Horizontal heterogeneity causes difficulties in the eddy covariance technique for measuring surface fluxes, related to both advection and the confounding of temporal and spatial variability. Our aim here was to address this problem, using statistical modelling and footprint analysis, applied to a case study of fluxes of sensible heat and methane in a subarctic mire. We applied a new method to infer the spatial heterogeneity in fluxes of sensible heat and methane from a subarctic ecosystem in northern Sweden, where there were clear differences in surface types within the landscape. We inferred the flux from each of these surface types, using a Bayesian approach to estimate the parameters of a hierarchical model which includes coefficients for the different surface types. The approach is based on the variation in the flux observed at a single eddy covariance tower as the footprint changes over time. The method has applications wherever spatial heterogeneity is a concern in the interpretation of eddy covariance fluxes.