Modelling fruit-temperature dynamics within apple tree crowns using virtual plants

BACKGROUND AND AIMS

Fruit temperature results from a complex system involving the climate, the tree architecture, the fruit location within the tree crown and the fruit thermal properties. Despite much theoretical and experimental evidence for large differences (up to 10 °C in sunny conditions) between fruit temperature and air temperature, fruit temperature is never used in horticultural studies. A way of modelling fruit-temperature dynamics from climate data is addressed in this work.

METHODS

The model is based upon three-dimensional virtual representation of apple trees and links three-dimensional virtual trees with a physical-based fruit-temperature dynamical model. The overall model was assessed by comparing model outputs to field measures of fruit-temperature dynamics.

KEY RESULTS

The model was able to simulate both the temperature dynamics at fruit scale, i.e. fruit-temperature gradients and departure from air temperature, and at the tree scale, i.e. the within-tree-crown variability in fruit temperature (average root mean square error value over fruits was 1·43 °C).

CONCLUSIONS

This study shows that linking virtual plants with the modelling of the physical plant environment offers a relevant framework to address the modelling of fruit-temperature dynamics within a tree canopy. The proposed model offers opportunities for modelling effects of the within-crown architecture on fruit thermal responses in horticultural studies.

Modelling fruit-temperature dynamics within apple tree crowns using virtual plants

BACKGROUND AND AIMS

Fruit temperature results from a complex system involving the climate, the tree architecture, the fruit location within the tree crown and the fruit thermal properties. Despite much theoretical and experimental evidence for large differences (up to 10 °C in sunny conditions) between fruit temperature and air temperature, fruit temperature is never used in horticultural studies. A way of modelling fruit-temperature dynamics from climate data is addressed in this work.

METHODS

The model is based upon three-dimensional virtual representation of apple trees and links three-dimensional virtual trees with a physical-based fruit-temperature dynamical model. The overall model was assessed by comparing model outputs to field measures of fruit-temperature dynamics.

KEY RESULTS

The model was able to simulate both the temperature dynamics at fruit scale, i.e. fruit-temperature gradients and departure from air temperature, and at the tree scale, i.e. the within-tree-crown variability in fruit temperature (average root mean square error value over fruits was 1·43 °C).

CONCLUSIONS

This study shows that linking virtual plants with the modelling of the physical plant environment offers a relevant framework to address the modelling of fruit-temperature dynamics within a tree canopy. The proposed model offers opportunities for modelling effects of the within-crown architecture on fruit thermal responses in horticultural studies.

Contributions of foliage distribution and leaf functions to light interception, transpiration and photosynthetic capacities in two apple cultivars at branch and tree scales

Both the spatial distribution of leaves and leaf functions affect the light interception, transpiration and photosynthetic capacities of trees, but their relative contributions have rarely been investigated. We assessed these contributions at the branch and tree scales in two apple cultivars (Malus x domestica Borkh. 'Fuji' and 'Braeburn') with contrasting architectures, by estimating their branch and tree capacities and comparing them with outputs from a radiation absorption, transpiration and photosynthesis (RATP) functional-structural plant model (FSPM). The structures of three 8-year-old trees of each cultivar were digitized to obtain 3-D representations of foliage geometry. Within-tree foliage distribution was compared with shoot demography, number of leaves per shoot and mean individual leaf area. We estimated branch and tree light interception from silhouette to total leaf area ratios (STAR), transpiration from sap flux measurements and net photosynthetic rates by the branch bag method. Based on a set of parameters we previously established for both cultivars, the outputs of the RATP model were tested against STAR values, sap fluxes and photosynthetic measurements. The RATP model was then used to virtually switch foliage distribution or leaf functions (stomatal and photosynthetic properties), or both, between cultivars and to evaluate the effects on branch and tree light interception, transpiration and photosynthetic capacities in each cultivar. 'Fuji' trees had a higher proportion of leaf area borne on long shoots, fewer leaves per unit shoot length and a larger individual leaf area than 'Braeburn' trees. This resulted in a lower leaf area density and, consequently, a higher STAR in 'Fuji' than in 'Braeburn' at both branch and tree scales. Transpiration and photosynthetic rates were significantly higher in 'Fuji' than in 'Braeburn'. Branch heterogeneity was greater in 'Braeburn' than in 'Fuji'. An analysis of the virtual switches of foliage distribution or leaf function showed that differences in leaf spatial distribution and functions had additive effects that accounted for the lower transpiration and photosynthetic rates of branches and trees of 'Braeburn' compared with 'Fuji'. Leaf distribution had a more important role at the branch scale than at the tree scale, but the leaf function effect exceeded the leaf distribution effect at both scales. Our study demonstrated the potential of FSPM to disentangle physiological differences between cultivars through in silico scenarios.

Simple equations to estimate light interception by isolated trees from canopy structure features: assessment with three-dimensional digitized apple trees

* Simple models of light interception are useful to identify the key structural parameters involved in light capture. We developed such models for isolated trees and tested them with virtual experiments. Light interception was decomposed into the projection of the crown envelope and the crown porosity. The latter was related to tree structure parameters. * Virtual experiments were conducted with three-dimensional (3-D) digitized apple trees grown in Lebanon and Switzerland, with different cultivars and training. The digitized trees allowed actual values of canopy structure (total leaf area, crown volume, foliage inclination angle, variance of leaf area density) and light interception properties (projected leaf area, silhouette to total area ratio, porosity, dispersion parameters) to be computed, and relationships between structure and interception variables to be derived. * The projected envelope area was related to crown volume with a power function of exponent 2/3. Crown porosity was a negative exponential function of mean optical density, that is, the ratio between total leaf area and the projected envelope area. The leaf dispersion parameter was a negative linear function of the relative variance of leaf area density in the crown volume. * The resulting models were expressed as two single equations. After calibration, model outputs were very close to values computed from the 3-D digitized databases.

A photographic gap fraction method for estimating leaf area of isolated trees: Assessment with 3D digitized plants

A method for computing leaf area of isolated trees from perspective photographs was developed. The method is based on gap fraction inversion. Photographs are discretized into picture zones where gap fraction is computed from image processing. Canopy volume and leaf area density associated with each picture zone are computed from geometrical considerations and inversion of gap fraction equations. Total leaf area and the vertical profile of leaf area are computed from the product of associated volume and its density. The method has been implemented in software called Tree Analyser, written in C++. The method has been tested by comparison with direct estimation of leaf area of three-dimensional (3D) digitized trees of walnut, peach, mango, olive and rubber. Estimated leaf area was sensitive to picture discretization, individual leaf size and leaf inclination distribution. Optimal size of picture discretization was 17 times projected leaf size. Total leaf area was estimated by using a set of eight photographs taken around the tree in the main horizontal directions: deviation ranged from -11% in peach tree to +5% in rubber tree. The method allows fast and nondestructive monitoring of leaf area of individual tree canopies. The next version of the method will include the estimation of 3D leaf area distribution within the canopy.

A method for 3D reconstruction of tree crown volume from photographs: assessment with 3D-digitized plants

We developed a method for reconstructing tree crown volume from a set of eight photographs taken from the N, S, E, W, NE, NW, SE and SW. This photographic method of reconstruction includes three steps. First, canopy height and diameter are estimated from each image from the location of the topmost, rightmost and leftmost vegetated pixel; second, a rectangular bounding box around the tree is constructed from canopy dimensions derived in Step 1, and the bounding box is divided into an array of voxels; and third, each tree image is divided into a set of picture zones. The gap fraction of each picture zone is calculated from image processing. A vegetated picture zone corresponds to a gap fraction of less than 1. Each picture zone corresponds to a beam direction from the camera to the target tree, the equation of which is computed from the zone location on the picture and the camera parameters. For each vegetated picture zone, the ray-box intersection algorithm (Glassner 1989) is used to compute the sequence of voxels intersected by the beam. After processing all vegetated zones, voxels that have not been intersected by any beam are presumed to be empty and are removed from the bounding box. The estimation of crown volume can be refined by combining several photographs from different view angles. The method has been implemented in a software package called Tree Analyzer written in C++. The photographic method was tested with three-dimensional (3D) digitized plants of walnut, peach, mango and olive. The 3D-digitized plants were used to estimate crown volume directly and generate virtual perspective photographs with POV-Ray Version 3.5 (Persistence of Vision Development Team). The locations and view angles of the camera were manually controlled by input parameters. Good agreement between measured data and values inferred from the photographic method were found for canopy height, diameter and volume. The effects of voxel size, size of picture zoning, location of camera and number of pictures were also examined.

Does variability in shoot carbon assimilation within the tree crown explain variability in peach fruit growth?

A three-dimensional model of radiative transfer and leaf gas exchange was used to quantify daily carbon (C) assimilation of all fruit-bearing shoots (FBS) in an early maturing 6-year-old peach tree (Prunus persica L. Batsch) with a heavy crop load. For a sample of FBS (n=36), growth of fruit and leafy shoots was measured every 1-2 weeks from 24 days after bloom (DAB) until harvest, between 93-101 DAB. The objective was to relate shoot C assimilation with harvested fruit mass for each shoot to test the hypothesis that variation in C supply contributes significantly to variation in fruit growth within and among FBS. Mean C assimilation of the sampled shoots was 0.07 g C fruit(-1) day(-1), but varied between 0.014 and 0.32 g C fruit(-1) day(-1). This indicates that C availability for fruit growth would have varied significantly among individual FBS if they were autonomous. Mean fruit dry mass on each FBS varied between 0.716 and 7.68 g C at harvest, and most of the variation originated among, not within, individual FBS. However, there were no correlations between the mean and standard deviation of fruit mass and fruit relative growth rate when each was plotted against shoot C assimilation, indicating that factors such as those regulating C demand of fruit, or C transfer among individual FBS, may be more important in controlling variability in fruit growth than intra-crown variability in shoot C assimilation. Under the study conditions, FBS were non-autonomous for C, because a model of fruit and leafy shoot growth was unable to reproduce the observed growth without supplementary contribution of C from shoots without fruit.

A biochemical model of photosynthesis for mango leaves: evidence for the effect of fruit on photosynthetic capacity of nearby leaves

Variations in leaf nitrogen concentration per unit mass (Nm) and per unit area (Na), mass-to-area ratio (Ma), total nonstructural carbohydrates (Ta), and photosynthetic capacity (maximum carboxylation rate, electron transport capacity, rate of phosphate release in triose phosphate utilization and dark respiration rate) were studied within the digitized crowns of two 3-year-old mango trees (Mangifera indica L.) on La Réunion Island. Additional measurements of Nm, Na, Ma, Ta and photosynthetic capacities were performed on young, fully expanded leaves of 11-year-old mango trees. Leaves of similar gap fractions were taken far from and close to developing fruits. Unlike Nm, both Na and Ta were linearly correlated to gap fraction. Similar relationships were found for all leaves whatever their age and origin, except for Ta, for which we found a significant tree effect. Photosynthetic capacity was nonlinearly correlated to Na, and a unique relationship was obtained for all types of leaves. Photosynthetic acclimation to light was mainly driven by changes in Ma, but allocation of total leaf N between the different photosynthetic functions also played a substantial role in acclimation to the lowest irradiances. Leaves close to developing fruits exhibited a higher photosynthetic capacity than other leaves, but similar Ta. Our data suggest that Ta does not control photosynthetic capacity in mango leaves. We used the data to parameterize a biochemically based model of photosynthesis and an empirical stomatal conductance model, allowing accurate predictions of net photosynthesis of leaves in field-grown mango trees.

Exploring within-tree architectural development of two apple tree cultivars over 6 years

The present study addresses the prediction of apple tree development, taking into account both the number and within-tree position of tree components. The architectural development of two trees per scion cultivar, 'Fuji' and 'Braeburn', was studied by describing all shoots over 6 years. Flowering and fruiting were observed over 3 years. The description included different scales [entire trees, axes, growth units (GUs) and metamers], and the analysis compared all axes of the trees as a function of their branching order and age. Three main aspects of vegetative development were investigated: the quantity of primary growth; the number and nature of developing axillary shoots; and meristem death. Results confirm the existence of within-tree morphological gradients, and show that the decrease in growth was comparable in magnitude for all axes and GUs, irrespective of their position. This decrease results from a reduction in the number of metamers per GU, which was modelled by an exponential function. The decrease in growth involved changes in the number and nature of the axillary shoots, which could be described by simple functions. The probability of spur death was constant over the years but differed according to cultivar and type of bearing shoot. The within-tree probability of flowering and fruiting was predictable for 'Braeburn' because axes, regardless of their position and type, had a high probability of flowering and a low probability of fruit set which led to a regular bearing habit. In contrast, 'Fuji' had an alternating bearing behaviour that was more complex to predict. This appeared to result from a synchronized increase in the probability that all GUs at tree scale are floral, combined with a high probability of fruit set. The consequences of these results for both yield prediction and architectural simulations are discussed.

Canopy structure and light interception in Quercus petraea seedlings in relation to light regime and plant density

Foliage structure was measured on 1- and 2-year-old Quercus petraea (Matt.) Liebl. seedlings grown in 100 or 18% sunlight at a planting density of 2.8 or 25 plants per m(2). A three-dimensional digitizing device was used to acquire the spatial position and orientation of all leaves within the seedlings and of all seedlings within the plot. The data were used to obtain (1) quantitative information on canopy structure, including leaf area index (LAI), seedling leaf area, number of leaves, leaf area density and leaf orientation; and (2) structural information on foliage arrangement from virtual images to estimate light interception by individual seedlings (STAR) and light partitioning among seedlings. During the second year, shading significantly reduced total leaf area and number of leaves but increased individual leaf area. The STAR was greater for seedlings in shade than in full sunlight because of the more horizontal orientation of leaves. Leaf area density was unaffected by the full sun treatments, and changes in leaf area dispersion had no effect on light-interception efficiency. No plant density effect was observed during the first year. During the second year, only the high plant density treatment induced mutual shading between seedlings, resulting in greater competition for light among seedlings in the full sun treatment than in the shade treatment. The small treatment-induced changes in light interception indicate that Q. petraea has low morphological plasticity of foliage structure compared with other species.

Photosynthetic light acclimation in peach leaves: importance of changes in mass:area ratio, nitrogen concentration, and leaf nitrogen partitioning

Photosynthetic light acclimation of leaves can result from (i) changes in mass-based leaf nitrogen concentration, Nm, (ii) changes in leaf mass:area ratio, Ma, and (iii) partitioning of total leaf nitrogen among different pools of the photosynthetic machinery. We studied variations in Nm and Ma within the crowns of two peach (Prunus persica L. Batsch) trees grown in an orchard in Portugal, and one peach tree grown in an orchard in France. Each crown was digitized and a 3-D radiation transfer model was used to quantify the intra-crown variations in time-integrated leaf irradiance, <PARi>. Nitrogen concentration, leaf mass:area ratio, chlorophyll concentration, and photosynthetic capacity were also measured on leaves sampled on five additional peach trees in the orchard in Portugal. The data were used to compute the coefficients of leaf nitrogen partitioning among carboxylation, bioenergetics, and light harvesting pools. Leaf mass:area ratio and area-based leaf nitrogen concentration, Na, were nonlinearly related to <PARi>, and photosynthetic capacity was linearly related to Na. Photosynthetic light acclimation resulted mainly from changes in Ma and leaf nitrogen partitioning, and to a lesser extent from changes in Nm. This behavior contrasts with photosynthetic light acclimation observed in other tree species like walnut (Juglans regia L.) in which acclimation results primarily from changes in Ma.

Spatial distribution of leaf dry weight per area and leaf nitrogen concentration in relation to local radiation regime within an isolated tree crown

To assess the spatial distribution of photosynthetic capacity within an isolated 20-year-old walnut tree (Juglans regia L.) crown, the distribution of relevant leaf characteristics was measured. Variations in leaf dry weight per area (W(a)), and nitrogen content on a weight (N(w)) and area basis (N(a)) were studied along two horizontal and one vertical gradients of leaf irradiance, at two dates (July 30 and September 3). In addition, the content of total nonstructural carbon on a weight (TNC(w)) and area basis (TNC(a)) was measured on July 30. Concurrently, the spatial distribution of daily integrated leaf irradiance within the crown was simulated by a three-dimensional radiation transfer model over a one week period before sampling at each date. High spatial heterogeneity was observed for W(a) (from 50 to 140 g m(-2)), TNC(a) (from 4 to 17 g m(-2)) and N(a) (from 1.2 to 3.6 g m(-2)) among the foliage. Although TNC(w) and N(w) were not correlated and only weakly correlated to daily leaf irradiance, respectively, W(a), TNC(a) and N(a) were strongly correlated to daily leaf irradiance. The relationship between observed N(a) and simulated daily leaf irradiance was used to assess the spatial distribution of N(a) within the crown at each date. Total leaf nitrogen in the foliage was estimated to be 339 g in late July and 317g in early September. For the whole crown (i.e., 1729 current-year shoots), N(a) increased strongly with basal shoot diameter (an index of "shoot vigor"), highlighting the fact that large shoots were mainly located in sunlit locations and exhibited high photosynthetic capacity.

Spatial distribution of leaf dry weight per area and leaf nitrogen concentration in relation to local radiation regime within an isolated tree crown

To assess the spatial distribution of photosynthetic capacity within an isolated 20-year-old walnut tree (Juglans regia L.) crown, the distribution of relevant leaf characteristics was measured. Variations in leaf dry weight per area (W(a)), and nitrogen content on a weight (N(w)) and area basis (N(a)) were studied along two horizontal and one vertical gradients of leaf irradiance, at two dates (July 30 and September 3). In addition, the content of total nonstructural carbon on a weight (TNC(w)) and area basis (TNC(a)) was measured on July 30. Concurrently, the spatial distribution of daily integrated leaf irradiance within the crown was simulated by a three-dimensional radiation transfer model over a one week period before sampling at each date. High spatial heterogeneity was observed for W(a) (from 50 to 140 g m(-2)), TNC(a) (from 4 to 17 g m(-2)) and N(a) (from 1.2 to 3.6 g m(-2)) among the foliage. Although TNC(w) and N(w) were not correlated and only weakly correlated to daily leaf irradiance, respectively, W(a), TNC(a) and N(a) were strongly correlated to daily leaf irradiance. The relationship between observed N(a) and simulated daily leaf irradiance was used to assess the spatial distribution of N(a) within the crown at each date. Total leaf nitrogen in the foliage was estimated to be 339 g in late July and 317g in early September. For the whole crown (i.e., 1729 current-year shoots), N(a) increased strongly with basal shoot diameter (an index of "shoot vigor"), highlighting the fact that large shoots were mainly located in sunlit locations and exhibited high photosynthetic capacity.

A theoretical analysis of radiation interception in a two-species plant canopy

Classical radiation interception laws for monospecific canopies cannot be used directly for bispecific canopies. They are always based on the gap frequency concept (i.e., the probability of no interception), which does not provide any information about the sharing of intercepted radiation between species. A theoretical analysis is reported that relates the radiation interception probabilities to the geometrical structure of the crop (i.e., the leaf area density and the leaf angle distribution of each component) and the foliage dispersion. The leaf dispersion globally describes the spatial relations between the leaf elements; it may be regular if the leaves avoid mutual shading, random, or clumped if they tend to overlap. For such two-species canopies, the leaf dispersions within each component (WSLD: within-species leaf dispersion) and between two species (BSLD: between-species leaf dispersion) are distinguished. Using bivariate multinomial distributions, general expressions for the gap frequency and the interception probabilities of a homogeneous vegetation layer were set as exponential functions of the foliage thickness, taking into account a number of dispersion parameters as small as possible. First, one WSLD for each species describes the rate of foliage overlap between the leaves of this species; it is quite similar to the leaf dispersion of single-species canopies. Second, the rate of foliage overlap between species is characterized by one BSLD. As in monospecific canopies, this parameter is positive, zero, or negative, respectively, for regular, random, or clumped BSLD. Third, another BSLD parameter has to be used if the foliage overlap between species is more than random (i.e., in the case of clumped BSLD); the latter shows the direction of overlap between species and may be taken as the probability of finding a leaf element of the first species in the case of marked overlapping. Suggestions for estimating the leaf dispersion parameters and possible uses of such relations are also discussed.