A method for detecting rapid mass flux of small glaciers using local sea level variations

Abstract

There is increasing evidence that the global reservoir of small (or mountain) glaciers is presently experiencing an accelerated phase of net melting, perhaps linked to climatic warming. We argue that relative sea level and sea surface fingerprints local to such events provide a potentially powerful, integrated diagnostic for the mass imbalance. For example, we demonstrate, using an inference of glacier mass balance near Alaska over the last 50 years, that the present-day relative sea level fall at nearby sites can reach amplitudes that are ∼2 orders of magnitude greater than the ongoing eustatic sea level rise associated with the melting. The peak sea surface subsidence is a factor of ∼15 greater than the eustatic amplitude. We find that the predicted present-day sea surface change arising from the 50-year loading history is sensitive only to the ongoing rate of accelerated melting. In contrast, the present-day relative sea level fingerprint becomes increasingly sensitive to the ‘history’ of the recent loading when the viscosity of the asthenosphere adopted in the prediction is progressively reduced below 10²⁰ Pa s. Specifically, the relative sea level fingerprint becomes more localized, and reaches higher amplitudes, close to the glacier system as viscous effects become active. Our results have application in efforts to constrain small glacier mass balance using tide gauge records of relative sea level change or satellite-derived constraints on sea surface (geoid) rates.

Introduction

The contributions to global sea level rise over the last century and at the present day from the Antarctic and Greenland ice sheets, other (henceforth ‘small’) glaciers and ocean thermal expansion are a matter of active research and debate [1]. Within this list, small glaciers are thought to be particularly sensitive to climate variations. Indeed, while these glaciers represent just 4% of the total glaciated land area, they may have contributed as much as ∼20% to the accumulated sea level rise over the last century [2], [3], [4]. Furthermore, recent research suggests that this net mass loss may have increased substantially since the mid-1990s [4], [5].

Estimating the regional or global mass balance of small glaciers is a difficult task (e.g., [1], [4]). One fundamental obstacle is the extremely poor sampling of the global glacier reservoir. Arendt et al. [5] have pointed out, for example, that only 40 of more than 160 000 small glaciers have been subject to continuous monitoring of mass changes for over 20 years (see also [3]). To overcome this difficulty, observational constraints obtained on a small subset of glaciers are commonly extrapolated over a given ‘climatic region’ [1]. For example, the inference of an acceleration in melting from glaciers in Alaska and Canada since the mid-1990s [5] was based on ‘reprofiling’ of 28 glaciers representing 13% of the total glacier cover. In addition, the current sampling of small glaciers is not geographically representative of the global network and is strongly biased toward smaller (<20 km² area) reservoirs [1], [5].

The accuracy of glacier mass balance estimates is also a function of the adopted measurement procedure. As an extreme example, inferences of glacier-scale mass balance based on a small set of point estimates of accumulation and discharge rates are prone to large errors [5]. The use of altimetry to measure ice height changes (e.g., [5]) improves the geographic sampling, but introduces complications involving ice-snow compaction and radial motions of the solid Earth. Clearly, it would be advantageous to apply techniques that directly estimate the integrated mass flux of a glacier or system of glaciers. Hager [6] argued that loading-induced radial motions in the vicinity of a glacier provide one such integrated measure, and he suggested that surveying these motions using the Global Positioning System would be an effective means of ‘weighing the ice sheets’ (see also [7]).

It has long been known that rapid melting or growth of ice sheets leads to non-uniform changes in sea level (e.g., [8], [9], [10], [11], [12], [13], [14], [15]). In this paper we explore, in detail, sea level variations driven by glacier flux of small spatial scale. We argue that these ‘fingerprints’, which are potentially observable using either local tide gauge records of relative sea level change or satellite-derived (e.g., GRACE) estimates of geoid or sea surface variations, provide a valuable, integrated diagnostic of changes in the ‘weight’ of small glacier complexes. To highlight the generic physics of the meltwater redistribution we present numerical predictions of sea level change associated with the recent, accelerated melting of Alaskan glaciers inferred (and tabulated) by Arendt et al. [5]. The characteristics of these results are relevant to all glacier complexes in that the basic physics of meltwater redistribution is universally applicable and we consider a realistic range of solid earth models.