Sensitivity analysis of the climate of a chaotic system

This paper addresses some fundamental methodological issues concerning the sensitivity analysis of chaotic geophysical systems. We show, using the Lorenz system as an example, that a naïve approach to variational ("adjoint") sensitivity analysis is of limited utility. Applied to trajectories which are long relative to the predictability time scales of the system, cumulative error growth means that adjoint results diverge exponentially from the "macroscopic climate sensitivity"(that is, the sensitivity of time‐averaged properties of the system to finite‐amplitude perturbations). This problem occurs even for time‐averaged quantities and given infinite computing resources. Alternatively, applied to very short trajectories, the adjoint provides an incorrect estimate of the sensitivity, even if averaged over large numbers of initial conditions, because a finite time scale is required for the model climate to respond fully to certain perturbations. In the Lorenz (1963) system, an intermediate time scale is found on which an ensemble of adjoint gradients can give a reasonably accurate (O(10%)) estimate of the macroscopic climate sensitivity. While this ensemble‐adjoint approach is unlikely to be reliable for more complex systems, it may provide useful guidance in identifying important parameter‐combinations to be explored further through direct finite‐amplitude perturbations.     

Continental/Cordilleran ice interactions: a dominant cause of westward super-elevation of the last glacial maximum continental ice limit in southwestern Alberta, Canada

In southwestern Alberta, Canada, a westward-rising last-glacial-maximum continental ice limit has been identified. This limit is defined by the upper elevation of Canadian Shield erratics deposited by last-glacial-maximum continental ice along the flanks of prominent ridges and buttes within the region. The interpolation between ice-limit data points has produced two distinct slope profiles: 2.9 m/km to the east, and 4.2 m/km to the west of Mokowan Butte. Three hypotheses are proposed to explain this westward rise of the last-glacial-maximum continental ice limit: (1) regional tectonic uplift, (2) glacio-isostatic uplift, and (3) continental ice-flow convergence due to topographic obstacles and interaction with montane ice. Inferred long-term rates of tectonic uplift and glacio-isostatic modelling show that these two mechanisms account for less than 25% of the observed absolute elevation increase of the limit between the Del Bonita uplands and Cloudy Ridge in southwestern Alberta. The remaining rise in elevation of the continental ice-sheet margin in this region is thought to result from continental ice-flow convergence due to the combined effects of the regional topography and interaction with montane glaciers to the west. The steeper rise in the former continental ice surface west of Mokowan Butte can be explained by the topographic obstruction and interaction with montane glaciers in the area of the Rocky Mountain front.     

Glacio-dynamic structures from the Blackwater Formation, Co. Wexford, Ireland

A series of large-scale glacio-dynamic structures exposed in 10 km of coastal cliff cut through the Screen Hills kame-morainc, Co. Wexford. Ireland, is descrihed. The structures range from simple ovcrfolds to complex multiple thrusts, have a consistent structural trend, and result from marginal deformation by an ice-sheet moving from the NE. The relationship between the structures and other, gcomorphic and stratigraphic components is resolved into a simple model of repeated ice-marginal oscillation during a phase of overall glacial retreat.