A mathematical approach to understandingemergent constraints
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Emergent constraints are one of the tools to reduce uncertainty in climate model projec-tions. These are physically explainable empirical relationships between characteristicsof the current climate and long-term behavior that emerge in ensembles of climatemodels, where the long-term behavior is constrained using observations. So far, nogeneral mathematical framework describing emergent constraints has been proposed.In this work, we introduce a classification for emergent constraints, depending on theprocess under consideration: we distinguish between emergent constraints that modelvariability, mean state or feedback strength. In addition we present a mathematicalframework making use of linear response theory and apply this description to a setof conceptual (climate) models. We specifically focus on an emergent constraint that waspreviously found for the snow-albedo feedback. We conclude by discussing if and howthis framework can be applied to GCMs.