Observations indicate that over the past several decades, geomorphic processes in the Arctic have been changing or intensifying. Coastal erosion, which currently supplies most of the sediment and carbon to the Arctic Ocean [Rachold et al., 2000], may have doubled since 1955 [Mars and Houseknecht, 2007]. Further inland, expansion of channel networks [Toniolo et al., 2009] and increased river bank erosion [Costard et al., 2007] have been attributed to warming. Lakes, ponds, and wetlands appear to be more dynamic, growing in some areas, shrinking in others, and changing distribution across lowland regions [e.g., Smith et al., 2005]. On the Arctic coastal plain, recent degradation of frozen ground previously stable for thousands of years suggests 10–30% of lowland and tundra landscapes may be affected by even modest warming [Jorgenson et al., 2006]. In headwater regions, hillslope soil erosion and landslides are increasing [e.g., Gooseff et al., 2009].

S U M M A R YMantle convection models require an initial condition some time in the past. Because this initial condition is unknown for Earth, we cannot infer the geological evolution of mantle flow from forward mantle convection calculations even for the most recent Mesozoic and Cenozoic geological history of our planet. Here we introduce a fluid dynamic inverse problem to constrain unknown mantle flow back in time from seismic tomographic observations of the mantle and reconstructions of past plate motions using variational data assimilation. We derive the generalized inverse of mantle convection and explore the initial condition problem in high-resolution, 3-D spherical mantle circulation models for a time period of 100 Myr, roughly comparable to half a mantle overturn. We present a synthetic modelling experiment to demonstrate that mid-Cretaceous mantle structure can be inferred accurately from fluid dynamic inverse modelling, assuming present-day mantle structure is well-known, even if an initial first guess assumption about the mid-Cretaceous mantle involved only a simple 1-D radial temperature profile. We also demonstrate that convecting present-day mantle structure back in time by reversing the time-stepping of the energy equation is insufficient to model the mantle structure of the past. The difficulty arises, because such backward convection calculations ignore thermal diffusion effects, and therefore cannot account for the generation of thermal buoyancy in boundary layers as we go back in time. Inverse mantle convection modelling should make it possible to infer a number of flow parameters from observational constraints of the mantle.

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This work presents numerical calculations of mantle convection that incorporate some of the basic observational constraints imposed by plate tectonics. The model is three‐dimensional and includes surface plates; it allows plate velocity to change dynamically according to the forces which result from convection. We show that plates are an effective means of introducing a toroidal component into the flow field. After initial transients the plate motion is nearly parallel to transform faults and in the direction that tends to minimizes the toroidal flow field. The toroidal field decays with depth from its value at the surface; the poloidal field is relatively constant throughout the layer but falls off slightly at the top and bottom boundaries. Layered viscosity increasing with depth causes the toroidal field to decay more rapidly, effectively confining it to the upper, low‐viscosity layer. The effect of viscosity layering on the poloidal field is relatively small, which we attribute to its generation by temperature variations distributed throughout the system. The generation of toroidal flow by surface plates would seem to account for the observed nearly equal energy of toroidal and poloidal fields of plate motions on the Earth. A low‐viscosity region in the upper mantle will cause the toroidal flow to decay significantly before reaching the lower mantle. The resulting concentration of toroidal flow in the upper mantle may result in more thorough mixing there and account for some of the geochemical and isotopic differences proposed to exist between the upper and lower mantles.

Regions of warm, thin, discontinuous permafrost have been observed to be experiencing rapid changes in lake and pond dynamics in recent decades. Even though surface water and groundwater interactions are thought to play a significant role in heat transport in these regions, the effect of these interactions on permafrost remains largely unquantified. In order to examine the influence of groundwater flow on permafrost dynamics, we modeled the development of a sub‐lake talik under permafrost conditions similar to those observed in the southern‐central Seward Peninsula region of Alaska using a numerical solution that couples heat transport and groundwater flow, including the effect of water phase changes on soil permeability and latent heat content. A comparison of model simulations, with and without near surface subpermafrost groundwater flow, indicates that stable permafrost thicknesses are 2 to 5 times greater in the absence of groundwater flow. Simulations examining the thermal influence of lakes on underlying permafrost suggest that a through‐going talik can develop in a matter of decades and that the incorporation of advective heat transport reduces the time to complete loss of ice beneath the lake by half, relative to heat transport by conduction alone. This work presents the first quantitative assessment of the rates of sub‐lake permafrost response to thermal disturbances, such as talik development, in systems with near‐surface groundwater flow. The results highlight the importance of coupled thermal and hydrologic processes on discontinuous permafrost dynamics.