IntroductionTranspiration rate depends on a balance among water supply to the plant, energy sup-ply to evaporate water within the leaf and the ease with which water vapour can escape from the leaves. These processes are dominated by two environmental factors, namely solar radiation and the water potential of the atmosphere. The ability to control stoma-tal aperture allows plants to respond quickly to changing environment, for example to avoid excessive water loss or limit uptake of liquid or gaseous pollutants through sto-mata. Stomatal opening and closing is modulated by uptake and loss of water in guard cells, which changes their turgor pressure. Canopy transpiration and stomatal conduct-ance are very useful plant-based stress indicators but continuous and real-time calcu-lations remains difficult and expensive. Calculation of potential evapotranspiration is based on physical analysis at three levels: (a) Penman equation; (b) Monteith-modified Penman equation; (c) Parameterization of P-M equation with respect to dependence of stomatal conductance on meteorological variables.

Material and MethodsPlant MaterialTwo–years old apple trees of cv. ‘Gala Galaxy’ on a M9 rootstock and trained accord-ing to a central leader system were used as replicates based on their equal values of trunk diameter and other biometric measurements, i.e. affinity index, vigour, number of branches and shoots, etc. Trees were planted 3 × 1 m apart, in a N–S orientation, at a small experimental orchard in Kosovo. The plots were regularly irrigated until the meas-urement period. Trees were not pruned during the experiment and their were yet in ju-venile (non-cropping) phase.

Experimental setupSF was measured using sap flow sensors EMS 62 (EMS Brno), based on SHB (stem heat bal-ance) method. Sensors were in-stalled on shoots (12 mm thick) on 8 trees at their trunk (Figure 1). The measuring interval was every minute with 1 s warm-up and storing interval every 15 minutes during July-September 2013. A portable meteorologi-cal station Minikin RTHi (EMS Brno, CZ) measured the Rs, Ta and RH. VPD was calculated from vapour pressure and rela-tive humidity. Plants were sub-ject to water stress, beside oth-ers (high radiation and temperature). Soil water potential values were kept around 0,5 MPa.

Modelling Penman equation describes water evaporation from a homogeneous short trimmed lawn well saturated with water accord-ing to the formula (here in terms of en-ergy)(1). The uncertain second “wind” part of Penman equation was replaced with a turbulent diffusion theory based expression(2). The (wind speed dependent) aerody-namic conductance was calculated from

canopy parameters(3).

Parameterization of Pen-man-Monteith equation is based on the assumption that the stomatal con-ductivity depends on solar radiation and VPD values according a suitable formula, e.g. Loham-mar, 1980. Parameterization process is usually

based on daily mean values of main environmental factors (R, VPD) and the most com-mon approach is to rearrange the P-M equation for stomatal conductance and than to find the best fit to R and VPD. The common Lohammar equation describing the R and VPD influence to stomatal conductance is written in the form(4) supposing stomata opening due to solar activity and clo-sure due to high evaporating demands. Differently from this approach, we have used diurnal courses of variables instead of commonly used daily means. We have used a different formula(5) describing the influence of VPD to stomata closure and the parameterization process is performed as a direct non-line-ar multi-regression analysis of P-M equa-tion.

Agricultural University of Tirana, Faculty of Agriculture & Environment, Department of Horticulture

Address: Koder-Kamez, Tirana, Albania www.ubt.edu.al

Modelling Canopy Transpiration and Stomatal Conductance of Young Apples Using a Parameterized Penman-Monteith Equation

E. Kullaj1, V. Avdiu, L. Lepaja, J. Kucera, and F. Thomaj 1Dep. Horticulture, Faculty of Agriculture and Environment, Agricultural University of Tirana, Kodër-Kamëz, 1010, Tirana, Albania Tel: +355684096186 Email: ekullaj@ubt.edu.al

Instead of standard rearrangement of P-M equation for gs calculation and following dis-crete regression analyses to R and VPD we wrote the complex P-M equation which already includes the gc as the function of R and VPD(6). Using a non-linear multiregres-sion analysis pro-vided by Mini32 software, PrgmClc module, parameters a, b, Ro, glim and gmin best fitting to (usually sap flow based) measured canopy transpiration and the one calculated by P-M equation are obtained. The P-M equation for the fit analysis was written but for faster analysis, the numerator is calculated separately.

Results and DiscussionThis fast modelling approach seem to properly calculate canopy transpiration (see Fig. 4 for comparison of measured and calculated values) and canopy conductance (see Fig. 5 for comparison between VPD and gcvalues). Fig. 6 shows the stomata response to in-creasing radiation and VPD.

ConclusionsUse of diurnal courses brings more details to the analysis of canopy transpiration and conductance and it perfectly shows the agreement between measured and calculated canopy transpiration (sap flow) patterns. This approach helps to understand canopy water status from the point of view of daily dynamics. The models offers an approach to study stomata behaviour to environmental variables and agricultural practices.

Fig. 4. (top) Dynamics of numerator used in the P-M equation and slope. (bottom) Actual and cal-culated transpiration using a scaling procedure from sap flow data (selected period)

Poster presented at the Physiological Principles and Their Application to Fruit Production

Geneva, NY, USA (March 26-28, 2014) http://events.cals.cornell.edu/ishsphysiology2014

Fig. 3. (top) Script for calculating variables necessary for para-metrization. (bottom) The “Fit”module in Mini32 software show-ing the initial param-eters for the procedure of finding the model which calculates canopy tran-spiration and stomatal conductance of apple trees. It shows both calculated values (blue) and the ac-tual (black) dots measured from sap flow and the correlation index (0.975)

Fig. 6. Simulation of stomata aperture and closure in response to global radiation (Rg) and vapour pressure deficit (VPD) respectively

where:Rn – net radiation [W/m2]G – soil heat flux [W/m2]D – vapor pressure deficit [Pa]w – wind speed [m/sec]γ - psychrometric constant [Pa/K]Δ – slope of saturation water vapor pressure deficit [Pa/K]λ – water heat capacity[J/kg]a, b – empirical parameters

where:cp – specific heat of air [J/m3]ρ – density of dry air [kg/m3]ga – aerodynamic conductance [s/m]gs – canopy (stomatal) conductance [s/m]k – von Karman constant [-]d – zero plane displacement [m]zo – canopy roughnes [m]z – wind speed measurement height [m]

Fig. 1. Particular EMS 62 on trunks of young apple trees

(6)

(1)

(2)

(3)

(4)

(5)

Fig. 5. Daily patterns of va-pour pressure deficit (VPD) and calculated canopy con-ductance (gc) during a se-lected measuring period. It is easily noticeable the reduction in stomata con-ductance when VPD values increases with radiation and temperature.