Stress-Gradient Coupling in Glacier Flow: II. Longitudinal Averaging in the Flow Response to Small Perturbations in Ice Thickness and Surface Slope

• Published in: Journal of Glaciology
• Main Authors: Echelmeyer, Keith A., Kamb, Barclay
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1986
• Subjects: Earth-Surface Processes; Blue Glacier; Journal of Glaciology
• Online Access: http://dx.doi.org/10.1017/s0022143000015616; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000015616

Abstract As a result of the coupling effects of longitudinal stress gradients, the perturbations ∆ u in glacier-flow velocity that result from longitudinally varying perturbations in ice thickness ∆ h and surface slope ∆α are determined by a weighted longitudinal average of ϕ h ∆ h and ϕ α ∆α, where ϕ h and ϕ α are “ influence coefficients ” that control the size of the contributions made by local ∆ h and ∆α to the flow increment in the longitudinal average. The values of ϕ h and ϕ α depend on effects of longitudinal stress and velocity gradients in the unperturbed datum state. If the datum state is an inclined slab in simple-shear flow, the longitudinal averaging solution for the flow perturbation is essentially that obtained previously (Kamb and Echelmeyer, 1985) with equivalent values for the longitudinal coupling length l and with ϕ h = n + 1 and ϕ α + n , where n is the flow-law exponent. Calculation of the influence coefficients from flow data for Blue Glacier, Washington, indicates that in practice ϕ α differs little from n , whereas ϕ h can differ considerably from n + 1. The weighting function in the longitudinal averaging integral, which is the Green’s function for the longitudinal coupling equation for flow perturbations, can be approximated by an asymmetric exponential, whose asymmetry depends on two “asymmetry parameters” μ and σ, where μ is the longitudinal gradient of ℓ(= dℓ/d x ). The asymmetric exponential has different coupling lengths ℓ + and ℓ − for the influences from up-stream and from down-stream on a given point of observation. If σ/ μ is in the range 1.5–2.2, as expected for flow perturbations in glaciers or ice sheets in which the ice flux is not a strongly varying function of the longitudinal coordinate x , then, when dℓ/d x > 0, the down-stream coupling length ℓ + is longer than the up-stream coupling length ℓ − , and vice versa when dℓ/d x < 0. Flow-, thickness- and slope-perturbation data for Blue Glacier, obtained by comparing the glacier in 1957–58 and 1977–78, ...