Controls on seasonal patterns of maximum 
ecosystem carbon uptake and canopy-scale 
photosynthetic light response: contributions 
from both temperature and photoperiod
Authors: Paul Stoy, Amy M. Trowbridge, and William 
L. Bauerle
The final publication is available at Springer via http://dx.doi.org/10.1007/s11120-013-9799-0.
Stoy, Paul, Amy M. Trowbridge, and William L. Bauerle. "Controls on seasonal patterns of 
maximum ecosystem carbon uptake and canopy-scale photosynthetic light response: 
contributions from both temperature and photoperiod." Photosynthesis Research 119, no. 1-2 
(2014): 49-64.
Made available through Montana State University’s ScholarWorks 
scholarworks.montana.edu 
Controls on seasonal patterns of maximum ecosystem carbon 
uptake and canopy-scale photosynthetic light response: 
contributions from both temperature and photoperiod
Paul C. Stoy • Amy M. Trowbridge •
William L. Bauerle
Abstract Most models of photosynthetic activity assume
that temperature is the dominant control over physiological
processes. Recent studies have found, however, that pho-
toperiod is a better descriptor than temperature of the sea-
sonal variability of photosynthetic physiology at the leaf
scale. Incorporating photoperiodic control into global
models consequently improves their representation of the
seasonality and magnitude of atmospheric CO2 concentra-
tion. The role of photoperiod versus that of temperature in
controlling the seasonal variability of photosynthetic func-
tion at the canopy scale remains unexplored. We quantified
the seasonal variability of ecosystem-level light response
curves using nearly 400 site years of eddy covariance data
from over eighty Free Fair-Use sites in the FLUXNET
database. Model parameters describing maximum canopy
CO2 uptake and the initial slope of the light response curve
peaked after peak temperature in about 2/3 of site years
examined, emphasizing the important role of temperature in
controlling seasonal photosynthetic function. Akaike’s
Information Criterion analyses indicated that photoperiod
should be included in models of seasonal parameter vari-
ability in over 90 % of the site years investigated here,
demonstrating that photoperiod also plays an important role
in controlling seasonal photosynthetic function. We also
performed a Granger causality analysis on both gross eco-
system productivity (GEP) and GEP normalized by photo-
synthetic photon flux density (GEPn). While photoperiod
Granger-caused GEP and GEPn in 99 and 92 % of all site
years, respectively, air temperature Granger-caused GEP in
a mere 32 % of site years but Granger-caused GEPn in 81 %
of all site years. Results demonstrate that incorporating
photoperiod may be a logical step toward improving models
of ecosystem carbon uptake, but not at the expense of
including enzyme kinetic-based temperature constraints on
canopy-scale photosynthesis.
Keywords Eddy covariance  Granger causality 
Gross ecosystem productivity  Light response curve 
Net ecosystem exchange  Seasonal variability
Abbreviations
AIC Akaike’s Information Criterion
C-LAMP Carbon Land Model Intercomparison Project
CLM Community Land Model
DOY Day of year
GEP Gross ecosystem productivity
GPPn Gross ecosystem productivity normalized by
photosynthetic photon flux density
GPP Gross primary productivity
HSD (Tukey’s) Honestly Significant Difference test
Jmax Rate of photosynthetic electron flow at light
saturation
L Maximum value of the likelihood function
LDay Day length
M Linear model
N Number of parameters
N Number of instances
NEE Net ecosystem exchange
P. C. Stoy (&)  A. M. Trowbridge
Department of Land Resources and Environmental Sciences,
Montana State University, Bozeman, MT 59717, USA
e-mail: paul.stoy@montana.edu
W. L. Bauerle
Department of Horticulture and Landscape Architecture,
Colorado State University, Fort Collins, CO 80523, USA
W. L. Bauerle
Graduate Degree Program in Ecology, Colorado State
University, Fort Collins, CO 80523, USA
PPFD Photosynthetic photon flux density
RE Ecosystem respiration
Ta Air temperature
Vc,max Maximum carboxylation capacity
a Initial slope of the light response curve
b Net ecosystem exchange at light saturation
c Ecosystem respiration calculated as the intercept
of the light response curve
hN Degree of curvature of the non-rectangular
hyperbola
M Referring to the Mitscherlich model
max Referring to the maximum seasonal value
calculated using a second-order polynomial
N Referring to the non-rectangular hyperbola
p Referring to a light response curve parameter
or combination of parameters
concentration (Bauerle et al. 2012; Bonan et al. 2011).
These results suggest that LDay may improve models of
gross ecosystem productivity (GEP) at the canopy scale
(Groenendijk et al. 2011). However, controls over the sea-
sonal pattern of GEP remain unclear because of the multiple
mechanisms that determine canopy photosynthesis. For
example, leaf area index varies over the course of the sea-
son, even in tropical canopies (van Schaik et al. 1993;
Wright and van Schaik 1994). Longer photoperiods corre-
spond to smaller minimum zenith angles and greater canopy
penetration of direct solar radiation (Song et al. 2009). Leaf
age and N allocation also influence the seasonal pattern of
photosynthetic parameters and photosynthetic rates (Wilson
et al. 2000; Reich et al. 1991), and incorporating this
information into ecosystem models improves their ability to
capture the seasonal dynamics and magnitude of photo-
synthetic uptake (Wilson et al. 2001). A number of mech-
anisms are thus responsible for seasonal variability of
canopy photosynthesis, and it is unclear if simply adding
LDay as an independent variable will improve model skill.
Incorporating canopy structure and nutrient allocation
into models of canopy photosynthesis remains a challenge
because it is difficult to observe the timing and magnitude of
canopy development and photosynthetic capacity at plot,
regional, and global scales (Fisher et al. 2007; Grace et al.
2007; Tian et al. 2002). These challenges remain despite
recent improvements in our ability to apply remote sensing
observations to quantify canopy function (Ryu et al. 2011;
Asner 1998), and remote sensing observations, like all
observations, contain important uncertainties (Foody and
Atkinson 2006). Uncertainties in the independent variables
of an ecological model introduce the well-known ‘‘errors in
x’’ problem (Chesher 1991; Fuller 1987) (also known as
‘‘regression dilution’’ or ‘‘attenuation’’), which add bias
error to the dependent variable, in our case GEP. Time, for
all intents and purposes, is without uncertainty for ecological
applications, excluding human error in timekeeping. If LDay
can be used as an explanatory variable for photosynthesis
models at the canopy scale, following the findings of Bauerle
et al. (2012) at the leaf and global scales, a variable that is
uniquely nearly error-free (at least for the purposes of eco-
logical studies) can be used to improve ecosystem models.
To explore the role of LDay in controlling seasonal vari-
ability in GEP and canopy-scale photosynthetic function, we
adopt a data-intensive approach (Gray 2009) to explore
patterns in large ecological datasets (Hunt et al. 2009). We
examined 385 site years of eddy covariance-measured net
ecosystem exchange (NEE) and estimated GEP from 81
research sites to test if adding time via LDay in addition to
temperature improves model prediction of maximum eco-
system-scale carbon uptake and the initial slope of the
light response curve. We chose to investigate the parameters
of simple light response curves to avoid introducing
Introduction
Chemical reactions, including those mediated by biological 
processes, are dependent on temperature. At the same time, 
organisms exhibit control over temporal aspects of reaction 
rates, the most familiar of which are the ca. 24 h period-
icities known as circadian rhythms that were described for 
stomatal conductance as early as Darwin (1898) and for 
photosynthesis as early as Hastings et al. (1961) (see Webb 
2003). Recent studies have even found evidence of circa-
dian patterns in carbon uptake at the ecosystem scale 
(de Dios et al. 2012), suggesting that models of canopy 
photosynthesis may benefit by simply including time as an 
independent variable.
The broader study of temporal changes in organismal 
function is known as chronobiology, and botanical exam-
ples include the seasonal variability in carbon and nutrient 
uptake and allocation. Despite chronobiological control 
over many aspects of plant function, the most common 
models of photosynthesis include parameters that are 
constant or are a function of temperature, leaf nitrogen 
concentration, and other factors (Farquhar et al. 1980), 
rather than photoperiod. These formulations follow from 
the fundamental rate laws of enzyme kinetics, but may be 
incomplete descriptions of the seasonality of photosyn-
thesis if chronobiological factors are also at play.
Recent research has shown that photoperiod (here 
abbreviated LDay for day length) is a better descriptor of the 
seasonal patterns of leaf-level photosynthetic activity than 
is temperature (Bauerle et al. 2012). Applying these find-
ings to the CLM global-scale terrestrial carbon cycle model 
improved its ability to replicate the observed global 
seasonal pattern and magnitude of atmospheric CO2
uncertainties from other variables (e.g., leaf area index) used
to infer Farquhar et al. (1980) model parameters (e.g.,
Vc,max) from eddy covariance data. Maximum ecosystem-
scale carbon uptake was chosen for this analysis because of
its importance in determining the magnitude of GEP across
ecosystem types (Desai et al. 2008a). Seasonality of the
initial slope of the light response curve was explored
because the GEP–light response relationship was identified
by a recent multi-site andmulti-model synthesis as a primary
source of model bias (Schaefer et al. 2012). Specifically, we
model carbon uptake as a function of photosynthetic photon
flux density (PPFD) for over 140,000 days of half-hourly (or
hourly) eddy covariance data and use information criteria
analyses and a well-established econometric analysis,
Granger Causality (Granger 1969; Detto et al. 2012), to
determine if information in LDay, air temperature (Ta), or a
combination of both better explain seasonal patterns of GEP
and canopy light response curve parameters. We also test if
the day of year (DOY) on which photosynthetic parameters
reach their seasonal maximum (DOYmax,p) occurs before or
after that of temperature (DOYmax;Ta ) and LDay (i.e., the
summer solstice, DOY 172 during non leap-years) to
explore how environmental variables contribute causal
information to seasonal patterns of parameter variability.
We further explore how climate zones and vegetation clas-
ses impact DOYmax,p. We hypothesize that there is infor-
mation in the LDay time series that helps explain seasonal
variability in canopy-level photosynthetic function follow-
ing Bauerle et al. (2012).
Methods
We first describe the eddy covariance and meteorological
data used here, followed by a description of the light
response curve analysis including the calculation of the
seasonal maxima of light response curve parameters. We
then describe the statistical analyses, information criteria
analyses, and Granger causality.
Eddy covariance
We analyzed patterns of NEE, GEP, Ta, and LDay using 385
site years of eddy covariance flux observations from81 forest
and shrub-dominated sites designated as Free Fair-Use in the
FLUXNET database (Fig. 1; Tables 1, 2). Grasslands and
Fig. 1 A global map of the Free Fair-Use eddy covariance research
sites in the FLUXNET database, excluding sites in Dry (Semi-Arid
and Arid) and Mediterranean climates where water availability is
likely a dominant control over seasonal patterns of canopy
photosynthesis, and grassland and crop ecosystems where ecosystem
management is likely a dominant control over seasonal patterns of
canopy photosynthesis (see Table 1)
Table 1 Vegetation (Veg.), climate (Clim.), years of available data (Years), latitude (Lat.), and longitude (Long.) for the 81 FLUXNET sites and
385 site years in the Free Fair-Use database analyzed here
Site Veg.a Clim.b Years Lat. Long. Reference
AUFog WET TR 2006–2007 -12.5425 131.307 Guerschman et al. (2009)
AUTum EBF T 2001–2006 -35.6557 148.152 Finnigan and Leuning (2000)
AUWac EBF T 2005–2006 -37.429 145.187 Beringer et al. (2006)
BEBra MF T 1997–2006 [1999, 2003] 51.3092 4.52056 de Pury and Ceulemans (1997)
BEJal MF T 2006 50.5639 6.07333 –
BEVie MF T 1996–2006 50.3055 5.99683 Aubinet et al. (2001)
BRSa3 EBF TR 2000–2003 -3.01803 -54.9714 Saleska et al. (2003)
CAMan ENF B 1994–2003 [1996] 55.8796 -98.4808 Sellers et al. (1995)
CAMer WET TC 1998–2005 45.4094 -75.5186 Lafleur et al. (2003)
CANS1 ENF B 2002–2005 55.8792 -98.4839 Goulden et al. (2006)
CANS2 ENF B 2001–2005 55.9058 -98.5247 Goulden et al. (2006)
CANS3 ENF B 2001–2005 55.9117 -98.3822 Goulden et al. (2006)
CANS4 ENF B 2002–2004 55.9117 -98.3822 Goulden et al. (2006)
CANS5 ENF B 2001–2005 55.8631 -98.4850 Goulden et al. (2006)
CANS6 OSH B 2001–2005 55.9167 -98.9644 Goulden et al. (2006)
CANS7 OSH B 2002–2005 56.6358 -99.9483 Goulden et al. (2006)
CAQcu ENF B 2001–2006 49.2671 -74.0365 Giasson et al. (2006)
CAQfo ENF B 2003–2006 49.6925 -74.3421 Bergeron et al. (2007)
CASF1 ENF B 2003–2005 54.4850 -105.818 Amiro et al. (2006)
CASF2 ENF B 2003–2005 54.2539 -105.878 Rayment and Jarvis (1999)
CASF3 ENF B 2003–2005 54.0916 -106.005 Rayment and Jarvis (1999)
CZBK1 ENF TC 2000–2006 49.5026 18.5384 Havrankova and Sedlak (2004)
CZwet WET T 2006 49.0250 14.7720 Dusˇek et al. (2009)
DEBay ENF T 1997–1999 50.1419 11.8669 Valentini et al. (2000)
DEHai DBF T 2001–2006 51.0793 10.452 Knohl et al. (2003)
DETha ENF T 1996–2006 50.9636 13.5669 Bernhofer et al. (2003)
DEWet ENF T 2002–2006 50.4535 11.4575 Anthoni et al. (2004)
DKSor DBF T 1996–2006 55.4869 11.6458 Pilegaard et al. (2001)
FIHyy ENF B 1996–2006 61.8474 24.2948 Suni et al. (2003)
FIKaa WET B 2000–2006 69.1407 27.295 Aurela et al. (2002)
FISod ENF B 2000–2006 67.3619 26.6378 Thum et al. (2007)
FRFon DBF T 2005–2006 48.4763 2.7801 Le Maire et al. (2005)
FRHes DBF T 1997–2006 48.6742 7.06462 Granier et al. (2000)
FRLBr ENF T 1996–2006 [1999] 44.7171 -0.7693 Berbigier et al. (2001)
IDPag EBF TR 2002–2003 2.3450 114.0360 Hirano et al. (2007)
ISGun DBF T 1996–1998 63.8333 -20.2167 Arado´ttir et al. (1997)
ITLav ENF T 2000–2006 [2003, 2005] 45.9553 11.2812 Cescatti and Marcolla (2004)
ITRen ENF T 1999–2006 46.5878 11.4347 Marcolla et al. (2003)
NLLoo ENF T 1996–2006 52.1679 5.74396 Dolman et al. (2002)
PLWet WET T 2004–2005 52.7622 16.3094 Chojnicki et al. (2007)
RUCok OSH A 2003–2005 70.6167 147.8830 van der Molen et al. (2007)
RUFyo ENF TC 1998–2004 56.46167 32.92389 Kurbatova et al. (2008)
RUZot ENF B 2002–2004 60.8008 89.3508 Kurbatova et al. (2002)
SEDeg WET B 2001–2005 64.1833 19.5500 Sagerfors et al. (2008)
SEFaj WET T 2005–2006 56.2655 13.5535 Lund et al. (2007)
SEFla ENF B 1996–2002 [1999] 64.1128 19.4569 Valentini et al. (2000)
SENor ENF TC 1996–2005 [2000–02, 2004] 60.0865 17.4795 Lagergren et al. (2008)
SESk1 ENF TC 2005 60.125 17.9181 Gioli et al. (2004)
croplands that are likely to experience substantial anthro-
pogenic management were excluded from the analysis, as
were ecosystems from Mediterranean and dry (arid and
semi-arid) climate classifications whose seasonal patterns of
ecological function are likely constrained by water avail-
ability (Ryu et al. 2008).
Eddy covariance is a standard methodology for mea-
suring ecosystem-level fluxes of carbon, water, and energy
(Baldocchi et al. 2001; Aubinet et al. 2000). Briefly, the
eddy covariance technique measures the turbulent
exchange of sensible heat, latent heat (i.e., evapotranspi-
ration), and trace gases including CO2 between the bio-
sphere and atmosphere. It does so by coupling high
frequency (usually 10 to 20 Hz) measurements of the
three-dimensional wind velocity with trace gas and water
vapor concentration measurements from a fast-response
infrared gas analyzer. Surface-atmosphere exchange of
mass and energy is well-represented by the turbulent flux
across a plane in the boundary layer above the surface plus
any changes in mass and energy storage underneath the
Table 1 continued
Site Veg.a Clim.b Years Lat. Long. Reference
SESk2 ENF TC 2004–2005 60.12967 17.8401 Lindroth et al. (2008b)
SKTat ENF TC 2005 49.1208 20.1635 Matese et al. (2008)
UKAMo WET T 2005 55.7917 -3.23889 Hargreaves et al. (2003)
UKGri ENF T 1997–2006 [1999, 2002–2004] 56.60722 -3.79806 Medlyn et al. (2005)
UKHam DBF T 2004–2005 51.1208 -0.8608 Wilkinson et al. (2012)
UKPL3 DBF T 2005–2006 51.4500 -1.26667 Herbst et al. (2008)
USBar DBF TC 2004–2005 44.0646 -71.2881 Richardson et al. (2007a)
USHa1 DBF TC 1991–2006 42.5378 -72.1715 Wofsy et al. (1993)
USHo1 ENF TC 1996–2004 45.2041 -68.7402 Hollinger et al. (1999)
USHo2 ENF TC 1999–2004 45.2091 -68.7470 Thornton et al. (2002)
USLos DBF TC 2001–2005 46.0827 -89.9792 Desai et al. (2008b)
USMMS DBF T 2001–2005 39.3231 -86.4131 Schmid et al. (2000)
USMOz DBF T 2004–2006 38.7441 -92.2000 Gu et al. (2006)
USOho DBF TC 2004–2005 41.5545 -83.8438 DeForest et al. (2006)
USPFa MF TC 1996–2003 [1998, 2001– 2002] 45.9459 -90.2723 Berger et al. (2001)
USSP1 ENF S 2000–2001, 2005 29.7381 -82.2188 Clark et al. (1999)
USSP2 ENF S 1998–2004 29.7648 -82.2448 Clark et al. (1999)
USSP3 ENF S 1999–2004 29.7548 -82.1633 Clark et al. (1999)
USSP4 ENF S 1998 29.8028 -82.2031 Fang et al. (1998)
USSyv MF TC 2002–2006 46.242 -89.3477 Desai et al. (2005)
USUMB DBF TC 1999–2003 45.5598 -84.7138 Curtis et al. (2002)
USWBW DBF S 1995–1999 35.9588 -84.2874 Verma et al. (1986)
USWCr DBF TC 1999–2006 45.8059 -90.0799 Cook et al. (2004)
USWi0 ENF TC 2002 46.6188 -91.0814 Desai et al. (2008a)
USWi1 DBF TC 2003 46.7305 -91.2329 Noormets et al. (2007)
USWi2 ENF TC 2003 46.6869 -91.1528 Noormets et al. (2007)
USWi4 ENF TC 2002–2005 46.7393 -91.1663 Noormets et al. (2007)
USWi5 ENF TC 2004 46.6531 -91.0858 Noormets et al. (2007)
USWi6 OSH TC 2002 46.6249 -91.2982 Noormets et al. (2007)
USWi7 OSH TC 2005 46.6491 -91.0693 Noormets et al. (2007)
USWi8 DBF TC 2002 46.7223 -91.2524 Noormets et al. (2007)
USWi9 ENF TC 2004–2005 46.6188 -91.0813 Noormets et al. (2007)
USWrc ENF T 1998–2006 [2003] 45.8205 -121.952 Chen et al. (2002)
Square brackets indicate years of observations that were not available for analysis
a Veg. vegetation following the International Geosphere-Biosphere Programme (IGBP) classification. DBF deciduous broadleaf forest, ENF
evergreen needleleaf forest, MF mixed forest, OSH open shrubland, WET wetland
b Climate group following the Ko¨ppen–Geiger classification scheme. A arctic, B boreal, S subtropical, T temperate, TC temperate continental, TR
tropical
sensor system during conditions of near-neutral atmo-
spheric stability (Aubinet et al. 2000; Foken et al. 2012).
The magnitude and direction of surface-atmosphere mass
and energy exchange is typically calculated over a half-
hourly or hourly time step, and eddy covariance measure-
ment systems are often run for multiple years or decades
(e.g., Urbanski et al. 2007; Baldocchi 2008) such that
patterns of ecosystem metabolism across diurnal, seasonal,
annual, and interannual time scales can be quantified
(Richardson et al. 2007b; Stoy et al. 2009; Desai 2010).
Eddy covariance measures NEE rather than GEP (see
Goulden et al. 1997, for a discussionof the distinction between
GEP and gross primary productivity, GPP). GEP is often
estimated as the difference between NEE and a model for
ecosystem respiration (RE) that is parameterized using
observationsofNEEat nightwhenGEP is negligible inC3 and
C4-dominated ecosystems following the definition equation:
NEE ¼ GEPþ RE ð1Þ
our GEP estimates with an uncertain temperature signal,
we used measured (i.e., not gap-filled) eddy covariance
data collected during both day time and night time and
estimated RE as the zero intercept of a light response curve
(Lasslop et al. 2010; Lee et al. 1999), an approach that was
found to better-match biometric estimates of ecosystem
carbon uptake across different ecosystem types than mod-
els based on the night time Ta–RE relationship (Stoy et al.
2006). We explore parameters from the Mitscherlich model
(Lindroth et al. 2008a; Aubinet et al. 2001):
NEE ¼ bM þ cMð Þ 1 exp
aMPPFD
bM þ cM
  
 cM ð2Þ
and the non-rectangular hyperbola (Gilmanov et al. 2003;
Lambers et al. 2000):
NEE ¼ 1
2hN
aNPPFD þ bN

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
aNPPFDþ bNð Þ24aNbNhNPPFD
q !
 cN
ð3Þ
where a is the initial slope of the light response curve (also
called apparent quantum yield), b is NEE at light satura-
tion, c represents RE, and h is the degree of curvature in the
non-rectangular hyperbola. Following equation 1, b ? c
represents GEP at light saturation, and we also examine b
(i.e., NEE at light saturation) for completeness. b is related
to the rate of photosynthetic electron flow at light satura-
tion, Jmax, of the Farquhar et al. (1980) photosynthesis
model (Lambers et al. 2000).
Mitscherlich model parameters were chosen to avoid
overestimates of b that can result from parameterizing the
simple rectangular hyperbola (Reichstein et al. 2012). The
non-rectangular hyperbola (Eq. 3) can further improve esti-
mates of b and also a (Gilmanov et al. 2003), but parameter
optimization routines often suffer from lack of convergence
when fitting the four-parameter non-rectangular hyperbola to
eddy covariance data (Stoy et al. 2006). By exploring both
models, we constrain our estimates of a, b, and b ? c for a
more conservative interpretation of their variability.
To quantify seasonal patterns of a, b, and b ? c from
hundreds of site years of observations, we fit the parame-
ters of Eqs. 2 and 3 with a nonlinear least squares algo-
rithm (MATLAB, Mathworks, Natick MA) using data from
a seven-day moving window centered about each DOY for
each site year as demonstrated in Fig. 2. Corresponding
parameter values for the models in Fig. 2 are listed in
Table 3. The seven-day window was chosen to obtain a
sufficient number of data points to fit the parameters of
Eqs. 2 and 3. Periods for which the parameter estimation
routine did not converge were excluded from the analysis,
Table 2 Summary table of the number of site years of eddy
covariance data available per vegetation and climate class in the Free
Fair-Use FLUXNET database, excluding Dry climate classes and
Crop, Grassland, and Savanna vegetation classes
T TC TR B A S Sum
DBF 46 40 0 0 0 5 91
EBF 9 0 6 0 0 0 15
ENF 65 48 0 76 0 17 206
MF 20 10 0 0 0 0 30
OSH 0 2 0 9 3 0 14
WET 7 8 1 13 0 0 29
Sum 148 108 7 98 3 22 385
Vegetation following the International Geosphere-Biosphere Pro-
gramme (IGBP) classification. DBF deciduous broadleaf forest, ENF
evergreen needleleaf forest, MF mixed forest, OSH open shrubland,
WET wetland
Climate group following the Ko¨ppen–Geiger classification scheme. A
arctic, B boreal, S subtropical, T temperate, TC temperate continental,
TR tropical
Carbon uptake by the biosphere is denoted as negative 
following the atmospheric convention used by most eddy 
covariance studies. Here we adopt the biological convention 
and denote ecosystem carbon uptake as positive such that 
GEP is defined as positive for consistency with studies of 
plant physiology.
Light response curves
Most RE models used for the purposes of estimating GEP 
from EC observations use Ta (or soil temperature) as an 
independent variable (Reichstein et al. 2005; Reichstein 
et al. 2012), which would add a temperature-based model 
into our estimate of GEP (Eq. 1). To avoid contaminating
as were days for which the estimated b or c parameters
exceeded 50 lmol CO2 m
-2 s-1, and for which the esti-
mated a parameter exceeded 0.2 lmol CO2 lmol pho-
tons-1. NEE observations whose magnitude exceeded
50 lmol CO2 m
-2 s-1 occurred very infrequently in the
dataset, and likely represent erroneous observations that
eluded standard filters (Papale et al. 2006).
Seasonal variability of light response curve parameters
We also used nonlinear least squares to fit the parameters
of a second-order polynomial with associated uncertainty
estimates in order to calculate the DOY for which Ta, a, b,
and b ? c are at their seasonal maximum using:
p1DOY
2 þ p2DOYþ p3 ð4Þ
where the DOY associated with the maximum parameter
values (DOYmax,p) and temperature (DOYmax;Ta ) is equal to
the vertical axis of symmetry for a parabola, - p2/2p1.
Site years for which less than 300 days of data were
measured were excluded from the analysis. An example of
the seasonal variability of LDay, Ta, and bM for a single site
year is demonstrated in Fig. 3. LDay was calculated fol-
lowing Campbell and Norman (1998) for each site year
using eddy covariance tower coordinates.
Statistical analysis
To quantify if DOYmax,p was significantly different among
vegetation and climate classes, we performed individual
one-way ANOVAs for the seasonal patterns of a, b, and
b ? c parameters of the Mitscherlich model. Mitscherlich
model parameters were chosen for this analysis because
parameter convergence occurred more frequently, which
resulted in more site years with sensible DOYmax,p estimates
(see Table 4). Arctic, Subtropical, and Tropical climate
classes are poorly represented in the Free/Fair-Use dataset
(Tables 1, 2; Fig. 1), but Boreal, Temperate, and Temperate
Continental classes all contain at least 82 site years of data
with which to interpret variability by vegetation type. To
explore differences among vegetation types within Boreal,
Fig. 2 Eddy covariance-measured NEE using the physiological
convention in which flux from atmosphere to biosphere is denoted
as positive as a function of photosynthetic photon flux density
(PPFD) for the period between day of year (DOY) 185 and 191 (i.e.,
July 4–10), 1999, at the Walker Branch Watershed (US-WBW) site in
eastern TN (Table 1). Corresponding parameters for the Mitscherlich
(Eq. 2) and non-rectangular hyperbola (Eq. 3) are presented in
Table 3
Table 3 Parameter values with 95 % confidence intervals (CI) for
the light response curves (Eqs. 2, 3) demonstrated in Fig. 2, corre-
sponding to the period between day of year (DOY) 185 and 191 (i.e.,
July 4–10), 1999, at the Walker Branch Watershed (US-WBW) site in
eastern Tennessee, USA (Table 1)
Parameter Value ± CI Units
aM 0.032 ± 0.0073 lmol CO2 lmol photons
-1
bM 31.6 ± 6.7 lmol CO2 m
-2 s-1
cM 3.3 ± 1.1 lmol CO2 m
-2 s-1
aN 0.026 ± 0.0081 lmol CO2 lmol photons
-1
bN 32.0 ± 11 lmol CO2 m
-2 s-1
hN 0.90 ± 0.30
cN 3.1 ± 1.1 lmol CO2 m
-2 s-1
Fig. 3 The seasonal pattern of maximum eddy covariance-measured
net ecosystem exchange (NEE) calculated by the Mitscherlich model
(bM, black dots) and the seasonal pattern of air temperature (Ta, gray
circles) for the Walker Branch Watershed study site (US-WBW,
Table 1) in 1999 with second-order polynomials as solid lines and
corresponding vertical dashed lines at the vertical axes of symmetry.
The data series and parabolas have been all scaled between 0 and 1 in
the vertical direction to simplify the visual display. Normalized day
length (LDay) is shown in the light gray line and the summer solstice
[day of year (DOY) 172] is indicated by the light gray vertical dashed
line
Granger causality
We performed a Granger causality analysis, a method based
on the understanding that causes precede effects (Granger
1969), on daily GEP from the Free Fair-Use FLUXNET
database (Table 1). Briefly, Granger causality employs a
series of t tests and F tests on lagged time series to quantify
if there is information in time series X that contributes to the
variability of an independent time series Y. Ta and LDay
were investigated as causal variables for GEP and GEP
normalized by PPFD (GEPn). GEPn was chosen for analysis
to account for the expectation that longer days that likely
have greater PPFD will also likely have greater GEP.
Daily data with a quality control value below 0.90 for
GEP (indicating a 90 % acceptance rate of half-hourly flux
measurements) and 0.95 for Ta were omitted from the
Granger causality calculation, as were site years that con-
tained less than 2/3 of potential data. FLUXNET quality
control criteria are described in Reichstein et al. (2005) and
Papale et al. (2006). Granger causality was determined to
be significant if the Granger F-statistic exceeded the critical
value from the F-distribution at the 95 % level. Site years
were considered statistically independent such that infer-
ence during years in which LDay or Ta did not Granger-
cause GEP or GEPn were not confounded by years during
which LDay or Ta Granger-caused GEP (i.e., we selected a
more conservative implementation of Granger causality).
The maximum lag time considered in the Granger causality
calculation was varied between one and 10 weeks to cal-
culate the uncertainty of the fraction of site years in which
a Granger causal relationship was observed.
Results
Seasonality of photosynthetic parameters
The 95 % confidence intervals about DOYmax;Ta exceeded
1 day in only five instances out of 385 site years, and the
95 % confidence interval about DOYmax,p did not exceed
1 day across all site years and parameters examined.
Subsequently, we focus our statistical analysis on patterns
among site years rather than uncertainty within site years.
DOYmax,p occasionally fell outside of the logical range of
0–365 (or 366), often due to incomplete measurements
across the site year. These site years were excluded from
further analyses.
As anticipated, the DOYmax,p for parameters of the non-
rectangular hyperbola could not be calculated for many
([70) site years due to difficulties in fitting the non-rect-
angular hyperbola to noisy eddy covariance data (Table 4).
We focus on parameters of the Mitscherlich model in
subsequent analyses to avoid excluding site years for this
Table 4 The mean and standard deviation of the day of year (DOY)
at which air temperature (Ta) and light response curve parameters
(collectively abbreviated ‘‘p’’) reach their maximum value (DOYmax)
for 385 site years of eddy covariance-measured net ecosystem
exchange (NEE)
DOYmax N DOYmax,p
\DOYmax;Ta
N DOYmax,p
[DOYmax;Ta
N for which
DOYmax,p
exceeded
logical
bounds
Ta 194 ± 29 – – –
aM 207 ± 47 105 230 13
bM 201 ± 39 129 218 19
bM ? cM 204 ± 32 113 231 20
aN 214 ± 48 71 209 72
bN 201 ± 26 106 192 71
bN ? cN 202 ± 25 102 196 73
N number of site years of occurrence
Temperate, and Temperate Continental climate zones, we 
performed a one-way ANOVA on DOYmax,p using vegeta-
tion class as the independent variable. If a main effect was 
significant, pairwise comparisons within vegetation types 
and climate classes were analyzed using Tukey’s Honestly 
Significant Difference (HSD) post hoc test. All statistical 
analyses were performed using R (R Development Core 
Team 2011) or MATLAB.
Information criteria analyses
We fit a suite of linear models to every site year of data to 
examine if incorporating LDay improves simple models of 
ecosystem-level photosynthetic parameter seasonality. 
Model 1 (M1) includes only Ta (i.e., daily values of the 
photosynthetic parameters are modeled as a function of a 
fitted slope, the independent variable in this case Ta, and a 
fitted intercept parameter), M2 includes only LDay, M3 is a  
function of Ta plus LDay, and M4 is equal to M3 plus an 
interaction term between Ta and LDay. We fit every model 
to every site year of available data and selected the model 
with the minimum Akaike’s Information Criterion (AIC) 
value (Akaike 1974). Briefly, AIC measures the relative 
amount of information lost (via information entropy) for a 
given model, and, therefore, the model with the minimum 
AIC value is preferred when discriminating amongst 
models. AIC penalizes against the number of parameters n 
and favors models with greater likelihood via:
AIC ¼ 2n  2 ln  Lð Þ
where L is the maximum value of the likelihood function of 
the model in question calculated using the output of the lm 
command in R.
reason. The mean DOYmax;Ta across all site years occurred
on average before the mean DOYmax,p for all parameter
combinations examined here (two-tailed t test, P\ 0.05;
Table 4). Maximum values of bM and bM ? cM occurred
on average 7–10 days after DOYmax;Ta , and maximum
values of aM occurred on average 2 weeks after DOYmax;Ta .
Despite statistically significant differences in mean
DOYmax;Ta and DOYmax,p across all site years, DOYmax,p
occurred earlier than DOYmax;Ta in 31–37 % of all instan-
ces, depending on the parameter chosen (Table 4).
Analysis of variance of parameter seasonality
by climate and vegetation type
DOYmax,p values below 150 and above 250 were identified
as outliers in an interquartile analysis, and excluding these
values resulted in a normal distribution of values for each
parameter as identified by Komolgorov–Smirnov tests.
Thus, we focus our statistical analysis of seasonal param-
eter variability by climate and vegetation type on site years
with DOYmax,p between 150 and 250. DOYmax,p for the
alpha parameter of the Mitscherlich model (aM) was sig-
nificantly different by vegetation type (F5,278 = 3.1;
P\ 0.01), but correcting for multiple comparisons using
Tukey’s HSD resulted in no pairwise comparisons that
were significantly different. DOYmax,p for both bM and
bM ? cM did not differ by vegetation type, but were sig-
nificantly different by climate type (bM: F5,311 = 8.1;
P\ 0.0001, bM ? cM: F5,319 = 13.6; P\ 0.0001).
Namely, DOYmax,p for bM in the Temperate climate zone
occurred nearly 11 days earlier than in the Boreal zone
(P\ 0.00001) and over 1 week earlier than in the Tem-
perate Continental zone (P\ 0.005; Fig. 4). DOYmax,p for
bM in the Tropical climate zone occurred nearly 1 month
earlier than in the Boreal zone and nearly 3 weeks earlier
than in the Temperate Continental zone (P\ 0.00001 in
both cases). DOYmax,p for bM ? cM was lower in the
Tropical zone than in all other climate zones investigated
by an average of 39 days (P\ 0.05 in all cases). DOYmax,p
for bM ? cM occurred ca. 2 weeks earlier in the Subtrop-
ical and Temperate zones than the Boreal climate zone
(P\ 0.01). DOYmax,p for bM ? cM occurred ca. 1 week
earlier in the Temperate zone than the Temperate Conti-
nental zone (P\ 0.0005). DOYmax,p for bM ? cM also
occurred 10 days earlier in wetland vegetation than in
evergreen needleleaf forests in the Boreal zone (P\ 0.05).
Minimal models for explaining the seasonal variability
of photosynthetic parameters
We were unable to calculate AIC values for only five of the
385 site years due to insufficient data. Results of the AIC
analysis for the aM, bM, and bM ? cM parameters were
similar (Table 5), and we discuss only bM parameter results
for simplicity. For bM, M1 had the lowest AIC value for 32
(of 380) site years, M2 had the lowest AIC value for 17 site
years, and M3 and M4 were the lowest for 51 and 280 site
years, respectively (Table 5). In other words, the preferred
model with the lowest AIC value included LDay (i.e., M2,
M3, and M4) in over 90 % (348/380) of all site years
examined here. On the other hand, excluding Ta (i.e., M2)
resulted in a preferred model less than 5 % of the time.
When considering only M1 and M2 (i.e., univariate linear
models of Ta and LDay, respectively), M1 had a lower AIC
value than M2 on 236 occasions (62 % of all site years)
and the opposite held on 144 occasions. The proportion of
sites for which the AIC value of M2 was less than the AIC
Fig. 4 A box-and-whisker plot for the day of year (DOY) of
maximum seasonal parameter values for the maximum ecosystem
CO2 uptake (bM) parameter for the Mitscherlich model grouped by
climate class. Climate group following the Ko¨ppen–Geiger classifi-
cation scheme. A arctic, B boreal, S subtropical, T temperate, TC
temperate continental, TR tropical
Table 5 The number of site years for which linear models (M) of the
seasonal variability different Mitscherlich model parameters (Eq. 2)
had the lowest value of Akaike’s Information Criterion (AIC),
including the number of site years for which the AIC value of model
M1 (i.e., a model that included only air temperature, Ta) was less than
M2 (a model with only day length, LDay)
Model Independent variables aM bM bM ? cM
M1 Ta 32 32 26
M2 LDay 23 17 15
M3 Ta ? LDay 68 51 68
M4 Ta ? LDay ? Ta 9 LDay 258 280 271
M1\M2 – 272 236 257
M2\M1 – 113 144 128
value of M1 (i.e., instances in which a model including
only LDay is preferred over a model including only Ta) is
significantly greater in the Temperate zone than in the
Temperate Continental zone (0.50 vs 0.26, P\ 0.0005) or
in the Boreal zone (0.50 vs 0.32, P\ 0.005).
Whereas simple linear models with only Ta (M1)
explained nearly 30 % of the variability of bM on average
and a model with only LDay (M2) explained 23 % of the
variability of bM, the model that included both Ta, LDay,
and an interaction term between the two (M4) explained an
average of 40 %, and up to 95 %, of the variability of bM.
The simple linear models explored here explained more of
the variability of bM ? cM than bM or aM (which was
similar to bM); M1 and M2 explained over 40 % and nearly
30 % of the variability of bM ? cM, respectively. The
model that included Ta, LDay, and an interaction term
between the two (M4) explained 53 % of the variability of
bM ? cM, on average.
Granger causality
LDay always Granger-caused Ta, as anticipated (Table 6).
LDay Granger-caused GEP (GEPn) in 99 % (92 %) of the
site years, and while temperature Granger-caused GEP in a
mere 32 % of site years, it Granger-caused GEPn in 81 %
of site years (Table 6). The proportion of site years in
which Ta Granger-caused GEP and GEPn are significantly
less than the percent of cases in which LDay Granger-caused
GEP and GEPn (P\ 0.05, Student’s t-test). We analyzed
opposite cases for completeness; GEP (GEPn) Granger-
caused LDay in 51 % (41 %) of all site years, but Granger-
caused Ta in 85 % (35 %) of all site years (Table 6). Ta
Granger-caused LDay in 40 % of site years.
Discussion
Photoperiod and temperature controls on canopy
photosynthetic function
Our results confirm that LDay improves our understanding of
the seasonal variability of maximum CO2 uptake, as also
demonstrated by studies at the leaf scale (Bauerle et al. 2012)
and ecosystem scale (Thum et al. 2007) using Farquhar et al.
(1980) model parameters. Results also demonstrate that LDay
should not be excluded from minimal models of parameter
variability in most cases (Table 5), offering support for our
experimental hypothesis. However, Ta tends to be a better
descriptor of the seasonal variability of canopy-scale photo-
synthetic parameters than LDay; for example, peak seasonal
values of aM, bM, and bM ? cM usually occur after the sea-
sonal peak of Ta (Table 4) and models with only Ta have
lower AIC values more often than models with only LDay
(Table 5). The best results occurred when Ta and LDay were
used in concert; M4 explained over 50 % of the variability of
bM ? cM, on average, before even considering hydrologic
stress (Yuan et al. 2007), leaf area index (Groenendijk et al.
2011), or other variables that are critical for explaining
canopy photosynthesis. In other words, results demonstrate
that most of the variability in maximum ecosystem-scale
carbon uptake can be explained using Ta and LDay in com-
bination without any other variables in the sites explored
here.
The Granger causality analysis also demonstrates that
LDay helps to explain the seasonal variability in GEP; LDay
Granger-caused GEP in almost all instances, even after
normalizing by PPFD (i.e., GEPn) to account for its role in
driving GEP. Ta Granger-caused GEPn in most instances as
well, but not as frequently as LDay (Table 6). Both the AIC
and Granger causality analyses substantiate that LDay
contributes to the seasonality of GEPn and the parameters
that determine the relationship between GEP and PPFD,
suggesting that the inclusion of LDay in photosynthesis
models at the ecosystem scale is likely to result in model
improvement, particularly in Temperate, Temperate Con-
tinental, and Boreal climate zones.
The role of ecosystem and climate type
Tropical, Subtropical, and Arctic climate zones had fewer
available site years for analysis, and we caution against
extrapolating our results beyond the Temperate, Temperate
Continental, and Boreal climate zones for which more data
were available. Results of the AIC analysis demonstrate that
univariate linear models with only LDay are preferred more
often in the Temperate zone than the Temperate Continental
or Boreal zone, where temperature variability and con-
straints on photosynthesis are likely to be more pronounced.
Table 6 The fraction of 385 site years of eddy covariance mea-
surements for which the explanatory variable (X) Granger-caused
causal variable (Y), considering all comparisons of day length (LDay,
as a surrogate for photoperiod), air temperature (Ta), gross ecosystem
productivity (GEP), and GEP normalized by photosynthetically active
radiation (GEPn)
X Y Fraction of site years for
which X Granger-caused Y
LDay GEP 0.99 ± 0.000
Ta GEP 0.32 ± 0.002
LDay GEPn 0.92 ± 0.006
Ta GEPn 0.81 ± 0.007
GEP LDay 0.51 ± 0.05
GEP Ta 0.85 ± 0.006
GEPn LDay 0.41 ± 0.05
GEPn Ta 0.35 ± 0.01
LDay Ta 1.00 ± 0
Ta LDay 0.40 ± 0.03
aM differed by vegetation type rather than climate type, but
without distinct differences among specific vegetation types
and we note that it is often treated as a near constant (albeit
dependent on temperature, Ehleringer and Bjo¨rkman 1977)
in leaf-level studies (Lambers et al. 2000). Maximum sea-
sonal values of bM and bM ? cM (i.e., DOYmax,p) often
peaked earlier in warmer regions like subtropical and
tropical climate zones as might be expected. Interestingly,
vegetation type itself rarely explained differences in
DOYmax,p, for bM and bM ? cM, except for wetland eco-
systems and evergreen needleleaf forests in the Boreal zone.
These results highlight the important role of climate on
controlling the seasonal variability of photosynthetic
physiology, and point to the emerging finding that plant
functional type schemes may not be the best way to partition
vegetation functioning in global models (Pavlick et al.
2012; Harrison et al. 2010) because they may not effectively
capture the variability of vegetation functioning within and
among vegetation classes (e.g., Kattge et al. 2011).
Results from different light response parameters
Both bM and bM ? cM are related to Jmax insomuch as they
are related to the maximum electron transport rate at high
irradiance. Jmax is known to be a function of temperature, as
is aM (Ehleringer and Bjo¨rkman 1977). However, M2
(the model with only LDay) was a better descriptor of bM and
bM ? cM more often than aM (Table 5), likely because aM
tends to be less-seasonal (Groenendijk et al. 2011). Results
also point to important differences between leaf-scale and
canopy-scale results; Bauerle et al. (2012) noted a decline in
Jmax and Vc,max in late June at the leaf scale across tree spe-
cies with average seasonal peaks around DOY 167–170 near
the summer solstice on DOY 172 (during most years). Our
estimated peaks in aM,bM, andbM ? cM occurred on average
over 1 month later, for reasons that remain unclear. We note
that our ecosystem-scale results inherently include photo-
synthetic contributions from shaded leaves and understory
species, when present, and fewer studies on photosynthetic
seasonality have been conducted on shaded and understory
leaves (Herrick and Thomas 2003). Care was taken to avoid
choosingmodels and approaches that drift extensively above
observed flux values when modeling light response (Fig. 3).
We chose multiple models to foster a conservative inter-
pretation of results, although we note that fitting light
response curves under conditions that are not light limiting
remains an ongoing challenge (Lasslop et al. 2010; Reich-
stein et al. 2012).
The ‘‘errors in x’’ problem and modeling implications
Our objective was to explore hundreds of site years of eddy
covariance data to uncover the role of LDay and Ta in
determining seasonal patterns of ecosystem-scale photo-
synthetic light response and GEP. We anticipate that
incorporating LDay into ecosystem-scale models will
improve their ability to simulate seasonal patterns in GEP,
but the steps that one might take to incorporate this
information depends on the type of model at hand. For
example, Schwalm et al. (2010) characterized GPP models
for the North American Carbon Program synthesis effort as
following either enzyme kinetic, stomatal conductance, or
light-use efficiency-based formulations, and noted that
more complicated model formulations need not lead to
improvement in performance. Light-use efficiency-based
models are arguably the simplest to modify, for example by
adding a multiplier based on LDay. Adjusting parameters of
enzyme kinetic-based models, for example Jmax, may also
improve model simulation estimates of the seasonal vari-
ability of photosynthetic function (Bauerle et al. 2012) as
demonstrated for the CLM (Bonan et al. 2011). Whether
these suggested improvements to photosynthetic subrou-
tines represent an improvement across different ecosystem
models for different biome types remains to be seen, but
large intercomparison efforts have demonstrated pro-
nounced model-data misfit (Schaefer et al. 2012; Schwalm
et al. 2010) at diurnal to interannual time scales (Dietze
et al. 2011), including models that used model-data fusion
schemes (Ricciuto et al. 2008). These observations suggest
that models still require mechanistic improvements to
capture the variability and magnitude of observed canopy-
scale CO2 uptake (Williams et al. 2009).
Our data-driven analysis does not suggest that simply
adding LDay to models of canopy photosynthesis should take
the place of mechanistic modifications to models of eco-
system-scale CO2 uptake (Ryu et al. 2011; Groenendijk et al.
2011; Krinner et al. 2005; Sitch et al. 2003; Baldocchi et al.
2002). Rather, adding LDay as an independent variable may
help to explain the variability of light response curve
parameters and thereby photosynthetic physiology. An
ongoing challenge with ecosystem-scale photosynthesis
models centers around uncertainties inmodel input variables
like leaf area index, canopy N, water status, and sunlit/sha-
ded leaf fraction. Since LDay can be computed with accuracy
at any point on the globe, and changes on timescales that are
longer than those explored bymost land surface models [i.e.,
thousands of years (Hays et al. 1976), incorporating LDay as
an independent model variable will likely improve models
of canopy photosynthesis. It is important to note that
including LDay can only aid a model of photosynthesis at the
time scales that LDay varies, in this case over the course of
seasons. Ta, on the other hand, varies across turbulent to
geologic time scales, and incorporating this rich, multi-scale
behavior into photosynthesis models can improve their fre-
quency response. We caution against extrapolating our
results, dominated by temperate and boreal ecosystems, to
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portions of the globe where seasonal LDay fluctuations are
small; the percent of variability in bM and bM ? cM 
explained by M4 rarely exceeded 40 % in sites at latitudes
below the 29th parallel. The amount of variability in bM or
bM ? cM explained by LDay alone (i.e., M2) at latitudes less
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moves away from the tropics and into ecosystems dominated
by seasonality in temperature. We also note that variability
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experience substantial anthropogenic management to the
degree of managed crops. We note that incorporating pho-
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Model Intercomparison Project (C-LAMP) metrics (Ran-
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geographic distinctions in our findings. Ideal approaches for
incorporating LDay into models of canopy photosynthesis 
remains an important topic for future research. Detailed
studies at well-characterized flux sites that include seasonal
observations of leaf area index and distribution, canopy N,
canopy light penetration, and water status are needed to
ascertain the degree of improvement that LDay may add in 
models of canopy photosynthesis.
Acknowledgments This work used eddy covariance data acquired 
by the FLUXNET community and in particular by the following 
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