A model of canopy photosynthesis and water use incorporating a mechanistic formulation of leaf CO2 exchange

l.i),-rst Ecolog?~ and hfunupetnet?r, 52 ( 1992) Elsevicr Science Publishers B.V., Amsterdam

26 l-27&

261

R.E. McMurtrie”.b, R. Letming”,‘, WA. Thompson”.’ and A.M. Wheeler” “CSIRO. Division qfforestrJ*. PO Box 4008, Queen Victoriu Terrace, Catzbewa, ACT 2600, Austrnlia hSchool qf Biologrcai Science, L~niversriyof NW: PO Box I, Kemingion, .WSM’ 2033. Australia (Accepted

30 December

199

I)

ABSTRACT McMurtrie, R.E., Leuning, R., Thompson. W.A. and Wheeler, A.M., 1992. A model of ,:anopy phctosynthesis and water use incorporating a mechanistic tormulation of leaf CQ exchange. For. Erol. JImage., 52: 261-278. A mode! of the carbon uptake and water balance of forest stands is described where leaf photosynthesis is represented by a mechanistic model of photosynthesis by C, plants. Data are presented IO support an empirical relationship linking stomata1 conductance, photosynthesis, relative htimidity and ambient CQZ concentration. The model was applied to stands of Pinus rudiata subject to extremes of water and nutrient availability. Simulated water storage in the root zone agreed with measurements condtnted over a 5 year period. Simulated and measured seasonal patterns of water use reached maximum rates of approximately 7 mm day- ’in summer for irrigated stands with projected leaf area indices of approximately 8. Simulated annual net photosynthesis (net ofphotorespiration and daytime fo!iar respiration) ranged from approximately ! 7 Mg C ha-’ year-’ for control stands to approximately 45 Mg C ha-’ year-’ for irrigated and fertilised stands.

In receQ years plant physioIogical ecologists have made significant advances in their capacity to describe and predict plant responses to the environmen’t (e.g. Mooney et al., 1987 ). Plant physiologists are now well placed to predict how %eaF-level gas exchange will respond to changes in cnvironmental conditions because established theories exist for leaf CO2 exchange of C3 Correspotldenceio; R.E. McMurtrie, School ofBiological Science, &iniversityof New South Wales, PO Box I) Kensington, iJSW 2033, AUSLdkL ‘Present addms: Centre for Environmental Mechanics, CSIRO, GPO Box 82 1,Canberra, ACT 260 I, Australia. ‘Present address: Department of Forest Sciences, Universjty of British Columbia, Vancouver, BC V6T lW.‘s, Canada.

plants (Farquhar

et al., 1988; Farquhar and Won Caemmerer, 1982) and for leaf energy balance (e.g. see review of this topic in Monteith and Unsworth, 1990). When, however, the objective is to quantify fluxes of carbon and water vapour for stands of trees, knowledge of leaf-level responses is of limited valae. The challenge we face is to extrapolate from the micro-environmental scale to the whole canopy. This requires integration over space and time, and sound formulations of the linkages between the various processes, tasks which can only be accomplished using process-based models. Several models have been developed tc address this task of scaling, including BACROS (De Wit et al., 1978; Goudriaen et al., 1984), FORCRO (Mohren, 1987 ), MAESTRO (Wang, _368; Wang and Jarvis, 1990 ), FOREST-KC (Running and Coughkm, 1988 ), BBOMASS (McMurtrie et al., 1989, 1990a,b; McMurtrie and Landsberg, 1992 ), QUINTA (Tenhunen et al., 1989). While the various models differ in the aspects of plant physiology emphasised and differ widely in levels of resolution, each simulates photosynthesis and water use of canopies (see review in Agren et al., 199 1 ). In this paper a model of canopy photosynthesis in relation to water use is described and applied to stands of Pinus radiata (D. Don ) growing near Canberra, Australia. The model is an enhancement of the BIOMASS mode! described by McMurtrie et al. ( i 990b) and McMurtrie and Lam&berg ( I992 ). One improvement is the formulation ol’photo:.ynthetic rates in terms of Farquhar and Van Caemmerer’s ( I982) biochemic~lllybased model for C3 plants. This development gives the model the capacity to scale up from knowledge of the biochemistry of photosynthesis to the canopy. The other major enhancement is the incorporaticm of the simplified stomata1 model of Ball et al. ( 1987) in ~~~~~S. To parmeterise Ball et al.‘s ( 1987) model, an empirical relationship between stomata! :snductLnce gs and net assimilation rate A was fitted to ?eld gas exchange data collected under a wi3.e range of conditions of nutrient and water status. The water balance model t5zs tested by comparing measrrred and simulated soil moisture contents, and rates of tree water use. The sffects o*‘irrigation and fer-tilisation on anmia! canopy net photosynthesis and its seasor& d~st~~~~t~o~were simulated.

The Biology of Forest Grow& (4333 ) gx~e~~rne~~ on the effects of fertilisation and irrigation in stands of P. ~~&tb x++asconducted al Pierce’s Creek ( 35’ 2 4‘S,, : 48” 54’E, eEevaBion 625 m above sea level )? near Canberra, Australia. Average aanual rainfa‘sallis 790 mm, but with Barge year-to-year varia-

MODELOFCARBON

UPTAKE

ANDWATEK

BALANCE

263

tions and w-ith summer droughts common. A detailed description of the site and experiment is given by Benson et al. ( 1992 ). The experiment commer,ced in 1983, 10 years after planting, when tree stocking was approximately 700 ha-‘. Treatments applied in the experiment were irrig ition (I), solid fertiliser (I?), irrigation plus solid fertiliser (IF ), and irrigation plus liquid fertiliser (IL), with the control (C) receiving no treatment. The irrigation treatment applied to I, IF and IL stands commenced in August 1984 with the aim of removing soi’ moisture as a growth-limiting variable. Water was applied by sprinklers at a i’-:‘tesufficient to maintain soil moisture at, or close to, field capacity. The solid fertiliser treatmer+ 1Lwan applied in two doses in Seplzmber and October 1983. The total supplied was 400 kg ha-’ of nitrogen an; 200 kg ha-’ of phosphorus (for other elements see Benson et al., 1992 ). The liquid fertiliser hreatment consisted of regular applications of a complete nutrient solution delivered weeklv through the irrigation system at rates designed to provide adequate nutrie& for tree growth throughout the season (see Benson et al., 4992 ). For the IL treatment annual ap;Aications of nitrogen were approximately 300 kg ha- ‘.

The pattern of leaf biomass development of tl.z_s:: P na;lds was estimated by Raison et a!. ( i Q92 ) using data derived from annual biomass harvests, fortnightly measureme&s of needle extension and monthly collections of litter fall. Specific leaf area (projected) was estimated to vary between 4 .O and 4.6 mz kg-‘. Projected leaf area iI:dices were approximately 2 in mid-1983 prior to treatment ard achieved maximulm values ofapprnximately 8, 8, 6, 5.5 and 5 for IL, IF, I, F and C. respectively. Gas exchange measurements were performed on trees of all treatments over a 4 month period commencing in October 1987 using a portable instrument (LCA Analytic Development Co. ktd, Hoddeson, Her&s, England) (see Thompson and Wheeler, 1992 for details ). Measurements were made at a range of irradiances on foliage of the two youngest age classes in the middls and upper canopy. Soil water contents were measured to a depth sf 2 m at ~o~~~~bt~y int -rvals with six access tubes per treatmznt using a soil moisture arrd density meter (CPN 501, Campbell Pacific, Pacheco, California, USA). See Myers srd Ta?sma ( 1992) for details.

264

13.E. McMUI.
the carbon and water balance of forest canopies. Th? model, consisting of a s+tem of difference equations with a daily time step, requires daily meteorological data (precipitation, air temperature, global radiation and humidity) and has been applied to stands of P. radiala (Booth and McMurtrie, 1988; McMurtrie et al., 1990a,b; McMurtrie and Landsberg, I992 ) and Eucalypttn (McMurtrie et al., 1989; Eeuning et al., 1991b). The canopy was represented in the model by three horizontal layers of equal depth. The model allows for a random array of conical or ellipsoidal crowns, the dimensions of which are based on knowledge of the time-course of height development, depth oflive crown, stoclnng, and fraction of ground area shaded by tree crowns. The instantaneous assimilation rate of foliage A, was estimated by dividing the canopy into sunlit aqd shaded foliage ( McMurtrie et al., 19SOb) and then calcuiating A using a simple two-parameter Blackman light response curve given by: A-min(j&&)--Rd

(1)

where the function min(x,y) represents the minimum of I-NOvariables x and ~1,Amax=&-& 3s the rate of net photosynthesis at light saturation and ambient CCL, @is absorbed photosynthetic photon flux density, f3 is the initial slope of the light response and Rd is the daytime rate of respiration. The Curve ( I ) gives a reasonable fit to light rca?onse data for P. rudinta needles (see Benecke, 1980 ). The proportion of sunlit foliage photosynthesising at the irradiance-saturated rate of nes ~~~otosy~t~~e~is(hmax) was calculated, while assimilation by I&Zremainder of the canopy (shade foliage a& s~~nlitfoliage below light saturaiion) was assumed to be proportional to radiation absorbed by that foliage. h radiation extinction coefficient C= 0.5 was assumed, corresponding to a s~~e~.~e~~~~ symmetl.i: leaf angle dlstrib:ltion. Details of the equations uced to estimate sun an shade foliage are ~~OViCkd by McMurtrie et al. ( 199cib )_ This jimpIe apprc?ach ma&es the modei kss computationally tlcmanding by ~crn~v~~g the need to simulate in detali the three-dim$:nsional radiation environment of 1% ‘*~Qv !iee Wang and Jarvis, 19910). Norman ( 19X8), Caidwell et al. ( 19& il al . Long ( 1991) adopted similar simplifications in their models.

MODELOF

CARBON

UPTAKE

&ND

WATER

265

BALANCE

Model qfstomatal conductance Analysing gas exchange iata from all treatments, Thompson and Wheeler ( 1992 ) fo,urd that the slope of the relationship between g, and A differed between irrigated and non-irrigated stands However Fig. I indicates that data co;lforrn to a single relationship when plotted in the form & =g0+g,AhlcS

(2)

as proposed by Ball et al. ( 1987), where h is relative humidity (O/o), c, is the concentration of COZ at the leaf surface and go and g, are empirically derived parameters. Though lacking a mechanistic base (Grantz, 1930; Aphalo and Jarvis, I99 1 ), this equation is able to describe much of the variability in several gas exchange data sets (Ball et al., 1987,* Graniz, 1990; teuning, 1990). The Relationship (2) is illustrated in Fig. I for Thompson and Wheeler’s ( 1992 ) gas exchange data for P. radiata. Da&adisp!ayed encompass all five treatments for measurements performed over the period October 198?-April 1988. The distinction between irrigated and non-irrigated trees in the relationship of g, to A (Thompson and Wheeler, 1992, Fig. ! ) is less pronounced when g, is rekted to the product (A h ). For reasons explained by Leuning ( 199(I), a small positive value for go is expected in eqn. (2 ). ‘When the Relationship (2) was fitted by linear regression to the pooled dsta of Figs. B(a,b and c) with go fixed at zero, the estimated value of the slope g, was 0.164 ( r2 = 0.9 I >, compared with slopes of 0.08-O. 164 reported for G, plants by Ball and Berry ( 1992 ) dnd 0.06-O. 10 obtained by Leuning ( 1990) for fieldgrown Eucalyptus grandis. Equality is assumed here between concentr&tions of CO2 at the leaf surface c, and in the ambient air stream c,, an assumption which is reasonable for aerodynamically rough canopies of pines with thin needles. Formulae for parameters oJphotosynthctic light response cwve Farquhar and 77011Caemmerer iu=(1_F*/ci)min(~a/,,W,)-Rcl

( 1982 ) express the assimilation

rate as (3)

where r+, 1s the C@ compensation point in the absence of &, c; is the intercellular co~ce~~~atio~ of COZYand B’, and !VJare the rates of carbcny:ation limited by ~ib~lose-b~s~~hosp~ate Carboxylase-Oxygesrase (Ruhisso ) and by IliiuBP regeneration respectively. Here

0

100

(Relative

300

200

humidity)

SOC

400

x (Assimilation

rate)

II 0

0

100 c,

i

c

ii

n ii 01

50

0

"_-__L'.--__L.____--. G

700

"> 200

'

I r i

300

0

w, =

300

200

100

(Relative

humidity)

x (Assimilation

rate)

JCi 4.5(Ci+7/3r*)

in which J iscalculated

as the solution of

&I’- (0.385~+J;,,;)J+0.385~~~,,=0.

(61

is the rate of electron transport at saturated irradiance and 8 is the curvature of the non-rectangular hyperbola gEven by eqn. (6 ). The constant value 0.355 is derived from the formulation of Farquhar and Wong ( 1984). Values of parameters and details of the assumed temperature dependence of .?,,,, VA,, 3k, and Rd are given in Appendix 1. is obtained from the limit of Sgh Cpwhen J approaches The value of&,, J,,,,. Leuning ( I 990) has solved eqns. ( 3 )- (6 : when stomata! conductance simultaneously satisfies eqn. (2) and the supply equation

J,,,

A=g,(c,--C,)/1.6

(7)

where the scalar I .6 reflects the relative diffusivities of stomata to CO2 versus water vapour. Again, eC.uality between c, and c, has been assumed in writing eqn, ( 7 1. Ef’assimilaiiou is Zimited by Rubisco activity. A,,, is given by the solution of (8)

ITassimilntion

Eslimited

by RuBP

regeneration, A,,, is givenby

Each of these equations can be expressed as a quadratic equation for c,. The appropriate solution for A,,,, is given by the minimum of solutions of eqns. (8) and (9). The quantum yield u can be obtained from eqns. (3 ), ( 5 ) and (6 ) as the limit of ;ow incident radialion (4 - 0, C,- c,) a=0,0857(c,-r*)/(~,t_7/3T*)

(10)

For parameter values specified in Appendix i, the theoretical quantum yield (eqn. ( 10) ) is cv= 0.062. The slope of the Blackman response p will generally be less than Q because of the approximation of a non-rectangular response with finite curvature by a pair of straight lines. i value 8~0.049 was estimated ny comparison of the Blackman function eqn. ( 1) with the non-linear relationship derived from eqns. (3), (4), ( 5 ) and (6) with EkO.8, using regression methods with A,,, fixed at the value derived from eqns. (8 1 and (9). Field measurements of needle gas exchange (Thompson and Wheeler, 1992) indicated that A,,, was approximately 25% higher fer needles of 116,trees than of I trees. Values of J,,, and f/,,,, are assumed in our simulations to be linearly related to average canopy nitrogen concentration (Field, I.983; Leuning et al., 1991a). Measured folk nutrient concentrations are given by Crane d Banks ( 9992 ). The assumed relationships between J,,, and VC,,,, and iV co~ce~trat~o~ within the canopy are presented in Appendix 1..

Tfg,e~~~~~~~v~~g sequence of calculations is adopted by the to obtam i~sta~tan~o~s rates of canopy net photosynthesis A, and transpiration. ~~~~~~~ evaluates A maxand p from the above model of leaf gas exchange and stomata1 conductance (eqns. (8 ), (9 ) and ( 1CI> ) ~Canopy assimilation A, is calculated separately for sunlit leaves above hghr satumtioa, cunlit leaves below hgh aturstion and for diffusely Bit leaves accofdlng to equati5ns given bj M urtrie et 31. ( 199Ob) ~Canopy c~~~~~~~a~~~,defined as the integral 631’9,over the canogpy of leaf area index L”, is calcu”rated from canogy assmailatnon:

MODELOF

CARBON

ILiPTAKE

AND

WATER

WALANCE

269

ductance are incorporated by observing that the slope g, does not differ be-, tween water-stressed and irrigated stands (Fig. I>, and assuming a simple functional dependence of conductance on plant-available soil water (see McMurtrie et al., l990b). From measurements at the BFG site, Myers and Talsrna ( 1992 ) found pre-dawn needle water potential was affected only when plant-available soil water declined below 40% of plant-available water when the so,al was at field capacity. We assume that conductance is unaffected by soi! water deficit until plant-available water has been reduced to 4OYo.Beyond that ;,oint conductance was assumed to decline linearly with available soil water (see McMurtrie et al., 1990b). According to eqn. ( 11) a concomitant decline will occur in canopy photosynthesis. This approach provides values of ,4, nnd c. T- !er water-stressed conditions. ‘The inst, .I:aneous rate of canopy transpiration is derived from the standard Pcnman-Monteith equation (e.g. Jarvis, 1985 1. The BIOIvIASS mode1 then employs six-point Gaussian quadrature to derive total daily fluxes of carbon and water for the canopy. In the water balance submodel, described by McMurtrie et al. ( l990b ), daily changes in soil water content of the rooting zone are obtained from the difference between rainfall and simulated rates of canopy interception, drainage, and evapotranspiration by trees and unde rstorey. MODEL SIMULATIONS

Ihe mode1 gave a good fit to measured soil moisture over successive cycles of wet and dry conditions for the C and F plots (Figs. 2a and 2b), respectivel.4). Figure 3 shows that simulated annua! rates of tree water use were consistent with t.hose derived by Myers and T&ma ( 1992 ) using soil moisture measurements over the period I July 1984 to 30 Sune 1987. Simulated annual totals for tree transpiration ranged between 500 and 600 mm for non. irrigated stands experiencing severe water limitations, and between 1 P50 and 1400 mm for irrigated stands experiencing no water limitation. The seasonal pattern of simulated canopy transpiration for the period I July 1986 to 30 June 1987 (Fig. 4 ) wp.s similar to that estimated by Myers and Talsma ( 1992) in summer, autumn and winter, though simulated rates were higher than mea.sured rates for F arid C treatments in September and October. Figure 2 suggests that the model overestimated canopy conductance in spring, causing soil .moisture to dechne too quickly, for C and to a lesser extem for F stands. Ssarni i provement may be achieved here by incorporating seasonality in the parameter g,. To achieve this, howeves. much more gas exchange data wouId be required to derive functions for the annual variation in $1 for each i,,ti* ~~~*rnent. ~~~t~sf~~~~~correspondence between measured and

/_<___ 1

Jan 85

!

I

----A 1

Jan

Jan

Jan

86

r7

08

1

271 1500 I3

IL

h

IF

i2

1

6C

A

F

Measured tree water use (mm year-’ ) Fig. 3. Relationship between simulated annual tree water use and rates estimated by klyers and Talsma ( 1992) from soil moisture measurements during the period 1July 1984-30 June 1987.

Fig. 4. Seasonal pattern oftree transpiration simulated fcr a i I month period ( 1 July 1966-30 June 1987 ) for IL. IF, 1, F and C stands. SimuiaM rates are month!y mean values of daily Iranspiration.

bU__ 0

-A

0

/

A% 0

.A

:0

5

0 Measured

cIaily transpiration

(mm)

Fig. 5. Comparison of simulated average monthly rates oftxe expcrimen?al!y by M! ers and Talsma C1992 ).

transpiration

with rates derived

273

Fig. 7. Seasonal pattern of rwt canopy assimilation simulated for a 12 month period (I July 1986-30 June 1987). Displayed rates of assimilation are monthly means of daily simulated totals.

Simulated canopy photoA.vnthessiy Values for simulated annual net canopy assrmilation (defined as assimilation derived after subtractian of photorespiration and daytime foliar respiration ) are presented in Fig. 6 as a function of leaf' area index. Simulated rates valry between 17 Mg C ha-’ year-’ and 45 Mg C ha- ’ year-’ for G and IL, respectively. Estimated annual totals for ‘IL and lF were more ihan double those f0r F and C. The seasonal pattern of net assimilation for the period 1 July 1986 to JO June 1987 is depicted in Fig. 7. The model suggests that canopy photosynthesis peaks in November for non-irrigated stands and in December for irrigated stands. For IL, IF and Iia depression occurred in January and February dr:e to low relative humidities. There lvas little net carbon r5roduction for nonirrigated stands in months of extreme -water clef&,. Canopy phot~sy~~~h~~~s of 1 is csnsistently absut ! S-28% behow that of IL, with that of IF intermedia?e between the two.

Modellers ~ornrno~~~ express stomata; ~~~~~~t~~~e as a non-linear function of measured ~~v~~~~rne~t~~ variables such as ieaf-air saturation deficit D, irradiance and plant water status. hn these mAeIs the relationship between J and A can depart ~~gr~i~~~~~t~~ from the !ixarity iktstrated in Fig. 1 and in OS the_ &as q exchange data of Thompsi;n antis V~keier [ 1992 ) ~Ho addition, para-

274

R.E. McMIJRTRIE

ET.4F.

~~.~~~~r~s~l~~ phencmenoiogical models depending on radiation, air saturation dciicit D and water status is not straightforward. For instance, seven parameters are required by McMurtrie et al. ( I990b) PO specify the dependence of gS on radiation, D and water stains (their eqns. ( 36 1-f 39) ) / in addSon to those r.equired to characterise assimilation. Models of water and carbo’n balance where the link between conductance and assimilation is explicit (Goudriaan, 1986; Mohren, 1987; Tr,r.hunen et al., 1989), have several potentiai advantages. The model described in this paper require: only three parameters (go, g,, and one parameter for the dependence ofgS on plant-available water). The uncertaintyin formulating functions relatingg, to radiation, D and water is greatly diminishe by imposing the ccastraint of eqn. (2). Furthermore the depentience of on D seems to vary seasonally and between treatments (Thompson and Wheeler, l?92) and between environments (e.g. ccmpare Whitehead a Ad Kelliher ( I39 I ‘I with Thompson and “WheeIer ( 1992 ) ) Data presented in Fig. i sL*ggest that less variability between seasons and treatments occurs in the Relationship (2). While some doubts have been expressed about the form of eqn. (2 f , particularly its dependence on relative humidity (e.g, Crantz, 1990; Aphalo and Jarvis, 199 1 ), an explicit link between gS and A has advamages in terms of theory. The incorporation of a mechanistic model of photosynthesis by leaves sf C3 pIants in the current model represents anotter significant advance. Thic ~rn~~eme~~tat~~~enhances the model’s capacity to rigorouslv predict canopy response to environmental variables such as temperature, C@ and irradiation. This paper presents simulations of carbon flux of forest stands (Figs. 6 and 7 ). Simulated rates of annual net photosynthesis for C and F stands (Fig. 5 ) were similar to rates simulated by McMurtiie et al. ( 1990a) using BIOMASS prior to the ~rn~~e~~e~~~o~of equation5 for Farquhar and von Caemmerer’s ( i9X!) photosynti eticmodel and SalI et al.‘s ( 1987) stomata1 model. Simulzted armua.l rates for IL3 IF and I were about 10% higher than values obm-tri~~et al. 1 i 390a). Experirqental validation of these simu-

275

ACKNOWLEDGEMENTS

The senior author Js grateful to Roberto Hnzunza for technical assistance and acknowledges support of the Australian Research Council and the NGAC Dedkated Greenhouse Research Grant Scheme.

REFERENCES Agrcn. G.I., McMurtric, R.E., Patton, W.J., Paster J. and Shugart, H.H., 199 I. State-of-the-art of models of production-decomposition linkages in conifer and grassland ecosysttms. Ecoi. Appi., I: I i8-i38. Aphalo. P.J. and Jarvis, P.G., 1991. Do stomata respond to relative humidity? Plant Cell Environ.. i 4: 137-i 32. Baldocchi, D.D., 1989. Turbulent transfer in a deciduous forest. Tree Physiol., 5: 357-377. Ball, J.T. and Berry, J.A., 1992. An analysis and concise description of stomata1 responses to multiple environmental factors. Planta, in press. Ball, J.T., Woodrow, LE. and Berry, J.A., 1987. A model prediciing stomata1 conductance and its contribution to the conrrol of photosynthesis under different environmental conditions. In: J. Biggins, (Editor), Progress in Photosynthesis Research. Vol. IV. Martinus Nijhoff, Dordrecht. pp. 22!-224. Benecke, U., 1980. Photosynthesis and transpiration of Pinzrs radiara D. Don under natural conditions in a forest stand. Oecologia (Berlin), 44: 192-198. Benecke, U., 1985. Tree transpiratton in steepland stands of Nozhqfagcls frurxata and Pinns roddata, Nelson, New Zealand. In: H. Turner and W. Tranquillmi (Editors), Establishment and Tending of Subalpine forest: Researcir and Management. Swiss Federal lnsti‘ute of Forestry, Birmensdot-f, Research Report 270, pp. 6 I-70. Benson. M.L., Landsberg, J.J. and Borough, C.J.. 1992. The Biology of Forest Growth experiment: an introduction. For. Ecol. Manage., 52: I- i6. Booth, T.H. and McMurtric, R.E., 1988. Climati: change and Pitrus vu&zlaraplantations in Australia. In: G.I. Pearman (Editor). Greenhouse: Planning for Climate Change. E.J. Brill, Leiden, pp. 534-545. Brooks, A. and Farquhar. T .D., 1985. Effect of temperature on the COz/OL specificity of ribulose-l .5-bipbosphate carboxylase/oxygenase and the rate of respiration in the light. Planta. 165: 397-406. Ca!dweII, M.M.. Meister, H.-P., Tenhunen, J.D. and Lange. O.L., 19S6. Canopy structure, light microclimate and leaf gas exchange of QI~(?T(,zIS lwcc~f~r;a L, in a Portuguese macchia: measurernerds in different canopy layers and simulations -with a canopy model. Trees, 1: 25-4 i Crane. \N.J.B. and Barks, J.C.G., lrt92. Accumtiiation and retranslocation of foliar nitrogen in fertilised and irrigated Ptnus radium. For. Ecol. Manage.. 52: 201 -223. De Wit, C.T. et a!., i978. Simulation of Assimilation, Respiration and Transpiration of Crops. PUDOC. Wa::eningen, 141 pp.

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--_ --~-. Fxqpra!ic~q c$e!:cajyp:an?.i".‘.%%_~uriJ .r-z-:~-r:--c-~*--CU.L>iCilllikllO

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1 Cl.l _~ c,;, ‘%.!l‘;-i-s. t3.J.and -r3!5ma.z : ‘40,- ‘iilC ;iZiCr b3lanCCand ITCCii’alii Si3iUSii1 iirigaiCd Zr,d i;~rliliscd 5i;ndY of I’ir:!r.i i.!.diiil‘:. i-w. Eu;l. Sian lge.. 52: i ‘4’. Y (-1 rjr>311,I.?\!. [?bil. Snrpriac!ngieaf 2nd light !nii’:‘r:epili.ri n?odeli. in: ‘I.D. Hc&ilih f’_:,~-

MODtL.

OF CAM%

.l\i 1 illTAKE

AND

WATER

277

BALANCE

and J.W. Joncc i Editors), Predicting Photosynthesis for Ecosystem Models. Vol II. CRC Press, noca rg?kXi, FL, pp. 49-67. Raison, X.J., ,&?:rira, P.K., Benson, ML., Myers, B.J.; McMurtrie, X.E. and Lang, A.R.G., 1992. Dynamics :rf Pirzus radium foliage in relation to water and nitrogen stress. II Needle loss and temporal changes in total foliage mass. For. Ecol. Manage., 52: 159-l 78. Running, S.W. and Coughlan, J.C., 1388. A general model of forest ecosystem processes for regional applications. I. Fydro!ogic balance. canopy gas exchange and primary production processes. EGOS.IModellinp., 42: 125-I 54. Tenhunen, J.D., Rcqnolds, J.F., Lange, O.L., Dougherty, R.L., Harley, P.C., K.ummerow, J. and Rambsl, S., 19&9. QIJI~TA: A physiologically-based growth simulator for drought adapted woody plant species. In: J.S. Fereira and J.J. Landsberg (Editors), Biomass Production by Fast-growing Trees. Kluwer, Dordrecht, pp. 135-l 68. Thomspon, W.A. and Wheeler, A.M., ! 992. Photosynthesis by mature needles of field-grown Pinks rudrara. For. Ecol. Manage., 52: 225-242. :vaog, Y.-P., lY85. Crown structure, radiation als;orption, photosynthesis and transpiration. Ph.D. Thesis, I Jmversity of Edinburgh, 138 pp. Wang, Y.-P. and jar’* is, P.C., 1990. Description and vahdatio, of an array model -- MAESTRO. Agric. For. Meteorol., 51: 257-280. Whitehead, D. and Kelliher, FM, 1991. A canopy water balar:ce model for a Pious radiata starid before and after thinning. Agric. For. Meteorol., 55: 109-l 26. AQPENDlX

I

PAP AMETERISATICiN OF MODEL OF PHG TOSYIL’THESIS

The temperature and nitrogen depxdence5

o,~J~~,~ V,,,, sre gi,ven by:

278

R.E. McMURTRlE

ET AL.

rhenius functions for the temperature dependences of k, and k0 are given by Harley et al. ( i 986). leading to an expression for kI,: ,4-,=k,0exp(25.88r)(lCI.127exp(-14.51z)) where r= (T-25)/( ‘The temperature

T+273.2) dependence

and k,0=252~mol mot-‘. of& is assumed to be:

& ==RJlL?IOT’1o (during dark period) =0.6R,oQlo

‘-“O (during daytime)

where values, R,,=O.O7,timol me2 s-’ and Qlo=2.3, were derived from Benecke (1985). The CO;, compensation point r* also depends on temperature (Brooks and Farquhar, 1985 ), but this dependence has been neglected here. Other parameter values assumed for these simulations were c,= 340pmol mol- ‘, go=0 and g, = 0.164.