Convective thermal evolution of the upper mantles of Earth and Venus

On Earth the present-day rate of heat loss is about twice the heat generation rate; on Venus it is about half. Though this rough balance may be due to a feedback mechanism between mantle temperature and heat loss, it is difficult to see how such a mechanism can occur on timescales of 1 Ga or less when the upper mantle of the Earth is thought to be cooling at about 40 degrees C Ga-1. On Venus a decrease in surface heat flux presumably occurred at the end of the catastrophic resurfacing event at similar to 500 Ma. Parameterized convection models relate heat flux to Rayleigh number by the exponent beta. Such models using a range of viscosities and values of beta from 0.2 to 0.3 show that the effect of a sudden decrease in surface heat flux is to cause an independently convecting upper mantle to increase in temperature by 100 - 500 degrees C over 1 Ga, whereas, if whole mantle convection occurs, the temperature change is less than 60 degrees C. An increase in mantle temperature of 200 degrees C or more will affect mantle viscosity, lithospheric thickness and melt generation rate, all of which may affect the feedback mechanism.