# Technologies for Forecasting Tree Fruit Load and Harvest Timing--From Ground, Sky and Time
## 2 Measurement of Fruit Number
### Tree Evaluation and Historical Knowledge  
Grower estimates of fruit load for a given orchard are often based on a visual assessment of current crop flowering or fruit load relative to previous years knowledge of historical yield for that orchard. For example, an experienced orchardist could associate the proportional area of fruit on canopy to yields of 20, 100 and 150 fruit per tree, or 8, 40 and 60 tonnes per ha, given a tree density of 400 trees/ha (Figure 2). An experienced 'eye' is needed for such estimates, both to gauge fruit load for a given tree, and to judge the average load per tree in the orchard. While such estimates can be very good, human error can also result in poor estimates, especially in the evaluation of extensive plantings and/or of large trees with dense canopies.  
\begin{table}
\begin{tabular}{c c c} \hline
**Term** & **Meaning** & **Equation** \\ \hline RMSE & The standard deviation of the prediction & \(RMSE=\sqrt{\frac{\sum_{i=1}^{n}\left(y_{i}-y_{i}\right)^{2}}{n}}\) \\  & weights & where \(y_{i}\) is the estimated value, \(y_{i}\) is the observed value and \(n\) is the sample size \\ \hline RRMSE & RMSE relative to mean & \(RMSE=\frac{RMSE}{X}\) \\ \hline MSE & The average squared errors of prediction & \(MSE=\frac{1}{n}\sum\limits_{i=1}^{n}\left(y_{i}-y_{i}\right)^{2}\) \\ \hline R\({}^{2}\) & The proportion of the variance of one variable & \(R^{2}=1-\frac{\sum_{i=1}^{n}\left(y_{i}-y_{i}\right)^{2}}{\sum_{i=1}^{n} \left(y_{i}-y_{i}\right)^{2}}\) \\  & that can be explained by the variance of the & \(R^{2}=1-\frac{\sum_{i=1}^{n}\left(y_{i}-y_{i}\right)^{2}}{\sum_{i=1}^{n} \left(y_{i}-y_{i}\right)^{2}}\) \\  & second variable & where \(\mu_{y}\) is the mean of observed values \\ \hline MAE & The average of the absolute values of prediction & \(MAE=\frac{\sum_{i=1}^{n}\left|y_{i}-y_{i}\right|}{n}\) \\ \hline MAPE & The average of the absolute values of prediction & \(MAPE=\frac{1}{n}\sum\limits_{i=1}^{n}\left|\frac{y_{i}-y_{i}}{y_{i}}\right|\) \\  & residuals divided by the actual values & \(CCC=\frac{2\mu_{y}c_{i}}{\mu_{y}^{2}+\sigma_{y}^{2}+(\mu_{y}-\mu_{y})^{2}}\) \\ \hline CCC & Interpreted similarly to R\({}^{2}\), but used to compare & where \(c_{y}\) represents the variability of either the observed value or another variable and \(\sigma_{y}\) and \(\mu_{y}\) the variability and the mean of either the estimated value or another variable \\ \hline RCV & The minimal significant difference between temporally different measurements & \(RCV=\pm q\sqrt{2\left(\sigma_{y}^{2}+\sigma_{y}^{2}\right)}\) \\  & where \(q\) is the quantile for the desired probability & from a standard normal distribution \\ \hline MCC & Measures the agreement of binary classifications & \(MCC=\frac{TP\times TN-FP\times FN}{\sqrt{\left(TP+FP\right)\left(TP+FN\right) \left(IN+FP\right)\left(TN+FN\right)}}\) \\  & where \(TP\) is true positives, \(TN\) is true negatives, \(FP\) is false positives and \(FN\) is false negatives of binary classification \\ \hline \end{tabular}
\end{table}
Table 2: Definition of evaluation metrics.  
Attempts have been made to adopt the use of a fruit load density factor within other methods. For example, [PERSON] et al. [9] described the use of a human expert to categorize fruit load density to one of four classes as one input to a model for fruit load estimation. [PERSON] et al. [12] described a machine vision-based classification of canopy images to three crop load densities using a 'Xception_classification' model and a Silhouette score as a first step in a pipeline for a machine vision-based estimation of tree fruit load (see later sections).