A framework for modelling spatio-temporal trends in crop production using generalised additive models

Satellite imagery provides opportunities for inference of trends in crop production across space and time. However, the large size of these datasets has made application of statistical modelling approaches computationally difficult. Recent advances in computational techniques and infrastructure have allowed generalised additive models to be fitted to very large datasets. We propose a framework for inferring trends in crop production across space and time using generalised additive models which accounts for inter-annual trends (main effect of year), spatial distribution (main effect of space), crop ontogeny (main effect of month), inter-annual changes in seasonality (interaction between year and month), and inter-annual changes in spatial distribution (interaction between year and space). Application of the proposed model to farm scale, multi-field sites in the Ord River Irrigation Area, Western Australia, demonstrates that this approach is able to decompose variation into the aforementioned effects. Furthermore, comparison of grain production observations and estimates for the Western Australian Wheatbelt as ground-truth data showed agreement with inferences drawn from the proposed model, with prediction terms for the main effect of year positively correlated with estimated tonnes produced from 2013 to 2021 (p = 0.03). Finally, application to Madagascar, which has been experiencing a food crisis, revealed a decreasing trend in cropland Normalised Difference Vegetation Index (NDVI) from 2014 to 2021 of 2.5%, raising concerns about ongoing food security. The proposed modelling framework is adaptable to numerous agricultural research problems.