	that typically	occur	over	a	multiyear period	due	to	a	direct	land	us e	or	land	use	management	change that	triggers	changes	in	car bon	stocks.	Similarly,	the AVOIDEMIT term	accounts	for	the	avoidance	of estimated	biogenic	emissions	tha t	could	have	occurred	on	the	fe edstock	landscape	without	biogenic

1 Note that under the retrospective reference poin t 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	feed stock)	or	per	an	alternative	ma nagement	strateg y	(e.g.,	waste‐ derived	feedstocks). LEAK represents	leakage	effects	that can	occur	from	feedstock	produ ction, including	indirect	land	use	chang es	that	could	affect	landscape CO 2 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	be low	integrates	future	multiye ar	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	annual ly)	for	illustrative	purposes. Note	that	the	need	to	integrate future	multiyear	fluxes	is	nece ssary	only	when	a	specific	application
of	the	framework	allows	for	or	re quires	consideration	of	counte rfactual	or	future	emissions	fluxes related	to	biogenic	feedstock	pr oduction	activities.	Again,	it is	not	necessary	to	integrate	these forward‐looking	temporal	element s	when	values	for	accounting	te rms	are	derived	through	a retrospective	reference point	baseline	approach.

The	three	potential	a pproaches	for	incorporating	multiyear	carb on	fluxes	into	th e	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	f ramework	application.	These illustrative	temporal	accounting approaches	are	(1)	front	loadi ng;	(2)	year‐to‐year	carryover;	and (3)	annualized	carryover.	Another	approach,	discounting,	is	dis cussed	in	a	separate	section	below. The	frontloading	approach	sums	all	future	estimated	net	emissio ns	associated	with	biogenic feedstock	production	and	accounts for	them	in	the	time	period	t he	biogenic	feedstock	is	used. Under	the	year‐to‐year	carryover approach,	emissions	are	tracke d	over	time	and	recorded	as	a cumulative	amount	as	they	occur over	time.	Under	the	annualized carryover	option,	estimated
cumulative	emissions	fluxes	are	an nualized	over	a	specific	time period	(which	can	be	the	time frame	in	which	the	emissions	impacts	are	expected	to	occur	or	s ome	other	determined	time	frame).

The	basic	advantages	and	disadva ntages	associated	with	each	of these	options	are	discussed	below. It	is	important	to	note	that	none of	these	three	approaches	inv olve	discounting	as	presented	here. This	means	that	net	biogenic	CO 2 fluxes	that	occur	many	years	in the	future	are	treated	identic ally as	net	emissions	that	occur	in	the	present	in	all	methods	discu ssed	below.	However,	discounting could	be	utilized	in	conjunction	with	any	of	the	three	approach es	outlined	below	(the	last	section	of this	appendix	discusses	discountin g).	Lastly,	the	methods	below include	some	estimation	of	future
conditions	and	related	emissions	f luxes,	which	may	over‐	or	und erestimate	future	emissions	fluxes
relative	to	actual	emission	fluxe s	trajectories	that	come	to	pa ss.



### 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	em issions	horizon	or	some	other specified	period	such	as,	for	ex ample,	20	years, 30	years,	or	1 00	years)	as	a	result	of	a	particular biogenic	feedstock	production	ac tivity	in	the	current	time	peri od	(for	example,	a	land	use	change	or residue	removal).	Then,	these	emissions	fluxes	can	be	summed	ov er	time	for	a	cumulative	estimate.
These	fluxes	are	then	accounted for	in	the	current	period,	or	p eriod	when	the	feedstock	is	used	(orNovember	2014	 	 B‐9 reported),	in	units	of	CO 2 e	per	ton	of	feedstock.	In	this	w ay,	the	total	carbon	fluxes	as sociated	with	a particular	unit	of	feedstock	pro duction	are	acco unted	for	up	fr ont,	before	the	estimated	future emissions/sequestration	associat ed	with	that	unit	of	feedstock actually	occur.

Under	the	front‐loading	approach, multiyear	net	biogenic	carbon fluxes	are	accoun ted	for	over	a specific	time	frame	but	attribut ed	to	a	single	(annual	or	other defined	reporting)	time	period.	The approach	captures	all	of	the	pre sent	and	future	estimated	net	e missions	associated	with	growth, harvest,	decay,	and/or	land	use changes	related to	the	biogenic feedstock	production,	processing, and	use.	Also,	economic	discount ing	could	be	incorporated	into the	front‐loading	approach	if	it	is
determined	that	future	carbon	fl uxes	should	not	be	treated	the same	as	current	fluxes,	or	if discounting	is	appropriate	in	a	s pecific	policy	o r	program	appl ication	of	the	framework.

Figure	B‐2	illustrates	the	calculations	of FCE t under	the	front‐loading	approach	in	the	context	of logging	residues.	For	a	100‐year	accounting	period,	the	front‐l oaded FCE t is	the	sum	of	annual FCE t values	over	100	years.	In	this	case,	the	front‐loaded FCE t equals	0.99.

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

.
There	may	be	policy	applications	or	other	framework	application s	in	which	the	a ssessment	horizon
is	shorter	than	the	emissions	h orizon.	For	instance,	the	emissi ons	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	fu ture	net	effects	may	not	be	i ncluded	in	an	analysis	using	this approach.

This	basic	method	for	incorporat ing	temporal	dynamics	is	relati vely	straightforward	in	that	all	or	a portion	of	the	estimated	future	net	biogenic	CO 2 emissions	fluxes	ar e	accounted	for	in a	single	time

2 The sum of the annual FCE values over 100 Years is th e front-loaded FCE over a 100-year accounting period.November	2014	 	 B‐10 step.	However,	there	are	inheren t	uncertainties	related	to	futu re	socioeconomic	and	biophysical projections	and	related	traject ories	of	estimated	net	emissions fluxes	related	to	the	biogenic feedstock	production	and	use.	Als o,	if	all	estimated	future	emi ssions	effects	are	captured	in	the current	time	period	or	when	the	b iogenic	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	CO 2 fluxes	associated with	a	unit	of	feedstock	producti on	in	the	current	period	are	a ccounted	for	in	the	year	in	which	the fluxes	actually	occur.	For	examp le,	land	use	change	that	occurs during	the	production	of	this	year’s biogenic	feedstock	might	generat e	a	small	increase	in	soil	carb on	sequestration	ea ch	year	for	the subsequent	20	or	30	ye ars.	In	this	accounting	approach,	the	acc ounting	for	the	subsequent	annual increment	of	change	in	emissions	occurs	in	the	year	of	the	emis sions	change.

In	the	year‐to‐year	carryover	a ccounting	approach,	net	emission s	from	feedstock	production	for	a given	year	are	reported	in	the	same	year	that	those	emissions	o ccur.	Any	net	carbon	fluxes	carried
over	from	feedstock	utilization in	previous	years	are	also	incl uded.	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	occu r.	Under	the	year‐to‐year	car ryover	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	feedstock s	used	over	multiple	prior	years	(the number	of	years	depends	on the	time	frame	chosen).

The	carryover	approach	may	increas e	the	complexity	of	accountin g	requirements	that	would	need to	be	implemented	by	stationary sources	and	program	administrat ors.	Under	the	year‐to‐year carryover	approach,	multiple	term s	in	the	framework	may	change from	one	year	to	the	next, thereby	complicating	the	calcula tions.	Also,	economic	discounti ng	could	be	incorporated	into	year‐ to‐year	carryover	if	future	carb on	fluxes	should	not	be	treated the	same	as	current	fluxes	or	if discounting	is	appropriate	in	a	s pecific	policy	o r	program	appl ication	of	the	framework.

Figure	B‐3	illustra tes	the	annual FCE t year	to	year	over	a	100‐year	ti me	frame	using	assumptions	of 5,	10,	and	25%	emissions	per	year in	the	case	of	logging	residu es.	The	annual	FCE	is	calculated	by subtracting	each	year’s FCR t value	from	the	previous	year’s FCR t value.	As	an	example	using	a	5% loss	per	year,	in	Year	1,	95%	o f	the	carbon	is	remaining	and	is subtracted	from	the	prior	year (100%),	which	gives	0.05	as	the	annual FCE t in	Year	1.	The	representative	values	depicted	in	Figure
B‐3	illustrate	that	the	annual FCE t 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 ( FCE t ) Depends on the Decay Rate.

This	method	could	allow	for	future	estimated	biogenic	CO 2 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	upd ates	to	future	trajectories	of
estimated	emissions	fluxes	relate d	to	the	biogenic	feedstock	pr oduction	and	use	in	case	initial estimated	trajectories	prove	to	differ	from	actual	emissions	fl ux	trajectories.	However,	the	values	of framework	equation	terms	for	a	given	year’s	feedstock	use	may	c hange	over	subsequent	years, which	may	cause	market	and	investment	uncertainty	(the BAF can	be	applied	onl y	to	the	annual emissions	from	a	stationary	source	in	a	given	year,	which	can	v ary). 3 As	a	result,	adjustment	of future‐year	stationary	source	biogenic	CO 2 emissions	may	not	capture	and	represent	the	actual	net emissions	impact	(on	a tonnage	basis)	of	future‐year	carbon	flu xes	related	to	previous‐year feedstock	consumption.



### 4.3. Annualized Carryover

The	annualized	carryover	approach accounts	for	cumulative	emiss ions	over	the	emissions	horizon
and	then	divides	those	emissions equally	over	th e	assessment	ho rizon.	Thus,	values	for	future
estimated	annual	net	emissions	a re	equal	across	the	assessment horizon	and	are	de termined	by	the annualized	value.	Depending	on	th e	dynamics	of	the	biogenic	CO 2 processes	on	the	landscape, annualized	carryover	may	over‐	or	underestimate	the	fluxes	at	t he	start	of	the	accounting	period compared	with	year‐to‐year	carryover	accounting. The	illustrative	exa mples	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	f uture	biogenic

CO 2 fluxes	were	not	be	treated	the	same	as	current	fluxes.	It	is	p ossible	that	a	specific	policy	or

3 If both the BAF and emissions varied each year, then these tw o 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	frame work	would	discount	future	biog enic	CO 2 fluxes	(discussed	in Section	5).

Under	the	annualized	carryover	a pproach,	the	values	of	future	e stimated	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	ba sed	on	new	reference	data)	and provide	simplicity	for application	of	the BAF equation.	However,	because	future	net	emissions
effects	related	to	a	c urrent	year’s	consumption	of	feedstock	ar e	accounted	for	in	future	years, applied	accounting	complications could	arise.	For	example,	as	w ith	year‐to‐year	carryover accounting,	future	flu xes	related	to	previou s	years’	feedstock consumption	would	need	to	be applied	in	each	year	when	calcu lating	a	stationary	source’s BAF related	to	the	use	of	a	feedstock.	If the	stationary	source	changes	ownership	or	operating	status,	pr operly	transferring	the	accrued future	emissions	accounting	value s	related	to	past	feedstock	co nsumption	may	prove	complex.

To	illustrate	these	dynamics,	Table	B‐2	presents	the	annualized FCE t over	a	100‐year	emissions horizon	for	a	representative	multiyear	carbon	flux	related	to	f orest	residue	decay,	with	different percentage	carbon	loss	assumpti ons	and	different	assessment	hor izons.	To	calcula te	annualized

FCE t 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 FCE t 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 ov er 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	e missions	horizon	is	truncated	at 20,	30,	and	100	years.	The	cumul ative	emissions	after	20,	30,	a nd	100	years	are	then	divided equally	over	the	same	time	periods.	Under	the	truncated	approac h,	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	c ase).	These	time	periods	were	c hosen	to	represent	different assessment	horizons	(e.g.,	facility	lifetimes)	that	could	be	ap plied	in	practice.	For	example,	the
annualized FCE t 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 Em issions 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	deter mining	appropriate	emission annualized	values,	it	is	importa nt	to	consider	both	the	emissio ns	horizon	for	the	feedstock	effects	as
well	as	the	assessment	horizon	fo r	the	reporting	of	those	emiss ions.	Specifically,	annualized
emissions	increase	as	the	emissi ons	horizon	increases;	for	exam ple,	under	a	5%	decay	rate	the	non‐
truncated	annualized FCE t for	a	100‐year	emissions	horizo n	and	20‐year	assessment	horizo n	(0.05) is	greater	than	the	truncated	annualized FCE t for	a	20‐year	emissions horizon	and	20‐year assessment	horizon	(0.0 3).	However,	as	the assessment	horizon	i ncreases,	annualized	emissions decrease:	for	example,	under	a	5%	decay	rate	the	non‐truncated annualized FCE t for	a	100‐year emissions	horizon	and	100‐year	a ssessment	horizon	(0.01)	is	les s	than	the	non‐truncated
annualized FCE t for	a	100‐year	emissions	horiz on	and	20‐year	assessment	horizo n	(0.05).

This	method	for	accounting	for	t ime	allows	for	inclusion	of	all emissions	fluxes	over	the	emissions
horizon	within	the	assessment	hor izon.	Also,	simi lar	to	the	yea r‐to‐year	carryover	approach,	this method	can	allow	updates	to	futur e	trajectories	of	estimated	em issions	fluxes	related	to	biogenic feedstock	production	activities	a nd	use	in	case	initial	traject ories	prove	to	differ	from	actual emissions	flux	trajectories.	However,	similar	to	the	year‐to‐ye ar	approach,	framework	equation term	values	for	a	given	year’s	feedstock	use	may	change	over	su bsequent	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	o f	future‐year	stationary

source	CO 2 emissions	may	not	capture	and	represent	the	actual	net	emissio ns	impact	(on	a	tonnage basis)	of	future‐year	carbon	fluxes	related	to	previous‐year	fe edstock	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	temp oral	dynamics	may	affect	the outcomes	(as	discussed	in	the	previous	subsection).	The	future anticipated	baseline	approach	as generally	discussed	in	this	repo rt	could	conceptually	apply	wha tever	future	time	horizon	is necessary	for	the	specific	progra m	or	policy	analysis	at	hand. This	report	does	not	apply	the framework	to	specific	policies	o r	programs	and	thus	has	no	spec ific	temporal	parameters	such	as

4 If both the BAF and emissions varied each year, then these tw o 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	r eporting.	For	illustrative	pu rposes	in	the	technical	future anticipated	baseline	appendices	o f	this	report	(Appendices	J,	K ,	and	L),	the	year‐to‐year	carryover	is applied	using	a	50‐year	simulati on	horizon.	This	assessment	tim e	scale	is	long	enough	to	capture significant	carbon	dynamics	of	l onger	rotation	feedstock	specie s,	land	use	and	land	use management	changes,	and	soil	car bon	pools.	Conversely,	it	is	sh ort	enough	to	detect	significant biogenic	CO 2 fluxes	related	to	bio genic	feedstock	prod uction	and	harvest.	T he	year‐to‐year carryover	approach	is	used	to	sho w	how	estimated	future	net	bio genic	CO 2 emissions	fluxes	could change	over	time	and	to	provide	insights	about	the	potential	fu ture	impacts	of	biogenic	feedstock production,	processing,	and	use. In	addition	to	annual	accounti ng	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	cum ulative	landscape	emissions projections	using	the	year‐to‐y ear	carryover	approach	can	be	fo und	in	Appendices	K	and	L.



## 5. Discounting and Its Relevance to the Framework

Broadly	speaking,	there	is	a	value	to	time.	For	example,	benefi ts	and	costs	are	typically	valued higher	if	they	are	experienced	s ooner	(OMB	Cir	A‐94).	This	valu e	of	time	is	usually	discussed	as	a
“discount”	of	what	the	future	ho lds.	Discounting	is	regularly	a pplied	in	finance	and	economics, where	it	represents	the	time	value	of	money,	and	quantitative	v alues	can	generally	be	assigned. Discounting	allows	for	assessmen t	of	the	future	value	in	today’ s	terms	(i.e.,	the net present value ). To	compute	net	present	value,	it	is	necessary	to	discount	futur e	benefits	and	costs.	The	discount rate	is	the	interest	rate	used	in	calculating	the	present	value of	expected	yearly	b enefits	and	costs (OMB	Cir	A‐94).

For	example,	money	invested	toda y	will	accrue	inte rest,	and	the quantity	of	money	will	grow	over time	according	to	the	interest	ra te.	Similarly,	a	debt	will	inc rease	over	time	accord ing	to	the	interest rate.	Money	received	t oday	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	mo netary	value	of building	and	maintaining	seawalls )	can	be	calcula ted,	as	can	th e	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	i n	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	raise s	difficult	and	controversial questions	of	science,	economics, philosophy,	and	law.	The	U.S.	fe deral	government reviewed	the	l iterature	on	intergenerational discounting	several	years	ago	wh en	developing	estimates	of	the social	cost	of	carbon,	i.e.,	the monetized	value	of	damages	associated	with	a	marginal	change	in CO 2 emissions.	The	federal government	found	that	although	it	is	well	understood	that	the	d iscount	rate	has	a	large	influence	on the	current	value	of	future	damages	from	GHG	emissions,	there	i s	no	consensus	about	what	rates	to
use	in	this	context.

Recognizing	the	lack	of	consensu s	about	an	appropriate	intergen erational	discount	rate	and uncertainty	regarding	how	intere st	rates	might	change	over	time ,	the	federal	government	selected three	rates	to	span	a	plausible range	of	certainty‐equivalent	c onstant	discount	rates:	2.5,	3,	and	5%November	2014	 	 B‐15 per	year.	In	sum,	average	return s	on	longer‐term	investments	we re	used	to	inform	selection	of certainty‐equivalent	discount	ra tes.	The	federal	government	vie wed	this	approach	as	defensible and	transparent	given	its	consis tency	with	current	benefit‐cost analysis	principles as	well	as	OMB’s guidelines	for	such	analysis	as embodied	in	OMB	Circular	A‐4.	T he	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	contin ued	to	research	alternative	ap proaches	for	intergenerational discounting.	In	particular,	a	gr oup	of	world‐recognized	experts convened	at	an	EPA‐funded workshop	in	2011 5 to	explore	what	principles	shou ld	be	used	to	determine	the	rat es	at	which	to
discount	the	costs	and	benefits of	regulatory	programs	when	cos ts	and	benefits	extend	over	very long	horizons.	The	charge	questions	that	were	the	subject	of	th e	workshop	discussion	focused	on three	main	areas:	(1)	whether	an d	in	what	contex t	it	is	appropr iate	to	apply	a	Ramsey	discounting framework	in	an	intergenerationa l	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‐generation ally	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	reg arding	how	to	establish	and implement	such	a	schedule	(Arrow	et	al.,	2013).

Discounting	is	more	challenging	when	applied	to	nonmonetary	qua ntities	where	there	is	not	a	clear interest	rate,	thereby	making	it	difficult	to	quantitatively	eq uate	present	and	future	events.	If	the
discount	rate	is	known	in	the	c ontext	of	avoiding	future	climat e	change	impacts,	the	net	present value	of	future	costs	(e.g.,	the	monetary	value	of	damages	asso ciated	with	climate	change	impacts) can	be	calculated,	as	can	the	future	value	of	benefits	(e.g.,	t he	monetary	value	o f	avoided	damages or	avoided	GHG	emissions.)	Also, if	carbon	emissions	have	monet ary	value	as	determined	through	a carbon	tax,	a	cap‐and‐ trade	system,	an	emissions	limit	or	permi t	system,	or	through	the	structure	of the	damages	caused,	then	quantit atively	discounting	the	value	o f	emissions	is	more straightforward.	However,	discou nting	becomes	more	challenging when	the	quantitative	links between	physical	emissions	and costs	or	benefits	are	less	clear

.

The	traditional	role	of	discount ing	is	to	compare	the	costs	and benefits	of	quantit ies	(such	as	money or	the	monetary	value	of	CO 2 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	preferenc e,	such	that	events	in	the	future,	for example,	are	given	far	less	valu e	than	those	occurring	today.	F ailure	to	discount	future	events assumes	a	discount	rate	of	0	and	implies	no	time	preference;	th at	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	carb on	accounting.	For example,	if	one	ton	of	CO 2 is	emitted	this	year	and	one	ton	of	carbon	is	sequestered	20	o r	100	years from	now,	the	treatment	or	valua tion	of	time	will	determine	if these	events	are	of	equal	and

5 Link to workshop summary: http://rff.org/Events/Pages/Intergenerational-Discounting-Workshop.aspxNovember	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 CO 2 

### Emissions

As	mentioned	above,	one	of	the	current	challenges	in	carbon	acc ounting	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	pat h	of	emissions	and	sequestratio n	matter?	Is	there	value	in delaying	emissions?	Is	there	value	in	temporary	storage	of	emis sions	if	they	will	be released	later? The	importance	of	the time	value	of	carbon	h as	been	recognized for	many	years	(e.g.,	Richards, 1997),	but	there	continues	to	be	much	debate	on	how	to	deal	qua ntitatively	with	time	and	what	the “appropriate”	discount	factor	is	in	the	context	of	monetizing	f uture	GHG	emissions.	A	recent advisory	group	to	the	California Air	Resources	Board	struggled with	this	topic	without	reaching consensus	but	did	provide	the	c onsensus	statement	that	“the	tim ing	of	emissions	[is]	important and,	as	a	general	goal,	policy	should	differentiate	based	on	ti ming	where	possible”	(Martin, Kloverpris,	Kline,	Mueller,	&	O’H are,	2011,	p.48).	The	group	al so	concluded	that	there	is	“no intellectually	supportable	escape from	the	universally	demonstr ated	judgment	of	society	that consequences	occurring	at	different	times	must	be	valued	with	r eference	to	the	time	of	occurrence,” but	the	group	acknowledged	the	d ifficulty	of	determining	approp riate	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	conclus ion	but	recommends	that	analyses “display	the	time	paths	of	benef its	and	costs	as	they	are	proje cted	to	occur	over	the	time	horizon	of the	policy...”

The	prevailing	view	is	that	phys ical	carbon	flows	should	not	be discounted	as	a	function	of	time	but
that—where	carbon	flows	have	ec onomic	value—the	monetary	value of	the	flows	should	be discounted.	As	O’Hare	et	al.	(20 09)	wrote	in	a	paper	on	their	v iew	of	the	proper	accounting	for	time in	biofuels	analyses,	“the	disco unting	model	applies	to	costs	a nd	benefits,	not	to	physical phenomena	that	generate	them,	unless	their	economic	value	is	ot herwise	stable	ove r	time”	(p.	3) and	“before	such	economic	analys is	can	be	meaningfully	pursued the	relationship	between	the physical	and	economic	quantities must	be	established”	(p.	4).	I f	carbon	emissions	were	currently subject	to	taxation,	for	example,	the	tax	rate	would	be	the	eco nomic	value	of	reducing	(or	avoiding) emissions	and	possibly	used	as	a discount	rate	in	net	present	v alue	calculations.	The	concept	of applying	a	discount	to	a	physica l	measure,	however,	is	difficul t	to	rationalize:	a	ton	of	carbon	is	a ton	of	carbon,	and	differences	a rise	only	from	its	equated	econ omic	value.

Any	program	or	policy	that	considers	effects	of	carbon	emission s	over	time	will	need	to	decide	on the	applicability	of	valuing	the se	emissions	and,	if	done	monet arily,	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	co nsidering	how	to	measure	the lifecycle	GHG	emissions	from	a	gi ven	type	of	renewable	fuel	rel ative	to	a	2005	petroleum	baseline, two	important	elements	were	cons idered	in	terms	of	how	to	estim ate	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	pr oposed	rule,	for	the	final	rule	EPA chose	a	30‐year	time	period	and a	0%	discount	rate.	Although	a relatively	short	t ime	period	of	30November	2014	 	 B‐17 years	was	chosen	becau se	it	was	similar	to	the	life	span	of	a	b iofuels‐producing	facility,	a	discount rate	of	0%	was	chosen	“due	to	the	many	issues	associated	with	a pplying	an	economic	concept	to	a physical	parameter”	(p.	423).	Th is	is	primarily	because	the	Ene rgy	Independence	and	Security	Act (EISA)	of	2007	did	not	establish any	monetary	valuation	of	carb on	emissions	for	the	RFS2	program,
as	well	as	the	“lack	of	consensu s	as	to	the	appropriate	discoun t	rate	to	apply	to	GHG	lifecycle emissions	streams	through	tim e”	(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	dir ect	in	its	opposition	to	discou nting physical	emissions,	stating	that	“all	reviewers	noted	in	some	w ay	that	a	discount	rate	should	only be	applied	to	a	monetary	unit,	ra ther	than	a	physical	unit	such as	a	carbon	emission.”	Similarly, “proper	discounting	...	can	only be	conducted	on	value	(i.e.,	d amages,	not	physical	quantities	such	as emissions)”	(p.	B‐2)	and	“discoun t	rates	are	only	justifiable	w hen	applied	to	monetary	impacts,	not physical	impacts”	(p.	13).	Furthe r,	“economic	discounting	canno t	logically	be	appl ied	to	physical quantities	such	as	GHG	emissions,	only	to	economic	quantities	s uch	as	climate	change	damages”	(p. B‐4).	Similarly,	Martin	et	al.	(2011)	wrote	that	“in	the	absenc e	of	agreement	on...values,	discount rates	become	meaningless”	(p.	27)	and	that	when	considering	dis counting,	“a	prerequisite	is	to begin	with	a	monetized	value	to discount”	(p.	26).	Other	source s,	such	as	the	Interagency	Review	on Social	Cost	of	Carbon	(Interagen cy	Working	Group,	2010)	and	Joh nson	and	Hope	(2012),	do	not address	the	concept	of	discounti ng	physical	emissions	and	focus on	damages,	costs and	benefits,	or other	concepts	of	monetized	value.

Although	the	literature	is	gener ally	opposed	to	the	concept	of discounting	physical	emissions,	some
sources	do	discuss	related	instan ces	where	the	strategy	may	be applicable.	First, as	noted	by	a	few respondents	in	the	peer	review	report	mentioned	above	(EPA,	200 9),	discounting	physical emissions	may	be	appropriate	if these	emissions	are	used	as	a	d irect	proxy	for	damages. Discounting	is	“justifiable	if	p hysical	emissions	were	being	us ed	as	a	proxy	for	economic	damages associated	with	warming”	(p.	15)	and	only	in	this	case	are	disc ount	rates	used	for	physical	carbon units	“analogous	to	monetary discount	rates”	(p.	22).

A	number	of	recent	efforts	have	attempted	to	describe	a	time‐de pendent	damage	function	for emissions,	that	is,	efforts	to	l ink	emissions	to	atmospheric	co ncentrations	and	subsequently	to	the climatic	effects	(damag es)	of	increasing	concentrations.	This	a pproach	encompasses	more	than	a time	preference,	because	it	can	include	recognition	of	the	dyna mics	of	changing	marginal	damages over	time	(i.e.,	the	notion	that	the	climate	impact	of	one	ton of	CO 2 emissions	today	is	not	equal	to the	impact	of	one	ton	of	emissions in	the	future	because	of	fac tors	such	as	the	persistence	of	GHGs in	the	atmosphere,	options	for	mitigation,	or	damages	that	are a	function	of	the	total	level	of atmospheric	CO 2 at	the	time).	Whereas	traditiona l	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	increa sing	faster	than	the	rate	of	time preference	(see,	for	example, Richards,	1997).	As	characterized by	Marshall	(2009),	“Ideally,	a	GHG accounting	method	...	should	expli citly	analyze	the	expected	dama ge	associated	with	flows	over time.	The	corresponding	monetary units	associated	with	this	dam age	can	then	be	discounted	to determine	how	the	impacts	of	fut ure	flows	compar e	to	those	of	t he	present.”	Fargione	wrote	that	“ifNovember	2014	 	 B‐18 EPA	is	not	willing	to	make	assump tions	about	the	relationship	b etween	emissions	and	damages, then	they	should	not	use	any	dis counting”	(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	CO 2 emissions”)	or	GWPbio	(defined	by	Cherubini	et	al.	as	“the	eff ective	climate impact”)	in	efforts	to	describe	a	damage	cost	that	reflects	the time	path	of	CO 2 emissions.	Similarly, Kendall	et	al.	(2009)	propose	a	“ time	correction	factor”	to	“pr operly	account	for the	timing	of	... greenhouse	gas	emissions	in	the	b iofuels	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,	discount ing	marginal	damages	is	relate d	to	traditional	discounting	in	that it	makes	assumptions	about	changing	values	over	time,	but	in	th is	case,	the	“value”	is	expressed	in terms	of	the	imp act	on	climate.

Ultimately	at	least	three	factor s	enter	into	considering	the	ti me	dependence	of	the	value	of	carbon flows:	(1)	the	monetary	values	potentially	captured	in	cost‐ben efit	analyses	(as discussed	above); (2)	the	existence	of	irreversibil ities	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	significan t	determinants	of	th e	expected	damage
function	for	GHG	emissions	that	must	be	considered	in	determini ng	how	to	compare	current	to future	emissions,	and	is	one	of	the	most	convincing	arguments	f or	the	need	to	make	some	sort	of
distinction	between	current	and future	...	emissions.”	Kolstad	(1 994)	includes	the	investment capital	of	mitigation	measures	a s	an	irreversibility.	On	the	ro le	of	learning,	Kolstad	(1993)	notes	the role	of	uncertainty	in	the	relat ive	value	of	current	and	future emissions	and	concludes	that “accelerated	learning	tends	to	re duce	current	period	optimal	em issions.”	That	is,	rapid	reductions in	uncertainty	tend	to	reduce,	b ut	not	eliminate,	expenditures to	reduce	current	emissions	as uncertainty	is	being	resolved.	Dornburg	and	Marland	(2008)	rais e	many	of	these	issues	in	the context	of	the	value	of	temporar y	carbon	sequestration	or	of	de laying	emissions.

Uncertainty	becomes	a	dominant	f actor	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	recogni tion	of	the	importance	of	deali ng	with	the	time	value	of	CO 2 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	corr ect	relationship	between	emissions and	damages,	and	the	potentially	long	times	involved	in	conside ration	of	climate	change	impacts.	It is	clear	that	application	of	cons tant	discount	rates	is	not	app ropriate	over	long	time	periods	(e.g., intergenerational	times)	(see,	f or	example,	EPA, 2009;	Schellin g,	1995).	There	is	the	suggestion	that
for	consideration	of	l ong	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	trad itional	measures	of	global	warm ing	potential)	to	limit
consideration	of	effec ts	after	a	specific	period	of	time	implic itly	assumes	that	the	discount	rate increases	to	100%	and	that	impact s	after	that	time	are	not	coun ted	at	all.

Ultimately,	O’Hare	writes	(pers onal	communication,	2012),	“at	l east	in	the	short	and	medium	term, something	like	compound	discounting	at	a	rate	in	the	3–7%	range is	necessary	to	rational	decisionNovember	2014	 	 B‐19 making	about	any	actions	with	consequences	that	occur	in	the	fu ture.	This	discounting	must	be applied	to	something	like	the	so cial	cost	and	not	mere	quantiti es	of	discharge.”	Richards	(1997) suggested	that	“at	a	minimum,	carbon	discount	rates	should	be	t ested	for	values	equal	to	the	social discount	rate	and	zero.”	In	2009,	Richards	(in	EPA,	2009)	sugge sted	discount	rates	of	2%,	3%,	and 5%.	The	specific	discount	rate	c hosen	depends	on the	circumstan ces.	Although	nearly	all individuals	possess	a	ti me	preference,	the	strength	of	this	pre ference	can	vary	greatly	and	with	it the	corresponding	disco unt	rate.	In	the	rea lm	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	horiz ons	associated	with	climate	chan ge	and	climate	cha nge	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	res ponses	that	criticize	its	use	of	very low	discount	rates	illustrate	the	large	impact	of	discount	rate s	over	long	time	periods	(see Nordhaus,	2007;	Stern,	2006).

Note	that	the	decision	to	ignore time	is	in	effect	a	decision	t o	assume	that	the	va lue	of	emissions	is not	affected	by	the	time	path	of	emissions	and	that	the	appropr iate	discount	rate	is	0.	Marland	et	al. (2010),	in	the	context	of	the	car bon	stored	in	durable	wood	pro ducts,	showed	that	where discounting	of	carbon	flows	is	i mplemented,	it	is	very	importan t	to	represent	the	time	path	of	CO 2 emissions	as	accura tely	as	possible.

There	is	much	discussion	and	uncertainty	about	appropriate	rate s	for	compounded	discounting,	but at	the	same	time	there	is	a	widespread	consensus	that	the	time value	of	carbon	emissions	is important.	Specifically,	as	Richa rds	wrote	in	1997,	“the	time	v alue	of	carbon	is	an	important	issue that	requires	an	explicit	decisi on.”	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	biogeni c	feedstocks	for	energy	can	in some	circumstances	have	emission implications	extending	well	into the	future.	Questions	then	ari se	about	whether	and	how	to	value
emissions	fluxes	that	occur	over time	in	present	terms.	Althoug h	there	is	no	single ,	scientifically correct	treatment	of	time,	the	choice	of	treatment	may	have	sig nificant	impacts	on	the	results	of	an accounting	framework	application.	It	is	important	to	consider	p ossible	treatments	of	time	and	the implications	of	different	treatm ents	in	terms	of	the	respective strategies	chosen	for	long‐term	and short‐term	emission	accounting.

The	prevailing	view	in	the	techn ical	literature	is	that	there	i s	a	value	of	time	that	can	have important	ramifications	for	prosp ective	accounting	and	analysis ,	that	it	ought	to	be	considered explicitly,	and	that	time	prefer ence	is	traditionally	viewed	as related	only	to	monetary	or	other values	and	is	not	inherent	in	physical	measures	of	carbon	emiss ions.	Aside	from	certain	financial
transactions	where	there	is	an	e xplicit	discount	rate	(the	inte rest	rate),	it	can	be	difficult	to determine	an	appropriate	discount rate	for	any	given	circumstan ce,	including	accounting	for	GHG
emissions	over	time.	The	debate	c ontinues	about	how	to	value	(i .e.,	what	discount	rates	to	choose) when	evaluating	the	future	value	of	biogenic	CO 2 emissions,	where	the	impacts	on	the	global	carbon cycle	may	occur	over	very	long	pe riods	of	time	and	the	impact	o f	small	changes	in	d iscount	rate	canNovember	2014	 	 B‐20 be	very	large.	The	scientific	li terature	does	not	provide	guida nce	on	selecting	one	appropriate discount	rate	but	does	suggest	using	multiple	values	to	illustr ate	the	great	importance	of	time.

The	decision	on	how	to	treat	the	time	value	of	biogenic	CO 2 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	emissi ons	over	time	is	an	effective	d ecision	to	select	a	discount	rate	of	0. For	the	purposes	of	acco unting	for	biogenic	CO 2 emissions	from	stationary sources,	the	framework application	in	this	report	focus es	primarily	on	the	physical	fl ows	of	biogenic	CO 2 and,	in	the forward‐looking	context,	the	comparison	of	different	potential flows	across	alternative	future scenarios.	Applications	of	the	framework	could	incorporate	disc ount	rates	into	calculations	of	the biogenic	assessment	fact or	as	appropriate	fo r	that	specific	app lication.



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