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Integrating discrete-return scanning LiDAR and spaceborne RADAR to support aboveground biomass assessments Tsui, Olivier W. L. 2013

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  INTEGRATING	DISCRETE‐RETURN	SCANNING	LIDAR	AND SPACEBORNE	RADAR	TO	SUPPORT	ABOVEGROUND	BIOMASS ASSESSMENTS   by  Olivier	W.L.	Tsui    B.Sc.,	McGill	University,	2000      A	THESIS	SUBMITTED	IN	PARTIAL	FULFILLMENT	OF THE	REQUIREMENT	FOR	THE	DEGREE	OF  MASTER	OF	SCIENCE in The	Faculty	of	Graduate	Studies (Forestry)      The	University	of	British	Columbia (Vancouver) March	2013 ©	Olivier	W	L	Tsui	2013  Abstract Forests	 are	 considered	 important	 reservoirs	 of	 organic	 carbon	 and	 have	 been	 identified	 as essential	in	moderating	climate	change.	Measuring	the	amount	of	carbon	stored	in	forests	helps improve	 our	 understanding	 of	 the	 carbon	 budget	 and	 help	 with	 climate	 change	 adaptation strategies.	 Therefore,	 effective	 and	 accurate	 methods	 in	 characterizing	 changing	 forest	 cover and	biomass	densities	are	needed. Both	LiDAR	(light	detection	and	ranging)	and	radar	(radio	detection	and	ranging)	technologies can	contribute	towards	the	study	of	forest	biomass	but	one	sensor	alone	cannot	provide	all	the information	necessary	to	monitor	forests.	Understanding	and	investigating	synergies	between different	 remotely	 sensed	 data	 sets	 provides	 new	 and	 innovative	 opportunities	 to	 monitor forests. The	overall	objective	reported	in	this	thesis	is	to	demonstrate	novel	methods	to	integrate	two remotely	sensed	data	sets	(i.e.,	radar	and	LiDAR)	for	the	application	of	biomass	estimation.	This research	 was	 divided	 into	 two	 main	 questions:	 (1)	 can	 shorter	 wavelength	 radar	 variables provide	improved	biomass	estimates	when	combined	with	LiDAR	data;	and	(2)	can	the	use	of space‐borne	 radar	 extend	 aboveground	 biomass	 estimates	 over	 a	 larger	 area	 using	 spatial modeling	methods. In	 the	 first	 study,	 relationships	 between	 biomass	 and	 biomass	 components	 with	 LiDAR	 and radar	 data	 were	 examined	 through	 regression	 analyses	 to	 determine	 the	 best	 combined parameters	to	estimate	biomass.	Results	indicated	that	integrating	radar	variables	to	a	LiDAR‐ derived	model	of	aboveground	biomass	helped	explain	an	additional	17.9%	of	the	variability	in crown	 biomass.	 This	 corresponded	 in	 an	 improvement	 in	 crown	 biomass	 estimates	 of	 10%  ii  RMSE.	Furthermore,	InSAR	coherence	magnitudes	from	C‐band	and	L‐band	radars	provided	the best	estimate	of	aboveground	biomass	using	radar	alone. In	 the	 second	 study,	 aboveground	 biomass	 transects	 derived	 from	 plot‐based	 field	 data	 and LiDAR,	 and	 wall‐to‐wall	 radar	 were	 spatially	 integrated	 using	 three	 kriging	 techniques.	 The results	indicated	the	importance	of	correlation	between	primary	and	secondary	variables	when using	these	kriging	approaches.	Also	a	1000	m	distance	between	biomass	transects,	was	found to	provide	reasonable	compromise	between	ease	of	use,	accuracy,	and	cost	of	obtaining	LiDAR data	 for	 the	 study	 area.	 Insights	 into	 other	 opportunities	 for	 further	 development	 in	 spatial modeling	techniques	are	discussed.     iii  Preface This	 thesis	 is	 the	 combination	 of	 two	 scientific	 papers	 of	 which	 I	 am	 the	 lead	 author.	 The structure	 and	 design	 of	 the	 project	 developed	 over	 time	 with	 guidance	 from	 Dr.	 Nicholas	 C. Coops,	 Dr.	 Michael	 A.	 Wulder,	 and	 Dr.	 Peter	 L.	 Marshall	 with	 the	 purpose	 of	 investigating methods	 to	 integrate	 different	 active	 remote	 sensing	 technologies	 for	 aboveground	 biomass assessments.  For	 both	 scientific	 journal	 submissions,	 I	 performed	 the	 primary	 research	 including	 data collection,	 data	 analysis,	 and	 interpretation	 of	 results	 and	 prepared	 the	 final	 manuscripts.	 	 A portion	of	the	data	analyzed	was	compiled	from	pre‐existing	sources	collected	by	Dr.	Nicholas C.	Coops	and	Dr.	Thomas	Hilker.		Overall	project	oversight,	advice	on	methodology	and	editorial comments	were	provided	by	Dr.	Nicholas	C.	Coops.		Dr.	Michael	A.	Wulder	provided	guidance	in forestry	 principles	 and	 on	 LiDAR	 technology	 and	 background	 as	 well	 as	 invaluable	 editorial comments.	Dr.	Peter	L.	Marshall	provided	suggestions	and	comments	on	statistical	analyses	and also	invaluable	editorial	comments.	Mr.	Adrian	McCardle	completed	all	InSAR	processing	for	the first	scientific	publication.	Mr.	Grant	Bruce	provided	suggestions	and	editorial	comments.  Publications	 arising	 from	 this	 thesis	 include	 (reprinted	 with	 the	 permission	 from	 the publishers):    Chapter	3:		Tsui,	O.W.,	Coops,	N.C.,	Wulder,	M.A.,	Marshall,	P.L.,	and	McCardle,	A.,	2012. Using	 multi‐frequency	 radar	 and	 discrete‐return	 LiDAR	 measurements	 to	 estimate aboveground	 biomass	 and	 biomass	 components	 in	 a	 coastal	 temperate	 forest.	 ISPRS Journal	of	Photogrammetry	and	Remote	Sensing	69,	121–133.    iv    Chapter	4:		Tsui,	O.W.,	Coops,	N.C.,	Wulder,	M.A.,	and	Marshall,	P.L.,	2013.		Integrating airborne	 LiDAR	 and	 space‐borne	 radar	 via	 multivariate	 kriging	 to	 estimate aboveground	biomass.	Remote	Sensing	of	Environment.	(submitted)        v  Table	of	Contents Abstract	..............................................................................................................................................................	ii Preface	...............................................................................................................................................................	iv Table	of	Contents	...........................................................................................................................................	vi List	of	Tables	................................................................................................................................................	viii List	of	Figures	..................................................................................................................................................	ix Glossary	............................................................................................................................................................	xi Acknowledgements	.....................................................................................................................................	xii Dedication	.....................................................................................................................................................	xiii 1. 	 INTRODUCTION	......................................................................................................................................	1  1.1 1.2 1.3 1.4 1.5  Terrestrial	Carbon	Cycle	.......................................................................................................................	1 Climate	Mitigation	....................................................................................................................................	1 Forest	Biomass	Estimation	..................................................................................................................	5 Data	Integration	.......................................................................................................................................	10 Research	Objectives	...............................................................................................................................	12  2. 	 STUDY	AREA	AND	DATA	SOURCES	................................................................................................	15  2.1 2.2  Site	Description	.............................................................................................................................	15 Data	Descriptions	.........................................................................................................................	16 2.2.1	 Plot	selection	and	inventory	measurements	.....................................................................................	16 2.2.2	 Radar	data	........................................................................................................................................................	17 2.2.3	 Airborne	LiDAR	data	....................................................................................................................................	20  3. 	 RADAR	AND	LIDAR	OBSERVATIONS	TO	ESTIMATE	ABOVEGROUND	BIOMASS	AND BIOMASS	COMPONENTS		...........................................................................................................................	22  3.1  Introduction	....................................................................................................................................	22 3.1.1	 Radar	remote	sensing	background	........................................................................................................	24 3.2	 Material	and	Methods	.................................................................................................................	25 3.2.1	 Study	site	............................................................................................................................................................	25 3.2.2	 Field	based	biomass	estimates	.................................................................................................................	25 3.2.3	 LiDAR	pre‐processing	...................................................................................................................................	26 3.2.4	 Radar	data	pre‐processing	........................................................................................................................	27 3.2.5	 Polarimetric	processing	..............................................................................................................................	28 3.2.6	 InSAR	processing	............................................................................................................................................	29 3.2.7	 Statistical	analysis	.........................................................................................................................................	29 3.3	 Results	...............................................................................................................................................	30 3.3.1	 Biomass	estimates	.........................................................................................................................................	30 3.3.2	 Regression	models	.........................................................................................................................................	31 vi  3.4  Discussion	........................................................................................................................................	40 3.4.1	 LiDAR	...................................................................................................................................................................	40 3.4.2	 Multi‐frequency	radar	.................................................................................................................................	40 3.4.3	 LiDAR	and	radar	integration	...................................................................................................................	42  4. 	 EVALUATING	MULTIVARIATE	KRIGING	TO	ESTIMATE	AND	MAP	ABOVEGROUND BIOMASS.		.......................................................................................................................................................	44  4.1  Introduction	....................................................................................................................................	44 4.1.1	 Geostatistics	......................................................................................................................................................	46 4.2	 Materials	and	Methods	..............................................................................................................	49 4.2.1	 Study	site	............................................................................................................................................................	49 4.2.2	 Data	description	.............................................................................................................................................	49 4.2.2.1	 Biomass	map	.....................................................................................................................................................	49 4.2.2.2	 Radar	data	..........................................................................................................................................................	50 4.2.3	 Aboveground	biomass	sampling	.............................................................................................................	51 4.2.4	 Biomass	modeling	..........................................................................................................................................	52 4.2.5	 Model	evaluation	............................................................................................................................................	55 4.3	 Results	...............................................................................................................................................	55 4.3.1	 Biomass	estimates	.........................................................................................................................................	58 4.3.2	 Biomass	mapping	models	...........................................................................................................................	62 4.4	 Discussion	........................................................................................................................................	63 4.4.1	 Future	considerations	..................................................................................................................................	64 4.4.2	 LiDAR	sampling	framework	......................................................................................................................	65 5. 	 CONCLUSION	.........................................................................................................................................	68  5.1 5.2 5.3  Key	Findings	...................................................................................................................................	69 Limitations	of	Study	....................................................................................................................	71 Future	Research	............................................................................................................................	72  REFERENCES	..................................................................................................................................................	74       vii  List	of	Tables Table	1.1		Benefits	and	limitations	of	airborne	LiDAR	and	spaceborne	SAR	in	estimating	forest biomass.	...................................................................................................................................................................	10 Table	1.2		Sample	studies	in	radar	and	LiDAR	for	forest	characterization,	including	AGB estimation,	and	their	key	research	findings..............................................................................................	11 Table	2.1		Summary	of	field	site	characteristics,	field	measurements,	and	derived	structural metrics	per	30	m	x	30	m	plot.	.........................................................................................................................	18 Table	2.2		Radar	data	sets	in	terms	of	products	type,	acquisition	dates	and	image	configurations. Complex	pairs	used	to	calculate	InSAR	coherence	are	denoted	by	*	and	†.	................................	20 Table	3.1		Summary	of	plot‐level	metrics	calculated	from	LiDAR	data	for	selected	plots representing	various	age	and	structural	classes.	...................................................................................	27 Table	3.2		LiDAR	biomass	models	developed	from	field‐measurements	and	LiDAR	canopy	height and	cover	metrics.	................................................................................................................................................	32 Table	3.3		Adjusted	R‐squared	values	from	linear	regression	of	forest	biomass	and	individual	L‐ and	C‐band	radar	variables.	Most	significantly	correlated	radar	variables	are	represented with	a	*.	....................................................................................................................................................................	33 Table	3.4		All	subsets	regression	biomass	models	developed	from	L‐	and	C‐band	radar	variables. 	.....................................................................................................................................................................................	36 Table	3.5		Final	biomass	models	developed	from	integrating	LiDAR	and	C‐band	radar	for aboveground,	stem	and	crown	biomass.		Significant	variables,	adjusted	R2,	RMSE	and relative	RMSE	are	shown	for	each	biomass	model.	...............................................................................	38 Table	4.1		Calculated	model	semivariograms	and	cross‐semivariogram	used	in	spatial predictions	for	each	variable	for	the	1000m	sampling	interval.	......................................................	56 Table	4.2		Evaluation	of	global	accuracy	for	co‐kriging,	regression	kriging,	and	regression	co‐ kriging	based	on	the	validation	dataset.	.....................................................................................................	58     viii  List	of	Figures Figure	2.1		Overview	of	the	Oyster	River	study	site	and	field	plot	locations.	.......................................	16 Figure	2.2		L‐	and	C‐band	colour	composites	of	the	Oyster	River	study	site.	Red,	green,	and	blue are	used	for	coding	HH,	HV	and	a	ratio	of	HH	and	HV	polarizations,	for	the	L‐band	image, and	for	coding	HH,	HV,	and	VV	for	the	C‐band	image.		The	images	cover	approximately	8 km	by	8	km	with	azimuth	direction	south	to	north	with	the	look	direction	towards	the	right (east).	........................................................................................................................................................................	20 Figure	3.1		Calculated	aboveground	biomass	(Mg	ha‐1)	and	individual	biomass	components	per plot	as	derived	by	species	specific	allometric	equations	published	by	Ung	et	al.	(2008).	.....	31 Figure	3.2		Comparison	of	adjusted	R2	values	for	the	LiDAR‐only,	LiDAR	+	C‐band,	and	LiDAR	+ L‐band	models.		LiDAR	+	C‐band	HH	backscatter	showed	the	best	adjusted	R2	for	stem	and total	biomass,	and	LiDAR	+	C‐band	entropy	showed	the	best	adjusted	R2	for	crown biomass.		LiDAR	+	L‐band	HV	coherence	showed	the	best	adjusted	R2	for	both	total	and component	biomass.	...........................................................................................................................................	37 Figure	3.3		Comparison	of	predicted	and	observed	aboveground	biomass	for	all	final	C‐	and	L‐ band	radar,	LiDAR,	and	LiDAR	+	C‐band	derived	models.	..................................................................	39 Figure	4.1		Location	of	study	site	and	aboveground	biomass	values	estimated	by	discrete‐return LiDAR.	.......................................................................................................................................................................	50 Figure	4.2		Sampling	strategies	tested	and	data	volumes	for	each	sample	forest	biomass	data set:	(a)	2000	m,	(b)	1000	m,	(c)	500m,	and	(d)	validation	points.		Shaded	grey	area represents	the	extent	of	the	reference	LiDAR	derived	aboveground	biomass	data	set.	........	52 Figure	4.3		Image	lattices	showing	characteristics	of	the	experimental	design	for	multivariate kriging.		Aboveground	biomass	transects	simulate	airborne	profiling	LiDAR	flight	lines	at 1000	m	intervals.	.................................................................................................................................................	54 Figure	4.4		Experimental	(black	points)	and	model	(black	line)	semivariograms	for	(a). aboveground	biomass,	(b)	radar	co‐variable,	(c)	cross‐semivariogram,	and	(d)	OLS residuals	for	the	1000m	sampling	interval.	..............................................................................................	57 Figure	4.5		Histograms	of	estimated	aboveground	biomass	values	(shaded	in	black)	for	all sampling	strategies	tested.	1.	co‐kriging	(a,b,c);	2.	regression	kriging	(a,b,c);	and	3. regression	co‐kriging	(a,b,c).		Histogram	of	reference	biomass	values	provided	as	reference (shaded	in	grey,	N=	80,025).	...........................................................................................................................	60 Figure	4.6		Scatterplots	of	estimated	vs.	observed	aboveground	biomass	values	for	all	sampling strategies	tested.	1.	co‐kriging	(a,b,c);	2.	regression	kriging	(a,b,c);	and	3.	regression	co‐ kriging	(a,b,c).		Pearson’s	correlation	coefficient	provided	for	each	sampling	strategy.  ix  Scatterplots	represent	accuracy	of	estimated	values	based	on	validation	points	(N	=	580). 	.....................................................................................................................................................................................	61 Figure	4.7		Violin	plot	showing	the	interquartile	range	(mid‐spread)	of	residuals	in	predicted biomass	for	all	sampling	strategies	tested.	OCK	‐	Ordinary	Co‐kriging;	RK	–	Regression kriging;	and	RCK	–	Regression	co‐kriging.	................................................................................................	62 Figure	4.8		Estimated	aboveground	biomass	maps	using	1.	co‐kriging	(a,b,c);	2.	regression kriging	(a,b,c);	and	3.	regression	co‐kriging	(a,b,c)	for	all	sampling	strategies	tested.	..........	63      x  Glossary Alpha: A	decomposition	variable	that	provides	the	dominant	scattering	mechanism	of	the	microwave pulse. Backscatter: The	 amount	 of	 energy	 returned	 to	 the	 radar	 sensor	 following	 an	 interaction	 (e.g.	 scattering) with	a	ground	target. Coherence: Parameter	that	describes	the	relative	difference	in	oscillation	between	two	microwave	pulses. In	other	words,	measures	the	degree	of	correlation	between	two	microwaves. Entropy: A	decomposition	variable	that	provides	a	measure	of	the	randomness	in	the	scattering	recorded by	the	radar	sensor. InSAR: Interferometric	 synthetic	 aperture	 radar	 (InSAR)	 is	 a	 radar	 processing	 technique	 to	 generate maps	of	surface	deformation	and	elevations	using	two	or	more	radar	images. LiDAR: Light	 Detecting	 and	 Ranging,	 an	 active	 optical	 remote	 sensing	 technology	 that	 measures	 the distance	to	targets	through	emitted	near	infra‐red	light	pulses. Polarimetry: The	measurement	and	interpretation	of	polarization	of	transverse	waves	(e.g.	microwaves). Polarization	(HH,	HV,	VV): Orientation	and	alignment	of	the	microwave	pulse	in	a	plane	perpendicular	to	the	direction	of propagation.	Radars	can	emit	microwaves	that	are	horizontally	oriented	or	vertically	oriented and	receive	the	same	or	different	orientation. Pol‐InSAR: Polarimetric	 interferometric	 SAR,	 is	 the	 processing	 of	 InSAR	 using	 radar	 data	 that	 is	 fully polarimetric	(e.g.	contains	all	information	on	the	polarization	of	the	microwave). Radar	bands: Categories	that	classify	the	microwave	portion	of	the	electromagnetic	spectrum	based	on	their frequency	or	wavelength	are	called	bands.	Most	common	spaceborne	remote	sensing	bands	are X‐,	C‐,	and	L‐band. RADAR: Radio	 Detecting	 and	 Ranging,	 an	 active	 microwave	 remote	 sensing	 technology	 that	 maps	 the electromagnetic	 scattering	 coefficient	 onto	 a	 2‐dimensional	 plane.	 Synthetic	 aperture	 RADAR (SAR)	is	similar	but	mainly	spaceborne	and	simulates	an	extremely	large	 antenna	to	generate high	resolution	images.   xi  Acknowledgements This	 research	 was	 undertaken	 with	 funding	 from	 the	 National	 Sciences	 and	 Engineering Research	Council	of	Canada	(NSERC)	Engage	Grant,	a	Discovery	grant	to	Dr.	Nicholas	C.	Coops, and	 Hatfield	 Consultants	 Partnership.	 All	 RADARSAT‐2	 data	 were	 provided	 through	 the Canadian	 Space	 Agency’s	 RADARSAT‐2	 Science	 and	 Operational	 Applications	 Research Education	Initiative	(SOAR‐E).	I	thank	Dr.	Andrew	Black	and	the	BIOMET	members	for	allowing us	access	to	the	FLUXNET‐Canada	site.	I	also	thank	the	forest	companies	Timberwest	and	Island Timberlands	 for	 providing	 their	 forest	 inventories	 and	 allowing	 access	 to	 their	 private	 lands. Furthermore	I	would	like	to	thank	Colin	Ferster,	Jean‐Simon	Michaud,	and	Martin	van	Leeuwen for	their	help	collecting	field	data,	and	to	3V	Geomatics	for	InSAR	processing	of	all	radar	data.  Special	thanks	to	my	supervisor,	Dr.	Nicholas	C.	Coops,	who	provided	his	time	and	a	great	deal of	patience	during	my	degree.		I	thank	each	of	the	committee	members,	Dr.	Michael	A.	Wulder, Dr.	Peter	L.	Marshall,	and	Mr.	Grant	Bruce	for	their	support	and	insight.	I	am	also	grateful	to	all partners	 at	 Hatfield	 Consultants	 for	 their	 encouragement	 and	 support	 throughout	 my	 degree. Lastly,	I	also	would	like	to	acknowledge	all	member	of	the	IRSS	lab,	past	and	present,	for	openly offering	their	knowledge,	support,	and	company.       xii  Dedication  To	my	family	and	friends	for	their	words	of encouragement,	and	to	Wanda	for her	love	and	support.   xiii  1. INTRODUCTION 1.1 Terrestrial	Carbon	Cycle The	 complex	 biogeochemical	 processes	 through	 which	 carbon	 is	 exchanged	 between	 the biosphere,	 geosphere,	 atmosphere,	 and	 hydrosphere	 is	 known	 as	 the	 global	 carbon	 cycle (Schlesinger	 and	 Andrews,	 2000).	 The	 exchange	 between	 atmospheric	 gasses	 and	 the terrestrial	biosphere	occurs	through	 carbon	uptake	by	vegetation	and	through	carbon	release by	 plant	 respiration,	 soil	 respiration,	 and	 land	 disturbance	 processes	 (Prentice	 et	 al.,	 2001). Plants	 convert	 carbon	 dioxide	 to	 organic	 carbon	 by	 absorbing	 solar	 radiation	 through	 the process	of	photosynthesis.	This	carbon	storage	in	the	form	of	vegetation	biomass,	accounts	for half	 of	 the	 living	 mass	 of	 terrestrial	 vegetation	 (Johnson	 and	 Sharpe,	 1983);	 therefore,	 forests are	 considered	 a	 large	 reservoir	 of	 carbon	 (Dixon	 et	 al.,	 1994).	 Current	 global	 forest	 carbon stocks	are	estimated	at	861	±	66Pg	C	(Pan	et	al.,	2011).	As	a	whole,	terrestrial	carbon	sinks	may be	 responsible	 for	 the	 uptake	 of	 one	 third	 of	 all	 carbon	 dioxide	 emissions	 released	 by anthropogenic	activities	(i.e.,	fossil	fuels	and	land	use	change)	into	the	atmosphere	(Canadell	et al.,	 2007).	 In	 contrast	 to	 other	 carbon	 pools	 (i.e.,	 soil	 carbon),	 forests	 can	 be	 more	 easily characterized	and	monitored	through	various	methods,	such	as	remote	observations	and	field inventories.	 Consequently,	 loss	 and	 gain	 dynamics	 in	 forest	 carbon	 can	 be	 quantified	 and	 the impacts	of	various	forest	land	management	approaches	on	carbon	storage	assessed.	Measuring the	 amount	 of	 carbon	 stored	 in	 forests	 can	 play	 an	 important	 role	 in	 improving	 our understanding	of	the	carbon	budget	and	help	with	strategies	aimed	at	mitigating	climate	change (Song,	2012).  1.2 Climate	Mitigation Due	to	increasing	CO2	levels	we	are	in	a	period	of	rapid	climate	change	(Peters	et	al.,	2013).	The impacts	 of	 climate	 change	 on	 many	 natural	 systems,	 such	 as	 increase	 shifts	 in	 species’  1  geographical	 ranges,	 increase	 wildfire	 risks,	 decrease	 water	 availability,	 etc.,	 are	 documented and	 reported	 by	 the	 Intergovernmental	 Panel	 on	 Climate	 Change	 (IPCC)	 (IPCC,	 2007). Atmospheric	concentration	of	greenhouse	gasses	(GHGs)	such	as	CO2	and	modified	land	cover are	key	drivers	of	these	changes	(Pan	et	al.,	2011;	Peters	et	al.,	2013).	Numerous	studies	have investigated	 the	 potential	 impacts	 and	 vulnerabilities	 of	 climate	 change	 on	 physical	 and biological	processes	(Bellard	et	al.,	2012;	Coops	and	Waring,	2011;	Parmesan	and	Yohe,	2003; Zhu	 et	 al.,	 2012).	 Impacts	 on	 forest	 vegetation	 from	 changing	 climate	 will	 increasingly	 affect forest	 ecosystems	 processes	 (Metsaranta	 et	 al.,	 2011),	 with	 gradual	 increases	 in	 temperature, changes	in	rainfall	patterns	or	modification	of	atmospheric	conditions	such	as	cloud	cover,	will also	likely	impact	vegetation	growth,	regeneration	and	natural	rates	of	mortality	(Chapin	et	al., 2010). A	 reduction	 in	 the	 rate	 of	 carbon	 accumulation	 in	 the	 atmosphere	 is	 required	 to	 mitigate climate	 change.	 This	 can	 be	 achieved	 through	 a	 decrease	 in	 GHG	 emissions	 generated	 from burning	of	fossil	fuels	and	by	increasing	the	net	uptake	(or	reducing	the	net	loss)	of	carbon	in terrestrial	 ecosystems	 (Kurz	 and	 Apps,	 2006).	 Information	 on	 the	 vertical	 and	 horizontal characteristics	 of	 forests	 is	 therefore	 increasingly	 important.	 Due	 in	 part	 to	 global	 initiatives, such	 as	 the	 UNFCCC	 (United	 Nations	 Framework	 Convention	 on	 Climate	 Change) (UNFCC,	2007),	and	international	reporting	obligations,	that	are	aimed	at	better	understanding global	GHG	sources	and	sinks,	detailed	information	on	forested	land	and	the	impacts	of	human activities	are	being	collected	that	will	facilitate	better	understanding	of	changes	in	forest	carbon stock. In	 Canada,	 forest	 carbon	 stock	 and	 its	 change	 are	 assessed	 through	 initiatives	 such	 as	 the national	 forest	 carbon	 monitoring	 accounting	 and	 reporting	 system	 (Kurz	 et	 al.,	 2009).	 This carbon	 accounting	 system	 integrates,	 at	 different	 temporal	 and	 spatial	 scales,	 information	 on  2  land	 use	 change,	 statistics	 on	 disturbance	 events,	 growth	 and	 yield	 information,	 and	 detailed forest	 inventory	 data,	 into	 a	 modeling	 framework	 (i.e.	 Carbon	 Budget	 Model	 of	 the	 Canadian Forest	Sector	‐	CBM‐CFS3)	to	estimate	carbon	stock	and	changes	in	carbon	(Kurz	et	al.,	2009). However,	in	contrast	to	countries	with	established	forest	inventories	and	monitoring	programs, such	 as	 Canada,	 many	 non‐annex	 I	 countries	 (i.e.,	 developing	 countries),	 have	 large	 forested areas	 that	 are	 not	 well	 characterized	 because	 of	 a	 lack	 of	 consistent	 and	 uniform	 systematic forest	 inventories	 (an	 important	 component	 for	 an	 operational	 measurement,	 reporting,	 and verification	(MRV)	system)(Grainger	and	Obersteiner,	2011). Under	 the	 UNFCCC,	 discussions	 are	 in	 progress	 to	 develop	 a	 mitigation	 strategy	 to	 reduce emissions	 from	 deforestation	 and	 forest	 degradation	 (REDD),	 and	 promote	 the	 role	 of conservation,	 sustainable	 management	 of	 forests	 and	 enhancement	 of	 forest	 carbon	 stocks	 in developing	 countries	 (REDD+).	 While	 the	 initial	 aim	 for	 REDD	 was	 to	 slow,	 halt,	 or	 reverse forest	 cover	 and	 carbon	 loss	 by	 placing	 monetary	 value	 on	 the	 amount	 of	 carbon	 stored	 in forest	 land	 (Pistorius,	 2012;	 Tacconi	 et	 al.,	 2010;	 van	 de	 Sand,	 2012),	 REDD+	 aims	 to	 also promote	 enhancement	 of	 carbon	 storage	 and	 conservation	 by	 including	 a	 wider	 range	 of stakeholders	 (Campbell,	 2009;	 Romijn	 et	 al.,	 2012).	 REDD+	 implementation	 is	 available	 to national	or	local	governments,	non‐governmental	organizations	(NGOs	–	CARE,	WWF),	and	the private	sector	who	are	interested	in	offsetting	their	carbon	footprint.	Through	the	retention	of carbon,	and	thus	the	avoidance	of	emissions	from	deforestation,	carbon	credits	produced	can	be traded	 on	 voluntary	 carbon	 markets	 (Corbera	 et	 al.,	 2009;	 Kimberly	 and	 Curran,	 2009;	 Miles and	Kapos,	2008). These	performance‐related	payment	schemes	for	environmental	services	(PES)	are	only	likely to	work	if	the	value	of	the	environmental	services	exceeds	opportunity	costs	of	the	land	holders (Campbell,	2009).	In	other	words,	if	it	is	financially	justifiable	to	diverge	from	business	as	usual  3  scenarios.	 While	 recognizing	 the	 limitations,	 problems,	 and	 current	 discussions	 on	 the effectiveness	associated	 with	placing	a	value	on	forests	and	their	carbon	 alone	(Kimberly	and Curran,	2009),	a	price	for	an	area	of	forest	can	only	be	assessed	if	the	carbon	stock	of	an	area can	be	accurately	determined	with	known	error.	In	order	to	determine	forest	carbon	stocks	per unit	area,	spatially	explicit	data	on	aboveground	biomass	are	important.	Guidelines	released	by the	 IPCC	 provide	 three	 tiers	 for	 carbon	 emission	 reporting,	 with	 Tier	 1	 having	 the	 highest uncertainty	 but	 being	 the	 easiest	 to	 implement	 and	 Tier	 2	 and	 Tier	 3	 having	 the	 lowest uncertainty	 but	 most	 difficult	 to	 implement.	 Recommendations	 are	 for	 higher	 tiers;	 however, higher	 tier	 methods	 require	 more	 data	 and	 are	 more	 expensive,	 because	 they	 involve monitoring	of	local	variables,	such	as	aboveground	biomass	and	carbon	stock	changes	(Romijn et	al.,	2012). Although	emission	reduction	activities	in	Canada	are	not	eligible	under	the	REDD+	framework, there	 are	 a	 number	 of	 voluntary	 carbon	 offset	 programs	 and	 protocols	 that	 have	 been developed	for	Annex	I	countries	(Ristea	and	Maness,	2009).	For	example,	the	Emission	Offsets Regulation	(British	Columbia,	2008)	and	the	Forest	Carbon	Offset	Protocol	of	British	Columbia (British	 Columbia,	2011)	 were	 designed	 to	 help	 guide,	 design,	 quantify,	 and	 verify	 carbon offsets	 projects	 on	 private	 and	 public	 land.	 In	 Canada,	 forested	 land	 are	 primarily	 owned	 and managed	 by	 the	 crown;	 therefore,	 provincial	 governments	 have	 the	 mandate	 to	 sustainably manage	 forest	 resources	 and	 promote	 a	 broader	 range	 of	 non‐timber	 services.	 Furthermore, sound	management	practices	are	driven	not	only	by	economic	evaluation	of	forests	but	social perception,	in	other	words	the	value	of	forests	for	non‐timber	values	(Harshaw	et	al.,	2009).	As a	 result,	 a	 wide	 spectrum	 of	 stakeholders,	 from	 regional	 to	 local	 governments,	 private	 sector entrepreneurs,	 conservation	 agencies,	 and	 First	 Nations,	 are	 interested	 in	 forest	 carbon	 offset projects	(Greig	and	Bull,	2011).		With	such	a	wide	range	of	stakeholders,	new	technologies	and innovative	methods	to	estimate	biomass	accurately	are	important.  4  1.3 Forest	Biomass	Estimation Components	 of	 forest	 biomass	 include	 aboveground	 (AGB)	 and	 belowground	 biomass	 (BGB). AGB	 consists	 of	 all	 living	 material	 above	 the	 soil,	 including	 stem,	 trunk,	 branches,	 bark,	 and foliage;	and	BGB	consists	of	all	live	roots	greater	than	2mm	in	diameter	(Penman	et	al.,	2003). Although	it	is	recognized	that	BGB	is	an	important	component	in	determining	the	entire	forest carbon	stock,	for	simplicity	the	term	biomass	will	refer	to	AGB	for	the	remainder	of	this	thesis. Accurate	estimates	of	biomass	play	an	important	role	in	understanding	the	carbon	cycle.	Direct measurements	 of	 AGB	 require	 destructive	 sampling	 of	 trees	 (i.e.,	 harvesting	 of	 trees,	 oven‐ drying	all	components,	and	then	weighing	them)	(Brown,	1997).	Given	the	inefficiency	of	this method,	a	more	practical	approach	in	estimating	biomass	is	to	use	allometric	equations,	which are	developed	from	destructive	harvesting,	and	relating	the	mass	of	foliage,	branches,	bark	and trunks	 to	 direct	 structural	 measurements,	 such	 as	 diameter	 at	 breast	 height	 (DBH)	 and	 tree height	 (Lambert	 et	 al.,	 2005).	 Information	 on	 forest	 and	 structural	 characteristics	 are	 often obtained	 by	 statistical	 sampling	 and	 the	 use	 of	 ground	 plots,	 which	 form	 the	 basis	 for	 forest inventories	(Kangas	et	al.,	2006).		Air	photos	are	also	commonly	used	to	aid	forest	inventories by	identifying	and	mapping	homogeneous	units	based	on	relevant	forest	attributes	such	as	age, species	composition,	volume,	and	stand	structure	(Gillis	and	Leckie,	1993).	However,	obtaining comprehensive,	spatially	complete,	and	accurate	forest	inventory	data	is	usually	costly,	labour intensive,	 and	 limited	 to	 smaller	 areas	 (Kangas	 et	 al.,	 2006).	 Remotely‐sensed	 data	 acquired from	 satellite	 or	 aerial	 platforms	 has	 provided	 a	 practical	 and	 economical	 means	 to	 measure and	monitor	vegetation	cover	and	structure,	especially	over	large	areas	(Xie	et	al.,	2008). Optical	 remote	 sensing	 data	 are	 commonly	 used	 for	 land	 cover	 mapping,	 capture	 of	 change, empirical	 estimates	 of	 structural	 attributes,	 and	 to	 provide	 strata	 for	 statistical	 attribute estimation.	The	estimation	of	biomass	with	optical	data	is	also	well	established;	see	Lutz	et	al.  5  (2008)	 for	 a	 review.	 However,	 direct	 biomass	 estimates	 at	 the	 landscape	 and/or	 the	 regional level	 still	 pose	 some	 challenges	 (Gibbs	 et	 al.,	 2007).	 Optical	 remote	 sensing	 data	 provides limited	 information	 on	 the	 vertical	 distribution	 of	 forest	 structure	 (Wulder,	 1998).	 Typically, once	crown	closure	is	reached	there	is	little	spectral	difference	between	stands	with	increasing structural	complexity	and,	as	a	result,	estimates	of	biomass,	leaf	area,	and	volume	derived	from optical	 imagery	 tend	 to	 reach	 an	 asymptote	 (i.e.,	 signal	 saturation	 level),	 whereby	 further increases	in	biomass	are	not	detectable	(Duncanson	et	al.,	2010).	While	experimental	trials	over smaller	areas	can	show	greater	range	(Song,	2012),	mapping	small	differences	at	high	biomass levels	 with	 optical	 sensors	 is	 difficult	 and	 have	 not	 proven	 to	 be	 consistent	 over	 large	 areas (Goetz	 et	 al.,	 2009).	 Furthermore,	 the	 presence	 of	 clouds,	 shadows,	 and	 haze	 can	 impact	 the quality	 and	 completeness	 of	 optical	 data,	 especially	 in	 tropical	 areas	 (Roy	 et	 al.,	 2010). However,	 new	 means	 of	 optical	 image	 processing	 are	 providing	 novel	 opportunities	 for composting	 that	 may	 mitigate	 the	 negative	 impacts	 of	 cloud	 cover	 (Hansen	 and	 Loveland, 2012). A	 number	 of	 remote	 sensing	 technologies	 that	 have	 experienced	 a	 great	 deal	 of	 scientific	 and operational	 attention	 in	 the	 last	 few	 years	 for	 forest	 biomass	 estimation	 include	 radar	 based approaches	including	space‐borne	synthetic	aperture	radar	(SAR)	(Santoro	et	al.,	2011;	Thiel	et al.,	2009),	and	interferometric	SAR	(InSAR)	(Simard	et	al.,	2006),	and	LiDAR	(light	detection	and ranging)	(Næsset	et	al.,	2011).	Unlike	optical	sensors,	which	passively	record	reflected	energy, active	 system	 supply	 their	 own	 energy	 and	 record	 the	 portion	 of	 the	 energy	 reflected	 back	 at the	sensor.	In	the	case	of	radars,	sensors	emit	microwave	pulses	and	records	the	strength	of	the returning	pulse,	also	known	as	backscatter,	after	some	surface	interaction	(Woodhouse,	2005). Backscatter	 is	strongly	dependent	on	radar	frequency,	polarization	of	the	 microwave,	and	the shape,	 size,	 and	 moisture	 content	 of	 the	 ground	 target.	 As	 a	 result,	 radar	 sensors	 are	 able	 to record	 direct	 interaction	 with	 groups	 of	 trees	 and	 can	 provide	 structural	 measurements  6  important	 in	 estimating	 forest	 biomass	 (Sader	 et	 al.,	 1989).	 Current	 SAR	 platforms	 operate	 at different	frequencies	or	microwave	wavelengths,	the	most	common	being:	X‐band	(3.0	cm);	C‐ band	 (5.6	 cm);	 L‐band	 (24	 cm);	 and	 P‐band	 (74	 cm).	 Theoretical	 scattering	 models	 of	 forest have	 shown	 that	 at	 longer	 wavelengths	 (L	 or	 P‐band),	 signal	 returns	 due	 to	 scattering	 result mainly	from	tree	branches,	trunks,	and	ground	surfaces;	while	at	shorter	wavelengths,	smaller branches	 and	 leaves	 drive	 the	 scattering	 (Kasischke	 et	 al.,	 1997).	 Provision	 of	 its	 own illumination	 source	 also	 allows	 SAR	 sensors	 to	 transmit	 microwave	 signals	 that	 are	 either horizontally	 (H)	 or	 vertically	 (V)	 polarized,	 relative	 to	 the	 Earth’s	 surface	 and	 record	 the returned	signal	in	either	of	these	polarizations.	This	ability	to	operate	in	multiple	polarization modes,	from	single	polarization	(transmit	H	or	V;	receive	H	or	V),	dual	polarization	(transmit	H or	 V;	 receive	 H	 and	 V),	 or	 quad‐polarization	 (transmit	 H	 and	 V	on	 alternate	 pulses;	 receive	 H and	 V	 on	 every	 pulse)	 provides	 additional	 information	 about	 forest	 and	 canopy	 structural characteristics. Scattering	 of	the	microwave	pulse	is	 strongly	dependent	on	the	frequency	and	polarization	 of the	microwave	pulse,	and	the	shape,	size,	orientation,	and	moisture	content	of	the	target.	Radar sensors	 are,	 therefore,	 able	 to	 record	 direct	 interaction	 with	 structural	 elements	 and	 can provide	 measurements	 important	 in	 estimating	 AGB	 (Sader	 et	 al.,	 1989).	 Quantifying	 biomass using	SAR	data	have	 been	demonstrated	by	many	studies	(Dobson	et	al.,	1992;	Le	Toan	et	al., 1992;	Lucas	et	al.,	2006).	Unfortunately,	signal	return	for	all	SAR	frequencies	saturate	and	limit the	predictive	capability	at	moderate	to	high	biomass	levels,	especially	when	higher	frequencies are	 used	 (Imhoff,	 1995a).	 In	 addition	 to	 saturation	 effects	 at	 high	 biomass	 levels,	 challenges with	 using	 SAR	 may	 include	 poor	 accuracy	 and	 temporally	 unstable	 relationships	 due	 to variability	 in	 weather	 conditions	 such	 as	 frost	 and	 wind	 (Kasischke	 et	 al.,	 2011;	 Ranson	 and Sun,	 1997).	 However,	 with	 its	 capacity	 to	 collect	 usable	 data	 over	 a	 wider	 range	 of	 weather  7  conditions	and	provide	frequent	observations,	SAR	data	can	provide	generalized	information	on the	horizontal	distribution	of	forests	at	stand	and	regional	scales	suitable	across	large	areas. The	 possible	 use	 of	 InSAR	 for	 assessing	 biomass	 is	 also	 of	 interest	 due	 to	 the	 demonstrated provision	 of	 height	 measurements	 with	 no	 apparent	 saturation	 limit.	 For	 example, Solberg	et	al.	(2010)	 showed	 the	 effective	 use	 of	 single‐pass	 X‐band	 InSAR	 data	 for	 measuring forest	 biomass	 in	 the	 boreal	 region	 of	 southern	 Norway	 and	 reported	 a	 linear	 relationship between	 biomass	 and	 InSAR	 heights	 with	 no	 apparent	 saturation	 effect.	 However,	 obtaining accurate	height	measurements	requires	reducing	or	compensating	for	temporal	decorrelation, which	 necessitates	 the	 use	 of	 multiple	 baselines	 to	 improve	 interferometric	 processing	 or	 the use	 of	 single‐pass	 interferometry.	 These	 requirements	 lower	 operational	 uptake	 given	 that there	are	no	space‐borne	L‐	or	P‐band	SAR	satellites	currently	operational,	and	no	SAR	sensors with	 single‐pass	 configuration,	 with	 the	 exception	 of	 TanDEM‐X	 lunched	 in	 2010,	 primarily designed	to	provide	detailed	digital	elevation	model	(DEM)	data. In	contrast,	airborne	laser	scanning	or	LiDAR	sensors	measure	the	distance	between	the	sensor and	 the	 target	 (e.g.,	 the	 ground	 or	 tree	 canopy)	 based	 on	 half	 the	 elapsed	 time	 between	 the emitted	laser	pulse	and	the	recorded	return	pulse	(Næsset,	1997).	This	allows	LiDAR	systems	to accurately	 measure	 the	 vertical	 structural	 characteristics	 of	 trees	 and	 use	 this	 information	 to estimate	 forest	 stand	 characteristics,	 such	 as	 stand	 density,	 aboveground	 biomass,	 and	 basal area	 (Lefsky	 et	 al.,	 1999;	 Lim	 and	 Treitz,	 2004;	 Næsset	 and	 Gobakken,	 2005;	 Næsset,	 2002). Published	 studies	 have	 demonstrated	 the	 non‐asymptotic	 relationship	 between	 LiDAR structural	 measurements	 and	 biomass	 (Lefsky	 et	 al.,	 1999)	 and	 the	 accuracy	 of	 canopy	 or individual	tree	height	measurements	(Næsset	and	Økland,	2002). Although	 accurate,	 the	 use	 of	 LiDAR	 data	 for	 large	 area	 monitoring	 is	 challenging	 because	 of operational	 considerations	 that	 limit	 widespread	 use,	 such	 as	 high	 data	 acquisition	 costs,  8  aircraft	scheduling	and	logistics,	and	large	data	volumes	(Wulder	et	al.,	2008a).	Although	costs have	generally	decreased,	a	review	by	Wulder	et	al.	(2008a)	discusses	several	factors	that	can affect	cost.		For	instance,	improvements	in	pulse	rates	enable	flying	higher	which	means	fewer lines	are	required	to	cover	an	area	with	the	desired	hit	density;	however,	fuel	costs,	especially for	 remote	 locations,	 can	 be	 a	 key	 cost	 driver.	 Given	 the	 inverse	 relationship	 between	 spatial coverage	 and	 spatial	 resolution	 (Franklin	 et	 al.,	 2002),	 cost	 may	 be	 the	 primary	 obstacle	 in using	 LiDAR	 for	 large‐area	 forest	 characterizations	 (Wulder	 and	 Seemann,	 2003).	 Even	 with anticipated	reductions	in	LiDAR	data	costs	in	the	near	future	(Li	et	al.,	2008),	it	is	still	unlikely that	 LiDAR	 data	 would	 be	 used	 to	 provide	 wall‐to‐wall	 forest	 characterization	 measurements for	large	or	remote	locations	(Wulder	et	al.,	2012b).	However,	there	are	an	increasing	number of	 examples	 where	 the	 expense	 in	 LiDAR	 collection	 is	 justified	 by	 information	 requirements, such	 as	 the	 motivation	 for	 elevation	 data	 (Woods	 et	 al.,	 2011).	 A	 summary	 of	 the	 advantages and	disadvantages	in	the	use	of	airborne	LiDAR	or	space‐borne	radar	to	estimate	forest	biomass are	provided	in	Table	1.1.      9  Table	1.1		Benefits	and	limitations	of	airborne	LiDAR	and	spaceborne	SAR	in	estimating forest	biomass. Advantages   Direct	biophysical	measurement of	vertical	structure.    High	accuracy	and	precision	in estimating	forest	biomass. Observations	over	large	areas. Acquire	usable	data	under	a range	of	weather	conditions. Able	to	provide	biomass	estimates for	different	components	(e.g., trunk,	branches,	canopy,	etc.).  Disadvantages   Small‐footprint	can	be	cost	prohibitive for	larger	areas	depending	on application.    Asymptotic	relationship	at	moderate	to high	biomass	levels.    Poor	accuracy	and	sensitive	to topography	and	moisture	content	due	to dielectric	properties.  LiDAR    SAR   1.4 Data	Integration Unfortunately,	 there	 is	 no	 single	 remote	 sensing	 technology	 capable	 of	 providing	 all	 the information	 necessary	 to	 characterize	 forests	 completely,	 and	 obtaining	 detailed	 vertical measurements	for	large	areas	(De	Sy	et	al.,	2012).	Therefore,	studies	conducted	in	the	last	two decades	have	focused	on	exploiting	the	strengths	of	each	of	these	remote	sensing	technologies. Although	studies	have	investigated	the	relationship	of	SAR	and	LiDAR	measurements	to	forest biomass	 separately	 (Koch,	 2010),	 recent	 studies	 have	 examined	 the	 benefits	 and	 synergies	 of integrating	 LiDAR	 and	 SAR	 data.	 Given	 the	 complimentary	 match	 of	 information	 that	 exists between	 radar	 and	 LiDAR	 data	 (Hyde	 et	 al.,	 2006;	 Wulder	 et	 al.,	 2012a),	 additional	 analysis options	 should	 be	 promoted	 and	 investigated.	 For	 example,	 forest	 biomass	 estimates	 derived from	LiDAR	data	can	be	used	to	calibrate,	and	subsequently	validate,	wider	area	observations made	 by	 radar.	 In	 general,	 the	 use	 of	 multiple	 data	 sources	 can	 increase	 cost‐efficiencies, resolve	 data	 coverage,	 and	 cloud	 cover	 issues;	 however,	 using	 multiple	 data	 sources	 also increases	complexity	of	the	analysis	(De	Sy	et	al.,	2012).	A	few	relevant	studies	on	LiDAR	and radar,	and	their	integration,	for	biomass	estimation	are	summarized	in	Table	1.2.  10  Effective	and	accurate	methods	in	mapping	and	monitoring	AGB	are	needed,	especially	for	areas where	limited	or	no	inventory	data	are	available	or	persistent	cloud	cover	is	an	issue.	The	large spatial	coverage	and	dynamic	nature	of	forests	can	also	complicate	quantifying	forest	biomass; however,	each	of	the	remote	sensing	technologies	presented,	provides	a	particular	advantage	in measuring	forest	biomass.	Integrating	the	complimentary	information	derived	from	LiDAR	and radar	has	the	potential	to	overcome	some	of	these	challenges	inherent	in	any	one	approach. Table	1.2		Sample	studies	in	radar	and	LiDAR	for	forest	characterization,	including	AGB estimation,	and	their	key	research	findings.  Author  Vegetation Type  Method  Data	Sources  Key	Findings  SAR	and	InSAR  Le	Toan	et al.,	1992  Maritime Pine  Regression analysis  SAR	(P,	L,C‐band at	HH,	HV,	VV polarization)  Treuhaft	et al.,	2004  N/A  Signal/noise modeling  InSAR	(P,	L,C‐ band)  Solberg	et al.,	2010  Norway spruce,	Scots pine,	and birch  Regression analysis  InSAR	(X‐band)  Lefsky	et	al., 2002  Mixed softwood  Regression analysis  LiDAR (Waveform)  Næsset	and Gobakken, 2008  Norway spruce, Scotch	pine  Regression analysis  LiDAR	(Discrete‐ return)  Asner	et	al., 2010  Tropical rainforest  Sampling	and LiDAR	(Discrete‐ Regression return analysis  ‐Strong	correlation	between	radar backscatter	and	trunk	biomass. ‐HV	polarization	is	most	sensitive to	trunk	biomass. ‐Phase	difference	between	HH and	VV	correlated	to	diameter	at breast	height	(dbh). ‐Forest	biomass	more	accurately determined	by	InSAR	coherence and	phase	than	by	backscatter. ‐Biophysical	properties	of vegetation	are	best	determined	by data	fusion	with	InSAR. ‐Relationship	between	biomass and	InSAR	height	is	linear	and	no apparent	saturation	detected.  LiDAR ‐Single	regression	equation	can	be used	to	relate	LiDAR	derived canopy	structure	to	AGB. ‐Below	ground	biomass	and	AGB can	be	estimated	from	LiDAR	data in	boreal	forest	with	good accuracy. ‐Use	of	LiDAR	as	sampling	tool	to support	broad‐scale	biomass assessment	in	Peru.  11  Table	1.2		Cont’d.  Authors  Vegetation Types  Methods  Data	Sources  Key	Findings  SAR/INSAR	&	LiDAR	Integration N/A  Data	fusion using	multi‐ scale	filter  LiDAR	(Disrete‐ return)	and InSAR	(C‐band)  Mangrove  Empirical calibration	of InSAR heights	using LiDAR  LiDAR	(Discrete‐ return)	and	C and	X‐band InSAR  Hyde	et	al., 2007  Ponderosa pine  Integration using regression analysis  LiDAR	(Discrete‐ return,	UHF	and VHF	SAR,	and	X, P‐band	InSAR  Sun	and Ranson, 2009  Mixed hardwood and	softwood  Correlation of	LiDAR LiDAR derived (Waveform)	and biomass	with	 SAR	(L‐band) SAR	data  Mitchard	et al.,	2012  Integration Savanna,	low	 of	biomass LiDAR (waveform)	and biomass,	and	 estimates tropical	forest	 with	SAR SAR	(L‐band) classification.  Slatton	et	al., 2001  Simard	et	al., 2006  -Combining physical modeling with multi-scale estimation can significantly improve estimates of tree heights over large areas ‐Biomass	can	be	accurately estimated	using	LiDAR measurements	to	calibrate	InSAR mean	heights	to	top	of	canopy heights. ‐LiDAR more	accurate	in predicting	forest	biomass compared	to	SAR. ‐LiDAR	derived	mean	height	is highly	correlated	to	biomass. ‐Addition	of	SAR	and	InSAR variables	only	slightly	improved biomass	estimates. -SAR data has the ability to extend biomass estimates to other forested areas, using collocated biomass samples derived from LiDAR. -Combining SAR derived land cover with accurate biomass estimates from LiDAR is a potential method to overcome challenges of high biomass and cloud cover.     1.5 Research	Objectives The	 objective	 of	 the	 research	 presented	 in	 this	 thesis	 was	 to	 investigate	 different	 methods	 of integrating	 LiDAR	 and	 SAR	 data	 to	 support	 forest	 biomass	 estimation	 and	 ultimately,	 carbon stock	assessment.	The	rationale	was	to	use	the	precision	and	accuracy	of	LiDAR	measurements to	 calibrate	 and	 enhance	 SAR	 measurements.	 The	 chapters	 in	 this	 thesis	 address	 the	 varying spatial	scales	at	which	forest	characterization	and	forest	biomass	can	be	measured.	It	begins	at  12  the	local	scale	with	an	analysis	of	forest	biomass	at	the	plot‐level	then	scales‐up	to	the	regional scale	with	a	quantification	of	forest	biomass	for	a	larger	area. To	support	the	research	objective,	two	specific	questions	were	posed: 1. Can	 LiDAR	 data,	 in	 combination	 with	 SAR	 data,	 provide	 more	 accurate	 estimates	 of forest	biomass,	and	individual	biomass	components,	compared	to	any	one	technology? 2. How	can	SAR	data	be	used	to	extend	biomass	estimates	over	large	areas	using	samples of	LiDAR	data,	and	at	what	accuracy? Chapter	2	describes	the	study	area,	including	the	regional	climate,	vegetation	communities,	and the	 disturbance	 processes	 within	 the	 area.	 In	 additional,	 this	 chapter	 provides	 a	 detailed description	of	the	various	remote	sensing	datasets	and	field	plots	used	throughout	this	thesis. Chapter	 3	 examines	 the	 correlations	 between	 forest	 biomass,	 and	 biomass	 components,	 and LiDAR	and	SAR	data	to	determine	the	combined	parameters	that	offer	the	best	relationship	to estimate	 forest	 biomass.	 Field	 measured	 biomass	 quantities	 were	 first	 related	 to	 a	 series	 of LiDAR	 metrics	 and	 radar	 variables	 separately	 to	 understand	 individual	 correlations.	 LiDAR metrics	and	radar	variables	were	then	combined	to	assess	the	relative	contribution	of	each	data source. Chapter	 4	 tests	 and	 demonstrates	 three	 data	 integration	 methods	 for	 producing	 spatially explicit	 biomass	 products	 suitable	 for	 application	 over	 a	 range	 of	 environments.	 Three geostatistical	 approaches	 were	 used	 to	 extend	 accurate	 biomass	 transects.	 These	 sampled transects	were	derived	from	plot‐level	and	LiDAR	 data,	and	were	extended	 over	a	larger	area through	the	integration	of	wall‐to‐wall	radar	data.  13  Finally,	chapter	5	discusses	the	overall	findings,	conclusions,	and	implications	of	this	work,	and makes	recommendations	for	future	research.  14  2. STUDY	AREA	AND	DATA	SOURCES1 2.1 Site	Description The	 study	 area	 is	 an	 intensively	 managed	 forest	 dominated	 by	 Douglas‐fir	 (Pseudotsuga menziesii	 (Mirb.)	 Franco)	 and	 western	 red	 cedar	 (Thuja	 plicata	 Donn	 ex	 D.	 Don)	 located	 on Vancouver	 Island,	 British	 Columbia,	 Canada.	 The	 area	 covers	 a	 5	 km	 by	 5	 km	 area	 around Oyster	 River	 (UTM	 Zone	 10,	 NAD83:	 Upper	 left	 329450E,	 5531300N;	 Lower	 right	 337550E, 5523500N),	with	a	mean	elevation	of	240	m	(range	of	120	m	to	460	m)	above	sea	level	(Figure 2.1).	 The	 site	 consists	 of	 predominately	 second‐growth	 coniferous	 forest	 of	 70%	 Douglas‐fir, 17%	 western	 red	 cedar,	 3%	 western	 hemlock	 (Tsuga	 heterophylla	 (Raf.)	 Sarg.),	 and	 10%	 red alder	(Alnus	rubra	Bong.).	It	is	highly	productive	compared	to	most	other	places	in	Canada,	with rotation	cycles	as	short	as	60	years	(Morgenstern	et	al.,	2004).	The	density	of	established	stands on	the	site	ranges	from	350	to	1200	stem	ha‐1,	with	tree	height	ranging	between	10.0	and	35.0 m	and	average	diameter	at	breast	height	(dbh)	between	12.0	cm	and	31.2	cm	(Tsui	et	al.,	2012). The	forest	is	the	result	of	harvesting	of	the	original	forest	from	1920	to	1950.	Much	of	the	area did	 not	 regenerate	 naturally	 (Goodwin,	 1937)	 and,	 as	 a	 result,	 some	 of	 the	 area	 was	 planted starting	in	the	late	1940s,	with	second	growth	harvesting	and	subsequent	planting	beginning	in 1989.	The	harvesting	history	has	resulted	in	a	patchwork	of	second	growth	stands	at	different successional	 stages.	 The	 site	 is	 located	 within	 the	 dry	 maritime	 Coastal	 Western	 Hemlock biogeoclimatic	subzone	(CWHxm),	of	the	biogeoclimatic	ecosystem	classification	(BEC)	system of	 British	 Columbia.	 This	 subzone	 is	 characterized	 by	 cool	 summers	 and	 mild	 winters	 with mean	 annual	 precipitation	 of	 1,500	 mm	 and	 a	 mean	 annual	 temperature	 of	 9.1	 0C	 (Meidinger                                                               1		A	version	of	this	chapter	has	been	published.	Tsui,	O.W.,	Coops,	N.C.,	Wulder,	M.A.,	Marshall,	P.L.,	and	McCardle,	A., (2012).		Using	Multi‐frequency	radar	and	discrete	return	LIDAR	measurements	to	estimate	aboveground	biomass	in a	coastal	temperate	forest.		ISPRS	Journal	of	Photogrammetry	and	Remote	Sensing,	69,	121‐133.   15  and	Pojar,	1991).	A	large	portion	of	the	forest	was	commercially	harvested	in	the	2011	winter and	replanted	during	the	2011	spring.   Figure	2.1		Overview	of	the	Oyster	River	study	site	and	field	plot	locations.  2.2 Data	Descriptions 2.2.1  Plot	selection	and	inventory	measurements  Field	 measurements	 on	 seven	 plots	 established	 in	 2005	 and	 2008	 were	 obtained.	 Complete descriptions	of	these	stands	and	plot	measurements	were	provided	by	Coops	et	al.	(2007)	and Hilker	et	al.	(2010),	respectively	for	the	two	measurement	dates.	An	additional	11	stands	were selected	and	visited	by	field	crews	from	July	to	September	2010,	to	capture	species	composition and	age	class	variability	at	the	study	site	(Table	2.1).	Forest	inventory	data	(derived	from	1996 aerial	 photography	 and	 updated	 in	 1999)	 were	 provided	 by	 the	 license	 holders,	 TimberWest Forest	 Corp.	 and	 Island	 Timberlands,	 and	 were	 used	 to	 support	 field	 plot	 selection.	 A	 high  16  spatial	resolution	optical	image	from	the	QuickBird	satellite,	acquired	August	14th,	2008,	was also	used.	30	m	 x	30	m	 fixed‐area	square	plots	 were	positioned	and	located	using	differential GPS	 (dGPS)	 for	 each	 of	 these	 stands.	 All	 trees,	 greater	 than	 10	 cm	 dbh,	 within	 the	 plot	 were measured	for	dbh,	height,	height	to	the	base	of	the	live	crown,	and	species. 2.2.2  Radar	data  To	investigate	the	sensitivity	of	multi‐frequency	radars,	five	radar	images	were	acquired:	three Fine	Beam	Dual	polarization	(FBD)	images	acquired	by	the	Phased	Array	type	L‐band	Synthetic Aperture	 Radar	 (PALSAR)	 instrument	 on	 the	 Advanced	 Land	 Observing	 Satellite	 (ALOS),	 and two	RADARSAT‐2	Quad‐pol	Fine	Beam	images	in	single	look	complex	(SLC)	format	(Table	2.2). The	 PALSAR	 sensor,	 is	 a	 fully	 polarimetric	 L‐band	 sensor	 able	 to	 operate	 in	 either	 single polarization	(HH	or	VV),	dual	polarization	(HH+HV	or	VV+VH),	or	quad‐pol	mode.	The	nominal ground	 resolution	 for	 single	 and	 dual	 mode	 is	 approximately	 10m	 to	 20m,	 respectively,	 and 30m	 for	the	 quad‐pol	 mode.	PALSAR’s	observation	strategy	provides	spatially	and	temporally consistent	 regional	 scale	 data	 through	 the	 limitation	 of	 its	 operational	 modes,	 e.g.,	 fixed incidence	 angles	 (34.3o),	 polarisations	 (single‐pol	 and	 dual‐pol),	 and	 ascending	 passes (Rosenqvist	et	al.,	2004). RADARSAT‐2	is	a	fully	polarimetric	C‐band	SAR	satellite	with	multiple	imaging	modes	ranging from	Spotlight	to	ScanSAR	mode,	with	nominal	ground	resolutions	of	1m	to	100m.	Information on	 the	 utilization	 of	 RADARSAT‐2	 is	 given	 by	 Van	 der	 Sanden	 (2004).	 Figure	 2.2	 presents	 a colour	 composite	 of	 the	 L‐band	 and	 C‐band	 images	 over	 the	 study	 site	 in	 2009	 and	 2010 respectively.	Different	polarizations	are	used	to	color	code	the	image:	RGB	(HH,	HV	and	a	ratio of	HH	and	HV	for	the	L‐band	image,	and	HH,	HV,	and	VV	for	the	C‐band	image).	Cut	blocks	and clearings	 are	 clearly	 visible	 in	 both	 radar	 images;	 however,	 younger	 stands	 and	 regenerating stands	are	less	evident	in	the	RADARSAT‐2	image.  17  Table	2.1		Summary	of	field	site	characteristics,	field	measurements,	and	derived	structural	metrics	per	30	m	x	30	m	plot. Plot ID  % DFa  % RAb  % WRCc  % WHd  Mean Height (m)  STD Height (m)  Mean DBH (cm)  1  52.5      33.8  12.3  2.1  12.0  3511  5.1  33.3  2  67.9      32.1  18.9  4.1  12.9  1200  7.7  31.0  3    84.3    15.6  20.0  4.4  24.9  356  18.2  16.1  4  100.0        18.1  2.8  17.5  733  18.4  22.9  5  46.4    25.0  28.5  19.6  7.2  19.2  622  21.0  20.8  6  11.8    67.7  20.3  20.7  8.6  24.2  467  25.8  16.5  7  97.2      2.7  28.9  6.5  27.4  355  23.2  14.6  8  41.4  2.9  54.3  1.4  22.6  6.3  21.8  722  30.5  18.3  9  61.7    19.1  19.1  27.1  5.7  27.1  488  29.1  14.8  10  19.6    58.9  21.4  26.4  7.7  26.4  522  34.0  15.2  11  39.6  58.6    1.7  16.9  6.5  21.8  950  33.9  18.3  12  98.1      1.8  28.7  4.7  26.9  589  35.3  14.9  13  14.8  85.1      20.7  6.5  27.7  700  46.4  14.4  14  80.8    19.1    20.9.  4.3  20.6  1325  49.3  19.4  aDF	=	Douglas‐fir bRA	=	red	alder     Total Tree Basal	Area Density (trees	ha‐1)	 (m2	ha‐1)  Vegetation Surface	Area	/ Veg.	Volume  Plot	Description Regenerating mixed	stand Regenerating mixed	stand Regenerating pure	stand Young	pure	stand Young	mixed stand Young	mixed stand Young	nearly	pure stand Young	mixed stand Young	mixed stand Young	mixed stand Young	mixed stand Young	nearly	pure stand Mature	mixed stand Mature	mixed stand  dWH	=	western	hemlock cWRC	=	western	red	cedar  18  Table	2.1			Cont’d   Plot ID  % DFa  % RAb  % WRCc  % WHd  Mean Height (m)  STD Height (m)  Mean DBH (cm)  15  80.4  9.9  9.6    26.1  4.9  27.7  575  38.8  14.4  16  81.2    15.0  3.7  25.2  7.9  25.7  855  60.6  23.2  17  55.8    36.3  5.1  23.5  10.0  27.7  866  76.3  14.4  18  81.9    18.1    26.5  6.3  31.2  556  79.3  12.8  aDF	=	Douglas‐fir bRA	=	red	alder     Total Tree Basal	Area Density (trees	ha‐1)	 (m2	ha‐1)  Vegetation Surface	Area	/ Veg.	Volume  Plot	Description Mature	mixed stand Mature	mixed stand Mature	mixed stand Mature	mixed stand  dWH	=	western	hemlock cWRC	=	western	red	cedar       19  Table	 2.2	 	 Radar	 data	 sets	 in	 terms	 of	 products	 type,	 acquisition	 dates	 and	 image configurations.	Complex	pairs	used	to	calculate	InSAR	coherence	are	denoted	by	*	and	†.  ID  SAR	Sensor  Product  Acquisition Date  Incidence Angle	(Deg)  Polarisations  Ground Resolution (m)  1  PALSAR  FBD  30‐Aug‐2008  34.3  HH+HV  ~20  2*    FBD  02‐Sep‐2009  34.3  HH+HV  ~20  3*    FBD  18‐Jul‐2009  34.3  HH+HV  ~20  4†  RADARSAT‐2  Fine‐Quad  07‐Aug‐2010  39.2  HH+HV+VH+VV  ~8  5†    Fine‐Quad  31‐Aug‐2010  39.2  HH+HV+VH+VV  ~8      Figure	 2.2	 	 L‐	 and	 C‐band	 colour	 composites	 of	 the	 Oyster	 River	 study	 site.	 Red,	 green, and	 blue	 are	 used	 for	 coding	 HH,	 HV	 and	 a	 ratio	 of	 HH	 and	 HV	 polarizations,	 for	 the	 L‐ band	 image,	 and	 for	 coding	 HH,	 HV,	 and	 VV	 for	 the	 C‐band	 image.	 	 The	 images	 cover approximately	 8	 km	 by	 8	 km	 with	 azimuth	 direction	 south	 to	 north	 with	 the	 look direction	towards	the	right	(east). 2.2.3  Airborne	LiDAR	data  Airborne	discrete‐return	LiDAR	data	was	acquired	on	14	August	2008,	using	a	Leica	ALS50‐II	at a	 mean	 flying	 altitude	 of	 2,303m.	 The	 sensor	 had	 a	 150	 kHz	 pulse	 rate,	 recording	 up	 to	 four returns	per	laser	pulse.	Based	on	the	pulse	frequency,	lowest	sustainable	flight	speed,	altitude,  20  and	when	both	ground	and	non‐ground	returns	were	considered,	the	data	had	an	average	point spacing	 of	 0.52	 m	 and	 an	 average	 point	 density	 of	 3.74	 points	 m‐2.	 These	 specifications	 are considered	 suitable	 to	 obtain	 detailed	 stand‐level	 structural	 measurements.	 	 Separation	 of ground	 and	 non‐ground	 (canopy)	 returns	 was	 completed	 using	 Terrascan	 v4.006	 (Terrasolid, Helsinki,	 Finland),	 which	 employs	 a	 series	 of	 iterative	 algorithms	 that	 combine	 filtering	 and thresholding	methods	(Kraus	and	Pfeifer,	1998).	After	final	processing,	the	bald	ground	density was	between	0.4	points	m‐2	and	1.0	points	m‐2	and	the	non‐ground	density	was	0.7	points	m‐2. For	additional	information	on	the	acquisition	parameters	of	the	scanning	laser	data	set,	please refer	to	Hilker	et	al.	(2010).     21  3. RADAR	AND	LIDAR	OBSERVATIONS	TO	ESTIMATE ABOVEGROUND	BIOMASS	AND	BIOMASS	COMPONENTS	2 3.1 Introduction Forest	 lands	 in	 coastal	 British	 Columbia	 are	 highly	 productive	 compared	 to	 most	 of	 Canada, valued	 for	 timber	 and	 biodiversity,	 with	 biomass	 levels	 that	 are	 comparable	 to	 productive tropical	forests.	Forest	resources	have	historically	been	managed	primarily	for	economic	value (i.e.,	 timber	 production);	 however,	 current	 sustainable	 forest	 management	 practices	 aim	 to provide	a	broader	range	of	goods	and	services	over	the	long	term	(Siry	et	al.,	2005).	Gathering data	and	reporting	on	the	extent,	quantity,	composition,	and	condition	of	forest	resources	has traditionally	 been	 completed	 using	 forest	 inventories	 (Kangas	 et	 al.,	 2006).	 These	 inventories then	 form	 the	 basis	 upon	 which	 forest	 management	 decisions	 are	 made,	 either	 at	 the operational	 level	 (e.g.,	 planning	 of	 silvicultural	 activities),	 or	 strategic	 level	 (e.g.,	 forest management	plans)	(Wulder	et	al.,	2008). Forest	biomass	can	be	sub‐divided	into	its	components	such	as	wood,	bark,	branch,	and	foliage (more	generally	the	crown	and	stem),	which	can	provide	additional	information	for	ecosystem management.	 For	 timber	 supply	 needs,	 merchantable	 stem	 volume	 is	 of	 importance,	 with relationships	 between	 stem	 and	 non‐stem	 biomass	 components	 established	 (i.e.,	 biomass expansion	factors)	enabling	estimation	of	biomass	(Lambert	et	al.,	2005).	Further	estimates	of biomass	 components,	 such	 as	 crown	 biomass,	 can	 aid	 in	 fuel	 load	 assessments	 and	 fire management	 strategies.	 Canopy	 fuel	 characteristics	 are	 the	 most	 important	 variables	 in predicting	fire	hazard	and	behavior,	making	predictions	of	canopy	biomass	important	for	many wildfire	models	(Saatchi	et	al.,	2007).                                                               2	A	version	of	this	chapter	has	been	published.		Tsui,	O.W.,	Coops,	N.C.,	Wulder,	M.A.,	Marshall,	P.L.,	and	McCardle,	A.,  (2012).		Using	Multi‐frequency	radar	and	discrete	return	LIDAR	measurements	to	estimate	aboveground	biomass	in a	coastal	temperate	forest.		ISPRS	Journal	of	Photogrammetry	and	Remote	Sensing,	69,	121‐133.  22  Combining	information	from	multiple	sensors,	or	data	integration,	can	be	an	optimal	strategy	to characterize	forest	land	and	provide	information	on	forest	biomass	components.	Investigations into	 data	 integration	 have	 yielded	 promising	 results	 when	 estimating	 forest	 structural characteristics.	 Hudak	 et	 al.	 (2002)	 combined	 regression	 and	 co‐kriging	 models	 from	 multi‐ spectral	 and	 LiDAR	 data	 to	 estimate	 forest	 canopy	 height	 at	 un‐sampled	 locations	 and	 found that	 an	 integrated	 modeling	 approach	 was	 suitable	 for	 estimating	 canopy	 height.	 	 When investigating	 the	 integration	 of	 Landsat	 TM	 data	 with	 polarimetric	 multi‐frequency	 radar, Moghaddam	et	al.	(2002)	found	that	accuracy	in	foliage	mass	estimates	were	notably	improved. Wulder	 et	 al.,	 (2007)	 showed	 the	 integration	 of	 profiling	 LiDAR	 and	 optical	 remotely	 sensed imagery	provides	improved	characterization	 of	 forest	canopy	attributes	 and	change	 dynamics over	a	large	area	of	the	boreal	forest	in	western	Canada. The	objective	of	this	chapter	was	to	investigate	the	relationships	between	forest	biomass,	and its	 components,	 across	 a	 range	 of	 structural	 age	 classes,	 with	 small‐footprint	 discrete	 return LiDAR	 and	 several	 C‐	 and	 L‐band	 radar	 variables	 (i.e.,	 backscatter,	 polarimetry,	 and interferometric	 coherence).	 High	 correlation	 between	 biomass	 components	 (e.g.	 crown biomass)	and	shorter	wavelength	radars	was	expected	given	the	predominate	scatterer	at	these frequencies	 are	 branches	 (Imhoff,	 1995b);	 therefore,	 the	 rationale	 was	 to	 examine	 the additional	information	provided	by	C	and	L‐band	to	determine	the	combined	LiDAR	and	radar parameters	 that	 offer	 the	 best	 relationship	 in	 estimating	 forest	 biomass	 and	 biomass components.	This	objective	was	accomplished	by	calculating	biomass	and	biomass	components values	using	species‐specific	allometric	equations.	These	quantities	were	first	related	to	a	series of	LiDAR	metrics	and	radar	variables	separately,	and	then	in	combination.	Multiple	regression analysis	 was	 then	 used	 to	 assess	 the	 relative	 contribution	 of	 each	 radar	 variable	 to	 a	 LiDAR derived	biomass	model	providing	to	obtain	the	best	estimates.  23  3.1.1  Radar	remote	sensing	background  Studies	by	Le	Toan	et	al.	(1992)	and	Dobson	et	al.	(1992),	demonstrated	the	response	of	radar backscatter	 interactions	 for	 various	 experimental	 forests	 stands	 using	 experimental	 airborne SAR	sensors	at	the	time.	Gaveau	et	al.	(2003)	studied	InSAR	coherence,	derived	from	ERS‐1	and ERS‐2,	 to	 help	 differentiate	 four	 categories	 of	 growing	 stock	 volume	 for	 an	 area	 in	 Central Siberia.	Thiel	et	al.	(2009)	studied	the	feasibility	of	summer	backscatter	intensities	and	winter coherence	to	operationally	delineate	forest	and	non‐forest	land	cover.	Some	studies	in	the	use of	SAR	for	forest	characterization	have	also	focused	on	the	relative	phase	information	(i.e.	the shift	 from	 horizontal	 or	 vertical	 in	 the	 transmitted	 microwave	 compared	 to	 the	 received microwave	signal)	in	polarimetric	data.	A	review	by	Treuhaft	et	al.	(2004),	suggested	that	the added	information	provided	by	the	phase	information	(InSAR	coherence	and	InSAR	heights)	for forest	monitoring	showed	promise	especially	with	the	fusion	with	optical	remotely	sensed	data. Availability	of	commercial	SAR	satellites	with	full	polarimetric	capabilities,	and	new	processing and	investigation	techniques	have	led	to	attempts	to	address	limitations	of	earlier	technologies (Cloude	and	Papathanassiou,	1998).	A	complete	overview	of	forest	biomass	estimation	through radar	 is	 provided	 by	 Koch	 (2010).	 In	 general,	 there	 are	 two	 methods	 to	 obtain	 estimates	 of aboveground	biomass,	direct	and	indirect.		Direct	methods	primarily	use	radar	responses	(e.g., backscatter,	SAR	coherence)	to	establish	relationships	with	forest	biomass	or	forest	structure. Indirect	 methods	 use	 radar	 derived	 forest	 structural	 estimates	 (e.g.,	 tree	 heights,	 or	 canopy heights	obtained	through	Interferometric	SAR	–	InSAR	or	Polarimeteric	InSAR	–	Pol‐InSAR)	to infer	forest	biomass	quantities. The	integration	of	radar	technology	with	other	sources	of	remotely	sensed	data,	even	with	the limitation	 of	 signal	 saturation,	 continues	 to	 be	 actively	 studied	 for	 forest	 biomass	 estimation and	 land	 use	 and	 land	 cover	 monitoring,	 especially	 for	 tropical	 regions	 where	 cloud	 cover hinders	 the	 operational	 effectiveness	 of	 optical	 remote	 sensing	 sensors	 (Zhang	 et	 al.	 2006).  24  Although	 previous	 studies	 by	 (Hyde	 et	 al.,	 2007;	 Nelson	 et	 al.,	 2007)	 have	 investigated	 the integration	 of	 these	 two	 data	 types	 through	 the	 use	 of	 co‐located	 datasets	 and	 aspatial regression	methods,	their	study	focused	on	airborne	radars	of	longer	wavelengths.	This	chapter aims	 to	 investigate	 the	 integration	 of	 LiDAR	 and	 shorter	 wavelength	 radars	 to	 better understand	 the	 potential	 synergies	 between	 these	 data	 sources.	 The	 wide	 area	 potential, frequent	collection	and	cloud‐free	nature	of	SAR	data	suggest	high	utility.  3.2 Material	and	Methods 3.2.1  Study	site  For	 a	 complete	 study	 site	 description,	 please	 consult	 Section	 2.1.	 The	 study	 area	 consists	 of several	 flux‐tower	 sites	 (DF49,	 HDF11,	 and	 HDF00)	 that	 are	 part	 of	 the	 Canadian	 Carbon Program	 (CCP)	 located	 on	 Vancouver	 Island,	 British	 Columbia,	 Canada.	 DF49	 was	 planted	 in 1949	and	is	a	mature	Douglas	fir	stand.	It	was	commercially	harvested	during	the	2011	winter and	replanted	during	the	2011	spring.	HDF‐11	was	replanted	during	the	spring	of	2011,	while HDF00	was	harvested	and	replanted	in	2000. 3.2.2  Field	based	biomass	estimates  Produced	from	national	archival	plot‐level	data,	Ung	et	al.	(2008)	developed	consistent	biomass equations	used	by	the	Canadian	Forest	Service	to	model	the	carbon	cycle	at	the	national	scale. This	study	calculated	tree	biomass	and	the	biomass	of	tree	components	(e.g.,	stem,	bark,	branch and	foliage)	using	these	species	specific	biomass	equations.	Aboveground	and	tree	component biomass	values	were	calculated	for	individual	trees	within	each	plot	and	then	summed	to	obtain a	 summary	 of	 the	 biomass	 for	 each	 plot.	 It	 is	 important	 to	 note	 that	 although	 field‐based biomass	measurements	date	back	to	2005,	only	a	relatively	small	increase	in	forest	biomass	is anticipated	 to	 have	 occurred	 between	 2005	 and	 2010.	 Comparison	 between	 the	 2008	 LiDAR data	 and	 the	 2004	 LiDAR	 data	 set	 described	 by	 (Coops	 et	 al.,	 2007),	 showed	 an	 average	 plot‐  25  level	 increase	 in	 stand	 height	 of	 1.4	 to	 2.8	 m.	 This	 corresponds	 to	 a	 change	 of	 approximately ±0.1	to	0.2	Mg	ha‐1	in	aboveground	biomass.	Furthermore,	a	study	conducted	by	Wulder	et	al. (2008),	 also	 reported	 a	 low	 annual	 increment	 in	 tree	 growth	 for	 this	 study	 site.	 We	 therefore conclude	that	only	small	increases	in	forest	biomass	occurred	between	the	date	the	field‐based measurements	were	collected	and	the	remotely	sensed	data	observations. The	field	data	collected	represented	a	range	of	structural	stages	from	regenerating	stands	with low	biomass	to	mature	stands	with	high	biomass	Table	2.1.	To	quantify	the	differences	between plots	and	obtain	a	consolidated	value,	two	structural	descriptors	presented	by	Imhoff	(1995b), vegetation	 surface	 area	 (SA)	 and	 vegetation	 volume	 (V),	 were	 calculated	 using	 the	 size	 and density	 of	 the	 stem	 and	 crown	 component.	 For	 each	 plot,	 the	 stem	 and	 crown	 volume	 were calculated	 using	 mean	 height,	 dbh,	 crown	 height	 and	 crown	 area	 and	 then	 summed.	 Surface area	for	stem	components	were	calculated	in	a	similar	fashion,	while	a	bulk	density	was	used	to calculate	the	surface	area	of	the	crown	component.	These	individual	surface	area	values	were also	then	summed.	The	ratio	of	these	two	descriptors	(SA/V)	was	then	used	as	a	measure	of	the geometric	 consolidation	 of	 the	 canopy	 component	 within	 the	 plot.	 	 As	 presented	 by	 Imhoff (1995b),	 a	 high	 SA/V	 value	 indicates	 a	 more	 diffuse	 or	 less	 consolidated	 structural	 type	 with many	 small	 components	 having	 a	 high	 surface	 area,	 while	 a	 low	 SA/V	 value	 indicates	 a	 high degree	 of	 consolidation	 with	 fewer	 but	 larger	 crown	 components	 resulting	 in	 a	 lower	 surface area	and	the	presence	of	canopy	gaps. 3.2.3  LiDAR	pre‐processing  The	 LiDAR	 data	 were	 processed	 using	 FUSION	 software	 (McGaughey,	 2009).	 A	 series	 of standard	 plot‐level	 LiDAR	 metrics	 were	 calculated,	 e.g.,	 mean	 first	 return	 height,	 standard deviation,	coefficient	of	variation,	percentile	of	first	return	heights,	percentages	of	first	return above	2m,	and	percentage	of	first	return	above	the	first	return	mean	height.	Table	3.1	provides  26  a	plot‐level	summary	of	the	various	metrics	calculated	for	select	field	plots	representing	a	range of	age	and	structural	classes.	Only	15	of	the	18	field	plots	were	within	the	spatial	extent	of	the LiDAR	data	and	these	were	used	in	the	statistical	analysis. Table	 3.1	 	 Summary	 of	 plot‐level	 metrics	 calculated	 from	 LiDAR	 data	 for	 selected	 plots representing	various	age	and	structural	classes. Plot Hmean	(m) ID  Hmax	(m)  Hstd	(m)  CV (m)  P90th (m)  CC2m (%)  CCmean (%)  3  26.44  39.85  2.33  0.09  28.27  98.38  46.11  8  22.88  34.65  3.88  0.17  27.75  100.00  52.77  9  25.80  35.08  5.51  0.21  30.84  94.39  60.91  11  16.42  33.27  4.32  0.26  21.76  99.86  41.86  13  19.36  33.00  4.14  0.21  24.78  98.70  51.18  14  17.04  28.61  4.48  0.26  22.87  95.92  48.49  15  25.10  36.83  5.29  0.21  31.32  99.48  53.83  16  27.86  42.38  4.72  0.17  32.88  96.95  53.04  17  27.51  41.79  7.15  0.26  35.31  96.77  57.11  18  28.24  41.20  5.08  0.18  33.80  96.56  52.54  Plot Description Regenerating pure	stand Young	mixed stand Young	mixed stand Young	mixed stand Mature	mixed stand Mature	mixed stand Mature	mixed stand Mature	mixed stand Mature	mixed stand Mature	mixed stand  Hmean	=	Mean	first	return	height CV	=	Coefficient	of	variation	of	the	first	return	heights Hmax	=	Max	first	return	height P90th	=	90th	percentile	of	the	first	return	heights Hstd	=	Standard	deviation	of	the	first	return	heights CC2m	=	Percentage	of	first	returns	above	2	m CCmean	=	Percentage	of	first	returns	above	first	return	mean	heights     3.2.4  Radar	data	pre‐processing  To	reduce	speckle,	the	PALSAR	and	RADARSAT‐2	data	were	multi‐looked	using	factors	of	2	and 8,	and	factors	of	1	and	2	respectively,	for	range	and	azimuth	directions	and	then	calibrated	to obtain	SAR	backscatter	images.	The	updated	calibration	factor	provided	by	JAXA	was	used	for absolute	 calibration	 of	 the	 PALSAR	 data	 sets	 (Shimada	 et	 al.,	 2009).	 For	 image	 geocoding,	 a  27  1:20,000	 scale	 Terrain	 Resource	 Information	 Management	 (TRIM)	 Digital	 Elevation	 Model (DEM),	with	25m	cell	size	was	used.	Radiometric	correction,	geometric	correction	and	terrain correction	of	the	ALOS‐PALSAR	and	RADARSAT‐2	data	was	performed	using	the	Alaska	Satellite Facility	(ASF)	MapReady	software	package. Studies	 have	 reported	 that	 areas	 of	 sloped	 terrain	 can	 induce	 2‐7	 dB	 dispersion	 on	 radar backscatter	 (Castel	 et	 al.,	 2001).	 Without	 radiometric	 normalization,	 areas	 with	 slopes	 facing the	radar	sensor	would	have	higher	backscatter	than	flatter	areas,	which	is	problematic	when assessing	 properties	 of	 backscatter.	 Topographic	 effects	 were	 therefore	 corrected	 by radiometric	 normalization	 of	 the	 backscatter	 coefficient	 using	 the	 method	 described	 by Kellndorfer	 et	 al.	 (1998).	 A	 simple	 normalization	 equation	 was	 used,	 where	 backscatter coefficients	 were	 corrected	 based	 on	 the	 true	 local	 incidence	 angle	 instead	 of	 the	 ellipsoidal “flat”	 surface.	 To	 obtain	 a	 better	 representation	 of	 the	 backscatter	 coefficients	 for	 distributed targets	 (i.e.,	 the	 forest),	 a	 conversion	 from	 sigma	 nought	 to	 gamma	 nought	 was	 also	 applied. This	allowed	for	a	normalized	radar	cross‐section	where	backscatter	remained	approximately constant	for	all	incidence	angles. 3.2.5  Polarimetric	processing  The	 relationships	 between	 a	 feature’s	 physical	 properties	 (i.e.,	 shape),	 and	 its	 polarimetric behavior	 can	 be	 interpreted	 by	 examining	 the	 underlying	 scattering	 mechanisms,	 with scattering	 processes	 changing	 between	 forest	 stands	 of	 different	 structural	 types	 and	 ages. Through	 a	 target	 decomposition	 technique	 or	 a	 means	 to	 interpret	 the	 scattering	 matrix,	 the degree	of	randomness	and	the	mean	scattering	mechanism	of	forest	stands	can	be	determined by	the	entropy	and	alpha	parameters	(Cloude	and	Pottier,	1997).	For	example,	high	entropy	is assumed	 to	 correspond	 well	 to	 high	 crown	 biomass	 (branch	 and	 foliage)	 at	 shorter wavelengths,	 given	 the	 main	 scattering	 mechanisms	 result	 from	 tree	 branches	 and	 smaller  28  twigs.	 Therefore,	 in	 addition	 to	 backscatter	 intensities	 of	 the	 different	 polarizations,	 a	 target decomposition	technique	was	applied	to	the	PALSAR	and	RADARSAT‐2	data	to	derive	a	series of	 polarimetric	 parameters.	 The	 entropy	 (H),	 alpha	 (α),	 and	 anisotropy	 (A)	 target decomposition	 parameters	 were	 calculated	 using	 PolSARPro	 provided	 by	 the	 European	 Space Agency	(ESA). 3.2.6  InSAR	processing  By	measuring	the	phase	difference	of	an	object	(e.g.,	a	tree	branch)	that	is	observed	by	an	InSAR pair,	the	degree	of	correlation	(coherence)	can	be	calculated.	 Typically,	as	the	phase	variation increases,	 mainly	 caused	 by	 random	 fluctuations	 (e.g.,	 wind	 induced	 movements),	 coherence decreases	 within	 a	 range	 from	 1	 to	 0.	 Vegetation	 causes	 coherence	 to	 decrease;	 therefore,	 in general	 coherence	 magnitudes	 are	 highest	 for	 open	 areas	 and	 decrease	 for	 areas	 of	 dense vegetation	(Rosen	et	al.,	2000).	Given	these	observations	high	biomass	areas	should	exhibit	low coherence	 and	 areas	 of	 low	 biomass	 should	 have	 higher	 coherence.	 The	 correlation	 and	 the magnitude	between	two	radar	images	with	similar	orbit	geometries	(e.g.	InSAR	coherence),	was calculated	using	the	L‐	and	C‐band	data	sets.	The	perpendicular	baselines	for	the	L‐	and	C‐band data	 sets	 were	 615m	 and	 280m	 respectively,	 both	 of	 which	 were	 suitable	 for	 processing	 and analysis.	 At	 46	 and	 24	 days	 respectively,	 the	 L‐	 and	 C‐band	 pairs	 had	 the	 shortest	 (best) possible	temporal	baselines	of	an	orbiting	cycle. 3.2.7  Statistical	analysis  Most	LiDAR	metrics	are	related	to	canopy	height	and	are	often	highly	correlated,	Li	et	al.	(2008) recommended	 the	 selection	 of	 specific	 candidate	 metrics	 to	 reduce	 redundant	 information while	 maintaining	 biological	 relevance.	 A	 subset	 of	 candidate	 LiDAR	 metrics	 was	 selected	 for use	 in	 further	 analysis.	 For	 the	 radar	 data,	 ground‐calculated	 biomass	 and	 all	 radar‐derived variables	were	plotted	to	verify	key	assumptions.	Non‐linear	relationships	were	noted	and	a	log  29  transform	 was	 applied	 to	 all	 ground	 based	 biomass	 estimates	 (Rignot	 et	 al.,	 1994).	 Both predictor	variables	and	plot‐level	biomass	were	transformed	to	their	natural	logarithms	before any	 analysis	 was	 conducted.	 Linear	 regression	 was	 used	 to	 create	 models	 of	 biomass	 as	 a function	 of	 the	 response	 variables	 using	 the	 statistical	 package	 R.	 Metrics	 were	 modeled	 for aboveground,	stem	and	crown	biomass	for	the	LiDAR	data	set	in	a	multiple	regression	analysis, using	 the	 regsubsets	 function	 from	 the	 Leaps	 package	 (Leaps	 2009).	 The	 regsubsets	 function performs	 an	 “all	 subsets”	 regression	 where	 all	 possible	 variable	 combinations	 are	 considered and	the	best	single	(independent)	variable	model	is	reported,	then	the	best	two‐variable	model, the	 best	 three‐variable	 model,	 and	 so	 on.	 Akaike’s	 Information	 Criterion	 (Akaike,	 1973)	 was employed	and	parsimony	was	used	to	determine	the	best	models. Linear	regression	was	also	used	to	create	models	of	biomass	as	a	function	of	all	radar	variables. Each	radar	variable	was	 modeled	separately	using	the	Linear	Model	(lm)	 function	and	also	in combination	with	other	variables	including	the	LiDAR	model	in	a	multiple	regression	analysis. The	adjusted	R‐squared	(adjusted	R2)	and	relative	root	mean	squared	error	(i.e.,	the	root	mean squared	error	divided	by	the	mean	biomass	value	–	relative	RMSE),	were	used	to	determine	fits for	both	LiDAR	and	radar	models.	Due	to	the	difference	in	spatial	coverage	between	the	LiDAR and	radar	data	sets,	three	field	plots	were	not	available	for	the	LiDAR	model.  3.3 Results 3.3.1  Biomass	estimates  Ground‐based	 biomass	 components	 calculated	 using	 field	 measured	 heights	 and	 DBH	 are presented	in	Figure	3.1.	Aboveground	biomass	ranged	from	20	Mg	ha‐1	for	regenerating	stands to	550	Mg	ha‐1	for	mature	stands.	On	average	68%	of	the	aboveground	biomass	of	a	 tree	was contained	within	the	stem,	16%	in	branches,	and	8%	in	bark	and	foliage.  30  3.3.2  Regression	models  The	final	LiDAR	models	explained	close	to	86%	of	the	variance	in	the	plot‐level	measurements, with	 all	 dependent	 variables	 predicted	 well	 by	 the	 LiDAR	 canopy	 height	 and	 cover	 metrics. Table	 3.2	 provides	 a	 summary	 of	 the	 final	 biomass	 models.	 Stem	 biomass	 had	 the	 highest relationship	with	the	LiDAR	data,	with	an	adjusted	R2	of	0.86	and	a	relative	RMSE	of	16%.   Figure	 3.1	 	 Calculated	 aboveground	 biomass	 (Mg	 ha‐1)	 and	 individual	 biomass components	 per	 plot	 as	 derived	 by	 species	 specific	 allometric	 equations	 published	 by Ung	et	al.	(2008).  31  Aboveground	 biomass	 showed	 an	 adjusted	 R2	 of	 0.82	 and	 a	 relative	 RMSE	 of	 18%.	 Crown biomass	 showed	 the	 lowest	 relationship	 with	 an	 adjusted	 R2	 of	 0.72	 and	 a	 relative	 RMSE	 of 22%.	For	aboveground	biomass	and	stem	biomass,	the	mean	first	return	height	and	percentiles (i.e.,	10th	and	90th)	of	first	return	heights	were	selected	as	predictor	variables	from	the	subset of	candidate	LiDAR	metrics.	For	crown	biomass,	the	percentage	of	first	returns	above	2m,	and 75th	and	90th	percentiles	of	first	return	heights	were	selected	as	predictor	variables. Table	3.2		LiDAR	biomass	models	developed	from	field‐measurements	and	LiDAR	canopy height	and	cover	metrics.    Aboveground Biomass  Variables	 Adjusted	R2 Lhmean	*** LhP10	**  0.82  LhP90	***   Root	Mean Square	Error (Mg	ha‐1)  Relative RMSE (%)  ‐7.144	‐	12.925x1	+ 2.239x2	+	14.019x3  56.43  17.9      Lhmean	*** Stem	Biomass  Model  LhP10	***  0.86  LhP90	***    CC2m	*  Crown	Biomass  LhP90	***  ‐7.965	‐	12.997x1	+ 2.281x2	+	14.218x3  40.09  16.4   0.72  LhP75	*** In	all	cases,	n=	15 *	Variable	is	significant	at	P	<	0.05 **	Variable	is	significant	at	0.001	<	P	<	0.05 ***	Variable	is	significant	at	P	<	0.001  7.350	‐	4.008x1	+ 17.601x2	‐	13.502x3  15.41  21.9  Lhmean	=	Mean	first	return	height LhP10	=	10th	percentile	of	the	first	return	heights LhP75	=	75th	percentile	of	the	first	return	heights LhP90	=	90th	percentile	of	the	first	return	heights CC2m	=	Percentage	of	first	returns	above	2	m   Final	individual	L‐	and	C‐band	biomass	models	are	summarized	in	Table	3.3.	The	relationship between	 C‐band	 backscatter	 and	 biomass	 was	 unexpectedly	 negative,	 (i.e.,	 decreasing	 as biomass	 increased),	 which	 differed	 from	 most	 reported	 results.	HH	 and	 HV	 data	 were	 weakly correlated	with	aboveground	biomass,	while	VV	polarization	was	not	significantly	correlated	to biomass	or	any	biomass	component.	HH	polarization	was	the	best	predictor	variable	(adjusted  32  R2	=	0.39).	C‐band	coherence	values	were	also	negative,	decreasing	as	biomass	increased.	The coherence	magnitudes	were	quite	low,	mean	(|γ|HV	=	0.34),	however,	C‐band	HV	coherence	had stronger	correlation	than	HH	backscatter	and	was	significantly	correlated	(adjusted	R2	=	0.71). Saturation	 of	 the	 HV	 coherence	 data	 occurred	 at	 approximately	 50	 to	 60	 Mg	 ha‐1.	 Although weak,	VV	coherence	showed	significantly	higher	correlation	to	forest	biomass	and	the	various biomass	 components	 than	 VV	 backscatter.	 Polarimetric	 decomposition	 variable	 (entropy	 and alpha)	 were	 not	 significantly	 correlated	 to	 forest	 biomass	 or	 any	 biomass	 component. Consistently,	higher	correlation	with	stem	biomass	and	lower	correlation	with	crown	biomass was	observed	for	most	of	the	C‐band	variables. Table	 3.3	 	 Adjusted	 R‐squared	 values	 from	 linear	 regression	 of	 forest	 biomass	 and individual	 L‐	 and	 C‐band	 radar	 variables.	 Most	 significantly	 correlated	 radar	 variables are	represented	with	a	*.  C‐Band	HH	Backscatter  Aboveground Biomass 0.39  C‐Band	HV	Backscatter  0.21  n/s  0.21  C‐Band	VV	Backscatter  n/s  n/s  n/s  C‐Band	HH	Coherence  0.31  0.32  0.28  C‐Band	HV	Coherence  0.71*  0.71*  0.68*  C‐Band	VV	Coherence  0.57  0.58  0.50  C‐Band	Entropy  n/s  n/s  n/s  C‐Band	Alpha  n/s  n/s  n/s  L‐Band	HH	Backscatter  n/s  n/s  n/s  L‐Band	HV	Backscatter  0.61*  0.63*  0.53*  L‐Band	HH	Coherence  0.40  0.41  0.34  L‐Band	HV	Coherence  0.47  0.47  0.44  L‐Band	Entropy  0.36  0.38  0.29  L‐Band	Alpha  0.37  0.40  0.30  Variable  Stem	Biomass  Crown	Biomass  0.39  0.38  In	all	cases,	n=	18 Variable	is	non‐significant	(n/s),	i.e.	p	>	0.05   33  The	 L‐band	 backscatter	 increased	 linearly	 with	 biomass	 and	 was	 generally	 more	 highly correlated	 than	 the	 C‐band	 backscatter.	 L‐band	 HV	 backscatter	 was	 strongly	 correlated	 with aboveground	biomass.	HV	polarization	was	observed	to	be	the	best	predictor	variable	(adjusted R2	 =	 0.61).	 Saturation	 of	 L‐band	 backscatter	 was	 approximately	 100‐120	 Mg	 ha‐1.	 As	 with	 C‐ band,	 correlation	 was	 slightly	 stronger	 for	 stem	 biomass	 than	 for	 crown	 biomass.	 L‐band coherence	 was	 also	 negative,	 decreasing	 as	 biomass	 increased	 and	 did	 not	 appear	 to	 be	 any more	sensitive	to	different	levels	of	forest	biomass	than	the	backscatter	variables.	HH	and	HV coherence	 were	 slightly	 less	 correlated	 with	 biomass	 than	 backscatter,	 with	 HV	 coherence	 as the	best	predictor	variable	(adjusted	R2	=	0.47).	In	contrast	to	C‐band	relationships,	moderate correlations	were	observed	for	the	L‐band	polarimetric	parameters	(entropy	and	alpha),	with the	alpha	angle	as	the	best	predictor	(adjusted	R2	=	0.37). Modeling	forest	biomass	as	a	function	of	both	L‐band	and	C‐band	variables	provided	improved fits	 relative	 to	 their	 respective	 individual	 values.	 Five	 separate	 models	 were	 evaluated,	 all variables	 from	 either	 L‐	 and	 C‐band;	 backscatter	 coefficients	 from	 L‐	 and	 C‐band;	 coherence from	 L‐	 and	 C‐band;	 and	 finally	 all	 L‐	 and	 C‐band	 variables.	 Significant	 variables,	 adjusted	 R2, RMSE,	 and	 relative	 RMSE	 for	 each	 model	 are	 presented	 in	 Table	 3.4.	 High	 relative	 RMSE	 was observed	 for	 the	 individual	 C‐band	 and	 L‐band	 models,	 53.6%	 and	 44.0%	 respectively. Combining	the	L‐band	and	C‐band	variables	provided	significant	improvement	in	the	predicted values	 and	 showed	 a	 lower	 relative	 RMSE.	 The	 L‐	 and	 C‐band	 coherence	 model	 provided	 the best	estimates	of	forest	biomass	with	a	relative	RMSE	of	35.7%	and	an	adjusted	R2=0.79.	The	L‐ and	C‐band	backscatter	model	had	slightly	higher	relative	RMSE	of	45.3%	compared	to	the	all	L‐ band	variable	model.	Although	the	all	variables	model	provided	a	higher	adjusted	R2,	a	higher relative	RMSE	(39.9%)	was	observed	when	compared	to	the	L‐	and	C‐band	coherence	model.  34  Overall	 results	 presented	 in	 Figure	 3.2,	 suggest	 that	 integrating	 L‐band	 coherence	 variables with	the	best	LiDAR‐only	model	showed	only	a	slight	increase	in	relationship	with	aboveground biomass	 and	 stem	 biomass	 with	 an	 adjusted	 R2	 =	 0.88	 and	 0.90	 respectively.	 L‐band	 HV coherence	 was	 only	 able	 to	 explain	 an	 additional	 2.4%	 and	 1.2%	 of	 the	 variability	 in aboveground	and	stem	biomass.	No	significant	improvement	was	observed	for	crown	biomass using	L‐band	radar.   35  Table	 3.4	 	 All	 subsets	 regression	 biomass	 models	 developed	 from	 L‐	 and	 C‐band	 radar variables.   C‐band	all variables  L‐band	all variables  Variables C.HH	Backscatter	*** C.VV	Backscatter	**  L.HV	Backscatter	*** L.HH	Backscatter	**  Model  Root	Mean Square	Error (Mg	ha‐1)  Relative RMSE (%)  0.76  4.046	‐	0.967x1	+ 1.157x2  119.61  53.6   0.83  L.Entropy	**    L‐	and	C–band	 L.HV	Backscatter	*** Backscatter C.HV	Backscatter	*   L‐	and	C‐ L.HV	Coherence	* band C.HV	Coherence	** Coherence   L.HV	Coherence	* All	variables  Adjusted	R2  C.HH	Backscatter	*** C.VV	Backscatter	**  24.892	+	1.728x1	‐ 1.432x2	‐	14.882x3  98.17  44.0   0.74  1.446	+	0.469x1	‐ 0.425x2  101.07  45.3          0.79  7.432	‐	1.379x1	‐ 13.297x2  79.79  35.7   0.87  4.159	‐	1.534x1	‐ 0.786x2	+	0.899x3  89.21  39.9  In	all	cases,	n=	18. *	Variable	is	significant	at	P	<	0.05 **	Variable	is	significant	at	0.001	<	P	<	0.05 ***	Variable	is	significant	at	P	<	0.001    36  In	 contrast,	 integrating	 C‐band	 backscatter	 and	 polarimetric	 entropy	 with	 the	 LiDAR‐only model	 showed	 significant	 improvement	 (P	 <	 0.05)	 for	 aboveground	 biomass,	 stem	 and	 crown biomass	with	an	adjusted	R2	=	0.94,	0.95,	and	0.89	respectively.	Relative	RMSE	for	aboveground biomass,	stem	and	crown	biomass	were	8.0%,	7.1%,	and	11.8%	respectively	(Table	3.5).	C‐band HH	 backscatter	 was	 able	 to	 explain	 an	 additional	 8.9%	 and	 6.5%	 of	 the	 variability	 in aboveground	 and	 stem	 biomass,	 while	 C‐band	 polarimetric	 entropy	 was	 able	 to	 explain	 an additional	 17.9%	 of	 the	 variability	 in	 crown	 biomass.	 Predicted	 vs.	 observed	 aboveground biomass	were	also	plotted	for	all	models	and	presented	in	Figure	3.3.   Figure	 3.2	 	 Comparison	 of	 adjusted	 R2	 values	 for	 the	 LiDAR‐only,	 LiDAR	 +	 C‐band,	 and LiDAR	+	L‐band	models.		LiDAR	+	C‐band	HH	backscatter	showed	the	best	adjusted	R2	for stem	 and	 total	 biomass,	 and	 LiDAR	 +	 C‐band	 entropy	 showed	 the	 best	 adjusted	 R2	 for crown	biomass.		LiDAR	+	L‐band	HV	coherence	showed	the	best	adjusted	R2	for	both	total and	component	biomass.    37  Table	 3.5	 	 Final	 biomass	 models	 developed	 from	 integrating	 LiDAR	 and	 C‐band	 radar	 for	 aboveground,	 stem	 and	 crown biomass.		Significant	variables,	adjusted	R2,	RMSE	and	relative	RMSE	are	shown	for	each	biomass	model.    Variables  Adjusted	R2  Model  Root	Mean	Square Error	(Mg	ha‐1)  Relative	RMSE	(%)  0.94  ‐14.439	+	2.745x1	–	8.311x2	+ 10.112x3	–	0.305x4  23.64  7.96  0.95  ‐14.886	+	2.628x1	–	8.045x2	+ 10.094x3	–	0.282x4  16.40  7.12  0.89  ‐21.164	+	3.153x1	–	9.373x2	+ 11.116x3	–	25.126x4  7.93  11.79  Lhmean	*** Total	Aboveground	 LhP10	** Biomass LhP90	*** HHc‐band*    Lhmean	***  Stem	Biomass  LhP10	*** LhP90	*** HHc‐band*    Crown	Biomass   CC2m	* LhP90	*** LhP75	*** Hc‐band	*  In	all	cases,	n=	15 *	Variable	is	significant	at	P	<	0.05 **	Variable	is	significant	at	0.001	<	P	<	0.05 ***	Variable	is	significant	at	P	<	0.001  Lhmean	=	Mean	first	return	height LhP10	=	10th	percentile	of	the	first	return	heights LhP75	=	75th	percentile	of	the	first	return	heights LhP90	=	90th	percentile	of	the	first	return	heights CC2m	=	Percentage	of	first	returns	above	2	m HHc‐band	=	C‐band	HH	backscatter Hc‐band	=	C‐band	polarimetric	entropy      38   Figure	3.3		Comparison	of	predicted	and	observed	aboveground	biomass	for	all	final	C‐	and	L‐band	radar,	LiDAR,	and	LiDAR	+ C‐band	derived	models.  39  3.4 Discussion 3.4.1  LiDAR  It	is	acknowledged	that	the	total	number	of	plots	used	in	this	study	was	small.	Additional	work field	work	could	have	added	more	plots	and	provided	additional	validation	and	robustness	to the	observed	relationships.	With	the	noted	limitations	of	the	sample	size,	this	study	was	able	to demonstrate	 	 the	 various	 relationships	 between	 forest	 biomass,	 and	 its	 components,	 with LiDAR	 and	 radar	 backscatter,	 polarimetry,	 and	 interferometric	 coherence	 from	 both	 C	 and	 L‐ band	radar	sensors.	It	confirmed	that	discrete‐return	LiDAR	height	measurements	perform	well in	determining	forest	biomass	and	biomass	components.	The	resulting	LiDAR	metrics	selected in	 this	 study,	 e.g.,	 mean	 height,	 90th	 percentile,	 75th	 percentile,	 and	 the	 percentage	 of	 first returns	 above	 2m	 were	 the	 main	 variables	 found	 to	 explain	 the	 majority	 of	 the	 variation. Overall	these	selected	metrics	are	consistent	with	previous	LiDAR	studies	(Hall	et	al.,	2005;	Li	et al.,	2008;	Næsset	et	al.,	2005).	Since	most	LiDAR	returns	result	from	hits	from	dominant	trees, especially	from	the	outer	canopy,	distribution	of	LiDAR	return	heights	is	weighted	toward	the tallest	trees	(Hall	et	al.,	2005).	Therefore	the	mean	and	90th	percentile	heights	likely	represent the	 height	 of	 the	 over‐story	 and	 the75th	 percentile	 and	 the	 percentage	 of	 first	 returns	 above 2m,	 provides	 a	 measure	 of	 the	 spatial	 variability	 in	 canopy	 heights	 (Li	 et	 al.,	 2008).	 	 For	 all models	 the	 combination	 of	 height	 metrics	 and	 canopy	 cover	 metrics	 provides	 the	 three dimensional	information	needed	to	estimate	the	different	components	of	forest	biomass. 3.4.2  Multi‐frequency	radar  As	 for	 L‐band	 and	 C‐band	 radar,	 the	 use	 of	 multi‐frequency	 radar	 performed	 better	 than	 any single	frequency	radar	with	respect	to	estimates	of	aboveground	biomass.	Modeling	individual biomass	 components	 (stem	 and	 crown)	 with	 L‐	 or	 C‐band	 backscatter,	 coherence,	 and polarimetric	variables	did	not	improve	the	relationship	compared	to	the	aboveground	biomass  40  model.	 Although	 combining	 L‐	 and	 C‐band	 variables	 produced	 a	 strong	 correlation	 with biomass,	 relative	 RMSE	 values	 were	 high	 due	 to	 saturation	 at	 higher	 biomass	 levels. Nonetheless,	 error	 levels	 obtained	 from	 this	 study	 were	 within	 the	 range	 of	 other	 studies	 for single‐date	 and	 multi‐temporal	 data.	 For	 example,	 relative	 RMSE	 values	 for	 C‐band	 estimates from	a	number	of	studies	reported	by	Santoro	et	al.	(2011),	ranged	from	49.6%	to	80.0%,	while relative	RMSE	values	from	this	study	ranged	from	35.7%	to	53.6%	for	C‐	and	L‐	band	estimates. For	polarimetric	parameters,	specifically	entropy	and	alpha	angle,	and	forest	biomass	showed moderate	 correlation.	 The	 degree	 of	 correlation	 between	 L‐band	 entropy	 and	 alpha	 angle	 is consistent	 with	 findings	 made	 by	 Melon	 et	 al.	 (2002),	 and	 suggested	 all	 polarimetric discriminators	 in	 L‐band	 data	 have	 similar	 sensitivity	 to	 forest	 biomass,	 when	 compared	 to backscatter.	 Therefore	 their	 use	 in	 forest	 parameter	 retrieval	 (e.g.,	 forest	 biomass)	 may	 not provide	additional	information. The	 dominant	 scattering	 within	 the	 crown	 layer	 can	 be	 associated	 to	 foliage	 and	 branches; therefore,	 a	 correlation	 between	 crown	 biomass	 and	 C‐band	 variables	 was	 expected.	 The absence	 of	 such	 a	 response	 may	 be	 a	 result	 of	 the	 structural	 components	 of	 the	 stands	 at	 the study	 site.	 Examining	 the	 ratio	 of	 vegetation	 surface	 area	 and	 vegetation	 volume	 (SA/V), younger	regenerating	stands	displayed	a	canopy	structure	containing	many	small	components, resulting	 in	 a	 high	 SA/V,	 while	 mature	 stands	 had	 lower	 SA/V	 indicating	 a	 canopy	 structure with	fewer	but	larger	crown	components.	Direct	volume	scattering,	as	described	by	Le	Toan	et al.	(1992),	from	the	crown	surface	would	be	higher	in	stands	with	diffuse	canopies	having	many smaller	 components	 than	 stands	 that	 have	 more	 consolidated,	 but	 bigger,	 components	 and larger	canopy	gaps.	As	a	result	the	structural	composition	of	this	study	site	may	provide	insight and	help	explain	the	observed	backscatter	response	from	the	C‐Band	radar.  41  3.4.3  LiDAR	and	radar	integration  Including	 a	 radar	 variable	 to	 the	 LiDAR	 biomass	 model	 showed	 a	 significant	 improvement	 in the	forest	biomass	estimates.	This	improvement	is	greatest	in	estimating	crown	biomass.	Given that	 the	 relationship	 between	 plot‐level	 measurements	 of	 canopy	 height	 metrics	 and	 biomass form	 the	 basis	 of	 estimating	 forest	 biomass,	 canopy	 heights	 may	 not	 be	 good	 predictors	 of crown	biomass	but,	as	we	have	seen	in	this	study,	are	more	sensitive	to	stem	biomass.	With	the dominant	scattering	process	associated	with	branches,	and	to	some	extent	foliage,	C‐band	radar appears	to	provide	additional	information	on	the	crown	components	to	a	LiDAR‐only	biomass model. Results	from	this	study,	however,	differ	from	others;	Hyde	et	al.	(2007)	and	Nelson	et	al.	(2007) investigated	LiDAR	and	radar	synergies	to	improve	forest	biomass	estimates	and	both	studies present	consistent	results.	LiDAR	estimated	biomass	more	accurately	and	precisely	than	any	of the	 radar	 variables	 used	 in	 their	 studies.	 The	 use	 of	 both	 LiDAR	 and	 radar	 jointly	 did	 not improve	 forest	 biomass	 estimation	 in	 a	 practical	 sense,	 even	 though	 the	 addition	 of	 radar variables	to	their	best	LiDAR‐only	model	was	statistically	significant	(Nelson	et	al.,	2007).	When examining	 the	 cross‐validated	 RMSE	 of	 both	 the	 LiDAR‐only	 and	 LiDAR‐radar	 models,	 an improvement	of	1.6%	(Nelson	et	al.,	2007)	and	7.8%	(Hyde	et	al.,	2007)	in	predictive	precision was	observed.	Both	studies	concluded	little	practical	utility	could	be	gained	by	combining	radar data,	considering	the	cost	of	acquisition	and	processing. For	this	study	site,	a	Douglas‐fir	and	western	red	cedar	dominated	forest,	the	addition	of	a	radar variable	 to	 the	 LiDAR‐only	 model,	 improved	 the	 results	 by	 reducing	 the	 relative	 RMSE	 of	 the predicted	 aboveground,	 stem,	 and	 crown	 biomass	 levels	 by	 approximately	 10%.	 Even	 with these	improved	accuracies	previous	conclusions	regarding	cost	implications	in	data	acquisition and	 data	 processing	 need	 to	 be	 considered.	 It	 is	 unlikely	 that	 the	 benefits	 obtained	 from	 the  42  inclusion	 of	 radar	 would	 justify	 its	 addition	 due	 to	 cost.	 However	 with	 the	 eventual	 launch	 of the	 European	 Space	 Agency’s	 Sentinel‐1	 mission	 and	 the	 Sentinel	 data	 policy,	 promoting	 full and	 open	 access	 to	 Sentinel	 data	 to	 all	 users,	 inclusion	 of	 C‐band	 radar	 with	 discrete‐return LiDAR	for	a	detailed	biomass	inventory	for	small	areas	should	be	possible.	The	mandate	of	the Group	 of	 Earth	 Observations’	 Forest	 Carbon	 Tracking	 (GEO‐FCT)	 Task,	 to	 facilitate	 access	 to time‐series	 SAR	 and	 optical	 satellite	 data,	 future	 integration	 of	 these	 two	 data	 sets	 is	 also encouraging.	 Although	 a	 detailed	 biomass	 inventory	 for	 small	 areas	 is	 possible,	 the	 high	 cost associated	with	wall‐to‐wall	LiDAR	data	collection	hinders	its	use	for	biomass	assessments	for larger	 areas.	 Future	 investigations	 in	 LiDAR	 and	 radar	 synergies	 for	 wide‐area	 biomass monitoring	 should	 be	 conducted.	 Sample	 observations	 provided	 by	 LiDAR	 transects	 could	 be integrated	with	large	area	radar	coverage	through	spatial	modeling	methods	(i.e.	geo‐statistical approach),	 rather	 than	 aspatial	 regression	 methods.	 For	 example,	 the	 known	 relationship between	 various	 radar	 variables	 and	 biomass	 can	 be	 exploited	 through	 sample	 observations provided	by	LiDAR	transects	and	a	co‐kriging	approach.     43  4. EVALUATING	MULTIVARIATE	KRIGING	TO	ESTIMATE	AND MAP	ABOVEGROUND	BIOMASS.	3 4.1 Introduction Forests	 are	 important	 at	 multiple	 scales,	 from	 providing	 habitat	 for	 animals	 and	 non‐timber products	 at	 local	 scales	 (Ahrends	 et	 al.,	 2010)	 to	 influencing	 climate	 systems	 and	 the	 carbon cycle	globally	(Lewis	et	al.,	2009).	Sequestered	carbon	in	the	form	of	vegetation	(i.e,	forests)	is both	 large	 and	 dynamic.	 Consequently	 forests	 are	 an	 important	 component	 in	 mitigating	 the effects	of	climate	change.	However,	when	forests	are	cleared	and	converted	to	other	land	types or	 degraded	 much	 of	 their	 stored	 carbon	 is	 released	 into	 the	 atmosphere	 as	 CO2.	 As	 of	 2007 deforestation,	including	decay	and	peat	fires	and	drained	peat	soils,	is	estimated	to	account	for approximately	 18	 %	 of	 global	 carbon	 emissions	 and	 is	 the	 second	 largest	 source	 of anthropogenic	GHG	emissions	(IPCC,	2007).	The	IPCC	has	also	shown	that	the	largest	source	of GHG	 emissions	 for	 most	 tropical	 countries	 is	 from	 deforestation	 and	 degradation.	 More damaging	 is	 that	 deforestation	 and	 degradation	 of	 tropical	 forests	 also	 removes	 globally important	 carbon	 sinks	 that	 currently	 sequester	 CO2	 from	 the	 atmosphere,	 and	 which	 are critical	 to	 future	 climate	 stabilization	 (Stephens	 et	 al.,	 2007).	 Spatially	 explicit	 maps	 of aboveground	biomass	are	essential	for	quantifying	the	amount	of	carbon	sequestered	in	forests, and	changes	in	forest	carbon	stocks	and	area. Frequent	 observation,	 demonstrated	 relationships	 with	 biomass,	 and	 an	 all‐weather	 data collection	capacity	encourage	further	research	with	radar	and	LiDAR	data.	SAR	and	InSAR	data provide	a	complimentary	match	of	information	with	LiDAR	data	for	biomass	monitoring	(Hyde et	 al.,	 2006;	 Wulder	 et	 al.,	 2012a).	 In	 an	 integrative	 framework,	 forest	 biomass	 estimates derived	 from	 LiDAR	 data	 can	 be	 used	 to	 calibrate	 (and	 subsequently	 validate)	 the	 wide	 area                                                              3	A	version	of	this	chapter	has	been	submitted	for	publication.		Tsui,	O.W.,	Coops,	N.C.,	Wulder,	M.A.,	and	Marshall,	P.L.  2013.		Integrating	airborne	LIDAR	and	spaceborne	radar	via	multivariate	kriging	toestimate	above‐ground	biomass. Remote	Sensing	of	Environment.  44  observations	made	by	radar.	For	example	Mitchard	et	al.	(2012)	combined	direct	observations of	 L‐band	 radar,	 space‐borne	 LiDAR,	 and	 ground	 data	 to	 map	 aboveground	 biomass	 for	 Lopé National	 Park	 (LNP)	 in	 Gabon,	 an	 area	 of	 5,000	 km2.	 PALSAR	 backscatter	 (HH	 and	 HV polarization),	 elevation	 data,	 and	 a	 radar‐derived	 forest	 degradation	 index	 (RFDI)	 (e.g.	 ratio between	 the	 HH	 and	 HV	 polsarization)	 were	 used	 to	 produce	 an	 unsupervised	 vegetation classification	 consisting	 of	 40	 classes	 for	 the	 entire	 national	 park.	 Each	 vegetation	 class	 was then	assigned	an	average	biomass	value	estimated	by	ground	and	LiDAR	data.	The	LiDAR	data consisted	 of	 sample	 profiles,	 covering	 only	 17.85	 km2	 but	 which	 intersected	 all	 40	 vegetation classes.	They	estimated	the	carbon	stock	of	the	LNP	to	be	173	Mg	C	ha‐1,	which	was	consistent to	the	field	data	average	of	181	Mg	C	ha‐1.	The	outcome	was	a	100	m	spatial	resolution	biomass map	for	the	LNP	with	an	estimated	uncertainty	of	±25.0%. LiDAR	is	sensitive	to	tree	level	characteristics	and	height	of	tress.	In	contrast,	radar	is	sensitive to	 the	 size	 and	 arrangement	 of	 structural	 elements	 of	 groups	 of	 trees	 with	 different	 levels	 of penetration	resulting	in	a	representation	of	a	mean	canopy	condition	(Sexton	et	al.,	2009;	Tsui et	al.,	2012).	Given	these	known	relationships	between	the	LiDAR‐derived	forest	biomass	and radar	 measurements,	 accuracy	 in	 predicted	 biomass	 over	 large	 areas	 is	 expected	 to	 improve compared	 to	 predictions	 using	 SAR	 data	 alone.	 The	 complimentary	 information	 content	 of LiDAR	 and	 radar	 promotes	 the	 investigation	 of	 additional	 analysis	 options,	 especially	 those incorporating	 spatial	 inter‐relationships.	 The	 use	 of	 geostatistics	 is	 one	 potential	 method	 to integrate	 these	 complimentary	 data	 sources.	 Through	 a	 LiDAR	 sampling	 framework, aboveground	biomass	predictions	can	be	estimated	for	un‐sampled	areas	aided	by	wall‐to‐wall radar,	using	multivariate	kriging	approaches	(i.e.,	co‐kriging	or	regression	kriging). The	overall	goal	of	this	chapter	is	to	test	and	demonstrate	three	spatial	integration	methods	to produce	 spatially	 explicit	 biomass	 products	 suitable	 for	 application	 over	 a	 range	 of  45  environments,	including	remote	or	less	data	rich	regions.	We	propose	that	samples	of	airborne LiDAR	data,	calibrated	with	field	data,	can	be	used	in	conjunction	with	space‐borne	radar	data to	 produce	 viable	 wall‐to‐wall	 maps	 of	 aboveground	 biomass.	 In	 support	 of	 this	 goal,	 we	 first provide	 background	 and	 context	 in	 geostatistics	 to	 fulfill	 this	 information	 need.	 Secondly,	 we suggest	 appropriate	 data	 sets	 and	 methods,	 followed	 by	 an	 implementation	 of	 the	 proposed approach.	 Finally	 we	 discuss	 the	 implementation	 opportunities	 and	 considerations	 for	 these integration	methods. 4.1.1  Geostatistics  Geostatistics	has	become	a	commonly	used	technique	to	 estimate	variables	that	vary	 in	space (Curran	 and	 Atkinson,	 1998).	 A	 fundamental	 difference	 between	 geostatistics	 and	 classical statistics	is	the	assumption	of	spatial	autocorrelation,	which	describes	the	correlation	between a	value	of	some	variable	at	one	location	and	nearby	values	of	the	same	variable.	Geostatistics	is based	 on	 the	 theory	 of	 regionalized	 variables	 (Matheron,	 1971),	 which	 assumes	 variables	 are stochastic	as	opposed	to	deterministic	(Olea,	1977). Semivariograms	 estimate	 the	 degree	 of	 dissimilarity	 (or	 variance)	 between	 pairs	 of measurements	and	provides	a	concise	scale	and	pattern	of	the	spatial	variance	(Curran,	1988). Given	 an	 array	 of	 sample	 sites,	 or	 in	 the	 case	 of	 remotely	 senses	 images,	 an	 array	 of	 pixels,	 h units	apart	and	the	difference	of	the	variable	of	interest	at	these	sites,	the	average	semivariance, γ	̂(h),	at	lag	h	is	given	by	(Yates,	1948):  γ h    1 2N h  N h    z xi  	z xi  h  2    i 1  where	xi	are	the	data	locations,	h	is	the	distance,	N(h)	the	number	of	sample	sites,	and	z	the	data value	 of	 interest.	 One	 of	 the	 main	 uses	 of	 the	 semivariogram	 is	 to	 allow	 extrapolation	 of	 that  46  variable	 to	 unsampled	 locations	 (Journel	 and	 Huijbregts,	 1978).	 Therefore	 to	 describe	 the semivariogram	and	apply	it	in	further	analysis,	it	is	necessary	to	fit	a	mathematical	model	to	the estimated	semivariances	(Webster,	1985).	The	variance	that	is	spatially	independent	is	given	by the	 nugget,	 the	 sill	 provides	 the	 maximum	 semivariance	 observed	 from	 the	 semivariogram where	 there	 is	 no	 spatial	 autocorrelation,	 and	 the	 range	 represents	 the	 lag	 value	 where semivariance	reaches	maximum. Ordinary	 kriging,	 the	 most	 common	 and	 robust	 form	 of	 kriging	 (Krige,	 1966),	 is	 a	 spatial modeling	 technique	 that	 provides	 optimal	 and	 unbiased	 estimates	 of	 unknown	 vales	 from sample	 data	 (Curran	 and	 Atkinson,	 1998).	 The	 technique	 is	 only	 appropriate	 when	 there	 is spatial	dependence	in	the	data	and	provides	estimates	by	assigning	weights	to	each	sample	data point	that	is	in	close	proximity	to	the	estimate	of	interest.	Key	to	this	process	is	that	the	weights are	 determined	 from	 the	 form	 of	 the	 spatial	 dependence	 represented	 by	 the	 semivariogram (Curran	 and	 Atkinson,	 1998).	 In	 this	 sense,	 estimation	 is	 optimal	 and	 unbiased	 since	 the variance	 is	 minimized	 and	 weights	 are	 chosen	 so	 that	 they	 sum	 to	 one.	 The	 ordinary	 kriging model	estimates	a	value	 	at	location  0  	and	takes	the	general	form:          where	 Z S 	 are	 the	 sampled	 data	 values,	 λi 	 are	 the	 weights	 assigned	 to	 each	 sampled	 data value,	 and	 n	 are	 the	 number	 of	 neighbouring	 samples	 used	 in	 the	 model	 (Goovaerts,	 1997). Given	 the	 existence	 of	 spatial	 dependence,	 sample	 data	 closer	 to	 the	 estimate	 are	 given	 more weight	because	they	are	more	likely	to	be	similar	to	the	unknown	value. Co‐kriging	extends	ordinary	kriging	to	account	for	one	or	more	variables	and	is	typically	more appropriate	when	the	primary	variable	to	be	estimated	(in	this	study,	forest	biomass)	is	under‐  47  sampled	with	respect	to	the	secondary	variable	(in	this	study,	the	radar	observations)	(Curran and	Atkinson,	1998).	Similar	to	kriging,	estimates	are	calculated	using	the	autocorrelation	of	the primary	variable;	however,	co‐kriging	also	exploits	the	inter‐variable	correlation	of	the	primary and	secondary	variable.	If	the	two	variables	are	cross‐correlated	(i.e.,	the	spatial	variability	of the	primary	variable	is	also	correlated	with	the	secondary	(auxiliary)	variable),	this	information can	 be	 used	 to	 make	 predictions	 of	 the	 primary	 variable	 (Bivand	 et	 al.,	 2008).	 Isotopic	 co‐ kriging	requires	that	data	for	the	primary	variables	and	auxiliary	variables	be	measured	at	all sampling	locations.	Heterotopic	co‐kriging	requires	that	each	variable	be	measured	on	different sets	 of	 sample	 points	 and	 where	 only	 some	 of	 the	 variables	 may	 share	 common	 sample locations	(Wackernagel,	2003).	In	cases	involving	remote	sensing	data,	collocated	co‐kriging	is	a particular	heterotopic	situation	and	is	often	used	where	auxiliary	variables	are	measured	at	all locations	 but	 the	 primary	 variable	 is	 available	 at	 only	 a	 few	 locations.	 Co‐kriging	 estimates	 a value	 	at	location  0  	and	takes	the	general	form:                Regression	 kriging	 is	 a	 hybrid	 approach	 that	 combines	 either	 a	 simple	 or	 multiple	 linear regression	 model	 with	 kriging	 of	 the	 regression	 residuals	 (Goovaerts,	 1997).	 The	 value	 of	 a target	 variable	 at	 some	 location	 can	 be	 modeled	 as	 a	 sum	 of	 deterministic	 and	 stochastic components.	Predictions	are	modeled	in	two	stages:	the	first	is	the	deterministic	part	obtained from	regressing	the	depended	variable	on	auxiliary	variables;	and	the	second	is	the	stochastic estimates	 of	 the	 model	 uncertainty	 (e.g.	 regression	 residuals)	 obtained	 through	 ordinary kriging.	Estimates	for	a	value  	at	location  	 		 ̂    0  	can	be	obtained	with	the	following:               48  where  0  	 is	 the	 fitted	 deterministic	 component	 and	 ̂  estimate	from	the	ordinary	kriging, variables	 (  	 is	 the	 interpolated	 residual  		are	the	estimated	regression	coefficients	for	 	auxiliary  	 is	 the	 estimated	 intercept),	 and  semivariogram	for	the	regression	residuals  	 are	 the	 weights	 determined	 by	 the  .  4.2 Materials	and	Methods 4.2.1  Study	site  For	a	complete	study	site	description,	please	consult	Section	2.1. 4.2.2  Data	description  4.2.2.1 Biomass	map The	spatially	explicit	predictions	of	aboveground	biomass	used	as	the	reference	data	set	for	this chapter	 is	 presented	 in	 Section	 3.3.2	 and	 was	 created	 from	 plot‐based	 field	 data	 and	 small‐ footprint	discrete‐return	LiDAR.	The	LiDAR	data	was	acquired	in	August	2008	at	a	mean	flying altitude	 of	 2,303m	 with	 a	 bald	 Earth	 density	 of	 between	 0.4	 ‐	 1.0	 pts	 m‐2	 and	 a	 non‐ground density	 of	 0.7	 pts	 m‐2.	 Standard	 plot‐based	 derived	 metrics	 (e.g.,	 mean	 first	 return	 height, standard	deviation,	coefficient	of	variation,	percentile	of	first	return	heights,	percentages	of	first return	 above	 2m,	 and	 percentage	 of	 first	 return	 above	 the	 first	 return	 mean	 height)	 were computed.	Biomass,	species	and	age	class	variability	were	determined	using	18	fixed	area	field plots	measuring	30	m	x	30	m,	with	all	trees	greater	than	10	cm	diameter	at	breast	height	within the	 plot	 measured	 for	 dbh,	 height,	 height	 to	 the	 base	 of	 the	 live	 crown,	 and	 species. Aboveground	 biomass	 for	 each	 tree	 was	 calculated	 using	 species‐specific	 biomass	 equations and	 then	 summed	 to	 obtain	 plot‐level	 biomass	 values.	 	 The	 final	 LiDAR‐based	 biomass	 model had	a	root	mean	squared	error	(RMSE)	of	56.43	Mg	ha‐1,	a	relative	RMSE	of	approximately	18%, and	an	adjusted	R2	of	0.82.  49  Mapping	of	the	empirical	model	produced	a	spatially	explicit	aboveground	biomass	image	at	a spatial	 resolution	 of	 20	 m,	 which	 matched	 the	 spatial	 resolution	 of	 the	 coarsest	 radar	 co‐ variable	used	in	this	study	(Figure 4.1).	Final	biomass	values	ranged	from	0	to	1100	Mg	ha‐1	with a	mean	biomass	value	of	304	Mg	ha‐1.   Figure	4.1		Location	of	study	site	and	aboveground	biomass	values	estimated	by	discrete‐ return	LiDAR. 4.2.2.2 Radar	data Co‐incident	to	the	LiDAR‐derived	biomass	data,	five	radar	images	were	acquired	over	the	study site.	 Three	 Fine	 Beam	 Dual	 polarization	 (FBD)	 images	 acquired	 by	 the	 Phased	 Array	 type	 L‐ band	Synthetic	Aperture	Radar	(PALSAR)	instrument	on	the	Advanced	Land	Observing	Satellite (ALOS),	 and	 two	 RADARSAT‐2	 Quad‐pol	 Fine	 Beam	 images.	 Both	 data	 sets	 were	 stored	 in single‐look	complex	(SLC)	format	(Table 2.2).  50  PALSAR	and	RADARSAT‐2	SLC	data	were	multi‐looked	using	factors	of	2	and	8,	and	factors	of	1 and	 2	 respectively,	 for	 range	 and	 azimuth	 directions	 and	 then	 calibrated	 to	 obtain	 SAR backscatter	 images.	 Radiometric,	 geometric,	 and	 terrain	 correction	 of	 the	 ALOS	 PALSAR	 and RADARSAT‐2	data	were	performed	using	the	Alaska	Satellite	Facility	(ASF)	MapReady	software package.	 Following	 radiometric	 and	 geometric	 correction,	 conversion	 from	 sigma	 nought	 to gamma	 nought,	 which	 normalizes	 the	 radar	 cross‐section	 where	 backscatter	 remains approximately	constant	for	all	incidence	angles,	was	completed	for	an	improved	representation of	backscatter	values	for	distributed	targets	such	as	forests.	In	addition	to	backscatter	images, InSAR	 coherence	 magnitudes	 were	 also	 calculated	 using	 PALSAR	 and	 RADARSAT‐2	 complex image	pairs	(i.e.	two	radar	images	of	similar	orbits	with	amplitude	and	phase	information).	By measuring	the	difference	in	the	phase	of	the	microwave	pulses	after	interacting	with	an	object (e.g.,	 a	 tree	 branch),	 the	 coherence	 of	 the	 phase	 can	 be	 calculated.	 As	 the	 phase	 difference	 or phase	 shift	 increases,	 mainly	 caused	 by	 random	 fluctuations	 (e.g.,	 wind	 induced	 movements), the	coherence	decreases	within	a	range	from	1	to	0.	Since	vegetation	causes	signal	coherence	to decrease	because	the	exact	point	of	scattering	and	the	travel	path	of	the	signals	vary	between the	 radar	 scenes,	 coherence	 is	 highest	 for	 open	 areas	 and	 decreases	 as	 vegetation	 increases (Rosen	et	al.,	2000).	Lastly,	the	RADARSAT‐2	data	were	down‐sampled	to	a	spatial	resolution	of 20	 m	 and	 reduced	 to	 a	 spatial	 subset	 equivalent	 to	 the	 extent	 of	 the	 estimate	 aboveground biomass	 data	 set.	 For	 a	 more	 complete	 description	 of	 the	 radar	 processing	 steps	 completed, please	refer	to	Section	3.2. 4.2.3  Aboveground	biomass	sampling  Sample	forest	biomass	values	were	extracted	from	the	processed	biomass	data	set	for	the	study area.	Sampling	of	these	data	comprised	of	both	a	north‐south	and	east‐west	continuous	transect with	each	transect	line	consisting	of	a	data	point	every	20	m.		Transect	lines	were	separated	by three	distances,	either	500	m,	1000	m,	or	2000	m	with	a	total	number	(n)	of	points	of	n=	5,540;  51  n=	 3,020;	 and	 n	 =	 1,512	 respectively	 (Figure  4.2).	 The	 histograms	 of	 the	 three	 forest	 biomass data	sets	exhibited	a	strong	positive	skew.	Therefore	each	data	set	was	normalized	with	a	log transformation	followed	by	a	normal	score	transformation	before	geostatistical	analyses	were performed.	The	purpose	of	the	normal	score	transformation	was	to	obtain	a	sample	distribution closely	resembling	a	standard	normal	distribution	with	mean	equal	to	zero	and	variance	equal to	 one	 (Olea,	 1977).	 After	 modeling,	 all	 predicted	 aboveground	 biomass	 values	 were transformed	back	to	the	original	units	(i.e.,	Mg	h‐1)	before	evaluating	the	accuracy	of	the	various spatial	models.   Figure	4.2		Sampling	strategies	tested	and	data	volumes	for	each	sample	forest	biomass data	set:	(a)	2000	m,	(b)	1000	m,	(c)	500m,	and	(d)	validation	points.		Shaded	grey	area represents	the	extent	of	the	reference	LiDAR	derived	aboveground	biomass	data	set. 4.2.4  Biomass	modeling  Aboveground	 biomass	 data,	 derived	 from	 LiDAR	 height	 measurements,	 were	 used	 as	 the primary	 variable,	 and	 backscatter	 intensities	 and	 coherence	 magnitudes	 from	 ALOS	 PALSAR and	 RADARSAT‐2	 data	 were	 used	 as	 wall‐to‐wall	 co‐variables.	 The	 PALSAR	 and	 RADARSAT‐2 radar	 backscatter	 coefficients	 and	 coherence	 magnitudes	 were	 also	 transformed	 to	 normalize all	 datasets	 prior	 to	 use	 in	 the	 estimation	 processes.	 Sampling	 of	 the	 primary	 variable	 was performed	 to	 simulate	 airborne	 profiling	 LiDAR	 observations.	 The	 three	 multivariate  52  geostatistical	 techniques	 were	 performed	 using	 algorithms	 found	 in	 the	 GSTAT	 package designed	for	the	statistical	package	R	(Pebesma,	2004). For	 each	 of	 the	 three	 forest	 biomass	 data	 sets,	 determining	 the	 most	 suitable	 mathematical model	 was	 assessed	 by	 fitting	 the	 most	 common	 semivariogram	 models	 to	 each	 of	 the estimated	 semivariograms	 using	 weighted	 least	 squares	 and	 evaluating	 the	 quality	 of	 fit through	 the	 residual	 sum	 of	 squares	 errors.	 To	 support	 the	 process	 of	 predicting	 biomass values	at	unsampled	locations,	wall‐to‐wall	coverage	of	the	secondary	variable	was	included	in the	 kriging	 process	 as	 illustrated	 in	 Figure  4.3	 for	 1000	 m	 transects.	 For	 co‐kriging	 a	 model semivariogram	was	also	calculated	for	the	secondary	variable,	as	well	as	a	cross‐semivariogram describing	the	cross‐correlation	between	the	primary	and	secondary	variable.	Even	though	it	is possible	 to	 model	 any	 number	 of	 variables,	 it	 has	 been	 shown	 that	 co‐kriging	 results	 are virtually	 identical	 to	 kriging	 outputs	 when	 spatial	 correlation	 between	 the	 primary	 and secondary	 variable	 is	 minimal	 or	 absent	 (Wackernagel,	 2003).	 Given	 that	 the	 correlation between	biomass	and	long	wavelength	radar	is	well	established	(Dobson	et	al.,	1992;	Le	Toan	et al.,	1992;	Rignot	et	al.,	1994),	PALSAR	HV‐polarization	was	used	as	the	secondary	variable	for co‐kriging.	 While	 developing	 the	 three	 semi‐variogram	 models	 required	 for	 each	 co‐kriging operation,	care	was	taken	that	each	followed	the	linear	model	of	co‐regionalization	(Goovaerts, 1997),	whereby	all	models	(direct	and	cross)	have	the	same	shape	and	range,	but	have	different sills	and	nuggets	to	ensure	that	the	covariance	matrices	are	always	positive. A	 three	 stage	 process	 was	 followed	 to	 obtain	 predictions	 from	 regression	 kriging	 and regression	 co‐kriging.	 First,	 the	 deterministic	 part	 of	 the	 predictions	 was	 performed	 by regressing	aboveground	biomass	on	the	various	radar	data	sets	using	ordinary	least	squares	to get	an	estimate	of	forest	biomass	for	the	study	area.	Secondly,	residuals	from	the	ordinary	least squares	regression	were	extracted	and	imported	into	GSTAT	and	interpolated	across	the	study  53  area	 using	 ordinary	 kriging.	 Lastly,	 the	 deterministic	 and	 stochastic	 components	 were combined	together	to	obtain	the	final	predicted	value.   Figure	 4.3	 	 Image	 lattices	 showing	 characteristics	 of	 the	 experimental	 design	 for multivariate	kriging.		Aboveground	biomass	transects	simulate	airborne	profiling	LiDAR flight	lines	at	1000	m	intervals. To	 determine	 which	 radar	 variables	 were	 significant	 for	 predicting	 biomass,	 a	 stepwise multiple	 regression	 analysis	 was	 employed	 using	 the	 regsubsets	 function	 from	 the	 Leaps package	 (Leaps	 2009)	 with	 a	 significance	 level	 of	 α	 =	 0.05.	 To	 interpolate	 the	 regression residuals	 for	 the	 study	 area,	 a	 model	 semivariogram	 was	 determined	 following	 the	 same procedures	 outlined	 for	 co‐kriging.	 The	 difference	 between	 regression	 kriging	 and	 regression co‐kriging	primarily	lies	in	the	interpolation	of	the	regression	residuals.	Instead	of	interpolating the	 residuals	 using	 ordinary	 kriging,	 regression	 co‐kriging	 uses	 a	 secondary	 variable	 for interpreting	the	residuals.	We	selected	PALSAR	HV	backscatter	as	the	secondary	variable	since this	data	set	had	the	highest	correlation	with	forest	biomass.  54  4.2.5  Model	evaluation  Discrepancies	 between	 actual	 and	 predicted	 forest	 biomass	 were	 evaluated	 based	 on	 the validation	sample	points	outlined	in	Figure 4.2d.	The	validation	data	set	consisted	of	580	forest biomass	points	extracted	from	the	reference	aboveground	biomass	data	set.	These	points	were outside	 the	 training	 data	 set	 used	 in	 the	 kriging	 process.	 Following	 (Alsamamra	 et	 al.,	 2009; Meng	et	al.,	2009;	Murphy	and	Katz,	1985)	three	different	and	common	indices	were	used:  Root	Mean	Squared	Error	 RMSE  Mean	Absolute	Error	 MAE  Mean	Error	 ME  1   1      1   〈            〉  where	N	is	the	size	of	the	validation	data	set,	xp	is	the	predicted	value	from	the	model,	and	xo	is the	 observed	 value	 from	 the	 validation	 data	 set.	 The	 ME	 provides	 an	 indication	 of	 bias	 in	 the predictions	and	it	should	be	close	to	zero	for	unbiased	methods.	The	RMSE	and	MAE	measure the	average	precision	of	the	prediction	and	provide	an	indication	of	how	close	the	predictions are	 to	 the	 observed	 values.	 Lastly,	 paired	 t‐tests	 were	 used	 to	 compare	 whether	 residuals	 in estimated	 biomass	 values	 differed	 statistically	 from	 one	 another	 for	 each	 of	 the	 transect distances	and	modeling	techniques.  4.3 Results Semivariograms	 were	 generated	 to	 analyze	 and	 assess	 the	 spatial	 properties	 of	 the	 sampled aboveground	 biomass	 transects,	 biomass	 residuals,	 and	 the	 radar	 co‐variable	 data	 sets.	 For aboveground	 biomass	 all	 sample	 intervals	 showed	 similar	 spatial	 dependence	 with	 similar  55  shape	and	nugget,	partial	sill	and	range	parameters.	Similar	results	were	found	for	the	biomass residuals	and	the	cross‐semivariogram	data	set.	For	the	aboveground	biomass	and	residual	data sets,	nugget	variance	increased	as	sample	interval	increased	from	500	to	2000	m.	The	distance where	maximum	semivariance	was	observed	ranged	between	328	to	374	m	and	313	to	324	m for	 the	 aboveground	 biomass	 and	 residuals,	 respectively.	 The	 cross‐semivariograms	 between the	 aboveground	 biomass	 and	 the	 secondary	 variable	 showed	 higher	 nugget	 variance	 and	 a range	distance	between	324	to	374	m.	Less	spatial	autocorrelation	was	observed	between	the primary	 and	 secondary	 variables,	 while	 spatial	 autocorrelation	 was	 evident	 for	 aboveground biomass	and	residual	datasets.	The	Whittle‐Matern	model	had	the	best	fit	for	all	cases	and	was selected	 as	 the	 theoretical	 mathematical	 model	 for	 the	 use	 in	 spatial	 predictions.	 	 Example model	semivariograms	for	each	variable	for	the	1000	m	sampling	interval	are	provided	in	Table  4.1	and	Figure 4.4. Point	 pairs	 for	 each	 variable	 were	 graphed	 to	 assess	 if	 any	 global	 trends	 existed.	 No	 obvious trend	 was	 found	 among	 the	 individual	 variables.	 Anisotropy	 was	 also	 checked	 in	 the semivariogram.	 Similar	 spatial	 dependence	 and	 semi‐variance	 for	 all	 sample	 intervals	 at directions	of	0,	45,	90,	135,	180,	225,	270,	and	315	degrees	were	found. Table	 4.1	 	 Calculated	 model	 semivariograms	 and	 cross‐semivariogram	 used	 in	 spatial predictions	for	each	variable	for	the	1000m	sampling	interval. Semi‐Variogram	Model (1000	m)  Model  Nugget  Partial	Sill  Range	(m)  Kappa  Aboveground	Biomass  Whittle‐Matern  0.116  0.877  387.493  0.30  Radar	co‐variable  Whittle‐Matern  0.156  0.807  519.417  0.20  Cross‐variogram	(biomass and	radar)  Whittle‐Matern  0.397  0.441  328.268  0.40  OLS	residuals  Whittle‐Matern  0.013  0.801  313.421  0.20  56    Figure	 4.4	 	 Experimental	 (black	 points)	 and	 model	 (black	 line)	 semivariograms	 for	 (a).	 aboveground	 biomass,	 (b)	 radar	 co‐ variable,	(c)	cross‐semivariogram,	and	(d)	OLS	residuals	for	the	1000m	sampling	interval.  57  4.3.1  Biomass	estimates  Aboveground	biomass	was	underestimated	in	all	cases.	Regression	kriging	at	a	sample	interval of	500	m	showed	the	smallest	RMSE	and	MAE	at	203.9	Mg	ha‐1	and	131.6	Mg	ha‐1	respectively. The	ME	showed	an	average	bias	of	‐14.0	Mg	ha‐1.	Moderate	correlation	(r	=	0.68	and	R2	=	0.46) was	 observed	 between	 predicted	 and	 reference	 aboveground	 biomass.	 Predictions	 using regression	 co‐kriging	 at	 a	 sample	 interval	 of	 2000	 m	 resulted	 in	 the	 highest	 RMSE	 and	 MAE values	 at	 238.2	 Mg	 ha‐1	 and	 164.6	 Mg	 ha‐1	 respectively.	 Prediction	 bias	 also	 was	 highest, averaging	 ‐37.4	 Mg	 ha‐1.	 Correlation	 between	 observed	 and	 reference	 aboveground	 biomass was	 also	 lower	 at	 r	 =	 0.52	 and	 R2	 =	 0.28	 (Table  4.2).	 Regression	 kriging	 generally	 showed	 the lowest	 RMSE,	 MAE,	 and	 ME	 for	 all	 transect	 distances.	 As	 expected,	 biases	 in	 aboveground biomass	predictions	decreased	as	transect	distances	decreased. Table	4.2		Evaluation	of	global	accuracy	for	co‐kriging,	regression	kriging,	and	regression co‐kriging	based	on	the	validation	dataset. Estimated	Aboveground	Biomass Prediction	method and	sampling strategy Ordinary	Co‐kriging 2000	m	transect 1000	m	transect 500	m	transect Regression	kriging 2000	m	transect 1000	m	transect 500	m	transect Regression	Co‐kriging 2000	m	transect 1000	m	transect 500	m	transect   RMSE (Mg	ha‐1)  234.750 219.413 205.00  237.759 218.729 203.900  238.228 221.940 205.613  Mean	absolute error	(MAE) (Mg	ha‐1)  162.370 142.802 126.758  161.951 147.638 131.643  164.621 152.050 134.259  Mean error	(ME) (Mg	ha‐1)  ‐22.730 ‐34.164 ‐24.362  ‐35.347 ‐19.523 ‐14.007  ‐37.349 ‐18.110 ‐15.690  Multiple	R‐ squared  0.285 0.383 0.458  0.255 0.380 0.460  0.276 0.364 0.449  Pearson’s correlation (r)  0.533 0.619 0.676  0.505 0.616 0.678  0.525 0.604 0.670  58  Histograms	 of	 aboveground	 biomass	 (Figure  4.5)	 were	 used	 to	 visualize	 the	 accuracy	 of	 the predicted	 values.	 Deviations	 of	 the	 predicted	 aboveground	 biomass	 histogram	 from	 the reference	 histogram	 provided	 further	 insight	 into	 where	 the	 majority	 of	 the	 prediction	 bias occurred.	 As	 indicated	 by	 ME	 values,	 all	 kriging	 methods	 and	 transect	 widths	 underestimated the	 biomass,	 with	 the	 majority	 of	 the	 deviations	 occurred	 at	 higher	 biomass	 levels.	 Mean predicted	 aboveground	 biomass	 for	 all	 methods	 ranged	 from	 255	 to	 278	 Mg	 ha‐1,	 a	 negative deviation	 of	 49	 Mg	 ha‐1	 to	 26	 Mg	 ha‐1	 from	 the	 mean	 aboveground	 biomass	 of	 the	 reference biomass	data	set.	The	histograms	also	showed	overestimation	of	predicted	biomass	for	areas	of low	biomass	values. Plots	of	reference	and	predicted	biomass	values	were	also	used	to	compare	the	different	kriging methods	 and	 transect	 widths	 (Figure  4.6).	 Improvements	 can	 be	 seen	 with	 shorter	 transect intervals	 (e.g.	 larger	 samples).	 None	 of	 the	 geostatistical	 methods	 predicted	 aboveground biomass	 above	 approximately	 1250	 Mg	 ha‐1	 with	 the	 exception	 of	 co‐kriging	 which	 had	 an outlier	above	1400	Mg	ha‐1. Residuals	 for	 aboveground	 biomass	 were	 also	 graphed	 for	 each	 scenario	 tested	 to	 investigate the	 distribution	 of	 prediction	 errors	 (Figure  4.7).	 Although	 the	 range	 in	 prediction	 errors	 was large	for	each	case,	the	majority	of	the	deviation	between	predicted	and	reference	aboveground biomass	 were	 between	 ‐100	 Mg	 ha‐1	 and	 100	 Mg	 ha‐1.	 The	 variance	 in	 residuals	 decreased	 as sampling	frequency	increased.		There	was	not	much	change	in	variance	among	the	geostatistical methods	within	the	same	sampling	frequency.	Differences	in	mean	prediction	errors	were	not significant	 between	 kriging	 methods.	 Co‐kriging	 also	 showed	 no	 significant	 change	 in	 mean predicted	errors	between	sampling	distances.		While	no	differences	were	observed	between	the 500	and	1000	m	for	regression	kriging	and	regression	co‐kriging	(n	=	580;	α	=	0.05;	p‐value	= 0.15	 and	 0.50	 respectively),	 significant	 differences	 were	 observed	 between	 the	 1000	 m	 and  59  2000	m	width	(n	=	580;	α	=	0.05;	p‐value	=	1.2	x	10‐3	and	5.7	x	10‐4	respectively),	and	the	500	m and	2000	m	width	(n	=	580;	α	=	0.05;	p‐value	=	3.7	x	10‐6	and	7.2	x	10‐6	respectively).   Figure	 4.5	 	 Histograms	 of	 estimated	 aboveground	 biomass	 values	 (shaded	 in	 black)	 for all	 sampling	 strategies	 tested.	 1.	 co‐kriging	 (a,b,c);	 2.	 regression	 kriging	 (a,b,c);	 and	 3. regression	 co‐kriging	 (a,b,c).	 	 Histogram	 of	 reference	 biomass	 values	 provided	 as reference	(shaded	in	grey,	N=	80,025).    60   Figure	 4.6	 	 Scatterplots	 of	 estimated	 vs.	 observed	 aboveground	 biomass	 values	 for	 all sampling	 strategies	 tested.	 1.	 co‐kriging	 (a,b,c);	 2.	 regression	 kriging	 (a,b,c);	 and	 3. regression	 co‐kriging	 (a,b,c).	 	 Pearson’s	 correlation	 coefficient	 provided	 for	 each sampling	 strategy.	 	 Scatterplots	 represent	 accuracy	 of	 estimated	 values	 based	 on validation	points	(N	=	580).      61   Figure	 4.7	 	 Violin	 plot	 showing	 the	 interquartile	 range	 (mid‐spread)	 of	 residuals	 in predicted	 biomass	 for	 all	 sampling	 strategies	 tested.	 OCK	 ‐	 Ordinary	 Co‐kriging;	 RK	 – Regression	kriging;	and	RCK	–	Regression	co‐kriging. 4.3.2  Biomass	mapping	models  The	 kriging‐based	 maps	 captured	 the	 overall	 variation	 in	 aboveground	 biomass	 in	 the	 study area	 (Figure  4.1	 vs.	 Figure  4.8).	 As	 expected,	 increase	 sampling	 frequency	 provided	 better definition	of	the	variation.	As	a	result	of	the	sampling	design,	artifacts	were	observed	in	the	co‐ kriging	 maps	 and	 were	 more	 pronounced	 at	 the	 smaller	 sampling	 distances.	 	 With	 the regression	 kriging	 and	 regression	 co‐kriging	 maps,	 these	 artifacts	 were	 virtually indistinguishable.	 Biomass	 maps	 produced	 by	 regression	 kriging	 and	 regression	 co‐kriging were	also	very	similar.  62   Figure	 4.8	 	 Estimated	 aboveground	 biomass	 maps	 using	 1.	 co‐kriging	 (a,b,c);	 2. regression	kriging	(a,b,c);	and	3.	regression	co‐kriging	(a,b,c)	for	all	sampling	strategies tested.  4.4 Discussion We	 found	 lower	 errors	 in	 predicted	 biomass	 with	 less	 distance	 between	 adjacent	 sampling transects.	Despite	some	differences	observed	between	kriging	methods	and	sampling	strategies, systematic	sampling	at	1000	m	intervals	and	the	use	of	regression	kriging	was	shown	to	be	a  63  possible	 compromise	 between	 ease	 of	 use,	 increase	 in	 accuracy,	 and	 cost	 of	 obtaining	 LiDAR data	for	this	study	area.	The	accuracy	of	all	predictions	suffered	from	low	correlation	between the	LiDAR‐derived	aboveground	biomass	estimates	and	the	radar	data,	which	was	reflected	in the	 cross‐semivariogram	 by	 the	 high	 nugget	 and	 partial	 sill	 value.	 Regardless	 of	 the	 sampling distance	 between	 transects,	 range	 values	 at	 which	 no	 spatial	 dependence	 was	 detected	 was consistently	 less	 than	 400	 m.	 As	 a	 result,	 the	 semi‐variogram	 had	 little	 influence	 on	 the estimation	 process	 beyond	 this	 distance.	 This	 resulted	 in	 a	 smoothing	 effect,	 particularly evident	 when	 co‐kriging	 was	 employed.	 This	 smoothing	 effect	 was	 less	 evident	 in	 regression kriging	 and	 regression	 co‐kriging	 due	 to	 the	 deterministic	 portion	 of	 these	 models. Furthermore,	 the	 high	 nugget‐effect	 at	 a	 lag	 distance	 of	 zero	 in	 the	 cross‐variogram	 also suggests	 large	 variability	 between	 the	 primary	 and	 secondary	 variable.	 The	 tendency	 for kriging	to	underestimate	large	values	and	overestimate	small	values	is	supported	by	previous studies	(Hudak	et	al.,	2002;	Meng	et	al.,	2009).	This	tendency	may	help	account	for	the	inflated RMSE	values,	given	that	large	errors	are	given	disproportional	weight	because	of	the	squaring of	the	differences. Ordinary	kriging	and	co‐kriging	are	the	best	approaches	in	cases	where	spatial	interpolation	is required,	since	kriging	coefficients	rely	on	the	spatial	variation	between	sample	points	(Hudak et	 al.,	 2002).	 However,	 for	 cases	 of	 spatial	 extrapolation	 however,	 regression	 kriging	 is	 better suited	 for	 spatial	 extrapolation,	 since	 the	 main	 kriging	 coefficients	 only	 depend	 on	 the correlation	between	the	dependent	variable	and	independent	variables	(Meng	et	al.,	2009). 4.4.1  Future	considerations  The	 techniques	 and	 sampling	 framework	 presented	 in	 this	 study	 are	 relevant	 to	 large	 area aboveground	 biomass	 assessments	 and	 identify	 multi‐variable	 kriging	 as	 a	 robust	 statistical technique	 for	 estimating	 forest	 biomass,	 provided	 that	 there	 is	 strong	 correlation	 between  64  biomass	and	the	secondary	variable.	Due	to	the	asymptotic	relationships	between	biomass	and radar	backscatter,	and	the	high	variance	between	the	two,	integrating	direct	radar	backscatter and	 LiDAR	 using	 a	 spatial	 modeling	 approach	 is	 likely	 more	 suited	 for	 large	 area	 mapping	 of moderate	 forest	 biomass	 levels	 where	 correlation	 would	 be	 expectedly	 higher.	 Integrating radar	 backscatter	 and	 LiDAR	 to	 estimate	 areas	 of	 high	 biomass	 could	 possibly	 benefit	 from aspatial	methods	as	shown	by	(Tsui	et	al.,	2012).	However,	such	an	approach	is	most	suitable for	smaller	areas	where	both	LiDAR	and	radar	data	are	available	at	all	locations. Given	 that	 tree	 heights	 are	 known	 to	 be	 highly	 correlated	 to	 biomass,	 the	 potential	 for integrating	 LiDAR	 with	 wall‐to‐wall	 canopy	 heights	 derived	 from	 Polarimetric	 InSAR	 (Pol‐ InSAR)	or	InSAR	is	high.	By	virtue	of	the	properties	of	radar,	InSAR	heights	usually	correspond to	 the	 location	 of	 the	 scattering	 phase	 center,	 which	 typically	 underestimates	 actual	 canopy heights	(Balzter	et	al.,	2007).	Therefore,	although	this	technique	is	able	to	obtain	canopy	height measurements,	integrating	them	with	highly	accurate	LiDAR	observations	is	one	way	to	obtain high	accuracy.	The	planned	suite	of	future	satellites	including	NASA’s	Deformation,	Ecosystem, Structure,	 and	 Dynamics	 of	 Ice	 –	 Radar	 (DESDynI‐R)	 L‐band	 mission,	 Japan’s	 ALOS‐2	 L‐band Mission,	 and	 ESA’s	 BIOMASS	 P‐band	 mission,	 in	 addition	 to	 the	 advancements	 in	 SAR interferometric	 processing,	 such	 as	 multiple	 baseline	 InSAR	 (Neumann	 et	 al.,	 2010),	 and	 SAR tomography	 (Reigber	 and	 Moreira,	 2000),	 should	 allow	 for	 future	 operational	 integration	 of SAR	 and	 LiDAR	 data.	 Additionally,	 new	 means	 of	 optical	 image	 understanding	 and	 processing are	 providing	 novel	 opportunities	 for	 composting	 that	 may	 mitigate	 the	 negative	 impacts	 of cloud	cover	(Hansen	and	Loveland,	2012). 4.4.2  LiDAR	sampling	framework  Regardless	 of	 which	 secondary	 variable	 is	 selected,	 highly	 accurate	 assessments	 of	 forest biomass	 for	 large	 areas	 will	 likely	 require	 integration	 with	 LiDAR	 observations,	 whether  65  airborne	 or	 spaceborne.	 Large	 area	 coverage	 of	 LiDAR	 requires	 a	 sampling	 framework,	 to capture	the	variation	and	structural	characteristics	of	the	forested	area	(Wulder	et	al.,	2012b). The	 cost/benefit	 of	 such	 a	 sampling	 framework	 can	 be	 illustrated	 by	 performing	 a	 basic	 cost comparison	for	this	study	area	using	the	approximate	costs	in	(Wulder	et	al.,	2008).	For	a	total area	of	25	km2,	complete	airborne	LiDAR	coverage	to	obtain	a	data	set	with	a	posting	size	of	30 cm	 would	 cost	 approximately	 $1000	 CAD	 per	 km2	 ($25,000	 CAD	 total).	 Implementing	 a sampling	framework	incorporating	continuous	profiling	transects	with	a	swath	size	of	100	m	at the	same	posting	size	for	every	1000	meters	would	cost	approximately	$6,000	CAD,	a	quarter	of the	 cost	 of	 full	 LiDAR	 coverage.	 If	 accurate	 tree	 or	 stand‐level	 height	 information	 is	 required, LiDAR	data	may	not	be	considered	expensive.	However,	if	lower	costs	are	needed,	yet	achieving reasonably	 accurate	 depiction	 of	 stand	 height	 or	 biomass,	 other	 data	 types	 or	 modeling approaches	may	be	preferred. Cost	savings	generated	from	a	LiDAR	sampling	framework	and	a	multi‐sensor	approach	would conceivably	 benefit	 activities	 like	 assessing	 aboveground	 carbon	 stocks	 and	 carbon	 stock change,	 particularly	 for	 tropical	 areas	 where	 forest	 lands	 are	regularly	 cloud	 covered	 and	 are inaccessible.	 Strategies	 for	 implementing	 a	 LiDAR	 sampling	 framework	 for	 such	 a	 scenario would	potentially	involve	several	general	steps: 1.  Stratify	 the	 land	 primarily	 into	 forest	 land	 (FL)	 and	 non‐forest	 land	 (NFL)	 using	 pre‐ existing	land	cover	data	if	available.		If	such	land	cover	data	is	not	available,	separation of	broad	land	cover	types	can	be	obtained	through	the	use	of	SAR	as	demonstrated	by Hoekman	et	al.	(2010)	for	the	island	of	Borneo.		Their	study	presents	a	potential	method for	differentiating	land	cover	types	through	the	use	of	single‐pol	and	multi‐pol	L‐band SAR	data.  66  2.  Acquire	space‐borne	radar	at	the	spatial	resolution	required	to	meet	information	need and	use	land	cover	data	to	mask‐out	(i.e.,	remove)	areas	identified	as	NFL.  3.  Establish	 a	 series	 of	 sample	 ground	 plots	 for	 all	 areas	 stratified	 as	 FL	 and	 ensure complete	 variation	 in	 biomass	 is	 captured	 to	 characterize	 the	 population.	 Then, calculate	 aboveground	 biomass	 through	 the	 use	 of	 appropriate	 allometric	 equations. The	 number	 of	 ground	 plots	 will	 depend	 on	 the	 size	 of	 the	 study	 area,	 but	 also	 must consider	 the	 spatial	 distribution	 of	 individual	 forest	 types	 and	 also	 the	 with‐in	 type variability	(Wulder	et	al.,	2012a).	A	complete	discussion	is	not	provided	here	given	the complex	nature	of	sampling	design	and	sampling	theory,	please	refer	to	Brown	(1999).  4.  Collect	 airborne	 LiDAR	 data	 to	 intersect	 each	 of	 the	 sample	 ground	 plots.	 Regress calculated	aboveground	biomass	data	with	the	 LiDAR	measurements	to	 obtain	sample aboveground	biomass	transects.	A	concise	discussion	on	the	use	of	profiling	LiDAR	as	a sampling	tool	is	provided	by	Nelson	et	al.	(2003).	Because	of	the	nature	of	how	airborne LiDAR	data	is	collected	(i.e.,	linear	flight	lines)	Wulder	et	al.	(2012a)	suggests	possible sampling	designs	that	can	be	used.  5.  Estimate	and	model	the	 semi‐variogram	 from	the	LiDAR	transects	and	in	 combination with	 SAR	 data	 and	 predict	 aboveground	 biomass	 for	 un‐sampled	 locations	 using regression	kriging.  6.  Finally,	 complete	 quantitative	 validation	 to	 compare	 predicted	 values	 to	 actual	 values. Reference	data	may	consist	of	new	ground	plot	data	or	an	independent	subset	of	LiDAR transects	not	used	in	the	modeling	processing.  .      67  5. CONCLUSION The	removal	of	terrestrial	carbon	through	the	conversion	of	forested	to	non‐forested	land	will continue	to	have	important	impacts	on	GHG	concentrations	in	the	atmosphere.	To	support	the reporting	 requirements	 of	 global	 climate	 change	 agreements	 and	 aid	 climate	 mitigation programmes,	 such	 as	 REDD+,	 use	 of	 Earth	 observation	 satellite	 data	 are	 increasingly	 crucial given	that	most	developing	countries	have	large	areas	of	forest	that	are	difficult	to	access	and systematically	 monitor	 (Grainger	 and	 Obersteiner,	 2011).	 There	is	 notable	 capacity	 for	 LiDAR and	 SAR	 technologies	 to	 provide	 objective,	 practical,	 and	 cost‐effective	 solutions	 to	 monitor changes	 in	 forest	 area	 and	 estimate	 aboveground	 carbon	 stocks.	 The	 IPCC	 Good	 Practice Guidelines	 for	 National	 Greenhouse	 Gas	 Inventories	 for	 Agriculture,	 Forestry,	 and	 Other	 Land Use	 (IPCC	 2006)	 and	 Global	 Observation	 of	 Forest	 and	 Land	 Cover	 Dynamics	 (GOFC‐GOLD) Sourcebook	(GOFC‐GOLD	2011)	recommend	the	use	of	both	LiDAR	and	SAR	to	support	carbon stock	 assessment	 among	 other	 data	 sources	 such	 as	 multi‐spectral	 data	 or	 targeted	 airborne surveys. The	overall	objective	of	this	thesis	was	to	demonstrate	novel	methods	to	integrate	two	remotely sensed	 data	 sets	 (i.e.,	 SAR	 and	 LiDAR)	 for	 the	 application	 of	 forest	 biomass	 estimation.	 This research	 was	 divided	 into	 two	 main	 questions:	 (1)	 can	 shorter	 wavelength	 radar	 variables provide	 improved	 biomass	 estimates	 when	 combined	 aspatially	 with	 LiDAR	 data;	 and	 (2)	 can the	 use	 of	 space‐borne	 radar	 extend	 aboveground	 biomass	 estimates	 over	 a	 larger	 area	 using spatial	 modeling	 methods.	 In	 addition	 to	 these	 two	 main	 questions,	 insights	 into	 the	 various relationships	between	biomass	and	SAR	polarimetry	and	coherence	were	gained,	while	a	new approach	was	investigated	to	predict	forest	biomass	from	LiDAR	data	across	the	landscape.  68  5.1 Key	Findings Results	from	chapter	3	suggest	that	integrating	radar	variables	into	a	LiDAR‐derived	model	of forest	 biomass	 can	 provide	 added	 explanatory	 information	 to	 biomass	 estimates,	 with improvements	in	relative	RMSE	of	approximately	10%.	It	also	showed	that	repeat‐pass	InSAR coherence	 magnitudes,	 from	 a	 combination	 of	 C‐band	 and	 L‐band	 radar,	 provides	 the	 best estimate	 of	 forest	 biomass	 and	 are	 the	 most	 significantly	 correlated	 radar	 variables.	 	 Similar observations	were	also	made	by	Delbart	et	al.	(2002)	for	L‐band	data.	In	contrast,	backscatter, polarimetric	decomposition,	and	interferometric	coherence	do	not	have	good	correlations	(i.e., 0.36	and	040	respectively)	to	with	biomass	components.	As	reported	by	Melon	et	al.	(2002),	a higher	 dynamic	 range	 is	 provided	 by	 backscatter	 than	 polarimetic	 measurements	 when assessing	forest	biomass.	Including	C‐band	radar	data	in	a	LiDAR‐derived	biomass	model	also indicated	that	additional	information	in	crown	biomass	was	obtainable. Cost	 implications	 are	 important	 factors	 to	 consider	 before	 applying	 these	 results.	 At	 current data	costs,	obtaining	both	LiDAR	and	radar	data	for	moderate	improvements	in	the	accuracy	of biomass	 estimates	 is	 not	 practical.	 However,	 movement	 towards	 open	 data	 policies	 for	 Earth observation	 data	 (Aschbacher	 and	 Milagro‐Pérez,	 2012)	 provide	 an	 exciting	 possibility	 for future	 use	 of	 radar	 and	 multi‐spectral	 sensors.	 This	 movement	 towards	 open	 exchange	 of remote	sensing	data	also	promotes	efficient	data	dissemination	and	advances	in	data	delivery technologies.		Also	open	data	policies	advance	data	processing	levels	to	provide	well	calibrated products	 to	 allow	 for	 wider	 public	 usage.	 The	 Sentinel‐1	 satellite,	 the	 first	 of	 a	 two	 radar satellites	planned	to	be	launched	in	mid‐2013,	carries	on	the	legacy	of	European	C‐band	radar sensors	 including	 the	 European	 Remote	 Sensing	 satellites	 (ERS‐1/2)	 and	 Envisat	 Advanced SAR.	With	planned	repeat	cycles	of	less	than	14‐days	and	average	revisits	of	2‐days	once	both satellite	 are	 operational	 (Torres	 et	 al.,	 2012),	 Sentinel‐1	 data	 can	 aid	 in	 global	 monitoring	 of forested	 land	 at	 high	 spatial	 resolution	 (Malenovský	 et	 al.,	 2012).	 Furthermore,	 NASA’s  69  proposed	 Deformation,	 Ecosystem	 Structure	 and	 Dynamics	 of	 Ice	 (DESDynI‐R)	 satellite	 will have	a	L‐band	SAR	system	with	a	potential	repeat	cycle	of	8	to	12‐days	and	will	offer	large	area observations	 (Eisen	 et	 al.,	 2012).	 Current	 agreements	 for	 open	 data	 access	 for	 Sentinel‐1	 and ongoing	discussions	for	DESDynI–R		and	the	next	generation	Advanced	Land	Observing	Satellite (ALOS‐2),	integrating	LiDAR	and	SAR	data	at	collocated	sites	has	greater	potential. Results	 from	 chapter	 4	 focused	 on	 the	 accuracy	 of	 three	 kriging	 techniques	 for	 estimating aboveground	biomass	at	a	spatial	resolution	of	30	m.	The	study	demonstrated	how	samples	of forest	biomass,	derived	from	airborne	LiDAR	and	plot	data,	can	be	combined	with	wall‐to‐wall spaceborne	 radar	 observations	 to	 achieve	 spatially	 continuous	 biomass	 estimates.	 In	 this integrative	 framework,	 spatial	 modeling	 methods	 provide	 an	 effective	 means	 to	 overcome challenges	in	the	application	of	large	area	biomass	assessments.	Through	additional	research	on the	 sampling	 design	 and	 on	 landscape	 stratification,	 accuracy	 of	 biomass	 estimates	 can potentially	 be	 improved.	 Integration	 of	 LiDAR	 and	 space‐borne	 radar	 data	 offer	 a	 different approach	for	direct	assessments	of	biomass,	especially	where	comprehensive	forest	inventory data	 do	 not	 exist	 or	 are	 too	 expensive	 to	 obtain,	 and	 where	 frequent	 cloud	 cover	 make	 other methods	 of	 quantifying	 forest	 biomass	 challenging.	 The	 wall‐to‐wall	 mapping	 opportunity enabled	 through	 integrating	 LiDAR	 and	 radar	 data	 provides	 additional	 value	 to	 existing	 data augmenting	 plot‐based	 biomass	 estimates	 (De	 Sy	 et	 al.,	 2012).	 Accurate	 biomass	 maps	 are possible,	 provided	 appropriate	 samples	 of	 LiDAR‐based	 biomass	 area	 available	 and	 these samples	represent	the	population	statistically	and	geographically.	Potential	next	steps	would	be to	compare	this	approach	to	the	more	common	“combine	and	assign”	or	“stratify	and	multiply” methods	 (Goetz	 et	 al.,	 2009)	 and	 examine	 the	 errors	 associated	 with	 each.	 Ultimately,	 any remote	sensing‐based	monitoring	system	must	be	able	to	measure	changes	in	forest	area	at	a fine	spatial	scale	(e.g.	~	1	ha)	and	carbon	stock	consistently	over	the	longer	term	to	be	able	to support	a	REDD+	MRV	system	(DeFries	et	al.,	2007;	GOFC‐GOLD,	2011).  70  5.2 Limitations	of	Study This	 thesis	 presented	 two	 potential	 methods	 for	 integrating	 LiDAR	 and	 radar	 data.	 Several limitations	and	caveats	for	each	study	are	described	below: Sample	 Size:	 	 The	 number	 of	 field	 plots	 used	 in	 the	 study	 presented	 in	 chapter	 3	 was	 small. Given	 the	 small	 sample	 size,	 all	 samples	 were	 used	 for	 model	 fitting.	 The	 robustness	 of	 the observed	 relationship	 and	 extrapolation	 of	 the	 results	 should	 be	 interpreted	 cautiously. Independent	 plots	 for	 validation	 could	 not	 be	 established	 and	 measured	 due	 to	 harvesting	 of the	study	site	in	2011. Misalignment	of	dates:	The	data	sources	used	in	chapter3	and	4	were	not	temporally	coherent (i.e.,	they	were	acquired	on	different	dates).	Although	discussed	and	addressed	in	section	3.2.2, the	 acquisition	 of	 data	 from	 different	 dates	 does	 introduce	 uncertainties	 in	 the	 estimates.	 No assessment	of	this	uncertainty	was	possible	given	no	LiDAR	and	PALSAR	data	was	available	for 2010. Co‐variance	of	LiDAR	and	SAR	data:	The	accuracy	of	forest	biomass	estimates	suffered	from low	correlation	between	the	LiDAR‐derived	aboveground	biomass	estimates	and	the	radar	data, as	 discussed	 in	 Section	 4.4.	 This	 in	 turn	 affected	 the	 distance	 where	 spatial	 dependency	 was observed	in	the	kriging	process.	The	full	potential	of	radar	data	(i.e.	InSAR	heights)	could	not	be investigated	given	that	appropriate	data,	such	as	single‐pass	InSAR	data,	were	not	available. Forest	 type:	 Integration	 approaches	 investigated	 in	 this	 thesis	 were	 applied	 to	 a	 coastal temperate	forest	which	had	high	levels	of	biomass.	The	portability	of	these	approaches	to	the boreal	 forest	 or	 tropical	 forest	 biomes	 was	 not	 investigated.	 The	 higher	 correlation	 between radar	measurements	and	low	to	moderate	biomass	levels	suggests	that	the	accuracy	in	biomass estimates	may	be	better	in	boreal	forests.	In	contrast,	dense	tropical	forests	with	a	substantially  71  dense	 understory	 may	 limit	 the	 information	 content	 from	 C‐band	 radar	 since	 the	 microwave pulse	would	be	mainly	attenuated	within	the	upper	canopy. Biomass	 monitoring:	 Although	 determining	 baseline	 carbon	 stocks	 is	 necessary,	 under	 the UNFCCC	REDD+,	monitoring	and	assessing	forest	carbon	stock	changes	is	required	to	measure emissions	across	time.	The	results	from	chapter	4	provided	carbon	stock	amounts	for	only	one time	period.	No	investigation	was	made	on	the	monitoring	capability	of	the	proposed	approach. However,	 the	 monitoring	 capacity	 of	 LiDAR	 reported	 by	 Bater	 et	 al.	 (2011)	 does	 suggest potential.  5.3 	Future	Research This	 research	 has	 highlighted	 the	 importance	 of	 exploiting	 the	 synergies	 between	 multiple sensors.	However,	potential	key	synergies	between	multiple	sensors	are	mainly	the	subject	of research	and	are	not	operationally	applied	(De	Sy	et	al.,	2012).	Acknowledging	the	limitations	of this	research,	a	number	of	areas	on	which	future	research	could	focus	on	are:   Determining	if	C‐band	radar	entropy	and	InSAR	coherence	provide	similar	relationships when	the	sample	population	size	is	increased;    Investigating	 the	 use	 of	 kriging	 with	 InSAR	 derived	 heights,	 to	 exploit	 the	 stronger correlation	 between	 the	 LiDAR	 and	 radar‐derived	 heights	 and	 thereby	 provide improved	accuracy	in	biomass	estimates.	However,	due	to	the	uncertainty	of	obtaining raw	 interferometric	 TamDEM‐X	 data,	 this	 investigation	 may	 be	 limited	 to	 airborne InSAR	data	collection	campaigns	or	future	space‐borne	radar	sensors;    Assessing	 the	 portability	 of	 these	 methods	 to	 other	 forest	 biomes,	 such	 as	 tropical	 or boreal	forests.	With	the	boreal	forest	covering	approximately	77%	of	Canada’s	forested land	(Wulder	et	al.,	2007)	and	providing	an	important	carbon	sink	(Apps	et	al.,	1995),  72  investigating	other	potential	methods	to	assess	this	large	forest	area	can	be	important in	understanding	forest	carbon	stocks	in	northern	Canada;	and   Determining	 if	 spatial	 modeling	 techniques	 are	 viable	 methods	 for	 monitoring	 and assessing	changes	in	carbon	stocks.	Although	LiDAR	data	collected	from	different	passes can	 provide	 similar	 vertical	 characteristics	 (Bater	 et	 al.,	 2011),	 determining	 whether spatial	kriging	can	measure	carbon	stocks	over	time	is	not	known.   Understanding	the	complementary	ways	in	which	accurate	LiDAR	data	can	be	integrated	with space‐borne	radar	to	characterize	forests	is	an	active	area	of	research.	In	this	thesis,	I	examined two	 areas	 of	 study	 related	 to	 data	 integration	 for	 biomass	 estimation.	 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