Timescale for oceans in the past of Titan

We estimate the past extent of liquid on the surface of Titan as a function of time assuming the current rate of destruction of methane and no sources or subsurface sinks. As methane increases for increasing past time the polar lakes expand equatorward. We use a spherical harmonics model for the surface topography to compute the fraction of the surface covered as the methane inventory increases. We find that substantial parts of the equator would have been flooded by a polar ocean 300 million years ago and that the equator would have been connected to a global ocean 600 million years ago. This provides one possible explanation for the fluvial features seen at the equator on Titan.