# Technologies for Forecasting Tree Fruit Load and Harvest Timing--From Ground, Sky and Time
## 2 Measurement of Fruit Number
### Correlative Methods
#### 2.5.4 Correlation to Canopy Structural Attributes  
The data of [PERSON] et al. ([PERSON], 2016) and [PERSON] et al. ([PERSON] et al., 2017) on mango fruit load and canopy volume per tree (re-plotted as Figure 7) provides a useful example of the limitations of correlation to canopy volume. There appears to be a maximum number of fruits per unit volume of tree canopy, at around 18 fruits per m\({}^{3}\), but many trees fail to achieve this maximum, i.e., a yield gap is demonstrated (Figure 7). Thus, while the potential for mango fruit number is set by the number of vegetative terminals, the correlation between fruit load and tree structure parameters can be poor, e.g., [PERSON] et al. ([PERSON], 2016) reported an R\({}^{2}\) of 0.21 and 0.17 for the correlation of fruit load to canopy volume measured using LiDAR and trunk circumference, respectively. For trees with a greater range in canopy volume, [PERSON] et al. ([PERSON] et al., 2017) reported an R\({}^{2}\) of 0.63 to 0.76 (\(p\)-values \(<\) 0.05) between mango fruit load and canopy volume, as measured using a UAV photogrammetry method.  
An MLR model was used for the prediction of mango orchard yield, utilizing six tree attributes (height, canopy size, stock girth, scion girth, and shoot length) and four meteorological parameters (maximum temperature, minimum temperature, rainfall, and sunshine hours) at five different development stages (flushing, bud differentiation, flow  
Figure 7: Relationship between tree fruit load and tree canopy volume as assessed using LiDAR for 494 trees of a single mango orchard. Line with slope of 18 fruit/m\({}^{3}\) bounds 99% of observations.  
ering, fruit set and fruit development stage) of 20 treatments at 10 sites across 9 seasons (n = 1800) [72]. The calibration R\({}^{2}\) for the fruit load prediction was 0.53, which the author noted was unsatisfactory. The identified constraints included the smallholder practice of interplanting tree crops and varieties and mixtures of tree ages in a given orchard and the reliability of yield data from growers.  
Similarly, while a relatively good correlation (R\({}^{2}\) = 0.80) was demonstrated for citrus canopy size and yield in a single season [73], another study demonstrated that the relationship was not consistent between seasons, orchards, time of imagery acquisition (twice per season) and the combined features of canopy area (pixel based) and spectral band, for a canopy area estimated from 0.2 m spatial resolution satellite imagery [74]. [PERSON] et al. [9] devised a methodology for yield modeling based on mango tree structural parameters and a fruit 'load index'. Mango tree structure parameters of height, crown area and volume were assessed by images collected by a UAV. These parameters were used together with cultivar information and a human-assessed 'fruit load index' per orchard as inputs to a second-degree polynomial predictive model. The fruit load index involved a visual assessment of the orchard to one of four classes (null, low, medium, high) based on the area of visible fruits to the overall crown area. This assessment was made of 50 trees located on a transect through the orchard, although this was recognized as a potential source of sampling error. Cultivar-specific models were developed, with an R\({}^{2}\) of 0.77 to 0.87 and RRMSE from 20-29% reported on validation sets. The load index was weighted higher than tree structure variables in all models.