Dynamic Simulation of Conductance in Apple Tree Canopy

Coupled model of canopy stomatal conductance (Gs) and photosynthesis (Pn) was presented. This model could simulate the response of Gs to microclimatic factors and the diurnal variation. These established models were tested by the observation data in an apple (Malus domestica Borkh. cv. ‘Fuji’) orchard (latitude 40 o 13' north, longitude 116 o 13′ east, altitude 79 m). The influences of the microclimatic factors on stomatal conductance were different. There were strong interactions among the various microclimatic factors. From this model, we can see that the diurnal course of Gs in the canopy showed a double-peak curve and Gs increased as the net radiation increased and decreased as the relative humidity and water potential decreased. There was a satisfactory correspondence between measured and simulated values of Gs with observation data in the apple orchard.


INTRODUCTION
Both photosynthesis and transpiration rates are regulated by stomatal conductance which depends on environmental factors and plant characteristics including solar radiation, air temperature, relative humidity, air CO 2 concentration, soil and leaf water potential (Damour et al., 2010;Naithani et al., 2012;Uddling and Wallin, 2012).The simulation models are very important for estimating stomatal conductance.Jarvis (1976) assumed that different environmental variables including solar radiation, air temperature, leaf water potential, vapor pressure deficit, soil moisture deficit and ambient CO 2 concentration acted independently in determining stomatal conductance.Therefore, the model could be expressed in a simple multiplicative form which has been widely used (Damour et al., 2010;Egea et al., 2011).However, more and more studies showed that stomatal conductance was subject to the feedback of photosynthetic activity (Ball et al., 1987;Leuning, 1990).Ball et al. (1987) proposed a semi-mechanistic model between stomatal conductance and photosynthesis.Some modified versions of this model were proposed by Collatz et al. (1991), Qian et al. (2012) and Gao et al. (2012).But this model had their defects as they cannot respond to the relationship of main environmental factors.A major challenge is to develop a model which accounts for all the factors which control stomatal conductance.The aims of our study are: • Design a coupled model of stomatal conductance which can simulate both the response of stomatal conductance to microclimatic factors and the feedbacks of photosynthesis and transpiration to stomatal conductance.• Simulate stomatal conductance (G s ) on canopy level in real environment.

Models and methods:
Stomatal conductance model: The model of g sc is given by Leuning (1990): where, a 1 , D 0 are constants, D is the vapor pressure deficit and Γ is the CO 2 compensation point.Assuming G sc = G s /1.56, G s is stomatal conductance for water, modified by the following equation: where, Ψ l is leaf water potential which is calculated by Penman-Monteith and water transport model in plant (Gao et al., 2010).G (Ψ l ) is a function of Ψ l (Jones 1992): where, b 1 , b 2 are constants.

Photosynthesis model:
The leaf photosynthesis model is based on the mechanistic understanding of C 3 photosynthesis encapsulated in the description of Farquhar et al. (1980) and modified by others (Leuning, 1990;Egea et al., 2011;Qian et al., 2012).The equations describing net photosynthetic rate (A) were given as follows: where, A c is the gross rate of photosynthesis limited by Rubisco activity, A q is the gross rate of RuBP regeneration through electron transport and R d is Respiration which is strongly dependent on leaf temperature.If I = I (i) the canopy photosynthesis (P n ) per unit ground area (m -2 ) is: where, l i is the leaf area (m 2 ) of the i th layer (which receives a light intensity I (i) on per unit ground area).
For the biochemical model, the driving variable c i was calculated according to: where, c a = Air CO 2 concentration g sc = Stomatal conductance to CO 2

MATERIALS AND METHODS
The experiment was carried out in a 'Fuji' apple (Malus domestica Borkh.cv.'Fuji') orchard from 2013 to 2014.The orchard is in the farm of 'Zhongri' Orchard (latitude 40 o 13′ north, longitude 116 o 13′ east, altitude 79 m) in Changping county of Beijing.The 'Fuji' apple trees were planted in 1994 in south-north rows at a density of 667 plants/ha.The planting spacing was 5×3 m.Each tree was trained as an open-center system.The soil of the orchard was loam soil and soil water was always adequate.
Leaf stomatal conductance was measured by an AP4 Porometer (AP4, Delta-T, UK).Leaf photosynthetic rate was measured by the Li-6400 Portable Photosynthesis System (LI 6400; LI-COR, USA).The canopy radiant interception was simulated by Beer's law (Johnson et al., 1989).The radiation in different layer of apple tree canopy was measured by LQF5 (Quantum Meter, USA).We presented 3D plots to describe the effects of microclimatic factors and their interaction.All the parameters were estimated with a nonlinear optimization technique or from previous reports (Leuning, 1990;Gao et al., 2010Gao et al., , 2012)).

RESULTS
The simulation of canopy stomatal conductance: The response of average G s of the apple tree canopy (LAI = 3) to the microclimatic factors was presented in Fig. 1.The results showed that G s were mostly affected by Radiation (R a ) and air Temperature (T a ).G s increased with the increase of R a .As T a increased, the change of G s followed a bell-shaped curve (Fig. 1A and  B).The influence of net Radiation (R a ) on G s depended on the net radiation flux density.When R a was below 200 W/m 2 , there existed a positive linear relationship between G s and R a .G s did not show a significant increase when R a increased from 200 to 800 W/m 2 (Fig. 1B and C).
Generally there was a negative correlation between CO 2 concentration and G s .The effect was stronger when CO 2 concentration was below 350 µmol/mol.However a positive correlation between CO 2 and G s was found when CO 2 concentration was below 100 µmol/mol (Fig. 1A and C).This was because under low CO 2 concentration the feedback of photosynthesis to G s was stronger than the effect of CO 2 concentration on G s .It should be noted that the temperature optimum of G s shifted to a higher temperature as PAR, CO 2 increased or RH decreased (Fig. 1A, B and D).Strong interactions existed in the various microclimatic factors, especially between T a and R a , R a and CO 2 .

Diurnal variation of stomatal conductance:
Diurnal changes of G s of apple trees were simulated by the models (Fig. 2).The microclimatic data used were from June 14 th to 19 th in 2013 during which it was clear from June 17 th to 19 th , cloudy from June 14 th to 16 th .The diurnal course of G s was simulated according to Eq. ( 1) and meteorological data.It showed a double-peak type curve on clear days.G s were at its peaking at midmorning about 9:30 and mid-afternoon about 15:00.The decline of G s at noon was caused by RH and Ψ l .On the cloudy day of 14 th to 16 th , lower R a and T a caused by less sunshine and more clouds led to a decrease in G s by about 66%, compared to the values on clear days.The change of T a depended on R a and had about 2 h lag from R a .The variation of RH was basically controlled by the variation of T a since e a (absolute humidity) remained as a constant.So the radiation intercepted by the canopy became the major factor that affected stomatal conductance in plant.The fluctuation of stomatal conductance was caused by the fluctuation of radiation, too.
The correlations between measured and simulated values of G s were shown in Fig. 3.For G s correlation coefficients of the linear regression equations between measured and simulated values was close to 1.The R values for the regressions were also high.Hence, the models and parameters used in this study were good enough to predict G s with different microclimatic

DISCUSSION
Implementing the coupled models of apple canopy has been successful in predicting the regulation of G s in response to various microclimatic factors.The models included the feedback of transpiration to stomatal conductance through leaf water potential and the feedback of photosynthesis to stomatal conductance through Ball et al. (1987).These models can be applied in the future for solving various theoretical and applied tasks, e.g., the study of plant physiological dynamic, water management in fruit orchards.In addition it can also be used to predict the responses of leaf photosynthetic rates to elevated atmospheric CO 2 concentration and increased temperature, which is fundamental to projecting the impact of global change on the biosphere (Damour et al., 2010;Uddling and Wallin, 2012).
The model of stomata is very important for simulating water loss and photosynthetic rates of the plant (Damour et al., 2010;Naithani et al., 2012;Qian et al., 2012).But both the empirical and semimechanistic models cannot respond to environmental variables and feedbacks of transpiration and photosynthesis at the same time.Our coupled model solved these problems.The feedback of transpiration to stomatal movement was described with the steady state water flow equation, stomatal model and P-M equation.And through semi-mechanistic model of stomatal conductance and biochemical model of photosynthesis the feedback of P n to stomatal behavior was described.Leaf water potential might have acted as a hydraulic signal to partly closing stomata (Shahnazari et al., 2007).Then the connection between T r and P n was established through the stomatal model.There were strong interactions between the various microclimatic factors.Therefore, we should consider the interactions when discussing the influences of environmental factors on stomatal conductance.In our study the maximum G s occurred at air CO 2 concentration of 100 µmol/mol because of the feedback of P n .This result is similar to other studies (Dubbe et al., 1978).

Fig. 1 :
Fig. 1: The response of stomatal conductance (G s ) per unit ground in apple orchard to net radiation flux density (R a ), air relative humidity (RH), air temperature (T a ) and air CO 2 concentration (CO 2 )