3D thematic maps of the chemical parameters of orange fruits

. Since orange is the most produced and consumed fruit in Brazil and since its position on the tree may influence its physical and chemical attributes, current assay modeled a three-dimension spatial variability of total soluble solids (TSS) and ascorbic acid (AA) contents of the fruit in an orange orchard according to fruit position (coordinates x, y and z) on the plant and analyzed solar radiation on them. The experiment was conducted in Nova Laranjeiras, Paraná State, Brazil, and analyzed 715 fruit (Monte Parnaso variety) from nine trees in 2011, 2012 and 2013. Results showed that high TSS contents were reported in the tree´s peripheral area in the two analyzed thirds due to a high solar radiation. Highest AA rates were reported in the apical third. In the case of quadrants, higher AA levels were found in SE and NE (morning sun) with regard to the apical third and in SW and SE (afternoon sun) with regard to the basal third. The three-dimension interpolation method displays the spatial variability of the fruit’s physical attributes by three-dimensional


Introduction
Knowledge on the spatial and temporal variability of fruits´ chemical attributes makes one decide on adopting a specific management of land, orchards or individual plants.Several studies have been carried out on this subject, including the distribution of the root system of a citrus crop under water stress (Alves Junior, Bandaranayake, Parsons, & Evangelista, 2012), relief and spatial variability of soil properties in an area cultivated with citrus (Leão, Marques Junior, Souza, Siqueira, & Pereira, 2011), citrus yield maps (Molin, Colaço, Carlos, & Mattos Junior, 2012) and the study on determinants of acceptability of orange tastes (Obenland et al., 2009).The states of São Paulo in Brazil and Florida in the United States are the largest producers of orange (Citrus sinensis (L.) Osbeck) in the world (Organização das Nações Unidas para a Alimentação e a Agricultura [FAO], 2014).
The chemical properties of fruits depend on weather conditions and on the exposure of plant and fruits to solar radiation during their formation and maturation (Lemos, Siqueira, Salomão, Cecon, & Lemos, 2012).As a rule, total solar radiation on a vertical surface depends on its azimuth angle (Mohammadi & Khorasanizadeh, 2015).According to Detoni, Herzog, Ohland, Kotz, and Clemente (2009), the size of trees, spacing, row orientation, canopy shape and type of planting system adopted influence the distribution of solar radiation on the plant.
Selecting the right time to harvest citrus fruits is highly important, although different stages of fruit maturation may occur on the same tree.The position of the fruit on the tree canopy is an important factor, with qualitative differences (Cronje, Barry, & Huysamer, 2011, Khalid et al., 2012).
According to Verreynne, Rabe, and Theron (2013), studies on the position of the fruit on the tree may define a fruit sampling plan for quality analysis and may serve as a guide for harvest and post-harvest.They may even be a help in the development of pruning strategies.Fruits facing west (morning sun) have higher levels of total soluble solids and maturity index.On the other hand, higher rates of total titratable acidity and ascorbic acid content may be found in fruits harvested inside the canopy, regardless of their height (Lemos et al., 2012).
Orange fruit is Brazil's most produced and consumed fruit and besides being an important source of vitamin C, it assists in one's resistance to infections, wound healing and burns.It strengthens bone structure, promotes the absorption of glucose and the functioning of the intestine, reduces cholesterol and neutralizes uric acid (Companhia de Entrepostos e Armazéns Gerais de São Paulo [Ceagesp], 2011).
Given the scarcity of studies involving 3D maps on the chemical characteristics of citrus fruits, methods already employed in the analysis of threedimensional variability of soil properties (Choi & Park, 2006, He et al., 2010), three-dimensional display of forest landscapes (Lim & Honjo, 2003) and ground magnitude and impedance (Karaoulis et al., 2011), albeit not in fruit culture, were used in current study to identify the spatial variability structure of the variables by means of geostatistics and ordinary kriging interpolation.
Thus, considering that the orange is the most produced and consumed fruit in Brazil and that the position of the fruit on the tree may influence its physical and chemical attributes, current analysis modeled a three-dimensional spatial variability of total soluble solids (TSS) and ascorbic acid (AA) contents of the fruit in an orange orchard according to fruit position on the plant and evaluated solar radiation on them.
Local climate is characterized as humid and very humid sub-montane (warm temperate), with an average annual temperature 19.5°C.The orange orchard was established in August 2005, with 4 x 6 m spacing.The rootstock used was Poncirus trifoliata L. Raf.grafted with Monte Parnaso variety (Citrus sinensis L. Osbeck).The orchard has 394 orange producing trees.
The UTM coordinates of the area were collected by GPS receiver with post-processing, at ± 30 cm precision, set to run Datum WGS84, by using the same reference ellipsoid in data processing.Considering each tree as a set of sampling units (oranges), nine trees were defined (Figure 1A) for spatial representation of the total area of the orchard, with minimum distance of 28 m and maximum distance of 44 m between the sampled trees.The 3D coordinates of the fruits (E -longitude, N -latitude and Altitude, further represented as local coordinates x, y and z) were collected with the aid of a total station with reading without the use of prism.Fruit were chosen randomly and identified (Figure 1B and C).Besides the coordinates of the fruit, the coordinate at the base of each tree was also collected.The collection of these coordinates occurred at an average of 30 days prior to fruit harvest.Further, 715 fruit were harvested (2011, 2012 and 2013) from the nine trees, ranging between 25 and 30 fruit per tree/year.
Harvest occurred simultaneously for all fruit each year at the end of May to visualize the heterogeneity of their chemical properties according to the position of each fruit on the tree.The instantaneous solar radiation was measured by a digital pyranometer, with a cloudless sky, just after noon.The trees were delimited into quadrants (NE, SE, SW and NW) to characterize the prevalence of solar radiation rates in relation to fruit arranged on the orange trees.
After harvest the fruit were stored in a refrigerator until laboratory tests, which took place within five days.Further, 203, 249 and 263 oranges were analyzed respectively for 2011, 2012 and 2013.
where: ND -normalized data at point i in year j; D -original data at point i in year j; D -average data of year j.Scrolling (transport) of the coordinates of the fruit of eight trees was employed to analyze the orchard´s overall model, or rather, a new arrangement was conducted so that the 715 samples (fruit) were analyzed as if they were all located in only one tree (E), which is the central tree in the orchard.
ArcGIS ® 10 and SGeMS ® (Remy, Boucher, & Wu, 2009) were used for the interpolation process and generation of the 3D thematic maps.Interpolation applied to three-dimensional map generation was done by the process commonly used for two-dimensional interpolation.However, computational processes completed the information in three dimensions and provided a 3D image using a group of 2D images.Tests of means aiming at assessing the statistical differences of TSS and AA attributes as to the thirds were not performed due to the spatial correlation among data.

Results and discussion
Daily average solar radiation from blossom to harvest presented minimum rates of 363.9, 351.8 and 308.3 W m -2 ; maximum values of 542.9, 515.0 and 495.9 W m -2 , and mean values of 425.1, 455.9 and 417.5 W m -2 for harvest in 2011, 2012 and 2013 respectively.
The average instant solar radiation in the three years under analysis was 951, 209, 56 and 592 W m -2 for quadrants NE, SE, SW and NW, respectively (Figure 3A). Figure 3B shows the planialtimetric map of the orange orchard in UTM coordinates oriented towards the north (N), south (S), east (E) and west (W).
The coefficient of variation (CV) was classified as low when CV ≤ 10% (homogeneous data); medium when 10 < CV ≤ 20%; high when 20 < CV ≤ 30%; very high when CV > 30% (heterogeneous data) (Gomes & Garcia, 2002).As to TSS content, CV was considered low for the nine trees analyzed.The lowest, medium and highest TSS rates were 7.0, 9.3 and 12.8 °Brix, respectively, for the group of 715 fruit analyzed.According to Brasil (2000), the minimum TSS content for industrialized orange juice must be 10.5 °Brix.Since the goal of current study was not only to gather ripe fruits but also to verify the heterogeneity of their chemical attributes in relation to their threedimensional position on the tree, the results are coherent.Rates ranging from 8.5 to 10.8 °Brix were found by Reis et al. (2008) also in an experiment with Monte Parnaso oranges in an orchard in Butiá, Rio Grande do Sul State, Brazil.
As to the thirds, AA rates ranged between 47.0 and 59.3 mg 100 mL -1 ; 48.0 and 60.2 mg 100 mL -1 and between 48.28 and 61.38 mg 100 mL on the basal, intermediate and apical thirds, respectively.Lemos et al. (2012) reported lower rates of AA content for Pêra oranges (32.0; 29.1 and 31.7 mg 100 mL -1 ) on the basal, intermediate and apical thirds respectively.
Results refer to the study of individual trees.Data of the localization (x, y and z) of the fruits on each tree were recalculated and transported to match only one point (tree) to have a general view of the behavior of chemical attributes of the fruit in the orchard (715 samples).The above preserves the vertical quotas and the normalized rates of the attributes, since the higher the number of points, the higher the number of pairs for the calculation of semivariances and, theoretically, the higher the precision in the estimation of the semivariances.
The TSS content averaged 9.3 °Brix within the general model of the orchard (Table 1), with rates ranging between 7.0 and 12.8 °Brix and CV equal to 9.4% (low), whereas the average AA content was 55.5 mg 100 mL -1 , with values ranging between 40.0 and 76.7 mg 100 mL -1 and CV of 13.1% (medium).Mean rates between the thirds were similar in TSS content, with a CV of 0.37%.These rates were lower to those found by Lemos et al. (2012) in a study on Pêra oranges: 10.6, 10.6 and 10.8 °Brix for the basal, intermediate and apical thirds, respectively.Lemos et al. (2012) reported AA content of 32.0, 29.1 and 31.6 mg 100 mL -1 respectively for the basal, intermediate and apical thirds.Rates were lower than those given in current study.Thus, the relationship between TSS increase and AA content as a function of the increase in fruit quota cannot be proved.The CV between thirds was 1.55% Table 2 shows the result of the geostatistical analysis and the best-adjusted model to each chemical attribute, estimated parameters and respective classification of spatial dependence.The best adjusted models were the exponential for SST and Gaussian for AA, as they presented the lowest CER rates.Spatial dependencies were classified as moderate by the SCI for both variables because the range (a) marks the distance from which a point of the variable under study has no more influence on the neighboring point.In current study, the ranges obtained were 0.09 and 0.08 meters for SST and AA, respectively, showing the distances within which the samples presented spatial autocorrelation.The experimental semivariances did not present anisotropy (Guedes, Uribe-Opazo, Johann, & Souza, 2008, Guedes, Uribe-Opazo, & Ribeiro Junior, 2013), since the semivariances behaved similarly in different directions, that is, they exhibit similar patterns of spatial dependence.As previously mentioned, the coordinates of the fruit of eight trees were recalculated and transported to coincide in only one point (base of tree E) to increase the number of samples and to ensure consistency of results.The analysis of the threedimensional spatial variability in the data group, with the nine trees superimposed, required the construction of a three-dimensional grid (Figure 4A).Thus, starting from the minimum local coordinates 0.000, 0.000 and 0.000 m, the new maximum local coordinates were 4.002, 3.966 and 2.269 m, accounting for 81, 80 and 46 voxels (volume x element) for x, y and z respectively.The two-dimensional representation of the fruit is illustrated in Figure 4B.
Figure 5 depicts the three-dimensional maps visualized from the y-axis (north-south), x-axis (east-west), z-axis (quota) and in cuts on the basal, intermediate and apical thirds.The analysis of the thematic map revealed that lower rates of TSS content are reported in the basal and intermediate thirds, as well as in the central and SW regions of the tree, whereas rates above the average are concentrated in the peripheral area of the tree in all thirds, with higher concentrations in the extreme north region, in the apical third and in the NW region of the basal third, or rather, the highest rates of solar radiation (quadrants NE and NW).
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Figure 4. Three-(A) and respective

Table 1 .
Mean rates of chemical attributes with regard to position of fruit on the thirds of nine trees in the orange orchard in 2011, 2012 and 2013 in Nova Laranjeiras, Paraná State, Brazil.

Table 2 .
Models and estimated parameters of the experimental semivariograms of the chemical attributes of fruit in the orange orchard in Nova Laranjeiras, Paraná State, Brazil.