Chaotic variability in a model of coupled ice streams

TL;DR

The paper addresses the intrinsic chaotic variability that can arise in ice streams due to base thermomechanical coupling. It develops a three-box, volume-conserving extension of the R13 ice-stream model to capture nonlinear coupling among upstream and downstream termini. The coupled model exhibits steady flow, build-up/surge oscillations, and temporal chaos across parameter ranges, with chaos arising via period-doubling and intermittency and accompanied by bistability and chaotic transients near crises. These results imply that coupled ice streams could introduce significant, intrinsic unpredictability into ice-sheet mass balance, underscoring the need for probabilistic frameworks in forecasting and interpretation of paleo-records.

Abstract

Regions of fast-flowing ice in ice sheets, known as ice streams, have been theorized to be able to exhibit build-up/surge oscillatory variability due to thermomechanical coupling at the base of the ice. A simple model of three coupled ice streams is constructed to replicate the spatial configuration of a single ice stream being bisected into two termini. The model is constructed to mimic existing branching ice streams in northern Greenland. This model is shown to exhibit both steady-flow and build-up/surge oscillations. Further, the variability can be chaotic due to the nonlinear coupling of three incommensurate frequencies. This provides a mode of chaotic internal variability for ice sheets that contain these types of ice streams.

Figures (9)

• Figure 1: (Top) Schematic of the fluxes for the R13 model of a single ice stream. Broad arrows represent mass fluxes and wiggly arrows represent energy fluxes. (Bottom) Schematic of the three cases of the till.
• Figure 2: Schematic of the geometry considered in the three-box split ice stream model. B1 gains volume from accumulation and loses volume to B2 and B3 due to streaming flow. B2 and B3 gain volume from accumulation and as volume flux from B1, and lose volume due to streaming flow.
• Figure 3: Time series of variables for the individual boxes in the chaotic regime. Black curves are B1 values, blue lines are B2, and red lines are B3. Parameter values are given in Tables 1 and 2 in the Appendix, with $T_{s,2} =15.085^{\circ}$C. The void ratio of B1 is arbitrarily large, so it is omitted for readability.
• Figure 4: Bifurcation diagram for $T_{s,2}$ from 0 to 27 (top) and a zoomed view of the chaotic window between 14.6 and 15.6 (bottom). Remaining parameters are given in Tables \ref{['tab:param_glob']} and \ref{['tab:param_box']} in the Appendix.
• Figure 5: Poincaré maps of the period-doubling route to chaos on decreasing $T_{s,2}$.