Agricultural and Forest Meteorology

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1 Agricultural and Forest Meteorology Contents lists available at ScienceDirect Agricultural and Forest Meteorology j ourna l ho me pag e: Empirical and optimal stomatal controls on leaf and ecosystem level CO and H O exchange rates Samuli Launiainen a,b,, Gabriel G. Katul c, Pasi Kolari d, Timo Vesala b, Pertti Hari d a Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 66, FI-8, Joensuu, Finland b Department of Physics, P.O. Box 48, FI-4, University of Helsinki, Helsinki, Finland c Nicholas School of the Environment, Duke University, Durham, NC, USA d Department of Forest Ecology, P.O. Box 7, FI-4, University of Helsinki, Helsinki, Finland a r t i c l e i n f o Article history: Received 9 June Received in revised form June Accepted 7 July Keywords: Photosynthesis Stomatal conductance Transpiration rate Scots pine Ball Berry model Optimality stomatal hypothesis a b s t r a c t Linkage between the leaf-level stomatal conductance g s response to environmental stimuli and canopylevel mass exchange processes remains an important research problem to be confronted. How various formulations of g s influence canopy-scale mean scalar concentration and flux profiles of CO and H O within the canopy and how to derive effective properties of a big-leaf that represents the eco-system mass exchange rates starting from leaf-level parameters were explored. Four widely used formulations for leaf-level g s were combined with a leaf-level photosynthetic demand function, a layer-resolving light attenuation model, and a turbulent closure scheme for scalar fluxes within the canopy air space. The four g s models were the widely used semi-empirical Ball-Berry approach, and its modification, and two solutions to the stomatal optimization theory for autonomous leaves. One of the two solutions to the optimization theory is based on a linearized CO -demand function while the other does not invoke such simplification. The four stomatal control models were then parameterized against the same shoot-scale gas exchange data collected in a Scots pine forest located at the SMEAR II-station in Hyytiälä, Southern Finland. The predicted CO and H O fluxes and mean concentration profiles were compared against multilevel eddy-covariance measurements and mean scalar concentration data within and above the canopy. It was shown that comparisons agreed to within % and comparisons to within 5%. The optimality approach derived from a linearized photosynthetic demand function predicted the largest CO uptake and transpiration rates when compared to eddy-covariance measurements and the other three models. Moreover, within each g s model, the CO fluxes were insensitive to g s model parameter variability whereas the transpiration rate estimates were notably more affected. Vertical integration of the layer-averaged results as derived from each g s model was carried out. The sensitivities of the up-scaled bulk canopy conductances were compared against the eddy-covariance derived canopy conductance counterpart. It was shown that canopy level g s appear more sensitive to vapor-pressure deficit than shoot-level g s. Elsevier B.V. All rights reserved.. Introduction The primary pathway by which gas molecules are exchanged between a leaf and the atmosphere was proposed to be through stomatal pores more than a century ago e.g. Blackman, 895. Since then, the precise regulatory mechanism controlling the opening and closure of a stoma continues to be the subject of intense research activity Cardon et al., 994; Parkhurst, 994; Fan et al., 4. Stomatal action is often studied with measurements of gas exchange conducted at a single leaf level. These measurements gen- Corresponding author at: Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 66, FI-8, Joensuu, Finland. Tel.: address: samuli.launiainen@metla.fi S. Launiainen. erally demonstrate that the response of stomatal conductance g s to environmental stimuli is well behaved when aggregated over numerous stoma Schulze et al., 97; Cowan and Farquhar, 977. This finding invites the interpretation of g s in the context of an effective or big stoma with an effective aperture Mott and Peak, 7. With conifers, a common practice is to use the shoot as the basic unit to determine the responses of stomatal conductance to microclimate Gower and Norman, 99, which involves aggregation of processes occurring at the needle surface elements. When aggregating to ecosystem level, the response of the canopy-scale conductance to environmental stimuli is more variable and not as well behaved as leaf- or shoot-level g s. However, clear deterministic trends do emerge also at such a scale Jarvis and McNaughton, 986 and these are commonly exploited in the so-called big-leaf representation. The aim of this work is to explore the connections 68-9/$ see front matter Elsevier B.V. All rights reserved. doi:.6/j.agrformet..7.

2 S. Launiainen et al. / Agricultural and Forest Meteorology between these deterministic trends at the canopy scale and the mechanisms governing the well-behaved leaf-level responses of g s to variations in its local microenvironment. The investigation of g s responses to environmental stimuli at the leaf scale appeared to have followed one of two broad model classes. The first describes g s as an empirical response to changes in photosynthetically active radiation, atmospheric vapor pressure deficit D, air temperature, leaf water potential, and the rate of leaf carbon assimilation Jarvis, 976; Ball et al., 987; Collatz et al., 99; Leuning, 995. These empirical and semi-empirical responses are often assigned to a plant functional type thereby allowing their routine use in climate or hydrological models Sellers et al., 996; Lai et al.,. The second approach is based on the socalled economics of gas exchange and assumes that the regulatory roles of the stomata are to autonomously maximize their carbon gains while minimizing water losses Givnish and Vermeij, 976; Cowan, 977, 98; Cowan and Farquhar, 977; Hari et al., 986; Berninger and Hari, 99; Mäkelä et al., 996. There are appealing attributes about this latter approach. First, the optimality hypothesis provides closed form analytical expressions for g s, assimilation rate and intercellular CO concentration. Second, these expressions require only one physiological parameter the marginal water use efficiency,. Third, the derived g s responses to several environmental stimuli can be viewed as an outcome of the optimization hypothesis thereby offering more transferability across plant functional types than empirical approaches, at least if the plant is operating its stomata optimally Hari et al., ; Katul et al., 9,. Although the behavior of g s to environmental stimuli are well described by both model classes, any general responses at the canopy scale can be obscured by highly inhomogeneous foliage distribution, complex wind and radiation fields, as well as the irregular variation in the mean atmospheric CO concentration within the canopy volume. The links between the responses of g s to variations in its local environment as described by these two model classes and the canopy scale processes including scalar fluxes and mean scalar concentration distribution within the canopy is explored. Three inter-related questions, labeled Q. Q., frame the scope of this exploration: Q. How sensitive are the modeled vertical CO and H O sink/source distributions, scalar fluxes, and mean ambient scalar concentrations within the canopy to the two commonly used model classes of g s? Q. How well do the up-scaled scalar fluxes compare against measured whole-canopy fluxes if only shoot-scale measurements are available and, in particular, how do models based on the optimality principle contrast against semi-empirical descriptions? Q. What are the effective properties of a big-leaf representation of this eco-system and how do they relate to the shoot-scale measurements? Q. is a generalization of a recent effort by Schymanski et al. 7, 8, who explored it in the context of H O and CO fluxes without considerations to predicted mean scalar concentration profiles used here as additional independent measures to evaluate the skill of the model. These three questions are addressed by combining a leaf photosynthesis model Farquhar et al., 98 and four commonly used descriptions of g s at the leaf scale, as recently done in Katul et al.. The up-scaling from leaf to canopy is carried out by incorporating a layer-resolving light attenuation model and a closure model for turbulent fluxes within the canopy air space, both dependent on the vertical leaf area density distribution. The parameters of the leaf-level photosynthesis and stomatal control models are independently inferred from leaf- and shoot-scale gas exchange measurements. The turbulent closure scheme and light attenuation model are tested against detailed velocity and radiation profiles collected in a Scots pine forest located at the SMEAR II-station in Southern Finland Vesala et al., ; Hari and Kulmala, 5; Launiainen et al., 7. The novelty of the present approach is that it deconstructs the predictive skills within and between-model variability using two scalars CO, H O and turbulent scalar fluxes as well as mean scalar concentration profiles. The advantages of including the scalar concentration profiles in such comparisons are generally attributed to the high vertical resolution that far exceeds those of eddy-covariance EC measurements within canopies. Hence, these measurements do serve as independent checks on how well the CO and H O source/sink distributions within the canopy are reproduced. The full scale-independency is retained by assessing the model predictions against independent EC and mean scalar concentration profile measurements noting that the physiological parameters are also independently inferred at the shoot-scale.. Theory The up-scaling from leaf to canopy using the mean scalar continuity equation and physiological principles that include the four g s models are considered next. The abbreviations used in the equations are listed in Table... The CO budget within a canopy layer For a stationary and planar homogeneous high Peclét number flow in the absence of subsidence, the one-dimensional mean CO continuity equation reduces to w c z z = S c z, where w c is the turbulent flux of CO, overbar represents and planar averaging Raupach and Shaw, 98; Finnigan,, primed quantities represent excursions from this space- average, S c is the mean uptake or emission rate sink or source strength of CO from the foliage at layer z, and z is the vertical direction with z = being at the forest floor. Representing the turbulent flux by first order closure principles results in w c z = K t z c az, z where K t is the turbulent diffusivity for CO, and c a is the mean atmospheric CO concentration. The necessary conditions for the application of such closure scheme inside canopies are discussed within the context of predictions from second and third - order formulations in Juang et al. 8 and Bash et al.. Assuming Fickian diffusion from the atmosphere into the leaf intercellular pores results in an expression for S c given by Katul et al., ci z S c z = azg s zc a z c a z, where az is the leaf area density, g s is the total leaf conductance, which is dominated by stomatal regulation vis-à-vis aerodynamic and mesophyll conductance, and c i is the mean intercellular CO concentration. Defining Rz = c i z/c a z so that S c z = az [g s z Rz c a z] and combining Eqs. and results in a homoge-

3 674 S. Launiainen et al. / Agricultural and Forest Meteorology Table List of abbreviations excluding those used only in Appendixes. Abbreviation Variable Value/units Source/reference z Height above ground m h Canopy height 5 m LAI Leaf-area index m m az Leaf area density m m Launiainen et al. 7 a c Ratio of molecular diffusivity of H O to CO in air.6 Campbell and Norman 998 g s Leaf-scale stomatal conductance mol m leaf s G s Big-leaf conductance mol m ground s Eq. 7 A max Light-saturated assimilation rate mol m leaf s A can Net canopy assimilation mol m ground s Eq. 8 S cz The net uptake S c < or emission of CO from the foliage at layer z mol m leaf s f c Net shoot CO flux mol m leaf s f e Shoot transpiration mol m leaf s Canopy net CO flux mol m ground s Canopy latent heat flux W m ground E s Soil evaporation W m ground R soil Soil respiration m olm ground s Soil chambers Pumpanen et al., R stem Trunk and branch respiration mol m ground s Kolari et al. 9, Hölttä and Kolari 9 R Trunk respiration at reference temperature C mol m trunk s Kolari et al. 9 Q Temperature sensitivity of trunk respiration Kolari et al. 9 WUE Water use efficiency leaf or canopy scale mol CO /mol H O Q p Photosynthetically active radiation mol m ground s Measured above the canopy at m height Uz Mean horizontal wind speed m s u * Friction velocity at highest grid-point m s Eddy-covariance,. m height w c z Turbulent vertical flux at height z l Mixing length m Appendix A K mz Turbulent eddy diffusivity for momentum m s Appendix A K tz Turbulent eddy diffusivity for scalars m s Appendix A S N Turbulent Schmidt number, K m/k t Appendix A c a Ambient CO mixing ratio ppm c i Internal CO mixing ratio ppm S Long-term mean c i /c a ratio in linearized optimality model Eq Shoot chambers, Appendix B e a Ambient H O mixing ratio mmol mol e i Leaf internal H O mixing ratio mmol mol D Ambient vapor pressure deficit, e st a e a kpa or mol mol D Ts True vapor pressure deficit, e st s e a kpa or mol mol RH Ambient relative humidity T a Air temperature C T s Leaf temperature C T stem Trunk temperature C Volumetric humus moisture content m m MLM Multi-layer model BB Ball Berry model Eq. a, Ball et al. 987 Leu Leuning model Eq. b, Leuning 995 Opti Optimal stomatal control model Eq. 4, Katul et al. 9 OptiL Linearized optimal stomatal control model Eq. 5, Appendix B neous second-order ordinary differential equation for the mean CO concentration given by Siqueira and Katul, c a z + Kt c a K t z z + az g s R c a = 4 Invoking first-order closure principles for momentum transfer see Appendix A and using a mixing length hypothesis leads to Harman and Finnigan, 7, K t = S N l U z, 5 where S N is the turbulent Schmidt number defined as the ratio of momentum to scalar turbulent diffusivities and need not be unity inside canopies, U is the mean velocity, and l is the effective mixing length. These first-order closure results link the mean momentum and mean scalar concentration budgets via c a z + U/ z U/ z ca a z z + gs R c a = 6 K t To solve Eq. 6 for c a at a given layer inside the canopy, additional equations describing the vertical variations of g s and R or c i /c a must be formulated from leaf-gas exchange principles considered next... Leaf- gas exchange principles As noted earlier, mass transfer of CO and H O through leaves i.e. expressed in m of leaf area occur via Fickian diffusion: f c = g s c a c i f e = a c g s e i e a a c g s D 7 where f c and f e are the CO and H O fluxes from the leaf surface i.e. S c z = azf c, a c =.6 is the relative molecular diffusivity of water vapor with respect to carbon dioxide in air, e i is the intercellular and e a the ambient water vapor mixing ratio and D is the vapor pressure deficit representing e i e a when the leaf is wellcoupled to the atmosphere. Furthermore, when leaf respiration is small with respect to f c and the mesophyll conductance is much larger than the stomatal conductance, the biochemical demand for CO is described by the Farquhar photosynthesis model given by Farquhar et al., 98: f c = a c i c p, 8 a + c i where c p is the CO compensation point, a and a are coefficients whose values depend on whether the photosynthetic rate is restricted by electron transport or Ribulose bisphosphate

4 S. Launiainen et al. / Agricultural and Forest Meteorology RuBP carboxylase or Rubisco. Under light-saturated conditions, a = V c,max maximum carboxylation capacity and a = K c + C oa /K O, where K c and K o are the Michaelis constants for CO fixation and oxygen inhibition, and C oa is the oxygen concentration in air. When light is limiting, a = pe m Q p = Q p and a = c p, where p is the leaf absorptivity of photosynthetically active radiation Q p, e m is the maximum quantum efficiency of leaves and is the apparent quantum yield determined from empirical light-response curves. Hence, expressed in terms of leaf stomatal conductance, g s, Eqs. 7 and 8 can be combined to yield the following leaf-level expressions: c i = c a + a a g s + f c = and a + a + c ag s a + a c a g s + 4g s a c p + a c a g s g s c a 9 a + g sa c a + 4g sa c p + a c ag s. These expressions do not assume any functional relationship for g s with its local environment. They show how f c and c i can be predicted from g s if c a and the physiological attributes of the leaf a, a, and c p are known or can be inferred from the local light regime and temperature. Eq. also shows that f c is non-linearly related to g s, with a convexity that is necessary for optimality solutions to exist as discussed later... The closure problem at the leaf scale semi-empirical formulations for stomatal conductance To mathematically close Eqs. 9 and, an independent formulation for g s is needed so that f c and c i can be computed. The so-called Ball Berry Ball et al., 987 and the Leuning 995 formulations can be used for such closure schemes in multi-layer biosphere-atmosphere models Baldocchi and Meyers, 998; Lai et al., ; Siqueira and Katul, ; Juang et al., 8. These formulations are, respectively: g s = m c a c p f c RH + b ; a and g s = m c a c p f c I LEU D + b ; I LEU D = + D D o b where RH is the mean air relative humidity, I LEU reflects the sensitivity of the stomata to vapor pressure deficit, D o is a vapor pressure deficit constant, and m, m, b, and b are empirical fitting parameters slope and residual conductance, respectively. Eqs. a and b provide the necessary mathematical closure i.e., three equations and three unknowns: f c c i and g s if c a, a, a, and c p are known. The formulations in Eqs. a and b assume a priori that g s is linearly related to f c /c a c p, a result that is supported from a large number of experiments e.g. Palmroth et al., 999. However, Eq. already suggests that a linear relationship between g s and f c can only be approximate..4. An optimality model An alternative formulation to Eqs. a and b can be derived from an optimality principle, originally proposed by Cowan 977 and Givnish and Vermeij 976 and retained in the work by Cowan and Farquhar 977, Hari et al. 986, Berninger and Hari 99, and more recently by Konrad et al. 8, and Katul et al. 9,. Assuming each leaf is autonomous, an objective function to be maximized at the leaf scale can be defined as f g s = f c f e = a + a + c a g s a + g s a c a + 4g s a c p + a c a g s a c g s D where Eq. was used to determine f c and Eq. 7 was used to determine f e. The premise here is that stomata regulate their aperture so as to maximize the carbon gain while minimizing water loss in units of carbon for a leaf specific cost parameter note that the notation by Hari et al. 986 is used here instead of the original notation proposed by Cowan and Farquhar, 977. Provided d/ << fe /f e, the g s that maximizes this objective function can be determined from f g s / g s = i.e., f g s is an extremum guaranteed to be a maximum given the expected convexity of f g s with respect to g s in Eq.. The optimization problem framed in Eq. does not a priori assume any functional response of g s to D or RH nor does it assume a priori any linear dependence between g s and f c /c a c p as in the case of Eqs. a and b. Instead, it assumes that excessive water losses can induce stomatal closure, which is consistent with the experimental findings of Mott and Parkhurst 99 who, using a helox gas medium, demonstrated that stomata appear to respond to transpiration rates rather than measures of air humidity. Differentiating Eq. with respect to g s results in Katul et al., f g s g s = a c D a + c a + a a + c a c p g s a + c a a + a c a g s + 4g s a c p + a c a g s. When setting f g s / g s = and solving for g s, we obtain: g s = a a c a + c p a + c a a c Da c a c p a +c p a +c a a c D a +c a a c D + a c Da +c a. a +c a a c D 4 This g s formulation is explicit in relating conductance to c a and D. However, unlike the empirical formulations in Eqs. a and b, both relating g s to the photosynthetic rate leaving two Ball Berry or three Leuning formulation unknown parameters, this formulation relates conductance to the three parameters of the photosynthesis model and leaving only one unknown physiological parameter related to conductance. Moreover, the model formulation in Eq. 4 suggests that cannot be entirely free and must be bounded to ensure real and positive conductance Katul et al.,. Linearizing the biochemical demand function in Eq. 8 results in a much simpler and insightful model for the optimal g s, f c, and subsequently c i given as see Appendix B for discussion g s = a + a + sc a [ f c = a c a c p a + sc a c i c a = c a c p a c D a c D c a c p a c D ca c p. c a c a ] 5

5 676 S. Launiainen et al. / Agricultural and Forest Meteorology Table Photosynthesis model and stomatal control model parameters. All values are given per projected leaf area. Abbreviation Variable Value Units Source V cmax,5 Maximum carboxylation velocity at 5 C C exp[ha/rt V cmax V T /T] c max,5, C = +exp[svt H d /RT]] + exp [S vt H d /RT 7 pine, understory mol m leaf s Wang et al. 996, Kolari et al. 6 mol m leaf s Wang et al. 996 p Absorptivity of leaves for PAR.8 Campbell and Norman 998 Apparent quantum yield.4 pine molco mol PAR Ciras- measurements pine, Kolari et al understory r d,5 Dark respiration at 5 C mol m leaf s Collatz et al. 99 r d,5 =.5V cmax,5 r d r d = mol m leaf s Wang et al. 996 exp /RT r d,5 exp /R 98.5 K c Michaelis Menten constant for 46 ppm Aalto 998 CO fixation K o Michaelis Menten constant for, ppm Aalto 998 oxygen inhibition C oa Oxygen consentration in air, ppm Aalto 998 c p CO compensation point ppm Campbell and Norman 998 Coa c p =.6 exp[.56 T T ] D o Vapor pressure deficit constant in Leuning model Eq. b. kpa Shoot chambers T Scaling temperature 5 C Campbell and Norman 998 m Slope in Ball Berry model Eq. Shoot chambers a m Slope in Leuning model Eq. Shoot chambers b b, b Residual conductance for CO. mol m leaf s Shoot chambers Eqs. a and b, LI Marginal water use efficiency molco mol H O Shoot chambers cost parameter for non-linear and linear optimality model, respectively a Coefficient of Farquhar-model mol m leaf s Eq. 8 a Coefficient of Farquhar-model ppm Eq. 8 The g s expression here is similar to the one in Hari et al Hereafter, we refer to the solution in Eq. 4 as the nonlinear model denoted by Opti and the result in Eq. 5 as the linear model OptiL. Eq. 5 reproduces a number of known stomatal responses documented across many species. For example, when expressed as g s /g s,ref with g s,ref defined as g s for D =. kpa, Oren et al. 999 found that g s /g s,ref = m o logd with m o [.5,.6]. Katul et al. 9 showed that OptiL is mathematically equivalent to this empirical formulation across a wide range of D values. Moreover, when increases linearly with c a i.e. = o c a /c o, where c a is a reference CO concentration at which o is known to have acclimated to, Eq. 5 can be re-arranged so that g s = fc D. 6 a c c a c p o This result shows that the assumed linear relationship between g s and f c /c a c p in Eq. a and b for the Ball Berry or the Leuning models is an outcome of OptiL. Moreover, it shows that there is a one-to-one mapping between OptiL and the Leuning 995 model of Eq. b when I LEU D = D / and b resulting in m = a c o /. In other words we do expect m to be inversely correlated with / in the OptiL framework. For the calculation of a, the vertical attenuation of photosynthetically active radiation and the estimation of the fraction of sun and shaded leaves at various depths within the canopy are needed and discussed in Appendix C. The gas-exchange calculations were performed separately for sunlit and shaded leaves to yield weighted averages at each layer. Here after, we refer to this combined radiative turbulence closure physiological conductance biosphere atmosphere transfer scheme as multi-layer model MLM..5. Effective big-leaf representation using MLM To derive the effective parameters of the big-leaf representation of ecosystem level fluxes from MLM, an integrated big-leaf conductance G s and c i /c a ratio are computed using the approach of Lai et al.. We assume that D does not vary appreciably within the canopy volume when compared to the light environment and thus G s for CO transport is G s = h azg s zdz, 7 where g s is given by the leaf-level solution derived by coupling the Farquhar photosynthesis model, Fickian diffusion, and one of the four stomatal conductance models described in previous section. Similarly, the net canopy assimilation A can is A can = G s c a h = h [ ] ci c a eff = h S c zdz [ ci ] z azg s zc a z dz, 8 c a z

6 S. Launiainen et al. / Agricultural and Forest Meteorology where c a h is the ambient CO mixing ratio at canopy top h. With G s inferred from Eq. 7, the c i /c a ratio characteristic for the big-leaf canopy is h azg s zc a z c i z/c a zdz ci =. 9 c a eff G s c a h How G s and the big-leaf c i /c a eff vary with environmental stimuli will be discussed using above formulations in the context of Q az Q p z/q p h. Measurements and model parameterization.8 The leaf-photosynthetic and stomatal conductance model parameters required in the MLM were determined using shoot gasexchange measurements conducted in a Scots pine Pinus sylvestris L. stand. This stand was sown in 96 and is currently serving as one of the long-term flux-monitoring sites SMEAR II station in southern Finland 6 5 N, 4 7 E, 8 m above sea level. In 6, the main canopy was characterized by the following: total leaf area index LAI 6.5 m m, stand density 4 ha, the mean tree height h 5 m and the mean diameter at breast height 6 cm. The forest floor vegetation is relatively low mean height.. m but dense total LAI.5 m m and is dominated by dwarf shrubs, mainly lingonberry Vaccinium vitis-idaea, blueberry V. myrtillus, and mosses Kolari et al., 6; Kulmala et al., 8... Leaf-level physiological measurements Photosynthetic parameters: The parameters a, a, and c p were taken either from the literature or defined using shoot-level gas-exchange measurements made at the site Table. The photosynthetic light response of the Scots pine was estimated from needle gas-exchange measurements. In July 6, shoot gas exchange measurements were made at different levels shading conditions in the canopy using a portable photosynthesis measuring device CIRAS-, PP Systems, Hitchin, UK. Apart from the irradiance, the conditions within the measuring cuvette were kept close to the ambient conditions. The quantum efficiency, per projected leaf area was determined by a non-linear regression fitting of a rectangular hyperbola Michaelis Menten-equation to each of the measurements and then averaged to obtain a representative value to be used in computing a from Q p z. The maximum carboxylation velocity V cmax, 5 and its temperature dependency is taken from Wang et al. 996 Table. The light response of the main forest floor species were measured in a previous study Kolari et al., 6. We use their biomass-weighted averages as an effective value in the MLM for ground vegetation. They reported values of the light-saturated assimilation rate A max instead of V cmax, 5, but we approximated the latter by A max Leuning, 997. Stomatal conductance parameters: The necessary parameters for the four leaf-scale g s models were determined using continuous shoot gas exchange chamber measurements Table. Two chambers, acrylic plastic boxes with a volume of dm, are located in the upper part of the canopy.9 h and open most of the thereby exposing the shoot in the chamber to ambient conditions. To measure the gas exchange, the chambers were closed 7 s a day for min. The details of chamber measurements are described in Hari et al. 999 and are not repeated here. The shoot-level g s parameters were estimated as follows: First, all the available chamber data in dry day conditions Q p > mol m s and RH < 9% were pooled together and the Ball Berry and Leuning model parameters Eqs. a and b, respectively were deter az/a max, Q p z/q p h Fig.. Profiles of normalized leaf area density, az, and radiation attenuation Q p. The circles with horizontal bars represent measured profiles mean ± Std based on Vesala et al.. mined using linear least square regression i.e. regressing g s against f c /c a c p. Then, the intercepts b, b and D o for Leuningmodel were fixed to their long-term mean values and the slope estimation was done separately for each measurement solving m and m from Eq.. We further averaged these to obtain daily values. Similarly, the average cost parameter was estimated from measured shoot water use efficiency WUE by regressing WUE against D / and solving for from the slope of the expression WUE = f c = c a f e [ = c i c a a c D ca c p a c = c a a c D ] a c D ca c p c a c a D /. In this computation, c a and c p were taken equal to their mean values over the period. Several studies have indicated that is nearly constant during a day whereas optimality can be achieved at longer scales only if varies as a response to changing environmental conditions, drought stress in particular Mäkelä et al., 996; Schymanski et al., 8; Manzoni et al.,. Therefore, we determined the temporal variability of as in Katul et al., their Eqs. 7, which included several approximations: First, in abundant light Q p > 6 mol m s the photosynthesis is Rubisco-limited and the parameter a V cmax in the Farquhar model Eq. 8. Second, we assumed that a and a follow their generic temperature dependencies, and c p is only a function of temperature Table. Using these simplifications, a can be solved for each gas exchange measurement by inverting Eq. 8. Finally, inverting Eq. 4 or Eq. 5 when determining LI from the linearized optimality model provides instantaneous. Also was further averaged to daily mean values to be used in MLM.

7 678 S. Launiainen et al. / Agricultural and Forest Meteorology g s mol m s a g s =. m =6.89 R =.88 g s mol m s b g =. m =6.46 D o =. R =.84 WUE mol CO mol H O.5..5 c λ =.9x...5. A n /C a C p *RH.5. A n /C a C p *+D/D o 5 5 D / kpa / d 8 7 e 7 x 6 5 f m m 5 4 λ LI DOY 6 8 DOY 6 8 DOY Fig.. Inferred shoot-scale parameter values for Ball Berry a and d, Leuning b and e and linear optimality models c and f. Top: data from days 5 pooled together, the dots and circles represent data from the two shoot chambers. Bottom: daily averaged slopes m, m and LI. Shoot gas-exchange data during days 79 9 was missing because of gas-analyzer malfunction. The vertical dashed line in d f represents end of the period considered in the latter analysis... Boundary conditions for the MLM The upper boundary conditions values at the highest layer above the canopy are based on series of half-hourly averaged friction velocity u * m s, measured by EC at. m height, ambient CO mixing ratio c a, ppm, atmospheric pressure P, kpa, air temperature T a, C, air relative humidity RH, % and diffuse and direct PAR Q p, mol m s determined from measurements made above the canopy. Instruments and details of the data acquisition are described elsewhere Hari and Kulmala, 5; Vesala et al., 998. During the model runs, T a and ambient RH and D were assumed to be vertically uniform within the canopy each / h thereby eliminating the need for a full leaf energy balance. This assumption is justified for the range of air temperatures considered here. Moreover, in this geographic region, the leaf satisfies its carbon demand first thereby incurring a concomitant water loss, with leaf temperature being a by-product via the leaf energy balance of these carbon uptake priorities. In other words, we are assuming here that g s is not operating to control the temperature status of the leaf. Moreover, measured mean air temperature and H O concentration profiles suggest that the vertical variability in D is about.5 kpa and hence does not exceed 5% in typical conditions within the stand. The woody biomass R stem and soil R soil respiration, and soil evaporation E s provide the necessary boundary conditions on the scalar budgets. The R soil was taken from the automated soil chamber measurements Pumpanen et al.,. The modeled stem respiration was computed as Kolari et al., 9: R = R Q T / where R =. mol m s is the base respiration rate at C per unit trunk area in July and Q the temperature sensitivity during typical June August. The stem temperature lags air temperature and was approximated as dt stem dt = T a T stem where is a constant estimated to be 4 h and discussed elsewhere Kolari et al., 9. The obtained R stem per m of stem surface area was scaled to per m ground area by multiplying it by

8 S. Launiainen et al. / Agricultural and Forest Meteorology BB Leu OptiL Opti.6.4 a.6.4 b.6.4 c A n μmolm - s - - S c μmolm - s g s molm - s d.6.4 e.6.4 f c/c i a μmolm - s Wm g.6.4 h.6.4 i WUE x - mol CO /mol H O C a ppm H O ppth Fig.. Within-canopy day 8: 8: profiles of a assimilation rate A n, b CO sink/source S c, c stomatal conductance of CO g s, d ratio of leaf internal to ambient CO c i /c a, e CO flux profile, f latent heat flux profile, g water use efficiency WUE, h ambient CO mixing ratio c a and i ambient H O mixing ratio. For reference, the leaf area density az dashed line is superimposed in panels a c, and measured canopy scale fluxes mean ± Std and concentrations mean ± S.E. are given. Only periods when the canopy was dry are included. the total stem and branch surface area.5 m m. The vertical distribution of R stem was based on measurements reported by Hölttä and Kolari 9. The CO efflux from the stem roughly scales with az in the crown peaking where az is at its highest value. The R stem below the foliage layer is roughly / of the maximum value. The E s was modeled assuming equilibrium evaporation e.g. Jarvis and McNaughton, 986 driven by radiation load computed at the forest floor. However, when the measured volumetric humus water content was below saturation, E s was reduced linearly with the decreasing water content... Canopy-scale flux and concentration measurements model evaluation data The MLM fluxes and corresponding mean scalar concentration profiles are compared against fully independent canopy-scale measurements made at the site. Continuous EC measurements of CO

9 68 S. Launiainen et al. / Agricultural and Forest Meteorology BB Leu OptiL Opti g s molm - s a.97 h f c μmolm - s b.97 h c/c i a c.97 h g s molm - s d.8 h f c μmolm - s e.8 h c/c i a f.8 h g s molm - s g.6 h f c μmolm - s h.6 h c/c i a i.6 h g s molm - s j.5 h f c μmolm - s k.5 h c/c i a l.5 h Fig. 4. Predicted stomatal conductance of CO g s, left and leaf net CO exchange f c, middle and c i /c a right at various levels within the canopy h = 5 m. All values are given per unit leaf area. and latent heat fluxes were carried out at.,.7 and. m.55,.78 and. s h, respectively using closed-path analyzers LI-66 and LI-7, Li-Cor Inc., Lincoln, NE, USA and the/ h average fluxes were calculated according to the standard FluxNet methodology Aubinet et al., and corrected for storage below the measurement height to allow comparison for night conditions. The details of the EC-measurements both above and below the canopy can be found in Launiainen et al. 5, 7 and Launiainen and are not repeated here. The ambient mean concentrations of CO and H O were measured at.6., 6.8, 8.4 and 4. m heights and are described in Rannik et al Model calculations The MLM was run for the period of st of June th of August, 6. The results were derived as follows: The canopy was first divided into horizontal layers and the radiative environment at each layer was solved. Second, initial guesses for the combined assimilation stomatal conductance transpiration were computed separately for sunlit and shaded leaves at each layer, assuming a constant c a and D profile values set to the measured ones above the canopy for each / h period. Then, the turbulent closure scheme was applied and the vertical c a profile following

10 S. Launiainen et al. / Agricultural and Forest Meteorology a y=.94 x.9, R =.8 5 b y=.96 x.47, R =.84 BB μmolm s 5 5 Leu μmolm s 5 5 EC μmolm s EC μmolm s 5 c y=. x.87, R =.84 5 d y=. x.66, R =.84 OptiL μmolm s 5 5 Opti μmolm s 5 5 EC μmolm s EC μmolm s Fig. 5. Comparison of measured abscissa and modeled ordinate / h average net CO exchange. The linear least-squares regression equation and proportion of explained variance R are given for comparison. The squares represent afternoon : 7: values and the dashed line gives : relationship. Only periods when the canopy was dry are included. from the sink/source distribution was calculated and then used to refine estimates on the f c, g s and f e iteratively. The iterations were continued until the results converged. Convergence was defined as the maximum difference between two successive iterations to be within.% for all the state variables and across all the layers. Within each iteration, the semi-empirical g s models Eq. were also solved iteratively while the two optimality models do not require any further iterations given their analytical form Eqs. 4 and 5, a decisive advantage in such model applications. For consistency between g s predictions of the optimality models and Ball Berry Leuning, the dark respiration r d was neglected when the f c to g s -relationship was iteratively optimized ; thus, r d was taken into account only in the sink/source profiles and neglected as the leaf s internal CO source. 4. Results and discussion Prior to addressing Q. Q., the environmental conditions above the canopy during the experiment period are first discussed. Next, the shoot-scale parameters and their daily variation reflecting the physiological states as computed from the shoot-scale gasexchange are presented. With these results, the predictions from the four leaf-level stomatal control models are integrated into MLM and compared against independently measured canopy-level mean scalar concentration and turbulent flux data. Note that the four versions of the g s models only differ in their canonical responses to humidity or vapor pressure deficit. Hence, differences among models in terms of canopy-scale predictions fingerprint the role of stomatal controls and any concomitant two-way coupling between the leaf and its micro-environment. All model versions significantly overpredicted the canopy scale gas exchange in August when drought stress was strongest, which hints that down-regulation of the photosynthetic capacity had occurred. Therefore, the analysis of MLM results are restricted to period during which the photosynthetic machinery was not significantly mediated by drought st June st July. 4.. Environmental conditions The growing season of 6 was very dry in Southern Finland; the cumulative precipitation from June to August was only about half of the typical 5 mm long-term value. Consequently, volumetric soil moisture content decreased from.4 m m in early June to. m m at end of July. The stand showed clear signs of drought stress in late July and during first half of August, manifested in leaf- and canopy scale reductions of photosynthesis, transpiration and also decreased rates of the decomposition of organic matter Duursma et al., 8; Kolari et al., 9; Launiainen,. The period of progressing drought provides a rather unique possibility to explore the stomatal control theories for a wide range of hydroclimatic conditions occurring in a boreal Pine forest. During the period of this study, air temperature varied between and 8 C and typical diurnal amplitude was 8 C. The first week of June was cooler and T a remained below 5 C. The diurnal amplitude of D was on the order of.5 kpa providing sufficient stimuli for stomatal opening and closure.

11 68 S. Launiainen et al. / Agricultural and Forest Meteorology a y=.75 x +., R =.76 5 b y=.89 x +.5, R =.78 BB Wm 5 Leu Wm EC Wm EC Wm 5 c y=. x + 7.8, R =.77 5 d y=.9 x + 9., R =.7 OptiL Wm 5 Opti Wm EC Wm EC Wm Fig. 6. Comparisons between measured abscissa and modeled ordinate / h latent heat fluxes above the canopy. The linear least-squares regression equation and proportion of explained variance R are given for comparison. The squares represent afternoon : 7: values and the dashed line gives : relationship. Only periods when the canopy was dry are included. 4.. Radiation attenuation and leaf-level parameters Because within-canopy radiation is needed to infer a, a brief validation of the radiation attenuation model used is presented here. Fig. shows the leaf area density profile and the light regime and demonstrates good agreement between measured and modeled Q p throughout the canopy. The measurements were conducted during one clear and one cloudy day from : to 6: in late June of 998 using a multi-point sensor system 48 sensors each level described in Vesala et al.. The measured az was not available for that 998 period and in the model data comparison here, the shape function of az was assumed to be stationary and only h was adjusted for the recorded changes from in 998 to 5 m in 6. The stand was partly thinned in Vesala et al., 5 but in 6 the leaf area index had recovered to its 998 level. The quantum yield estimated from shoot gas-exchange measurements was nearly constant.4 ±. mol mol, mean ± Std irrespective of the shading conditions the shoot had acclimatized to. The light-saturated assimilation A max at the needle level showed marked difference between the lightshoots 7.6 ±.4 mol m s, mean ± Std and shoots growing in shaded conditions 4.7 ±. mol m s in the lower canopy the degree of shading was determined from hemispherical photographs but the difference was statistically non-significant p >.5 justifying the use of uniform photosynthesis parameters for this Scots pine canopy. The average matches the values in Palmroth and Hari measured in June. However, they found higher.54 in July, a similar value to the one.57 reported in Leverenz 987 for Scots pine. The stomatal conductance parameters were determined from linear regression analysis for all models as described in Section. and the results are shown in Fig.. There was distinct temporal Fig. d and e and shoot-to-shoot variability both in m and m. As a response to a progressive drying of the soil, increased and m and m decreased significantly during the last weeks of the experiment when decreased below. m m not shown. The similarity in the temporal courses of and m is expected given their unambiguous dependency as earlier discussed Eq. 6. In contrast, there was no significant correlation between m and m for the same period. The marginal water use efficiency determined from OptiL, LI, was 7% higher than the obtained from the non-linear model R =.98, in qualitative agreement with Katul et al. in a Loblolly pine stand in the Southeastern U.S. 4.. Addressing Q. To address Q., modeled scalar sources, fluxes and mean concentration profiles are considered in detail followed by a direct comparison between the aggregated and eddy-covariance measured canopy-level fluxes. In addition, differences between the models and the measurements are discussed. Fig. shows the ensemble-averaged day canopy profiles between 8. and 8.. The net leaf CO exchange f c profile Fig. a shows rapid

12 S. Launiainen et al. / Agricultural and Forest Meteorology μmolm s Wm a +/ σ EC EC BB Leu OptiL Opti b Fig. 7. Ensemble diurnal variation of canopy-scale fluxes: a CO -flux and b latent heat flux. The grey dots and shaded area represent the above-canopy eddy-covariance data mean ± Std. Only dry-canopy conditions are included. decrease in photosynthesis rates per leaf area below z =.8 h. Within the pine canopy, the f c decrease more than by a factor of two in all models, while Q p is reduced by a factor of 5 Fig.. The kink closest to the ground results from the higher quantum efficiency of the shade-adapted forest floor vegetation. When f c is multiplied by az and R stem is taken into account, the vertical canopy source/sink distribution of CO can be computed and is shown Fig. b. The Ball Berry model and the linear optimality model predict the lowest and highest f c at all levels, respectively. This is caused by differences in g s and consequently the c i /c a Fig. c and d between the models. The g s of OptiL is significantly higher throughout the canopy than predicted by other models and thus the modeled c i /c a ratio becomes fairly invariant with height. The shapes of g s, f c and c i /c a profiles predicted by OptiL and Leuning models are close to each other but OptiL predicts higher g s, f c and c i /c a at each height. The vertical gradient of g s is strongest in the non-linear optimality model, which predicts that g s decreases by a factor of. between the uppermost and lowermost shoots while all other models estimate a reduction factor of.9.. In addition, the most striking difference is that non-linear optimum model predicts the opposite curvature of the c i /c a ratio inside the pine canopy. In contrast, the other formulations predict increased c i /c a when descending deeper into the canopy volume. Recall that the nonlinear model is the only model that does not assume or produce a linear dependence between g s and f c. The increase in c i /c a with depth inside the canopy is however what can be expected based on carbon isotope data presented in the literature. For instance, Ellsworth 999, explored c i /c a ratios in Loblolly pine Pinus taeda and found that it varied between.66 and.75, the latter measured in the shaded shoots in the lower canopy. Despite these differences, the flux profiles i.e. scalar flux at each height represents the net effect of the sources and sinks per m ground below the height of interest behave consistently and compare well with the EC data Fig. e and f. The forest floor contributes, in an ensemble sense, about % of the canopy scale photosynthesis despite the fact that it represents some % of the total LAI. This MLM estimate is similar to what was reported by Kolari et al. 6 who concluded that forest floor GPP was % of the stand GPP during the period from th of April to November th in. All the models overpredicted the ensemble averaged canopy net CO exchange by.5.9 mol m s 6 % of the measured. The crown and trunk-space EC measurements were well matched Fig. e. During nocturnal conditions, the ensembles of measured and modeled were rather well balanced average difference <. mol m s indicating that the respirative components were adequately described in the model and thus the mismatch of day fluxes was mainly due to assimilation rates. Because of the assumption of a depth-constant D set to its value above the canopy, the water vapor sources are simply slaved to the carbon fluxes and modeled as the leaf conductance profile multiplied by az and D. Hence, the models predicting highest g s also resulted in highest water vapor fluxes, shown here in terms of latent heat flux f e, Fig. f. In relative terms, the combined understory transpiration and soil evaporation was 7 9% of the stand-scale values, slightly less than the fraction % measured by the EC systems. The correspondence between the ensemble averaged ECdata and MLM results was encouraging considering that the models were only calibrated with the shoot chamber data independent of any canopy level mean concentration or EC flux measurements. The water use efficiency profiles show highest WUE at the top, ranging from 4.8 to 5.8 mol CO mol H O followed by estimates of the order of 5 4 drop within the crown indicating that assimilating a unit of CO becomes more uneconomical in terms of water loss deeper in the canopy Fig. g. Again, the non-linear optimum model is an exception and predicts strong WUE increase within these canopy layers. At the shaded forest floor, the higher quantum efficiency enhances f c per leaf area and WUE becomes comparable to its upper canopy value except for Opti. The various stomatal closure schemes only resulted in minor differences for ambient mean scalar concentrations. The predicted c a and H O profiles Fig. h and g show rather good agreement with the measured concentrations considering the small scalar gradients caused by strong mixing during day. Although the MLM assumes the photosynthesis and stomatal conductance model parameters remain uniform with height within the canopy, the importance of stomatal control on regulating f c diminishes deeper inside the canopy Fig. 4. The fraction of sunlit foliage degreases rapidly in the crown and the transition from primarily temperature to light limited assimilation occurs accordingly. Thus, in the deeper layers, the diurnal pattern of g s becomes more symmetrical since any alteration in Q p creates a linear change in f c thereby explaining the lesser WUE in the lower canopy predicted by the majority of the g s -schemes. Because of the compensating effects of c i, the diurnal patterns of f c are more symmetrical during the day than those of g s. The fingerprint of stomatal regulation is hardly visible in g s below.6 h. A notable difference is that the non-linear optimality model predicts smaller g s during the morning