Numerical and experimental methodsExperimental methods have been implemented independently for many years in wind engineeringWind engineering applications. Their combination, using data assimilationData assimilation (DA), is a relatively recent development in the field in order to provide an improved solution. In this scope, a DA method is developed based on the employment of the Best Linear Unbiased Estimator (BLUEBest Linear Unbiased Estimator (BLUE)) equations together with an ensemble-based strategy for the quantification of the underlying uncertaintiesUncertainty in a localised framework. For a steady-state laminar flow past a square cylinder, synthetic measurements of the two velocity components and pressure, originating from a fine mesh CFDComputational Fluid Dynamics (CFD) solution, are assimilated into a model state derived from a coarser mesh solution, using the same OpenFOAM solver. Spatial discretisation is considered as the only source of relative uncertaintyUncertainty between the two solutions and therefore is perturbed for the generation of the ensemble at a Reynolds number of Re = 10. The extracted ensemble is also used for DAData assimilation for an order of magnitude of Reynolds numbers, for which the flow regime remains the same. Significant model error reduction is achieved, even with a limited number of assimilated measurements and even though they are derived at a different Reynolds number.