Characterization of canopy structure for high‑yield performance of greenhouse‑grown satsuma mandarins using direct measurements and indirect estimations

Under assuming that high‑yield canopy structure would be simply explained by a given index, orchard productivity of greenhouse‑grown early‑flowering satsuma mandarins “Miyagawa wase” was assessed using conventional modified‑open‑center‑training and trellis‑training methods. This was done by using universal indices that assist with determining yield in relation to canopy structure. Leaf area index was the optimum index for determining fruit yield. Empirical extinction coefficients showed negative linear trends with yield. Either plant area index, estimated by using a plant canopy analyzer, and crown cover showed poor correlation with fruit yield. To effectively predict yield from leaf area index, a direct measurement is recommended rather than an indirect optical method. Trellis‑trained trees were superior to modified‑open‑center‑trained trees. This is because trellis‑trained trees had higher fruit productivity up untill 10 yeas old, and because 15‑year‑olds had better canopy light distrubution patterns when compared with modified open‑center‑trained trees. Based on the costs associated with planting seedlings and the labor‑efficiency due to width of free alley, trellis‑training 2.2 m × 1.0 m plots was optimum for planting. In this study, even when accounting for the measurement error of woody elements, empirical extinction coefficients was a good index to base yield productivity. This is because this index directly represents vertical canopy light distribution. Additionally, the clumping index, calculated by using direct measurement and indirect optical method, was suggested to relate to canopy light distribution, however, further study must be essential.


Introduction
Satsuma mandarin Citrus unshiu Marcow. is a major fruit crop sold year-round in local markets in Japan. From the months of September to March, satsuma mandarin fruits are produced in an open field, and from April to August, the fruits are produced by early-flowering satsuma mandarins grown in a heated greenhouse. The cultivation of greenhouse-grown early-flowering satsuma mandarins hereafter refered to as "greenhouse-grown satsumas" has several merits including a larger yield and higher trade price than those grown in open fields Nii et al., 1984;Morinaga and Ikeda, 1991 . In 2018, the cultivation area and fruit production of greenhouse-grown satsumas were estimated to be 400 ha and 20,000 t 5.0 t per 1,000 m 2 , respectively Ministry of Agriculture, Forestry and Fisheries of Japan, 2019 . However, both the area and amount of fruit produced have decreased since 1993. This is largely in response to high fuel requirements, lack of labor for cultivationparticularly harvestingand yield limitations within conventional cultivation methods. To overcome these problems, the establishment of high-yield and low-labor cultivation methods is required. Such methods include reductions in fuel costs through various methods involving improving temperature controls Yano et al., 2014 . Training systems used for fruit tree cultivation are critical factors in determining orchard productivity. When compared with deciduous fruit trees, there have been relatively few reports on training systems specifically targeted at optimizing citrus tree production Morinaga et al., 1982;Ono et al., 1987;Rabe, 2000;Toyohuku et al., 2019;Kawasaki et al., 2020 . A major training system used for citrus trees is the modified-open-center-training method, which is based on the natural tree form. The summary of this method is to form semispherical crowns with three main stems and to decrease plant density from 200 -250 trees per 1,000 m 2 to 50 trees per 1,000 m 2 as an increment of canopy cover Yakushiji, 1970 . One of the reasons for the sparsity in available reports on these training systems is the requirement for a high degree of horticultural skill to manage the growth of the canopy Robinson et al., 1991 , which balancing vegetativei.e., mothershoots with reproductivei.e., bearingshoots. Specifically, this balance is important for satsumas cultivated under open field conditions, because the unbalance on amounts of mother and bearing shoots results in biennial cropping Nishikawa et al., 2012 . By contrast, shoot management among summer harvesting crop types is a much simpler process. Summer shoots that sprout by August are typically able to flower by December. This means that pruning was conducted immediately following fruit harvest in August, resulting in no need to balance between mother and bearing shoot. This simple trait of summer harvesting crops is exceptionally advantageous when developing new training methods, especially when adapting methods for greenhouse cultivation. Based on summer harvesting, strong interference by pruning can be applied for maintenance and modification of trees when necessary.
In this study, to produce high yields with low-labor costs required for summer harvest cropping types of greenhouse-grown satsumas, the efficiency of shoot management was optimized. This efficiency was attempted although greenhouse-grown citrus fruits are known to have more active vegetative growth Yano et al., 2018aYano et al., , 2018b and excessive tree vigor Tachibana and Yahata, 2007 than citrus grown in open-field conditions. To account for and regulate tree vigor, a high-density trellis training system was tested that involved multiple leadersi.e., three to four leaders per tree Micheli, 2014, 2015 . However, the fruit productivity and effectiveness of this trellis-training system are still unknown, because of a lack of available research and data.
To determine orchard productivity, in this study, a select number of effective indices were recorded and reported. This action was made on the basis of previous fruit tree research that reported orchard productivity being determined through geometrical indicessuch as tree density Sansavini and Musacchi, 2002;Hampson et al., 2004;León et al., 2007;Robinson, 2007, canopy cover Yakushiji, 1970Ono et al., 1987;Tachibana andNakai, 1989 , canopy volume Yakushiji, 1970 , and canopy surface area Yakushiji, 1970;Hutton, 1986 . However, these indices were conducted on single strains and were thus too simple to be used to explain the universal productivity of fruit trees. This was true even when accounting for multiple growth training systems Wünsche et al., 1996 . Thus, more appropriate and universally applicable quantative factors are requied to effectively determine fruit tree parameters that specifically include factors such as canopy photosynthesis and/or dry matter production theory Higashide, 2018;Nabeshima et al., 2019;Nomura et al., 2020 . Total dry matter production of a particular crop is described as a function of intercepted lighti.e., as a product of light use efficiency and intercepted light - Scholberg et al., 2000;Higashide and Heuvelink, 2009;Higashide, 2018 . The ability to intercept light by a crop is a function of the incident solar radiation on the plants, known as the leaf area index LAI and the light extinction coefficient K . LAI is the main variable used for numerous biological process models, including photosynthesis and evapotranspiration. As the light extinction coefficient, K is based on Beer's Law Monsi and Saeki, 1953 and is a key index of canopy light distribution. Zhang et al. 2014 described how to interpret K as follows: "a low K indicates that large amout of radiation can reach the bottom of the canopy, and conversely, a high K indicates that only a small amout of radiation can penetrate into the understory of the canopy." Theoretically, K is determined by leaf inclined angle and solar zenith angle Monsi and Saeki, 1953;Campbell, 1986 . When modeling canopy light interception, K = 0.5 is often used, which assumes a spherical leaf angle distribution Green et al., 2003;Annandale et al., 2004 . However, several previous reports have empirically shown K with a wide range Kubota et al., 1994;Zhang et al., 2014 . In relation to the empirically derived K, there are two main procedure categories used to estimate LAI: namely, direct measurement and indirect estimation methods Jonckheere et al., 2004 . Direct methodssuch as leaf collectionare the most accurate; however, they require a large amount of effort Jonckheere et al., 2004 . By contrast, indirect methodssuch as optical methodsare easier, but several reports have shown that they underestimate LAI when compared with direct measurements Jonckheere et al., 2004;Weiss et al., 2004 . Several factors have been identified as possible sources for the underestimation of LAI in indirect methods. The first factor being clumping Nilson, 1971;Bréda, 2003 ;Nilson 1971 defined the clumping index as the nonrandom distribution of canopy elements Bréda, 2003 . When a canopy displays random dispersion, is unity, whereas when a canopy has nonrandom dispersion, is higher or lower than unity Bréda, 2003;Chen et al., 2005 . The more clumped a canopy is, the smaller the value, and generally, most natural forest and shrub canopies are assumed to be clumped Chen et al., 2005 . The second factor is the contribution of stems and branches, where the indirect method measures all canopy elements intercepting radiation. This means that all canopy elements have often previously been defined as one plant area index PAI , with PAI then being devided into LAI and wood area index WAI; Bréda, 2003. Bréda 2003 illustrated that the WAI of oak stands ranged from 0.43 m 2 m -2 to 2.45 m 2 m -2 , with the ratio of WAI to PAI further ranging from 7 to 40 . Thus, for an accurate estimation of LAI, a study requires the contributions from both clumping and woody parts to be determined Bréda, 2003 . Further to this, it is important to elucidate the relationship between orchard productivity and the contributions of clumping or woody elements.
The main objectives of this study were as follows: 1 to discover universal indices related to yield, beyond-the-site-specific, seasonal, and geometrical variations of tree canopy; 2 to compare orchard productivity with conventional modified-open-center-training and trellis-training methods; and 3 to discuss optimized planting and canopy structures for greenhouse-grown satsumas. To achieve these objectives, 16 greenhouses with varying tree ages -5 -42 years oldwere utilized. Fifteen of the selected greenhouses had modified-open-center-trained trees that were used to produce commercial fruits, with fruit productivity being assessed in one season from 2005 to 2006. The final greenhouse was operated with test treatments: four different spacing patterns for trellis-trained trees with multiple leaders, as well as a control treatment with modified-open-center-trained trees. Seasonal changes in fruit production among the test treatments were assessed over the long term, from 2 to 17 years of age, over a 15 year period from 2005 to 2020.
Raf. ] rootstocks, were tested. The first was a conventional modified-open-center-training method Fig. 1a , with spacing 2.7 -4.5 m interrow spacing 1.4 -4.4 m intrarow spacing . Trees were planted in 15 greenhouses hereinafter refered to as "commercial trees" located in Kitsuki, Oita, Japan. Greenhouses were heated from autumn to spring, and fruits were harvested from early June until early August. A summary of their cultivation is provided in Table 1. To minimize sampling error, four representative sample trees per greenhouse were selected. Generally, cultivation followed traditional practices, with the quantities of flower buds and fruit sets were sufficient to producing commercial fruits.
The second method was a trellis-training method with multiple leaders Fig. 1b, Fig. 2 , trialed in a test greenhouse in the Fruit Tree Group, Oita Prefectural Agriculture, Forestry, and Fisheries Research Center 33 32 N; 131 43 E, Kunisaki, Oita . The greenhouse was 33 m 30 m in size, divided into five subfields 6.6 m 30 m using arches, roofed with 0.15-mm-thick polyester film, and walled off by 0.15-mm-thick vinyl sheets. To assess the seasonal change in productivity for the trellis-training with multiple leaders, 2-year-old satsuma mandarin seedlings were planted in the greenhouse in March 2005, as shown in Fig. 3. We compared four types of configuration for the trellis-trainings: 2.2 m 1.0 m Fig. 3a, 390 trees per 1,000 m 2 , 2.2 m 1.5 m Fig. 3b, 283 trees per 1,000 m 2 , 1.6 m 1.0 m Fig. 3c, 558 trees per 1,000 m 2 , and 1.6 m 1.5 m Fig. 3d, 378 trees per 1,000 m 2 , oriented in a northsouth direction Fig. 3 . In the same subfield, modified-open-center-training trees Fig. 3e were also planted as a control, spaced at 2.2 m 2.0 m 207 trees per 1,000 m 2 . After the harvest in 2010, filler trees were thinned to a spacing of 3.1 m 2.8 m 104 trees per 1,000 m 2 . The calculations for tree numbers per 1000 m 2 are provided in Supplementary Fig. S1. The disagreement between the configurations and planting distancescaused by the averaging row width in Fig. S1 are illustrated in Fig. 3 e.g., 1.6 m and 1.5 m, or 2.2 m and 2.0 m . During the experimental years, the subfield was sandwiched on both sides by similarly cultivated subfields, which cultivated trellis-trained early-flowering satsuma mandarins Fig. 3 . These trees served only as "guard" trees Nabeshima et al., 2019 to ensure that the experimental trees experienced a uniform microclimate and were consequently not sampled. All cultivation variables including air temperature and irrigation followed traditional practices Tachibana and Yahata, 2007 . During the experimental period, harvest days were conducted from June  8 to July 30 for all years, with flower buds and fruit sets were generally suitable for commercial fruit production.

Measurements 2.2.1 Plant area index
According to previous reports on forests and shrubs Holst et al., 2004;Sano et al., 2012;Sun et al., 2020 , PAIincluding the contributions of leaf, stems, and branchescan be indirectly estimated using LAI-2000 Li-Cor, Lincoln, Nebraska, USA . PAI measurements were conducted when there were diffused light conditions, such as on overcast days. The effect of steel framesof roofs or sides of a greenhouseon the LAI-2000 measurement was assumed to be negligible by the routine background correction.
The preliminary basic performance of the LAI-2000 for use with greenhouse-grown satsumas was confirmed in a leaf-thinning test conducted from June 2 -6, 2005. The tested canopy, which was assumed to be closed, included two neighboring 11-year-old modified-open-center-trained trees. The whole canopy of the two trees was then divided into five vertical layers at 0.0 -0.5, 0.5 -1.0, 1.0 -1.5, 1.5 -2.0, and 2.0 -2.5 m heights. Leaf-thinning tests were performed by alternating leaf collection from the vertical layers and LAI-2000 measurements in turn repeatedly. LAI-2000 performance was determined by comparing the leaf area for vertical layers with the LAI-2000 measurement. The test ignored stems and branches. To eliminate the effect of gap spacei.e., space outside the tree canopyan optical sensor for the LAI-2000 was equipped with a 45 view cap. The LAI for the detached leaves was determined using the leaf area meter LI-3000A; Li-Cor, Lincoln, Nebraska, USA . All LAI-2000 measurements performed well for the leaves r 2 = 0.88, P < 0.001, n = 44; Fig. 4 .
For commercial trees, the LAI-2000 measurements were taken beneath the canopy of each of the representative trees. Measurements were performed from November 2 to December 14, 2005. To collect information for the tree canopy on a wider scale, the optical sensor for the LAI-2000 was equipped with a 180 view cap. PAI data were averaged using 40 -64 samplesmeasured at 0.5 m 0.5 m grid-point inside tree canopy shilhouette area, with including at near the origin of stockviewed equally from north, south, east, and west, for each greenhouse. For trellis-trained trees, it was assumed that the tree canopy was a row, and thus, the measurements were made in groups of diagonal transects, following the manufacturer instructions for the LAI-2000. PAI data were averaged over 30 samplesmeasured at point simmilar to commercial treeswith viewing occurring along each row for each plot. Measurements at 5 and 15 years old were performed October 17 -23, 2007 and November 6, 2017, respectively.  Circles with dashed lines indicate filler trees that were thinned at 7 years of age, postharvest. Black circles indicate trees sampled for destructive measurements at 10 years of age, postharvest. Triangles indicate permanent trees. The east and west sides of the experimental plot were sandwiched by guard trees gray rectangles , which were not sampled, to ensure that experimental trees experienced a uniform microclimate.

Leaf area index
LAI was directly determined using either nondestructive or destructive methods. For the commercial trees and for the 5-year-old trellis-trained treesincluding the control treatmentthe LAI values were determined using a nondestructive method, which was conducted just before heating, from October to December. This method involved estimating the leaf area as a product of the number of leaves, by using a representative leaf area value for a single leaf. The values were estimated using a portable leaf area meter LI-3000A; Li-Cor, Lincoln, Nebraska, USA , averaged over 400 leaves. LAI for the 10-year-old trellis-trained treesincluding control treatmentwas determined by a destructive method, which was conducted just after harvest. For this, leaf area was estimated as the product of the dry mass for all detached leaves from a single tree as well as the specific leaf areaestablished as 8.1 10 -3 m 2 g -1 in a previous report Yano et al., 2013 . The LAI for the 15-year-old trellis-trained trees also used a destructive method, in which the leaves were detached from a tree and the leaf area was measured using a portable leaf area meter LI-3000A; Li-Cor, Lincoln, Nebraska, USA . Measurements at 10 and 15 years old were performed August 1 -31, 2013 and June 13 -22, 2018, respectively.

Wood area index and clumping index (Ω)
If PAI > LAI, it was assumed that the WAI could be estimated using the following formula: If PAI < LAI, it was assumed that the leaf distribution was clumped Chen et al., 2005 , and the clumping index could be estimated using the following formula: 2 LAI

Canopy light interception fraction
Light interception fraction fIPPFD was calculated using the following formula: where PPFD in is the incoming photosynthetic photon flux density PPFD, μmol m -2 s -1 measured at a point between the ceiling of the greenhouse and the top of the tree canopy and PPFD tr is the PPFD transmitted through the canopy. All the sensors used to measure the fIPPFD were fixed horizontally to the ground. Measurements were performed from November to December. Measurement instruments were selected on the basis of canopy type. First, for commercial trees and for 5-year-old trellis-trained treesincluding control treatmenttwo-point PPFD sensors LI190SA; Li-Cor Inc. were used that were connected to the LAI-2070 control unit of the LAI-2000. One PPFD sensor was mounted to a treetop, with another mounted to the side of the LAI-2050 optical sensor. The instantaneous PPFD data were collected by the LAI-2070 control unit. Thus, measurement point for the fIPPFD data corresponded to that for the PAI data. Second, for the 15-year-old trellis-trained trees, assuming that there was a row canopy, a PPFD bar made from a 2 m aluminum bar and six PPFD sensors MIJ-14PAR Type2/K2; Environmental Measurement Japan, Co., Ltd. evenly spaced along the bar were used. The PPFD bar was designed as a substitute for a line -PPFD sensor, and the PPFD bar could be hung in the greenhouse. The PPFD bar was placed perpendicular to the rows. Instantaneous light interception was obtained using one set of the alternate PPFD in measurements at the top of the canopy and for the PPFD tr just below the canopy. Each measurement spanned 3 -5 min, with measurements taken at 5 s intervals. By using either measurement instrument, the instantaneous fIPPFD was measured on overcast days during the off-crop season at the preflowering growth stage.

Canopy light extinction coefficient (K)
Despite the training methods, the light extinction coefficient, K, was empirically derived using the classic exponential formulation to modify Beer's Law Monsi and Saeki, 1953 : where fIPPFD is the fraction of light interception calculated by Equation 3. Measurements were performed from November to December. LAI was determined by the methods aforementioned at 2.2.2, with assuming that LAIs before heating and after harvest have no difference in greenhouse-grown satsumas.

Geometrical canopy description
Canopy geometry of modified-open-center-trained treesincluding tree heightwas assumed as a discontinuous hemisphere; an average of the horizontal crown radius was determined by the maximum among tree crown radiuses measured at heights of 0, 0.5, 1.0, 1.5, 2.0, and 2.5 m. Canopy cover was determined by using the average of horizontal radius, following methods described in previous studies Yakushiji, 1970;Tachibana and Nakai, 1989 . Free alley width was determined by a deduction of the average planting distance and average horizontal radius. For commercial trees, canopy geometry was estimated by using four representative sample trees per greenhouse. Canopy geometry of trellis-trained treesincluding tree heightwas assumed as a continuous canopy like with a triangle prism; thus, the canopy cover and free alley width were determined by using the product of canopy width and length, and a deduction of the average of planting distance and canopy width, respectively. For trellis-trained trees, canopy geometry was estimated by using all sample trees.
Measurements for both modified-open-center-trained and trellis-trained trees were performed from November to December.

Other indices
Duration of sunshine h from January to June 2006 for commercial trees was estimated using AMEDAS data for Kitsuki Oita, Japan . Duration of sunshine h and solar radiation Rs, MJ m -2 from January to June 2008 2020 for trellis-trained trees were estimated using meteorological observation system M-801; Yokogawa Electric Corp., Japan in the Fruit Tree Group, Oita Prefectural Agriculture, Forestry, and Fisheries Research Center 33 32 N; 131 43 E, Kunisaki, Oita . Both of duration of sunshine and solar radiation were directly estimated by using raw data of the AMEDAS or meteorological observation system. Yields were estimated by using data with four representative sample trees per greenhouse for commercial trees and by using data with all sampled trees in Fig. 3 for trellis-trained trees, respectively. Soluble sugar content SSC for juice produced by cultivated fruits was measured with a digital refractometer PR-101, ATAGO Co., Ltd. . Acidity of the fruit juice was measured through titration. SSC, acidity of the fruit juice, and fruit weight were sampled at harvest peak day, which generally corresponded to from early June to early August. Data analysis was performed using R-3.6.1 R Development Core Team, 2019 .

Variation in sites and research years
Generally, cultivation in the commercial trees and the trellis-trained trees followed traditionally observed practices. However, light conditions fluctuated somewhat between year and site. The seasonal sum for the duration of sunshine from January to June was 18 larger in Kunisaki City for trellis-trained trees than in Kitsuki City for commercial trees Table 2 . Consequently, the trellis-trained trees received slightly better light for fruit production than the commercial trees.

Productivity of commercial trees
A summary of the commercial satsuma mandarin trees assessed is presented in Table 1. The average of fruit weight was at ~90 g, with SSC at ~12 Brix, and the acidity at ~0.8 . These values met the general commercial requirements for satsuma mandarin fruits in Japan. With conventional shoot managementwhere stems and branches were spread horizontallyalmost all greenhouses had narrow free alley widths 0.2 0.05 m; Table 1 . The maximum yield and LAI were 7.6 t per 1,000 m 2 and 3.6 m 2 m -2 , respectively. Tree height ranged from 2.1 to 2.8 m.

Productivity of trellis-trained trees
A summary of the productivity of the satsuma mandarin trellis-trained trees is shown in Table 3 and Figure 5. Until 10 years of age, fruit yield was proportional to the planting density with a logarithmic trend Fig. 5 , in which some factors or single factor can fluctuate the yield. For example, for the 6-to 8-year-old trees, an unplanned water deficiency due to a lack of irrigation resulted in underestimations of the fruit yield, as shown   Fig. 6a c . However, overall, fruit productivity for the trellis-trained trees mainly followed LAI Fig. 6a and 6e , and a tendency of biennial fruiting was not recognized Fig. 6a . Five-year-old trees had a narrow free alley width of 0.5 m or less, although 15-year-old trees had a wide free alley width of 0.8 -0.9m Table 3 . The wide free alley was obtained by training and trimming tree canopy. Tree height ranged from 2.3 to 2.7 m Table 3 . Additionally, during the experimental years, solar radiation Rs from January to June only affected acidity, although it did not show a significant correlation to the other indices of fruit production Table 4 .

Comparison of indices affecting yield
During experimental years, Rs did not show a significant correlation to fruit yields, by using averaging data of trellis-training 2.2 m 1.0 m and 2.2 m 1.5 m Table 4 . The reason for using the averaging data was to grasp general effect  of environment on fruit productivity. Additionally, both of the trellis-training 2.2 m 1.0 m and 2.2 m 1.5 m also showed similar results data not shown . LAI showed a significant positive correlation with fruit yield, with a similar pattern for both trellis-trained and modified-open-center trees Fig. 7b . To assess the differences or correspondence of the linear trends of LAI with yields for trellis-trained and modified-open-center trees, the slopes and intercepts of the linear models were compared using an analysis of covariance. The slopes of the two regression lines Fig. 7b were not significantly different P = 0.60 , with the trees of the two training methods having a common intercept in the regression line P = 0.16 . Therefore, a relationship between LAI and yield could be simply described using a common regression line for both training methods. Thus, yield Y, t per 1,000 m 2 can be modeled by the following formula, and the model explained 72 of the variation of yield. Y = 1.56 LAI + 2.16 n = 27, R 2 = 0.72, P < 0.001 5 The extinction coefficient K showed a significant negative correlation with fruit yield; however, there was a slightly different pattern between the trees from the two training methods Fig. 7c . The slopes of the two regression lines Fig. 7c were not significantly different P = 0.075 , and the trees of the two training methods had a common intercept in the regression line P = 0.96 . Thus, yield Y can be modeled by the following formula, and the model explained 47 of the variation of yield. Y = 0.91 K + 7.15 n = 22, R 2 = 0.47, P < 0.001 6 Both the PAI and canopy cover showed a poor correlation than LAI with fruit yield Fig. 7a and 7d .

Light interception pattern and canopy structure
To characterize the canopy structure of greenhouse-grown satsumas, a comprehensive investigation was conducted on  several canopy features. The light interception fraction fIPPFD was over 0.8 and was near constant when compared against LAI Fig. 8a . The relationship between LAI and the empirically derived extinction coefficient K showed a negative trend, in which a nonlinear pattern can be fitted Fig. 8b . K increased with the ratio of WAI to PAI Fig. 9 . These results indicated that although LAI was low, the contribution of WAI was large, consequently increasing K. Furthermore, when PAI > LAI with a clumping index > 1 -which included trees from the modified-open-center training method as well as the 5-year-old trellis-training methodthe K values were high at over 1.0 Table 1 and 3 . Another situation in which PAI < LAI and the clumping index < 1, was with the 15-year-old trellis-trained trees, where K was close to 0.5 Table 3 . The different trends for the indices suggest a change in the canopy architecture for the greenhouse-grown satsumas.

Discussion
Overall, in greenhouse-grown satsumas, results showed usefulness of selected indices for explaining fruit yields, and of trellis-training method for high-yield. In this section, three objectives, which were mentioned at introduction, and one subject, which requires further study on characterizing detailed canopy structure, were discussed.

Universal indices related to yield
In trellis-trained greenhouse-grown satsumas, solar radiation from January to June did not show a significant correlation to fruit yield Table 4 . Taniguchi 1983 showed that combination of 95 shading and high air temperature above 25 C from flowering to the end of June-drop term affected fruit set. In the present study, from January to February, air temperature was conventionally controlled less than 25 C, and difference of solar radiation among plots was not the level as affecting fruit set Table 2 . After the June-drop term, previous reports on modified-open-center-trained trees reveal that 60 shading from March to May did not show significant differences in the yield compared with trees with no shading Yano et al., 2013 . In the present study, the whole fluctuation level of sunshine duration from January to June was at most 30 Table 2 . Therefore, this fluctuation level of sunshine duration was not assumed as a factor affecting yield.
LAI correlated linearly with fruit yield Fig. 7b . Analysis of covariance revealed that fruit yield was explained by LAI with a linear regression line, regardless of the training used for the trees.   1970;Ono et al., 1987;Tachibana and Yahata, 2007 and natural tree forms Tachibana and Nakai, 1989 . However, the present study measurement method for LAIsuch as leaf collection or leaf countingrequired destructive sampling or a significant amount of effort. For an effortless and practical estimation of LAI, other direct or indirect methods must be established, such as allometric techniques Jonckheer et al., 2004 . Extinction coefficient K also showed a significant correlation with fruit yield Fig. 7c . Similar to LAI, analysis of covariance revealed that the fruit yield was explained by K with a linear regression line, regardless of the training used for the trees Fig. 7c . However, the model explained the lower variation of yield rather than that of LAI, thereby inferring that the extinction coefficient K was a secondary effective index related to yield. Furthermore, the relationship between K and fruit yield may be spurious correlation, because K and LAI showed a significant correlation Fig. 8b .
The PAI determined by the LAI-2000 showed a narrower range than the LAI and poor correlation against the fruit yield Fig. 7a . In this study, it was assumed that the poor correlation was mainly due to an error in the information calculated for the stems and branches and thus calculated a WAI using Equation 1. Bréda 2003 questioned whether the PAI equals the sum of LAI and WAI Lang, 1991;Chen, 1996 or this equality is not a general assumption because of the overlapping of branches by leaves Dufrêne and Bréda, 1995;Gower et al., 1999 . Through this study, estimation on WAI were made according to Lang 1991 andChen 1996 . Therefore, close attention must be paid to the measurement error when using an indirect method, for example, PAI is constructed with at least two different measurement elements.
Canopy cover did not show a universal relationship against yield Fig. 7d . The reasoning for this was different for each training method. First, in trellis-trained trees, 5-year-old trees with wide canopy width large canopy cover and low LAI resulted in low fruit yields Table 3, Fig. 7b . Conversely, 15-year-old trees with narrow canopy width small canopy cover and high LAI resulted in high fruit yields Table 3, Fig. 7b . Thus, the relationship in trellis-trained trees between canopy cover and yield showed a negative trend Fig. 7d . Second, in the modified-open-center-trained trees, canopy cover and yield did not show a significant correlation Fig. 7d . In the open field, Ono et al. 1987 highlighted that yield fluctuation among sites increased when both canopy cover and LAI were over 60 and 2.5 m 2 m -2 , respectively. In this study, the most canopy cover recorded was over 60 Table 1 ; thus, a worse canopy light distribution originating from a horizontal crown spread might partly cause yield fluctuation. Therefore, canopy cover is simply too one-dimensional to accurately describe the yield of greenhouse-grown satsumas.

Orchard productivity of modified-open-center-training
and trellis-training methods Through this study, it was concluded that trellis-trained trees were superior to modified-open-center-trained trees. The first reason for this being fruit productivity. Until 10 years of age, fruit yield per unit area under the greenhouse-grown trellis-trained trees exceeded that of the modified-open-center-trained trees per unit area Fig. 5 . Under open field conditions, previous reports also showed superior productivity of trellis-trained trees when compared with modified-open-center-trained trees. For example, Ono and Kudo 1983 showed that fruit yield per unit area and uniformity of fruit quality under trellis-trained trees 300 trees per 1,000 m 2 exceeded those of modified-open-center-trained trees 82 -300 trees per 1,000 m 2 . Morinaga et al. 1982 showed similar results in trellis-trained trees 125 -165 trees per 1,000 m 2 against modified-open-center-trained trees 36 trees per 1,000 m 2 . These trends in fruit yield were explained by LAI related to planting density.
The second reason is canopy light distribution. In open field, Ono et al. 1987 showed that canopy light distribution of modified-open-center-trained trees was maintained at a good level when the canopy cover was under 60 . Several previous studies showed that low K related to good canopy light distribution and high plant productivity Higashide, 2018;Higashide and Heuvelink, 2009;Kubota et al., 1994;Monsi and Saeki, 1953 . In this study, at 5 years of age, trellis-trained trees spread branches horizontally, meaning they showed high canopy cover at 78 -88 Table 3 and high extinction coefficient K at 1.89 -6.35 Table 3 . Furthermore, 15-year-old trellis-trained trees showed lower K, at 0.49 -0.51, with a low canopy cover of 59 Table 3 when compared with modified-open-center-trained trees Table 1 . Data from this study showed that the canopy light distribution of 15-year-old trellis-trained trees must be superior compared with 5-year-old of those and modified-open-center-trained trees Fig. 7c , with supporting previous observations. Additionally, Ono et al. 1980 showed that the utilization of solar radiation and photosynthesis rates were greater in the trellis-trained trees than modified-open-center-trained trees. This result also supports the good canopy light distribution of trellis-trained trees.
The third reason is capacity for increasing LAI. This is explained by the goodness of canopy light distribution. Low K conditionlarge amount of radiation to the near bottom of canopyis advantageous for sprouting new bud and increment of LAI. In open field, Ono 1982 showed the threshold level of relative light intensity for active vegetative growth as 10 -14 . In this study, 15-year-old trellis-trained trees showed large amount of radiation to the bottom of canopy as 12 -16 percentage of 1-fIPPFD , whereas modified-open-center-trained trees showed small amount of that as 1 -8 Fig. 8a . Therefore, 15-year-old trellis-trained trees had high capacity for increasing LAI as 4.0 m 2 m -2 Fig. 7b , which was supported by low K condition with distributing large amount of radiation to the near bottom of canopy. The fourth reason is labor cost. In this study, 15-year-old trellis-trained trees showed wide free alley width Table 3 , whereas modified-open-center-trained trees showed narrow free alley width Table 1 . The wide free alley width helps to save on labor costs for harvesting, transportation, and pesticide spraying.

Optimized planting and canopy dimensions
In the open field, early-flowering satsuma trees showed optimum LAI that maximized yields at 6.8 m 2 m -2 when tree height was over 3 m with a closed canopy Tachibana and Nakai, 1989;Tachibana, 1998 . Similarly, in the heated greenhouse, the optimum LAI was reported at 5.7 -5.9 m 2 m -2 with near closed canopy Tachibana and Yahata, 2007 . However, in the greenhouse, to achieve both high fruit productivity and low-labor cost, optimizing planting and canopy dimensions must be an important criterion in the experimental process. When comparing the spacing of trellis-trained trees, the present study results showed that both the 1.6 m 1.0 m and 2.2 m 1.0 m had high fruit yields per year, averaged until 10 years of age Fig. 5 . The 1.6 m 1.0 m had only narrow free alley width similar to modified-open-center-trained trees Table 1 and 3 , with planting tree numbers per unit area of 1.6 m 1.0 m 43 larger than that of 2.2 m 1.0 m Table 3 . Therefore, based on these costs for planting seedlings and the labor involved with fruit production, the 2.2 m 1.0 m was optimum. However, even when planting was 2.2 m 1.0 m, low LAI with large tree volumes or narrow free alley widthssuch as the 5-year-old trees or modified-open-center-trained treeswould show worse canopy light distribution, represented by high K Table 3 . Additionally, for such high K situations, shading by woody elements must be marginal Fig. 9 . Hence, to decrease the negative effect of woody elements on fruit productivity, the compactness of a tree and increment of LAI is important for high productivity in trellis-trained trees.
Recently, studies on apples have revealed that the cultivation system has advantages for management and mechanization that enable narrow and planar canopies to be contained under 1.0 m width with 2.7 m tree height was developed Dorigoni and Micheli, 2015 . In the present study, the canopy width of trained trees was set to 1.3 -1.5 m. If more narrow and planar canopies were established for greenhouse-grown satsumas, optimum planting and canopy dimensions might be discovered and consequently used to update cultivation techniques.

Subjects for future study and short conclusion
In this study, the factors of LAI, extinction coefficient K, and clumping index were focused on as indices to characterize canopy structure. Here, to understand the availability of the indices in the greenhouse-grown satsumas, a more detailed discussion is needed. The first discussion point is the fluctuation of the K value. Different to modeling studies assuming K = 0.5 Green et al., 2003;Annandale et al., 2004 , the present study direcrly measured the light absorption and LAI to estimate K. A relationship between K and LAI was fitted to nonlinear functions Fig. 8b , which is similar to several previous studies Binkley et al., 2011;Brown and Parker, 1994;Sampson andSmith, 1993 . Binkley et al. 2011 divided the patterns of light absorption in relation to leaf area into three patterns. According to these divisions, present study results Fig. 8 were classified into the respective patterns instead of based on Beer's Law. However, even when measurement error by a woody elements exists, in this study, empirical K was at a good index. This could be because the index represented vertical canopy light distribution directly. Thus, a difference of K between 15-year-old trellis-trained trees average 0.5, Table 3 and modified-open-center-trained trees average 1.6, Table 1 was considerable.
The second point is the clumping index. Generally, most natural forest and shrub canopies with high LAI values over 4.0 m 2 m -2 were assumed to be clumped < 1; Bréda, 2003;Chen et al., 2012 . However, results for the greenhouse-grown satsumas differed to this; trellis-trained trees had low clumping indices < 1 , whereas modified-open-center-trained trees, which based on natural tree form, showed high clumping indices > 1 . To sufficiently understand and describe the canopy structure for high-yield, further examination for analyzing relationship among and light distribution factors, such as K and/or other indicesi.e., leaf inclination angle Ryu et al., 2010 -must be essential.
In conclusion, LAI was the optimum index for determining fruit yield in greenhouse-grown satsumas. Though empirical K included some mesasurement error caused by woody elements, K was a good index to represent vertical canopy light distribution directly. From fruit productivity, canopy light distribution, and labor-cost, trellis-training method was superior to modified-open-center-training method.