On the origin and significance of subadiabatic temperature gradients in the mantle

It is well established that the temperature gradients in the interiors of internally heated mantle convection models are subadiabatic. The subadiabatic gradients have been explained as arising because of a balance between vertical advection and internal heating; however, a detailed analysis of the energy balance in the subadiabatic regions has not been undertaken. In this paper, we examine in detail the energy balance in a suite of simple, two-dimensional convection calculations with mixed internal and basal heating, depth-dependent viscosity, and continents. We find that there are three causes of subadiabatic gradients. One is the above mentioned balance, which becomes significant when the ratio of internal heating to total surface heat flow is large. The second mechanism involves the growth of the overshoot'' of the geotherm near the lower boundary where the dominant balance is between vertical and horizontal advection. The latter mechanism is significant even in relatively weakly internally heated calculations. For time-dependent calculations, we find that local secular cooling can be a dominant term in the energy equation and can lead to subadiabaticity. However, it does not show its signature on the shape of the time-averaged geotherm. We also compare the basal heat flow with parameterized calculations based on the temperature drop at the core-mantle boundary, calculated both with and without taking the subadiabatic gradient into account, and we find a significantly improved fit with its inclusion.