*4.5. Potential of S1 Backscatter and VIs for Precise Yield Mapping in Rainfed Areas Using the CatBoost Algorithm*

VIs have been widely utilized in PA for various purposes such as yield estimation, SSMZ delimitation, and water stress estimation. For its part, S1 backscatter information has been used for crop classification or for measuring land transformation changes. However, its use for yield estimation is not common. As previously mentioned, its relationship with growth is not direct, but it has been associated with key factors such as soil moisture, roughness or crop height. Therefore, it is imperative to conduct new studies to understand the underlying relationship between wheat yield and the S1 backscatter signal.

This study represents a preliminary step towards the goal of modulating fertilizer application according to crop needs. The underlying theoretical basis of this approach is that in rainfed areas, the fertilizer needs of the crop are generally associated to the potential yield. The high resolution of this study allowed for the estimation of precise yield maps. In this sense and according to Figure 9, the average %MAE was 4.38%, equivalent to an error of 0.31 t ha<sup>−</sup>1. This level of precision would enable farmers to adjust fertilizer rates at the plot level with an acceptable margin of error. Figure 10 takes this approach one step further by comparing the yield maps generated from the yield monitor data with those generated using the proposed methodology. The classification of pixels was found to be consistent between the two maps in 91.4% of cases, suggesting that this approach captures intra-plot yield spatial variability. Therefore, this would enable farmers who do not have a yield monitor installed on their harvesters but have a variable rate fertilizer applicator to create and employ intra-plot prescription maps based on estimated yield maps. In addition, thanks to the auxiliary information source used (VI and backscatter derived from satellites), this methodology can be scalable and applicable to larger areas. The results, however, were obtained using satellite images acquired between Day 1 (GS30) and Day 3 (GS69-75), with the latter date being too late to increase yield by fertilizing. Considering this, the authors believe that future works should be directed at studying the combined capability

of CatBoost with remote sensing data at early phenological stages of the crop to vary the fertilization strategy during the growing cycle.

Finally, it is worth noting that the results presented in this study are promising, but only correspond to one year. Thus, future works should encompass data from several years to verify that the results remain consistent across all campaigns. Furthermore, it would be interesting in future studies to incorporate high resolution climate and soil information in order to better understand the reasons behind yield spatial variability.

#### **5. Conclusions**

The models developed to estimate yield using information from S1 and S2 satellites showed better results than the correlation analysis. Among the evaluated models, CatBoost, which is still relatively underutilized in agriculture, provided the best results. Furthermore, using all available images that correspond to the GS30, GS39-49 and GS69-75 wheat phenological phases improved the performance of the models. Additionally, combining images from S1 and S2 substantially improved predictions, providing a level of precision sufficient to consider yield maps for fertilizer adjustment. This is an important aspect because most farmers in the area do not have yield monitors.

Despite its potential, the methodology proposed in this article has some limitations. Operationally, the biggest challenge lies in the clouds that impact the usability of the S2 images. While, theoretically, S2 provides an image every five days, in reality only three images were obtained throughout the whole crop growing cycle which were free of clouds and hence suitable for analysis. Moreover, to effectively train the algorithm, it is imperative to have access to high resolution yield data, such as that provided by yield monitors, although the use of such equipment is not yet widespread.

Combining the backscatter information of S1 with that of S2 resulted in improved outcomes of only using data from S2. However, further research is necessary to gain a better understanding of the relationship between backscattering and crop yield. In addition, this study focused solely on VIs and backscattering as they provide information on crop status. Future research could benefit from incorporating high resolution meteorological and edaphic variables, such as temperature, precipitation, and soil moisture, to better comprehend the factors influencing crop yield.

**Author Contributions:** A.U. worked in the following: Conceptualization, Methodology, Software, Data Processing, Formal Analysis, Original Draft Preparation, Visualization, Investigation, Interpretation. A.C. worked in the following: Methodology, Data Acquisition, Results Analysis, Resources. A.A. worked in the following: Conceptualization, Methodology, Writing, Reviewing and Editing, Supervision of Parameter Computing, Funding Acquisition, Project Administration. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the AgritechZeha project of the Basque Government, Department of Economic Development, Sustainability and Environment. It also was partially elaborated in the context of the CLIMALERT project SOE3/P4/F0862 UNION EUROPE. So, we want to express our gratitude to Interreg Sudoe Programme which a is part of the European territorial cooperation objective known as Interreg (financed by one of the European structural funds: the European Regional Development Fund (ERDF)).

**Data Availability Statement:** Data are available in a publicly accessible repository that does not issue DOIs. The raw satellite information data can be found in https://scihub.copernicus.eu/dhus/ #/home, accessed on 30 January 2023.

**Acknowledgments:** The authors would like to thank Javier Alava, a farmer in the GARLAN cooperative, for providing the possibility to carry out the research in his plots and giving us high resolution yield information.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study, in the collection, analyses, or interpretation of data, in the writing of the manuscript, or in the decision to publish the results.
