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Advantages of diffuse radiation for terrestrial ecosystem productivity Verma, Shashi B.; Baldocchi, Dennis; Gu, Lianhong; Vesala, TImo; Black, T. Andrew; Dowty, Peter R.; Falge, Eva M. 2002

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Advantages of diffuse radiation for terrestrialecosystem productivityLianhong Gu,1Dennis Baldocchi,1Shashi B. Verma,2T. A. Black,3Timo Vesala,4Eva M. Falge,5and Pete R. Dowty6,7Received 8 August 2001; revised 19 October 2001; accepted 21 October 2001; published 29 March 2002.[1] Clouds and aerosols alter the proportion of diffuse radiation in global solar radiation reachingthe Earth’s surface. It is known that diffuse and direct beam radiation differ in the way they transferthrough plant canopies and affect the summation of nonlinear processes like photosynthesisdifferently than what would occur at the leaf scale. We compared the relative efficiencies of canopyphotosynthesis to diffuse and direct photosynthetically active radiation (PAR) for a Scots pineforest, an aspen forest, a mixed deciduous forest, a tallgrass prairie and a winter wheat crop. Thecomparison was based on the seasonal patterns of the parameters that define the canopyphotosynthetic responses to diffuse PAR and those that define the responses to direct PAR. Theseparameters were inferred from half-hourly tower CO2flux measurements. We found that: (1) diffuseradiation results in higher light use efficiencies by plant canopies; (2) diffuse radiation has muchless tendency to cause canopy photosynthetic saturation; (3) the advantages of diffuse radiationover direct radiation increase with radiation level; (4) temperature as well as vapor pressure deficitcan cause different responses in diffuse and direct canopy photosynthesis, indicating that theirimpacts on terrestrial ecosystem carbon assimilation may depend on radiation regimes and thus skyconditions. These findings call for different treatments of diffuse and direct radiation in models ofglobal primary production, and studies of the roles of clouds and aerosols in global carboncycle. INDEX TERMS: 4806 Oceanography: Biological and Chemical: Carbon cycling; 0315Atmospheric 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 cycle1. Introduction[2] A plant canopy consists of an assemblage of plants, whoseleaves possess a particular spatial distribution and assortment ofangle orientations [de Wit, 1965; Monsi and Saeki, 1953]. How acollection of leaves intercepts sunlight and uses light energy toassimilate carbon dioxide (CO2) is the basis of canopy photosyn-thesis. The radiation environment inside a plant canopy is dynamicin both time and space (vertically as well as horizontally), owing totemporal changes in the solar elevation angle, the presence ofclouds, the motion of the canopy, and spatial variations in plantcanopy physical structure and physiological capacity. Interactingwith this dynamic radiation environment are several vertical bio-logical and environmental gradients within plant canopies, includ-ing profiles of leaf nitrogen content, photosynthetic capacity,temperature, humidity, wind speed, CO2concentration, etc. Thesecanopy structure-induced complexities can lead to emergent prop-erties that are not expected from photosynthesis of a single leaf.One such example is the differentiation in impacts of diffuse anddirect photosynthetically active radiation (PAR) on canopy photo-synthesis.[3] Crop scientists have long realized that radiation-use effi-ciency (RUE, defined as the ratio between grams of biomassaccumulated and total solar radiation intercepted) or light useefficiency (LUE, similar to RUE, but based on PAR only) is higherfor diffuse radiation than for direct radiation [de Wit, 1965; Allen etal., 1974; Goudriaan, 1977; Norman, 1980; Norman and Arke-bauer, 1991; Sinclair et al., 1992; Sinclair and Shiraiwa, 1993;Rochette et al., 1996; Healey et al., 1998]. Sinclair et al. [1992]speculated that higher diffuse RUE might explain why some cropspecies growing under glasshouses show higher RUE than thosegrowing in open fields. However, they did not quantitativelycompare the inside radiation with the outdoor environment. Youngand Smith [1983] reported that an understory herb in a mixedspruce stand gained more carbon on representative cloudy daysthan on clear days. They suggested that this could be due to greaterdiffuse PAR flux density and increased plant water potentialsunder cloudy sky conditions. With increasing interests in terrestrialecosystem carbon sequestration and new technologies available formeasuring fluxes over tall canopies [Verma et al., 1986; Baldocchiet al., 1988], observational studies on the relationship between theradiation environment and CO2exchange of forests becamepossible. Numerous researchers have since reported significantlyhigher radiation use efficiencies during cloudy days than duringclear days for both coniferous and deciduous forests [Price andBlack, 1990; Hollinger et al., 1994; Fan et al., 1995; Fitzjarrald etJOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D6, 4050, 10.1029/2001JD001242, 20021Ecosystem Science Division, Department of Environmental Science,Policy and Management, University of California, Berkeley, California,USA.2School of Natural Resource Sciences, University of Nebraska, Lincoln,Nebraska, USA.3Faculty of Agricultural Sciences, University of British Columbia,Vancouver, British Columbia, Canada.4Department of Physical Sciences, University of Helsinki, Helsinki,Finland.5Department of Plant Ecology, University of Bayreuth, Bayreuth,Germany.6Department of Environmental Sciences, University of Virginia,Charlottesville, Virginia, USA.7Now at Puget Sound Water Quality Action Team, Office of theGovernor, Olympia, Washington, USA.Copyright 2002 by the American Geophysical Union.0148-0227/02/2001JD001242$09.00ACL 2 - 1al., 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 isshown by the alienation of light responses of net ecosystemexchange (NEE) of CO2between clear and cloudy days withcloudy days having a higher NEE rate (in terms of the absolutevalue) than clear days for the same solar irradiance level.[4] It is important to compare RUE, or LUE, at the sameirradiance level because both variables decrease with increasingirradiance level due to light saturation effect. A somewhatunexpected finding reported by some of these studies is thatthe highest rate of forest NEE of CO2(that is, the most negativevalue, following the NEE sign convention) often occurs oncloudy rather than on sunny days even through solar radiationis substantially lower on cloudy days than on sunny days [Priceand 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. [1999] showed that themaximum carbon sequestration by two temperate forest ecosys-tems happened under sky conditions with a solar radiation levelequivalent to about 70–80% of clear-sky solar irradiance andclouds reduced the solar irradiance by as much as 50% withoutlowering the capacity of these two forests in carbon sequestrationas compared with clear days. Except for a few cases [e.g.,Freedman et al., 1998, 2001], most of these studies used changesin surface solar irradiance as a measure of cloudiness and did notactually conduct cloud observations.[5] Clouds reduce the global solar radiation but increase therelative proportion of diffuse radiation at the Earth surface. Acritical aspect of cloud modulation of surface solar radiation is thatclouds can also increase the absolute amount of diffuse radiation ifthe sky is not too cloudy [Gu et al., 1999]. Because of the higherRUE of diffuse radiation, clouds can actually enhance terrestrialecosystem carbon assimilation if the photosynthetic gains ofincreased diffuse radiation exceed the photosynthetic losses ofreduced direct beam radiation. This line of reasoning has led someresearchers to use increased diffuse radiation to explain enhancedecosystem carbon sequestration under cloudy sky conditions [Priceand Black, 1990; Hollinger et al., 1994; Fan et al., 1995; Gouldenet al., 1997]. However, it should be pointed out that increaseddiffuse radiation might not be the only factor responsible for theenhanced ecosystem carbon assimilation observed under cloudysky conditions [Young and Smith, 1983; Baldocchi, 1997; Gu et al.,1999]. In addition to changes in surface solar radiation, the presenceof clouds can be both causes and consequences of changes in manyatmospheric factors such as temperature, moisture, and latentheating, precipitation, etc. These factors all have direct or indirectinfluences on terrestrial ecosystem carbon assimilation [Gu et al.,1999]. Therefore some researchers emphasized decreases in therespiration of sunlit leaves due to reduced leaf temperature [Bal-docchi,1997], reduction in vapor pressure deficit (VPD) [Freedmanet al., 1998, 2001], stomatal dynamics associated with lightfluctuations [Fitzjarrald et al., 1995; Sakai et al., 1996]. We mayalso 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 netecosystem carbon uptake on clear days. Because of these consid-erations, Gu et al. [1999] stressed the multiplicity of environmentalfactors influencing ecosystem carbon sequestration under cloudyconditions. In this paper, however, we focus on detecting thedifferences in the effects of diffuse and direct radiation.[6] Much understanding on the canopy differential responses todiffuse and direct radiation has been gained from numerous canopyphotosynthesis 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 Puryand Farquhar, 1997; Baldocchi, 1997; Choudhury, 2000; Choud-hury, 2001a, 2001b]. Although it is a general agreement amongthese models that canopy RUE is higher for diffuse radiation thanfor direct radiation, different models may have different sensitiv-ities on the separation of diffuse and direct radiation for predictingcanopy photosynthetic productivities. For example, the model ofde Wit [1965] showed only a slight dependence of RUE on thefraction of diffuse radiation, which led de Wit [1965 p. 37] toconclude ‘‘it is not worthwhile to spend much energy on measuringthe fraction of diffuse light in order to improve on the calculationof photosynthesis.’’ On the contrary, the model of Goudriaan[1977] sensitively depended on the separation of diffuse and directradiation for canopy photosynthesis, and the author stated that‘‘separate measurements of diffuse and direct radiation are almostas important as measuring the total solar radiation’’ [Goudriaan,1977, p. 192]. Considering the complexities involved in predictingcanopy photosynthesis, this type of disagreement is not surprising,especially for early models. With better understanding and quanti-tative treatments in canopy radiative transfer, leaf photosynthesis,transpiration, stomatal conductance, energy balance, etc., morerecent models generally reveal high sensitivities of canopy photo-synthesis 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 Puryand Farquhar, 1997; Choudhury, 2000; Choudhury, 2001a,2001b]. Norman and Arkebauer [1991] used the Cupid model toshow that canopy LUE increases nearly linearly with the fraction ofdiffuse PAR. Using a different model, Choudhury [2000, 2001a,2001b] came to similar conclusions. According to the predictionsof these studies, LUE of diffuse PAR can be several times higherthan LUE of direct PAR.[7] The sensitive dependence of canopy photosynthesis on thefraction of diffuse radiation as revealed by modern biophysicalcanopy models is apparently in consensus with the scenario thatuses enhanced diffuse radiation to explain field observation ofsignificantly higher RUE on cloudy days than on clear days.However, experimental studies, which go beyond simple compar-isons between cloudy and clear days and directly address thecanopy photosynthetic differences between diffuse and directradiation, are still needed. This is important since a variety ofenvironmental factors can differ and no conclusive statements canbe made on which factors are responsible for the differences inlight response curves between cloudy and clear days. Gu et al.[1999] elaborated this point.[8] Conceptually, the differences of canopy photosyntheticresponses to diffuse and direct PAR are relatively easy to under-stand. They result from the differences in diffuse and directradiative transfer regimes in plant canopies coupled with thenonlinearity of photosynthesis. While the irradiance from thediffuse skylight on all leaves at a given canopy depth is nearlythe same [Gutschick, 1991], the irradiance on sunlit leaves, whichare illuminated by both the direct beam and diffuse radiation andrepresent only a fraction of all leaves in the canopy, ranges fromthe level of a shaded leaf to full light, depending on the anglesbetween leaf orientation and beam propagation direction. Mean-while, as the irradiance level increases, leaf photosynthesis shiftsfrom RuBP regeneration (electron transport) limitation to Rubisco(CO2diffusion) control [Farquhar et al., 1980]. This leads tophotosynthetic saturation and decrease in RUE under high irradi-ance levels. Therefore the transfer regime of direct beam radiationwastes photons by concentrating the light resource to only afraction of all leaves, leading to a less efficient photosyntheticuse of light by plant canopies. Diffuse radiation, however, effec-tively avoids the light saturation constraint by more evenlydistributing radiation among all leaves in plant canopies, and leadsto a more efficient use of light.[9] A closely related issue is the necessity of separating leavesinto sunlit and shaded groups to predict canopy photosynthesis.This has been well recognized by terrestrial ecosystem biophysicalACL 2 - 2 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONmodeling communities [Sinclair et al., 1976; Norman, 1980; Wangand Jarvis, 1990; Wang et al., 1992; De Pury and Farquhar, 1997;Baldocchi, 1997; Wang and Leuning, 1998]. The distribution ofsunlight in canopies is bimodal: most leaves are shaded with low-intensity light or sunlit with high-intensity light. Few if any areexposed to the mean light level. The light responses of the groupsof shaded and sunlit leaves are distinctively different from eachother. The light response for the group of sunlit leaves quicklysaturates with increasing light level because the light is concen-trated among a relatively small number of leaves. Further increasein radiation can even lead to decreases in photosynthesis becauseof elevated temperature and enhanced respiration. In contrast, thelight response curve for the group of shaded leaves is very linear asthe light is shared by a relatively large amount of leaves and eachleaf tends to inhabit the linear portion of the leaf-level lightresponse curve [Baldocchi, 1997]. Therefore proper treatment ofthese two groups of leaves is important for accurately predictingcanopy photosynthesis. To determine the fractions of sunlit andshaded leaves in a canopy, one needs to deal with the issue of leafclumping as natural canopies often have leaves clumped, whichcan have significant effects on canopy photosynthesis [Baldocchiand Wilson, 2001].[10] However, the issues of separating leaves into sunlit andshaded groups and incident solar radiation into direct and diffusecomponents are not identical. Without separating sunlit fromshaded 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 ofsunlit leaves) and light constraint (in the case of shaded leaves)cannot be captured by such schemes. In contrast, failure topartition incident solar radiation into diffuse and direct compo-nents by treating the global radiation as direct beam radiationwill lead to underestimating canopy photosynthesis, especiallyunder cloudy conditions, because the higher diffuse radiation useefficiency is missed [Gu et al., 1999]. Therefore it is desirablefor biophysical canopy models to do both separations properly.However, models that address only one of these two issues butnot both are likely to perform worse than models that addressnone of them due to their opposite impacts on canopy photo-synthesis estimation.[11] Although the underlying mechanism for the differentia-tion in impacts of diffuse and direct PAR on canopy photosyn-thesis has been understood quite well, quantifying thisdifferentiation from measurements is difficult and can only bedone indirectly. This is because solar radiation at the Earthsurface is always composed of diffuse and direct PAR simulta-neously even on sunshine or overcast days. Further complicatingthis issue is that a variety of environmental factors, in additionto diffuse and direct radiation, can change with sky conditions.Thus complete pictures of canopy photosynthetic responses todiffuse PAR or direct PAR cannot be obtained directly undernatural conditions. To overcome this problem, new analysisapproaches are needed. To our knowledge, there have been nosystematic analyses on the behaviors of canopy photosyntheticresponses to diffuse or direct PAR based on field flux measure-ments in the literature. However, large-scale models such asregional or global gross primary production (GPP) models oftenrely on our quantitative understandings of canopy photosynthesisderived from light response curves. For example, many GPPmodels use LUE modulated by environmental stress functions topredict primary productivity [Monteith, 1977; Prince, 1991; Lawand 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 LUEsfor diffuse and direct PAR in their algorithms with only a fewexceptions that rely on results from canopy biophysical models[Anderson et al., 2000; Choudhury, 2000, 2001a, 2001b; Roder-ick et al., 2001]. A quantitative understanding of the differencesin the behaviors of canopy photosynthesis between diffuse anddirect PAR that is supported directly by field flux observationsis much needed.[12] There are three main objectives in this paper: (1) tointroduce a method for inferring canopy photosynthetic charac-teristics of both diffuse and direct PAR from tower fluxmeasurements; (2) to use the developed method to test theprevious modeling finding of the advantages of diffuse PARby evaluating the differences in canopy photosynthetic effectsbetween diffuse and direct PAR for a Scots pine forest, a mixeddeciduous forest, an aspen forest, a tallgrass prairie, and a winterwheat crop; and (3) to examine differences, similarities, andenvironmental controls in canopy photosynthetic characteristicsof diffuse and direct PAR for these ecosystems. To achieve theseobjectives, we take advantage of long-term tower flux measure-ments at these sites. We base our analyses on the seasonaldynamics of characteristic canopy photosynthetic parameters fordiffuse and direct PAR derived from flux measurements. TheTable 1. Locations, Climates, and Vegetative and Edaphic Characteristics of the Five Sites Investigated in This StudyaScots PineForestAspen Forest Tallgrass Prairie Mixed Forest WheatLocation 61C176510N,24C176170E,Finland53C176630N,106C176200W,Canada36C176560N,96C176410W,United States35C176580N,84C176170W,United States36C176460N,97C176080W,United StatesMean annualtemperature, C176C3 1 15 13.9 15Annual precipitation, mm 700 400 1103 1372 1044Canopy height, m 13 22 0.6 at maximum 26 0.9 at maximumStand age 35 70 55Maximal LAI 9.0 4.5 3.0 4.9 5.0Stem density or basal area 2500 stem haC01830 stem haC0123 m2haC01Dominant species Pinus sylvestris L. Populus tremuloidesMichx. Corylus cor-nuta (understory)little bluestem, bluegrama, big bluestem,Indiangrass, povertydropseedQ prinus L., Q albaL., Acer rubrum L.,A. saccharum, Lir-iodendron tulipi-fera, Carya sp.winter wheatSoil type Haplic Podzol, coarse,silty, glacial tillOrthic Luvisol, silty-clay texturesilty clay loam ofWolco-Dwight com-plex (thermic PachicArgiustolls andmesic Typic)Fullerton cherty siltloam (Typic Paleu-dult)silty clay loamof Poncreek andKirkland complexes(Typic and PachicArgiustolls)aData 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 deciduousforest site are used in the analyses.GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 3findings presented in this paper will provide a basis for globalGPP models to apply different treatments for diffuse and directPAR in their algorithms.2. Sites and Measurements[13] This study was conducted at five sites: a Scots pine forestin Finland, an aspen forest in Canada, a mixed deciduous forest, anative tallgrass prairie, and a cultivated winter wheat crop in theUnited States (Table 1). We selected these five locations from thetower sites in the FLUXNET project (http://public.ornl.gov/FLUXNET/) [Running et al., 1999; Baldocchi et al., 2001] tocover a broad vegetation spectrum and climate conditions. Table 1summarizes locations, climate conditions, and vegetative andedaphic characteristics of these five sites.[14] The data from the Scots pine forest were collected at theStation for Measuring Forest Ecosystem-Atmosphere Relations(SMEAR II) field measurement station, which is located inHyytia¨la¨, southern Finland [Vesala et al., 1998]. The stand ishomogeneous for about 200 m in all directions from themeasurement site, extending to the north for about 1.2 km(60C176 sector). The terrain is subject to modest height variation.An eddy covariance (EC) system, which included an ultrasonicanemometer and a closed-path infrared gas analyzer, wasinstalled to measure the net ecosystem CO2exchange at 23 mabove the ground (10 m above the canopy). Detailed descrip-tions on the site conditions, the setup of the eddy covariancesystem, and the microclimate measurements have been givenelsewhere [Vesala et al., 1998; Rannik, 1998; Rannik andVesala, 1999; Rannik et al., 2000].[15] Located in the southern part of Prince Albert National Park,Saskatchewan, Canada, the aspen forest site was in a horizontallyextensive and homogeneous even-aged stand. This mature aspenforest was regenerated after a natural fire in 1919 [Weir, 1996].Half-hourly fluxes of CO2were measured using the EC techniqueat 39.5 m above the ground (17.5 m above the canopy, see Table1). The EC sensors consisted of a three-dimensional sonic ane-mometer 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. [1996], Blanken et al. [1997],Chen et al. [1999], and Black et al. [2000].[16] The mixed deciduous forest site is located at the WalkerBranch Watershed in eastern Tennessee. This forest has regen-erated from agricultural land. The EC instruments, whichincluded a three-dimensional sonic anemometer and an openpath, infrared absorption gas analyzer, were placed on a scaffoldtower 36.9 m above the surface (10 m above the canopy, seeTable 1). The topography of this site is a challenge for fluxstudies. Its landscape is undulating. The vegetation around thetower changes systematically (E. M. Falge, unpublished data).As a consequence, there is a relatively large variability in fluxmeasurements as compared with other more flat sites. At thissite, diffuse PAR measurements are available through the Inte-grated Surface Irradiance Study (ISIS) program (http://www.atdd.noaa.gov/isis/isis.htm) [Hicks et al., 1996]. Detailedinformation on the measurements, the site condition, and thevegetation characteristics is provided by Wilson and Baldocchi[2000] and Johnson and Van Hook [1989].[17] The native tallgrass prairie and the winter wheat crop sitesare located in north central Oklahoma, United States, in theDepartment of Energy (DOE) Atmospheric Radiation Measure-ment-Cloud and Radiation Testbed (ARM-CART) region. Theformer is near Shidler, and the latter is near Ponca City, both withflat terrains. The prairie, dominated by warm season C4grasses, istypical of the central Kansas/northern Oklahoma region. The wheatcrop was planted mid October, emerged 2 weeks later, and reachedmaturity in late May. It was harvested early July. Fluxes of CO2,sensible heat, latent heat, and momentum were measured at aheight of 4.5 m in the center of a quarter section field (65 ha) usingthe EC technique. The EC array of sensors included a three-dimensional sonic anemometer, a Krypton hygrometer, and aclosed-path CO2analyzer. Further information on methodologyand measurements at the tallgrass prairie and winter wheat sites isgiven by Suyker and Verma [2001].[18] The Scots pine forest site belongs to CarboEurope (http://www.bgc-jena.mpg.de/public/carboeur/), while the other four sitesare 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 instrumentsto other regional networks. It has been found that intercompar-ability among different sites/sensors is good [Baldocchi et al.,2001].[19] This study involved one growing season of measurementsfrom each of these five sites (Scots pine forest in 1997, aspenforest in 1996, mixed deciduous forest in 1995, and tallgrassprairie and winter wheat in 1997). The analyses were based onhalf-hourly measurements of NEE, air temperature, vapor pres-sure deficit (VPD), soil temperature, and global PAR. At eachsite, global PAR, air temperature, and VPD were measured abovethe canopy, and soil temperature was taken at the soil surface(C245 cm deep). We also needed diffuse and direct PAR informa-tion in this study. Unfortunately, measurements of diffuse anddirect PAR were available only at the mixed deciduous forestsite. So we used a radiation partitioning model to calculatediffuse and direct PAR for the other four sites from measuredglobal PAR, global solar radiation, air temperature, and humidity.The model couples several well-tested relationships published inthe literature and is described in Appendix A. We tested thediffuse and direct PAR calculations using measurements from themixed deciduous forest site and found good agreement (FigureA1 in Appendix A).3. Data Analysis Method[20] As we pointed out in the Introduction, it is impossible todirectly compare canopy photosynthesis of diffuse radiation withthat of direct radiation under natural conditions. However, byinferring parameters that exclusively define canopy photosyntheticresponses to diffuse and direct light from canopy CO2fluxmeasurements, we can construct the canopy photosyntheticFigure 1. Effects of the parameter b in the rectangular hyperbola(equation (2)) on the response of canopy photosynthesis to theincident PAR.ACL 2 - 4 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONresponses to diffuse or direct light through the parameters inferred.We can then examine the differences or similarities of canopyphotosynthesis of diffuse and direct light based on the constructedresponses. In this section we will derive a canopy photosyntheticresponse function that allows us to infer parameters that exclu-sively define canopy photosynthetic responses to diffuse and directlight from tower flux measurements. Procedures to test the derivedresponse function will be outlined.3.1. A Generalized Rectangular Hyperbola[21] For the purpose of this study, the NEE of CO2(Fc)measured over a plant canopy can be considered as consisting oftwo components: canopy photosynthetic flux density (P)andecosystem respiration rate (Re):Fc¼ ReC0P: ð1ÞBy writing NEE in the form (1) we adopt the sign convention usedby the flux community for NEE: positive upward. Ecosystemrespiration (Re) consists of carbon loss by autotrophs (roots, plants)and heterotrophs (microbes, fungi, bacteria, etc), but a gain ofcarbon by the atmosphere. In many empirical analyses [e.g., Fan etal., 1990; Hollinger et al., 1994; Ruimy et al., 1995; Hollinger etal., 1998; Wofsy et al., 1993; Goulden et al., 1997; Chen et al.,1999; Lindroth et al., 1998; Lee et al., 1999], a rectangularhyperbola has been used to describe canopy photosynthetic fluxdensity P:Model 1ðÞP ¼aItbbþaIt; ð2Þwhere Itis the global PAR incident on the canopy; a is thecanopy quantum yield on an incident PAR basis when Itapproaches zero [Wofsy et al., 1993], and we call it the initialcanopy quantum yield; b is another empirical coefficient.Equation (2) is designated as Model 1. In previous studies, bhas been explained as the maximum canopy photosynthetic fluxdensity or canopy photosynthetic flux density at saturationbecause P ! b as It!1. In fact, this is not an appropriatedescription for this coefficient. For many crops, for example,canopy photosynthesis does not saturate at the natural range ofPAR. Instead, crops show an almost linear relationship with PAR[Ruimy et al., 1995]. Equation (2) itself is very flexible. Figure 1illustrates the relationship between P and Itfor different valuesof b.Asb increases, the curve becomes closer to being linear. Atb = 1, the curve is linear. Therefore b actually describes thecloseness to linear response of the canopy photosyntheticresponse curves, that is, the capacity of a canopy to resistphotosynthetic saturation at high levels of PAR. In other words,b is not necessarily the real canopy photosynthetic rate atsaturation, and does not have to be within ranges of commonlyobserved canopy photosynthetic flux densities. For semanticclearness, b will be referred to as Closeness to Linear Response(CLR) coefficient thereafter.[22] Previous studies have always treated a and b as purelycanopy properties and fixed them for a given plant canopy understudy. Such a view needs to be changed. Because of the differentialresponses of canopy photosynthesis to diffuse and direct PAR, aspointed out in the Introduction, these two parameters likely dependon sky conditions as well. Norman and Arkebauer [1991] andChoudhury [2000, 2001a, 2001b] showed that modeled LUE at thecanopy level increases linearly with the diffuse fraction. Torepresent this modeling finding, Anderson et al. [2000] describedcanopy LUE by the product of the nominal LUE and a linearfunction of diffuse fraction with the nominal LUE equal to canopyLUE when the diffuse faction is 0.5. In this study, we generalizethe results of these researchers and assume that both a and b arelinear functions of the fractions of diffuse and direct light in globalPAR. Thusa ¼ afIfItþarIrIt; ð3Þb ¼ bfIfItþ brIrIt; ð4Þwhere afand arare the initial canopy quantum yield for diffuse (If)and direct (Ir) PAR, respectively, and bfand brare the CLRcoefficient for diffuse and direct PAR, respectively. Our treatmentof a (equation (3)) is similar to the treatment of LUE by Andersonet al. [2000] in the sense that both are linear functions of the diffusefraction. To our knowledge, the introduction of (4) is new in thispaper. Substituting (3) and (4) into (2), we haveModel 2ðÞP ¼afIfþarIrC0C1bfIfþbrIrC0C1bfIfþbrIrC0C1þ afIfþarIrC0C1It: ð5ÞEquation (5), which is designated as Model 2, can be considered asa generalization to the commonly used rectangular hyperbola(Model 1, equation (2)). At the extreme condition when the canopyreceives only purely diffuse (direct) radiation, Ir=0(If= 0),equation (5) reduces to the exact form of equation (2). If there areno differences between diffuse and direct PAR for canopyphotosynthesis, ar= afand br= bf, equation (5) also returns toequation (2). Therefore af(ar) and bf(br) in equation (5) have thesame meanings with a and b, respectively, in equation (2). Theydescribe the characteristics of canopy photosynthetic responses todiffuse and direct PAR, respectively. Later we will examine thedifferences in canopy photosynthetic efficiencies between diffuseand direct PAR by comparing arwith afand brwith bf. Highervalues of ar(af)orbr(bf) indicate better efficiencies.[23] The dependence of ecosystem respiration rate Reisdescribed by the following function:Re¼ c1ec2c3Taþ 1C0c3ðÞTs½C138þd1ed2Ts; ð6Þwhere c1, c2, c3, d1, and d2are regression coefficients, Tsis soiltemperature, and Tais air temperature. The first term on the right-hand side of equation (6) is expected to capture abovegroundbiomass respiration, while the second is expected to capture soilrespiration. Instead of using only air temperature in the first termon the right-hand side of (6), we employ c3Ta+(1C0 c3)Tsto reflectthe effects of vertical temperature gradient on abovegroundbiomass respiration. Obviously, 0 C20 c3C20 1.3.2. Statistical Model Testing Procedures[24] 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 effec-tively for a wide range of vegetation types? (2) By includingdiffuse and direct PAR information in the model, do we improvemodel performance?[25] To answer these questions, we divided the growing seasonsof the five sites into 11-day moving windows (see the followingsection). For each window we randomly separated the measure-ments into two parts: one part for estimating coefficients throughnonlinear regression procedures (regression data set), and the otherfor independently validating models (validation data set). We usedboth the measured and calculated diffuse and direct PAR in the testof Model 2 for the mixed deciduous forest site.[26] To examine the importance of separating diffuse and directPAR in predicting canopy photosynthesis, we compare the newmodel with the conventional rectangular hyperbola (Model 1),GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 5which assumes the same canopy photosynthetic effects for diffuseand direct PAR (photosynthetic parameters are therefore treated asconstants for a given canopy).[27] For reasons explained later, we do not intend to introduceeffects of temperature (except on ecosystem respiration) and VPDexplicitly into Model 2. To examine how critical the roles oftemperature and VPD are in the regression scheme, we comparedModel 2 with a multiple response function that is similar to thoseused 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 functionhas the following form:Model 3ðÞP ¼aItbbþaItfTaðÞfVðÞ; ð7Þwhere V is VPD. The parameters f(Ta) and f(V) are environmentalresponse functions to modulate canopy photosynthetic responses tolight given byfTaðÞ¼expa1TaC0TrðÞRTrTaC16C171þexpa2TaC0TmðÞRTrTaC16C17fVðÞ¼11þb1exp C0b2=VðÞ;where a1, a2, Tm, b1, and b2are coefficients to be estimated throughregression, Tris the reference temperature (25C176C), and R is the gasconstant. The term f(Ta) has been widely used to describe leafphysiological response to changes in temperature [Harley andTenhunen, 1991]. The VPD response function has a feature ofbeing equal to unity when the air is saturated (V = 0) anddecreasing when VPD increases. The design of f(V) reflectsconsiderations of results published in the literature concerningresponses of plant physiological activities to VPD [Runyon et al.,1994; Law and Waring, 1994; Hogg et al., 2000].[28] Following the recommendations of Willmott [1981, 1982],we employed three statistical indices together in the model testingand comparisons in order to give adequate evaluation on theoverall 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 bothdifferential (as opposed to r2) and bounded (no agreement 0 C20IOA C20 1 complete agreement, as opposed to RMSE) and thereforecomplements r2and RMSE. For each moving window, values ofr2, RMSE, and IOA were calculated for each of the three modelsand for both regression and validation data sets. The paired t testwas then conducted to evaluate the significance regarding thedifferences in r2, RMSE, and IOA between Model 2 and Model1 and Model 3 for both model regression and validation.3.3. Obtaining Seasonal Dynamics[29] After the new model (Model 2) was tested, the measure-ments were merged. To get the seasonal dynamics of the initialcanopy quantum yield and CLR coefficient for both diffuse PAR(afand bf) and direct PAR (arand br), we applied an 11-daymoving window technique. The obtained values from a given 11-day window were treated as the values for the central day of thewindow (5 days before and after the central day). The length of this11-day window is a trade-off between two competing require-ments. The first requirement is that it must be short enough so thatno significant changes in canopy structure and leaf physiologyFigure 2. Changes of VPD and air temperature with the ratio of diffuse to global PAR at (a and b) the aspen forestsite (calculated diffuse PAR, solar elevation 50C176–60C176) and (c and d) the mixed deciduous forest site (measured diffusePAR, solar elevation 60C176–70C176). Data were moving-averaged with 11 points. In the moving average the ordering wasdone on the fraction of diffuse PAR, and the averaging was done on VPD and air temperature.(8)ACL 2 - 6 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONoccur during this period. The second requirement is that it must belong enough to have sufficient data points for regressional analy-ses. The length scale of 11 days also covers frontal passages thatoften cause large flux spectral variance [Baldocchi and Wilson,2001]. This coverage is important for this study since it widens therange of sky conditions and therefore the ranges of diffuse anddirect PAR in the moving window and increases the stability andreliability in the estimates of photosynthetic parameters throughnonlinear regressions. The seasonal courses were obtained bymoving the window day by day.[30] We examined how errors in the calculated diffuse and directPAR affect the estimates of af, bf, ar, and br. We determined theseasonal patterns of af, bf, ar, and brusing both measured andcalculated diffuse and direct PAR for the mixed deciduous forestsite. A sensitivity analysis was conducted to see how the estimatesof the parameters change in responses to ±15% variation in thecalculated diffuse PAR (direct PAR varied accordingly so thatglobal PAR is unchanged).3.4. Nonlinear Regression[31] A nonlinear regression software package called ODRPACKwas used in this study. ODRPACK can be freely downloaded fromhttp://www.netlib.org/. Although the major feature of this softwareis its weighted orthogonal distance regression, we chose to use itsordinary least squares function after numerous trials. This isbecause in our regression the measurement errors of the dependentvariable (NEE) are much greater than the measurement errors ofexplanatory 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 bothdependent and explanatory variables, which is very difficult to do.In the end, we concluded that the weighted orthogonal distanceTable 2. Statistics of the Paired t Tests on the Differences Between Model 2 and Model 1, Model 2 and Model 3 in the r2for ModelRegression (Reg.) and Validation (Val.)MixedaMixedbAspen Scots Pine Prairie WheatModel 2 – Model 1Reg.t stat 11.70 9.67 21.15 20.12 13.96 4.07t0.051.65 1.65 1.66 1.66 1.66 1.66P value 0.00 0.00 0.00 0.00 0.00 0.00Val.t stat 12.45 8.46 17.20 9.44 12.28 5.43t0.051.65 1.65 1.66 1.66 1.66 1.66P value 0.00 0.00 0.00 0.00 0.00 0.00Model 2 – Model 3Reg.t stat 1.42 C02.15 13.28 10.34 5.84 C01.10t0.051.65 1.65 1.66 1.66 1.66 1.66P value 0.08 0.80 0.00 0.00 0.00 0.86Val.t stat 5.05 1.41 12.85 7.16 7.92 1.88t0.051.65 1.65 1.66 1.66 1.66 1.66P value 0.00 0.08 0.00 0.00 0.00 0.03aUsing measured diffuse/direct PAR.bUsing calculated diffuse/direct PAR.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-Mean-Square Error (RMSE) for Model Regression (Reg.) and Validation (Val.)aMixedbMixedcAspen Scots Pine Prairie WheatModel 2 – Model 1Reg.t stat C011.78 C010.56 C021.27 C019.95 C015.64 C06.32t0.05C01.65 C01.65 C01.66 C01.66 C01.66 C01.66P value 0.00 0.00 0.00 0.00 0.00 0.00Val.t stat C013.70 C07.96 C019.37 C09.43 C014.87 C08.41t0.05C01.65 C01.65 C01.66 C01.66 C01.66 C01.66P value 0.00 0.00 0.00 0.00 0.00 0.00Model 2 – Model 3Reg.t stat C02.16 1.24 C012.21 C011.54 C07.63 C02.59t0.05C01.65 C01.65 C01.66 C01.66 C01.66 C01.66P value 0.02 0.89 0.00 0.00 0.00 0.006Val.t stat C03.61 C03.92 C015.62 C08.15 C09.83 C05.37t0.05C01.65 C01.65 C01.66 C01.66 C01.66 C01.66P value 0.00 0.00 0.00 0.00 0.00 0.00aRMSE is in units of mmol mC02sC01.bUsing measured diffuse/direct PAR.cUsing calculated diffuse/direct PAR.GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 7regression does not necessarily provide better estimations ofparameters than the ordinary least squares regression in our caseand the ordinary least squares regression (no weights applied todata points) is sufficient for our analyses.[32] The regression was conducted for each window. In thenonlinear regressions it is necessary to pick up a set of initialguesses for the parameters that are to be estimated. Sometimes thenonlinear regression cannot end with the desired sum of squaresconvergence with one trial of initial guesses. To deal with thisproblem, we employed a repetitive regression procedure. If theregression fails to converge, the procedure goes back and reiniti-alizes the regression with a different set of initial guesses. Theinitial guesses are picked up randomly from the preset reasonableranges (based on previous knowledge). The process repeats untilthe proper convergence is reached, or until the maximum of 50cycles is reached. If the latter case happens, the current window isabandoned, and the regression moves to the next window.3.5. Some Additional Points About the GeneralizedRectangular Hyperbola[33] It is important to point out that the initial canopy quantumyield of direct PAR (ar) is not equivalent to the initial canopyquantum yield for clear days. Under clear skies the fraction ofdiffuse radiation changes with solar elevation angles. This fractionapproaches unity when solar elevation is less than 5C176 but decreasesas solar elevation increases [Goudriaan, 1977]. The initial canopyquantum yield is determined from the initial response of canopyphotosynthesis to PAR when PAR is low. Under clear skies, lowlevels of global PAR can only occur in early morning and lateafternoon when the Sun is near the horizon. Since a high fraction ofglobal PAR at the Earth surface is diffuse under these solarpositions, the initial slopes of the curves of canopy photosynthesisagainst global PAR obtained from clear days would typically havea diffuse ‘‘signature.’’ Therefore the light response curves obtainedseparately from clear and cloudy days should converge at the lowlight level, and they both should be close to the slope of purelydiffuse PAR (af).[34] In theory, both arand brshould depend on solar elevationangles since the fraction of sunlit leaves in canopies changes withthe direct beam incidental angle. However, our analyses usingmodels of Ross [1981] showed that the fraction of sunlit leaves issensitive to changes in solar elevation angles only when the Sun isnear the horizon. As the solar elevation increases, the fraction ofsunlit leaves increases but quickly saturates and is not sensitive tochanges in solar elevation angles at high solar positions. Undernatural conditions, direct beam radiation dominates only at highsolar elevation angles. Therefore we expect that the dependence ofarand bron solar elevation angles is small.[35] Diffuse and direct PAR, temperature, and VPD are corre-lated with each other under natural conditions (Figure 2). Becauseof this correlation, applying additional temperature and VPDresponse functions to Model 2 may result in multicollinearity[Ratkowsky, 1989; Myers, 1990] and confound the estimates ofinitial canopy quantum yield and CLR coefficient through non-linear regression. This is not desirable because we are not onlyinterested in the overall performance of Model 2 but also want tomake sure that its parameters have clear biophysical meanings.Therefore it serves the particular goal of this paper by keepingregressors simple and independent in Model 2.[36] Since Model 2 does not explicitly consider the effects oftemperature and VPD on canopy photosynthesis, they must bereflected through the parameters of af, ar, bf, and br. A questionarises naturally: Are the differences between afand ar, bfand brattributable to the differences in the canopy photosynthetic effectsof diffuse and direct PAR? The answer is yes. Note that values ofaf, ar, bf, and brare determined at the same time domain fordiffuse and direct PAR through Model 2. If at a certain time ofthe growing season, a certain environmental condition (e.g.,water stress or no water stress) affects the photosynthesis ofdirect PAR, this same condition affects the photosynthesis ofdiffuse PAR also. What interests us are the relative magnitudesof afagainst ar, bfagainst br. Therefore the dependence of af, ar,bf, and bron temperature, VPD, or any other environmentalconditions does not pose any problem to our analyses as long asthey are always compared with each other under the sameenvironmental conditions.[37] It should be clear that the differences between afand ar,bfand bras estimated from Model 2 are not the same as thedifferences between cloudy and clear days in a and b asestimated from Model 1. As we explained in the Introductionand also in the work of Gu et al. [1999], many environmentalfactors can differ between cloudy and clear days. It would bedifficult to identify environmental factors that are responsible forthe differences in a and b of Model 1 between cloudy and clearTable 4. Statistics of the Paired t Tests on the Differences Between Model 2 and Model 1, Model 2 and Model 3 in the Index ofAgreement for Model Regression (Reg.) and Validation (Val.)MixedaMixedbAspen Scots Pine Prairie WheatModel 2 – Model 1Reg.t stat 12.40 9.79 22.49 15.90 15.84 6.23t0.051.65 1.65 1.66 1.66 1.66 1.66P value 0.00 0.00 0.00 0.00 0.00 0.00Val.t stat 12.06 8.83 18.71 5.44 14.76 5.96t0.051.65 1.65 1.66 1.66 1.66 1.66P value 0.00 0.00 0.00 0.00 0.00 0.00Model 2 – Model 3Reg.t stat 0.54 2.04 12.60 11.70 5.51 0.46t0.051.65 1.65 1.66 1.66 1.66 1.66P value 0.29 0.98 0.00 0.00 0.00 0.32Val.t stat 4.42 0.33 13.17 7.85 8.57 4.08t0.051.65 1.65 1.66 1.66 1.66 1.66P value 0.00 0.63 0.00 0.00 0.00 0.00aUsing measured diffuse/direct PAR.bUsing calculated diffuse/direct PAR.ACL 2 - 8 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONdays. This is why we used Model 2 and did not group days forcloud types in this study.4. Results4.1. Model Test and Comparisons[38] Results of the paired t tests on the differences in all threestatistics (r2, RMSE, and index of agreement) between Model 2and Model 1 indicate that Model 2, which has higher r2and indexof agreement and smaller RMSE, consistently performs better thanModel 1 with statistical significance for all five sites and for bothregression and validation (see Table 2 for r2, Table 3 for RMSE,and Table 4 for index of agreement). In all these tests the P valuesare smaller than 0.0001.[39] For the comparisons between Model 2 and Model 3 thestatistical test results are mixed. For the sites of aspen forest, Scotspine forest, and tallgrass prairie, results of the paired t tests on thedifferences in all three statistics between Model 2 and Model 3show that Model 2 consistently performs better than Model 3 withstatistical significance for both regression and validation (seeTables 2, 3, and 4). In these tests the P values are also smallerthan 0.0001. For the winter wheat site the validation tests on allthree statistics indicate that Model 2 works better than Model 3.The regression test on RMSE also supports this statement. How-ever, the regression tests on r2and index of agreement indicate thatthere are no significant differences between Model 2 and Model 3.For the mixed deciduous forest site, both measured and calculateddiffuse and direct PAR were used in the model comparisons. Forthis site the following paired t tests suggest that Model 2 is better:r2with validation data set and measured diffuse and direct PAR,RMSE with regression data set and measured diffuse and directPAR, RMSE with validation data set and both measured andcalculated diffuse and direct PAR, index of agreement withvalidation data set and measured diffuse and direct PAR. However,other tests at this site indicate no significant differences betweenModel 2 and Model 3. The mixed results in the statistical tests ofr2, RMSE, and index of agreement suggest that the recommenda-tions made by Willmott [1981, 1982] on model evaluations areprobably valid.[40] Although we expect that Model 2 is better than Model 1,the better performance of Model 2 than Model 3 for most casestested is somewhat surprising since Model 3 has more drivingvariables and free regression coefficients than Model 2. Theseresults indicate that it is important to separate diffuse and directPAR in interpreting NEE measurements. For some ecosystems theimportance of doing so may even exceed the inclusion of temper-ature and VPD in the predicting schemes of NEE. The reason forthat is diffuse radiation is correlated with VDP and temperature andrepresents a combined measure of both effects (Figure 2).[41] By comparing the t statistics and P values for the tests ofusingmeasureddiffuseanddirectPARandthoseofusingcalculated diffuse and direct PAR for the mixed deciduous forestsite, one finds that using measured diffuse and direct PAR increasesthe differences between Model 2 and Model 1 as well as thedifferences between Model 2 and Model 3 (see Tables 2, 3, and 4).[42] The effectiveness of the generalized rectangular hyperbola(Model 2) in predicting NEE can also be examined in Figures 3and 4 for model fitting and independent model validation, respec-tively. In general, the calculated NEE closely agrees with themeasured NEE. The values of r2, RMSE, and index of agreementindicate that the generalized rectangular hyperbola works well forthe five sites. The values of the three statistical indices vary fromsite to site, which reflects variations in site complexity. The mixeddeciduous forest site, which is the most complex site, has thelowest values of r2and index of agreement and largest RMSEamong the five sites studied. The model tends to underestimate themagnitude of unusually large fluxes (positive or negative). This isprobably not caused by the model. For example, ecosystemrespiration rates, which are shown to exceed 10 mmol mC02sC01insome measurements, are hard to explain ecologically for thesenorthern sites. It is known that occasionally the eddy covariancetechnique obtains unusually large fluxes (either positive or neg-ative). However, these points are sporadic and more likely due tocertain atmospheric turbulent events than to any real ecological orphysiological processes.4.2. Advantages of Diffuse PAR: InitialCanopy Quantum Yields Afand Ar[43] All five sites show that the initial canopy quantum yield ofdiffuse PAR (af) is consistently higher than the initial canopyquantum yield of direct PAR (ar) (Figure 5). For the mixeddeciduous forest in Oak Ridge, Tennessee, the seasonal patternsusing measured diffuse and direct PAR (Figure 5a) are similar tothose using calculated diffuse and direct PAR (Figure 5b) althoughsometimes using calculated diffuse and direct PAR leads to smallerestimates for afand larger estimates for ar(for example, comparevalues of afand araround day 200 in Figures 5a and 5b). Again,vegetation and land complexities and perhaps variable weatherconditions at this mixed deciduous forest site lead to large day-to-day variations in the estimates of afand ar, while at other sites(Figures 5c–5f) changes are smoother. Seasonality of afand arcan be clearly seen at the tallgrass prairie site (Figure 5e) and thewinter wheat site (Figure 5f). At the tallgrass prairie site, both afand arincrease during the spring period and reach the maximum inthe midsummer and then decrease toward the end of the growingseason (Figure 5e). Several developmental stages in the growth ofwinter wheat are revealed by the temporal patterns of afand ar(Figure 5f). In early growth stages of winter wheat, afand ar,which are both small, do not differ very much. As the wheatdevelops, both afand arincrease as well as the differencesbetween them. However, as it approaches maturity, the twoparameters converge again and then decrease rapidly toward theend of May (Figure 5f). The seasonality of afand arat the Scotspine forest site (Figure 5c) and the aspen forest site (Figure 5d) isnot as clear as at the tallgrass prairie site or the winter wheat sitealthough increases during spring and decreases during autumn canstill be seen at the two sites.[44] The sensitivity test shows that ±15% variations in thecalculated diffuse PAR and accordingly in the calculated directPAR have hardly any effects on the estimates of arand onlyTable 5. Average Diffuse and Direct Canopy Photosynthetic Parameters and Their Standard ErrorsaMixedbMixedcAspen Scots Pine Prairie WheatMean af4.93 ± 0.14 4.34 ± 0.14 2.90 ± 0.05 2.89 ± 0.06 2.19 ± 0.07 2.08 ± 0.14Mean ar2.33 ± 0.09 2.43 ± 0.12 1.35 ± 0.04 1.83 ± 0.06 1.62 ± 0.06 1.58 ± 0.13Mean af/ arratio 2.81 ± 0.17 3.49 ± 0.53 2.50 ± 0.21 1.67 ± 0.04 1.41 ± 0.03 1.66 ± 0.08Mean bf69.7 ± 5.6 63.8 ± 5.4 239.2 ± 17.2 80.0 ± 5.3 238.0 ± 9.6 95.3 ± 6.3Mean br20.4 ± 0.84 22.7 ± 1.1 25.8 ± 2.3 20.0 ± 0.7 20.1 ± 1.1 24.0 ± 2.5Mean bfand brratio 4.7 ± 0.7 3.6 ± 0.3 15.4 ± 1.5 6.3 ± 0.8 13.9 ± 0.5 8.2 ± 0.7aAveraging periods are the same as in Figures 5 and 8. Units of initial canopy quantum yields afand arare in 100 C2 mol CO2/mol photon; CLRcoefficients bfand brare in mmol mC02sC01.bUsing measured diffuse/direct PAR.cUsing calculated diffuse/direct PAR.GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 9slightly 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 estimatesof af, and a C015% change slightly increases the estimates of af,while the effects on arare hardly detectable (Figure 5d). Togetherwith the results from the mixed deciduous forest site where bothmeasured and calculated diffuse and direct PAR are used, wetherefore conclude that errors in the calculated diffuse and directPAR are unlikely responsible for the differences between afand arobtained here.[45] The ratios of afto arat the five sites are compared inFigure 6. Although there are a lot of scatterings in the datapoints, the afto arratio is generally greater than 1. The meanvalues of af, ar, and the afto arratio at the five sites are foundin Table 5. The mixed deciduous forest has the largest mean af(0.049 and 0.043 mol CO2/mol photon using measured andcalculated diffuse and direct PAR, respectively) and ar(0.023and 0.024 mol CO2/mol photon using measured and calculateddiffuse and direct PAR, respectively). The winter wheat has thesmallest mean af(0.021 mol CO2/mol photon), while the aspenFigure 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.ACL 2 - 10 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONforest has the least mean ar(0.014 mol CO2/mol photon). Themixed deciduous forest also has the largest mean afto arratio(2.81 and 3.49 using measured and calculated diffuse and directPAR, respectively), while the tallgrass prairie has the least meanafto arratio. Because of the strong seasonality in afand aratthe tallgrass prairie and winter wheat sites, these mean values arefor references only.4.3. Effects of Temperature and VPD on InitialCanopy Quantum Yields Afand Ar[46] As we pointed out earlier, effects of temperature and VPDon canopy photosynthesis are implicitly expressed in the values ofthe parameters in Model 2. From Figure 5 we see that both afandarvary a lot over the season. Although the overall seasonalpatterns may be controlled by leaf phenology, short-term variationsare likely caused by changes in weather conditions.[47]Sinceafand arare estimated through 11-day movingwindows, it is not possible to conduct a strict analysis on howenvironmental factors control them. However, if we focus on thegeneral patterns and prominent features only and refrain frominterpreting details, we may still be able to get some insights onthis issue by examining how afand archange with daily meanvalues of air temperature and VPD. An initial examination onFigure 5 encourages this effort. For example, a sharp drop in afanda somewhat less significant drop in aroccurred early in thegrowing season, around day 172, in the aspen forest (Figure 5d).The temporal records of surface meteorological variables indicatedthat this was associated with the passage of a cold front. DuringFigure 4. Same as Figure 3, but for model validation.GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 11this period, surface air pressure increased, and the wind directionshifted from steady southwesterly to northwesterly wind. In themeantime, mean daily air temperature dropped 12C176C in less than 3days and reached a minimum of less than 4C176C. We noticed that thehighest afbefore this event was about 0.046 mol CO2/mol photon.Such a high value was never reached again after the cold weatherfront was past (Figure 5d). In the following, we will analyzechanges of afand arwith air temperature and VPD using data fromthe mid growing seasons at the five sites (days 150–275 for theScots pine forest, 160–270 for the aspen forest, 110–270 for themixed deciduous forest, 160–260 for the tallgrass prairie, 110–150 for the winter wheat) to minimize the impact of phenology.[48] Among the five sites, Scots pine forest appears to be mostsensitive to changes in air temperature (Figure 7a). However, theFigure 5. Seasonal dynamics of diffuse and direct initial canopy quantum yields afand arfor the mixed deciduousforest 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 isvaried accordingly to keep the measured global PAR unchanged. The obtained seasonal patterns are shown along withthe original calculations. For clarity, sensitivity test results for other sites are not shown. Most missing points are dueto gaps in the original measurements. A few are due to unsuccessful convergence in the regression.ACL 2 - 12 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONoptimum temperatures for afand ar, which are about 10C176C, aresurprisingly low. The afand arof the aspen forest respond weaklyto changes in temperature (Figure 7c). Nevertheless, it can still beseen from the exhibited patterns that low or high temperatures tendto reduce afand ar. The optimum temperatures for afand arappear to be around 15C176C. The afand arof the mixed deciduousforest (Figure 7e) respond to temperature differently at low temper-ature range. While afis higher for temperature <20C176C than fortemperature >20C176C, the opposite is true for ar. No clear depend-ence of afand arof the tallgrass prairie on temperature isidentifiable (Figure 7g). Similar to the mixed deciduous forest(Figure 7e), the afand arof winter wheat (Figure 7i) also responddifferently to temperature. While the dependence of afon temper-ature is weak, the arstrongly depends on temperature.[49] The responses of afand arto VPD unavoidably carry somesimilarities with the responses to temperature since the twovariables are correlated. For example, the initial increases in afand arof the Scots pine forest (Figure 7b) and the aspen forest(Figure 7d) with VPD are probably a reflection of the correspond-ing temperature responses in Figures 7a and 7c, respectively.However, the mixed deciduous forest (Figures 7e and 7f) andthe tallgrass prairie (Figures 7g and 7h) show signs of independentVPD and temperature effects. In the case of the mixed deciduousforest, no clear signs of VPD effects on afand arare visible at lowVPD (Figure 7f), while low temperature affects afand ar(Figure7e). Although the afand arof the tallgrass prairie apparently donot depend on temperature (Figure 7g), high VPD tends todecrease them (Figure 7h).[50] The revelation that afand arsometimes respond to temper-ature as well as VPD in different ways is interesting. It explainssome contrasting features between afand arin Figure 5. Althoughafand arshow some degree of parallel changes with time in theirseasonal dynamics, especially for the overall patterns, out-of-phasefluctuations in the two parameters do occur. This may indicate thatenvironmental controls on afand arcan differ.4.4. Advantages of Diffuse PAR:CLR Coefficients Bfand Br[51] The relative effectiveness of diffuse and direct PAR forcanopy photosynthesis can also be examined through bfand brwith greater values indicating lower tendency to saturation underhigh levels of light (see equation (4) and Figure 1). Advantagesof diffuse PAR over direct PAR for canopy photosynthesis areagain demonstrated by the much larger bfthan brfor all five sitesstudied (Figure 8). For these sites, direct PAR more easily causescanopy photosynthetic saturation than diffuse PAR. Because bfcan be several orders of magnitude larger than br, the logarithmicscale is used in Figure 8. All five sites show strong seasonality inthe estimates of bfand br. This is in contrast with afand ar,which exhibit clear seasonality only at the tallgrass prairie andwinter wheat sites. The five sites have distinctively differentfeatures in the seasonal patterns of bfand br. At the mixeddeciduous forest site (Figure 8a, using measured diffuse anddirect PAR; Figure 8b, using calculated diffuse and directPAR), bfand brincrease quickly during the springtime, reachthe maximum around mid May, and then gradually decrease. Themaximal bfseems to be around late July or early August for theScots pine forest (Figure 8c), while the pattern is not clear for br.The seasonal patterns of bfand brof 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 theformer. At the tallgrass prairie site the seasonal patterns of bfandbr(Figure 8e) are in contrast with those of afand ar(Figure 5e).While afand arof the tallgrass prairie keep changing in the midgrowing season, there is a quite long period in which bfand brare relatively constant. bfand brof the winter wheat increase as itapproaches maturity (Figure 8f). Just like afand ar(Figure 5f),bfand brof the winter wheat also converge and then decreasewhen maturity is reached.[52] The revealed seasonal patterns of bfand brindicate thatcanopy photosynthesis may shift between nonlinear and linearresponses to PAR during the growing period. The general trendof transition from nonlinear response early in the growing seasonto more linear response in the middle of growing season and thenback to nonlinear response late in the growing season may reflecttemporal changes in a variety of biotic factors. Baldocchi andAmthor [2001] used a model to show that canopy photosyntheticlight responses are nonlinear at low LAI but become more linearat high LAI. The seasonal dynamics in leaf nitrogen content mayalso affect the seasonal patterns of bfand br. The maximumcatalytic activity of Rubisco (Vcmax) increases with leaf nitrogencontent [Wilson et al., 2000], while bfand brshould increase withVcmax.[53] Using the measured and calculated diffuse and direct PARlead to similar seasonal patterns in the estimates of bfand brforthe mixed deciduous forest although sometimes the use of calcu-Figure 6. Ratios of diffuse to direct initial canopy quantum yields af/arfor the (a) mixed deciduous forest (usingmeasured diffuse and direct PAR) and Scots pine forest and (b) aspen forest, tallgrass prairie, and winter wheat.GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 13lated values tends to decrease the differences between the esti-mates of bfand br(Figure 8a, using measurements; Figure 8b,using calculation). Also, the sensitivity test shows that ±15%variations in the calculated diffuse PAR and accordingly directPAR have a negligible effect on the estimates of both bfand br(see Figure 8d). Therefore we feel confident that the differencesbetween the estimated bfand brreflect the differences in canopyphotosynthetic effects between diffuse and direct PAR.[54] Figure 9 plots the ratio of bfto brfor the five sites.Although variations of the bfto brratio are large with time andfrom site to site, almost all points are larger than 1. Table 5summarizes the mean bf, brand bfto brratio for the five sites.The aspen forest has both the highest mean bf(239 mmolmC02sC01) and br(26 mmol mC02sC01) as well as the highestmean bfto brratio (15). The mixed deciduous forest has thesmallest mean bf(70 mmol mC02sC01if using measured diffuseFigure 7. Responses of diffuse and direct initial canopy quantum yields afand arto changes in daily mean airtemperature 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 arestandard error bars. Data were moving-averaged.ACL 2 - 14 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONand direct PAR, 64 mmol mC02sC01if using calculated diffuse anddirect PAR) and smallest mean bfto brratio (5 if usingmeasured diffuse and direct PAR, 4 if using calculated diffuseand direct PAR). It is interesting that while there are consid-erable differences in the mean values of bf(from about 60 to240 mmol mC02sC01) among the five sites, the mean values of brare much closer (from about 20 to 25 mmol mC02sC01).4.5. Effects of Temperature and VPDon CLR Coefficients Bfand Br[55] Similar to what we did for afand ar, we also examine howbfand brchange with daily mean air temperature and VPD (Figure10). 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 bfand bron temperatureexcept for the tallgrass prairie site where no clear dependence isidentifiable (Figure 10g). While the bfof the Scots pine foresttends to increase with temperature, the brshows the opposite trend(Figure 10a). A similar pattern is found for the aspen forest (Figure10c). The brof the mixed deciduous forest tends to decrease withtemperature, but the dependence of bfon temperature appears to benonmonotonic with the optimum temperature around 20C176–25C176C(Figure 10e). Both bfand brof the winter wheat (Figure 10i)appear to decrease with temperature. For all five sites the responsesof bfand brto temperature are similar to those to VPD (Figures10b, 10d, 10f, 10h, and 10j), again reflecting the correlationbetween temperature and VPD.[56] Similar to what we observed for afand ar, environmentalcontrols on bfand brdo not always exhibit the same patterns.The divergence in the effects of temperature (or VPD) on bfandbras revealed in Figures 10a, 10c, and 10e (or Figures 10b, 10d,and 10f) explains why sometimes out-of phase fluctuationsoccur in the seasonal dynamics of bfand brat these sites (Figure8). We will discuss the importance and implications of thesefindings later.4.6. Effects of Light Level on the Advantagesof Diffuse PAR[57] The initial canopy quantum yields (afand ar) reflect thelight use efficiencies by the canopy under a ‘‘purely’’ diffuse ordirect radiation environment when the incident light levelapproaches zero. As the light level increases, the canopy lightuse efficiency decreases because of the saturation effects. Since bfand brare different, we expect that the rate of decrease in canopylight use efficiency with the light level differs between diffuse anddirect PAR. Consequently, the differences in the canopy photo-synthetic effects of diffuse and direct PAR change with the lightlevel. According to Model 2, under a purely diffuse radiationenvironment with any light level If, the diffuse canopy quantumyield af(If) is found to beafIfC0C1¼afIf¼ 0C0C1bfIf¼ 0C0C1afIf¼ 0C0C1þbfIf¼ 0C0C1If¼afbfafþbfIf: ð9ÞFigure 7. (continued)GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 15A similar expression can be found for the direct canopy quantumyield at any light level Irunder a purely direct radiationenvironment. Now let us assume If= Ir= I and obtain the ratio:afIðÞarIðÞ¼afbfarþbrIðÞafþbfIC0C1arbr: ð10ÞUsing the mean values of af, ar, bf, and brgiven in Table 5, weexamine how the above ratio changes with the light level I, eitherpurely diffuse or purely direct (Figure 11). All five sites showthat the ratio af(I)/ar(I) increases almost linearly with I. FromFigure 11 it is clear that it is necessary to examine both a and bsimultaneously for the differences in radiation use efficienciesFigure 8. Seasonal dynamics of diffuse and direct CLR coefficients bfand brfor 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 thesensitivity test the diffuse PAR is varied by ±15% over the calculated values, and the direct PAR is varied accordinglyto keep the measured global PAR unchanged. The obtained seasonal patterns are shown along with the originalcalculations. For clarity, sensitivity test results for other sites are not shown. Most missing points are due to gaps inthe original measurements. A few are due to unsuccessful convergence in the regression.ACL 2 - 16 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONbetween diffuse and direct radiation since radiation useefficiencies change with radiation level.5. Discussion and Conclusions[58] Using tower flux measurements, we demonstrated theadvantages of diffuse PAR over direct PAR for forcing canopyphotosynthesis for five vegetation sites, covering a broadecosystem spectrum and climate conditions. We found that (1)diffuse radiation results in higher light use efficiencies by plantcanopies; (2) diffuse radiation has a much less tendency tocause canopy photosynthetic saturation; (3) the advantages ofdiffuse radiation over direct radiation increase with radiationlevel; (4) temperature as well as vapor pressure deficit cancause different responses in diffuse and direct canopy photo-synthesis, indicating that their impacts on terrestrial ecosystemcarbon assimilation may depend on radiation regimes and thussky conditions.[59] These findings have implications for studies of the globalcarbon cycle. To explain recently observed increases in photo-synthetic activities in the Northern Hemisphere, researchers havebeen looking at nitrogen deposition, CO2fertilization, globalwarming, reforestation, and regrowth of secondary forests foranswers [Keeling et al., 1996; Myneni et al., 1997; Fan et al.,1998]. The findings in this study highlight the necessity ofexamining yet another factor for temporal variations of carbonsequestration in the Northern Hemisphere: changes in cloudinessand aerosol concentration. Variations in cloudiness and aerosolconcentration not only change the total solar radiation at theEarth surface but also alter the relative proportions of diffuseand direct solar irradiance. Hollinger et al. [1994] suggested thatincreased haze might have enhanced terrestrial CO2uptake inthe northern Temperate Zone. Cloudiness has increased overbroad regions of the world since the beginning of the twentiethcentury [McGuffie and Henderson-Sellers, 1988; Henderson-Sellers, 1989; Abakumova et al., 1996; Russak, 1990; Karland Steurer, 1990; Angell, 1990], while atmospheric aerosolconcentration has substantially increased due to anthropogenicemissions of SO2, for example, especially in the NorthernHemisphere [Andreae, 1995]. Increased cloudiness and aerosolconcentration may have already altered the nature of solarradiation received at the Earth’s surface. Data from the formerSoviet Union showed that increases in cloudiness and atmos-pheric turbidity were accompanied by decreases in global solarradiation and direct beam solar radiation but increases in diffusesolar radiation [Abakumova et al., 1996]. Gilgen et al. [1998]also reported significant decreases in solar irradiance on mostcontinents. If the benefit of increases in diffuse solar radiationovercompensates the loss caused by decreases in direct beamsolar radiation for vegetation photosynthetic activities, increasedcloudiness and aerosol concentration could have enhanced car-bon sequestration of terrestrial ecosystems in the NorthernHemisphere during the last several decades [Gu et al., 1999;Roderick et al., 2001]. Further studies are needed to clarify thisissue.[60] Traditionally, light use efficiency or radiation use efficiencyat the canopy level has been considered to be independent of thedirectional 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 assumptionin this definition is that plant canopies behave like one single leaf.Under this assumption, what matters is the amount of radiationabsorbed by the canopy, and how the canopy absorbs the radiationis irrelevant. Such an assumption goes against the long practice bycrop scientists using leaf orientation, plant geometry, and cropcanopy as indicators in their breeding programs to identify superiorvarieties [e.g., Pendleton et al., 1968; Yoshida, 1972]. The resultspresented in this paper directly supports the modeling findings ofNorman and Arkebauer [1991] and Choudhury [2000, 2001a,2001b] that light use efficiency strongly depends on the diffuseand direct composition of the incident global PAR. Clearly, lightuse efficiency must be treated as a function of sky conditions. It is achallenge for the next generation of regional and global primaryproduction models, which rely on the concept of light use effi-ciency, to develop new algorithms to accommodate these newfindings.[61] Another finding with important implications for globalprimary production studies is that the dependence of canopyquantum yields on temperature (VPD) can be complicated and isvegetation (species functional type)-specific. Ehleringer andPearcy [1983] and Ehleringer et al. [1997] reported the leaf-levelmeasurements of quantum yield for a number of C3and C4mononcot and dicot grass species. They found that the quantumyield of C3species is generally driven by photorespiration andtherefore decreases with temperature while temperature has noclear effects on the quantum yield of C4species. However, thetemperature ranges reported by Ehleringer and Pearcy [1983]Figure 9. Ratios of diffuse to direct CLR coefficients bf/brfor the (a) mixed deciduous forest (using measureddiffuse/direct PAR) and Scots pine forest and (b) aspen forest, tallgrass prairie, and winter wheat.GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 17were mostly >15C176C. Our results suggest that cautions should betaken when one generalizes the conclusions of Ehleringer andPearcy [1983] and Ehleringer et al. [1997] to the canopy scale orextrapolates them into lower temperature ranges. The canopyquantum yields of Scots pine forest (Figure 7a), aspen forest(Figure 7c), and winter wheat crop (Figure 7i) increase withtemperature when temperature is low. Nevertheless, we obtaineda tendency for decrease in canopy quantum yields of the Scotspine forest with increasing temperature when temperature islarger than 10C176C and no dependence for the canopy quantumyields of the tallgrass prairie. This is in agreement withEhleringer and Pearcy [1983] and Ehleringer et al. [1997] eventhrough the two studies worked at different scales and useddifferent approaches.[62] It is somewhat unexpected that impacts of temperatureand VPD on the initial canopy quantum yields afand ar(Figure7) and CLR coefficients bfand br(Figure 10) can divergebetween diffuse and direct PAR. Obviously, this kind of phe-nomenon cannot happen at the leaf level. Although more studiesare needed to find a sound explanation for it, we suspect that itmight be related to differences in the microenvironment thatsunlit and shaded leaves experience. Sunlit leaves receive notFigure 10. Responses of diffuse and direct CLR coefficients bfand brto changes in daily mean air temperature andVPD for the (a and b) Scots pine forest, (c and d) aspen forest, (e and f) mixed deciduous forest (using measureddiffuse and direct PAR), (g and h) tallgrass prairie, and (i and j) winter wheat. Also shown are standard error bars.Data were moving-averaged.ACL 2 - 18 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATIONonly more PAR but also more near-infrared radiation thanshaded leaves do. Therefore temperatures of sunlit leaves areexpected to be higher than shaded leaves. This leads to greatertemperature gradients between sunlit leaves and surrounding air[Young and Smith, 1983]. Consequently, an air temperature thatis too low for shaded leaves and thus limits their photosyntheticactivities might be within the right range for sunlit leaves.Conversely, an air temperature in the right range for shadedleaves might be too high and therefore limit photosyntheticactivities of sunlit leaves. Differences in leaf temperature canalso result in differences in VPD at the leaf surface and thusaffect stomatal conductance [Collatz et al., 1991; Baldocchi,1997; Baldocchi and Harley, 1995]. Therefore responses ofcanopy photosynthetic parameters of diffuse and direct PAR toenvironmental factors may not always parallel with each other,and for certain ranges of environmental conditions divergenceamong diffuse and direct photosynthetic parameters can occur.The differences in environmental responses of canopy photo-synthetic characteristics for diffuse and direct PAR indicate thatthe underlying mechanisms of terrestrial ecosystem carbonassimilation are likely a function of sky conditions. For example,we may expect that environmental controls of net ecosystemexchanges of carbon dioxide follow different patterns betweencloudy and clear days.[63] This study reiterates the conclusion of Goudriaan [1977]that diffuse PAR is an important variable in interpreting vegetationphotosynthetic activities. Its impact depends on vegetation struc-ture and climate conditions. However, currently diffuse PAR is nota variable commonly measured by tower flux communities.Instead, most teams measure only total PAR. As shown in thispaper, a single measurement of total PAR, which masks skyconditions, hinders accurate interpretation of CO2flux measure-ments. Therefore we recommend routine measurements of diffuseradiation, particularly diffuse PAR, in tower flux measurements. Inconjunction with diffuse radiation measurements, cloud observa-Figure 10. (continued)Figure 11. Changes of diffuse to direct canopy quantum yieldratio af(I)/ar(I) with the incident PAR (diffuse or direct) for thefive study sites. Mean values of af, ar, bf, and brgiven in Table 5were used in the calculation. See equation (10) and text forexplanation.GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION ACL 2 - 19tion is also desirable. By linking measured radiation components atthe surface with cloud variables such as cloud cover, which may beobservable from space, potential algorithms for remote sensingapplications can be developed. Future generations of regional andglobal primary production models may use these algorithms toderive surface diffuse and direct radiation conditions from satelliteobservations of cloudiness to estimate terrestrial ecosystem pro-ductivities. An advantage of such a strategy is that it is applicableto all-weather conditions, including cloudy skies that currentremote sensing based algorithms tend to avoid.Appendix A: Estimating Diffuse and Direct PAR[64] Currently, diffuse and direct PAR are not variables com-monly measured by flux towers or meteorological stations. How-ever, several models that partition measured global PAR intodiffuse 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. [1999]coupled several relationships published in open literature todecompose measured global PAR and solar radiation into diffuseand direct components. In this study, we adopt a similar approach.For completeness, these relationships are given here.[65] The radiation decomposition model first computes thetotal diffuse (diffuse PAR plus diffuse near-infrared) fraction inglobal solar radiation from clearness index (kt), solar zenithangle (q), ambient temperature (Ta), and relative humidity (f)by using relationships reported by Reindl et al. [1990]. Clearnessindex is defined as the ratio between the global solar radiationreceived at the Earth surface and the extraterrestrial solarradiation. The corresponding equations are [Reindl et al., 1990]Interval: 0 C20 ktC20 0.3; constraint: Sf/S0C20 ktSfC14S0¼ kt1C00:232ktþ0:0239cosq½C06:82C210C04Taþ0:0195fC3;ðA1aÞInterval: 0.3 < kt< 0.78; constraint: 0.1 ktC20 Sf/S0C20 0.97 ktSfC14S0¼kt1:329C01:716ktþ0:267cos q½C03:57C210C03Taþ0:106fC3;ðA1bÞInterval: ktC21 0.78; constraint: Sf/S0C21 0.1 ktSfC14S0¼kt0:426ktC00:256cos q½þ3:49C2C03Taþ0:0734fC3; ðA1cÞwhere Sfdenotes the total diffuse radiation received by a horizontalplane at the Earth surface (JmC02sC01); S0denotes the extraterrestrialirradiance at a plane parallel to the Earth surface (JmC02sC01), and isgiven by [Spitters et al., 1986]S0¼ Ssc1þ0:033cos 360td=365ðÞ½C138cos q; ðA2Þwhere Sscis the solar constant (1370 J mC02sC01); tddenotes the dayof year.[66] From the total diffuse radiation, diffuse PAR is calculatedby using relationships reported by Alados and Alados-Arboledas[1999]:IfC14Sf¼ 2:282C00:78C1þ0:067ln eþ0:007Td; ðA3Þwhere Tdis dew point temperature (C176C), Ifhas the unit of (mmolmC02sC01), and e andC1are sky clearness and brightness of skylight,respectively, and are given bye ¼1þ StC0SfC0C1C14Sfcos qC0C1þ1:041q31þ1:041q3; ðA4ÞC1¼ SfC14S0; ðA5Þwhere Stis the global solar irradiance at the Earth surface. Afterdiffuse PAR is obtained, direct PAR is calculated from thedifference between the calculated diffuse PAR and the measuredglobal PAR.[67] These empirical relationships have been tested in the citedpapers. We also tested the calculated diffuse and direct PAR againstthe 1995 measurements from the mixed deciduous forest site atWalker Branch in Tennessee, United States, and found goodagreement for both diffuse and direct PAR (Figure A1).Figure A1. Relationship between measured and calculated (a) diffuse and (b) direct PAR for the mixed deciduousforest site in Walker Branch in 1995.ACL 2 - 20 GU ET AL.: ADVANTAGES OF DIFFUSE RADIATION[68] Acknowledgments. This study was a contribution from theFLUXNET project sponsored by NASA’s EOS Validation Program. D.D. Baldocchi received additional support for his study at the WalkerBranch Watershed from the U.S. Department of Energy’s TerrestrialCarbon Program. T. A. Black received support from the ClimateResearch Branch of the Meteorological Service of Canada, the NaturalSciences and Engineering Research Council of Canada, the CanadianForest Service, and Parks Canada; S. B. Verma received support fromthe 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, ProgrammeEnvironment and Climate 1994–1998 (project EUROFLUX under con-tract ENV4-CT95-0078), and the Academy of Finland (project 33687); P.R. Dowty was supported through the NASA grant NAG5-7956 (Land-Surface Characterization of South African Savannas). We give specialthanks 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 ODRPACKpackage. 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