## 4 Discussion  
A generic example of the application of N-PLS algorithm to time-series of multispectral images was provided in the form of an agricultural study. This paper showed the potential for methods originally developed in the spectrometry/chemometrics domains to be applied to a time-series of Sentinel-2 data. The application showed the value of considering simultaneously the temporal and spectral dimensions with a sensor whose band repartition was partly optimised for vegetation monitoring. The application of N-PLS to characterize and estimate the impact of an extreme event, such as a heat wave on grapevines, showed that it was possible to predict yield losses with a performance (\(R^{2}\)) of 0.66 and a RMSE of approximately 10%. The theory for the use of remote sensing instruments to monitor electromagnetic radiation reflectance changes in crops is well demonstrated in the scientific literature [38]. In situations where crops interact with any given aspect of their environment, such as seasonal climatic variations or meteorological extreme events, the interactions between plants and light reflectance translates into changes in plant signal patterns that can be interpreted using satellite data [39]. Besides the model of yield loss estimation, the N-PLS analysis showed the interest of adopting a systemic analysis which accounts simultaneously for the spectral and temporal characteristics of the considered data. The approach allowed the identification of the spectral bands that responded most strongly to the phenomenon of interest while keeping the information of the period of influence. Previous studies have reached similar accuracies to assess the effects on heat stress on grapevines [23]. However, notably, the linear nature of the dimensionality reduction in the method presented here allowed for a simple interpretation using the computed \(b\)-coefficients, which are directly related to the importance of the explanatory variables, i.e., to the best spectral signature related to the event under study. Since \(b\)-coefficients have the same dimension as the spectral-temporal profile, spectral bands around Red Edge (700 nm) and the SWIR region (1600 nm) in late June and early July, were considered relevant to quantify the effect of a heat wave that occurred in late June. It has already been demonstrated that the Red Edge band has a good potential for estimating plant stress, either due to water loss or to leaf pigment modifications [23; 40; 41]. In particular, this band has been useful for studying how experimental water deficits change the characteristics of plant physiology (e.g., chlorophyll a/b ratio), as plants experiencing a water deficit change their foliar chlorophyll composition, resulting in a shift of red-edge reflectance towards shorter wavelengths [42]. Regarding the shortwave infrared region (SWIR), from approximately 1300 nm to 2500 nm, the absorption of radiation is largely dominated by water [39]. These results generally supported the prediction that wavelengths, where the water absorption coefficient is weak, will penetrate further into canopies and thus will be best for estimations of water content, as is the case in the 1600 nm region [43]. This implied that the SWIR region of the spectrum may potentially be efficient for drought stress detection and resulting changes in canopy tissues [23]. The results of the current analysis confirmed, with a data-driven approach, that a combination of Red Edge and SWIR regions was a valuable indicator in identifying grapevine heat stress on a regional scale. It is essential to place the results presented in this paper within the reality of multitemporal satellite data. Satellite observations are heavily conditioned by cloud coverage over the acquisition period. Despite this, this method was able to manage a time-series dataset with different sets of missing values by means of an interpolation on a date grid that was regularly spaced and optimised over the period of interest.