New insights into the drainage of inundated ice-wedge polygons using fundamental hydrologic principles

The pathways and timing of drainage from the inundated centers of ice-wedge polygons in a warming climate have important implications for carbon flushing, advective heat transport, and transitions from methane to carbon dioxide dominated emissions. Here, we expand on previous research using a recently developed analytical model of drainage from a low-centered polygon. Specifically, we perform (1) a calibration to field data identifying necessary model refinements and (2) a rigorous model sensitivity analysis that expands on previously published indications of polygon drainage characteristics. This research provides intuition on inundated polygon drainage by presenting the first in-depth analysis of drainage within a polygon based on hydrogeological first principles. We verify a recently developed analytical solution of polygon drainage through a calibration to a season of field measurements. Due to the parsimony of the model, providing the potential that it could fail, we identify the minimum necessary refinements that allow the model to match water levels measured in a low-centered polygon. We find that (1) the measured precipitation must be increased by a factor of around 2.2, and (2) the vertical soil hydraulic conductivity must decrease with increasing thaw depth. Model refinement (1) accounts for runoff from rims into the ice-wedge polygon pond during precipitation events and possible rain gauge undercatch, while refinement (2) accounts for the decreasing permeability of deeper soil layers. The calibration to field measurements supports the validity of the model, indicating that it is able to represent ice-wedge polygon drainage dynamics. We then use the analytical solution in non-dimensional form to provide a baseline for the effects of polygon aspect ratios (radius to thaw depth) and coefficient of hydraulic conductivity anisotropy (horizontal to vertical hydraulic conductivity) on drainage pathways and temporal depletion of ponded water from inundated ice-wedge polygon centers. By varying the polygon aspect ratio, we evaluate the relative effect of polygon size (width), inter-annual increases in active-layer thickness, and seasonal increases in thaw depth on drainage. The results of our sensitivity analysis rigorously confirm a previous analysis indicating that most drainage through the active layer occurs along an annular region of the polygon center near the rims. This has important implications for transport of nutrients (such as dissolved organic carbon) and advection of heat towards ice-wedge tops. We also provide a comprehensive investigation of the effect of polygon aspect ratio and anisotropy on drainage timing and patterns, expanding on previously published research. Our results indicate that polygons with large aspect ratios and high anisotropy will have the most distributed drainage, while polygons with large aspect ratios and low anisotropy will have their drainage most focused near their periphery and will drain most slowly. Polygons with small aspect ratios and high anisotropy will drain most quickly. These results, based on parametric investigation of idealized scenarios, provide a baseline for further research considering the geometric and hydraulic complexities of ice-wedge polygons.