# Mapping Smallholder Yield Heterogeneity at Multiple Scales in Eastern Africa
## 1 Introduction  
Low crop yields in smallholder farming systems of Africa are widely acknowledged as an impediment to improving food security and reducing poverty in this region [1]. One reason for low productivity is the limited access of farmers to high-yielding varieties, fertilizers, and modern management technologies [2]. Another important reason is the tremendous heterogeneity of soils and weather in the local cropping systems, which precludes any single strategy from working over a broadregion. Despite the urgent need and the complexity of closing yield gaps in this region, however, the productivity of individual smallholder farms remains poorly measured. Lacking accurate field-level yield estimates is a serious constraint to both researchers and policy-makers, making it difficult to identify the causes of yield gaps, track progress in response to extension or other interventions, and to evaluate the impact of a particular policy. Although significant efforts have been proposed on ground, such as designing and implementing nationally representative household surveys [3], these approaches are often labor-intensive and, hence, have limited coverage.  
By their nature, satellite data can be used to characterize crop production across a large area and through time with low cost [4]. The recent advent of new satellite sensors with both high spatial (less than 10 m) and temporal resolution (less than 2 weeks) as well as the powerful geospatial big-data platform such as Google Earth Engine (GEE) brings an opportunity to routinely observe millions of individual smallholder farms and increases the possibility of accurately mapping crop type [5] and field-level crop productivity [6]. Recently, reference [7] demonstrated the potential to estimate smallholder maize yield variation in a \(\sim\)400 km\({}^{2}\) region within western Kenya, using a combination of 1-m Terra Bella Skysat imagery and hundreds of field plots. In their paper, satellite-based estimates were able to explain up to 40% of variations in ground-based yield measures. Reference [7] further showed that these estimates were able to detect positive yield responses to fertilizer applications and hybrid seed adoption. However, the proposed approach in [7] was only tested for a single set of sensors (i.e., Skysat) and for a small region for two years (2014-15), and, therefore, it remains unclear whether the approach is generally applicable to the eastern Africa smallholder farming system.  
This study aims to expand the evaluation of satellite-based yield estimates to a broad region in western Kenya. The work presented here has advanced those in ref. [7] in at least three substantial ways. First, utility of different sensors was investigated, including the commercial Skysat and RapidEye satellites and the publically accessible Sentinel-2. Second, we tested multiple possibilities for improving yield estimation accuracy, including using alternate vegetation indices, updating the phenology process in the crop model used for yield estimation, and implementing alternative approaches to modeling the ratio of yield to total biomass (following reference [8]). Third, the methodology was tested with substantially more data across a broader region for the 2016 growing season, including: (i) farmer interviews and plot outlines for 766 maize fields in a sub-region of western Kenya, and (ii) nearly 4000 crop cuts collected throughout a \(\sim\)40,000 km\({}^{2}\) western Kenya region.