# Technologies for Forecasting Tree Fruit Load and Harvest Timing--From Ground, Sky and Time
## 2 Measurement of Fruit Number
### Manual Fruit Count
#### 2.3.2 Sampling Approaches
[22] demonstrated a 20-35% decrease in the sample size required for peach fruit load estimation by use of a stratified sampling based on tree size and canopy density compared to an SRS strategy. Tree size and canopy density were estimated by means of multispectral indices obtained from UAV imagery. [PERSON] et al. [16] compared several sampling strategies for a mango orchard (site 1 in Table 1) in which the fruit load of every tree was known. Stratification to three classes based on canopy area or volume did not result in a reduced total sample number (Equation (2)), due to the poor correlation of these attributes to fruit load on a per tree basis in this orchard. Stratification on the basis of fruit load resulted in a 10% reduction in the overall sampling effort compared to classless random sampling. These data were reworked for a comparison of the efficiency of RS and SUR sampling of trees for the prediction of the total fruit load from counts of an RS of 26 trees and a sampling fraction of 1/18 using SUR (providing an average sample size of 26 trees (Figure 3). Under RS, the true CE was estimated to be 16.5%, whereas under SUR, it was 11.5%. Doubling the sampling size to 52 trees under RS decreased the CE from 16.5 to 11.6%, whereas increasing the average SUR sample size to 47 by sampling more trees per row reduced the CE from 11.5 to 6.6% (equivalent to a maximal error of 10.8% with 90% probability). Thus, in this case, an RS sampling strategy requires double the sample size of that required by a SUR strategy, for a similar sampling error, and increasing sample size reduced the error at a higher rate for SUR than SR. This example demonstrates the potential for SUR sampling to provide a significant decrease in sampling effort compared to RS in an orchard with high spatial variability. SUR is most efficient when units in a sample are as heterogeneous as possible. Procedures to accomplish this aim based on systematic or non-uniform sampling designs and ancillary measurements that do not require stratification are reviewed by [PERSON] [14]. A multistage approach to sampling trees was described by [PERSON] [14] and [PERSON] et al. [24]. Sampling effort was reduced using a nested SUR methodology for the sampling of branches and subunits. Rather than counting all fruit on sampled trees, fruits were counted on every \(j\)th primary branch and every \(k\)th secondary branch of those primary branches of the sampled tree from uniform random starting positions. The extra effort of distinguishing the fruit associated with the sub-canopy sections was claimed to be more  
Figure 3: Comparison of two sampling strategies, RS and SUR, in estimation of total fruit load (N\({}_{(\text{ffr})}\)) in a mango orchard in which the fruit number on every tree is known (site 1 in Table 3). The orchard has 469 trees and high variability in tree fruit load, with an average of 88 and SD = 89 fruit per tree (CV = 81%). The boxplots present estimates of fruit loading based on 250 realizations of 26 random samples using RS, compared to SUR sampling of rows with period 2 and trees-in-rows with period 9, for a mean sample size of 26 trees. than offset by the reduced total sampling effort. The methodology avoids two sources of sampling bias that are common in traditional methods used by the industry: the surveyor does not decide what trees or fruit to sample, as that is decided by a sampling algorithm, and low counts are made on small portions of plants spread over the three-dimensional (3D) orchard space, avoiding counting errors common when many fruits must be counted. A handheld app was developed to assist in-field implementation, calculating the position of the next sample and allowing for data entry, randomized start allocations and the use of semi-empirical error models to predict the sample size required to achieve a desired confidence criterion, typically a CE of 6-10% [25]. [PERSON] et al. [15] demonstrated the methodology in the estimation of the fruit load of apple, grape and kiwifruit.