This study presents a Bayesian framework for generalising SCADA-calibrated wake-model tuning parameters across offshore wind farms. The framework infers cluster-wide, farm-specific, and new-farm parameter distributions while accounting for calibration uncertainty, intra-farm variability, inter-farm variability, and residual model-data mismatch. It is applied to the Jensen and Gaussian TurbOPark wake models and extended to condition the central tuning parameter on atmospheric stability, represented by the bulk Richardson number and the inverse Monin-Obukhov length. For both wake models, unstable conditions are associated with larger tuning parameters, indicating faster wake expansion and recovery, whereas stable conditions yield smaller tuning parameters and more persistent wakes. The results show that the globally pooled stability-independent parameter should not be interpreted as a neutral-stability parameter because it reflects the stability mix at the case-study offshore site. Propagating representative stability-class-specific parameters to wake-loss estimates shows that atmospheric stability substantially affects predicted wake losses, with model differences becoming more pronounced when external wakes from surrounding wind farms are included.