Continental lithosphere influences heat loss by acting as a local insulator to the convecting mantle and by sequestering heat-producing radioactive elements from the mantle. Continental heat production can have a two-part effect since it decreases the amount of internal heat driving convection, which lowers mantle temperature, while also increasing the local insulating effect of continental lithosphere, which raises mantle temperature. We explored these competing effects using simulations that incorporated enriched continents within a mixed internal- and bottom-heated convecting mantle. Increasing continental surface area was found to enhance global heat loss for a range of heat production distributions and Rayleigh numbers. The effect of enriched continents was evident as a double peak in the continental surface area values that maximize global heat loss. That the presence of continental lithosphere could increase average mantle temperature despite the mantle being depleted suggests that continents can significantly influence mantle potential temperature.
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 For example, Lenardic et al.  demonstrated that increasing continental surface area could actually buffer or increase mantle heat loss. This counterintuitive response relies on the ability of continental insulation to directly impact oceanic heat flux. This is important for a mantle with a strongly temperature-dependent rheology. If the continental lithosphere sufficiently insulates the mantle and the mantle tends toward a thermally well-mixed state, then the increased temperature can decrease mantle viscosity. This allows for more rapid overturn of oceanic lithosphere, which can, depending on continental area, increase global heat loss.
 Continental lithosphere, as well as insulating the mantle, also serves as a sink for heat producing elements (HPE). Increasing the continental crust volume depletes the mantle of HPE. This has a potential two part effect: (1) depleting the mantle of HPE removes a portion of the heat sources driving convection and (2) enriching the continental crust with HPE increases its local insulating effects.
 To explore the two part effect, we began by defining a reference case in which the total amount of heat production in the continent-mantle system is partitioned between the continental crust and the mantle based on estimated present day values [Rudnick et al., 1998]. That is, continental crust is enriched in heat production density by 40 times that of the mantle. Continental crust surface area within the reference case also reflects present day conditions (36% of the surface). From the reference case, we varied the crustal heat production enrichment and continental lateral extent (thickness remains fixed) while maintaining constant total heat production within the system. In other words, within our models, placing more heat production within the continent (either through increased enrichment or surface area) comes at the expense of mantle HPE enrichment. Maintaining constant total heat production for all simulations allowed us to explore the effects of relative partitioning of HPE between the mantle and continents that would be induced by continental growth. Time dependent disintegration of HPE was not included within the simulations. For all simulations, the continental crust resides within the upper thermal boundary layer of the convecting mantle (Figure 1) and is free to drift. To avoid crustal remixing and maintain constant continental extent within a simulation, we set the crust's rheological properties such that model continents resist deformation. We use a finite element code [Moresi et al., 2003] to solve the governing equations of convection, i.e., conservation equations of mass, momentum, and energy for an incompressible fluid with mixed internal- and bottom-heating.
 The vigor of the bottom-heated component of convection is represented by the Rayleigh number, Rab,
where ρ0 is average mantle density, α is coefficient of thermal expansion, ΔT is temperature drop across convecting layer, d is convecting layer depth, μ is mantle viscosity at the system base, and κ is thermal diffusivity. For each heat production distribution scenario, we varied the Rab from 2 × 107–108.
 The internal heating Rayleigh number, RaH, is defined as
where Hm is the rate of internal heat generation per unit mass within the mantle and k is thermal conductivity. The internally-heated Rayleigh number within our simulations depends on the amount of mantle heat production. This in turn depends on the volume and enrichment of continental crust since the total amount of heat production within the system is held constant. Within the mixed heating mode of convection, the ratio between the two Rayleigh numbers parameterizes the degree of internal to basal heating. For our reference case, this ratio was set to one (or non-dimensionally Hm = 1). As crustal volume and enrichment increases, the ratio, RaH/Rab, and the degree of internal mantle heating decreases as more HPE are removed from the mantle (non-dimensional Hm minimum = 0.3). The degree of internal mantle heating is highest when there is no continental crust (non-dimensional Hm maximum = 1.842).
 A viscoplastic rheology was used to model plate-like behavior. Above a specified yield stress, material deforms according to a continuum representation of Byerlee's Law [Byerlee, 1968; Moresi et al., 2003]. Deformation in this plastic regime occurs within localized shear bands (bright white zones in Figure 1). If the yield stress is not exceeded, then the material deforms viscously following an exponential temperature-dependent viscosity law given by
where T is temperature, A is a prefactor, Q is activation energy, R is the gas constant, ΔT is the temperature drop across the system and Ti is the temperature of the interior of the convecting system. Within the mantle, the non-dimensional viscosity ranges from 1 at the hottest temperature to 105 at the coldest temperature allowing the upper thermal boundary to behave as an internally rigid lithosphere. The yield stress within the model oceanic lithosphere is set to a constant and low value such that stagnant lid convection is avoided and the oceanic lithosphere can be recycled into the mantle.
 Top and bottom boundaries are both free slip and isothermal. Wrap around side boundary conditions were applied allowing the continent to drift freely across the surface while minimizing boundary effects. All simulations were run to a statistical steady state.
3.1. Global Heat Flux
Figure 2 shows time and space averaged global heat flux versus continental extent for simulations with variable ratios of continental to mantle heat concentration (Hc/Hm) and variable Rab. The first order trends confirm the results of Lenardic et al. ; increasing continental extent can increase total heat loss up to a point at which the oceanic lithosphere area decreases such that its contribution to total heat flux does not offset the reduced continent heat flux. This trend holds for the full range of Hc/Hm and Rab explored. This suggests that heat production distribution has a smaller effect on total heat flux variations than continental surface area.
 However, heat production distribution does influence the continental extent for which global heat flux is maximized (Figure 2). Of particular interest, global heat flux can undergo a double peak at continental lateral extents of 18% and 36% for intermediate crustal enrichment ratios. This is more pronounced for higher Rab.
 The competing effects of continental insulation and enrichment are also observed in the mantle heat flux. Figure 3a shows the mantle heat flux variations with increasing continental extent for simulations with a Rab of 108. Again, increasing continental surface area enhances mantle heat loss until the point at which the oceanic surface area is too small to offset the insulation effect of continental crust. The second order variations due to heat production distribution are also highlighted for mid-range Hc/Hm. The similarity between global surface and mantle heat flux trends confirms that the main variations in total surface heat flux are not predominantly influenced by variations due to greater continental heat flow resulting from an enriched crust. Rather, they reflect the feedback between increased mantle temperatures and oceanic surface heat flux driven by continental insulation.
3.2. Oceanic vs. Continental Surface Heat Flux
Figure 3b shows oceanic and continental surface heat flux versus continental extent for simulations with variable ratios of Hc/Hm and Rab of 108. An increase in continental area increases oceanic surface heat flux while continental surface heat flux remains relatively constant. Both trends are weakly dependent on HPE distribution and Rab. As with global total heat flux, the smaller scale variations within oceanic surface heat flux are influenced by heat production distribution.
3.3. Mantle Average Internal Temperature
Figure 3c shows the average mantle internal temperature versus continental lateral extent for simulations with variable Hc/Hm and Rab of 108. Mantle internal temperatures are horizontally averaged at mid-depth and are presented non-dimensionalized relative to the total system temperature drop. In general, mantle internal temperature increases with continental extent. Only the cases with the highest crustal enrichment allowed for second order variations on this trend for which increased extent could lower mantle temperature.
 As continental crust volume grows the mantle becomes more depleted in HPE, which has the potential to lower internal mantle temperatures. However, within our simulations as the mantle becomes more depleted, due to greater extent of continental crust, the average internal mantle temperature shows a generally increasing trend approaching a value near the system's total temperature drop. This suggests that the insulating effect of continents overrides the thermal signature due to changes in the ratio of internal to bottom heating within the mantle driven by continental growth. Therefore, the ratio of internal mantle temperature to core-mantle boundary temperature may not be as effective an indicator of the mode of mantle heating (bottom vs. internally-heated) as has been assumed. Further, our results suggest that if enriched continental crust was mixed back into the mantle, then the mantle potential temperature would decrease due to the decreased continental insulation (Figure 3). This opens the possibility that continental growth could have offset the effects of decaying mantle heat sources and, thus, maintained near constant mantle potential temperatures over geologic time.
 Increased internal mantle temperature is tied to the increased global and oceanic heat flux with increased continental extent, observed within our simulations. As argued by Lenardic et al. , increased mantle temperature, caused by continental insulation, decreases the temperature-dependent mantle viscosity, thus allowing oceanic lithosphere to overturn and lose heat more rapidly. Our results confirm this trend and show that it is robust for mixed heating convection. An unexpected new result is that the mixed heating system allows for a double peak in the global heat loss versus continental extent curve over a range of crustal enrichment that is in line with present day estimates. A physical scaling analysis, along the lines of that presented by Lenardic et al.  for the simpler bottom heated system, is required to understand the combination of factors that allow for this behavior.
 The increased efficiency in heat loss due to viscosity reduction can be limited by the onset of stagnant lid convection, which occurs if viscosity is reduced to the point that convective stresses do not exceed the oceanic lithosphere yield stress. For our study, the yield value was set low enough to avoid this potential. Future work will relax this restriction. Stagnant lid convection will also occur if the oceanic lithosphere is too buoyant to subduct back into the mantle. Mantle internal temperature determines the oceanic lithosphere's chemical buoyancy as it affects the degree of melting and thus, thickness of oceanic crust and melt-depleted residuum. This suggests another interesting feedback as our models show that the extent of continents strongly affects mantle internal temperature.
 Continental lithosphere influences global heat loss by locally insulating the mantle as well as depleting the mantle of heat producing elements. Simulations exploring the coupling of these effects confirm that increasing continental surface area can enhance global heat loss. This result is shown not to be overly sensitive to heat production distribution or bottom-heated Rayleigh number. Heat production distribution was found to influence the continental surface area at which global heat loss is maximized. For mid-range ratios of continental to mantle heat production, the dependence of global heat loss on continental surface area showed two peaks. This double peak effect could reflect trade off between mantle heat production depletion and the increased continental insulation. The insulating effect of continents was shown to alter the temperature signature associated with bottom- vs. internally-heated convection.
 We would like to thank the anonymous reviewer for constructive comments and suggestions. This work was supported by NSF-Career grant EAR-0448871 and Australian Research Council Discover grant DP0449979.