Figure 4A visualizes the calibration of the VO estimated fPAR against the lightbar estimated midday fPAR over all varieties on June 26. Again, reasonably high R2 (0.91) and low RMSE (2.94%) from data points to the 1:1 line suggested that both methods estimate the actual canopy fPAR. However, one method estimated fPAR with lower accuracy or more error since some data points were slightly off the 1:1 line (in the dashed red). For instance, we observed that the regression line (in the dashed blue) was not completely overlapped with the 1:1 line with the slope of 0.91 in the clockwise direction of rotation (the difference was significant as shown in Table 3), indicating that most of the data points were below the 1:1 line. The result suggested that the lightbar tended to underestimate the canopy fPAR or the VO method tended to overestimate it (mean of absolute errors to the regression line: 1.97 +- 1.85%; to the 1:1 line: 5.09 +- 2.55%). Over different almond varieties, 6-year-old 'Nonpareil' trees intercepted more fPAR than others, which is reasonable because of their larger canopy size (up to 73% fPAR). Figure 4B visualized a similar calibration for 'Nonpareil' only with a better R2 of 0.96 and a lower RMSE of 2.06% to the 1:1 line (the difference was significant as shown in Table 3). This improved correlation might be due to the uniformity of the tree canopy from a single variety (mean of absolute errors to the regression line: 1.58 +- 1.00%; to the 1:1 line: 6.59 +- 2.47%). We scanned all three orchards using the aerial photogrammetry method within a day for each data collection from May to August. However, the lightbar method needed multiple days to complete the same tasks. Therefore, the VO method we offered in this study is practically easier and faster to conduct than a mobile lightbar platform to estimate canopy fPAR in the orchard environment.
Figure 5 shows the overall correlations of VO estimated fPAR over the growing season in 2019. We observed a good correlation among the data collected at different dates, with Pearson's r ranged between 0.92 and 0.99. Based on the scatter plots in the lower-left half, we could find better correlations when the two dates were closer. The highest Pearson's r of 0.99 was from the dates between July 26 and August 7. One possible reason could be the proximity of data collection dates (only 10-d difference). Besides, the histograms on the diagonal illustrate that all sampled trees were normally distributed, and the majority of the sampled trees were 'Nonpareil' and 'P16.013'. Lastly, the kernel-density-estimate plots in the upper right half show that the variations of VO estimated fPAR decreased from May to August with more data points aligned on the 1:1 line. Figure 5 illustrates the results of 12 different flights, image processing, and feature extractions conducted by the VO pipeline. High correlations in Figure 5 show the robustness and replicability of the VO methodology that consistently and accurately estimated fPAR in all 12 datasets. While we observed some canopy development over the season that leads to minor changes in the canopy profile, no major observational error (variation in measurement) was noticed for the same tree profile features measured during the season. To explore which method is more reliable, we further compared the VO and lightbar methods in estimating the actual almond yield from different spatial precision levels: per-row, per-block, and per-tree (VO only) level.
To test which method could better estimate actual almond yield, we compared the scatter plots of actual yield vs. canopy fPAR estimated by the mobile lightbar and VO methods on a per-row basis. Figure 6 summarizes the overall results, and Figure 7 shows more details in Supplementary Material. The results indicated that canopy fPAR estimated by VO is a more accurate indicator of almond actual yield than lightbar. Both R2 and predictive R2 are higher with the VO method (0.37 and 0.34 for VO; 0.34 and 0.31 for lightbar) on June 26. Both regression lines in Figures 7B,E had similar slopes (32 for VO; 36 for lightbar) and intercept on the y-axis. We may accept either method since both RMSEs were lower than the standard deviation of the actual yield (484.14 lb acre-1) with all varieties. We did not find any statistical difference between the means of absolute errors in predicting actual almond yield by the VO and mobile lightbar models. So, the VO method is statistically as good as the lightbar measurement but with potentially better performance as the VO models presented insignificantly smaller errors. One possible reason might be the higher spatial resolution of the VO method (0.01-0.02 m) compared with the mobile lightbar (~0.4 m). In general, the R2 of 0.34 estimated by the lightbar in our study agreed with the findings from Zarate-Valdez et al., who reported that mobile lightbar estimated midday fPAR was an indicator of almond kernel yield with R2 in the range of 0.16-0.36. A better correlation between VO estimated fPAR suggested that light interception, or fPAR, is not only a good indicator of potential (maximum) yield but also a possible good estimator of actual yield for almond (particularly the 'Nonpareil' variety).
We conducted separate analytics for 'Nonpareil' since it is the leading and most profitable almond variety in California. Results indicated better fits for both models if we only analyze the 'Nonpareil' variety. For example, we achieved a better R2 of 0.83 and predictive R2 of 0.79 for the 'Nonpareil' yield prediction than the model for all varieties (0.37 and 0.34, respectively). One reason might be that the sampled trees are more uniform when we tested with only one variety. This better performance on the 'Nonpareil' variety is also valid for using lightbar estimated midday fPAR. However, the achieved R2 (0.70) and predictive R2 (0.65) are notably lower than those from VO. Pearson's r followed a similar pattern. RMSEs for both methods with 'Nonpareil' only were lower than the standard deviation (497.64 lb acre-1) of actual almond yield at the per-row level. However, the RMSE of VO estimated fPAR (199.26 lb acre-1) was notably smaller than the mobile lightbar (265.73 lb acre-1) in June. These results reiterated the possibility that fPAR alone could be an accurate indicator of actual almond yield if it is estimated accurately. We may accept both VO and lightbar results in explaining 'Nonpareil' yield, but apparently, the result from VO seemed more accurate and reliable. Overall, we suggest that the VO method offers a more accessible and accurate (with smaller errors) alternative for estimating canopy fPAR than the mobile lightbar platform since the VO model showed a better correlation to actual yield. Therefore, we can use this VO technology as a reliable indicator for predicting actual almond yield, particularly with the 'Nonpareil' almond variety.
In addition to comparing VO estimated fPAR with lightbar data, we compared the yield prediction models based on data at a different time of the season. Interestingly, a descending trend of yield prediction accuracy is present from May to August when we tested all varieties (Figure 6). In other words, we found that we achieved a better actual yield prediction in May comparing to June, July, or August using VO estimated fPAR model for all varieties. The overall trend was in a reverse direction when we only tested 'Nonpareil'; the prediction accuracy on 'Nonpareil' improved as we got closer to the harvest time in August. This discrepancy of accuracy changes between all varieties and 'Nonpareil' suggests that a single comprehensive model cannot accurately predict yield for different almond varieties, and the yield prediction model should be calibrated for each variety. It might be more reasonable to develop models separately for each variety, such as 'Nonpareil', to explain the variations of actual almond yield.
The yield prediction accuracy with VO for 'Nonpareil' improved from May to June but did not change much after June 26. The source-sink interaction theory during plant growth may better explain it (Allen et al.,). Starting from the bloom in almonds (around February in a year), the reproductive growth (with reproductive organs: flower and fruit) is becoming more competitive with vegetative growth (with vegetative organs: branches and leaves) for absorbing the nutrients. Therefore, midseason (June/July) measurement might be more accurate for predicting actual almond yield when both growths are dominant. This deduction was verified because the midday fPAR was mostly measured with a lightbar system in midseason (June and July) for almond orchards (Lampinen et al.,; Rubke,). Lastly, the similarity of actual yield prediction results on June 26 between the lightbar (R2 = 0.34 for all varieties; R2 = 0.70 for 'Nonpareil' only) and VO method (R2 = 0.37 for all varieties; R2 = 0.83) also verified the strong correlation between these two methods of fPAR measurement as discussed earlier.
It was also interesting to notice that the regression lines (dashed blue line in Figure 8) had a smaller angle to the 1:1 line for 'Nonpareil' than all varieties combined in Figure 7. First of all, all data points (at the per-row level in Figure 7) were below the 1:1 line, indicating that none of the samples reached the potential yield in this study. Specifically, with the increase of estimated fPAR on the x-axis (0-100%), the slope of the regression lines moved farther (35.6 in Figure 7A to 29.0 in Figure 7D) from the potential yield line over the season for all varieties, suggesting that the actual yield prediction became less accurate. Comparatively, the regression lines directions were closer to the 1:1 line for 'Nonpareil' only (Figures 8A-D). Although the actual yield of 'Nonpareil' was also far less than the potential yield, the changing patterns were more comparable. We believe that the proposed model could be used as a good yield forecasting tool for 'Nonpareil' trees with an acceptable accuracy of R2 = 0.84 and RMSE = 195 lb acre-1 at the per-row precision level, where the standard deviation of the yield (498 lb acre-1) was about 2.5 times greater than RMSE. Besides, we analyzed the VO estimated fPAR with higher spatial precision (at the per-tree level) in the next section, but no corresponding lightbar data at this level of precision was available for comparison.
Figure 9 visualizes the regressions between per-tree fPAR (estimated by VO) and almond kernel yield over the season in 2019. Figure 10 provides in-depth details. As discussed for the per-row level results, the accuracy (R2) decreased for all-varieties-model from May (May 28; with R2 of 0.31 and RMSE of 504.88 lb acre-1) to August (August 7; with R2 of 0.24 and RMSE of 532.37 lb acre-1). The result at the per-tree level had a relatively poorer R2 (0.29), and RMSE (514.31 lb acre-1) with a greater standard deviation of the yield (609.38 lb acre-1) compared with the per-row analysis (R2 = 0.37 and RMSE = 38.18 lb acre-1 for VO; R2 = 0.34 and RMSE = 389.49 lb acre-1 for lightbar; the standard deviation was 484.14 lb acre-1) in June. This result is reasonable because we expected a greater variation in the dataset for the high-spatial-precision level of per-tree data. For instance, we observed a huge range of yield from 10.81 to 5094.49 lb acre-1 at a per-tree precision level. Given this large variation in per-tree yield data, VO estimated fPAR still offered a reasonable accuracy with higher spatial precision than lightbar data, which is mainly available at the per-row level.
When we only considered the 'Nonpareil' variety, we observed an increasing trend in accuracy (R2) similar to the per-row models (Figure 6). On July 26, the R2 was up to 0.62, and RMSE was 351.25 lb acre-1 for the 'Nonpareil' per-tree yield prediction. As expected, these results were not as good as the per-row model (R2 = 0.84 and RMSE = 195.01 lb acre-1). The RMSE from per-tree data were also much greater than that from per-row data due to the more diversity in the yield data. The differences were only significant between the two scenarios (i.e., all varieties and 'Nonpareil') when we tested the means of absolute errors using ANOVA (p < 0.05). In general, we conclude that the VO method provides an acceptable yield prediction accuracy (R2) at the per-tree level; a level of spatial precision in yield forecasting that has not been offered by the mobile lightbar platform or any other yield prediction methodologies.
It was important to note that more scattered points were getting closer to the potential yield line (Jin et al.,) due to the more variation in per-tree yield data. Two 'Monterey' trees (in yellow "x" symbol) yielded (5094.49 and 3801.04 lb acre-1) more than their potential yields (i.e., the two symbols were above the potential line in Figures 10A-D). Jin et al. found that the variation of the almond yield gap from actual yield to the potential yield (pass or not reach) was mainly driven by tree age and other factors if the orchards were located in different geographical areas. Since our three orchards were located close to each other, and all trees were mature, this gap was probably triggered by different orchard management and practices.
Orchards 1 and 3 contain several blocks in each row, consisting of three to eight trees based on the orchard configuration. Therefore, we also analyzed the data based on the per-block level, where the lightbar data were available to compare. Figure 11 compares the accuracies (R2) of the different measuring levels [per-tree (VO only), per-block, and per-row] in explaining almond actual kernel yield on June 26. In general, as the precision level decreased from per-block to per-row, the accuracy (R2) increased for both methods. For example, R2 increased from 0.29 to 0.37 using VO estimated fPAR in June. We expected this trend since the dataset contained more errors or extreme values when the precision level was higher. Subtle changes, such as a tree being shaded from neighboring trees, can cause biased data collection. We observed that even with the highest level of precision (at the per-tree level), the VO method achieved better accuracies (R2) than that of lightbar at a lower level of precision (at per-block level) for all varieties (R2 = 0.29 for VO at tree level; R2 = 0.23 for lightbar at block level). In other words, VO estimated fPAR could better explain the actual kernel yield with both higher accuracy and spatial precision than lightbar. Regarding 'Nonpareil', the per-tree VO method (R2 = 0.59) performed only slightly worse than the lightbar at the per-block level (R2 = 0.64). Overall, we can conclude that the correlation (R2) between the two measures (i.e., VO and lightbar estimated fPAR) can be up to 0.96, in which the VO method even better explained the almond actual kernel yield with up to 0.83 of R2 on the leading variety of 'Nonpareil' in June. The estimation accuracy was further improved for 'Nonpareil' toward the end of the season using the VO data.
In future work, we will consider adopting the DSM model generated by the LiDAR sensor instead of RGB photogrammetry, where LiDAR has much higher pixel resolutions. It is expected that fractional absorbed PAR (fAPAR) is highly correlated to fPAR due to fAPAR is strongly correlated to transmittance. In the PAR domain, the fAPAR is very close to the fPAR, corresponding to the canopy transmittance in the sun direction (Todd et al.,). Although only fPAR was considered in this work, we already tested the relationship between accumulated PAR (in the unit of mole) and fPAR using some preliminary datasets, where sun angle and sunlight directions were precisely modeled from sunrise to sunset at the specific locations of almond orchards. Per accumulating the total PAR over the entire growing season (four months from April 1 to July 31), we achieved a very high correlation (R2 = 0.97-0.99) between accumulated PAR and fPAR. Such information and results are out of the scope of this work and, therefore, will be presented in our future publications. We will also take the nitrogen and irrigation scheduling effects on the plants into account when we evaluate the correlation between estimated fPAR and almond yield. Besides, we will consider employing spectral reflectance (Moghimi et al.,) to determine tree nitrogen status and to better explain the yield variations in trees of similar size.