## 5 Conclusions  
In this study, we have developed a novel approach to using Landsat temporal series to evaluate changes in the illumination conditions and vegetation indices in forested areas in irregular terrain. We used Google Earth Engine to analyze 397 images for 28 years (1984-2017) of the latest Landsat Surface Reflectance collections. The main conclusions of our work can be described as follows:  
1. In summary, the illumination condition of Landsat scenes can be easily calculated using Landsat image information and an elevation model of the same resolution. Changes in illumination condition and its relation to vegetation indices can be evaluated effectively at the pixel level without needing to use ancillary data from other sensors or simulating data.
2. The analysis at the pixel level showed correlations between illumination conditions and vegetation indices with a strong effect in EVI and less in NDVI. Moreover, positive correlations were found in shadowed areas, whereas neutral to negative correlations were found in sunlit areas, This, is a crucial finding to interpret vegetation indices derived from Landsat data in irregular terrain. In this regard, our analysis at the pixel level revealed patterns that could not be detected using only solar angle information.
3. Our long-term analysis revealed that there is an increasing trend in illumination conditions, EVI, and NDVI associated with the improvement in the position in Landsat sensors over time. These trends calculated at selected images at varying seasons were significant when placed in chronological order. This effect cannot be overlooked when employing vegetation indices in the study of phenology patterns or aboveground net primary productivity. The incorporation of illumination condition into time-series analysis according to this method can provide additional data to understand the behavior of vegetation indices in irregular terrain.  
[PERSON] and [PERSON] conceptualized the research ideas and supervised the research activity. [PERSON], designed the methodology, analyzed the data and wrote the paper. [PERSON] and [PERSON] revised the manuscript and provided useful suggestions on the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research has been conducted as part of a Ph.D. thesis project supported by the Agricultural Transformation by Innovation (AGTRAIN) Erasmus Mundus Joint Doctorate Programme, EU Framework Partnership Agreement 2011-1530/001-001-EMJD (2011.0019)--Contract AGTRAIN NO. 2015-005 funded by the EACEA (Education, Audovisual and Culture Executive Agency) of the European Commission  
The authors would like to thank the anonymous reviewers in their effort of reading and giving constructive feedback on the manuscript. We also acknowledge the institutional support of the Department of Forest and Environmental Engineering and Management of Universidad Politecnica de Madrid, Montpellier SupAgro, CIRAD, UMR Innovation and Centro Agronomico Tropical de Investigacion y Ensenanza (CATIE). We would also like to thank feedback from the Google Earth Engine team on the code and from anonymous users in the GEE forum.  
The authors declare no conflicts of interest.