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Venus may have had both an Earth-like climate as well as extensive wateroceans and active (or incipient) plate tectonics for an extended interval ofits history. The topographical power spectrum of Venus provides important cluesto the planet's past evolution. By drawing detailed contrast with the stronglow-order odd-$l$ dominated global topography of Earth, we demonstrate that therelatively flat Venusian topography can be interpreted to have arisen from thetransition from active terrestrial-like plate tectonics to the current stagnantlid configuration at a time $\tau = 544^{+886}_{-193}$ million years beforepresent. This scenario is plausible if loss of oceans and the attendanttransition to a CO$_2$-dominated atmosphere were accompanied by rapidcontinental-scale erosion, followed by gradual lava resurfacing at an outflowrate $\sim$ 1 km$^{3}$ yr$^{-1}$. We study Venus' proposed topographicalrelaxation with a global diffusion-like model that adopts terrestrial erosionrates scaled to account for the increased rainfall and temperatures that wouldaccompany a planet-wide transition from an Earth-like climate to the runawaygreenhouse climate that could ultimately yield present-day Venus, with anestimate of $5.1^{+1.8}_{-1.1}$ Myr if the global erosion operated asefficiently as that of a typical bedrock river basin on Earth.

Turning Earth into Venus: A Stochastic Model of Possible Evolutions of Terrestrial Topography