We introduce the “replicate Earth” ensemble interpretation framework, based on theoretically derived statistical relationships between ensembles of perfect models (replicate Earths) and observations. We transform an ensemble of (imperfect) climate projections into an ensemble whose mean and variance have the same statistical relationship to observations as an ensemble of replicate Earths. We use a ‘perfect model’ approach to test whether this Ensemble Dependence Transformation (EDT) approach can improve 21st century CMIP projections.