Dynamic Simulation of Transpiration and Water Use Efficiency in Apple Tree Canopies

We developed a model that couples canopy stomatal conductance, transpiration and canopy Water Use Efficiency (WUE) in an apple orchard (Malus pumila Mill. ‘Fuji’). The model used the Penman-Monteith equation to compute effects of the interaction between canopy transpiration rate (Tr) and microclimatic factors. For convenience, WUE was expressed as the ratio of photosynthesis to transpiration rate; we simulated the relationship between WUE and microclimatic factors. Models developed were tested against observational data from an apple orchard (latitude 40° 13 ' N, longitude 116° 13 ′ E, altitude 79 m). The models and parameters well simulated Tr and WUE in apple trees. The mathematical simulation showed strong interactions among various microclimatic factors and indicated that transpiration was driven mainly by Vapor Pressure Deficit (VPD) and stomatal conductance. During the course of 1 day, transpiration increased (decreased) as net radiation and stomatal conductance increased (decreased). Maximum transpiration rates of experimental trees (leaf area index, LAI = 2.53) were about 8 mmol/m 2 /s on clear days and about 3 mmol/m 2 /s on cloudy days. Over 24 h, an apple tree (leaf area = 37.95 m -2 ) lost 50 to 70 L of water in clear weather and about 15 L in cloudy weather. On clear days, the peak of WUE was reached early after sunrise; it then decreased to a stable level maintained through most of the day until falling to zero at sunset.


INTRODUCTION
Water vapor exchange between plant surfaces and the atmosphere is the most important component to agricultural production (Naithani et al., 2012).The Penman-Monteith equation has been widely used to estimate plant transpiration from intercellular to canopy (Green et al., 2003;Pereira et al., 2006;Teixeira et al., 2008).This equation is based on net radiation and the resistance from cell to air.The parameters of canopy resistance and stomatal resistance needed for the Penman-Monteith equation are difficult to acquire.For convenience, WUE is expressed as the ratio of photosynthesis to transpiration rate, based on fundamentals underlying leaf gas exchange (Hsiao and Xu, 2000).Although the equation is simple, many factors in the equation have major impacts on WUE, such as soil water moisture, air relative humidity, light interception, leaf temperature and canopy characteristics (Alarcón et al., 2006).
Apples are very important economic crops, with orchards covering nearly 5,000,000 ha worldwide.Many orchards are in arid or semiarid areas.Modeling studies of regional water balance in dry regions can assess the importance of orchards in water exchange.
Transpiration in fruit trees has been modeled many times, especially for predicting diurnal variation in water exchange (Green et al., 2003;Pereira et al., 2006).Little literature is available on the fluxes of water loss for apple trees exposed to varying microclimate factors.
The objective of this study was to develop a coupled model to simulate the variation of canopy transpiration (T r ) and WUE in a natural environment including the interaction between T r , WUE and microclimatic factors, such as net radiation flux density (R a ), air Relative Humidity (RH), air temperature (T a ), air CO 2 concentration (CO 2 ) in order to simulate diurnal variations of T r and WUE in an apple canopy under different weather conditions.

Models and methods:
Transpiration model: Evaporation of water from a plant can be effectively modeled using the Penman-Monteith equation (Monteith, 1965): where, E is the transpiration rate per unit leaf area, R n is the net radiation flux density absorbed by the leaf, ρ is air density, c p is specific heat capacity of air, λ is the latent heat of evaporation of water, γ is the psychrometer constant, s is the slope of the curve relating saturation vapor pressure to temperature, D a is the vapor pressure deficit of the air, r a is the leaf boundary layer resistance and r s is stomatal resistance.Use of the factor 0.93 is based on the assumption that boundary layer resistance for vapor is 0.93 times that of sensible heat (Caspari et al., 1993).Leaf boundary layer resistance (r a ) was calculated from the empirical relation, derived by Perrier (1975).
Darcy's law was used to simulate sap flow within an apple tree, which was described by following equation (Jones and Tardieu, 1998;Dauzat et al., 2001): where, Ψ s and Ψ l are soil and leaf water potential, R sp is the resistance of the whole soil-plant pathway.Maximum soil water potential under optimal conditions is zero, so that: Water use efficiency model: At the physiological level, WUE may be defined as the ratio of photosynthesis and transpiration rate, which is difficult to monitor over long periods and is sensitive to changes in environmental factors.Canopy WUE is defined as the ratio of canopy photosynthetic rate (P n ) to canopy transpiration rate (Warren and Adams, 2006): The canopy photosynthesis is simulated by C 3 photosynthesis model (Farquhar et al., 1980;Gao et al., 2012), Using the above models, we can calculate effects of environmental factors on WUE.

MATERIALS AND METHODS
The experiment was carried out in a 'Fuji' apple (Malus domestica Borkh.cv.'Fuji') orchard from 2004 to 2007.The orchard is in the farm of The Ming Tombs (latitude 40° 13′ north, longitude 116° 13′ east, altitude 79 m) in Changping county of Beijing.The 'Fuji' apple trees were planted in 1985 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 framework structure of the traditional open-center tree and principles underlying its training and pruning were reported by Kikuchi and Shiozaki (1992).The soil of the orchard was loam soil and soil water potential was always controlled greater than -10 kPa.
Leaf stomatal conductance was measured by an AP4 Porometer (AP4, Delta-T, Cambridge, UK).Leaf net photosynthetic rate was measured by the Li-6400 Portable Photosynthesis System (LI 6400; LI-COR, Inc., Lincoln, NE, USA).Canopy was simulated by the model of Gao et al. (2012) In order to test the transpiration models the sap flow at the base of the tree stem was measured routinely using the Compensation Heat-pulse Technique (Swanson and Whitfield, 1981).In the trunk 2 sets of probes were installed into parallel holes drilled radially into the tree stem at heights of about 0.6 m above the ground.Sap velocity was measured at radial depths of 10 and 30 mm following the procedure given by Green and Clothier (1988) and using the theoretical calibrations of Swanson and Whitfield (1981) to account for the probe-induced effects of wounding.Volume sap flow rates were calculated in the tree stem by integrating the radial profile of sap velocity over the sapwood cross-section.The total leaf area of 10 apple trees was measured at the end of the experiment by removing all the leaves and measuring the leaf area of 3% (by weight) of the leaves using the scanned images with Optimas software (v6.5, Media Cybernetics, Silver Spring, MD).
A meteorological station was installed close to the trees recording 30 min averages of incoming radiation, wind speed, air temperature, relative humidity and CO 2 concentration.The instruments were mounted in the middle of the canopy at a height of about 1.5 m above the ground except for the wind sensor at 2 m above the ground.The canopy radiant interception was simulated by a multi-layer canopy model.The radiant flux density absorbed in canopy was assumed to be 65% of the top canopy radiant flux density, with 10% reflected to the atmosphere and 25% on the ground.The leaves in any given layer were regarded as being exposed to the same air temperature, relative humidity, CO 2 concentration and wind speed.Leaf temperature was assumed equal to air temperature.Radiation was the only variable.
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.

RESULTS
When R a was <200 W/m 2 , T r increased sharply with increasing R a , which is connected to the increase in G s (Fig. 1B and C).A higher leaf temperature results in more dramatic canopy transpiration.However, after optimum leaf temperature was exceeded, G s decreased with increasing leaf temperature.The optimum T a for T r was higher than that for G s due to the increase in Vapor Pressure Deficit (VPD).The optimum T a for T r was >40°C under low radiation conditions and 37°C under high radiation conditions (Fig. 1B and C).This difference was caused by the feedback from photosynthesis to stomatal conductance.
T r increased rapidly when CO 2 concentration decreased from 350 to 100 µmol/mol (Fig. 1A).However, T r decreased when CO 2 concentration decreased from 100 to 0 µmol/mol because of the feedback from photosynthesis to stomatal conductance.
When CO 2 concentration was >400 µmol/mol, T r became slightly reduced with increasing CO 2 concentration.VPD was the driving factor for T r , which increased linearly as RH decreased from 100 to 0 (Fig. 1B and D).
From Eq. (3), canopy WUE was completely determined by canopy photosynthesis (P n ) and transpiration (T r ).As a result, WUE and CO 2 concentration showed a nearly linear relationship (Fig. 2).As shown in Fig. 2B and D, WUE was highly sensitive to RH, especially when RH was in the range of 50-95%.RH affects WUE both through the physical process of evaporation from the canopy and by acting upon stomatal resistance to CO 2 exchange.These effects produce the non-linear relationship depicted in Fig. 2B and D. Both P n and T r increased with increasing R a ; when R a was >200 W/m 2 (Fig. 2B and C), P n increased exponentially as R a increased from 0 to 200 W/m 2 .As a result, WUE had a linear relationship with R a only when R a increased from 0 to 200 W/m 2 .Due to the feedback of T r to P n , there was a slight decrease in WUE when R a was >600 W/m 2 .
Figure 2A, B and D shows the effect of T a on WUE when T a varied from 10 to 40°C.It was apparent that the effect of T a became stronger when T a , CO 2 concentration and RH were all high.Although there were optimum temperatures for G s , T r and P n , WUE was linearly related to T a .An increase in T a caused a linear decrease in WUE because the increase in T r was steeper than that of P n with increasing T a .
Diurnal variations in canopy transpiration (T r ) were simulated in Fig. 3 (LAI = 2.53).The diurnal change in T r was similar to those of R a and P n , following monotonic curves on clear days.The microclimatic data used were from 14 to 20 June 2007; conditions were clear from June 14 th to 17 th and cloudy June 18 th to 20 th .The maximum T r values for experimental trees (LAI = 2.53) were about 8 mmol/m 2 /s on clear days and about 3 mmol/m 2 /s on cloudy days.Over 24 h, one apple tree (leaf area = 37.95 m 2 ) lost 50 to 70 L of water on clear days and about 15 L on cloudy days.In general, over 1 day, T r was 300% higher under clear conditions than under clouds.
The pattern of variation in WUE from June 14 th to 17 th in 2007 is shown in Fig. 4. On clear days, a typical WUE pattern was found in most measurements.The peak of WUE was reached early after sunrise, decreasing to a stable level and maintaining this during most of the day, until finally decreasing to zero at sunset.RH was much larger and T a smaller in the early morning than during the remainder of the day, so that there was a peak of WUE in the early morning.Both P n and T r increased with R a , so that a stable level existed across almost the whole day.On the cloudy days of 19 and 20 June, lower R a and T a due to reduced sunshine and increased cloudiness led to a decrease in photosynthesis and water loss by about 70 and 60%, respectively, compared to values on clear days.Thus the WUE on clear days was >25% higher than on cloudy days.

values in apple canopy
There is a satisfactory correspondence between measured and simulated values of transpiration in Fig. 5.The relationship between estimated transpiration (T r ) and measured Sapflow (S) is expressed as follows: S = 1.038T r (r 2 = 0.9095, n = 1245).The p value for the regressions was very high.Hence, the models and parameters we used were good enough to predict T r in apple tree canopies.

DISCUSSION
A coupled model was developed to incorporate apple tree G s and T r for assessing effects of the interaction between tree canopy and microclimatic factors on T r and the interactions between themselves.The models can be applied at different validation scales from leaf to orchard.We have demonstrated that these models were also of value in estimating diurnal variations under different weather conditions.
The Penman-Monteith equation was successful in simulating plant water use in our study and in others (Teixeira et al., 2008).It is based on the energy balance using the "big-leaf" approach and requires micrometeorologial and canopy variables to estimate evaporative losses from plant communities (Irmak et al., 2008).However, canopy variables, such as stomatal resistance (r l ) and canopy resistance (r c ) are difficult to measure.Some studies have evaluated different methods of scale-up as a function of different microclimatic, soil and crop characteristics.
WUE is defined as the amount of dry matter produced by a crop per unit of water transpired over a season (Ma et al., 2008).However, WUE can also be understood in terms of physiological and biochemical processes that determine the state of the plant canopy (Kumar et al., 1996), including microclimate and stomatal conductance.WUE is related to individual weather parameters, such as interception of radiation, relative humidity, soil moisture, temperature and wind velocity.The diurnal course of WUE was simulated by using our models and the microclimatic data from the canopy.WUE was sensitive to RH, T a and CO 2 concentration (Fig. 2).However, it was not sensitive to R a , because both transpiration and photosynthesis increased linearly with increasing R a (Fig. 2).Moreover, peak WUE was reached in early morning, followed by decreases to a stable level over most of the day.The results were similar to those of Testi et al. (2008).
The stomatal conductance was the key factor to simulate water evaporation and assimilation (Naithani et al., 2012).But the regulation of photosynthesis and transpiration by stomatal conductance was different.This difference could maximize the assimilation and avoid excessive loss of water in the plant.Upadhyaya et al. (1983) reported that transpiration rate is directly correlated with stomatal diameter when stomatal diameters are <10 µm, but photosynthesis rate is directly correlated with stomatal diameter only when stomatal diameter is <2 µm.Our simulation also showed the different influence of stomata on CO 2 and water vapor fluxes.

Fig. 1 :
Fig. 1: The response of transpiration rate (T r ) 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 )

Fig. 3 :
Fig. 3: The diurnal variation of transpiration rate (T r ) per unit ground in apple orchard from June 14 th to 20 th (LAI = 2.53)