## 3 Results
### Quality of the N-PLS Model  
The quality and performance of the N-PLS model with 5 latent variables is presented in terms of \(R^{2}\), the bias and the standard error of prediction of yield losses in the calibration (Figure 10a) and validation (Figure 10b) analyses. The N-PLS model showed a performance accuracy (\(R^{2}\)) of 0.56 in the calibration set and 0.66 in the validation set, with a standard error of cross-validation in the calibration set of 12.4% and a standard error of prediction of losses in validation set of 10.7%. A standard error of prediction over the prediction set of 10.7% (Figure 10b) was consistent with the initial variability of the ground truth data (Section 2.4.3) and also with the information needed by the growers to characterize the level of yield loss in a block that was caused by the heat wave. These results demonstrated the relevance of the approach to detect incidences of heat waves in viticulture and in particular to estimate the yield loss based on spectral and temporal attributes of the images. The results were further validated by the calibration data. Figure 8: Evolution of RMSECV as a function of varying intervals between dates (\(N\)) and Gaussian filter width (\(P\)) obtained for 2 blocks repeated 5 times with a N-PLS performed with a \(\underline{\mathbf{X}}\) cube and the \(\mathbf{y}\) yield losses. Parameter optimisation was achieved at, \(P\) = 30 and \(N\) = 15 as indicated by the white dash circle. Figures 11 and 12 show plots of the coefficients \(\mathbf{B_{\text{nPLS}}}\) corresponding to the 5 latent variables selected for the model. The N-PLS model estimated yield loss for each block by making the inner product of \(b\)-coefficients with a spectral-temporal profile (7 \(\times\) 12) contained in the cube \(\mathbf{X}\) (107,7,12). Thus, the \(b\)-coefficients had the same dimension as the spectral-temporal profile and could be analysed to identify how specific parts or periods of the spectral-temporal profile were more or less related to yield losses. Figure 10: Results of the N-PLS prediction of losses on individuals in the calibration set (**a**), with 80 vineyard blocks and in the validation test (**b**), with 27 vineyard blocks. The standard error of cross-validation in the calibration set was 12.4 and the standard error of prediction of yield losses in validation set was 10.7. Figure 9: Evolution of the RMSEC and the RMSECV for a cross-validation of 2 blocks repeated 10 times of a N-PLS between the \(\mathbf{X}\) cube and the \(\mathbf{y}\) losses. The black frame indicates the optimal number of latent variables (5 LV). Figure 11: N-PLS \(b\)-coefficients corresponding to 5 latent variables and the following two different dimensions: (**a**) plotted according to the spectral dimension and (**b**) plotted according to the temporal dimension. Black dot-dash line highlights the most relevant date of the heat wave. Figure 12: Combined representation of the temporal and spectral profiles as a 3D view of N-PLS \(b\)-coefficients corresponding to 5 latent variables. Black dot-dash line to highlight the most relevant date of the heat wave. Figure 11 shows the spectral profiles for each spectral band (Figure 11a) and the temporal profiles by date (Figure 11b) of the \(b\)-coefficients. Regarding the spectral profile (Figure 11a), the spectral bands were clearly organized into the following three groups: (i) bands B1 and B2 (442.7 and 492.4 nm), which presented no variations throughout the study period, (ii) bands B3, B9 and B12 (559.8, 945.1 and 2202.4 nm), which showed a slight decrease by the end of June and, (iii) the remaining bands B4, B5, B6, B7, B8, B8A and B11 (663.5, 704.1, 740.5, 782.8, 832.8, 864.1 and 1613.1 nm), which presented a very pronounced V-shaped profile with a minimum \(b\)-coefficient observed on the 20 th of June, identifying these spectral bands as significant in order to identify and characterize the heat stress. Regarding the temporal profiles (Figure 11b), they were very similar in shape and mainly differed in translation.