Emergent constraints use relationships between future and current climate states to constrain projections of climate response. Here we introduce a statistical, hierarchical emergent constraint (HEC) framework in order to link future and current climates with observations. Under Gaussian assumptions, the mean and variance of the future state are shown analytically to be a function of the signal-to-noise ratio between current climate uncertainty and observation error and the correlation between future and current climate states. We apply the HEC to the climate change, snow-albedo feedback, which is related to the seasonal cycle in the Northern Hemisphere. We obtain a snow-albedo feedback prediction interval of (−1.25,−0.58)%/K. The critical dependence on signal-to-noise ratio and correlation shows that neglecting these terms can lead to bias and underestimated uncertainty in constrained projections. The flexibility of using HEC under general assumptions throughout the Earth system is discussed.