Unformatted text preview: JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D6, 4050, 10.1029/2001JD001242, 2002 Advantages of diffuse radiation for terrestrial
Lianhong Gu,1 Dennis Baldocchi,1 Shashi B. Verma,2 T. A. Black,3
Timo Vesala,4 Eva M. Falge,5 and Pete R. Dowty6,7
Received 8 August 2001; revised 19 October 2001; accepted 21 October 2001; published 29 March 2002.  Clouds and aerosols alter the proportion of diffuse radiation in global solar radiation reaching
the Earth’s surface. It is known that diffuse and direct beam radiation differ in the way they transfer
through plant canopies and affect the summation of nonlinear processes like photosynthesis
differently than what would occur at the leaf scale. We compared the relative efficiencies of canopy
photosynthesis to diffuse and direct photosynthetically active radiation (PAR) for a Scots pine
forest, an aspen forest, a mixed deciduous forest, a tallgrass prairie and a winter wheat crop. The
comparison was based on the seasonal patterns of the parameters that define the canopy
photosynthetic responses to diffuse PAR and those that define the responses to direct PAR. These
parameters were inferred from half-hourly tower CO2 flux measurements. We found that: (1) diffuse
radiation results in higher light use efficiencies by plant canopies; (2) diffuse radiation has much
less tendency to cause canopy photosynthetic saturation; (3) the advantages of diffuse radiation
over direct radiation increase with radiation level; (4) temperature as well as vapor pressure deficit
can cause different responses in diffuse and direct canopy photosynthesis, indicating that their
impacts on terrestrial ecosystem carbon assimilation may depend on radiation regimes and thus sky
conditions. These findings call for different treatments of diffuse and direct radiation in models of
global primary production, and studies of the roles of clouds and aerosols in global carbon
INDEX TERMS: 4806 Oceanography: Biological and Chemical: Carbon cycling; 0315
Atmospheric Composition and Structure: Biosphere/atmosphere interactions; 1851 Hydrology:
Plant ecology; 1610 Global Change: Atmosphere (0315, 0325); KEYWORDS: diffuse and direct PAR,
terrestrial ecosystem productivity, clouds, aerosols, global carbon cycle 1. Introduction
 A plant canopy consists of an assemblage of plants, whose
leaves possess a particular spatial distribution and assortment of
angle orientations [de Wit, 1965; Monsi and Saeki, 1953]. How a
collection of leaves intercepts sunlight and uses light energy to
assimilate carbon dioxide (CO2) is the basis of canopy photosynthesis. The radiation environment inside a plant canopy is dynamic
in both time and space (vertically as well as horizontally), owing to
temporal changes in the solar elevation angle, the presence of
clouds, the motion of the canopy, and spatial variations in plant
canopy physical structure and physiological capacity. Interacting
with this dynamic radiation environment are several vertical biological and environmental gradients within plant canopies, includ1
Ecosystem Science Division, Department of Environmental Science,
Policy and Management, University of California, Berkeley, California,
School of Natural Resource Sciences, University of Nebraska, Lincoln,
Faculty of Agricultural Sciences, University of British Columbia,
Vancouver, British Columbia, Canada.
Department of Physical Sciences, University of Helsinki, Helsinki,
Department of Plant Ecology, University of Bayreuth, Bayreuth,
Department of Environmental Sciences, University of Virginia,
Charlottesville, Virginia, USA.
Now at Puget Sound Water Quality Action Team, Office of the
Governor, Olympia, Washington, USA. Copyright 2002 by the American Geophysical Union.
0148-0227/02/2001JD001242$09.00 ACL ing profiles of leaf nitrogen content, photosynthetic capacity,
temperature, humidity, wind speed, CO2 concentration, etc. These
canopy structure-induced complexities can lead to emergent properties that are not expected from photosynthesis of a single leaf.
One such example is the differentiation in impacts of diffuse and
direct photosynthetically active radiation (PAR) on canopy photosynthesis.
 Crop scientists have long realized that radiation-use efficiency (RUE, defined as the ratio between grams of biomass
accumulated and total solar radiation intercepted) or light use
efficiency (LUE, similar to RUE, but based on PAR only) is higher
for diffuse radiation than for direct radiation [de Wit, 1965; Allen et
al., 1974; Goudriaan, 1977; Norman, 1980; Norman and Arkebauer, 1991; Sinclair et al., 1992; Sinclair and Shiraiwa, 1993;
Rochette et al., 1996; Healey et al., 1998]. Sinclair et al. 
speculated that higher diffuse RUE might explain why some crop
species growing under glasshouses show higher RUE than those
growing in open fields. However, they did not quantitatively
compare the inside radiation with the outdoor environment. Young
and Smith  reported that an understory herb in a mixed
spruce stand gained more carbon on representative cloudy days
than on clear days. They suggested that this could be due to greater
diffuse PAR flux density and increased plant water potentials
under cloudy sky conditions. With increasing interests in terrestrial
ecosystem carbon sequestration and new technologies available for
measuring fluxes over tall canopies [Verma et al., 1986; Baldocchi
et al., 1988], observational studies on the relationship between the
radiation environment and CO2 exchange of forests became
possible. Numerous researchers have since reported significantly
higher radiation use efficiencies during cloudy days than during
clear days for both coniferous and deciduous forests [Price and
Black, 1990; Hollinger et al., 1994; Fan et al., 1995; Fitzjarrald et 2-1 ACL 2-2 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION al., 1995; Sakai et al., 1996; Baldocchi, 1997; Baldocchi et al.,
1997; Goulden et al., 1997; Lamaud et al., 1997; Freedman et al.,
1998; Gu et al., 1999; Freedman et al., 2001]. Typically, this is
shown by the alienation of light responses of net ecosystem
exchange (NEE) of CO2 between clear and cloudy days with
cloudy days having a higher NEE rate (in terms of the absolute
value) than clear days for the same solar irradiance level.
 It is important to compare RUE, or LUE, at the same
irradiance level because both variables decrease with increasing
irradiance level due to light saturation effect. A somewhat
unexpected finding reported by some of these studies is that
the highest rate of forest NEE of CO2 (that is, the most negative
value, following the NEE sign convention) often occurs on
cloudy rather than on sunny days even through solar radiation
is substantially lower on cloudy days than on sunny days [Price
and Black, 1990; Hollinger et al., 1994; Fitzjarrald et al., 1995;
Sakai et al., 1996; Freedman et al., 1998; Gu et al., 1999;
Freedman et al., 2001]. Gu et al.  showed that the
maximum carbon sequestration by two temperate forest ecosystems happened under sky conditions with a solar radiation level
equivalent to about 70 – 80% of clear-sky solar irradiance and
clouds reduced the solar irradiance by as much as 50% without
lowering the capacity of these two forests in carbon sequestration
as compared with clear days. Except for a few cases [e.g.,
Freedman et al., 1998, 2001], most of these studies used changes
in surface solar irradiance as a measure of cloudiness and did not
actually conduct cloud observations.
 Clouds reduce the global solar radiation but increase the
relative proportion of diffuse radiation at the Earth surface. A
critical aspect of cloud modulation of surface solar radiation is that
clouds can also increase the absolute amount of diffuse radiation if
the sky is not too cloudy [Gu et al., 1999]. Because of the higher
RUE of diffuse radiation, clouds can actually enhance terrestrial
ecosystem carbon assimilation if the photosynthetic gains of
increased diffuse radiation exceed the photosynthetic losses of
reduced direct beam radiation. This line of reasoning has led some
researchers to use increased diffuse radiation to explain enhanced
ecosystem carbon sequestration under cloudy sky conditions [Price
and Black, 1990; Hollinger et al., 1994; Fan et al., 1995; Goulden
et al., 1997]. However, it should be pointed out that increased
diffuse radiation might not be the only factor responsible for the
enhanced ecosystem carbon assimilation observed under cloudy
sky conditions [Young and Smith, 1983; Baldocchi, 1997; Gu et al.,
1999]. In addition to changes in surface solar radiation, the presence
of clouds can be both causes and consequences of changes in many
atmospheric factors such as temperature, moisture, and latent
heating, precipitation, etc. These factors all have direct or indirect
influences on terrestrial ecosystem carbon assimilation [Gu et al.,
1999]. Therefore some researchers emphasized decreases in the
respiration of sunlit leaves due to reduced leaf temperature [Baldocchi, 1997], reduction in vapor pressure deficit (VPD) [Freedman
et al., 1998, 2001], stomatal dynamics associated with light
fluctuations [Fitzjarrald et al., 1995; Sakai et al., 1996]. We may
also expect that sparse and dense canopies behave differently.
Under a sparse canopy, much solar radiation can reach the soil,
heat it, and promote soil respiration, resulting in reduced net
ecosystem carbon uptake on clear days. Because of these considerations, Gu et al.  stressed the multiplicity of environmental
factors influencing ecosystem carbon sequestration under cloudy
conditions. In this paper, however, we focus on detecting the
differences in the effects of diffuse and direct radiation.
 Much understanding on the canopy differential responses to
diffuse and direct radiation has been gained from numerous canopy
photosynthesis models [e.g., de Wit, 1965; Allen et al., 1974;
Goudriaan, 1977; Norman, 1980; Ross, 1981; Jarvis et al., 1985;
Wang and Jarvis, 1990; Gutschick, 1991; Norman and Arkebauer,
1991; Sinclair et al., 1992; Sinclair and Shiraiwa, 1993; De Pury
and Farquhar, 1997; Baldocchi, 1997; Choudhury, 2000; Choud- hury, 2001a, 2001b]. Although it is a general agreement among
these models that canopy RUE is higher for diffuse radiation than
for direct radiation, different models may have different sensitivities on the separation of diffuse and direct radiation for predicting
canopy photosynthetic productivities. For example, the model of
de Wit  showed only a slight dependence of RUE on the
fraction of diffuse radiation, which led de Wit [1965 p. 37] to
conclude ‘‘it is not worthwhile to spend much energy on measuring
the fraction of diffuse light in order to improve on the calculation
of photosynthesis.’’ On the contrary, the model of Goudriaan
 sensitively depended on the separation of diffuse and direct
radiation for canopy photosynthesis, and the author stated that
‘‘separate measurements of diffuse and direct radiation are almost
as important as measuring the total solar radiation’’ [Goudriaan,
1977, p. 192]. Considering the complexities involved in predicting
canopy photosynthesis, this type of disagreement is not surprising,
especially for early models. With better understanding and quantitative treatments in canopy radiative transfer, leaf photosynthesis,
transpiration, stomatal conductance, energy balance, etc., more
recent models generally reveal high sensitivities of canopy photosynthesis to the fraction of diffuse radiation [Jarvis et al., 1985;
Wang and Jarvis, 1990; Gutschick, 1991; Norman and Arkebauer,
1991; Sinclair et al., 1992; Sinclair and Shiraiwa, 1993; De Pury
and Farquhar, 1997; Choudhury, 2000; Choudhury, 2001a,
2001b]. Norman and Arkebauer  used the Cupid model to
show that canopy LUE increases nearly linearly with the fraction of
diffuse PAR. Using a different model, Choudhury [2000, 2001a,
2001b] came to similar conclusions. According to the predictions
of these studies, LUE of diffuse PAR can be several times higher
than LUE of direct PAR.
 The sensitive dependence of canopy photosynthesis on the
fraction of diffuse radiation as revealed by modern biophysical
canopy models is apparently in consensus with the scenario that
uses enhanced diffuse radiation to explain field observation of
significantly higher RUE on cloudy days than on clear days.
However, experimental studies, which go beyond simple comparisons between cloudy and clear days and directly address the
canopy photosynthetic differences between diffuse and direct
radiation, are still needed. This is important since a variety of
environmental factors can differ and no conclusive statements can
be made on which factors are responsible for the differences in
light response curves between cloudy and clear days. Gu et al.
 elaborated this point.
 Conceptually, the differences of canopy photosynthetic
responses to diffuse and direct PAR are relatively easy to understand. They result from the differences in diffuse and direct
radiative transfer regimes in plant canopies coupled with the
nonlinearity of photosynthesis. While the irradiance from the
diffuse skylight on all leaves at a given canopy depth is nearly
the same [Gutschick, 1991], the irradiance on sunlit leaves, which
are illuminated by both the direct beam and diffuse radiation and
represent only a fraction of all leaves in the canopy, ranges from
the level of a shaded leaf to full light, depending on the angles
between leaf orientation and beam propagation direction. Meanwhile, as the irradiance level increases, leaf photosynthesis shifts
from RuBP regeneration (electron transport) limitation to Rubisco
(CO2 diffusion) control [Farquhar et al., 1980]. This leads to
photosynthetic saturation and decrease in RUE under high irradiance levels. Therefore the transfer regime of direct beam radiation
wastes photons by concentrating the light resource to only a
fraction of all leaves, leading to a less efficient photosynthetic
use of light by plant canopies. Diffuse radiation, however, effectively avoids the light saturation constraint by more evenly
distributing radiation among all leaves in plant canopies, and leads
to a more efficient use of light.
 A closely related issue is the necessity of separating leaves
into sunlit and shaded groups to predict canopy photosynthesis.
This has been well recognized by terrestrial ecosystem biophysical ACL GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION 2-3 Table 1. Locations, Climates, and Vegetative and Edaphic Characteristics of the Five Sites Investigated in This Studya
Annual precipitation, mm
Canopy height, m
Stem density or basal area
Dominant species Soil type Aspen Forest Tallgrass Prairie Mixed Forest Wheat 61°510N,
2500 stem haÀ1
Pinus sylvestris L. 400
830 stem haÀ1
Michx. Corylus cornuta (understory) 1103
0.6 at maximum 1044
0.9 at maximum Haplic Podzol, coarse,
silty, glacial till Orthic Luvisol, siltyclay texture silty clay loam of
Wolco-Dwight complex (thermic Pachic
mesic Typic) 1372
23 m2 haÀ1
Q prinus L., Q alba
L., Acer rubrum L.,
A. saccharum, Liriodendron tulipifera, Carya sp.
Fullerton cherty silt
loam (Typic Paleudult) 3.0
little bluestem, blue
grama, big bluestem,
winter wheat silty clay loam
of Poncreek and
(Typic and Pachic
Data from 1997 at the Scots pine forest, tallgrass prairie, and winter wheat crop sites, 1996 at the aspen forest site, and 1995 at the mixed deciduous
forest site are used in the analyses. modeling communities [Sinclair et al., 1976; Norman, 1980; Wang
and Jarvis, 1990; Wang et al., 1992; De Pury and Farquhar, 1997;
Baldocchi, 1997; Wang and Leuning, 1998]. The distribution of
sunlight in canopies is bimodal: most leaves are shaded with lowintensity light or sunlit with high-intensity light. Few if any are
exposed to the mean light level. The light responses of the groups
of shaded and sunlit leaves are distinctively different from each
other. The light response for the group of sunlit leaves quickly
saturates with increasing light level because the light is concentrated among a relatively small number of leaves. Further increase
in radiation can even lead to decreases in photosynthesis because
of elevated temperature and enhanced respiration. In contrast, the
light response curve for the group of shaded leaves is very linear as
the light is shared by a relatively large amount of leaves and each
leaf tends to inhabit the linear portion of the leaf-level light
response curve [Baldocchi, 1997]. Therefore proper treatment of
these two groups of leaves is important for accurately predicting
canopy photosynthesis. To determine the fractions of sunlit and
shaded leaves in a canopy, one needs to deal with the issue of leaf
clumping as natural canopies often have leaves clumped, which
can have significant effects on canopy photosynthesis [Baldocchi
and Wilson, 2001].
 However, the issues of separating leaves into sunlit and
shaded groups and incident solar radiation into direct and diffuse
components are not identical. Without separating sunlit from
shaded leaves, canopy photosynthesis is overestimated [Spitters,
1986; De Pury and Farquhar, 1997, 1999; Wang and Leuning,
1999] because the effects of light saturation (in the case of
sunlit leaves) and light constraint (in the case of shaded leaves)
cannot be captured by such schemes. In contrast, failure to
partition incident solar radiation into diffuse and direct components by treating the global radiation as direct beam radiation
will lead to underestimating canopy photosynthesis, especially
under cloudy conditions, because the higher diffuse radiation use
efficiency is missed [Gu et al., 1999]. Therefore it is desirable
for biophysical canopy models to do both separations properly.
However, models that address only one of these two issues but
not both are likely to perform worse than models that address
none of them due to their opposite impacts on canopy photosynthesis estimation.
 Although the underlying mechanism for the differentiation in impacts of diffuse and direct PAR on canopy photosynthesis has been understood quite well, quantifying this differentiation from measurements is difficult and can only be
done indirectly. This is because solar radiation at the Earth
surface is always composed of diffuse and direct PAR simultaneously even on sunshine or overcast days. Further complicating
this issue is that a variety of environmental factors, in addition
to diffuse and direct radiation, can change with sky conditions.
Thus complete pictures of canopy photosynthetic responses to
diffuse PAR or direct PAR cannot be obtained directly under
natural conditions. To overcome this problem, new analysis
approaches are needed. To our knowledge, there have been no
systematic analyses on the behaviors of canopy photosynthetic
responses to diffuse or direct PAR based on field flux measurements in the literature. However, large-scale models such as
regional or global gross primary production (GPP) models often
rely on our quantitative understandings of canopy photosynthesis
derived from light response curves. For example, many GPP
models use LUE modulated by environmental stress functions to
predict primary productivity [Monteith, 1977; Prince, 1991; Law
and Waring, 1994; Runyon et al., 1994; Ruimy et al., 1994;
Landsberg et al., 1995; Prince and Goward, 1995; Ruimy et al.,
1995]. Currently, GPP models rarely implement different LUEs
for diffuse and direct PAR in their algorithms with only a few
exceptions that rely on results from canopy biophysical models
[Anderson et al., 2000; Choudhury, 2000, 2001a, 2001b; Roderick et al., 2001]. A quantitative understanding of the differences
in the behaviors of canopy photosynthesis between diffuse and
direct PAR that is supported directly by field flux observations
is much needed.
 There are three main objectives in this paper: (1) to
introduce a method for inferring canopy photosynthetic characteristics of both diffuse and direct PAR from tower flux
measurements; (2) to use the developed method to test the
previous modeling finding of the advantages of diffuse PAR
by evaluating the differences in canopy photosynthetic effects
between diffuse and direct PAR for a Scots pine forest, a mixed
deciduous forest, an aspen forest, a tallgrass prairie, and a winter
wheat crop; and (3) to examine differences, similarities, and
environmental controls in canopy photosynthetic characteristics
of diffuse and direct PAR for these ecosystems. To achieve these
objectives, we take advantage of long-term tower flux measurements at these sites. We base our analyses on the seasonal
dynamics of characteristic canopy photosynthetic parameters for
diffuse and direct PAR derived from flux measurements. The ACL 2-4 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 1. Effects of the parameter b in the rectangular hyperbola
(equation (2)) on the response of canopy photosynthesis to the
incident PAR. findings presented in this paper will provide a basis for global
GPP models to apply different treatments for diffuse and direct
PAR in their algorithms. 2. Sites and Measurements
 This study was conducted at five sites: a Scots pine forest
in Finland, an aspen forest in Canada, a mixed deciduous forest, a
native tallgrass prairie, and a cultivated winter wheat crop in the
United States (Table 1). We selected these five locations from the
tower sites in the FLUXNET project (http://public.ornl.gov/
FLUXNET/) [Running et al., 1999; Baldocchi et al., 2001] to
cover a broad vegetation spectrum and climate conditions. Table 1
summarizes locations, climate conditions, and vegetative and
edaphic characteristics of these five sites.
 The data from the Scots pine forest were collected at the
Station for Measuring Forest Ecosystem-Atmosphere Relations
(SMEAR II) field measurement station, which is located in
Hyytiala, southern Finland [Vesala et al., 1998]. The stand is
homogeneous for about 200 m in all directions from the
measurement site, extending to the north for about 1.2 km
(60° sector). The terrain is subject to modest height variation.
An eddy covariance (EC) system, which included an ultrasonic
anemometer and a closed-path infrared gas analyzer, was
installed to measure the net ecosystem CO2 exchange at 23 m
above the ground (10 m above the canopy). Detailed descriptions on the site conditions, the setup of the eddy covariance
system, and the microclimate measurements have been given
elsewhere [Vesala et al., 1998; Rannik, 1998; Rannik and
Vesala, 1999; Rannik et al., 2000].
 Located in the southern part of Prince Albert National Park,
Saskatchewan, Canada, the aspen forest site was in a horizontally
extensive and homogeneous even-aged stand. This mature aspen
forest was regenerated after a natural fire in 1919 [Weir, 1996].
Half-hourly fluxes of CO2 were measured using the EC technique
at 39.5 m above the ground (17.5 m above the canopy, see Table
1). The EC sensors consisted of a three-dimensional sonic anemometer and a closed-path infrared gas analyzer [Chen et al.,
1999]. For detailed information on the site and measurements,
readers are referred to Black et al. , Blanken et al. ,
Chen et al. , and Black et al. .
 The mixed deciduous forest site is located at the Walker
Branch Watershed in eastern Tennessee. This forest has regen- erated from agricultural land. The EC instruments, which
included a three-dimensional sonic anemometer and an open
path, infrared absorption gas analyzer, were placed on a scaffold
tower 36.9 m above the surface (10 m above the canopy, see
Table 1). The topography of this site is a challenge for flux
studies. Its landscape is undulating. The vegetation around the
tower changes systematically (E. M. Falge, unpublished data).
As a consequence, there is a relatively large variability in flux
measurements as compared with other more flat sites. At this
site, diffuse PAR measurements are available through the Integrated Surface Irradiance Study (ISIS) program (http://
www.atdd.noaa.gov/isis/isis.htm) [Hicks et al., 1996]. Detailed
information on the measurements, the site condition, and the
vegetation characteristics is provided by Wilson and Baldocchi
 and Johnson and Van Hook .
 The native tallgrass prairie and the winter wheat crop sites
are located in north central Oklahoma, United States, in the
Department of Energy (DOE) Atmospheric Radiation Measurement-Cloud and Radiation Testbed (ARM-CART) region. The
former is near Shidler, and the latter is near Ponca City, both with
flat terrains. The prairie, dominated by warm season C4 grasses, is
typical of the central Kansas/northern Oklahoma region. The wheat
crop was planted mid October, emerged 2 weeks later, and reached
maturity in late May. It was harvested early July. Fluxes of CO2,
sensible heat, latent heat, and momentum were measured at a
height of 4.5 m in the center of a quarter section field (65 ha) using
the EC technique. The EC array of sensors included a threedimensional sonic anemometer, a Krypton hygrometer, and a
closed-path CO2 analyzer. Further information on methodology
and measurements at the tallgrass prairie and winter wheat sites is
given by Suyker and Verma .
 The Scots pine forest site belongs to CarboEurope (http://
www.bgc-jena.mpg.de/public/carboeur/), while the other four sites
are within the network of AmeriFlux (http://cdiac.esd.ornl.gov/
programs/ameriflux/). To ensure network intercomparability,
AmeriFlux circulates a set of reference sensors to its members,
and FLUXNET sponsors the circulation of this set of instruments
to other regional networks. It has been found that intercomparability among different sites/sensors is good [Baldocchi et al.,
 This study involved one growing season of measurements
from each of these five sites (Scots pine forest in 1997, aspen
forest in 1996, mixed deciduous forest in 1995, and tallgrass
prairie and winter wheat in 1997). The analyses were based on
half-hourly measurements of NEE, air temperature, vapor pressure deficit (VPD), soil temperature, and global PAR. At each
site, global PAR, air temperature, and VPD were measured above
the canopy, and soil temperature was taken at the soil surface
($5 cm deep). We also needed diffuse and direct PAR information in this study. Unfortunately, measurements of diffuse and
direct PAR were available only at the mixed deciduous forest
site. So we used a radiation partitioning model to calculate
diffuse and direct PAR for the other four sites from measured
global PAR, global solar radiation, air temperature, and humidity.
The model couples several well-tested relationships published in
the literature and is described in Appendix A. We tested the
diffuse and direct PAR calculations using measurements from the
mixed deciduous forest site and found good agreement (Figure
A1 in Appendix A). 3. Data Analysis Method
 As we pointed out in the Introduction, it is impossible to
directly compare canopy photosynthesis of diffuse radiation with
that of direct radiation under natural conditions. However, by
inferring parameters that exclusively define canopy photosynthetic
responses to diffuse and direct light from canopy CO2 flux
measurements, we can construct the canopy photosynthetic ACL GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION
responses to diffuse or direct light through the parameters inferred.
We can then examine the differences or similarities of canopy
photosynthesis of diffuse and direct light based on the constructed
responses. In this section we will derive a canopy photosynthetic
response function that allows us to infer parameters that exclusively define canopy photosynthetic responses to diffuse and direct
light from tower flux measurements. Procedures to test the derived
response function will be outlined.
3.1. A Generalized Rectangular Hyperbola
 For the purpose of this study, the NEE of CO2 (Fc)
measured over a plant canopy can be considered as consisting of
two components: canopy photosynthetic flux density (P) and
ecosystem respiration rate (Re):
Fc ¼ Re À P: ð1 By writing NEE in the form (1) we adopt the sign convention used
by the flux community for NEE: positive upward. Ecosystem
respiration (Re) consists of carbon loss by autotrophs (roots, plants)
and heterotrophs (microbes, fungi, bacteria, etc), but a gain of
carbon by the atmosphere. In many empirical analyses [e.g., Fan et
al., 1990; Hollinger et al., 1994; Ruimy et al., 1995; Hollinger et
al., 1998; Wofsy et al., 1993; Goulden et al., 1997; Chen et al.,
1999; Lindroth et al., 1998; Lee et al., 1999], a rectangular
hyperbola has been used to describe canopy photosynthetic flux
ðModel 1Þ P¼ a It b
b þ a It ð2Þ where It is the global PAR incident on the canopy; a is the
canopy quantum yield on an incident PAR basis when It
approaches zero [Wofsy et al., 1993], and we call it the initial
canopy quantum yield; b is another empirical coefficient.
Equation (2) is designated as Model 1. In previous studies, b
has been explained as the maximum canopy photosynthetic flux
density or canopy photosynthetic flux density at saturation
because P ! b as It ! 1. In fact, this is not an appropriate
description for this coefficient. For many crops, for example,
canopy photosynthesis does not saturate at the natural range of
PAR. Instead, crops show an almost linear relationship with PAR
[Ruimy et al., 1995]. Equation (2) itself is very flexible. Figure 1
illustrates the relationship between P and It for different values
of b. As b increases, the curve becomes closer to being linear. At
b = 1, the curve is linear. Therefore b actually describes the
closeness to linear response of the canopy photosynthetic
response curves, that is, the capacity of a canopy to resist
photosynthetic saturation at high levels of PAR. In other words,
b is not necessarily the real canopy photosynthetic rate at
saturation, and does not have to be within ranges of commonly
observed canopy photosynthetic flux densities. For semantic
clearness, b will be referred to as Closeness to Linear Response
(CLR) coefficient thereafter.
 Previous studies have always treated a and b as purely
canopy properties and fixed them for a given plant canopy under
study. Such a view needs to be changed. Because of the differential
responses of canopy photosynthesis to diffuse and direct PAR, as
pointed out in the Introduction, these two parameters likely depend
on sky conditions as well. Norman and Arkebauer  and
Choudhury [2000, 2001a, 2001b] showed that modeled LUE at the
canopy level increases linearly with the diffuse fraction. To
represent this modeling finding, Anderson et al.  described
canopy LUE by the product of the nominal LUE and a linear
function of diffuse fraction with the nominal LUE equal to canopy
LUE when the diffuse faction is 0.5. In this study, we generalize
the results of these researchers and assume that both a and b are 2-5 linear functions of the fractions of diffuse and direct light in global
a ¼ af If
þ ar ;
It ð3Þ b ¼ bf If
þ br ;
It ð4Þ where af and ar are the initial canopy quantum yield for diffuse (If)
and direct (Ir) PAR, respectively, and bf and br are the CLR
coefficient for diffuse and direct PAR, respectively. Our treatment
of a (equation (3)) is similar to the treatment of LUE by Anderson
et al.  in the sense that both are linear functions of the diffuse
fraction. To our knowledge, the introduction of (4) is new in this
paper. Substituting (3) and (4) into (2), we have
À ðModel 2Þ P¼À ÁÀ
af If þ ar Ir bf If þ br Ir
bf If þ br Ir þ af If þ ar Ir It ð5Þ Equation (5), which is designated as Model 2, can be considered as
a generalization to the commonly used rectangular hyperbola
(Model 1, equation (2)). At the extreme condition when the canopy
receives only purely diffuse (direct) radiation, Ir = 0 (If = 0),
equation (5) reduces to the exact form of equation (2). If there are
no differences between diffuse and direct PAR for canopy
photosynthesis, ar = af and br = bf, equation (5) also returns to
equation (2). Therefore af (ar) and bf ( b r) in equation (5) have the
same meanings with a and b, respectively, in equation (2). They
describe the characteristics of canopy photosynthetic responses to
diffuse and direct PAR, respectively. Later we will examine the
differences in canopy photosynthetic efficiencies between diffuse
and direct PAR by comparing ar with af and br with bf. Higher
values of ar (af) or br (bf) indicate better efficiencies.
[ 23 ] The dependence of ecosystem respiration rate R e is
described by the following function:
Re ¼ c1 ec2 ½c3 Ta þð1Àc3 ÞTs þ d1 ed2 Ts ; ð6Þ where c1, c2, c3, d1, and d2 are regression coefficients, Ts is soil
temperature, and Ta is air temperature. The first term on the righthand side of equation (6) is expected to capture aboveground
biomass respiration, while the second is expected to capture soil
respiration. Instead of using only air temperature in the first term
on the right-hand side of (6), we employ c3Ta + (1 À c3)Ts to reflect
the effects of vertical temperature gradient on aboveground
biomass respiration. Obviously, 0 c3 1.
3.2. Statistical Model Testing Procedures
 Two questions need to be answered in the model testing: (1)
Does the generalized rectangular hyperbola (Model 2, equation
(5)), which treats diffuse and direct PAR explicitly, work effectively for a wide range of vegetation types? (2) By including
diffuse and direct PAR information in the model, do we improve
 To answer these questions, we divided the growing seasons
of the five sites into 11-day moving windows (see the following
section). For each window we randomly separated the measurements into two parts: one part for estimating coefficients through
nonlinear regression procedures (regression data set), and the other
for independently validating models (validation data set). We used
both the measured and calculated diffuse and direct PAR in the test
of Model 2 for the mixed deciduous forest site.
 To examine the importance of separating diffuse and direct
PAR in predicting canopy photosynthesis, we compare the new
model with the conventional rectangular hyperbola (Model 1), ACL 2-6 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 2. Changes of VPD and air temperature with the ratio of diffuse to global PAR at (a and b) the aspen forest
site (calculated diffuse PAR, solar elevation 50° – 60°) and (c and d) the mixed deciduous forest site (measured diffuse
PAR, solar elevation 60° – 70°). Data were moving-averaged with 11 points. In the moving average the ordering was
done on the fraction of diffuse PAR, and the averaging was done on VPD and air temperature. which assumes the same canopy photosynthetic effects for diffuse
and direct PAR (photosynthetic parameters are therefore treated as
constants for a given canopy).
 For reasons explained later, we do not intend to introduce
effects of temperature (except on ecosystem respiration) and VPD
explicitly into Model 2. To examine how critical the roles of
temperature and VPD are in the regression scheme, we compared
Model 2 with a multiple response function that is similar to those
used by global GPP models [e.g., Reed et al., 1976; Prince, 1991;
Law and Waring, 1994; Runyon et al., 1994; Landsberg et al.,
1995; Prince and Goward, 1995]. The multiple response function
has the following form:
ðModel 3Þ P¼ a It b
f ðTa Þf ðV Þ;
b þ a It ð7Þ where V is VPD. The parameters f (Ta) and f (V) are environmental
response functions to modulate canopy photosynthetic responses to
light given by
exp a1 ðTarÀa r Þ
f ðTa Þ ¼
1 þ exp a2 ðRTrÀTm Þ
Ta (8) 1
f ðV Þ ¼
1 þ b1 expðÀb2 =V Þ
where a1, a2, Tm, b1, and b2 are coefficients to be estimated through
regression, Tr is the reference temperature (25°C), and R is the gas
constant. The term f (Ta) has been widely used to describe leaf
physiological response to changes in temperature [Harley and Tenhunen, 1991]. The VPD response function has a feature of
being equal to unity when the air is saturated (V = 0) and
decreasing when VPD increases. The design of f (V ) reflects
considerations of results published in the literature concerning
responses of plant physiological activities to VPD [Runyon et al.,
1994; Law and Waring, 1994; Hogg et al., 2000].
 Following the recommendations of Willmott [1981, 1982],
we employed three statistical indices together in the model testing
and comparisons in order to give adequate evaluation on the
overall performance of these models. The three indices are r2,
root-mean-square error (RMSE), and index of agreement (IOA)
[Willmott, 1981, 1982]. IOA has the advantage of being both
differential (as opposed to r2) and bounded (no agreement 0
IOA 1 complete agreement, as opposed to RMSE) and therefore
complements r2 and RMSE. For each moving window, values of
r2, RMSE, and IOA were calculated for each of the three models
and for both regression and validation data sets. The paired t test
was then conducted to evaluate the significance regarding the
differences in r2, RMSE, and IOA between Model 2 and Model
1 and Model 3 for both model regression and validation.
3.3. Obtaining Seasonal Dynamics
 After the new model (Model 2) was tested, the measurements were merged. To get the seasonal dynamics of the initial
canopy quantum yield and CLR coefficient for both diffuse PAR
(af and bf) and direct PAR (ar and br), we applied an 11-day
moving window technique. The obtained values from a given 11day window were treated as the values for the central day of the
window (5 days before and after the central day). The length of this
11-day window is a trade-off between two competing requirements. The first requirement is that it must be short enough so that
no significant changes in canopy structure and leaf physiology 2-7 ACL GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Table 2. Statistics of the Paired t Tests on the Differences Between Model 2 and Model 1, Model 2 and Model 3 in the r2 for Model
Regression (Reg.) and Validation (Val.)
Model 2 – Model 1
Model 2 – Model 3
b Mixedb Aspen Scots Pine Prairie Wheat 11.70
0.03 Using measured diffuse/direct PAR.
Using calculated diffuse/direct PAR. occur during this period. The second requirement is that it must be
long enough to have sufficient data points for regressional analyses. The length scale of 11 days also covers frontal passages that
often cause large flux spectral variance [Baldocchi and Wilson,
2001]. This coverage is important for this study since it widens the
range of sky conditions and therefore the ranges of diffuse and
direct PAR in the moving window and increases the stability and
reliability in the estimates of photosynthetic parameters through
nonlinear regressions. The seasonal courses were obtained by
moving the window day by day.
 We examined how errors in the calculated diffuse and direct
PAR affect the estimates of af, bf, ar, and br. We determined the
seasonal patterns of af, bf, ar, and br using both measured and
calculated diffuse and direct PAR for the mixed deciduous forest
site. A sensitivity analysis was conducted to see how the estimates
of the parameters change in responses to ±15% variation in the calculated diffuse PAR (direct PAR varied accordingly so that
global PAR is unchanged).
3.4. Nonlinear Regression
 A nonlinear regression software package called ODRPACK
was used in this study. ODRPACK can be freely downloaded from
http://www.netlib.org/. Although the major feature of this software
is its weighted orthogonal distance regression, we chose to use its
ordinary least squares function after numerous trials. This is
because in our regression the measurement errors of the dependent
variable (NEE) are much greater than the measurement errors of
explanatory variables (direct PAR, diffuse PAR, air temperature,
VPD, etc.). To invoke the weighted orthogonal distance regression,
one must be very careful in selecting the delicate weights for both
dependent and explanatory variables, which is very difficult to do.
In the end, we concluded that the weighted orthogonal distance Table 3. Statistics of the Paired t Tests on the Differences Between Model 2 and Model 1, Model 2 and Model 3 in the Root-MeanSquare Error (RMSE) for Model Regression (Reg.) and Validation (Val.)a
Model 2 – Model 1
Model 2 – Model 3
P value Mixedc Aspen Scots Pine Prairie Wheat À11.78
0.00 RMSE is in units of mmol mÀ2 sÀ1.
Using measured diffuse/direct PAR.
Using calculated diffuse/direct PAR.
b ACL 2-8 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Table 4. Statistics of the Paired t Tests on the Differences Between Model 2 and Model 1, Model 2 and Model 3 in the Index of
Agreement for Model Regression (Reg.) and Validation (Val.)
Model 2 – Model 1
Model 2 – Model 3
b Mixedb Aspen Scots Pine Prairie Wheat 12.40
0.00 Using measured diffuse/direct PAR.
Using calculated diffuse/direct PAR. regression does not necessarily provide better estimations of
parameters than the ordinary least squares regression in our case
and the ordinary least squares regression (no weights applied to
data points) is sufficient for our analyses.
 The regression was conducted for each window. In the
nonlinear regressions it is necessary to pick up a set of initial
guesses for the parameters that are to be estimated. Sometimes the
nonlinear regression cannot end with the desired sum of squares
convergence with one trial of initial guesses. To deal with this
problem, we employed a repetitive regression procedure. If the
regression fails to converge, the procedure goes back and reinitializes the regression with a different set of initial guesses. The
initial guesses are picked up randomly from the preset reasonable
ranges (based on previous knowledge). The process repeats until
the proper convergence is reached, or until the maximum of 50
cycles is reached. If the latter case happens, the current window is
abandoned, and the regression moves to the next window.
3.5. Some Additional Points About the Generalized
 It is important to point out that the initial canopy quantum
yield of direct PAR (ar) is not equivalent to the initial canopy
quantum yield for clear days. Under clear skies the fraction of
diffuse radiation changes with solar elevation angles. This fraction
approaches unity when solar elevation is less than 5° but decreases
as solar elevation increases [Goudriaan, 1977]. The initial canopy
quantum yield is determined from the initial response of canopy
photosynthesis to PAR when PAR is low. Under clear skies, low
levels of global PAR can only occur in early morning and late
afternoon when the Sun is near the horizon. Since a high fraction of
global PAR at the Earth surface is diffuse under these solar
positions, the initial slopes of the curves of canopy photosynthesis
against global PAR obtained from clear days would typically have
a diffuse ‘‘signature.’’ Therefore the light response curves obtained
separately from clear and cloudy days should converge at the low
light level, and they both should be close to the slope of purely
diffuse PAR (af).
 In theory, both ar and br should depend on solar elevation
angles since the fraction of sunlit leaves in canopies changes with
the direct beam incidental angle. However, our analyses using
models of Ross  showed that the fraction of sunlit leaves is
sensitive to changes in solar elevation angles only when the Sun is near the horizon. As the solar elevation increases, the fraction of
sunlit leaves increases but quickly saturates and is not sensitive to
changes in solar elevation angles at high solar positions. Under
natural conditions, direct beam radiation dominates only at high
solar elevation angles. Therefore we expect that the dependence of
ar and br on solar elevation angles is small.
 Diffuse and direct PAR, temperature, and VPD are correlated with each other under natural conditions (Figure 2). Because
of this correlation, applying additional temperature and VPD
response functions to Model 2 may result in multicollinearity
[Ratkowsky, 1989; Myers, 1990] and confound the estimates of
initial canopy quantum yield and CLR coefficient through nonlinear regression. This is not desirable because we are not only
interested in the overall performance of Model 2 but also want to
make sure that its parameters have clear biophysical meanings.
Therefore it serves the particular goal of this paper by keeping
regressors simple and independent in Model 2.
 Since Model 2 does not explicitly consider the effects of
temperature and VPD on canopy photosynthesis, they must be
reflected through the parameters of af, ar, bf, and br. A question
arises naturally: Are the differences between af and ar, bf and br
attributable to the differences in the canopy photosynthetic effects
of diffuse and direct PAR? The answer is yes. Note that values of
af, ar, bf, and br are determined at the same time domain for
diffuse and direct PAR through Model 2. If at a certain time of
the growing season, a certain environmental condition (e.g.,
water stress or no water stress) affects the photosynthesis of
direct PAR, this same condition affects the photosynthesis of
diffuse PAR also. What interests us are the relative magnitudes
of af against ar, bf against br. Therefore the dependence of af, ar,
bf, and br on temperature, VPD, or any other environmental
conditions does not pose any problem to our analyses as long as
they are always compared with each other under the same
 It should be clear that the differences between af and ar,
bf and br as estimated from Model 2 are not the same as the
differences between cloudy and clear days in a and b as
estimated from Model 1. As we explained in the Introduction
and also in the work of Gu et al. , many environmental
factors can differ between cloudy and clear days. It would be
difficult to identify environmental factors that are responsible for
the differences in a and b of Model 1 between cloudy and clear ACL GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION 2-9 Table 5. Average Diffuse and Direct Canopy Photosynthetic Parameters and Their Standard Errorsa
af / ar ratio
bf and br ratio Mixedc Aspen Scots Pine Prairie Wheat 4.93 ± 0.14
2.33 ± 0.09
2.81 ± 0.17
69.7 ± 5.6
20.4 ± 0.84
4.7 ± 0.7 4.34 ± 0.14
2.43 ± 0.12
3.49 ± 0.53
63.8 ± 5.4
22.7 ± 1.1
3.6 ± 0.3 2.90 ± 0.05
1.35 ± 0.04
2.50 ± 0.21
239.2 ± 17.2
25.8 ± 2.3
15.4 ± 1.5 2.89 ± 0.06
1.83 ± 0.06
1.67 ± 0.04
80.0 ± 5.3
20.0 ± 0.7
6.3 ± 0.8 2.19 ± 0.07
1.62 ± 0.06
1.41 ± 0.03
238.0 ± 9.6
20.1 ± 1.1
13.9 ± 0.5 2.08 ± 0.14
1.58 ± 0.13
1.66 ± 0.08
95.3 ± 6.3
24.0 ± 2.5
8.2 ± 0.7 a
Averaging periods are the same as in Figures 5 and 8. Units of initial canopy quantum yields af and ar are in 100 Â mol CO2/mol photon; CLR
coefficients bf and br are in mmol mÀ2 sÀ1.
Using measured diffuse/direct PAR.
Using calculated diffuse/direct PAR. days. This is why we used Model 2 and did not group days for
cloud types in this study. 4. Results
4.1. Model Test and Comparisons
 Results of the paired t tests on the differences in all three
statistics (r2, RMSE, and index of agreement) between Model 2
and Model 1 indicate that Model 2, which has higher r2 and index
of agreement and smaller RMSE, consistently performs better than
Model 1 with statistical significance for all five sites and for both
regression and validation (see Table 2 for r2, Table 3 for RMSE,
and Table 4 for index of agreement). In all these tests the P values
are smaller than 0.0001.
 For the comparisons between Model 2 and Model 3 the
statistical test results are mixed. For the sites of aspen forest, Scots
pine forest, and tallgrass prairie, results of the paired t tests on the
differences in all three statistics between Model 2 and Model 3
show that Model 2 consistently performs better than Model 3 with
statistical significance for both regression and validation (see
Tables 2, 3, and 4). In these tests the P values are also smaller
than 0.0001. For the winter wheat site the validation tests on all
three statistics indicate that Model 2 works better than Model 3.
The regression test on RMSE also supports this statement. However, the regression tests on r2 and index of agreement indicate that
there are no significant differences between Model 2 and Model 3.
For the mixed deciduous forest site, both measured and calculated
diffuse and direct PAR were used in the model comparisons. For
this site the following paired t tests suggest that Model 2 is better:
r2 with validation data set and measured diffuse and direct PAR,
RMSE with regression data set and measured diffuse and direct
PAR, RMSE with validation data set and both measured and
calculated diffuse and direct PAR, index of agreement with
validation data set and measured diffuse and direct PAR. However,
other tests at this site indicate no significant differences between
Model 2 and Model 3. The mixed results in the statistical tests of
r2, RMSE, and index of agreement suggest that the recommendations made by Willmott [1981, 1982] on model evaluations are
 Although we expect that Model 2 is better than Model 1,
the better performance of Model 2 than Model 3 for most cases
tested is somewhat surprising since Model 3 has more driving
variables and free regression coefficients than Model 2. These
results indicate that it is important to separate diffuse and direct
PAR in interpreting NEE measurements. For some ecosystems the
importance of doing so may even exceed the inclusion of temperature and VPD in the predicting schemes of NEE. The reason for
that is diffuse radiation is correlated with VDP and temperature and
represents a combined measure of both effects (Figure 2).
 By comparing the t statistics and P values for the tests of
using measured diffuse and direct PAR and those of using
calculated diffuse and direct PAR for the mixed deciduous forest
site, one finds that using measured diffuse and direct PAR increases
the differences between Model 2 and Model 1 as well as the
differences between Model 2 and Model 3 (see Tables 2, 3, and 4).  The effectiveness of the generalized rectangular hyperbola
(Model 2) in predicting NEE can also be examined in Figures 3
and 4 for model fitting and independent model validation, respectively. In general, the calculated NEE closely agrees with the
measured NEE. The values of r2, RMSE, and index of agreement
indicate that the generalized rectangular hyperbola works well for
the five sites. The values of the three statistical indices vary from
site to site, which reflects variations in site complexity. The mixed
deciduous forest site, which is the most complex site, has the
lowest values of r2 and index of agreement and largest RMSE
among the five sites studied. The model tends to underestimate the
magnitude of unusually large fluxes (positive or negative). This is
probably not caused by the model. For example, ecosystem
respiration rates, which are shown to exceed 10 mmol mÀ2 sÀ1 in
some measurements, are hard to explain ecologically for these
northern sites. It is known that occasionally the eddy covariance
technique obtains unusually large fluxes (either positive or negative). However, these points are sporadic and more likely due to
certain atmospheric turbulent events than to any real ecological or
4.2. Advantages of Diffuse PAR: Initial
Canopy Quantum Yields Af and Ar
 All five sites show that the initial canopy quantum yield of
diffuse PAR (af) is consistently higher than the initial canopy
quantum yield of direct PAR (ar) (Figure 5). For the mixed
deciduous forest in Oak Ridge, Tennessee, the seasonal patterns
using measured diffuse and direct PAR (Figure 5a) are similar to
those using calculated diffuse and direct PAR (Figure 5b) although
sometimes using calculated diffuse and direct PAR leads to smaller
estimates for af and larger estimates for ar (for example, compare
values of af and ar around day 200 in Figures 5a and 5b). Again,
vegetation and land complexities and perhaps variable weather
conditions at this mixed deciduous forest site lead to large day-today variations in the estimates of af and ar, while at other sites
(Figures 5c – 5f ) changes are smoother. Seasonality of af and ar
can be clearly seen at the tallgrass prairie site (Figure 5e) and the
winter wheat site (Figure 5f ). At the tallgrass prairie site, both af
and ar increase during the spring period and reach the maximum in
the midsummer and then decrease toward the end of the growing
season (Figure 5e). Several developmental stages in the growth of
winter wheat are revealed by the temporal patterns of af and ar
(Figure 5f ). In early growth stages of winter wheat, af and ar,
which are both small, do not differ very much. As the wheat
develops, both af and ar increase as well as the differences
between them. However, as it approaches maturity, the two
parameters converge again and then decrease rapidly toward the
end of May (Figure 5f ). The seasonality of af and ar at the Scots
pine forest site (Figure 5c) and the aspen forest site (Figure 5d) is
not as clear as at the tallgrass prairie site or the winter wheat site
although increases during spring and decreases during autumn can
still be seen at the two sites.
 The sensitivity test shows that ±15% variations in the
calculated diffuse PAR and accordingly in the calculated direct
PAR have hardly any effects on the estimates of ar and only ACL 2 - 10 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 3. Agreement between the Model 2 calculated and measured NEE for the mixed deciduous forest using (a)
measured diffuse and direct PAR and (b) calculated diffuse and direct PAR, (c) Scots pine forest, (d) aspen forest, (e)
tallgrass prairie, and (f ) winter wheat for model fitting.
slightly affect the estimates of af. For clearness, we show the
±15% test curves only for the aspen site in Figure 5. A +15%
change in the calculated diffuse PAR slightly reduces the estimates
of af, and a À15% change slightly increases the estimates of af,
while the effects on ar are hardly detectable (Figure 5d). Together
with the results from the mixed deciduous forest site where both
measured and calculated diffuse and direct PAR are used, we
therefore conclude that errors in the calculated diffuse and direct
PAR are unlikely responsible for the differences between af and ar
obtained here.  The ratios of af to ar at the five sites are compared in
Figure 6. Although there are a lot of scatterings in the data
points, the af to ar ratio is generally greater than 1. The mean
values of af, ar, and the af to ar ratio at the five sites are found
in Table 5. The mixed deciduous forest has the largest mean af
(0.049 and 0.043 mol CO2/mol photon using measured and
calculated diffuse and direct PAR, respectively) and ar (0.023
and 0.024 mol CO2/mol photon using measured and calculated
diffuse and direct PAR, respectively). The winter wheat has the
smallest mean af (0.021 mol CO2/mol photon), while the aspen GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 4. ACL 2 - 11 Same as Figure 3, but for model validation. forest has the least mean ar (0.014 mol CO2/mol photon). The
mixed deciduous forest also has the largest mean af to ar ratio
(2.81 and 3.49 using measured and calculated diffuse and direct
PAR, respectively), while the tallgrass prairie has the least mean
af to ar ratio. Because of the strong seasonality in af and ar at
the tallgrass prairie and winter wheat sites, these mean values are
for references only.
4.3. Effects of Temperature and VPD on Initial
Canopy Quantum Yields Af and Ar
 As we pointed out earlier, effects of temperature and VPD
on canopy photosynthesis are implicitly expressed in the values of
the parameters in Model 2. From Figure 5 we see that both af and
ar vary a lot over the season. Although the overall seasonal patterns may be controlled by leaf phenology, short-term variations
are likely caused by changes in weather conditions.
 Since af and ar are estimated through 11-day moving
windows, it is not possible to conduct a strict analysis on how
environmental factors control them. However, if we focus on the
general patterns and prominent features only and refrain from
interpreting details, we may still be able to get some insights on
this issue by examining how af and ar change with daily mean
values of air temperature and VPD. An initial examination on
Figure 5 encourages this effort. For example, a sharp drop in af and
a somewhat less significant drop in ar occurred early in the
growing season, around day 172, in the aspen forest (Figure 5d).
The temporal records of surface meteorological variables indicated
that this was associated with the passage of a cold front. During ACL 2 - 12 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 5. Seasonal dynamics of diffuse and direct initial canopy quantum yields af and ar for the mixed deciduous
forest using (a) measured diffuse and direct PAR and (b) calculated diffuse and direct PAR, (c) Scots pine forest, (d)
aspen forest, (e) tallgrass prairie, and (f ) winter wheat. The sensitivity test results are shown for the aspen forest
(Figure 5d). In the sensitivity test the diffuse PAR is varied by ±15% over the calculated values, and the direct PAR is
varied accordingly to keep the measured global PAR unchanged. The obtained seasonal patterns are shown along with
the original calculations. For clarity, sensitivity test results for other sites are not shown. Most missing points are due
to gaps in the original measurements. A few are due to unsuccessful convergence in the regression. this period, surface air pressure increased, and the wind direction
shifted from steady southwesterly to northwesterly wind. In the
meantime, mean daily air temperature dropped 12°C in less than 3
days and reached a minimum of less than 4°C. We noticed that the
highest af before this event was about 0.046 mol CO2/mol photon.
Such a high value was never reached again after the cold weather
front was past (Figure 5d). In the following, we will analyze changes of af and ar with air temperature and VPD using data from
the mid growing seasons at the five sites (days 150 – 275 for the
Scots pine forest, 160 – 270 for the aspen forest, 110 – 270 for the
mixed deciduous forest, 160 – 260 for the tallgrass prairie, 110 –
150 for the winter wheat) to minimize the impact of phenology.
 Among the five sites, Scots pine forest appears to be most
sensitive to changes in air temperature (Figure 7a). However, the GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 13 Figure 6. Ratios of diffuse to direct initial canopy quantum yields af /ar for the (a) mixed deciduous forest (using
measured diffuse and direct PAR) and Scots pine forest and (b) aspen forest, tallgrass prairie, and winter wheat. optimum temperatures for af and ar, which are about 10°C, are
surprisingly low. The af and ar of the aspen forest respond weakly
to changes in temperature (Figure 7c). Nevertheless, it can still be
seen from the exhibited patterns that low or high temperatures tend
to reduce af and ar. The optimum temperatures for af and ar
appear to be around 15°C. The af and ar of the mixed deciduous
forest (Figure 7e) respond to temperature differently at low temperature range. While af is higher for temperature <20°C than for
temperature >20°C, the opposite is true for ar. No clear dependence of af and ar of the tallgrass prairie on temperature is
identifiable (Figure 7g). Similar to the mixed deciduous forest
(Figure 7e), the af and ar of winter wheat (Figure 7i) also respond
differently to temperature. While the dependence of af on temperature is weak, the ar strongly depends on temperature.
 The responses of af and ar to VPD unavoidably carry some
similarities with the responses to temperature since the two
variables are correlated. For example, the initial increases in af
and ar of the Scots pine forest (Figure 7b) and the aspen forest
(Figure 7d) with VPD are probably a reflection of the corresponding temperature responses in Figures 7a and 7c, respectively.
However, the mixed deciduous forest (Figures 7e and 7f ) and
the tallgrass prairie (Figures 7g and 7h) show signs of independent
VPD and temperature effects. In the case of the mixed deciduous
forest, no clear signs of VPD effects on af and ar are visible at low
VPD (Figure 7f ), while low temperature affects af and ar (Figure
7e). Although the af and ar of the tallgrass prairie apparently do
not depend on temperature (Figure 7g), high VPD tends to
decrease them (Figure 7h).
 The revelation that af and ar sometimes respond to temperature as well as VPD in different ways is interesting. It explains
some contrasting features between af and ar in Figure 5. Although
af and ar show some degree of parallel changes with time in their
seasonal dynamics, especially for the overall patterns, out-of-phase
fluctuations in the two parameters do occur. This may indicate that
environmental controls on af and ar can differ.
4.4. Advantages of Diffuse PAR:
CLR Coefficients Bf and Br
 The relative effectiveness of diffuse and direct PAR for
canopy photosynthesis can also be examined through bf and br
with greater values indicating lower tendency to saturation under
high levels of light (see equation (4) and Figure 1). Advantages
of diffuse PAR over direct PAR for canopy photosynthesis are again demonstrated by the much larger bf than br for all five sites
studied (Figure 8). For these sites, direct PAR more easily causes
canopy photosynthetic saturation than diffuse PAR. Because bf
can be several orders of magnitude larger than br, the logarithmic
scale is used in Figure 8. All five sites show strong seasonality in
the estimates of bf and br. This is in contrast with af and ar,
which exhibit clear seasonality only at the tallgrass prairie and
winter wheat sites. The five sites have distinctively different
features in the seasonal patterns of bf and br. At the mixed
deciduous forest site (Figure 8a, using measured diffuse and
direct PAR; Figure 8b, using calculated diffuse and direct
PAR), bf and br increase quickly during the springtime, reach
the maximum around mid May, and then gradually decrease. The
maximal bf seems to be around late July or early August for the
Scots pine forest (Figure 8c), while the pattern is not clear for br.
The seasonal patterns of bf and br of the aspen forest (Figure 8d)
appear to be similar to those of the mixed deciduous forest
(Figures 8a or 8b), but the changes with time are gentler in the
former. At the tallgrass prairie site the seasonal patterns of bf and
br (Figure 8e) are in contrast with those of af and ar (Figure 5e).
While af and ar of the tallgrass prairie keep changing in the mid
growing season, there is a quite long period in which bf and br
are relatively constant. bf and br of the winter wheat increase as it
approaches maturity (Figure 8f ). Just like af and ar (Figure 5f ),
bf and br of the winter wheat also converge and then decrease
when maturity is reached.
 The revealed seasonal patterns of bf and br indicate that
canopy photosynthesis may shift between nonlinear and linear
responses to PAR during the growing period. The general trend
of transition from nonlinear response early in the growing season
to more linear response in the middle of growing season and then
back to nonlinear response late in the growing season may reflect
temporal changes in a variety of biotic factors. Baldocchi and
Amthor  used a model to show that canopy photosynthetic
light responses are nonlinear at low LAI but become more linear
at high LAI. The seasonal dynamics in leaf nitrogen content may
also affect the seasonal patterns of bf and br. The maximum
catalytic activity of Rubisco (Vcmax) increases with leaf nitrogen
content [Wilson et al., 2000], while bf and br should increase with
 Using the measured and calculated diffuse and direct PAR
lead to similar seasonal patterns in the estimates of bf and br for
the mixed deciduous forest although sometimes the use of calcu- ACL 2 - 14 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 7. Responses of diffuse and direct initial canopy quantum yields af and ar to changes in daily mean air
temperature and VPD for the (a and b) Scots pine forest, (c and d) aspen forest, (e and f ) mixed deciduous forest
(using measured diffuse and direct PAR), (g and h) tallgrass prairie, and (i and j) winter wheat. Also shown are
standard error bars. Data were moving-averaged. lated values tends to decrease the differences between the estimates of bf and br (Figure 8a, using measurements; Figure 8b,
using calculation). Also, the sensitivity test shows that ±15%
variations in the calculated diffuse PAR and accordingly direct
PAR have a negligible effect on the estimates of both bf and br
(see Figure 8d). Therefore we feel confident that the differences
between the estimated bf and br reflect the differences in canopy
photosynthetic effects between diffuse and direct PAR.  Figure 9 plots the ratio of bf to br for the five sites.
Although variations of the bf to br ratio are large with time and
from site to site, almost all points are larger than 1. Table 5
summarizes the mean bf, br and bf to br ratio for the five sites.
The aspen forest has both the highest mean bf (239 mmol
mÀ2 sÀ1) and br (26 mmol mÀ2 sÀ1) as well as the highest
mean bf to br ratio (15). The mixed deciduous forest has the
smallest mean bf (70 mmol mÀ2 sÀ1 if using measured diffuse GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 7. and direct PAR, 64 mmol mÀ2 sÀ1 if using calculated diffuse and
direct PAR) and smallest mean bf to br ratio (5 if using
measured diffuse and direct PAR, 4 if using calculated diffuse
and direct PAR). It is interesting that while there are considerable differences in the mean values of bf (from about 60 to
240 mmol mÀ2 sÀ1) among the five sites, the mean values of br
are much closer (from about 20 to 25 mmol mÀ2 sÀ1).
4.5. Effects of Temperature and VPD
on CLR Coefficients Bf and Br
 Similar to what we did for af and ar, we also examine how
bf and br change with daily mean air temperature and VPD (Figure
10). The Scots pine forest (Figure 10a), aspen forest (Figure 10c),
mixed deciduous forest (Figure 10e), and winter wheat (Figure 10i)
all show some levels of dependence of bf and br on temperature
except for the tallgrass prairie site where no clear dependence is
identifiable (Figure 10g). While the bf of the Scots pine forest
tends to increase with temperature, the br shows the opposite trend
(Figure 10a). A similar pattern is found for the aspen forest (Figure
10c). The br of the mixed deciduous forest tends to decrease with
temperature, but the dependence of bf on temperature appears to be
nonmonotonic with the optimum temperature around 20° – 25°C
(Figure 10e). Both bf and br of the winter wheat (Figure 10i)
appear to decrease with temperature. For all five sites the responses
of bf and br to temperature are similar to those to VPD (Figures
10b, 10d, 10f, 10h, and 10j), again reflecting the correlation
between temperature and VPD. ACL 2 - 15 (continued)  Similar to what we observed for af and ar, environmental
controls on bf and br do not always exhibit the same patterns.
The divergence in the effects of temperature (or VPD) on bf and
br as revealed in Figures 10a, 10c, and 10e (or Figures 10b, 10d,
and 10f ) explains why sometimes out-of phase fluctuations
occur in the seasonal dynamics of bf and br at these sites (Figure
8). We will discuss the importance and implications of these
4.6. Effects of Light Level on the Advantages
of Diffuse PAR
 The initial canopy quantum yields (af and ar) reflect the
light use efficiencies by the canopy under a ‘‘purely’’ diffuse or
direct radiation environment when the incident light level
approaches zero. As the light level increases, the canopy light
use efficiency decreases because of the saturation effects. Since bf
and br are different, we expect that the rate of decrease in canopy
light use efficiency with the light level differs between diffuse and
direct PAR. Consequently, the differences in the canopy photosynthetic effects of diffuse and direct PAR change with the light
level. According to Model 2, under a purely diffuse radiation
environment with any light level If, the diffuse canopy quantum
yield af (If) is found to be
a f If ¼ À
af If ¼ 0 bf If ¼ 0
af þ bf If
a f If ¼ 0 þ b f If ¼ 0 If ð9Þ ACL 2 - 16 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 8. Seasonal dynamics of diffuse and direct CLR coefficients bf and br for the mixed deciduous forest using
(a) measured diffuse and direct PAR and (b) calculated diffuse and direct PAR, (c) Scots pine forest, (d) aspen forest,
(e) tallgrass prairie, and (f ) winter wheat. The sensitivity test results are shown for the aspen forest (Figure 8d). In the
sensitivity test the diffuse PAR is varied by ±15% over the calculated values, and the direct PAR is varied accordingly
to keep the measured global PAR unchanged. The obtained seasonal patterns are shown along with the original
calculations. For clarity, sensitivity test results for other sites are not shown. Most missing points are due to gaps in
the original measurements. A few are due to unsuccessful convergence in the regression. A similar expression can be found for the direct canopy quantum
yield at any light level Ir under a purely direct radiation
environment. Now let us assume If = Ir = I and obtain the ratio:
af ð I Þ af bf ðar þ br I Þ
ar ð I Þ
af þ bf I ar br Using the mean values of af, ar, bf, and br given in Table 5, we
examine how the above ratio changes with the light level I, either
purely diffuse or purely direct (Figure 11). All five sites show
that the ratio af (I )/ar(I ) increases almost linearly with I. From
Figure 11 it is clear that it is necessary to examine both a and b
simultaneously for the differences in radiation use efficiencies GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 17 Figure 9. Ratios of diffuse to direct CLR coefficients bf /br for the (a) mixed deciduous forest (using measured
diffuse/direct PAR) and Scots pine forest and (b) aspen forest, tallgrass prairie, and winter wheat. between diffuse and direct radiation since radiation use
efficiencies change with radiation level. 5. Discussion and Conclusions
 Using tower flux measurements, we demonstrated the
advantages of diffuse PAR over direct PAR for forcing canopy
photosynthesis for five vegetation sites, covering a broad
ecosystem spectrum and climate conditions. We found that (1)
diffuse radiation results in higher light use efficiencies by plant
canopies; (2) diffuse radiation has a much less tendency to
cause canopy photosynthetic saturation; (3) the advantages of
diffuse radiation over direct radiation increase with radiation
level; (4) temperature as well as vapor pressure deficit can
cause different responses in diffuse and direct canopy photosynthesis, indicating that their impacts on terrestrial ecosystem
carbon assimilation may depend on radiation regimes and thus
 These findings have implications for studies of the global
carbon cycle. To explain recently observed increases in photosynthetic activities in the Northern Hemisphere, researchers have
been looking at nitrogen deposition, CO2 fertilization, global
warming, reforestation, and regrowth of secondary forests for
answers [Keeling et al., 1996; Myneni et al., 1997; Fan et al.,
1998]. The findings in this study highlight the necessity of
examining yet another factor for temporal variations of carbon
sequestration in the Northern Hemisphere: changes in cloudiness
and aerosol concentration. Variations in cloudiness and aerosol
concentration not only change the total solar radiation at the
Earth surface but also alter the relative proportions of diffuse
and direct solar irradiance. Hollinger et al.  suggested that
increased haze might have enhanced terrestrial CO2 uptake in
the northern Temperate Zone. Cloudiness has increased over
broad regions of the world since the beginning of the twentieth
century [McGuffie and Henderson-Sellers, 1988; HendersonSellers, 1989; Abakumova et al., 1996; Russak, 1990; Karl
and Steurer, 1990; Angell, 1990], while atmospheric aerosol
concentration has substantially increased due to anthropogenic
emissions of SO2, for example, especially in the Northern
Hemisphere [Andreae, 1995]. Increased cloudiness and aerosol
concentration may have already altered the nature of solar
radiation received at the Earth’s surface. Data from the former
Soviet Union showed that increases in cloudiness and atmos- pheric turbidity were accompanied by decreases in global solar
radiation and direct beam solar radiation but increases in diffuse
solar radiation [Abakumova et al., 1996]. Gilgen et al. 
also reported significant decreases in solar irradiance on most
continents. If the benefit of increases in diffuse solar radiation
overcompensates the loss caused by decreases in direct beam
solar radiation for vegetation photosynthetic activities, increased
cloudiness and aerosol concentration could have enhanced carbon sequestration of terrestrial ecosystems in the Northern
Hemisphere during the last several decades [Gu et al., 1999;
Roderick et al., 2001]. Further studies are needed to clarify this
 Traditionally, light use efficiency or radiation use efficiency
at the canopy level has been considered to be independent of the
directional nature of solar radiation and vegetation structure
[Monteith, 1972, 1977; Prince, 1991; Prince and Goward, 1995;
Goetz et al., 1999; Ruimy et al., 1999]. A fundamental assumption
in this definition is that plant canopies behave like one single leaf.
Under this assumption, what matters is the amount of radiation
absorbed by the canopy, and how the canopy absorbs the radiation
is irrelevant. Such an assumption goes against the long practice by
crop scientists using leaf orientation, plant geometry, and crop
canopy as indicators in their breeding programs to identify superior
varieties [e.g., Pendleton et al., 1968; Yoshida, 1972]. The results
presented in this paper directly supports the modeling findings of
Norman and Arkebauer  and Choudhury [2000, 2001a,
2001b] that light use efficiency strongly depends on the diffuse
and direct composition of the incident global PAR. Clearly, light
use efficiency must be treated as a function of sky conditions. It is a
challenge for the next generation of regional and global primary
production models, which rely on the concept of light use efficiency, to develop new algorithms to accommodate these new
 Another finding with important implications for global
primary production studies is that the dependence of canopy
quantum yields on temperature (VPD) can be complicated and is
vegetation (species functional type)-specific. Ehleringer and
Pearcy  and Ehleringer et al.  reported the leaf-level
measurements of quantum yield for a number of C3 and C4
mononcot and dicot grass species. They found that the quantum
yield of C3 species is generally driven by photorespiration and
therefore decreases with temperature while temperature has no
clear effects on the quantum yield of C4 species. However, the
temperature ranges reported by Ehleringer and Pearcy  ACL 2 - 18 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION Figure 10. Responses of diffuse and direct CLR coefficients bf and br to changes in daily mean air temperature and
VPD for the (a and b) Scots pine forest, (c and d) aspen forest, (e and f ) mixed deciduous forest (using measured
diffuse and direct PAR), (g and h) tallgrass prairie, and (i and j) winter wheat. Also shown are standard error bars.
Data were moving-averaged.
were mostly >15°C. Our results suggest that cautions should be
taken when one generalizes the conclusions of Ehleringer and
Pearcy  and Ehleringer et al.  to the canopy scale or
extrapolates them into lower temperature ranges. The canopy
quantum yields of Scots pine forest (Figure 7a), aspen forest
(Figure 7c), and winter wheat crop (Figure 7i) increase with
temperature when temperature is low. Nevertheless, we obtained
a tendency for decrease in canopy quantum yields of the Scots
pine forest with increasing temperature when temperature is
larger than 10°C and no dependence for the canopy quantum
yields of the tallgrass prairie. This is in agreement with Ehleringer and Pearcy  and Ehleringer et al.  even
through the two studies worked at different scales and used
 It is somewhat unexpected that impacts of temperature
and VPD on the initial canopy quantum yields af and ar (Figure
7) and CLR coefficients bf and br (Figure 10) can diverge
between diffuse and direct PAR. Obviously, this kind of phenomenon cannot happen at the leaf level. Although more studies
are needed to find a sound explanation for it, we suspect that it
might be related to differences in the microenvironment that
sunlit and shaded leaves experience. Sunlit leaves receive not GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 19 Figure 10. (continued)
only more PAR but also more near-infrared radiation than
shaded leaves do. Therefore temperatures of sunlit leaves are
expected to be higher than shaded leaves. This leads to greater
temperature gradients between sunlit leaves and surrounding air
[Young and Smith, 1983]. Consequently, an air temperature that
is too low for shaded leaves and thus limits their photosynthetic
activities might be within the right range for sunlit leaves.
Conversely, an air temperature in the right range for shaded
leaves might be too high and therefore limit photosynthetic
activities of sunlit leaves. Differences in leaf temperature can
also result in differences in VPD at the leaf surface and thus
affect stomatal conductance [Collatz et al., 1991; Baldocchi,
1997; Baldocchi and Harley, 1995]. Therefore responses of
canopy photosynthetic parameters of diffuse and direct PAR to
environmental factors may not always parallel with each other,
and for certain ranges of environmental conditions divergence
among diffuse and direct photosynthetic parameters can occur.
The differences in environmental responses of canopy photosynthetic characteristics for diffuse and direct PAR indicate that
the underlying mechanisms of terrestrial ecosystem carbon
assimilation are likely a function of sky conditions. For example,
we may expect that environmental controls of net ecosystem
exchanges of carbon dioxide follow different patterns between
cloudy and clear days.
 This study reiterates the conclusion of Goudriaan 
that diffuse PAR is an important variable in interpreting vegetation
photosynthetic activities. Its impact depends on vegetation structure and climate conditions. However, currently diffuse PAR is not
a variable commonly measured by tower flux communities.
Instead, most teams measure only total PAR. As shown in this
paper, a single measurement of total PAR, which masks sky conditions, hinders accurate interpretation of CO2 flux measurements. Therefore we recommend routine measurements of diffuse
radiation, particularly diffuse PAR, in tower flux measurements. In
conjunction with diffuse radiation measurements, cloud observa- Figure 11. Changes of diffuse to direct canopy quantum yield
ratio af (I ) /ar(I ) with the incident PAR (diffuse or direct) for the
five study sites. Mean values of af, ar, bf, and br given in Table 5
were used in the calculation. See equation (10) and text for
explanation. 2 - 20 ACL GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION tion is also desirable. By linking measured radiation components at
the surface with cloud variables such as cloud cover, which may be
observable from space, potential algorithms for remote sensing
applications can be developed. Future generations of regional and
global primary production models may use these algorithms to
derive surface diffuse and direct radiation conditions from satellite
observations of cloudiness to estimate terrestrial ecosystem productivities. An advantage of such a strategy is that it is applicable
to all-weather conditions, including cloudy skies that current
remote sensing based algorithms tend to avoid. Interval: kt ! 0.78; constraint: Sf /S0 ! 0.1 kt
Sf S0 ¼ kt ½0:426kt À 0:256cos q þ 3:49 Â À3 Ta þ 0:0734f ; ðA1cÞ
where Sf denotes the total diffuse radiation received by a horizontal
plane at the Earth surface (JmÀ2 sÀ1); S0 denotes the extraterrestrial
irradiance at a plane parallel to the Earth surface (JmÀ2 sÀ1), and is
given by [Spitters et al., 1986]
S0 ¼ Ssc ½1 þ 0:033cosð360td =365Þcos q; Appendix A: Estimating Diffuse and Direct PAR
 Currently, diffuse and direct PAR are not variables commonly measured by flux towers or meteorological stations. However, several models that partition measured global PAR into
diffuse and direct components are available in the literature
[Goudriaan, 1977; Weiss and Norman, 1985; Spitters et al.,
1986; Alados and Alados-Arboledas, 1999]. Gu et al. 
coupled several relationships published in open literature to
decompose measured global PAR and solar radiation into diffuse
and direct components. In this study, we adopt a similar approach.
For completeness, these relationships are given here.
 The radiation decomposition model first computes the
total diffuse (diffuse PAR plus diffuse near-infrared) fraction in
global solar radiation from clearness index (kt), solar zenith
angle (q), ambient temperature (Ta), and relative humidity (f)
by using relationships reported by Reindl et al. . Clearness
index is defined as the ratio between the global solar radiation
received at the Earth surface and the extraterrestrial solar
radiation. The corresponding equations are [Reindl et al., 1990]
Interval: 0 kt 0.3; constraint: Sf /S0 where Ssc is the solar constant (1370 J mÀ2 sÀ1); td denotes the day
 From the total diffuse radiation, diffuse PAR is calculated
by using relationships reported by Alados and Alados-Arboledas
If Sf ¼ 2:282 À 0:78Á þ 0:067ln e þ 0:007Td ; ðA3Þ where Td is dew point temperature (°C), If has the unit of (mmol
mÀ2 sÀ1), and e and Á are sky clearness and brightness of skylight,
respectively, and are given by e¼ À
Sf cos q þ 1:041q3
1 þ St À Sf
1 þ 1:041q3 ;
Á ¼ Sf S0 ; ðA4Þ ðA5Þ kt
Sf S0 ¼ kt ½1 À 0:232kt þ 0:0239cos qÀ6:82 Â 10À4 Ta þ 0:0195f ;
Interval: 0.3 < kt < 0.78; constraint: 0.1 kt ðA2Þ Sf /S0 0.97 kt
Sf S0 ¼ kt ½1:329 À 1:716kt þ 0:267cos qÀ3:57 Â 10À3 Ta þ 0:106f ;
ðA1bÞ where St is the global solar irradiance at the Earth surface. After
diffuse PAR is obtained, direct PAR is calculated from the
difference between the calculated diffuse PAR and the measured
 These empirical relationships have been tested in the cited
papers. We also tested the calculated diffuse and direct PAR against
the 1995 measurements from the mixed deciduous forest site at
Walker Branch in Tennessee, United States, and found good
agreement for both diffuse and direct PAR (Figure A1). Figure A1. Relationship between measured and calculated (a) diffuse and (b) direct PAR for the mixed deciduous
forest site in Walker Branch in 1995. GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION
 Acknowledgments. This study was a contribution from the
FLUXNET project sponsored by NASA’s EOS Validation Program. D.
D. Baldocchi received additional support for his study at the Walker
Branch Watershed from the U.S. Department of Energy’s Terrestrial
Carbon Program. T. A. Black received support from the Climate
Research Branch of the Meteorological Service of Canada, the Natural
Sciences and Engineering Research Council of Canada, the Canadian
Forest Service, and Parks Canada; S. B. Verma received support from
the National Institute for Global Environment Change through the U.S.
Department of Energy (cooperative agreement DE-FC03-90ER61010). T.
Vesala received support from the European Commission, Programme
Environment and Climate 1994 – 1998 (project EUROFLUX under contract ENV4-CT95-0078), and the Academy of Finland (project 33687); P.
R. Dowty was supported through the NASA grant NAG5-7956 (LandSurface Characterization of South African Savannas). We give special
thanks to David Fitzjarrald for his critical comments on this paper.
Nancy Kiang is also thanked for her helpful comments. P. T. Boggs, R.
H. Byrd, J. E. Rogers, and R. B. Schnabel developed the ODRPACK
package. Measurements of diffuse PAR at the Walker Branch site were
obtained from the NOAA Integrated Surface Irradiance Study (ISIS)
program. We thank Detlef Matt and Kell Wilson for their assistance in
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ÀÀÀÀÀ D. Baldocchi and L. Gu, Ecosystem Science Division, Department of
Environmental Science, Policy and Management, 151 Hilgard Hall,
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T. Vesala, Department of Physical Sciences, University of Helsinki,
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