Global Change Biology (2002) 8,124-141

Modelling night-time ecosystem respiration by aconstrained source optimization method

C H U N - T A LAI’, G A B R I E L KATULt, J O H N BUTNORf, DAVID ELLSWORTH~ andRAMORENt‘Depurtnlent of Biology, University of Utah, 257s. 1400E Salt L.&e City, UT 843 2 2-0840, USA; tDepartnlent of the Environmenf,Duke University, Durham NC 27708-0328, USA; $U.S.D.A Forest Service, Southern Research Station, 3041 Cornwallis Road,Research Trianngle Park, NC 27707, USA; 9 School o/ Nntural Resources and the Environment, University of Michigan, DanaBuilding, 430 East University Avenue, Ann Arbor, Ml 48709-1175, USA

Abstract

One of the main challenges to quantifying ecosystem carbon budgets is properly quanti-fying the magnitude of night-time ecosystem respiration. Inverse Lagrangian dispersionanalysis provides a promising approach to addressing such a problem when measuredmean CO2 concentration profiles and nocturnal velocity statistics are available. An in-verse method, termed ‘Constrained Source Optimization’ or CSO, which couples a Jocal-ized near-field theory (LNF) of turbulent dispersion to respiratory sources, is developedto estimate seasonal and annual components of ecosystem respiration. A key advantage tothe proposed method is that the effects of variable leaf area density on flow statistics areexplicitly resolved via higher-order closure principles. In CSO, the source distributionwas computed after optimizing key physiological parameters to recover the measuredmean concentration profile in a least-square fashion. The proposed method was field-tested using lyear of 30-min mean CO* concentration and CO;, flux measurementscollected within a 17-year-old (in 1999) even-aged loblolly pine (Pinus taeda L.) stand incentral North Carolina. Eddy-covariance flux measurements conditioned on large frictionvelocity, leaf-level porometry and forest-floor respiration chamber measurements wereused to assess the performance of the CSO model. The CSO approach produced reason-able estimates of ecosystem respiration, which permits estimation of ecosystem grossprimary production when combined with daytime net ecosystem exchange (NEE) meas-urements. We employed the CSO approach in modelling annual respiration of above-ground plant components (c. 214 g C m-* year-‘) and forest floor (c. 989 g C me2 year-‘)for estimating gross primary production (c. 1800gCm- *year ~‘1 with a NEE ofc. 605gC m-’ year-’ for this pine forest ecosystem. We conclude that the CSO approachcan utilise routine COZ concentration profile measurements to corroborate forest carbonbalance estimates from eddy-covariance NEE and chamber-based component flux meas-urements.

Keywords: local ized near f ie ld theory, inverse methods, ecosystem respirat ion, net ecosystemexchange, forest carbon budget

Received 13 November 2000; revised version received and accepted 17 April 2001

Introduction

Est imating monthly to annual ecosystem respirat ion (RE)i s essent ia l in l ight of the pre-eminence of respirat ion inaffecting net ecosystem COz exchange (Baldocchi ef RI.

Correspondence: ChumTa Lai, tel. -t 801 581 8917, fax 801 581

4665, e-mail Iai@biology.utah.edu

1997; Valentini et al. 2000). Long-term covariancemeasurements of net ecosystem exchange (NEE) arecritical to estimating ecosystem carbon budgets, yetlarge errors arising from micrometeoroIogical measure-ments of respirat ion under night- t ime condit ions maycorrupt NEE est imates (e .g . Wofsy et al. 1993; Baldocchiet al. 1996; Goulden et al. 1996; Moncrieff c,t al. 1996;Lindroth ef al. 1998; Law et al. 1999a,b; Schmid ef al.2000; Valentini ef nl. 2000). Vertical subsidence, lack of

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steadiness in mean atmospheric conditions and in-termit tent turbulent t ransport contr ibute to increase the‘de-coupling’ between night-t ime net ecosystem respir-ation and the CO2 flux above the canopy measured bycovariance methods. Instrument limitations, such asseparation between sensors that are assumed to measurethe same parcel of air, attenuation of fluctuation inthe tube, volume averaging by anemometers, and f initesampling per iods that may be too short to resolve a l l theeddy sizes, further compound the random and systematicerrors in night-time fhrx measurements (Kaimal &Gaynor 1991; de Bruin ef al. 1993; Kaimal & Finnigan1994; Leuning & Judd 1996; Moncrieff ef al. 1996;Massman 2000).

An al ternative approach to est imating RE i s t o u t i l i z e afunctional relationship between CO* sources, S(t,z), orf luxes , F(t,z), and a re lat ively s imple quanti ty to measuresuch as mean CO;! concentrat ion, C(t,z), within the canopyvolume, where t is time and z is the height from the forestf loor. This approach has the added benefi t of permitt ingdetai led part i t ioning of S(f,z) between different canopylevels and between the vegetation and the forest floorefflux F(t,O).

Early research ef forts der ive these funct ional re lat ion-ships by assuming F(t,z) i s re lated to dC/dz via an effect-ive turbulent diffusivity (K-Theory). Over the past30 years , theoretical developments and many laboratoryand field experiments have demonstrated that scalar andmomentum f luxes within many canopies do not obey K-Theory (e.g. Deardorff 1972, 1978; Corrsin 1974; Shaw1977; Sreenivasan ef ai. 1982; Denmead & Bradley 1985;Finnigan 1985; Raupach 1988; Wilson 1989). To alleviateK-Theory limitations, other theoretical and practicalmethods were developed without resorting to a Iocafeddy diffusivity approximation (e.g. Raupach 1988,1989a,lb; Katul & Albertson 1999; Katul et al. 2000a;Siqueira et al. 2000).

This study builds on these recent advances to develop amethod capable of inferr ing F(f ,O) and S(f,z) f rom meas-ured C(f,z) for long- term es t imat ion of n ight - t ime Rr. Tosuccessfully reproduce F(f,z) from measured C(t,z), thefol lowing condit ions must be sat is f ied: ( i ) accurate de-scription of the flow statistics inside the canopy for stableatmospher ic condi t ions , ( i i ) expl ic i t account ing of s toragef luxes within the canopy volume, and ( i i i ) constrainingthe estimation of S(l,z) so as to minimize the effect ofinherent measurement and sampling errors in C(f,z) onthe computed S(f,z). The objective of this study is todevelop a method, termed ‘Constrained Source Opti-mizat ion’ or CSO, capable of reproducing night- t ime eco-system f luxes and XII components from measured C(t,z).The method is tested using 1 year of 30-minute measuredmean CO? concentrat ion prof i les C(t,z) co l lec ted wi th in a17-year-old (in 1999) even-aged loblolly pine (Pinus faeda

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L.) stand at the Duke Forest. Rather than propose a rc-placenrent method to night-time covariance, chamber-scalemeasurements , or other establ ished respirat ion measure-ment methods, we propose here a complementary methodthat can independently assess monthly to annual RE es t i -mates from routinely measured C(r,z). Such an assess-ment is essential because forest floor respiration is amajor component of forest gross pr imary product ion (Bal-docchi et al. 1997; Law et al. 1999b; Valentini ef al. 2000).

Theory

In order to estimate Rr, both the source S(f,z) in thecanopy and the forest floor CO* flux F(t,O) are requiredbecause

II

KE =.[

S(f,z)dz+F(t,o) (1)0

where h is the mean canopy height. Measured C(t,z) canbe related to S(t,z) or F(f,z) using the time and horizontallyaveraged one-dimensional continuity equation for aplanar homogeneous f low,

K(t) 2) i>F(l,z)- = - 7 + S(f,z)at (2)

Equation 2 has two unknowns, S(r,z) and F(f,z), and re-quires one addit ional prognost ic equat ion to solve for RE.One approach to establish this requisite equation is toconsider the interdependency between S(t,z) and C(t,z)via Lagrangian dispersion theory, which is considerednext .

Lqrangian Dispersion Theo y

The local ized near-f ield theory (LNF) proposed by Rau-path (1989a,b) can be used to describe a canonical rela-tionship between S(t,z) and C(f,z). According to Raupach(1989a,b), C(t,z) can be decomposed into far-f ield (C,) andnear-f ield (C, , ) concentrat ions, with the near-f ield concen-trat ion at z g iven by

where Az,, is the vertical interval between source locations,n,(z) is the standard deviation of the vertical velocityat height z, k,,(c) = -0.39891n(l -e-lo) - 0.15623e.ICI isa near-f ield kernel function, and < is a dummy variable .This analyt ical approximation to the kernel and result -ing errors (< 6%) are discussed in Raupach (1989a,b,1998) and Gu (1998). Given a reference concentration

126 C.-T. LA1 etal.

(C,) at z/h > 7, the diffusive, far-field concentration (C,)can be expressed as:

cf(z, = c,(zR) - Cn(ZR) + $$$A2 (4)

where Za is a reference (or measurement) height , and

f$(z) = a2,(ZVL(Z)is the far-f ield eddy diffusivity in a steady, homogeneousturbulent flow, and 7’t* is the Lagrangian integral timescale. We emphasize here that while steady-state diffu-sion is assumed in equations 3 to 5, the mass conservationequation in equation 2 is non-steady.

Many laboratory and f ield experiments demonstratedthat LNF is a significant improvement over gradient-diffusion theory (Raupach et al . 1992; Denmead & Raupach1993; Denmead 1995; Katul et al. 1997a; Massman & Wei l1999; Leuning 2000; Leuning et al. 2000; Siqueira et al.2000). Therefore, LNF was used to describe the scalartransport in the GO. Other models equal ly sui table toCSO include the Eulerian closure approach of Katul &Albertson (1999) and Katul ef al . (ZOOOa), the Hybrid ap-proach of S iqueira et al. (ZOOO), or the recent revis ion toLNF by Warland & Thurtell (2000).

For LNF, given ‘IL and ow, equations 3-5 provide theindependent formulation necessary to relate C to S and F ,thereby ‘c losing’ equation 2 and, in principle , permitt ingnight- t ime RE to be computed from measurements of C.As discussed in Katul et al. (1997a, ZOOOa), the conven-tional inverse LNF approach is not suff ic ient ly ‘ robust ’ tomeasurement errors because, in pract ice , the dif ferencebetween the number of source layers and the number ofconcentrat ion measurement layers is typical ly smal l . Nat-ural ly , such a smal l di f ference implies l imited degrees offreedom (usual ly 5 3) in the est imat ion of S f rom C. Wedescribe next the CSO, which is a variant on Raupach’s(1989b) invers ion to generate the des irable robustness inthe inference of S from C.

Constrained Source Optimization (CSO) method

As described by Raupach (1989b), i t i s poss ib le to so lvefor the source S and the f lux F from the mean CO2 con-centrat ion profi le C by the so-cal led ‘ inverse’ approach.In this method, the canopy is first divided into m’source layers, where m’ C- m, and m is the number oflevels where C(zJ are measured (i = 1, 2.. m). Thechal lenge is to determine the opt imum source dis tr ibu-tion S(zr) (j = 1, 2. m’) that best recovers the measuredC(z,) using LNF and prescribed f low stat ist ics (e .g . o , , , (z) ,T,). As discussed in Katul et al. (1997a) and Siqueira et al .(2000), this inverse procedure is very sensitive to thechoice of nr’ and m, as well as to the random measurement

errors in C(z,). With m-m’ < 3 for most field studies,spurious sources and sinks may be produced from meas-urements and sampling errors in C (see Katul et a l . 2000a;Siqueira ef al. 2000). To minimize such sensitivity andincrease the degrees of freedom in the estimation of Sfrom C, an alternative approach that utilizes knowncanopy physiological properties and attributes is pro-posed.

Total above-ground plant respiration (= $ S(t, z)dz)

can be decomposed into woody t issue and fol iage respir-ation (Ff). According to Law er al. (1999b), wood respir-ation accounted for about 6% of total RE in a ponderosapine ecosystem, while fol iage respirat ion accounted forabout 18%, despite the re lat ively low leaf area densi ty inthat forest . In our region, atmospheric demand for vapouris lower than that in the Oregon ponderosa pine ecosys-tem, thus requir ing less woody water t ransport systemper unit of leaf area (Oren et al. 1986). Therefore, weassumed the contr ibution of wood respirat ion would beeven less important re la t ive to the fo l iage respirat ion incomparison to the ponderosa pine ecosystem. Conse-quently, the contribution of woody components toabove-ground ecosystem respirat ion was not expl ic i t lyseparated from foliage in this study. In a nearby standof s imi lar character is t i cs , the contr ibut ion of woody sur-face area to plant area density was 18% (Pataki ef al. 1998).This is an underest imate of the total woody surface areain the stand and hence the actual amount of respiringwoody biomass . This was part ia l ly compensated for inthe calculat ions of respirat ion by assuming that the ent ireplant area density was composed of fol iage with i ts char-ac ter is t i ca l ly h igher respirat ion ra tes .

With th is s impl i f i ca t ion , a f i rs t order es t imate of thevertical distribution of S can be specified a priori as

S(z) = 4z)Rn(z) (6)

where a(z) is the plant area density and Rd is the darkrespiration per unit plant area modelled after Collatz et al.(1991) as

R&Z) = ~Vcn&)

where c1 is, in our approach, an unknown constant andV~,&Z) is the maximum catalyt ic capaci ty of Rubisco perunit leaf area. The scaling between Rd and V,,,,, assumesthat respirat ion is mainly a funct ion of enzyme turnoverassociated with the maintenance of photosyntheticenzymes, pr incipal ly r ibulose 1,5-bisphosphate carboxy-lase as represented by V,,,,. Natural ly , other models forRd can be readily implemented in such a framework. BothV cmax and a are temperature-dependent (Campbell &Norman 1998). Typical a values at 25°C are assumedbetween 0.011 and 0.015 (Farquhar et al. 1980; Collatzef al. 1991). Here, the temperature dependency of V,,,,can be calculated from

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V’ max(Ta) =

V c max, 25 exph 6 - 25111 + exp[a2(T, - 55)] (8)

wlwre, Vcmax,25 is the maximum cata lyt ic rate of Rubiscoat 25”C, I’, is the air temperature (which approximatesthe plant t issue temperature during night t ime), and a,and a2 are species-specific coefficients as discussed byLai rt al. (2OOOa), which were reported, respectively, as0.051 and 0.205 for overstorey pine (0.4 < z/h < 1) and as0.088 and 0.290 for the understorey hardwood (0 < .z/h < 0.4) . Long-term averaged values of Vcm.1x,2s = 59 umolm -* s’ for pines and 30 nmol me2 s-’ for the hardwoodspecies are used, as discussed by El lsworth (1999), DeLu-cia & Thomas (2000) and Naumburg & Ellsworth (2000).

We define the constrained source optimizat ion (CSO)method as the combination of tl and forest floor flux F(f,O)used in equations 2-5 to recover the measured C(z,) i n aleast-square manner (e .g. optimized) every 3Omin. Whencompared to Raupach’s (1989b) inverse method, this ap-proach offers several advantages for night- t ime sourcecalculat ions :

1. The proposed CSO modelling approach prescribedand constrained S(z) by our understanding of the ver-tical distribution of a(z) and Vcmax(z), both measuredquanti t ies , but a l lowing determinat ion of ecosystemrespira tory f luxes F(f,z) via opt imizing C L and F(f ,O) toreproduce the CO1 concentrat ion f ie ld for a wide rangeof stable atmospheric conditions. In essence, thenumber of unknowns was greatly reduced to M’ =2.The redundancy in the proposed optimization isgreater ( typical ly , m - 2 varies from 6 to 8) when com-pared to Raupach’s (1989b) method (m - m’ 5 3 fornearly all LNF field studies conducted thus far).Hence, with such redundancy, S and F(t,O) are nolonger ‘hypersensit ive’ to random measurement andsampl ing errors in C(Zi).

2 . Because the number of parameters is small (only a andF(t,O)), a global optimization method can be efficientlyimplemented. This global search can be readily con-strained by the maximum range in C L and F(t,O) f r o mli terature values . For example, a global search with nbetween 0.001 and 0.05, and F( t,O) between 0 and 30 nmolm-* s-i, should yield reasonable sources and forest floorfluxes observed in majority of field experiments.

3. The method takes advantage of the measured plantarea density a(t,t) dynamics when computing thecanopy sources. Plant area density distribution anddynamics are not well uti l ized in the LNF approachof Raupach (1989a, b) .

The velocity statistics and integral time scale

Ideally, the measured o, , (z) should be used in equation 3and 5. However, these measurements are rarely available

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on a routine basis on monthly to annual time scales.Higher-order Eulerian c losure models provide an altema-t ive to routine est imation of o , (z) provided that they canbe val idated via short intensive f ie ld campaigns. A keyadvantage to such a model framework is its ability to mapvariability in a(z,f) to variability in cr,,(z,f).

In order to model the u,, within the canopy volume, wechose the second-order closure approach by Wilson &Shaw (1977) (hereafter referred to as WS77; see Appendix1 for details). The ability of this model to reproducemeasured CT, inside forested canopies was found to becomparable to third-order closure schemes (Katul &Albertson 1998) and other multiscale second orderclosure schemes (Katul & Chang 1999). Furthermore,obtaining the numerical solution to the WS77 closureequations does not require complex numerical integra-t ion algori thms, at least when compared to the recentlyproposed c losure model of Ayotte et al. (1999). Althoughthe WS77 assumes neutral atmospheric conditions, theeffects of atmospheric stability can be indirectly ac-counted for by revis ing the upper boundary condit ionsto evolve with h/L, where L is the Obukhov lengthtypically measured at a reference height above thecanopy-atmosphere interface.

With regards to the integral time scale, Raupach(1989a,b) suggested that v z 0.3 as a constant withinthe canopy volume, where U S is the friction velocity.While the 0.3 value appears reasonable for unstable andnear-neutral a tmospheric s tabi l i ty condit ions (Katul cf a l .1997a), l i t t le evidence is avai lable to support such a con-stant value for s table condit ions. In this s tudy, we assessthe sensitivity of the RE calculation to three differentformulat ion of b.h .

--=I0.3

h7-Llf* 41 L

h0 (9)

where, $i and $2 are determined from detailed Eulerianvert ica l veloc i ty integral t ime-scale measurements (TJand assuming T,, = f TL (Tennekes & Lumley 1972). Esti-mates of T,, can be derived from the autocorrelat ion func-t ion plo(r) o f the vert ica l ve loc i ty f luctuat ions 70’:

(10)

where overbar represents t ime averaging ( i .e . iii’ = 0), andT is the time lag. The above integration is commonlyterminated at the first zero crossing of pi,(r). If such acrossing is not wel l def ined (as may be the case for some

128 C.-T. LA1 etnl.

very stable runs), the integration is terminated at the firstT for which pi,,(~) i s no longer s ta t i s t i ca l ly d i f ferent f romzero at the 99% probability level. This probability limit onpJr) can be determined from Salas et al. (1984):

P!&%(T) =-1 f 2.32$/N-

N-ifs(11)

where N is the number of sample points, and fs is thesampling frequency (e.g. N = 18000 forf5 = 1OHz and a 30min sampling durat ion) . Hence, for consistency, the inte-gration in equation 10 is terminated when pU,(r) =: p%“,,(r)(rather than zero) for all runs.

Study site and measurements

study siteThe measurements are conducted at the Blackwood Div-ision of Duke Forest in Orange County, near Durham,NC, USA (36’2 N, 79% W) as part of the AmeriFluxlong- term CO2 f lux monitor ing in i t ia t ive (Kaiser 1998) .The s i te i s a uni formly planted loblol ly pine (Pinus taedaL.) forest that extends 300-600m in the east-west direc-tion and 1OOOm in the north-south direct ion. The meancanopy height was 14 m ( k 0.5 m) at the end of 1998. Thechange of topographic s lope is smal l (< 5%) so that theturbulent transport is not confounded by terrain (Kaimal& Finnigan 1994). All the measurements and parameter-izations in this study were from the tower in ambientcondit ions .

Eddy covariance flux measurements

The COZ, latent and sensible heat f luxes above the canopywere measured by a conventional covariance systemcomprising of a Licor-6262 C02/H20 infrared gas ana-lyser (Li-Cor Inc., Lincoln, NE, USA) and a CampbellScient i f ic sonic anemometer (CSAT3, Campbel l Sc ient i f icInc. , Logan, UT, USA). The sonic anemometer was pos-it ioned just above the canopy (z = 15.5 m). The infraredgas analyser was housed in an enclosure on the tower4.5 m below the inlet cup, which was co-located with theanemometer. The sampling f low rate for the gas analyseris9Lmin-‘, suff ic ient to maintain turbulent f lows in thetubing. A krypton hygrometer (KH20, Campbel l Scien-t i f ic) was posi t ioned with the anemometer to assess themagnitude of the tube attenuation and time lag betweenvert ical veloci ty and scalar concentrat ion f luctuat ions asdiscussed in Katul et al. (1997a, 2000a).

The f lux measurements were sampled at 10 Hz using aCampbell Scientific 21X data logger with all digitizedsignals transferred to a portable computer via anoptical ly isolated RS232 interface for future processing.

Detai ls about the process ing and correct ions to these highfrequency measurements are described in Katul et al.(1997a,b).

Mean CO2 and water vapour concentration profiles withinthe canopy

Another LiCor-6262 gas analyser was used to measureCO* and water vapour concentration profiles at 10levels (z,=O.l, 0.5, 1.5, 3.5, 5.5, 7.5, 9.5, 11.5, 13.5 and15.5 m, i.e. m = 10). This profiling system includes a multi-port gas sampling manifold to sample each level for 1 min(45s sampling and 15s purging) at the beginning, themiddle, and the end of 30-minute sampling duration.In 1999, the experiment resulted in 4850 30-minutesnight- t ime runs for which s imultaneous COz concentra-tion and flux measurements were available between 2030and 0430 EST.

Other meteorological and biological variables

In addit ion to the covariance f lux measurements above thecanopy, a HMP35C Ta/RH probe (Campbell Scientific)was also positioned at z = 15.5 m to measure mean airtemperature (T,) and mean relative humidity. A non-l inear thermistor (Campbel l Sc ient i f ic ) was posi t ioned at15cm below the forest floor, adjacent to the tower, tomeasure mean soil temperature (T,). All the meteoro-logical variables were sampled at 1 s and averaged every30min using a 21X Campbell Scientific data logger. Atotal of 45 leaf- level CO* ass imi la t ion (A,,,) responses to02 supply (A”,, - C; curves), conducted within a 14-month period between 1998 and 1999, were also used toest imate V,,, using the least -square regression proced-ure described by Wullschleger (1993) and Ellsworth(2000), where C, is the leaf internal CO2 mole fraction.Further details about the gas exchange measurementsand sampling methodology can be found in Ellsworth(1999, 2000) and Katul et al. (2000b).

Plant area density

The vertical variat ion of the leaf area plus branches wasmeasured by gap fraction techniques as described byNorman & Welles (1983) . A pair of opt ical sensors withhemispherical lenses (LAI-2000, Li-Cor) was used forcanopy light transmittance measurements from whichgap fraction and plant area densities were calculated.The measurements were made at 1 m intervals fromthe top of the canopy to 1 m above the ground to pro-duce the vertical profile in plant area index (PAI). PA1measurements were made routinely during the ex-perimental periods, from the same tower used for meas-ur ing f low s ta t i s t i cs , COz concentration and covariance

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measurements . For t ime increments between these meas-urements, the PA1 values were linearly interpolated.The vertical foliage distributions a(z) were generatedusing three canonical PA1 prof i les representing winter(December to Apri l ) , summer ( June to October) and tran-si t ion periods (May and November) .

Soil respiration measlrrements

Soil respiration F(t,O) was measured with a customdesigned, chamber based system - Automated CarbonEfflux System (ACES) - based on principles used inMaier & Kress (2000) . ACES is a multiport , dynamic gassampling system that utilizes an open flow-throughdesign to measure carbon dioxide f luxes from the forestf loor. Each chamber was equipped with a pressure equil i -brat ion port , ensuring that the chamber pressure was heldnear ambient (Fang & Moncrieff 1996) . Fif teen soi l cham-bers (25cm diameter , 1Ocm height , 4909cm3) were meas-ured sequentially using a single infrared gas analyser(EGM-3, PP Systems Inc . , Haverhi l l , MA, USA) integratedinto the system. Each chamber was sampled for 10 min-utes to ensure steady state conditions, and a value of F(t,O)was recorded on the tenth minute of the cycle. Ninecomplete runs (135 measures) were recorded every day.When not being actively sampled, all chambers werecontinuously supplied with ambient air to prevent COz.bui ld-up. Data were col lected cont inuously from Apri l toMay 2000. To lessen chamber induced impacts on the soilsurface, chambers were moved twice a week between twofixed sample points .

Velocity statistics measurementsfir testing WS77

To estimate 4, and Qz in equation 9 and test the WS77model performance for s table atmospheric condit ions , anintensive field experiment was conducted. The threeveloci ty components and vir tual potent ia l temperatureinside the canopy were measured at eight levels (z = 1.3,2.9, 4.8, 6.5, 8.5, 10.7, 12.1, 15.5m) from 23-30 August1999 with a vert ical array of eight CSAT3 sonic anemom-eters . Each sonic anemometer was anchored on a horizon-tal bar extending 1 m away from the walkup tower. Thesampling frequency was 10 Hz for al l sonic anemometers .All analogue s ignals were digit ized by a Campbell Scien-t i f ic CR-9000 data logger and transferred to a laptop com-puter for future processing. This experiment wasperformed at the same f lux tower s i te used to measureplant area density, the long-term scalar f luxes and con-centrat ion prof i les thereby permit t ing to assess the WS77performance of reproducing a , , (z) using the local ly meas-ured a(z). The velocity statistics were collected over awide range of atmospheric s tabi l i ty condit ions ; however ,here we focus only on stable atmospheric condit ions .

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Results and discussion

We assessed the performance of the CSO by ( i ) comparingthe predicted night-t ime ecosystem f luxes with eddy cov-ariance measurements collected at z/h = 1.1 for high u.(> 0.15 m s--l), (ii) verifying whether the optimized a isbounded by leaf- level measurements, and ( i i i ) evaluatingthe s imi lar i ty o f fores t f loor resp i ra t ion-so i l t emperatureresponse function computed with the CSO to functionsderived from chamber measurements. Final ly, the sea-sonal dynamics of RE and its components, as modelledby the CSO, are discussed in the context of the annualcarbon budget and gross primary production (GPP) ofthis forested ecosystem. Before present ing the modelledRE results, we consider the estimation of the flow statisticsinside the canopy that are essential to drive the CSOmethod.

Velocity statistics for nocturnal conditions

To model night- t ime RE using LNF, the veloci ty s tat is t icso,,, and TL are required. Figure 1 shows the measured qand o,,/u. at z/h = 1.1 for a wide range of stable atmos-pheric condit ions. Here, TL i s der ived from the Eulerianintegral time scale (T,,) described in equation 10. Theapparent increase of o,,/u. from the value of 1.1 forlarge h/L is attributed to the fact that random errorstend to increase o, but decrease 14. over very stableconditions. Hence, we assumed that CT,,/II. = 1.1 for theent ire h/L range. This is consistent with the f indings ofLeuning (2000) that thermal strat i f icat ion has l i t t le ef fecton (5,.

While the normalized o, remains nearly constant(c. l.l), the rp is greatly reduced with increasingstability (a reduction factor of 10 for two decades of h/L). Based on these field observations, F was made tovary with h/L. This variation is also consistent withfindings in a recent study by Leuning (2000) in whichthe LNF performance was significantly improvedwhen T, was corrected based on atmospheric s tabi l i ty .To quantify the stability effects on Tb we fitted anexponential curvef&/L) to the measurements in Fig. 1.The fitted curve was used to compute TL based on meas-ured h/L at z/h = 1.1. The above analysis completes thedescription of the upper boundary condition for thecanopy volume in order to generate the flow statisticsfor LNF.

The within-canopy vert ical variat ion of CT, and FL a r econsidered using the intensive velocity statistics measure-ments collected inside the canopy. Figure 2 shows the nor-malized ensemble o,, and ‘FL prof i les inside the canopyfor nocturnal conditions collected in August 1999.Although WS77 does not expl ic i t ly account for densi tygradients , i t can reproduce night- t ime CT,, reasonably wel l

1 3 0 C . - T . LA1 etal.

100-I

-------_--------

10-Z. . ,.

....* .J10-a 1 o-2 10-l 100 1 0 '

2

1.5

.

$1

0.5

0

. . . i: .. .

- - -..- ---

10-" 10-z 10-l

hll

10"

-

_1 0 '

Fig. 1 Normalized Tr (top) and CT,, (bottom) measured (0) at z/h = 1 .I for different stable conditions. Solid line is the fitted curveused in the CSO calculation. Dashed lines are the values for near-neutral conditions within the canopy sublayrr.

if the empirical constant in the characteristic length scale

is varied from its neutral value to match best the meas-ured mean wind field (see Appendix 1). The ozU profilefrom WS77, obtained with the revised length scale con-stant , is used in the LNF calculat ion for the entire studyperiod.

While the vertical variation in Tt. cannot be directlymeasured, i t may be inferred from measured T,, shownin Fig. 2. The fact that the measured T,,, profile is notconstant within the canopy volume motivated us to con-sider three possible scenarios for the space-time variationin ri*, shown in Fig. 3, and described below in thefo l lowing three cases .

1. 9 = 0.3, constant throughout the canopy without anystabilitv correction.

2, Ii& =i’, where f@ = 4, (1) = exp (- 0.0695x*

-‘0.6454x - 3.8516), x = ln($‘-and L is calculatedfrom the sensible heat and friction velocity measure-ments collected at the canopy top. Here, Tt, i s a lsoassumed constant within the canopy but varies withatmospher ic s tabi l i ty a t z / h = 1.1.

Finally, the case for which TL varies with both atmos-pheric stability h/L and z/h as derived from T, measure-ments is also shown. This case can be approximated by

3 . =f~-o.l55x(z,-l),

where

2, = 0 . 4 if z/h < 0.4z, = z/h ifz/h > 0.4

I.1 -

l-

I.5

O0- 1.5

I i--t- I

---.-[-.-..-jI II0 . 3 0 . 5

T.uJh

Fig. 2 Comparison between ensemble averages of within canopyTL (right) and oU, (left) profiles measured in August 1999 andmodelled based on WS77. For reference, the profiles suggestedby Kaupach (1989a,b) are also shown.

I0 I I0 0.05 0.1 0.15 0 . 2 0 . 2 5 0 . 3

TLuJh

Fig. 3 Three plausible 7’~ profiles tested in the CSO approach. Forthe Ti u./h =ji(&, &), we present as a sample 7’,-u./h = 0.044 atz/h = 1.1 derived from the long-term mean value in Fig. 2.

02002 Blackwell Science Ltd, Global Cbmge Biology, 8, 124-141

MODELLING N I G H T - T I M E E C O S Y S T E M R E S P I R A T I O N 1 3 1

Again, we emphasize that this profile assumes T,,, zz~TL and is based on the measurements shown in Fig. 2 .From the analysis in Appendix 2, we found that case 2provides the most reasonable result , a l though the dif fer-ences between cases 2 and 3 was at most 10%. For theremaining discuss ion the Ti+ profi le of case 2 was used.

Model optimization

Given the modelled veloci ty f ie ld and assuming some C Iand F(t,O), the night-time CO* concentration profile can becomputed using equations 3-5. The SL and F(f,O) are thenal lowed to vary unti l the root-mean square error (RMSE)between predicted and measured CO* concentra t ions a t 9levels i s minimized.

The optimization was conducted for each 30 min runwith

1. 1 > 0 , ( i .e . s table atmospheric condit ions)2. measured F(t,h) > 0 (ecosystem respiration exceeds

photosynthesis) , and

Jan. & Feb.1 61 4

1 2

-10E8%6

4

2

0350 400 450 500 r

1 61 4

1 2

-10E 6

'64

2

0350 400 450 500 !

Sep. ik Oct.IO

1 41 2

-10E6;;

64

2

0350 400 450 500

C (Iimol me2 s-l)

1 6Mar. & Apr.

14

1 2

1 06

64

2

0350 4Ga 450 500

1 61 4

1 2

1 06

64

2

0350 4M) 450 500 c

1 6

1 41 2

IO6

6

42

0350 400 450 500

C (Irmol me2 s-l)

Fig.4 Comparison between measured and CSO modelled en-semble averaged C(f,z) within the canopy. The comparison isreported for data combined over two consecutive months,thereby allowing demonstrating seasonal variations.

3. RMSE < 10~ mol mall’ (i.e. LNF reproduces well themeasured concentrat ion) .

These three criteria resulted in 2418 30-minute eveningruns between 2030 and 0430. The resulting optimizedconcentrat ion prof i les are shown in Fig . 4 af ter ensembleaveraging every 2 months ( to i l lustrate seasonal patterns) .As evidenced from Fig. 4 , the C profi les computed withC’S0 from opt imized a and F(f,O) are in good agreementswith the ensemble-averaged C measurements.

Model validation

To assess how well CSO reproduced RE, we consider thefo l lowing:

1. Comparisons between predicted and measured en-semble of F(t,h) for u. > 0.15m s-i. The latter u. condi-tion is used to ensure that the measured F(t,h) re l iab lyrepresents net ecosystem exchange (NEE) (Falge et a l .2000).

2. A comparison between modelled forest-floor-temperature function and chamber-measured re-sponse funct ions.

3. Whether the optimized c( value is bounded by theporometry chamber measurements of leaf Rd.

4. On longer time scales, whether the modelled ratio offorest floor to total ecosystem respiration is consistentwith independently established estimates derivedfrom biomass increment and other ecological measure-ments .

Comparisons between modelled and covariance measuredF(t,h)

A number of previous studies have found that duringnight-t ime condit ions, the NEE measurements by eddycovariance may not be reliable (e.g. Wofsy et al. 1993; Hol-linger et ul. 1994; Black ef al. 1996; Goulden et al. 1996;Baldocchi et nl. 1997; Lavigne et nl. 1997; Law et al. 1999a).For example, when eddy covariance measurementswere compared to the chamber-estimated soil surfaceeff lux in a ponderosa pine forest in Oregon, the under-estimation was as large as 50% (Law EI al. 1999b). On theother hand, other field experiments did not find suchdiscrepancies (Grace et al. 1996). Uncertainty in thesecomparisons may be complicated by the storage flux(F,,), which is g iven by

t 2F,, =

002)

Greco & Baldocchi (1996) reported that F,, averages tonear zero on a dai ly basis , a l though i t may be s ignif icant

1 3 2 C . - T . LA1 etnl.

in the evenings. Previous measurements at this s i te a lsoshowed that F,, averages to zero on a daily basis but issignificant during sunrise and sunset periods (Lai et al.2000b). For this study, F,, was calculated usingmeasured mean COz concentrat ion every 30min for theselected night-time runs (from 2030 to 0430) and wasincluded for reference in the comparison between meas-ured and modelled ecosystem respirat ion.

Upon integrating equation 2 with respect to 2, weo b t a i n

h h

IaC(t.2)tdz +F(t,h) = F(f,O) +

IS(t,z)dz. (13)

0 0

in equation 13, the left-hand side represents the measuredecosystem respirat ion and the r ight-hand s ide representsthe so-called ‘biotic’ fluxes. To illustrate the seasonal vari-at ion in these components , we report the ensemble aver-ages of measured F,, + F(t,h) a n d CSO-modclledF(t, 0) + i! S (t, z) dz every 2 months for evening runsbetween 2030 and 0430 in Fig. 5. For 14. > O.l5ms-’ (athreshold used by several investigators including

Jan. & Feb.15Y

512 2 0 0 2 4 0 0 2 0 0 4 0 0

May & Jun.

5-2 2 0 0 2400 2 0 0 4 0 0

5-2 2 0 0 2 4 0 0 2 0 0 4 0 0

5-2 2 0 0 2 4 0 0 2 0 0 4 0 0

hour hour

Mar. & Apr.

2 2 0 0 2 4 0 0 2 0 0 4 0 0

1 5 ,Jul. & Aug.

I

512 2 0 0 2 4 0 0 2 0 0 4 0 0

Nov. & Dec.1 5 , 1

Fig. 5 Comparison between measured (0 with one standard de-viation) and CSO modelled (solid line) f(f,h). The measured F,,(f)(thick solid line) is also shown for reference.

Goulden et al. 1996 and Clark et al. 1999), our modelcalculation agrees closely with measured F,, + F(t,h) fort h e w i n t e r p e r i o d s . H o w e v e r , modelled F(t,O) -t-$ S( t, z)dz tends to be greater than measured F,, + F(t,h)by up to 30% in the summer. This discrepancy may be anartifact of the modelled time scale (TL), or an indication ofmissing f luxes which are not wel l captured by ei ther eddycovar iance system or the prof i l ing system used to es t i -mate the storage f lux. General ly Fst are smal l except forsummer months, when mean CO* concentrat ion near thefores t f loor (z < 10 cm) is large and dynamic. We empha-size that both measured F(t,k) and F,, suffer f rom randomand sampling errors .

Optimizedforest-floor respiration

In order to compare the CSO model results with otherstudies and chamber measurements avai lable at this s i te ,the O-optimized forest floor respiration are presentedas a funct ion of soi l temperature (e .g . Raich & Schlesinger1992; Wofsy et ai. 1993; Hollinger et al. 1994; Lloyd &Taylor 1994; Fan et nl. 1995; Lindroth et ~1. 1998; Lawet al. 1999a,b). Regressing the CSO modelled F(t,O) withsoi l temperature (TJ measured at 15cm below the groundsurface resul ted in

F(f, 0) = 7.198 exp (0.054Ts) (14)

This regression was performed with bin-averagedrespiration values for 5°C increments of T, (Fig. 6a).Figure 6(b) shows the comparison between this funct ionand functional relat ionship derived from the ACES cham-ber measurements , a long with funct ions reported in otherstudies. We note that nearly 70% of our measured Ts i sbetween 5 “C and 15 “C, where the discrepancy betweenmodelled and measured F(t,O) - T, is no greater than 7%(Fig. 6b) . Such discrepancy can be attr ibuted to a combin-ation of model underestimation and statistical uncer-tainty in aggregating chamber measurements (e.g.Lavigne ef nl. 1997).

We estimated the Qlo value of the CSO-modelledF(f,O) - T, re lat ionship in two ways. The f i rs t ut i l izes a l lthe 30-minute runs and the second is based on bin-averages of modelled respiration and soil temperatureevery 5 “C (Fig. 6a). The Qlo values derived from the CSOand the ACES chamber measurements are presented inTable 1. The agreement between the chamber-measuredand CSO-modelled Qlo is within 6%. The resul t f rom thebin-averaged approach is better behaved and is usedthroughout. Both QIo values derived from ACES chambermeasurements and the CSO are also well within the rangereported in other studies (Raich & Schlesinger 1992;Lavigne ef nl. 1997). However, these QIo estimates arelower than those calculated using data from Andrews &

icZOO2 Blackwell Science Ltd, Global Cluqy Biology, 8, 124-141

M O D E L L I N G N I G H T - T I M E E C O S Y S T E M R E S P I R A T I O N 1 3 3

Table I Estimates of Q10 and Relo from different experiments at the pine forest stand, Re ,” is the forest floor respiration at 10 “C. Andrews& Schlesinger’s (2001) QIo and ReIo are derived from SRC-1 chamber measurements (PI’ Systems) collected at three plots (FOURchambers per plot) within the forest, once a month (at noon) from 1996 to 1999. The ACES estimates of Qlo and Relo are from N-minute

forest floor flux and soil temperature (TJ measurements conducted in April-May (60days) at one plot (14 chambers per plot). The rangeof values from Andrews & Schlesinger (2001) are due to spatial variability in Qto and Relo among plots

Reference/approach QIIj/RelL) using 7’, Q3cm Qlo/Relo using T, @15cm

Andrews & Schlesinger (2001)Automated Chambers (ACES)

CSO Model

2%2.7/2..5-2.6

**I*l ***

2.3-2.9/2.5-2.6

1.8/2.1 (April-May 2000, 14 chambers)1.7/2.0 (using 5 “C bin averages)1.5/ 1.9 (using all 30 min runs)

0 5 1 0 1 5 2 0 2 5

0 5 1 0 1 5 2 0 2 5

T,(‘C)

Fig.6 (a) The 30-minute CSO modelled F(f,O) as a function ofmeasured T, (dots) at 15 cm below the soil surface. Bin-averagingof F(f,O) along T, in 5°C increments is also shown ( with onestandard deviation). The dashed and solid lines represent the

best-fit exponential functions to the raw 30-minute F(f,O) and tothe bin-averaged F(t,O), respectively. (b) Comparison behveenthe ACES measured and CSO modelled F(I,O) - T, curves (bin-averaged). The respiration functions of Law et al. (1999a,b) andLloyd 81 Taylor (1994) are also presented for reference. Forthe Lloyd & Taylor (1994) equation, the fitted regressioncoefficient (To= 209.58 K) to the bin-averaged CSO-modelledF(f,O) was used.

Schlesinger (2001) for the same stand. The data ofAndrews & Schlesinger (2001) resulted in Qlo= 2.9 inthe vicinity of the flux tower and a mean of 2.5 (whensoil temperature measurements at 15cm are used) for thestand in general (see Table 1) . These est imates, higher bymore than 30% of a l l the est imates in Fig. 6 , may ref lectbiases in the measurement system (SRC-1, PP Systems,Haverhill, MA, USA) used by Andrews & Schlesinger(2001). Such discrepancies have been observed in directf ie ld comparisons of the SRC-1, Li -Cor 6400-09 (L i -Cor ,Inc.) and ACES (J. Butnor, unpublished data).

rind plant respiration

The optimized 30-minute cx values were averaged overtwo-month period to obtain mean bi -monthly C L values forthe ent ire year . A constraint on C L could be derived fromdaytime A,,, - C, curves collected around noon for theupper fol iage (z = 12m). Upon f i t t ing these curves to theFarquhar et al . (1980) model , the maximum possible a canbe determined after Rd and V,,,, are computed. Extrapo-lating the A,,, - C, curves to determine Rd f rom a smal lmagnitude of Anet can, in itself, introduce systematicoverest imat ion in Rd because of ( i ) the l inear form of theextrapolating function and (ii) small and unavoidableleaks within gas-analysers tend to increase the value ofKd (Villar cf al. 1995; Amthor 2000). Based on the sunlitleaf- level A,,, -C, measurements and a linear extrapo-lation for Rd, we found as expected that the meana = 0.025 is larger than the CSO-optimized a(= 0.012) byabout 50%, for the same range in temperature in whichthe A,,, - C, curves were collected. We explored a quad-rat ic extrapolat ion with the fo l lowing constra ints a t theCOZ compensat ion point (I-),

and at C, = O,t$~c = 0, where V’,,,, is V,,,, computedwith al l kinet ic correct ions. The fundamental dif ferencebetween l inear and quadratic extrapolat ions is the s lopecondit ion at C, = 0, which assumes Rd independent of C,for small C; in the quadratic form. With this quadraticextrapolation, we calculated Rd that is 50% smaller thanthe linearly extrapolated Rd (Fig. 7) thereby reducinga from 0.025 to 0.0125. The latter a i s in excel lent agree-ment with the CSO-computed a, and is in accordancewith reported physiological repression of respirationby leaf carbohydrates (Azcon-Bieto 1983; Villar et al.1995). Both the quadratic interpolation for Rd and theCSO calculation produced estimates of a within therange of reported values of 0.011-0.015 (e.g. Farquharet nl. 1980; Collatz ef al. 1991).

(c‘p2W2 Blackwell Science Ltd, Clobc~l C/IQ~~P Bu~l~~~y, 8, 124-141

1 3 4 C . - T . LA1 &al

0.2

0 F- 0 . 2

7u) - 0 . 4

f - 0 . 6

: - 0 . 8E

-zj -1E3 - 1 . 2

u - 1 . 4

- 1 . 6

- 1 . 8

- 2 I

10 2 0 3 0 40 5 0 6 0 7 0 8 0

C, (p mol mod-‘)

Fig. 7 Estimation of dark respiration (R,) by extrapolating dny-time Anrl - C,. The solid line is linear extrapolation leading to (1x 0.025. The dotted line is a quadratic extrapolation leading to(x = 0.0725 that is consistent with the CSO-modelled a. Thequadratic extrapolation includes repression of respiration byc a r b o h y d r a t e s a t v e r y l o w C , .

Seasonal varintion of modelled plant and forest jloorrespiration

To summarize, we show the relative contribution ofCSO-modelled plant and forest floor respiration to thetotal ecosystem respiration in Fig. 8a-d along with time-matching primary driving variables for different times ofthe year. The modelled F(f,O) increased with mean soiltemperature (Fig. 8c), reaching a near maximum rateof 3.8 pm01 m -*s-’ in mid-summer (see Fig. 8a). Themodelled plant respiration has a similar pattern, andalso peaked in mid-summer with a maximum rate3.1 ~molm~2s~’ as a result of the high leaf area density(see Fig. 8d) and high plant tissue temperature. Figure 8bshows the ratio of modelled F(I,O)/R, in 1999 for differenttimes of the year. This ratio varied from 0.82 to 0.56 fromwinter to summer, suggesting that the contribution ofplant respiration to total ecosystem respiration is muchless in the winter when both air temperatures and the leafarea density are low. These model results suggest thatestimates of F(~,O)/RE derived from short field campaigns(even up to 2months) should not be extrapolated toannual ratios.

Implications for annual ecosystem carbon balance

Based on the GO-modelled F(t,O) - T, relationship, meanc( values and measured daytime covariance fluxes, themajor components of the annual carbon balance of thepine forest ecosystem can be quantified. To estimate day-time net COz exchange, we regressed measured CO*fluxes with photosynthetically active photon flux density

1

,w (b)

2 1 JF e b Apr Jun Au9 Ott Dee

Fig.8 Seasonal variation of (a) modelled F(r,O) and F,, and (b)moclelled ratio of F(t,O)/Kr. For reference, we also show meas-ured T, and T, in (c), and measured plant area index (PAI) in (d).For comparison, the ensemble-averaged F(t,O) from chambermeasurement is also shown in (a) with one standard deviation.

(IJPFD) measurements using a nonlinear F(t,h) - PPFDresponse curve (Landsberg 1986; Ruimy et al. 1995;Clark et nl. 1999; Law et al. 1999a), given by:

F(t. h) =cry PPFDF,,

q, PPFD -t F,, - Ro

For this simple analysis, it is assumed that forest carbonassimilation is principally driven by light only with noother limitations (temperature, vapour pressure deficit,drought stress, etc.) explicitly considered. We employthis analysis here only for the purposes of comparingnet C assimilation with other forest sites because lightinterception and radiation use are major determinants offorest productivity (‘Jarvis & Leverenz 1982; Ruimy et at.1995). The estimated mean apparent quantum yield (ap),net CO2 flux at light saturation (F,,), and the mean netCO2 flux at PPFD=O (Ro) are all close to the valuesreported by Clark ef nl. (1999) for a 24-year-old Floridaslash pine forest of a similar leaf area index and height(see Table 2). The F(t,h) - PPFD curve is shown in Fig. 9,and the regressed coefficients are compared in Table 2with the Florida slash pine stand. The F(t,h) - PPFD

02002 Blackwell Science Ltd, C/oh/ Chnge Biology, 8, 124-141

MODELLING NIGHT-TIME ECOSYSTEM RESPIRATION 135

equation was combined with continuous PPFD and othermeteorological measurements to yield a net carbon gainof 1342gCm-*year’, which is within 10% of the meanvalue reported by Clark et al. (1999).

Using equation 14 and measured soil temperature,F(t,O) was estimated to be 989 g C m-* year-‘, well withinthe range of temperate coniferous forest reported byRaich & Schlesinger (1992). DeLucia cf nl.‘s (1999) studyat this site reported a soil efflux as 1066 rt 46 and928 + 9gCm-*year’ in 1997 and 1998, respectively,consistent with the C’S0 estimates. Based on the cham-ber-measured respiration-temperature curve of Fig. 6(parameters in Table l), F(t,O) = 1063gCm-m2yearm’,only 8% higher than the CSO modelled F(f,O).

Combining modelled CL, measured plant area densityand temperature-adjusted V,,,, F, was estimated to be214gCm-‘year’, slightly greater than the combinedfoliage and woody respiration reported by Law et al.(1999b) for a stand with a lower leaf area density thanthe loblolly pine ecosystem. The annual NEE of the lob-1011~ pine forest, estimated as the difference between

35

f25

-1010 200 400 600 600 1000 1200 1400 1600

PPFD (nmol m-* s-l)IO

Fig. 9 The whole-ecosystem light response (i.e. F(t,h) - PPFDrelationship) derived from the eddy covariance measured F(t,h)at z/h = 1.1 (0 with one standard deviation) for the Pims taedaecosystem. For reference, the F(t,h) - PPFD curve for Pinusrlliotii reported in Clark et al. (1999) is also shown (dot-dashedline).

Table 2 Comparisons of study site characteristics, F(t,h) and coefficients in F(f,k) - PPFD curve between two south-east pine ecosystems.The data for the North Carolina site are for 1999 (also see DeLucia cf al. 1999 and Ellsworth 2000)

Study site North Carolina FloridaLoblolly pine forest Slash pine forest

LocationVegetation typeMean canopy height (m)Maximum leaf area indexMinimum leaf area indexSite index at 25 years oldLong-term mean air temperature (“C)WinterSummer

36L2’ N, 798 W 29’ 44’ N, 82”9’ WI’?-year-old Pinus tmda L. 24-year-old (in 1996) Pinus elliotii var. elliotii14 f 0.5 (in 1998) 19.2 -t 1.0 (in 1996)5 . 0 6 . 52 . 4 3 . 716m 15m

Long-term mean annual rainfall (mm)

%F,,, (urn01 m-* s-‘)K, (urn01 m-‘s-‘)Ecosystem light compensation point (umol rn-.‘s- ‘)Total daytime net F(t, h) exchange &Cm ‘year ‘)

7 . 62 7 . 21 1 5 40 . 0 2 93 1 . 23 . 91 5 61.342

Total plant respiration (g C m ‘year ‘) 214Total forest floor respiration (g Cm ‘year-‘) 989Total night time F(I/r) release (g C m ‘year-‘) 737

NEE (gC rn-’ year- ‘) 1.342 - 737 = 605

GPP @Cm-‘yearr’) 214 t 989 t 605= 1808

142 713320 . 0 4 42 6 . 54 . 61 2 51529 (1996)1416 (1997)******

1400 + (1995-96)789 (1996)808 (1997)740 (1996)608 (1997)> 2008

+ Estimated by Moncrieff & Fang (1999) from chamber measurements and model simulations

02002 Blackwell Science Ltd, G&r/ Clrntr~e Biobgy, 8, 124141

136 C.-T. LA1 etal.

daytime CO:, gains and night t ime CO* release, was605gCm-2year--‘, also similar to that of the Floridaslash pine forest. More importantly, this estimate(605gCm-’ year-‘) is also very close to the NEE esti-mated by the eddy covariance measurements correctedfor mean u* with no gap-filling (630 g C rn- ’ year-‘).

With these estimates of RE and NEE, the estimatedGPP = HE + NEE is 1800 g C rn--’ year-’ for 1999. For thepurpose of this study, we define GPP to be carbon assimi-lation by photosynthesis ignoring photorespiration(Schulze et al. 2000). To contrast this estimate with otherindependent GPP estimates, we consider the measurednet primary production (NPP) along with theproposed NPP/GPP of = 0.47 from Waring it a/. (1998).Based on this ratio and an NPI’ z8OOgC me2 year ’reported by DeLucia cf al. (1999) for this pine forest,GPP-1702gCm-*year--‘, within 6% of the GPPdetermined from measured NEE and CSO-modelled RE(see Table 3).

Another independent check on the forest GPP can bederived from the ratio of autotrophic respiration (R,,,) tonet photosynthesis (A, = GPP). Using isotopic carbon la-belling, Andrews ef al. (1999) estimated the rootcontribution to be 55% of F(t,O). Combined with ourestimate of F(r,O) n. 989 g C me2 year- ‘, this yields a con-tribution by root respiration (RR) of 544gCm-‘year-‘.When combined with the above-ground respiration(=F,=214gCm-2year-‘), RA -F,+ RK=758gCme2year-‘. Based on our estimate of GPP, RA/GPP=0.42,which is well within the range of ratios reported byRyan et al. (1994) for pine forests (0.33-0.63, with a mean

= 0.49; see Table 3). Additionally, we consider the hetero-trophic respiration RH estimated from 45% of F(t,O) as inAndrews et al. (1999) and the independently measuredroot turnover (TOK) and litter turnover (TOL) reported byDeLucia et al. (1999). Given the measurement uncertainty

in these terms, the agreement between estimatedRt, (- 445 g C m--* year- ‘) and measured TOR + TOL(-- 400 g C rn--* year--‘) is remarkably good ( < 10%) asshown by the summary results in Table 3.

As a final test, the net photosynthesis A, can be esti-mated from a simple Fick’s law formulation

A,, = gcC, 1 - ;iL Ia

where, gc is the bulk canopy conductance, directly esti-mated from sapflux measurements as described in Ewerset nl. (1999) and Oren et nl. (1998, 1999), C, and C, are theinternal and atmospheric COZ concentrations, respect-ively. Using the approach of Lai rt al. (2000a), the verti-cally averaged Ci/C, equals 0.70 for the entire stand. Thelatter estimate is well within the range of the isotopiccarbon analysis reported by Ellsworth (2000) and Katulet al. (2000b) for which C,/C, = 0.66 for sunlit and 0.76 forshaded foliage, respectively. The mean annual sapfluxestimated gc of 70mmol/m* 5-l and C, = 370pmolmol ’ , leading to an estimate of A, (= GPP, as per Schulzeef al. 2000) of 1825gCm.‘year--‘for 1999, which is inexcellent agreement with the CSO model calculations.

Having demonstrated the consistency between ourNEE measurements and modelled F(f,O) with a varietyof experiments and literature data, we note that our esti-mated GPJ’ (c. 1800 g C m -* year ‘) is much larger (c. 25%)than the modelled GPP (c. 1200-1300gCm-*year -‘)reported in Luo at al. (2001) for this pine ecosystem. InLuo et a/. (2001), a multilevel photosynthesis model(MAESTRA) with an empirical parameterization of sto-matal resistance, calibrated with porometry measure-ments collected at 12m height, was used to estimateGPP. According to Luo ef al. (2001), the MAESTRAmodel calculations reproduced measured NEE bythe covariance system. Given that the MAESTRA model

Table3 Comparison between ecosystem respiration components as modelled by CSO and estimated from published experiments. Theunits for respiration and GPP are in gCm-‘year-’

Ecosystem Component CSO Model Literature Estimates

GPP 1 8 0 0

Forest Floor Respiration 989Total Root Respiration (RR) 5 4 4Autotrophic Respiration (RJ 7 5 8R,IGPP 0 . 4 2

Heterotrophic Respiration (RI+) 44.5

1700 derived from measured NI’P = 800 by DeLucia rt nl. (1999)and estimated NPP/GI’P = 0.47 by Waring ef al. (1998).928 from l&Lucia ef 01. (1999)= 0.55 x 989, the 55% is from Andrews cl al. (1999)- 544 + 214; the 214 is from GO modelled plant respirationR,IGPP = 0.33-0.63 reported by Ryan ef al. (1994) for pineforests (mean = 0.49)= 0.45 x 989; the 45% is from Andrews et nl. (1999)Measured litter turnover = XXI (&Lucia ef al. 1999)Measured rout turnover 7 100 @Lucia et al. 1999)Hence, estimated RI, = 400 (for 1998 measurements)

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M O D E L L I N G N I G H T - T I M E E C O S Y S T E M R E S P I R A T I O N 1 3 7

reproduced measured NEE (c. 630 g C me2 year-‘), themodel calculations must have underestimated RE. Forinstance, combining the measured NEE with measuredforest floor respiration from DeLucia et al. (1999)(c. 928gCm-*year-~’m 1998) results in a GPP of at least1558gCm-*year-’ without accounting for plant respir-at ion (c. 200 g C me2 year- ’ based on the CSO modelcalculat ions) . Furthermore, a GI’P of 1200 g C rn-’ year- ’and a measured NPI’ of 800 g C me 2 year-’ (DeLucia et al.1999) produce a ratio of NPP/GPP =0.66, 40% higherthan the rat io reported by Waring el a l . (1998), in contras tto good agreement with the results based on the CSOmodel. Thus the CSO model combined with simplephotosynthesis formulat ions as wel l as the mass-balanceof this forest suggest GPI’ values between 1800 and2000gCm--2year-‘.

Conclusions

This study proposed a method to estimate components of

ecosystem respirat ion f rom readi ly avai lable COz concen-tration profile measurements. Applying this method to apine forest in North Carolina, we demonstrated the

fo l lowing:

For nocturnal condit ions and close to the canopy-atmosphere interface, 9 was < 0.3 and sensitive tovariations in atmospheric stability h/L. However, y

did not vary appreciably within the canopy ( < 200/o), atleast when assuming TL N ‘F,.Unlike v, qo/u. remained nearly a constant (= 1.1)for a wide range of h/L evaluated at the canopy top.This constant ratio of o,/u. is consistent with a recent

study by Leuning (2000) and perhaps suggests thatmodel l ing o,/u. for nocturnal condit ions may be s i m -pler than unstable condit ions.The second-order closure model of Wilson & Shaw(1977) successfully reproduced the measured verticalvariation of o,,/u* for a wide range of h/L conditions.

The combination of LNF and the proposed optimiza-t ion scheme, termed CSO, reproduced well ecosystemrespiration measured with the covariance systemunder conditions of large IIS. The modelled forest-floor respiration F(f,O) by the CSO approach was inclose agreement with the chamber measurementswhen the night-time CO:! fluxes are described as afunction of soil temperature.Using ecosystem respiration modelled based on theCSO and daytime net CO2 exchange measured witheddy covariance, we estimated GPP = 1800 g C rn- *year- ’ and NEE =605 g C mm2 year-’ for this temper-ate loblol ly pine forest . The rat io of measured NPP tomodelled GPP (= 0.44) is close to the general ratio(= 0.47) reported by Waring et a l . (1998). Furthermore,

the modtlled plant and forest floor respiration areconsistent with measured litter and root turnoverrates reported by DeLucia ef al. (1999), and with iso-topic analysis of root : microbial respiration reported inAndrews et al. (1999).

The broader implicat ions of this s tudy, when combinedwith the recent NEE measurements reported in Clark et al.(1999) from a Florida s lash pine forest ecosystem, is thatyoung (15- to 25-year-old) south-eastern pine forestsappear to be among the largest atmospheric terrestr ialcarbon sinks when compared to other flux sites withpublished NEE data in Europe and North America (e.g.Wofsy et a l . 1993; Holl inger ef a l . 1994; Greco & Baldocchi1996; Valentini et al. 2000). These two pine forestsalong with the Picca s i f c h e n s i s conifer plantat ion in Valen-tini et al . (2000) exhibi t GPP values from 1800 to2000gCm- 2year-‘. Warm temperate conifers at an ageclose to crown c losure are l ike ly to be among the mostproductive forest ecosystems because their leaf areaindex is close to maximum and the growing season isvery long (El l sworth 2000), assuring an ef f ic ient absorp-t ion of photosynthet ical ly act ive radiat ion. In addit ion,

according to Waring & Schles inger (1985), the amount ofnon-photosynthet ic b iomass is not very large at this s tageof stand developments, assuring l imited carbon con-sumption in respirat ion.

Acknowledgements

The authors thank Yavor Parashkevov and Andrew Palmiotti fortheir help during the experiment, the Duke Forest staff for main-taining facilities, and Keith Lewin and John Nagy for their assist-ance in the COz/H20 multiport design and setup. This projectwas funded, in part, by the National Science Foundation (NSF-BIR 9512333 and EAR-Y805395), and the US Department ofEnergy (DOE) through the FACE-FACTS project under contractDE-FG05-95ER62083, and through the National Institute forGlobal Environmental Change, South-east Regional Center atthe University of Alabama, Tuscaloosa (DOE cooperative agree-ment DE-FC03Q-90ER61010).

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M O D E L L I N G N I G H T - T I M E E C O S Y S T E M R E S P I R A T I O N 1 4 1

Appendix 1: Second Order Closure Model of Wilson& Shaw (1977)

The following is summarized from Katul & Albertson (1998,1999) and Katul et al. (2000a); for completeness, the final meanmomentum and Reynolds stress equations are repeated. In orderto model the vertical variation in CT,, the second order closuremodel of Wilson & Shaw (1977) is used and is briefly describednext. Upon time and horizontally averaging the mean momen-tum and Reynolds stresses equations, and after performing thesimplifications of (i) steady-state adiabatic flow, (ii) assumingthat the form-drag by the canopy can be modelled as a dragforce, (iii) neglecting the viscous drag relative to the formdrag, (iv) closing all the triple-velocity products by agradientdiffusion approximation (Donaldson & Du 1973; Mel-lor 1973; Mellor & Yamada 1974; Shaw 1977; Wilson & Shaw1977; Wilson 1988; Wilson 1989; Andren 1990; Canuto et nl.1994; Abdella & McFarlane 1997), (v) modelling the pressure-velocity gradients based on return-to-isotropy principles, (vi)assuming the viscous dissipation is isotropic and dependent onthe local turbulence intensity (Mellor 1973), and (vii) assuminghorizontal homogeneity, the second-order closure model ofWilson & Shaw (1977) reduces to:

where L(, (u, = u, uz = v , us = w) are the instantaneous velocitycomponents along x,, Y, (x1 = Y, x2 =y, x3 = z) are the longitudinal,lateral, and vertical directions, respectively, (T) denotes both timeand horizontal averaging (Raupach & Shaw 1982; Raupach et al.1991), and primes denote departures from the temporal aver-aging operator, q= fi is a characteristic turbulent velocity,I,, hZ and 1s are characteristic length scales for the triple-velocitycorrelation, the pressure-velocity gradient correlation, and vis-cous dissipation, respectively (Katul & Chang 1999), K (- 0.4) isVon Karman’s constant, C,, is the foliage drag coefficient, y is an

Table4 The closure constants cr. c2, cs, C, and y used in theWS77. Their estimation is discussed in Katul & Albertson (1998)and Katul & Chang (1999)

Closure constant R e m a r k s

cl = 0.302

c2 = 2 .313c3 = 24.296c,, = 0 .099y = 0 .07Cd T 0.25

Estimated by matching the WS77 equations,in the absence of flux divergences,to established similarity relations, namely:Q = 2.4$1.9z” = 1.25

and that the mixing length is K(Z d), whereK = 0.4 and d is the height of zero-planedisplacement

empirical constant, and cr, c2, cs, and C, are closure constants thatcan be determined such that the flow conditions well above thecanopy reproduce established atmospheric surface layer similar-ity relations. With estimates of these five constants (cr. cz, ca, C,a n d y), t h e f i v e o r d i n a r y d i f f e r e n t i a l e q u a t i o n s l i s t e d a b o v e c a n b e- -solved for the five flow variables ti, u’ur’. F. I@. UP if appropriateboundary conditions are specified. The flow boundary condi-tions are assumed to approach the theoretical values of neutralatmospheric surface layer similarity (Panofsky & Dutton 1984)well above the canopy (z/h > 2), and zero gradients for allsecond moments, as well as zero mean velocity at the forestfloor. Table 4 summarizes the closure constants used in WS77.

Appendix 2: Sensitivity Analysis of TL profile

T h e r e s u l t s o f CS4I i n F i g . 5 w e r e d e r i v e d b y a s s u m i n g a v e r t i c a l l yconstant Tr profile inside the canopy with a correction for ahnos-pheric stability. We repeated the optimization using the threeplausible Tt- schemes described in the section ‘Velocity statisticsof nocturnal conditions’ to assess how sensitive modelled F(f,h)a n d F(t, 0) a r e t o s u c h a n a s s u m p t i o n . A s s h o w n i n T a b l e 5 , b a s e don r+ = 0.3, the model over-predicted F(t,h) and f(f,O) b y afactor of 5 and 3, respectively. It clearly shows that such Tr.profile is not reasonable for nocturnal conditions. Our calculationimproved significantly after T, was corrected for stability, withcase 2 and 3 providing comparable results.

Table5 Comparisons between modelled to measured ratios of F(t,h) and F(t,O) for the 3 different 7’tprofiles on annual time scales

Case

12

3

q!L F(t,h) FV,O)

0 . 3 5 . 0 3 . 0f*; wheref, = 0, [8] L exp(--0.0695x2 0.64541 - 3.8516), 1 . 2 0 . 9 2x=ln$]f0 --0.155(2, - 1); where{% BG 1.37 0 . 9 6

82002 Blackwell Science Ltd, Cl&r,rrl Cltllttxc Biology, 8, 124741