Modeling Hydraulic Dynamics at Different Levels of Fruit Tree Canopies under Abiotic Stress

Fruit production provides an important contribution in the agricultural sector in Albania, providing about 20 percent of the total agriculture output. Apple is not only the main fruit produced in Albania, but its production has marked the highest growth by quadrupling between 1985 (18200 tons) and 2012 (71300 tons). Use of sap flow for either studying plant water relations or plant water use has received particular research and practical importance [1,2]. Various methods have been conceived attempting to increase the accuracy of measurement in a wide variety of species, organs and climatic or technological conditions.


Introduction
Fruit production provides an important contribution in the agricultural sector in Albania, providing about 20 percent of the total agriculture output. Apple is not only the main fruit produced in Albania, but its production has marked the highest growth by quadrupling between 1985 (18200 tons) and 2012 (71300 tons). Use of sap flow for either studying plant water relations or plant water use has received particular research and practical importance [1,2]. Various methods have been conceived attempting to increase the accuracy of measurement in a wide variety of species, organs and climatic or technological conditions. Climatic variables like solar radiation (Rs), air temperature (Ta), canopy temperature (Tc), vapour pressure difference (VPD) and reference evapotranspiration (ET 0 ) drive or relate to sap flow. Solar radiation within the 400-700 nm wavebands (photosynthetic photon flux, PPF) drives the photosynthetic process, and global radiation (300-2500 nm waveband) provides the energy for transpiration activity [3]. The relationship is positive because increasing the radiation load on the leaf results in an increase in the dissipation of sensible heat and latent heat, even at constant levels of Ta and VPD [4][5][6]. Plant canopy geometry determines the spatial and temporal interaction between incoming radiation flux and foliage, and therefore plays a central role in quantifying the driving force for leaf physiological processes [7][8][9][10]. Effect of air temperature (and obviously canopy temperature) on SF is even higher and proportional. Varying levels of the latest influences relative humidity (RH) and consequently changes VPD altering the transpiration flow (and sap flow rates).
Most these variables change significantly within fruit tree canopies and depending on the level of canopy, their effect on sap flow could be different [11]. The purpose of the research presented here was to unravel the relationship between sap flow and the above (micro) meteorological variables at various levels of a tree canopy to demonstrate which of them better predicts sap flow and at what respective canopy level. Models that predict sap flow and therefore transpiration have important applications in many areas including agricultural production, automated irrigation, tree ecophysiology, climate change, hydrology, etc.

Plant material
Eight-years old apple trees of cv. 'Golden Delicious' on a dwarfing M9 EMLA rootstock and trained according to a central leader system were used as replicates based on trunk diameter and other biometric measurements, i.e. affinity index, vigour, number of branches and shoots, etc. Homogeneity of these trees was evaluated under another study [12]. Trees were planted 3 × 1 m apart, in an N-S orientation, at a 6 ha commercial orchard in Lushnja (40°58'31.90"N 19°40'15.76" E). The plots were regularly irrigated until the measurement period. Trees were not pruned during the experiment, and crop load was adjusted by manual thinning in accordance with commercial practice. The division of tree canopies into three layers was based on their position relative to the main leader and their training in relation to the wires.

Discretization of the canopy
The division of tree canopies into layers was based mainly on light interception and canopy temperature. Light interception was characterized as silhouette to total area ratio (STAR) [13] using a modified 3-D mock up of an 8 -years old apple tree [14]. Canopy layer temperature was measured with an infrared radiometer (Apogee SI 100, www.apogeeinstruments.com). Using a combination of PAR values calculated from STAR and Tc, three classes or layer of canopy were defined, pertaining approximately to the division into upper, middle and lower canopy. Shadowing of adjacent rows and upper part of the canopy were the major factors determining the belonging of branches to the lower and medium layer.
Simplifications and codes chosen for multi scale descriptions of tree topology were used in previous studies [13,[15][16][17]. On the basis of above canopy discretization, shoots about 12 mm thick belonging to each class of layer were labelled accordingly for SF measurement. Shoots chosen had an equal leaf area (LA). As the scope of this research was not to quantify the total SF but rather to predict it by meteorological variables, SF measured represent the average SF rate (kg/h) of 12 mm thick shoots belonging to a certain canopy layer but from different positions distances from the main leader as well as cardinal points.(upper = twigs coming out the bottom scaffold branches, at the level of the bottom wire support; middle = twigs coming out the middle primary branches at the level of the middle wire support; lower = twigs coming out from almost the top of the central leader, at the level of the third wire support).

Measurement of sap flow and (micro)meteorological variables
SF was measured using sap flow sensors EMS 62 (EMS Brno), based on SHB (stem heat balance) method [18,19]. Sensors were installed on shoots (12 mm thick) on 5 trees at three levels of the canopy. The measuring interval was every minute with 1 s warm-up and storing interval every 15 minutes during July 2012. Infrared radiometers (Apogee SI 100) continuously measured Tc respectively at these three canopy levels. A portable meteorological station Minikin RTHi (EMS Brno, CZ), located in the centre of the orchard, measured the Rs, Ta and RH. Calculation of VPD from relative humidity and PET (potential evapotranspiration) was implemented in Mini 32 (EMS Brno, CZ). The closest state meteorological station measured wind speed, rainfalls and ET 0 .

Experimental design and statistical analysis
The design of the experiment was completely randomized with four replications, each replication consisting of three adjacent rows of five trees. Measurements were taken in the inner tree of the central row of each replicate, the other trees serving as borders. All the measurements were taken in the same tree in each replicate. Values for each day and replicate were averaged before the mean and the standard error were calculated.
Considering that the relationship between the series of predictor or explanatory variables (GR, PAR, Ta, Tc, RH, VPD and ET 0 ) and the response variable (SF) is linear, the experiment was designed as a simple linear regression analysis [20]. As the predictor variables are random, the method used was reduced major axis (RMA) regression. Regression lines between the three data sets representing the three levels of the canopy were compared using the analysis of covariance. To model the relationship between the series of predictor/explanatory variables (Rs, Ta, Tc, VPD and ET 0 ) and the response variable (SF), regressions of various orders were computed using R statistical software. Regression lines were compared using various statistical techniques from R packages.   All the parameters concerning the evaporative demand where relatively constant during the measurement period with an obvious daily fluctuation trend (Figure 1a-1d). During the experimental period, in both years, there was not rainfall event allowing us to maintain the water stress conditions in the experimental site area. Rs levels were high with maximum levels as high as 986. 7   Mean daily air temperature (Tm) and midday air temperature (Tmd) presented a similar daily trend. During the experiment, average Tm and average daily minimum temperatures were 25 and 13°C, respectively (Figure 1b), and average mean relative humidity was 66%. Mean VPD values presented a similar seasonal trend (Figure 1c). Intercorrelations shown in Figure 2 using a correlogram indicate a stronger correlation of SF low and SF upper with Rs and ET 0 and less with VPD and Tc whilst for SF middle a higher correlation with VPD and ET 0 . SF tree was more correlated with VPD and Tc. In general, increases in predictor variables were associated with increases in SF until reaching high values, after which SF levelled off as they increased, thus, departing from linearity.

Results and Discussion
The correlogram in Figure 2 shows intercorrelations between sap flow (SF) at various levels of the canopy (SF Low , SF Middle , SF Upper and of the whole tree (SF Tree ) and environmental parameters (Rs, Tc, VPD, ET 0 ). Rows and columns have been reordered using principal components analysis (PCA). All correlations are positive (blue); the darker and more saturated the color, the greater the magnitude of the correlation. The upper triangle of cells displays the same information using pies. The strength of the correlation is displayed by the size of the filled pie slice. Positive correlations fill the pie starting at 12 o'clock and moving in a clockwise direction.
Residuals versus Fitted graph indicates evidence of curved relationship, suggesting the addition of the quadratic or cubic term. Thus, best-fit curve using polynomial regression, a secondorder (quadratic) and third-order (cubic) yielding equations with a higher determination coefficient. However, only in few cases these coefficients were significantly higher. The study confirmed that Ta [21,22] and Tc are not an accurate indicator of the evaporative demand of the atmosphere. (Figure 3) Probability plot of studentized residuals against a t distribution with n-p-l degrees of freedom (n = sample size, p = number of regression parameters, including intercept). A 95 per cent confidence envelope is produced using a parametric bootstrap.

Agricultural Research & Technology: Open Access Journal
Of the relationships between the water status indicator (SF) and the predictor variables (covariates), Ta presented the weakest r 2 value. In general, a cubic fit of the regression between SF and environmental variables yielded equations with a determination coefficient higher than those found for the first and second order regressions. However, it was statistically significant only in few cases described below. For the lower part of the apple canopy (Figure 4a), the cubic fit regression between SF and Rs was characterized by a higher correlation (r 2 = 0.91) than other predictors, especially Ta and VPD (r 2 = 0.49 and 0.48 respectively). SF was also highly related to changes in ET 0 (r 2 = 0.87).   Regressions of SF values of the middle part of the canopy (Figure 4b) against evaporative demand parameters found that VPD, ET 0 and Rs could predict almost similarly SF (r 2 = 0.89, 0.88 and 0.86 respectively). As for the lower part of the canopy, Ta was not a good predictor. The regression analysis for the purposes of modelling SF of the upper part of the apple canopy (Figure 4c) found again VPD, Rs and ET 0 as very good predictors of SF also for this part of the canopy (r 2 = 0.95, 0.95 and 0.94). Again, Ta was not a well correlated with SF (Figure 4d).

Conclusion
The above mentioned results indicate that baselines or reference values for sap flow rate as a plant-based water status indicators can be obtained for apple trees, even though there was a certain scattering in the relations between the plant-based measurements and the environmental variables. The regression analysis indicated that the highest coefficients of determination were obtained for the regressions of S Flow against Rs, SF middle and SF upper against VPD and SF tree against ET 0 . However, these correlations must be used within their confidence levels.
Notwithstanding, at the current level of this research, the best-fit regression approach of modeling can offer a proxy of daily SF values but, in general, they hardly simulate the daily SF dynamics, especially when the evaporative parameters highly fluctuate during the day or especially for the middle and bottom part of the canopy. This gross estimation of SF could be used in automatic irrigation scheduling in apple trees [23].