Effects of mutual shading of tree crowns on prediction of photosynthetic light-use efficiency in a coastal Douglas-fir forest.

Abstract

Gross primary production (GPP) is often expressed as the product of absorbed photosynthetically active radiation and the efficiency (epsilon) with which a plant community uses absorbed radiation in biomass production. Light-use efficiency is affected by environmental stresses, and varies diurnally and seasonally. Uncertainty about epsilon can be a serious limitation when modeling GPP. An important determinant of epsilon is the amount and type of solar radiation incident on a canopy, because an abundance of light can trigger a photo-protective reaction, diminishing GPP. The radiation regime in a forest canopy is determined by the predominant sky conditions and by mutual shading of tree crowns. Shading effects, producing shifts in the amount of incident direct and diffuse solar radiation, have been largely ignored, however, because they depend on forest structure and are difficult to measure. We describe a new approach for estimating changes in mutual canopy shading throughout the day and year based on a canopy structure model derived from light detection and ranging (LiDAR). Proportions of canopy shading were then combined with eddy covariance data to assess the explanatory power for variance in epsilon by regression tree analysis over half-hourly, daily and weekly time scales. The approach explained between 75 and 97% of variance in epsilon, representing an increase of between 5 and 16% compared with models driven solely by meteorological variables.

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Summary
pressed as the product of absorbed photosynthetically active
radiation and the efficiency (ε) with which a plant community
uses absorbed radiation in biomass production. Light-use effi-
ciency is affected by environmental stresses, and varies diur-
nallyandseasonally.Uncertaintyaboutεcanbeaseriouslimi-
tation when modeling GPP. An important determinant of ε is
theamountandtypeofsolarradiationincidentonacanopy,be-
causeanabundanceoflightcantriggeraphoto-protectivereac-
tion,diminishingGPP.Theradiationregimeinaforestcanopy
is determined by the predominant sky conditions and by mu-
tual shading of tree crowns. Shading effects, producing shifts
in the amount of incident direct and diffuse solar radiation,
have been largely ignored, however, because they depend on
foreststructureandaredifficulttomeasure.Wedescribeanew
approach for estimating changes in mutual canopy shading
throughoutthedayandyearbasedonacanopystructuremodel
derived from light detection and ranging (LiDAR). Propor-
tionsofcanopyshadingwerethencombinedwitheddycovari-
ance data to assess the explanatory power for variance in ε by
regression tree analysis over half-hourly, daily and weekly
time scales. The approach explained between 75 and 97% of
variance in ε, representing an increase of between 5 and 16%
compared with models driven solely by meteorological vari-
ables.
Gross primary production (GPP) is often ex-
Keywords: GPP, LiDAR, regression trees.
Introduction
Global modeling of plant photosynthesis, or gross primary
production (GPP), is a critical aspect of climate change mod-
eling, because it predicts the amount of atmospheric CO2ab-
sorbed by terrestrial ecosystems(Hamilton et al. 2002, Janzen
2004). Existing models often express GPP as the product of
photosynthetically active radiation (PAR), defined as solar ra-
diationbetween400and700nm,thefractionofPARabsorbed
by the plant canopy ( fPAR), and the efficiency (ε) with which
fPARis used in the production of biomass (Monteith 1972,
1977):
GPPPAR
PAR
= ε f
(1)
Our ability to measure fPARand PAR globally by satellite re-
mote sensing has improved significantly in recent years; how-
ever, the determination of ε over space and time remains chal-
lenging (Running et al. 2004, Hall et al. 2006). Physiologi-
cally,εisdeterminedbythemostlimitingofalargenumberof
environmental stresses, some of which may have only short-
term effects on photosynthesis (photo-inhibition), whereas
others can have longer-term effects on GPP, even after the
stress event has ended (Adams et al. 1999, 2002). Conse-
quently, ε is highly variable and differs among sites, species
and individuals (Demmig-Adams 1998). Uncertainty about ε
can be a serious limitation when modeling GPP (Running et
al. 2004).
Existing satellite-based measures of GPP incorporate ε ei-
ther explicitly or implicitly from environmental stresses, typi-
cally focusing on a few globally measurable meteorological
variables. In temperate climates, the prevailing atmospheric
sky condition, driven by cloudiness, water vapor content or
smog, is a key factor influencing photosynthesis (Turner et al.
2003, Lagergren et al. 2006, Schwalm et al. 2006), because it
controlstheamountandtype(directordiffuse)ofradiationin-
cident on a plant canopy. The influence of radiation on GPP is
twofold: (1) light can be a limiting factor to photosynthesis, in
which case almost all absorbed solar energy is used in carbon
assimilation (ε ≈ 100%); and (2) abundant light can trigger
a photo-protective reaction, down-regulating photosynthesis
and lowering ε (Demmig-Adams 1990, Demmig-Adams and
Adams 1996).
A common approach to describing radiation regimes is the
ratio of direct to diffuse radiation (Q) available from instru-
mentation at flux tower sites (Turner et al. 2003, Schwalm et
al. 2006). In a forest canopy, however, the amount of radiation
Tree Physiology 28, 825–834
© 2008 Heron Publishing—Victoria, Canada
Effects of mutual shading of tree crowns on prediction of
photosynthetic light-use efficiency in a coastal Douglas-fir forest
THOMAS HILKER,1,2NICHOLAS C. COOPS,1CHRISTOPHER R. SCHWALM,3RACHHPAL
(PAUL) S. JASSAL,4T. ANDREW BLACK4and PRAVEENA KRISHNAN4
1Faculty of Forest Resources Management, University of British Columbia, 2424 Main Mall, Vancouver, BC V6T 1Z4, Canada
2Corresponding author (thilker@interchange.ubc.ca)
3Department of Natural Resources, University of Minnesota, St. Paul, MN 55155, USA
4Faculty of Land and Food Systems, University of British Columbia, 2357 Main Mall, Vancouver, BC V6T 1Z4, Canada
Received April 16, 2007; accepted November 29, 2007; published online April 1, 2008
at University of Portland on May 22, 2011
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received by a tree crown is dependent not only on atmospheric
conditions,butalsooncanopystructure,whichdeterminesthe
degree of mutual shading between and within individual tree
crowns. These shading effects may produce significant shifts
intheeffectiveproportionofdirecttodiffuseradiation(Qe)re-
ceived, especially in the morning and late afternoon when so-
lar elevation is low (Li and Strahler 1992). Consequently,
shading within forest canopies determines the distribution of
energy incident on trees, and may therefore significantly af-
fect ε. Additionally, the capacity of leaves to dissipate excess
radiant energy thermally varies within the canopy (vertically
and horizontally), because shaded leaves are more susceptible
to photoinhibition than sunlit leaves (Demmig-Adams 1998).
Finally, shading effects are a major determinant of the surface
conductance of canopy foliage (Brooks et al. 1997), which in
turn controls the availability of CO2to photosystem II. Al-
though the effects of mutual shading on canopy illumination
have been acknowledged in several studies (Li and Strahler
1992, Li et al. 1995), the resulting effect on ε has been largely
ignored.
We introduce a new approach to assess mutual shading of
forest canopies (hereafter canopy shadow fraction) and its ef-
fect on ε based on airborne laser scanning (referred to as light
detection and ranging, LiDAR). We modeled canopy shading
over a 6-year period (May 1, 2000 to August 31, 2006) to cal-
culate Qeincident on a Douglas-fir (Pseudotsuga menziesii
var.menziesii(Mirb.)Franco)dominatedforeststand.Shadow
proportions were combined with several meteorological vari-
ables to assess, by regression tree analysis, their relative ex-
planatory power for variance in ε observed over different time
scales. The results were compared with a second set of regres-
sionsbasedonmeteorologicalvariablesalone(i.e.,notconsid-
ering shadow fraction (σc)). In addition, the potential of up-
scaling canopy shading and modeling it as a function of struc-
ture and stand age to facilitate application over larger areas
was demonstrated for clear-cut, young, intermediate-aged and
mature forest stands.
Materials and methods
Research site
The study area is a Canadian Carbon Program (CCP) site
(hereafterDF-49site)locatedontheeasternsideofVancouver
Island, British Columbia, Canada (49°52′ N, 125°20′ W,
300 m a.s.l.). It is within the dry maritime Coastal Western
Hemlock biogeoclimatic subzone (CWHxm), characterized
by cool summers and mild winters with occasional drought
during late summer (mean annual precipitation = 1500 mm
and mean annual temperature = 8.5 °C; Humphreys et al.
2006). The forest stand consists of 80% Douglas-fir, 17%
western red cedar (Thuja plicata Donn ex D. Don) and 3%
western hemlock (Tsuga heterophylla (Raf.) Sarg.) (Morgen-
stern et al. 2004, Humphreys et al. 2006). The soil is a humo-
ferricpodzolwithagravellysandyloamtextureoverlainbyan
organic surface layer ranging from 1 to 10 cm in depth.
Flux tower data
Carbon dioxide and heat flux measurements
half-hourly fluxes of CO2and water vapor were measured
above the canopy by the eddy covariance (EC) technique
(Morgenstern et al. 2004, Humphreys et al. 2006) for the
2000–2006 growing seasons (defined as days of year (DOY)
between 105 and 288). Net ecosystem exchange (NEE) was
calculated as the sum of half-hourly fluxes of CO2and the rate
ofchangeinCO2storageintheaircolumnbetweentheground
and the EC measurement level (42 m), measured with a three-
axissonicanemometer-thermometer (SAT,ModelR3,Gill In-
struments, Lymington, U.K.) and a closed-path CO2/H2O in-
frared gas analyzer (Model LI-6262, Li-Cor). Incident and re-
flected PAR were measured with upward and downward look-
ing Li-Cor quantum sensors (Model 190 SZ), installed above
and below the canopy. Gaps in data of less than 2 h were filled
by linear interpolation. Half-hourly measures of daytime GPP
were derived from:
Continuous
GPPNEP
d
=+ R
(2)
where NEP = –NEE and Rdis daytime ecosystem respiration
(Morgenstern et al. 2004, Jassal et al. 2007). Light-use effi-
ciencywascalculatedfromEquation1withPARmeasureddi-
rectly by the downward-looking quantum sensor and half-
hourly fPARdetermined from incident and reflected PAR above
and below the canopy (ρ1(θ) and ρ2(θ), respectively), solar ze-
nith angle (θ) and the effective leaf area index (LAIe) (Chen
1996):
( ) (
−
)
fe
G
PAR
LAI
θ
te
=−−
−
11
12
ρ θ
( )
ρ θ
θ
cos
( )
( )
(3)
where Gt(θ) is the projection coefficient for total PAR trans-
mission approximated by a constant of 0.5 (Chen 1996, Chen
etal.2006)andLAIe=4.3isderivedfromground-basedmeth-
ods (Chen et al. 2006). Sensible (H) and latent (λE) heat
fluxes were calculated as described by Humphreys et al.
(2006) and Jassal et al. (2007).
Weather measurements
with a “sunshine sensor” (Model BF3, Delta-T Devices) and
upwelling (L↑) and downwelling (L↓) thermal infrared radia-
tion(definedasradiationofwavelengthλ>4000nm)werede-
termined above the canopy with pyrgeometers (Model CNR1,
Kipp & Zonen B.V., Delft, The Netherlands). Above-canopy
airtemperature(Ta)andrelativehumidityweremeasuredwith
temperature and humidity probes (HMP45CF, Vaisala Oyj,
Helsinki,Finland)housedinaspiratedshields(Model076Bra-
diationshield,Met-OneInstruments,GrantsPass,OR)(Hum-
phreysetal.2006).Atmosphericvaporpressuredeficit(D)was
computed from Taand relative humidity (Buck 1981).
Half-hourly means of volumetric soil water content in the
0–60 cm soil layer (Θ60) were derived from measurements
made at two locations and four depths between 2 and 100 cm
with water content reflectometers (Model CS-615, Campbell
Incident diffuse PAR was measured
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Scientific) and at 11 stations with time domain reflectometry
(TDR) probes (Hook and Livingston 1996). Soil water
content–soilmatricpotentialrelationshipsweredeterminedin
the laboratory on intact soil cores from 0–60 cm layers with a
pressure plate apparatus. The resulting field capacity and per-
manent wilting point were 0.25 and 0.10 m3m– 3, respectively
(Coops et al. 2007).
LiDAR data
LiDAR is an airborne remote sensing technology that deter-
mines distances to an object or surface with laser pulses. First
pulse returns are reflected from the highest surface (e.g., tree
canopies), whereas last hit returns are reflected from the low-
est points in the landscape, most often the terrain surface.
LiDAR data were acquired on June 8, 2004, by Terra Remote
Sensing (Sidney, BC, Canada) with a ground return density of
0.7hitm–2andafootprintdiameter(spotsize)of0.19m.Clas-
sification of LiDAR data into either ground or non-ground re-
turns was carried out with Terrascan v. 4.006 software
(Terrasolid, Helsinki, Finland) (Kraus and Pfeifer 1998).
Modeling shadow fractions within the canopy
Model development
steps. First, non-ground LiDAR returns were extracted and
used to generate a three-dimensional forest canopy structure
model(CSM)(spatialresolutionis30cm)ataradiusof500m
around the tower to approximate the eddy flux footprint
(Blanken et al. 2001, Kljun et al. 2004). This CSM was as-
sumed to be representative and constant over the entire 6-year
period, because the structure of the coniferous forest was not
expectedtochangesignificantlyduringthistime(Klinkaetal.
1991).Second,thegeneratedCSMwasusedtosimulateσcper
half-hour time step based on a hillshade algorithm (ArcGIS,
Esri, Redlands, CA). Hillshades are panchromatic rasters that
modelilluminationconditionsforagivensurfacebasedonsun
position (Reda and Andreas 2004) and are commonly used in
spatial mapping (Van Den Eeckhaut 2005). Assuming clear
sky conditions, canopy shadow fractions can be computed
from hillshadesas the proportion of sunlit to shadedpixels de-
rived from binary classification. For a canopy surface, σcis
likelytooverestimateshadowingeffects,becausetheCSMde-
scribesthecanopyasanopaquesurface,whereastreecanopies
aretranslucent.Tomitigatethiseffect,aweighting,ortranspar-
ency, factor (p) was introduced, which reduced the effective
shading within the canopy. The transparency factor was de-
fined corresponding to the probability of canopy gaps P at a
given solar zenith angle (θ) (Chen 1996):
Canopy shading was computed in two
Pe
G
( )
θ
( )
cos
θ
θ
=
−
te
LAI
(4)
where LAIeand Gt(θ) were used in conformity with Equa-
tion 3. To verify modeled σc, digital images were acquired
from the 45-m flux tower in 24 directions around the mast
(horizontal offset between pictures was 11.5°, beginning at
313° to avoid blocking by the tower) at a constant vertical ze-
nithangleof118°withaSonydigitalcamera(ModelDSCT7)
underaclearsky.Imagehistogramswerecomputedandasim-
ple threshold defined to classify pixels as either sunlit or
shaded. A hillshade for the same half-hour interval was com-
puted and the shadow fractions compared.
Implementing shadow fractions in the canopy radiation re-
gime
The value of Q (without considering σc) is defined as:
Q =
−ρρ
ρ
tot diff
diff
(5)
where ρtotand ρdiffare total and diffuse incident PAR, respec-
tively. Mutual shading of tree crowns affects Q incident on a
leaf by increasing the diffuse and decreasing the direct radia-
tion components,hence the effective amount of direct PAR in-
cident on the canopy (ρe,dir) can be obtained from
ρσ
e,dirc
()1− p
,wherepσcistheweightedshadowfraction.The
amount of effective diffuse radiation (ρe,diff) is then calculated
from,andbothtermssubstitutedin,Equation5toyieldQeas:
( )()
σ
Q
p
−
1
e
e,dir
ρ
ρ
e,diff
e,dir
−
tot
ρ
e,dir
ρ
1
tot
(
diff
−
c
p
==
=
−
ρ
−
ρ
ρ
ρ
−
σ
)()
ρρ
tot totdiffc
(6)
Assessing the power of Qeto account for variation in
Regression tree analysis
by regression tree analysis. Regression trees are created by
non-parametric data mining and can be considered as a se-
quence of binary nodes (yes/no queries) splitting dependent
variables using optimal predictor variables based on least
squares (Melendez et al. 2006). The proportion of variation in
each response variable predicted by each measurement vari-
able is assessed on a linear scale from 0 to 100. All regression
treeswerecomputedbasedona10-foldcrossvalidation,witha
maximum tree depth of 16 and a minimum splitable node size
of10.Treepruningwassettotheminimumcrossvalidationer-
ror (Witten and Frank 2005).
The effect of σcon ε was assessed
Contribution of Qeover different time scales
to predict variation in ε was assessed by regression tree analy-
sis, relative to the power of additional predictor variables in-
cludingTa,L↓,L↑,H,λE,Θ60andD(Schwalmetal.2006).Be-
cause these variables change diurnally and seasonally (Fig-
ure 1), the proportion of variation in ε explained was expected
to change with the temporal scale observed. To investigate
these changes, four regression trees were constructed for
half-hourly (non-water-stressed and water-stressed), daily and
weekly time intervals (hereafter referred to as regression trees
A1–A4):
A1.Regressiontreeanalysisforhalf-hourlyvariationsinε:
The power of Qe
ελ=↓↑
f Q T L
(,
e
LHD
,,,,,, )
a
E
Θ60
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A2. Regression tree analysis for half-hourly variations of
ε of plants subject to water stress using values acquired with
Θ60 < 0.1:
ε
λ
Θ <
<
<<<
<
=↓↑
0 1.
0 1.
0 1.
,
0 1.0 1.
)
0 1.
,
,
(,,,,
f QTLL
ea
E
Θ
ΘΘΘ
Θ
,,
.,..
HD
ΘΘΘ
Θ
<<<
0 1600 1 0 1
A3. Regression tree analysis investigating daily (d) aver-
aged data:
εd=↓↑
f Q
(
TLLHD
)
edad
dddd
60d
d
,,, , E ,
λ
,,
Θ
A4. Regression tree analysis investigating weekly (w) aver-
aged data:
εw=↓↑
f Q
(
TLLHD
)
ewaw
wwww
60w
w
,,, , E ,
λ
,,
Θ
(εdand εwwere computed as the ratio of summed totals di-
vided by the relevant time frame).
The benefit of considering σcto explain variations in ε was
assessedinasecondanalysis,withthesametimeintervals,set-
tingsandinputvariables,butsubstitutingQewithQ,thatis,ig-
noring σc(hereafter referred to as regression trees B1–B4).
Upscaling shadow fractions
Modeling shadow fractions from stand parameters
LiDARdatacanbeusedtoestimatecanopyshadingoversmall
areas, large area coverage of LiDAR is relatively expensive.
Thus,itisimportanttodetermineifbroaderspatialestimatesof
σccan be developed from more easily measured parameters,
suchassolarpositionandstandtype.Toassessthepotentialof
modeling shadow fractions from stand parameters, we com-
puted σcfor three addition stands adjacent to DF-49 (a clear-
cut, a young forest planted in 1990 and a 38-year-old stand;
Figure2) andcomparedσcathalf-hourlyanddailytimesteps.
Although
The potential of
The standard GPP algorithm of the moderate resolution imag-
ing spectro-radiometer (MODIS) uses 8-day means of fPAR,
PAR and ε, where ε is a biome-specific constant, representing
theoptimalpotentialofavegetationtypeforconvertingPARto
cin satellite-based GPP products
828HILKER ET AL.
TREE PHYSIOLOGY VOLUME 28, 2008
Figure 1. Half-hourly, daily and weekly means (± standard deviation) of latent (λE) and sensible (H) heat fluxes, vapor pressure deficit (D) and
half-hourlymeansofvolumetricsoilwatercontentinthe0–60cmsoillayer(Θ60)forthe2005growingseason(daysofyear,DOY105–288).For
daily means, only every 7th day is displayed.
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biomass(Turneretal.2003,Runningetal.2004),whichisad-
justed using daily mean D to account for water/humidity re-
lated stress factors, and minimum daily air temperature (Tmin)
to account for thermal stresses (Heinsch et al. 2003). We as-
sessedthepotentialofimprovingMODIS-basedpredictionsof
ε by including shadow fractions as an additional explanatory
variable:
εεσ
MODIS min
d
cd
,,
=
max ()
f TD
where σcdis mean daily shadow fraction. The explanatory
power of this regression tree (named A5) was compared with
the current approach (named regression tree B5), expressing ε
as:
εε
MODIS min
d
,
=
max ()
f TD
Results
Modeling shadow fractions
Figure 3a illustrates the CSM for the DF-49 site derived from
LiDAR observations. Photographically estimated shadow
fractions and those modeled from hillshades were signifi-
cantly correlated (r2= 0.7, P < 0.05, n = 24; Figure 3b), with
CSMshadowfractionsrangingbetween10and90%andshad-
ing fractions obtained from digital photography ranging be-
tween 20 and 80%. Figure 4 illustrates how the computed
shadow fractions vary over a growing season at different time
scales. Half-hourly means showed up to 99% mutual shading
at sunrise and sunset, and between 58 and 77% at solar noon.
Daily and weekly means ranged between 65 and 95%, with
minimum values at summer solstice. Light-use efficiency var-
iedbetween0.05and4.0gCMJ–1,andwaslowestintheafter-
noon and highest in the early morning (Figure 5), especially
under cloudy conditions.
Regression tree analysis
Regression trees
treecomputedforweeklyaverageddata(regressiontreeA4)is
shown in Figure 6 to illustrate how the algorithm splits the de-
pendent variable (ε) into homogeneous subsets based on
thresholding. The success of splitting is used to assess the im-
portance of each predictive variable. For example, the tower-
based weekly estimates of ε were largely explained by
Qew60w
,and L
Θ↓ .
A schematic representation of a regression
w
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MUTUAL CANOPY SHADING AND PHOTOSYNTHETIC LIGHT-USE EFFICIENCY829
Figure 2. Sites selected for acquisition of shadow fractions using
LiDAR drawn overa Quickbirdpanchromaticsatelliteimage(ground
resolution: 0.61 m). Coordinates are projected in UTM Zone 10. The
circular shape of the main site approximates the footprint of the eddy
covariance measurements.
Figure 3. (a) LiDAR-derived canopy structure model within a radius
of 1 kmfromthetower. The heightof thetower (center)isoverdrawn.
(b) Correlation between photographically derived shadow fraction
(σc, red channel) versus σcmodeled by hillshade analysis (r2= 0.7, P
< 0.05). The threshold value separating shadow from light in the digi-
tal images was selected independently from that of the hillshade
model,thus,adirectcomparisonofabsolutevaluesmustbemadecau-
tiously. Each valuerepresentsanobservationatonerotationangle,and
the dotted line represents the 1:1 line.
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