Can we estimate farm size from field size? An empirical investigation of the field size to farm size relationship.

CONTEXT: Farm size is a key indicator associated with the environmental, economic, and social contexts and outcomes of agriculture. Farm size data is typically obtained from agricultural censuses or household surveys, but both are usually only available in infrequent time intervals and at aggregate spatial scales. In contrast, spatially explicit and detailed data on individual fields can be continuously derived from Earth observation data. Assuming a field size to farm size relationship (FFR) exists, assessing field sizes and their changes over time using Earth observation could enhance our understanding of the spatial patterns and dynamics of farm size. However, current empirical knowledge does not allow characterizing this FFR over large spatial extents. OBJECTIVE: To address this knowledge gap, we here provide a quantitative assessment of the FFR using Germany as a case study. METHODS: We developed a Bayesian multilevel model and a machine learning model to estimate farm size based on field size, controlling for a set of contextual factors such as crop types, topography, and neighborhood effects. RESULTS AND CONCLUSIONS: We found that farm size generally increased with field size for almost all federal states and crop type groups, but the FFR varied considerably in magnitude. Farm size predictions were accurate for medium sized and large farms (50-7,000 ha, representing 66% of the data) with mean absolute percentage errors of 40-114% but estimates for smaller farms had higher errors. Spatially aggregating predictions to 15 km diameter hexagons resulted in more accurate predictions (mean absolute percentage errors of 37%) compared to the field-level. SIGNIFICANCE: Our study presents the first empirical insights into the FFR, opening future research directions towards producing spatially explicit farm size predictions at scale. Such information is key for monitoring scale transitions in agricultural systems, facilitating the design of timely and targeted interventions, and avoiding undesired outcomes of such processes.