We present a new parameterisation that relates surface mass balance (SMB: the sum of surface accumulation and surface ablation) to changes in surface elevation of the Greenland ice sheet (GrIS) for the MAR regional climate model. The motivation is to dynamically adjust SMB as the GrIS evolves, allowing us to force ice sheet models with SMB simulated by MAR while incorporating the SMB–elevation feedback, without the substantial technical challenges of coupling the two models. This also allows us to assess the effect of elevation feedback uncertainty on the GrIS contribution to sea level, using multiple global climate and ice sheet models, without the need for additional, expensive MAR simulations. We estimate this relationship separately below and above the equilibrium line altitude (ELA, separating negative and positive SMB) and for regions north and south of 77° N, from a set of MAR simulations in which we alter the ice sheet surface elevation. These give four "SMB lapse rates", gradients that relate SMB changes to elevation changes. We assess uncertainties within a Bayesian framework, estimating probability distributions for each gradient from which we present best estimates and credibility intervals (CIs) that bound 95% of the probability. Below the ELA our gradient estimates are mostly positive, because SMB usually increases with elevation: 0.54 (95% CI: 0.22 to 1.34) kg m 3 a 1 for the north, and 1.89 (1.03 to 2.61) kg m 3 a 1 for the south. Above the ELA the gradients are much smaller: 0.09 ( 0.03 to 0.22) kg m 3 a 1 in the north, and 0.06 ( 0.07 to 0.56) kg m 3 a 1 in the south, because SMB can either increase or decrease in response to increased elevation. Our statistically based approach allows us to make probabilistic assessments for the effect of elevation feedback uncertainty on sea level projections. In a companion paper we use the best estimates and upper and lower CI bounds in five ice sheet models, and the full probability distributions in another, to adjust simulated SMB from MAR forced by two global climate models for the SRES A1B scenario (Edwards et al., 2013).