Parameterization of a coupled CO 2 and H 2 O gas exchange model at the leaf scale of Populus euphratica

The following two models were combined to simultaneously predict CO 2 and H2O gas exchange at the leaf scale ofPopulus euphratica : a Farquhar et al. type biochemical sub-model of photosynthesis (Farquhar et al., 1980) and a Ball et al. type stomatal conductance sub-model (Ball et al., 1987). The photosynthesis parameters [including maximum carboxylation rate allowed by ribulose-1,5bisphosphate carboxylase/oxygenase (Rubisco) carboxylation rate (Vcmax), potential light-saturated electron transport rate (Jmax), triose phosphate utilization (TPU) and day respiration (Rd)] were determined by using the genetic algorithm (GA) method based on A/Ci data. Values of Vcmax andJmax standardized at 25 C were 75.09±1.36 (mean± standard error), 117.27±2.47, respectively. The stomatal conductance sub-model was calibrated independently. Prediction of net photosynthesis by the coupled model agreed well with the validation data, but the model tended to underestimate transpiration rates. Overall, the combined model generally captured the diurnal patterns of CO 2 and H2O exchange resulting from variation in temperature and irradiation.


Introduction
Recently, simultaneous estimations of CO 2 and H 2 O gas exchange coupling the Farquhar et al. (1980) type biochemical model of photosynthesis and the Ball et al. (1987) type stomatal conductance model have been reported in many articles Correspondence to: G. F. Zhu (syh@lzb.ac.cn) (e.g.Tenhunen et al., 1990;Collatz et al., 1991;Harley et al., 1992;Leuning, 1995;Sellers et al., 1996;De Pury and Farquhar, 1997;Baldocchi and Meyers, 1998;Wilson et al., 2001;Kosugi et al., 2003;Kim and Lieth, 2003).Although combined models have become an important tool for understanding the CO 2 and H 2 O gas exchange at both the leaf and canopy scales, the parameterization of these models is still insufficient and further studies of the variations in the parameters of both the photosynthesis and stomatal conductance models among species and environmental conditions are still needed (Cannell and Thornley, 1998;Kosugi et al., 2003).There are only a few lists of these parameters for SiB2 (Sellers et al., 1996), one of the famous global scale land surface models, which uses a Farquhar et al. (1980) type net assimilation model and a Ball et al. (1987) type stomatal conductance model.Moreover, the methods used in estimating the parameters have not received much attention and need further studies (Dubois et al., 2007).
Over the past two decades, the responses of net photosynthesis (A) to the leaf intercellular concentration (C i ), i.e. the A/C i curve fitting analyses, have been widely used to parameterize leaf photosynthesis.These analyses have been invaluable for elucidating and quantifying in vivo the fundamental biochemical processes underlying the photosynthetic responses of plants to various environmental conditions (von Caemmerer, 2000).However, this procedure of parametrization requires that each A/C i curve be first divided into several segments.The parameters for the model are then estimated through separate fitting of the component functions corresponding to the segments, rather than fitting all parameters simultaneously based on the entire data set (Kim and Lieth, 2003).It should be noted that the identification of the Published by Copernicus Publications on behalf of the European Geosciences Union.G. F. Zhu et al.: Parameterization of a coupled CO 2 and H 2 O gas exchange model cut-off point between different segments is usually arbitrary, in essence at the discretion of the investigator.The consequence of arbitrary subsetting of the data is that it creates an entry for systematic deviation from the true parameter values (Dubois et al., 2007).Moreover, measurement noise is inevitable in realistic testing conditions.However, the A/C i curve fitting method is sensitive to noisy data, and small or noisy data sets will be subject to significant estimation problems (Sharkey et al., 2007).Therefore, we set out to find an innovative method to parameterize the Farquhar et al. (1980) photosynthesis model, which can overcome the flaws of the A/C i curve fitting method.
In general, parameter estimation can be viewed as an optimization problem.The goal is the determination of a set of parameters which, substituted into a mathematical model, generate results consistent with measured experimental data.During the last three decades, there has been a growing interest in solving optimization problems by mimicking natural processes, such as biological evolution and metal annealing (Ooka and Komamura, 2009).Among them, the Genetic Algorithms (GA) pioneered by Holland (1975) is such a technique that has received considerable attention (Lee et al. 2006).Compared with traditional optimization methods (e.g.ordinary least squares, weighted and generalized least squares, Bayesian, and maximum likelihood) relating to the parameter estimation, the GA is more appropriate when the function includes some complexities and/or discontinuities (Barth, 1992).Major advantages of the GA include the following: (1) it has very good characteristics of robustness and global convergence; (2) it can process a large number of variables at the same time; (3) it can handle the nonlinearity between the model and its parameters; (4) it can be computed simply and has a high implicit parallelism (Holland, 1975;Hu et al., 2007).
Populus euphratica, one of the oldest species of Populus in Salicaceae, is the sole species of the genus naturally growing at the edge of barren and semi-barren deserts (Gu et al., 2004).Its high survival and biomass production in the arid areas of Mongolia, China, Pakistan, Iraq, and Iran is acclaimed (Sharma et al., 1999).P. euphratica is characterized by a great resistance to drought, high irradiance and temperature, wind, and salinity in the soils, and is very important in maintaining ecosystem function in arid and semi-arid regions (Chen et al., 2004).Comparative studies have been carried out to determine the responses of P. euphratica to salt and drought stress (Ma et al., 2002;Chen et al., 2004Chen et al., , 2006)).However, efforts to use the gas-exchange data of P. euphratica leaves to determine the biochemical model parameters and their temperature dependences are lacking.Furthermore, coupled gas exchange models have not been developed for P. euphratica.
In this study, the well-know combined model that simulates both CO 2 and H 2 O gas exchange on a leaf scale was applied to several data sets obtained from in situ leaf-scale observations of CO 2 and H 2 O gas exchange of P. euphratica leaves, to parameterize the leaf characteristics related to the gas exchange using the GA method.Also, some details of the model implementation were provided.This information should be of interest to physiologists who seek to understand the enzymatic and photochemical events regulating CO 2 assimilation of the species, and modelers searching for speciesspecific estimates of photosynthesis parameters for use in describing large scale CO 2 and H 2 O exchange.

Photosynthesis, stomatal conductance and transpiration sub-models
The combined model used for the estimation consists of a Ball et al. (1987) type stomatal conductance sub-model (BWB model), a Farquhar et al. (1980) type biochemical submodel of photosynthesis for C 3 plants (FvCB model) and the integrated sub-model of transpiration.
In the FvCB model, the net CO 2 assimilation rate A could be modeled as the minimum of two limiting rates: A c is the rate of photosynthesis when Rubisco activity is limiting, A j is the rate when ribulose-1,5-bisphosphate (RuBP)regeneration is limiting by electron transport, and A p is the rate when triose phosphate utilization (TPU) is limiting.R d is the day (non-photorespiratory) respiration rate.Rubiscolimited photosynthesis is given by: where V c max is the maximum rate of carboxylation, C i and O are the intercellular concentrations of CO 2 and O 2 (which is considered to remain 21 kPa), respectively, K c and K o are the Michaelis-Menten coefficient of Rubisco activity for CO 2 and O 2 , respectively, and * is the CO 2 compensation point in the absence of mitochondrial respiration.This formulation of the model assumes that the cell-wall conductance, the conductance between the intercellular space and the site of carboxylation, is negligible.Some authors have argued that this conductance is significant and may vary with leaf temperature (e.g.Makino et al., 1994).For the species considered here, we did not have access to appropriate data to evaluate the cell-wall conductance and hence were obliged to use the form of the model given above.The rate of photosynthesis when RuBP regeneration is limiting is given by: where J is the rate of electron transport.J is related to incident photosynthetically active photo flux density, Q, by: where J max is the potential rate of electron transport, θ (0.90) is the curvature of the light response curve (Evans, 1987), ε (0.86) is the leaf absorbance of Q (von Caemmerer, 2000), f (0.3) is the fraction of photosynthetically active radiation (εQ) loss (Evans, 1987;Long et al., 1993).These parameter values have only a slight effect on the estimated value of J max (Medlyn et al., 2002).
When the rate of photosynthesis is limited by TPU, it is simply: where TPU is the rate of use of triose phosphates but can also be any export of carbon from the Calvin cycle, including direct use of photorespiratory glycine or serine.
The accuracy of the photosynthesis model depends on proper representation of the kinetic properties of Rubisco.Fortunately, the kinetic properties of Rubisco among C 3 plants have been shown to be relatively conserved and thus we use a general set of kinetic parameters (Table 1; see also von Caemmerer, 2000; Kattge and Knorr, 2007;Sharkey et al., 2007) but with caution (Tcherkez et al., 2006).There are four parameters that need to be estimated.These are V c max , J max , A p and R d corresponding to measurement temperatures, thus comparisons between two treatments are often made at a single temperature.Representative temperature responses of the fitted parameters are used to adjust these values to a single temperature in this case 25 • C. The dependence of reaction rates on temperature is described by either exponential or peaked exponential functions.The equations used here can be found in Harley et al. (1992): where c is a scaling constant, H a is the enthalpy of activation, H d is enthalpy of deactivation, S is the entropy, T k denotes leaf temperature in K and R is the universal gas constant (8.314J mol −1 K −1 ).The scaling constant for the equations used to adjust the parameters is chosen to cause the results to be 1 at 25 • C and the calculated value at other temperature can be used to scale the parameter to 25 • C. Equation 7 is essentially the exponential equation (Eq.6) modified by a term that describes how conformational changes in the enzyme at higher temperature start to negate the on-going benefits that would otherwise come from further increasing temperature.The exponential function is used for the temperature dependences of parameters K c , K o , * , J max , V c max  Bernacchi et al. (1992Bernacchi et al. ( , 2001Bernacchi et al. ( , 2002)), Bernacchi et al. (2003) and also see Sharkey et al. (2007).
and R d , and the peaked exponential function is used for the temperature dependence of g m .The values used in this paper are presented in Table 1.
In sub-model BWB, the stomatal conductance is estimated from the net assimilation rate (A), relative humidity (h), and CO 2 concentration at the leaf surface (C s ) using, where g sw is the stomatal conductance of H 2 O, m is the slope of the relationship between the stomatal index (Ah/C s ) and the stomatal conductance and g sw min is the minimum stomatal conductance.The CO 2 concentration at the leaf surface C s is calculated using the CO 2 concentration of the air in the chamber.
Under steady-state conditions, C i can be estimated using the stomatal conductance of CO 2 (g sc ): where, g sc is the stomatal conductance to CO 2 such that g sc = g sw 1.6 .The transpiration rate, E, can be calculated as, where, VPD s is the water vapor pressure deficit between intercellular space and the air layer just above the leaf surface.

Coupling the models
The FvCB model uses C i , among others (T k and Q), as driving variables.The BWB model requires the net photosynthesis A as an input, while C i results from the interaction of A and g sw .Therefore, the two sub-models are interdependent.
A nested iterative procedure was used to solve this relation numerically (Fig. 1).In finding the solution, the value of C i was assumed to be equal to 0.7C a , and substituted into the biochemical photosynthesis model (Eq. 1) to obtain an estimate of A. Then stomatal conductance (g sc ) was calculated from the stomatal model (Eq.8), and a new C i was estimated using the resulting A and g sc (Eq.9).This process was solved iteratively using the Newton-Raphson method until the change in C i was less than a certain small value of allowance.It should be noted that the parameters of the FvCB sub-model must be calibrated first (discuss below).

Plant materials
The experiment was conducted at Qidaoqiao Populus euphratica Oliv.forest reserve, Ejina county, Inner Mongolia, China (42 • 21 N, 101 • 15 E; elevation 920.5 m above sea level; 13.33 km 2 ).This is one of the most arid regions in China, with potential evaporation exceeding 3500 mm year −1 and mean annual rainfall, 84% of which occurs during the growing season (May-September), less than 50 mm year −1 .The annual mean air temperature is about 8.1 • C. A winter minimum temperature of −38.5 • C (17 January 1996) and a summer maximum of 43.1 • C (21 July 1980) have been recorded, with an average diurnal temperature range of 28-30 • C (Su et al., 2007).Prevailing winds are northwesterly in winter and spring, and southwesterly to southerly in summer and fall.Annual mean wind velocity ranges from 3.4 to 4.0 m s −1 .Total annual sunshine time is from 3170 to 3444 h, the accumulated temperature Populus euphratica Oliv. is the dominant native woody species in the reserve, whose average age is 25 years, and their growth status is good.The stem density was 500 plants ha −1 .Mean tree height is 10 m and men breastheight diameter is 12 cm.The understory includes the species Tamarix ramosissima and Sophora alopecuroides L., the former is an invasive xerophytic woody shrub species, which can form monospecific stands at a maximum height varying between 2 and 3 m; the latter is a perennial legume drought-resistant forage species infested to the reserve, commonly, 30-60 cm in height.The trees were accessed via a canopy access tower.Three to four intact dentate broad-ovate leaves on the exposed side were selected for measurements.The measurements were conducted on 8, 10, 17 July 2006 which were all clear days.

Gas exchange measurement
A photosynthesis system (LI-6400; LI-COR, Lincoln, NE, USA) with a red/blue light source (LI6400-02B) mounted onto a 6-cm 2 clampe-on leaf chamber was used to determine light and A/C i responses under various environment conditions.For the construction of A/C i response curves, three leaf replicas were used.Prior to the measurement the leaf was acclimated to saturating irradiance (1500 µmol m −2 s −1 ) and measurement temperature for half an hour.The CO 2 concentration in the cuvette was gradually decreased from 360 µmol mol −1 to about 20 µmol mol −1 through five steps, increased back to 360 µmol mol −1 and then the leaf was allowed to acclimate for at least five minutes.Upon completion of this sequence, the CO 2 concentration was increased to about 1200 µmol mol −1 through six steps.The light response of leaves was determined at several irradiance levels between 0 and 1800 µmol m −2 s −1 at 25 • C leaf temperature and 360 µmol mol −1 CO 2 inside the leaf chamber.For light response curves, measurements started with a leaf equilibrated to high light and the light level was then gradually decreased.
The A/C i response of leaves was investigated at various leaf temperatures (10,15,20,25,30,35 and 40 • C) to determine the temperature dependence of the photosynthetic parameters.The leaf chamber was modified by replacing the peltier external heat sink with a metal block containing water channels, which in turn were connected to a heating/cooling circulating water bath (Endocal RTE-100, Neslab Instruments, Newington, USA).The modified heating/cooling blocks, used in conjunction with the peltier temperature controls, provided leaf temperature control at any preset value between 10-45 • C. Leaf temperatures were measured using a chromal-constantin thermocouple pressed to the lower leaf surface.The temperatures reported by this particular thermocouple were cross-checked against standard mercury-in-glass thermometers in a controlled temperature chamber and found to be within ±0.4 • C (Bernacchi et al., 2003).
Using 99 leaves, the response of g sc to relative humidity (0.05-0.90), irradiance (>100 µmol m −2 s −1 ), leaf temperature (10-40 • C) and a range of CO 2 levels (>50 µmol mol −1 ) was determined to calibrate the stomatal conductance model.Relative humidity was controlled by adjusting the flow rate of air through the leaf chamber.Measurements used to calibrate the stomatal conductance model were collected by waiting until the rate of C i , transpiration and CO 2 assimilation had stabilized before taking the reading; this wait-time ranged from 5 to 30 min depending on the leaves and the environmental conditions of the camber.

Parameter estimation
The objective of parameter calibration is to determine the parameters is the input variables.We define our objective function that derives the optimization procedure as, where l is the estimated outputs, N 0 is the number of data sets, and w j (j = 1,2,•••,l) is the weighting factor for the j th estimated outputs.In the present work we used the GA to find a vector − → β in the given search space, which is defined by providing the lower and upper bounds for each of the The GA is an effective stochastic global that mimics biological evolution.As they are robust, i.e. they use only objective function information and not other auxiliary information, they has been successfully applied to various problems, such as function optimization and combinatorial optimization, especially when a rigorous mathematical model is too complicated to be practically implemented (Goldberg, 1989).The basic operations involved in a GA include three basic operators: selection, crossover, and mutation.The linkage between the coupling model and the GA is shown in Fig. 2. The procedure is summarized as follows: First, an initial set (called a "population") of vectors (called "individuals") whose elements (called "genomes") are the values of the parameters is generated.This population is a representative set of solutions to the problem under investigation.Each individual is evaluated on its performance with respect to the fitness function.For parameter estimation problems, the fitness of a particular individual is roughly proportional to the inverse of the errors between experimental and predicted values (S( − → β )).Using this measure, the individual competes in a selection process where the fittest survives and is selected to enter the mating pool; the lesser-fit individual dies.The selected individuals (parents) are assigned a mate randomly.Genetic information is exchanged between the two parents by crossover to form offspring.The parents are then killed and replaced in the population by the offspring to keep the population size stable.Reproduction between the individuals takes place with a probability of crossover.If a random number generated is less than the probability of crossover, crossover happens, otherwise not, and the parents enter into the new population.GA is very aggressive search techniques; they tend to converge quickly to a local optimum if the only genetic operators used are selection and crossover.The reason is that GA eliminates rapidly those individuals with poor measures until all the individuals in the population are identical.Without a fresh influx of new genetic materials, the solution stops there.To maintain diversity, some of the genes are subjected to mutation to keep the population from premature convergence (Goldberg, 1989;Cieniawski et al., 1995).Selection, crossover and mutation are repeated for many generations, with the expectation of producing the best individual(s) that could represent the optimal or near optimal solution to the problem under study.

Calibration of the sub-models
A/C i response of P. euphratica leaves, examined at an irradiation of 1500 µmol m −2 s −1 and leaf temperature 25 • C, followed typical A/C i response patterns of C 3 plants (Fig. 3a).Estimates of the photosynthesis parameters were 75.09±1.36(approximated standard error), 117.27±2.47,8.21±0.10,and 5.81±0.08µmol m −2 s −1 for V c max , J max , TPU, and R d at 25 • C, respectively.The FvCB sub-model described the photosynthetic response very well over a range of measured C i at 25 • C. The transition points from A c to A j and from A j to A p occurred at 23.2 and 88.3 Pa, respectively (Fig. 3a).The model response to irradiation was also examined at C i of 38 Pa at 25 • C. From Fig. 3b, we can  see that the model simulated fairly well and transition from RuBP-limited to Rubisoco-limited or TPU-limited photosynthesis did not occur during doing light response curves under these circumstances.
Figure 4a shows the relationship between stomatal conductance (g sw , mol m −2 s −1 ) and the stomatal index ( Ah C s ) of the BWB sub-model of P. euphratica.The optimized values for parameters m and g sw min (mol m −2 s −1 ) are 11.32 and −0.0091, respectively.The BWB sub-model was capable of accounting for 92% of the observed variation in measured stomatal conductance of calibration data (Fig. 4b).Figure 4c shows the diurnal change in relative humidity (h) at the leaf surface.The h value decreased slowly from 43.6% at 08:00 to 18.83% at 11:00 and leached a plateau about 14.3% from 12:00 to 14:00.After that the h value slowly increased from 19.61% to 21.03% from 15:00 to 16:00.Analysis of the response of the rate of photosynthesis rate (A, µmol m −2 s −1 ) to relative humidity (h, %) for leaves at the field site showed that there was positive relationship between A and h (Fig. 4d).

Prediction of A by the FvCB model
Predicted A by the FvCB model is represented graphically against calibration data (Fig. 5).At 10 • C, A was insensitive to high CO 2 levels.The FvCB sub-model simulated this observed pattern well; that is, an increase of photosynthesis rated up to the CO 2 concentration level about 20.7 Pa, followed by a flat line as CO 2 increased further (Fig. 5a).The model predicted a flat response at high CO 2 levels as a result of a limitation due to A p .At 10 • C, the model predicted a nearly direct transition from the Rubisco-limited (A c ) to the TPU-limited (A p ) region, with a brief period of RuBP limitation (A j , 10.4-20.7 Pa of C i ) between the two regions.At 20 • C, the model behaved such that the transition from A c to A j occurred around 17.6 Pa and the transition between A j and A p took place around 54.2 Pa (Fig. 5a).At 30 • C, the limitation due to A j was recognized over a board range of CO 2 pressure from 23.8 Pa to 87.6 Pa (Fig. 5b).At 40 • C,  the model predicted a directly transition from A c to A p occurred at 29.9 Pa and the limitation due to A j was not realized (Fig. 5b).The model successfully reproduced the observed pattern of A/C i responses at all four leaf temperatures.The photosynthesis response to leaf temperature was simulated fairly well over the entire range of temperatures at various ambient CO 2 concentrations (Fig. 5c).At C i =100 Pa, the optimal leaf temperature that yields the maximal net photosynthetic rate of 24.59 µmol m −2 s −1 was around 32 • C. At C i =38 Pa, the optimal leaf temperature increased to 34 • C with a maximal photosynthetic rate of 21.32 µmol m −2 s −1 .At C i =20 Pa, the optimal leaf temperature decreased to 23 • C with a maximal photosynthetic rate of 10.0 µmol m −2 s −1 .The model response to irradiation was also simulated fairly well.At 20 • C, the model predicted that A was solely limited by A j throughout all irradiation levels (Fig. 5d).At 30 • C, the transition from A j to A c occurred around Q=820 µmol m −2 s −1 .At 40 • C, the transition from A j to A c occurred at lower irradiation (Q=621 µmol m −2 s −1 ).

Coupling model validation
Having parameterized the combined model as described above, we simulated the diurnal courses of photosynthesis and evapotranspiration on a leaf scale, using as driving variables the measured values of the leaf temperature and irradiation, as well as measured C s and h.The resulting simulations were compared with the measure rates of net photosynthesis (Fig. 6a) and transpiration (Fig. 6b).The combined model successfully reproduced the observed response in A. Of note, the observed net assimilation rate of the P. euphratica leaves peaked at 10:00 o'clock and declined gradually until 15:00 o'clock with a slightly increase after that.The regression line slope between the observed and modeled values was 1.01 with an intercept of −0.0807, corresponding to a Root Mean Squared Errors (RMSE) of 3.12 (Fig. 7a).
However, the combined model generally tended to underestimate the transpiration (Fig. 6b) and the regression line slope deviated significantly from unity, corresponding to a RMSE=1.62 (Fig. 7b).Comparing the daily integrated totals of carbon fixed and water lost, the model overestimated daily CO 2 fixation by 0.44% and underestimated water loss by 9.31%, respectively.Overall, the combined model generally captured the diurnal patterns of CO 2 and H 2 O exchange resulting from variation in temperatures and irradiation.

Model parameterization
The major advantage of the proposed method is its global nature, and its ability to outperform simultaneous estimates of the photosynthetic parameters (e.g.V c max , J max , TPU and R d ).Our experiments showed that the appropriately identifying bounds on parameters for minimization in proximity to the global minimum were indispensable.Wide parameter searching bounds for the GA may result in parameters drifting into nonsensical ranges.For example, in very rare circumstances, data include samples of two segments (A c and A j ), but wide bounds result in an A/C i set for which one of the two functions (e.g.A j ) happens to provide a better fit than two functions combined, despite the underlying presence of two phases (Su et al., 2009).In this circumstance, we say the GA method obtained biologically implausible estimates for the parameters of the FvCB model.
It is possible to prohibit the estimation procedure from reaching biologically implausible values by constraining the range of a parameter.Knowing the initial value of A/C i curve, one can use the following equation to get an approximate estimation for V c max (when C i equals to the CO 2 compensation point *): where V c max ,0 is the primary estimation of V c max , dA dC i is the initial slope of the A/C i curve, which can be calculated from the difference quotient of the first two points of the A/C i curves.
When C i → +∞, A j in Eq. 3 becomes lim where lim C i →+∞ A j is the limit of the RuBP-limited photosynthesis rate function when C i → +∞, which can be approximately evaluated from the last two end points on the A/C i curves.Thus J max can be approximately estimated by: where J max,0 is the primary estimation of J max .If TPU-limited photosynthesis occurs as no increase in A with increasing CO 2 concentration, approximate TPU value can be easily obtained: Generally, R d is constrained to be greater than 0 and less than 10 µmol m −2 s −1 (Sharkey et al., 2007).Thus, for any given A/C i curves, the bounds for parameters V c max , R d , J max and TPU are [V c max ,0 − 30,V c max ,0 + 40], [0, 10], [J max,0 −40, J max,0 +70] and [TPU 0 − 3, TPU 0 +3].Our experiences showed that at these search spaces the optimum parameters were all successfully found at one time.
The BWB model is empirical and has received wide attention, analysis, acceptance and applications (Muchow, 1985;Lhomme et al., 1998).The applications of the model to CO 2 and H 2 O exchange studies result in coupled equations which required recursive or iterative computation.Thus, it may not be favourable for large-scale ecosystem simulations.Also, the empirical nature of the BWB model makes it difficult to extrapolate the model into future environmental regimes.For example, the effect of the soil water stress on stomatal conductance was not explicitly included in the model.(Wullschleger, 1993).Our values of V c max and J max for P. euphratica is very close to Wullschleger's two values for Populus species (Table 2).The optimal V c max and J max for P. euphratica in this study are also close to Wullschleger's values for hardwood in temperate forests of Betura pendula and Quercus rubra.
Various functions have been used to describe the temperature dependence of V c max and J max .For example, Harley et al. (1992) and Leuning (1995) employed a compound function with an optimum for both V c max and J max , whereas de Pury and Farquhar (1997) used an exponential growth function for V c max .Leuning (1995) reported that functions describing temperature responses of the photosynthetic parameters V c max and J max at 25 • C showed little variation between different species at leaf temperatures <30 • C, while above this temperature variation was large and speciesdependent.Under the natural condition, better predictions of Rubisoc-limited photosynthesis are necessary because of the synchronous variations of temperatures and irradiation which range from 24.0 to 40.98 • C and from 934.82 to 166.8 mol m −2 s −1 during the diurnal course, respectively (Fig. 4c).Thus, photosynthesis in field condition is commonly Rubisco-limited (Fig. 5d).In our experiments, we found a slight decline of V c max when the temperature was greater than 40 • C.However, we opted to use the exponential function because it resulted in better overall performance for the typical diurnal gas exchange on a leaf scale.The leaf nitrogen content can also be linked to key photosynthetic model parameters such as V c max and J max (Gonzalez-Real and Baille, 2000).Therefore, further studies are still needed to reveal these relationships.

Parameters of BWB sub-model
Table 3 compared the optimized values of parameters m and g sw min for BWB sub-model with other studies.Parameter m in the BWB sub-model for P. euphratica is 11.31.This value is in the range of values for C 3 tree species listed in Table 3. Parameter g sw min , the minimum stomatal conductance to H 2 O when A=0 at the light compensation point, should be nonnegative in the sense of biological realities.Although g sw min is negative in our study, it was noticed that its value is relative low (−0.0091mol m −2 s −1 ) and has small effect on the estimated g sw .Thus, we thought it is acceptable to use the negative g sw min value to predict the values of g sw in the coupled models.Evidence from gas exchange measurements suggests that the value of m occupies a relatively narrow range for all C 3 species.Based on this, some noteworthy studies simulating canopy fluxes used a constant m of around 9 (see also Table 3).Nevertheless, parameter m has a significant physiological meaning related to the intrinsic water use efficiency, indicating a plant-specific manner of regulating the fluxes, and the importance of slight fluctuation in parameter m should not be undervalued (Kosugi et al., 2003).Studies have reported that the soil and plant water status might effect m through regulating leaf water potentials.Results showed that m became small during soil drought conditions (Sala and Tenhunen, 1996) and in old tress (Falge et al., 1996).Thus, Gao et al. (2002) derived a new model for the plant stomatal conductance and transpiration as a function of the soil water stress, vapour pressure deficit and photosynthetically active radiation.In the applications of the model, some additional experiments are needed in future studies.

Conclusions
This paper applied a combined model to simulate CO 2 and H 2 O fluxes at the leaf scale for P. euphratica.The parameters of the FvCB sub-model were estimated by using the GA method.It is demonstrated that this method can effectively find higher quality parameter values of the FvCB sub-model based on the entire A/C i curves data sets while obviating the need for arbitrary determination of transition points and subsetting of the data before analysis.Moreover, the present coupled gas exchange model for P. euphratica leaf is capable of predicting photosynthesis, the stomatal conductance and transpiration as a function of radiation, leaf temperatures, ambient CO 2 , and relative humidity, but predictions of the stomatal conductance and transpiration are less satisfactory.
In the present study, the FvCB sub-model was parameterized by using A/C i data sets under a controlled environment.Recent advances in potable equipment enabled us to make longterm field gas exchange measurements and we have been accumulating data.What about the GA method using the longterm data obtained from in situ observations of the diurnal changes in the CO 2 and H 2 O fluxes in the parameterization of the FvCB model?A comprehensive study is still required.

Fig. 2 .
Fig. 2. Flow chart of the GA estimator for parameter estimation of the coupling

Fig. 2 .
Fig. 2. Flow chart of the GA estimator for parameter estimation of the coupling models.

Fig. 3 .Fig. 4 .
Fig. 3. Examples of genetic algorithms (GA) to A/C i curve in parameter estimations (a) and corresponding light response curves (b).For the A/C i curve, the data set was properly subdivided into three segments by GA with the photosynthesis parameters were 75.09±1.36,117.27±2.47,8.21±0.10,and 5.81±0.08 for V c max , J max , TPU, and R d at 25 • C, respectively.Points below 23.2 Pa was regarded as Rubiscolimited and above 88.3Pa as TPU-limited; points between 23.2 and 88.3 Pa might be RuBP-regeneration-limited-the arrow indicates the transition points between different segments.Light response curve at C i of 36.4Pa at 25 • C.

Fig. 5 .Fig. 5 .
Fig. 5. Prediction of net photosynthesis ( A ). Lines represent the FvCB model prediction; symbols are observations of calibration data.(a) A/Ci responses at 10 and 20ºC; (b) A/Ci responses at 30 and 40ºC; (c) Temperature response at three Ci levels (20, 38, and 100 Pa); (d) Light responses at Ci=38 Pa at three leaf temperature levels (20, 30 and 40 ºC) Fig. 5. Prediction of net photosynthesis (A).Lines represent the FvCB model prediction; symbols are observations of calibration data.(a) A/C i responses at 10 and 20 • C; (b) A/C i responses at 30 and 40 • C; (c) Temperature response at three C i levels (20, 38, and 100 Pa); (d) Light responses at C i =38 Pa at three leaf temperature levels (20, 30 and 40 • C).

Fig. 6 .Fig. 6 .
Fig. 6.Comparison of the observed and estimated (a) net assimilation rates, (b) transpiration rates using the optimized parameters obtained by GA method.

Fig. 6 .
Fig. 6.Comparison of the observed and estimated (a) net assimilation rates, (b) transpiration rates using optimized parameters obtained by GA method.

Fig. 7 .Fig. 7 .
Fig. 7. Linear regression of (a) predicted A on measured A; (b) predicted transpiration on measured transpiration.Dashed line indicates one to one relationship.

Fig. 7 .
Fig. 7. Linear regression of (a) predicted A on measured A; (b) predicted transpiration on measured transpiration.Dashed line indicates one to one relationship.

Table 1 .
The

Table 2 .
A comparison of V c max and J max of the investigated tress with the results of other studies.

Maximum carboxylation rate, V c max and maximum rate of electron transport, J max
Values for V c max of 75.09±1.36and J max of 117.27±2.47µmol m −2 s −1 were obtained for P. euphratica leaves at 25 • C. It should be noticed that the assessed values of V c max and J max at a reference temperature dependent on the choice of the Rubisco kinetic parameters and temperature dependence functions in each model.Therefore, care should be needed for the comparison of the V c max and J max with other studies.Wullschleger's list of V c max and J max for 109 species estimated from the A/C i curves included five species from the genus Populus

Table 3 .
A comparison of the parameters for BWB submodel with other studies.