Modelling the soil-plant-atmosphere continuum in a Quercus-Acer stand at Harvard Forest: the regulation of stomatal conductance by light, nitrogen and soil/plant hydraulic properties

Our objective is to describe a multi-layer model of C 3 -canopy processes that effectively simulates hourly CO 2 and latent energy (LE) fluxes in a mixed deciduous Quercus-Acer (oak-maple) stand in Massachusetts, USA. The key hypothesis governing the biological component of the model is that stomatal conductance (g(s)) is varied so that daily carbon uptake per unit of foliar nitrogen is maximized within the limitations of canopy water availability. The hydraulic system is modelled as an analogue to simple electrical circuits in parallel, including a separate soil hydraulic resistance, plant resistance and plant capacitance for each canopy layer. Stomatal opening is initially controlled to conserve plant water stores and delay the onset of water stress. Stomatal closure at a threshold minimum leaf water potential prevents xylem cavitation and controls the maximum rate of water flux through the hydraulic system. We show a strong correlation between predicted hourly CO 2 exchange rate (r 2 = 0.86) and LE (r 2 = 0.87) with independent whole-forest measurements made by the eddy correlation method during the summer of 1992. Our theoretical derivation shows that observed relationships between CO 2 assimilation and LE flux can be explained on the basis of stomatal behaviour optimizing carbon gain, and provides an explicit link between canopy structure, soil properties, atmospheric conditions and stomatal conductance. ABSTRACT Our ohjective is to descrihe a multi-layer model of C.r canopy processes that effectively simulates houri)' C0 2 :uul latent energy (U~) lluxcs in a mixed deciduous Quercus-Acer (oak- maple) st'.111d in c~ntral l\l~1ssac~1u­ selts, US/\. The key hypothesis J!OVernmg the b1oloA1cal component of the model is Urnt stomata! conductance (g,.) is varied so that daily carbon uptake per unit of foliar nit roj:!en is maximized within the limitations of ca1101>Y water avr1ilability. The hydraulic system is modelled as :m analo~ue to simple electrical circuits in parallel. includinJ! a separate soil hydraulic resistance. plant resistance and plant capacitance for each c:m opy layer. Stomata! openin(! is initially controlled to conserve plant water stores and delay the onset or water stress. Stomata! closure at :i threshold minimum l~1f water potential prevents xylem cavitation and controls the maximum r:itc of water llux through the hydraulic system. We show a strong correla tion between predicted hourly C0 2 exchange rate (r2 = 0·86) and LE (r 2 = 0·87) with independent whole-for est measurements made by the eddy correlation method during the summer of 1992. Our theoretical derivation shows that observed relationships between C0 2 assimila tion and LE nux can he explained on the basis of stomata! behaviour 01>timizing c:irhon gain, and provides mt exi>licit link hetwecn canopy structure, soil pro1>erties. atmospheric conditions and stomatal conductance. is resistant to drought. Epron & Dreyer 1993) have shown thal, in lhe leaves of young oak saplings (Q11errns petraea) subjected to water slress, there was only a limilcd decline in maximum photosynthetic rates, and the photochemistry of pholosystcrn II and the yield or ligl11-drivcn electron transport remained stable. We therefore water s1ress affects only gs. and 1101 1hc photosynthe1ic mechanism.

Quercus-Acer (oak-maple) st '.111d in c~ntral l\ l~1ssac~1u selts, US/\. The key hy pothesis J!OVe rnmg the b1oloA1cal component of the model is Urnt stomata! conductance (g,.) is var ied s o that d ail y carbon uptake per unit of foliar nit r oj:!en is maximized wit hin the limitations of ca1101>Y water avr1ilability. T he h ydraulic system is modelled as :m a nalo~ue to simple electr ical circuits in parallel. includinJ! a separate soil hydraulic resistance. plant resistance and plant capacitance for each c:m op y layer. Stomata! openin(! is initially controlled to conserve plant water stores and delay the o nset or water stress. Stomata! clos ure at :i threshold minimum l~1f water potential prevents xyle m cavitation and contr ols the maximum r:itc of wate r llux through the h ydraulic system. We show a strong correlat ion between predicted hourly C0 2 exchange rate (r2 = 0·86) and LE (r 2 = 0·87) with independent whole-forest measurements made by the eddy correlation method during the s ummer of 1992. Our theoretical derivation s hows that observed relationships between C0 2 assimilation a nd LE nux can he explained on the basis of s tomata! behaviour 01>timizing c:irhon gain, and provides mt exi>licit link hetwecn canopy structure, soil pro1>erties. atmos pheric conditions and stomatal conductance.

INTRODUCTION
Eco-physiological processe:-. such as photosynthesis and lc;if e nergy balance. arc now relatively well understood Ctll'/'l'SflOlldi!llCl '.' M(lf/Jew Williw11.... 711e Ecm..~1·sre111.1· renlt'I', Marine /Jiological La/111ra111ry. Wood ... llolc. MA 02543, USA. <D 1996 Blackwell Science Ltd (Mt.:Murtric 1993). Whal n:mains elusive is a sound understanding or how these processes integrate over space and time. and interact within a community of plams . lmcre:-i in scaling. canopy processes derives in pan from question~ raised about the global carbon (C) cycle. and the nature ol the missing. terrestrial C si nk (Schimel 1995). One approach to this problem uses models that allow scaling of processes at the leaf level to whole canopies (Jarvis C't al. 1985: Running & Coughlan 1988: McMurtrie 1993. Such models closely predict hourly co~ llm, measurements in temperate grasslands (Norman & Policy 1989). a soybean crop (Baldocchi 1992). and 1cmpcratc forest (Amthor \ 994). although the latter model 1endcd to ov1.:restimate CO~ uptake in the afternoon (Amthor et al. 1994). Our goal in this paper is to describe <t process-based model that accurately predicts whole-forest carbon and water exchange, and explains these 11uxes in terms of optimal water and nitrogen (N) use. Such a model both improvt.:~ o ur understanding or key factors in forest growth and ecosystem function, and provides a synthetic tool with which to investigate the behaviour of canopies al different sites.
Both aggregated (e.g. 'big-leaf) and distributed (e.g. multi-layer) approaches arc commonly applied in modelling canopy proce!'>scs (Raupach & Finnigan 1988). There arc costs and benefit~ to both (0' eill & Ru~t 1979: Rastetter et al. 1992). Dbtrihuted simula1ions require a~sumptions about the uistribution of key parameters in space. but allow model parametriLation using fine-scale (e.g. leaf-level) data. Aggregation avoids the need for ~pa tlal deiai ls by bui ld ing the dTcc1s of non-linearities into the model parameters: however. line-scale data arc not dircc1ly applicahlc to cstima1io11 of these coarse-scale parameters. These parameters must therefore be estimatcu directl) from coarse-scale data (e.g. canopy rather than leaf-level data).
Big-leaf mode Iii ng is an aggregated approach commonly applied in simulations of canopy processes (Sinclair er al. 1976): photosymhetic propcnie. or individual lc;ives an: assumed 10 be scaled with depth in Lhe canopy in rela-Lion to pholosynthetic photon nux density (PPFD) pro files (Farquh ar 1989;Field 1991 ). If this is so, then details o f the canopy profile can be ignored in many cases, and the modelling approach can be simplified to treat on ly a single layer. However, if the interaction between microcl imate and physiology is or interest, then it is important LO resol ve detail within Lhe canopy using a distributed approach (Raupach & Finn igan 1988). The model we present is based in part on a hypothesized spatial independence o f stomata! control, and therefore precludes an aggregated approach. Atmospheri c saturation defi cit. net radiati on and leaf boundary layer conductance al l vary with clcplh in the canopy; also. the rate or water supply may depend on the height of the leaves above the ground. This means we expect vertical variation in patterns of water stress, and thus the degree or stomata l limitation may vary wi th height in the canopy. To investigate and account for this phenomenon, we employ a I 0-layer canopy model.
Our model is a new synthesis, combining simple models of plant and soil hydraul ics, carbon assimilation. gas diffusion and vegetation/environment interactions to produce a robust model of the soil-plant-atmosphere continuum. The model is unique in that~. for each layer is calculated to maximize daily C gain per unit leaf N, withi n the limitations of canopy wa ter storage and soil-to-canopy water transport. Transpiration is ultimately limited by the rat e of water supply imposed by plant hydraulics (Tyree 1988) and soil water avai labil ity (Golian et al. 1985). Cowan ( 1977) has proposed a mechanism or optimal stomata! variation that regulates the relationship bet ween water loss and carbon gain. We employ a similar mechanism that operates to ensure the efficient use of canopy stored water so it can be more optimally employed ameliorating afternoon water stress. Once stored water is ex hausted, leaves must be irrigated by wuter transported from the soil (M einzer & Grantz 1990): g, adjusts so that tran spiration equals the rate of water supply (Aston & Lawlor I 979). The maximum rate of water supply is determined by the minimum sustainable lea f water potemial. canopy capaci tance. root water uptake, soil wa ter avai lability, and stem hydraul ic conductance (M einzer & Grantz 199 I ). Stomata! closure at a threshold mini rnum leaf water potential prevents xylem ca vi Lat ion and controls the maximum ra1e or water l"lux through the hydraulic system (Jones I 992) . We parametrize and drive the model wilh meteorologica l data and measurements of vegeta1ion structure collected at Harvard Forest, Petersham, M A (42 ' 54°N. 72 ' I 8°W , eleva1ion. 340 111) du ring the summer of J 992. The model then predicts the C0 2 exchange rate and transpiration rate o f each canopy layer; from measurements or other lluxes within the system (e.g. soil respiration and evapora1ion), we can predict the diurnal course of wholefores t lluxes. The eddy correl ation method (Baldocchi e t al. 1988) has provided independenl measurements of the hourly !luxes of carbon and latent energy from the forest canopy for entire growing seasons at Harvard Forest ( Wofsy et al. 1993). We compare the simulated and rnea-sured diurnal nuxes o f C0 2 and latent energy (LE). and discuss the influence of' plant hydraulics on llows. W e use sensiti vity analysis to determine the most influential sci or parameters, and discuss future directions for model dcvelopmclll and application.

MODEL STRUCTURE
The model (Fig. I ) consists or various sub-models, which can be roughly divided into physical and biological components. The physical components specify the structure of the canopy, dclcrmi ne the absorption or bol h photosynthetically active radiation (PAR) and other wavelength s in each canopy layer, calculate leaf boundary layer conductance, and determine soil water avai lability. The biological components determine how leaf' water potential vari es w ith transpiration, the variation of lear biochem ical parameters with foliar N contcnl , irradiance and leaf temperature. and the diurnal course of gs in each layer. which controls C uptake and water loss.

Physical sub-models
The physicul sub-models arc calculated only once per time step (30 min). Hourly meteorologica l data collected al Harvard Forest were linearly interpolated Lo estimate conditions on the half-hour. In the physica l components we h::ive four sub-models as follows.

(A) Canopy structure
The canopy is divided into IO layers. with equal leaf area per layer, spaced equally belwecn the top (24 m) and bottom ( I 0·5 m) of the canopy. El ls worth & Reich ( 1993) and Aber ( 1979) have shown that such a leaf area distribution is a reasonable assumption in closed deciduous forests. We analysed data from Ellsworth & Reich ( I 993) showing the variation in N concentration (g m-2 l el!/'area) w ith height in a deciduous forest. and fitt ed an exponential decay !"unction that effectively described this relationship (see Eqn A I ). We used this fun ction to alloca te the total canopy N measured at the site among Lhe I 0 canopy layers.
reflecrance and absorptance of NIR, PAR and longwave radiati on. Reflectivity and trunsmissivity of leaves and soils were esrimated from data provided by Baldocchi et al. ( 1985). We assumed a spheri cal leaf angle distribution (Russell et al. 1989 • On this evidence, we w ill <1ssumc that conductan ce across the canopy boundary layer is high enough to be ignored.

(C) Soil 111a1er f'lwracreri.wics
Soil water potential ( lfJJ and soil hydraulic conductivi ty (/~0;1) were not measured directly. bul can be estimated from soil sand. clay and water content using empirical relationships (Saxton e1 al. 1986). Evaporation or water from the soi l surface is determined from soil rndiation balance (calcul< 1ted in the radiation regime) and soil wt\ler content (Amthor et al. 1994 ). Soi I moisture levels arc high around the study site at Harvard Forest (sec below). so we expect soil water to be freely available throughout the growing season in this case.

Biological sub-models
The key hypothesis governing the biological components of the model is that J:, is controlled 10 maximize c~1 rbon gain per unit N within the limit:-; set by the rate of water uptake and canopy water storage. Studies on Querc:u. 1· rnbro (Ren & Sucoff 1995) and other species ( Kuppcrs 1984: Mein:r.cr & Grantz 1990) have shown a coordinati on of vapour-phase and liquid-phase conductances. M einzer & Grantz ( 1991) hypothesize that J:, will ideally remain in balance with the hydraulic capaci ty of the soil and roms to supply th e leaves with water. avoiding leaf desiccation al one extreme and the unnecessary restriction of' C0 2 uptake al the oth er. W e model this explicitly. and also include the impacts of water stored by plants.
Component plants are assumed w open their stomata until either ( I ) further opening docs not constitute an effective use of stored water in terms of carbon gain per unit water loss, or (2) runher opening causes a drop in leaf water potential below th e limit that c.iuses xylem cavi tation. Plant water rel ations arc mocklled as an analog ue to a simple electrical circuit (Cowan 1965: Passioura 1982 Whitehead & Hinckley 199 1 ). Each canopy layer is assumed to have an independent connection to soil water. Therefore, each layer is modelled separately.

Soil resistance
We use a single soil layer steady-state model (Newman 1969: Federer 1979 10 estimate th e hydraulic resistance of the soil around the roots that supply each canopy layer (R, 11 : MPa s 111 2 mmol-1 ). The model i s dependent on root dimensions and soil hydrau lic conductivity (sec A ppendi x). W e assume that each canopy layer is supplii:d by an equal proportion or the total root length, and so R, 11 is invari ant among layers. The single soil layer is an appropriate ap[>roximation for Harvard Forest because of high moisture levels (see below). but a more detailed soil prolile might be needed in dry soi ls.

Plant hydra11lics
The highes t layers in Lhe canopy arc subject to lhe greatest resistance 10 xylem water supply ( Hellkvist el al. 1974}. Thus. xylem hydraulic resistance per unit leaf area for layer n in the canopy (Rr 11 ; MPa s m 2 mmol 1 ) i ncreases with the h1yer height (11). W e make various simplifying assumptions in our representation of plant hydraulics.
Analogous w ith a pipe model (Shino7.aki el al. 1964). each l ayer is ser ved by an independent water supply system. W e employ an unbranched model , rather than a branched catcna (Tyree 1988). because of its greater simplici ty. and because wc arc representing a canopy of many indi viduals. rather th:m modelling a single tree. The whole canopy can be visualized as a set of I 0 parallel circuits (only one of which is shown in Fig. I ). /\ separate branch hydraulic resistance is not specified, but is assumed 10 be included with the value or /?pn· The water in the xylem can rupture under the extreme tensions th at occur naturnlly -there is often a threshold water potenti<il for such cavitation (Jones 1992).

Dy11amicjlow
The rel ationship between the nux of water through the plant and the water potential drop is not unique; ini1ially water is drawn from stores within plant I issues. so thai liquid fl ow lags the transpirativc demand (Landsberg el al. 1976: Schul.~e el al. 1985 ). This hysteresis can be modelled by incorporating capaci tors into the circuit analogue to represent canopy water storage capacity (Jones 1978). Assuming constant capacitance (C 11 ). the change in leaf water potential or canopy layer 11 over a time step Ll1 can he described by where Pw is the density of liquid water (kg m-3 ). g is gravitational acceleration (9·8 m s-2 ) and h is the height (m) of the canopy layer 11 (see Appendix for derivation). The response times or both crop plants (Jones 1978) and 1rees (Schulze e1 nl. 1985) indicate thal a time step or 30 min is adequate to resolve the dynamic behaviour using this equation.
Jones ( 1978) used a similar lumped-parameter model 10 simulate diurnal trends of '1' 1 in transpiri ng wheat. and round 1ha1 it could account for more 1han 90% or the variation in hourly means of 'l'r· However, we do nol believe th<ll this approach has been used 10 predict g,. and thus determine the hypo1he1ical water supply limitations to productivity.
Tyree & Sperry ( 1988) undcnook hydraulic measurements for Acer .wcclwrum in Vermont and estimated the hydraulic conductivity (Gr) to be 4·0 mmol s-1 m 1 MPa 1 (RP"= h/Gp: sec l\ppendix). The conducti vity of Q11erc11.1· ni/Jra is of similar magnitude (Cochnrd & Tyree I 990). We assume that ring-porous Q11errn.1 · will have a slightly higher conducti vity than Acer. and so we use an es1im<11e of 4.5 for model testing. This figure gives /? 1 ,,. values close 10 those measured for larger Q. mlmt seedlings (Ren & Sucoff 1995). Schulze el ul. ( 1985) have estimated total Lrce stored water usage f'or adu lt Picea nbies. An individual P. nhies used 16·2 kg of stored water in a day: needle biomass was 13· I kg. Using leaf mass per unit area relationships for I '. abies (Oren el al. 1986). we estimate the amou111 or stored water per unit leaf area as 8·8 mol m 2 • The drop in leaf water potential during stored water usage was I · I MPa. so we estima1e capacitance (C 11 ) at 8·0 mol MPa 1 m 2 . A lthough C 11 is expressed on a leaf' area basis. the stored water is distributed in both foliage and the woody 1issuc of the crown. Landsberg el al. ( 1976) estimated the capacitance of polled apple trees 10 be si milar. around 5·0 mot MPa 1 m 2 • The value of Schulze er al . ( 1985) is probably more applicable to this model because i1 was measured for full -sized canopy trees in the licld. However. because of the uncertainty associated with this value. a sensitivity analysis has been performed on ell (see below).

Leaf /Jioclie111ical 1u11·t1111e1ers
The model used 10 delennine photosynthesis is described elsewhere (Farquhar & Von Cacmmercr 1982). but the calculation or lhc parameters required is detailed below. Pho1osyn1hesis is limited by the minimum of the rihul ose bisphosphate carboxylation rate and the rate of ribulosc bisphosphate (Ru BP) regeneration. The maximum rates of these two processes and their temperature and N dependences must be calculated.

l111pac1.1· of waler s/a/us
Following Cornie e1 al. ( 1989), we assume 1ha1 1he pholosynthelic apparatus is resistant to drought. Epron & Dreyer ( 1993) have shown thal, in lhe leaves of young oak saplings (Q11errns petraea) subjected to water slress, th ere was on ly a limilcd decline in maximum photosynthetic rates, and th e photochemistry of pholosystcrn II and the quan1um yield or ligl11-drivcn electron transport remained stable. We therefore assume that water s1ress affects only gs. and 1101 1hc photosynthe1ic mechanism.

Leqf /elle/ proce.ues
For each canopy layer. once every 30 min nn iterative procedure is used to determine the maxi 111um stomata I conductance in this layer (g, 11 ) and the assimi lation rate associated with this conductance (see Fig. I ).
The iterative procedure is as follows, starting from a very low g,. (2) Determine lea f temperature (T 1 , °C) resulting from th e leaf energy balance al this x"' using a steady-state approximation (Jones 1992). (4) Determine lhe equi librium rncsophyll C0 2 concentra-1ion <Cc) lhat satisfies both diffusion from 1he atmosphere 10 1hc mcsophyll (sec Appendix) and metabolic uptake. as described by Farquhar & Von Caemmerer ( 1982).  -fJ, 11 ) afler one time step (Lll. 1800 s) or transpiration at 1he specified g , 11 , using Eqn I . (7) Return to step I (for a funher increment o f g,n), unless either: (a) previous Rsn increment foiled to raise assimi lation appreci ably (sec below). or (/3) l/~1 1 has reached i1s specified cavitaiion limil ( IP 1111 ; 11 ) . The water supply system is now operating al its maximum rate: any furth er increase in gsn would take the xy lem beyond its threshold !'or cavitation , and result in a ca tastrophic failure in water supply.
II is 1his i1 erati vc procedu re of sell ing x,, especially as relates 10 step (7), 1hat sets our canopy model apart from sim ilar models. Embedded in 1his procedure is our underlying hypothesis tha1 stomata} variation operates 10 minimize waler s1ress, by effectively using stored water to maximize C gained per unit water loss over lhe course of a day, and by preventing xylem cavi1 a1ion. Figure 2 shows 1hc response of ne1 lea f layer C0 2 assimi lation rate (/\) and lranspiration 10 g,. in the topmos1 canopy layer at noon on a reprcscn1a1ivc day (sec Fig. 5. day 2 15, for prevailing environmcnlal condilions -1hese are held constant through lhc i teration). After an initially rapid increase, 1he response or/\ become:-; asy111p101ic, and the carbon gain per uni I water loss declirn.:s. We argue 1hu1 plan1s use their water s1ore conservati vely: it is more efficient to limi1 Csn when almosphcric saiuration deficits arc low (morning), so that stored water can be uti l ized later to   19. 9 t l-IJ27 buffer the impac ts of hig h a f"l c rnoon almosphe ric saturaiion deficits. For lhis reason. optimal g· "' is fix ed when an im:re111c nl in g"' (

Site description
The mode l results were compared with hourly measureme nts of whole-canopy exchange made al Harvard Forest d uring the 1992 g rowing season (Wol'sy el al. 1993al. : GoulJen et 111. 1996. The experimcnlal mc thous used al I larvard Forest. and the accuracy of the mcasurc me111s. are described by Goulden e l 111. ( 1996). Individual hourly tlux measureme nts a rc s ubject 10 random variability or or<ler ± 20% because o f the finit e s ampling period used ( Baldocchi et al. 1988). T his c reates scatter in 1he compariso n between predic ted and measured fluxes that over time ave rage to 1.ero. Systematic errors during Lhe day. which re!lcct a consiste nt discrepancy be tween Lhc true flux and the meas ured !lux (e.g. a c alibration error). arc no g reater than l 0-20% (Gou Iden et al. 1996 ).
Me as ure me nts s howe<l that te mperature (°C) and atmosphe ric saturation defic it (kl'a) varied s lig htl y between the 1op and bo 1tom of the c:rn opy: val ues for the midd le layers were de rive d by ime rpolation . Inc ident PPFD (J-1 mo l m ~ s 1 ) was measure<l at :w m and use d to c alc u- Modelling the soil-plant-atmosphere continuum 917 (Rich Boerne. Harvard Forest. personal communic ation). This secti o n of rorest seems to be we ll s upplied with water throughout the growing season. so we assume that soils are at !ic l<l capacity in mo de l runs. Therefore. water limitati ons of canopy processes in these simulations arc the resu lt of restricted conductance thro ug h the soil-root-stem syste m. not the result of low soi l moisture. Soil maps at Harvard Forest indicate that sandy loams lie south-west of the wwcr. with .::60% s and conte nt and I Oo/ r c lay content.

RESULTS AND DISCUSSION
The model predicts d iurnal vari a ti on in o ne parameter (gJ in e ach canopy laye r. In combi nation with environme ntal conditions. g, determines the magnitude of canopy water and carbon fluxes . Modelled rates of soil evapora1ion arc a<ldcd to the transpira ti o n rates of the canopy layers to give whole-forest LE. The net or individual layer CO~ exchan!!e rates ;md soil and stem respira1ion rates prnvid~s our cs~i matc or NEE. The model was tested against hourly llux measurements from 25 d wi th complete <lata sets and varying weather conditio ns l'rnm the summer o f 1992 (Fi!!. 3). From re!!rcss io n analysis or 111casure<l versus prcdi~ted lluxcs d~ring daylight hours (11 = 3 17). the r 1 values were O·l:\3 for LE (slo pe 0·85 ± 0·02) and 0·82 for NEE (slope I ·O:'i ± 0·02).
The model tended to underpredicl LE in :;ome instances.
T he wino quadrnnL for each llux reading is indicated by the symbols in Fig. 3. Beeau:;c the model was parametrized w ith data l'rolll the canopy !'OU th-west of the tower. WC reanalyscd the data for periods in which winds were solely fro m this direction (11 = l :-19): the r 2 values were 0·87 l'or LE (slo pe I ·O I ±().()2) a nd 0·86 fo r NEE (slope I ·03±().()2 ).
Thus. whe n winds arc l'rom the south-west the model makes more accurate predictions. and the s lopes or the regression lines do no! differ significantl y from l ·O. The mo del unde restimates LE when wi nds arc from the nonhwesl. an area with swampy conditions. and where key parameters like LAI may <lirfcr from those used in the model. Prediction:; for four day:; between the e nd of Jul y an<l early Sep1e mbc r. with winds consis1emly from the southwest. arc examined in detail (Fig. 4). T he only differences among the modelled days are the measured environmental conditions and calculated diurnal varia1ion in :;olar elevation. The full set o r parame ters used in the mo<lcl runs arc shown in Table I. In discussing model output. we s how predictions at the whole-canopy level (Fig. 4) and also for individual canopy layers (Figs 6 & 10). Our model is designed to make predictions at the whole-forest level. and thus Fig.4 is used for quanti tative model conlirmation. In presenting data for the individual layers. the details of mo <lcl be haviour arc displayed. A degree of aggregation has been e mployed in paramc1ri1.ing each canopy layer: a s imple weighted average was applied 10 take accoun1 of species <lifferenccs. Thus. we use the 1.:omparison or cano py layer level predic ti o ns with leaf level darn purely as a qualitative confirmatio n of the model.

Whole-forest hourly C0 2 exchange
During the course of' the day. canopy processes arc initially driven hy the interception of incident radiation (Figs 4 & 5). As s tomata open. CO! assimilation rises more rapidly than l~E'. because atmospheric saturation defic it is low in the cool of the morning (Fig. 5). With rising air temperatures. atmos pheric demand for water. and thus transpiration, arc increased. As light becomes saturating. leaves arc no longer limited by potential electron transport. Instead. RuBP carboxylation activity becomes limiting. which in turn is related to leaf N content. Figure 6 shows diurnal rates Of assimilation (µ 11101 CO~ S I pe r layer) and internal CO~ concentrations CC,. pmol mo l 1 ) in selected layers on day 2 15.
After midday a third factor becomes limiting. In the first few hours of daylight the transpirational demand created by sto matnl opening i~ met from water stored in the leaves and the crown (i.e. capacitance). 1 lowever. once the stored water is exhaus ted. the leaves must he supplied by water transported from the roots. In the upper canopy. over 20 111 above the forest noor. xylem hydrau lic resistance is significant and stonwta arc forced to close to maintain turgor ;rnd 11void xy lem cavi tation. Because aftern oon atmospheric saturation de ficits arc high in the upper canopy, the degree of stomata! closure required to maintain tunrnr has a significant effect on C0 1 di trusion i 1110 upper ca1~opy layers~ Further factnr!I involved in reducing afternoon NEE include the measured drop in ambient C0 1 concentration result ing from co~ uptake by the canopy. and the recorded increase in soil respiration caused hy higher afternoon soil temperat ure~. I lowcver. the model suggests that the overriding reduction in afternoon C0 1 uptake results from stomata! closure in the upper canopy caused by restrictions in water s uppl y. Measured anu modelled NEE show a similar hyperbolic n.:spon:.e to incident PPFD during the four d:iys wc examined (Fig. 7). and both shO\\ the :;amc hyl>-tercsi~. with afternoon co~ uptake lower than morning uptake at a similar PPFD.
Deeper in the can<'PY· there arc different limitations to productivity. Light level~ arc lower. but so also are atn10spheric :.aturation delicih. temperatures and wind :;pceds. and hydraulic.: rc:.istance i:. reduced in layers nearer the ground. Therefore water demand in the lower canopy never exceeds supply. and there is no stomata! closure during the aftern oon according to the model.
In their s tu dies on gas exchange in mature Q11rrc11s mhm. We ber & Gates ( 1990) showed that a marked middny depression in C0 2 assimilation commonly occurred C0 2 at 25· C lnh1h111on const:rnt ol Ruh"co by 0~ a1 25"C Leaf area index Fine root length per m 2 ground area: total/layer Soil hydrauli e conducti vit y /\rc:il con1.:cntration or leaf" N h>liar N concentration in layer 11 Proponion of total canopy Nin top layer Slope coefficient of ca nopy N di,trihtt11on i\t111n,1>heric pre,sure Rc,piration rate Canopy layer hydr.iulic rc'i'tancc Soil hydrnulic rcsiMance 111 <.::inopy layer /1 G:" con,tanl Fine roo1 radiu' Rml iu' of soil cylinder ex ploited hy a mm /\ir 1crnpera ture I .cuf 1cmpcra1Urc Sor I temperature /\clUal ral e or carbox ylat ion Ru BP carhoxylation capacily Canopy layer waler con ten I /\tnm,pheric ,a1ura1ion deficll 111 c:111opy layer C0 2 compcn~ati on poinl wilh H, 1 = 0 al 25' C 8No1:, 1hre,hold for ~ioma1al 01>cning RuUP carhox ylation ca1aly1ic ra1c coefli cicnl a1 JO' C Electron 1r:111,porl r;1te coeflicic111 ;1t 30"C l)c11si1y of waler Minimum suMai nahlc leaf water po1e111ial Lear water po1en1ial in layer 11 Soi l waler potenlial  Kir ... chhaum & Farquhar ( 1984)   rates were generally lower. but less variable throughout the day. and an at'temoon dcc.:line in uptake was not indicated. These data provide qualitati ve substantiation for lhe model results al the canopy layer level. Bearing in mind the mag nitude of the erro r associated with eddy corre lation methods. il is also instructi ve 10 examine where modelled and measured results for the whole canopy diverge. For day 253 (Fig.. -l-) the model underestimates C0 1 uplake and LE during the middle of 1he day. However. this day wa~ c. :haracterized by a g rcal degree or variability in flux measurements. and by rcla-1ivcly high soil temperatures. II seems likely that our estimates or soi l respiration arc an overestimate. The morning peak in measured U ;' is explained by evaporati on from wet leaf s urfac.:cs resulting from rainfal l a l 0600 h.
Internal C0 2 concentration ( C 1 ) Figure 6 traces the diurnal course or predicted internal CO~ concentrations (C,) for live canopy layers on day 2 15. Tenhuncn et al. ( 1984) ob~c1vc 1ha1 C; tends to remain essentially consttlll\ despite stomata! closure. so that assimilation and conductance change in conc.:ert. This observation is the basis or some empirical models or g, (Ball et al. 1987 ).
(f) 1996 lllackwcll Science Lid. P/11111, Cr/I mu/ E111'irm11111•111. 19. 91 1 927 A similar coordination between assimilation and stomatal conductance arises because of the optimization we u~e lO calculate g, in our model. Thus. in our model C, remains relat ively c.:ons1an1 for much of the day and in mos1 layers. between 260 and 280 pmol mol 1 • a typical range for C, leaves. However. in topmost layers. where afternoon g, i~ set to avoid cavitation rather than optimise C uptaJ..c. C, falls as diffusion becomes limiting 10 assimilation. In studies of gas exchange in malllre Q11l'rrns rubra . Weber & Gatci. ( 1990) shO\H:d that C, did decline during the middle or the day. though not to the extent of our predictions for the upper canopy.
The stable C, values predicted for each layer arc simi lar. their exact values dependent on fo liar N concentration and im:idcnt radia1ion. However. because the impacts of s1om-:11al closure due 10 water s1rc:.s are confined 10 the uppt:r canopy. the average daily C; will decline with hcig.hl. Carbon isotope ratios in leave~ can provide an indication of long-tern1 aggregated C, values (Farquhar et al. 1989). U:.ing 1his technique. Yoder"' al. ( 1994) have sho\\ n thal in upper canopy tree~ there i~ C\'idence of reduced C,. which they trace 10 hydraulic.: limi1a1ions. Although their data pe1 1ain to a conifcrou:. stand at a dry site. they do provide some suppor1 for our simulated vertica l distribution of average C; in developed stands.
The model can also be used to examine how g, varies within the plant canopy. Daylight average and maximum g, are plolled against leaf height for the same day (Fig. 9). Maximum g, declines deeper into the canopy. However. lhe grealer water slress in the upper canopy and the resulting aftern oon stomatul closure mean that average gs i s highesl below lhe 1opmos1 layer. These predictions are in agreement with the measurements of Roberts et al . ( 1990)  These data do indicate that the predicted patterns arc consistc nl with obsc rvalions from other 1all-sta1Urc forests.

Nitrogen use efficiency
Nitrogen use efficiency (NUE) of each canopy layer through a single day is dc1crmined as the total gross co~ assimilation per g foliar N. Integrated daily NUEs or 1he c:.lllopy layers are simi lar (sec Fig. I 0). suggesting that the N distribution we applied is close 10 optimal. Upper layers arc the most e ffi cicn1 earl y and tare in the day. when they arc belier il luminated and least water-stressed. Lower layers arc the mosr effi cient around noon, when irradiance is highest.  19. 911 -927 Modelling the soil-plant-atmosphere continuum 923 may be import:ml in de1ermining the optimal distribution of N within the canopy.

Sensitivity analysis
The parame1ers 1es1ed ror sensi1i vi1y are those related 10 the hydraulic model and stomata! variation that were nol measured al the site: C,,. 'i/ 1111111 • G" and 1. The model was rerun for the 25 d. wi1h 1hese parameters varied individually by at least ±30% (according to uncertainty abou1 the parameter estimates). Table 2 shows the / and slopes ± s1andard errors of the measured versus predicted fluxes when winds were from the south-west. There was o nl y a small alteration in model respunse wi1h varia1ion in canopy hydraulic conductivi1y (G 1 ,), and canopy layer capacitance (C,,). There was more si.:nsi ti vity 10 changes in minimum sustai nable leaf waler pote111ial ( '¥ 1111111 ). When this was increased to -1 ·5 MPa. 1ranspira1ion and photo· synthesis were significan1l y reduced. because s1omatal opening is constrained as '¥ 1111111 becomes le:::~ negati ve. The layers arc numbered from the 1opmo~1 ( I ) 10 the second from bottom (9).  Live values of 'P_. Thus. sensitivity analysis of l/~min also serves as a sensitivity analysis on soil water availability.

NEE
LE showed more sensi ti vity than NEE 10 variati on in 1.
the stomata! threshold parameter that controls water use efficiency. We have used t 10 cons train g,. arguing that conservati on of the plant water store ameliorates afternoon water stress. The sensi1ivi1y of this parameter (set 10 0·07% in the model run s) and this assumption were tested in more detail. r:or day 2 15 the canopy model was rerun wi th a varic1y oft values. ranging from 0·00 I 10 0·2% (Fig. 1 I ).
With lower t values, GPP (gross primary productivity) was stimulated in the morning because stomata opened wider. The model then forecast a rapid exhaustion of the water store, causing stomata I closure to occur earlier and to affect more of the canopy. Afternoon GPP was significant ly reduced. and so in balance there was minimal improvement (less than 1 %) in daily total GPP with less con-Mraincd g,. With higher values of 1. the model predicted that !.tomata opened less widely in the morning; water stress was ameliorated in the afternoon. but this highly conserva ti ve strategy reduced daily GPP overall. The hydraulic model docs set short-term limits on productivi1y. but suggests that conservative g, limits the degree of canopy water stress.

Further directions
The model docs not include any representation or waler dynamics around roo ts or the impacts of root clumping (Tardicu el al. 1992). W<1ter uptake rates may be affected by the development and enlargement of water-depletion zones around roots during the course of the day. If morning photosynthesis relics large I y on stored water. these depiction zones around roots arc expected to affect only afternoon transpiration and therefore might explain the tendency o f the model to overestimate late afternoon LE.
A lso. we did not simulate the variation in soil moisture at differcnL depths. To test and apply this model further. we require data l'rom a water-s tressed site. so that the impacts of low soil moisture on canopy processes can be examined. The major objective or th is work was to develop predictions or canopy 11uxes. both for use in investigation of the stand-level response 10 global change. and for application to ecosystem models (e.g. Part on el al. 1988: Rastetter el al. 199 1 ). Having confirmed model predictions against whole-forest measurements. we can reliably use the model to develop more aggregated representations of canopy processes. These arc much simpler sets of equations. operating like a simplified 'big-lear model. that capture the behaviour of the process-based formulation while requiring many fewer parnmctcrs and much reduced computing power.