Heat flow scaling for mantle convection below a conducting lid: Resolving seemingly inconsistent modeling results regarding continental heat flow

Numerical models of mantle convection below a conducting lid, meant to mimi c a continent, have been used 1) to argue that heat how variations in stabl e continental regions result principally from lithospheric thickness variat ions, and 2) to argue that the relationship between lithospheric thickness and continental heat how is too weak to allow for this. We reconcile these results using a theoretical heat flow scaling which shows that the relation ship between heat flow and lid thickness can take on two end-member forms. As the ratio of lid thickness to convecting layer depth increases, the effe cts of lid thickness variations on heat how move from weak to strong. Model ing studies that concluded that lithospheric thickness variations could lea d to significant continental heat flow variations assumed a convecting laye r depth appropriate to upper mantle convection and, thus, maximized the rel ative thickness of the continental lithosphere, i.e., the conducting lid. S tudies that concluded that the relationship is weak assumed whole mantle co nvection which placed them on the flatter end of the heat flow versus relat ive lid thickness curve.