# Interpretable Machine Learning for Legume Yield Prediction Using Satellite Remote Sensing Data
## 1 Introduction  
Legumes constitute an integral part of sustainable agriculture, providing an important source of plant-based protein identifying them as a foundational component in the protein intake of both humans and domesticated animals [1, 2]. They also improve soil health through biological nitrogen fixation, thus lowering the need for chemical-based nitrogen fertilizers [3]. Dryland legume crops, including lupin, hold a key position in cropproduction across Mediterranean-type climates. These climates, characterized by cool, wet winters and hot, dry summers, present unique agricultural challenges that lupin is well-adapted to withstand [4]. Its resilience to water-limited conditions, combined with their ability to enrich soil fertility, makes it ideal for enhancing both productivity and environmental sustainability in these areas. Additionally, its suitability for crop rotation contributes significantly to food security and soil conservation in semi-arid and temperate regions. As a consequence, accurate yield prediction for this crop is essential to optimize production, mitigate food insecurity risks, and guide climate adaptation strategies [5]. By predicting yields with precision, farmers can make informed decisions about pest control, irrigation management, and resource allocation [6]. Furthermore, reliable yield forecasts can help policymakers and implement better-targeted support, especially in regions facing growing challenges of climate change [7]. Traditional methods for estimating crop yields, including field surveys, meteorological statistical methods, and governmental reports, struggle with key limitations that impede their utility [8]. Primarily, they are often time-consuming, expensive, and susceptible to errors due to inconsistent data or incomplete coverage [9]. Field surveys are labor-intensive and influenced by seasonal factors, while agro-meteorological models may fail to account for localized conditions or sudden weather events [10]. These persistent shortcomings emphasize the critical need for more advanced and scalable crop monitoring solutions that can deliver timely and accurate yield predictions. Satellite remote sensing has become a game-changing solution, providing the ability to monitor crops frequently and with high resolution [11; 12]. Specifically, it constitutes a necessary tool in crop yield monitoring, providing various levels of detail in terms of location, timing, and spectral resolutions. Remote sensing relies on the electromagnetic spectrum, such as visible, thermal, and infrared radiation, to examine how this energy interacts with different features on Earth's surface [13]. For the effective utilization of satellite remote sensing in agriculture, precise and dependable quantitative analysis of the acquired data is paramount. The spectral reflectance signature of vegetation is modulated by a complex interplay of factors inherent to plant development, including root system attributes, leaves, soil background influences (like moisture content), canopy structure, and spatial arrangement [14]. Multispectral sensors quantify crop health through vegetation indices (VIs), which are mathematical combinations of spectral bands. In essence, VIs serve as statistical proxies that can be correlated with biophysical variables like Leaf Area Index (LAI), representing the amount of leaf material, and fraction of Absorbed Photosynthetically Active Radiation (fAPAR), showing how much sunlight the plants absorb for photosynthesis. These data are integrated with several crop models to enhance yield predictions [15]. For example, [PERSON] et al. [16] assimilated remote sensed LAI and soil moisture into the DSSAT-CERES model. In addition, [PERSON] et al. [17] incorporated LAI and Canopy Nitrogen Accumulation (CNA) into the aforementioned crop model stressing that the model performed better than when only one variable was used. Finally, [PERSON] et al.