Statistical Modelling of the Incidence of Glacier Surging in Svalbard

Hester Jiskoot, Paul Boyle and Tavi Murray
School of Geography, University of Leeds, Leeds LS2 9JT, United Kingdom

Glacier surging is a cyclic flow instability in which long periods of quiescence are interspersed by short periods of rapid flow 10-1000 times faster. Glaciers showing evidence of unstable flow behaviour of this type are called surge-type glaciers. Surging may occur in all types and sizes of glaciers, but the spatial distribution of surge-type glaciers is markedly non-uniform, at both global and regional scales. This spatial clustering implies that there are environmental controls on surge behaviour; identifying these factors would provide vital clues to the surge mechanism and trigger.

We use data from one of the key-areas for surge-type glaciers, Svalbard, an archipelago in the European high Arctic. The glacier data were retrieved from a glacier inventory published in the Glacier Atlas of Svalbard and Jan Mayen (Hagen et al., 1993), and additional information was collected from aerial photographs, geology maps and published material. From literature reviews of observations and theories on glacier surging we selected a key-set of glacier and environmental variables and derivatives likely to control or influence surge mechanics. These variables can thus be used for testing theories on surging. In this research surge-type and non-surge-type glaciers were tested against variables such as: glacier length, area, slope, elevation, orientation, glacier-type, geographical position, and bedrock lithology.

At regional scales, research on the distribution and characteristics of surge-type glaciers have been performed in recent decades, using conventional statistical analysis methods (Glazyrin, 1978; Clarke et al., 1986; Wilbur, 1988; Clarke, 1991; Hamilton, 1992). However, these statistical methods are problematic: firstly there are statistical significance problems with conventional tests when using small data sets; secondly the variables used in the testing vary widely, for example some are continuous (e.g. glacier length) while others are categorical (e.g. lithology type). Conventional statistical correlation tests are unable to cope with these mixtures of data types. To overcome these problems, this research utilises recent developments in data analysis techniques in both geographical sciences and other disciplines: (i) case-control studies, which overcomes the problems of small data sets, and (ii) multivariate logit regression analysis, which can cope with mixed data types.

In method (i) we analysed the associations between variables and surging, by stratifying classes of cases (surge-type glaciers) and controls (non-surge-type glaciers) on the basis of each of the variables. By dichotomising on the presence or absence of variables, and thus creating a 2x2 matrix, we tested each variable or class of variables against the prevalence for surging. We used method (ii) to disentangle multiple correlations between variables, in order to find primary correlations between variables and surging. For this analysis we used the computer package GLIM (Generalised Linear Interactive Modelling), which includes parametric and nonparametric analysis techniques.

The results of our data analysis show the advantages of these methods over the conventional statistical methods previously used. Both methods distinguish variables related to surging; case-control studies provide a simple way of initial analysis of complex interrelationships, while multivariate logit regression analysis can deal with multicollinearity in finding correlations between mixed variable types and surging.

Clarke, G.K.C. 1991. "Length, width and slope influences on glacier surging", J. Glaciol., 37 (126), 236-246.

Clarke, G.K.C., Schmokk, J.P., Ommanney, C.S.L. and Collins, S.G. 1986. "Characteristics of surge-type glaciers", J. Geophys. Res., 91 (B7), 7165-7180.

Glazyrin, G.E. 1978. "Identification of surging glaciers by morphometric characteristics", Mater. Glyatsiologicheskikh Issled. Khronika, 33, 136-137.

Hagen, J.O., Liestøl, O., Roland, E., and Jørgensen, T. 1993. "Glacier atlas of Svalbard and Jan Mayen", Meddelelser, 129, Norsk Polarinstitutt.

Hamilton, G.S. 1992. Investigations of surge-type glaciers in Svalbard, Unpublished PhD dissertation, Scott Polar Research Institute, Cambridge.

Wilbur, S.C. 1988. Surging versus nonsurging glaciers: a comparison using morphometry and balance, Unpublished MSc. thesis, University of Alaska, Fairbanks.