Methods

2.3.1 Crevasse stratigraphy method

To determine the degree of spatial variability in net accumulation, crevasse stratigraphy was conducted in the accumulation area (~2000-2400 m a.s.l.) of both glaciers in March 2007-2009. Each year the same circuit is walked around the accumulation areas by two rope teams surveying as may crevasses as possible. Access, weather, and snow

conditions influence the number of crevasses that can be surveyed each year. A low-accumulation year (e.g. 2008) tends to have more exposed crevasses by the end of summer whereas an early snowfall (e.g. 2009) can cover crevasse walls on some aspects, reducing the number of crevasses available for accurate measurement.

The crevasse stratigraphy method is well suited for high accumulation glaciers, and has been utilised by researchers for over 30 years (Pelto, 1988; Ruddell, 1995; Pelto, 1996;

Anderson et al., 2006). Crevasse stratigraphy utilises ablation surfaces formed by summer melt and sedimentation, which are preserved by winter snowfall. These horizons are observed down crevasse walls and can be easily measured (Post and

LaChapelle, 2000). The method is fast, so large areas can be surveyed, and multiple measurements can often be taken from each crevasse, due to the clarity of the annual layer sequence. At FJG only top annual layers were measured, but at TG, measurements for both 2007 and 2008 include some data from second annual layers. The estimated error in measuring annual layer depth by this method is ±0.05 m.

The high precipitation in the Southern Alps results in large annual accumulation, often in excess of 10 m snow depth. This factor renders traditional measurement techniques such as stakes and snow-pits unsatisfactory. In addition, the maritime climate means that it is common for a number of ice layers to be present in the snow pack, thereby making probing potentially inaccurate unless combined with another method to verify depth. Certainly, by only sampling crevassed areas some bias will occur (Appendix A3), but similar bias applies to other techniques, for example, digging snow-pits requires a safe, crevasse free spot. Snow-pits are usually dug at a ‘representative’ location, somewhere relatively flat, providing a single point measurement for many hours work.

Crevasses occur over a variety of terrain enabling researchers to choose flat

‘representative’ areas, or include crevasses in depressions, on slopes, and on convex or concave surfaces, thereby providing a detailed spatial assessment of accumulation.

In order to determine net annual accumulation, depth measurements from crevasse stratigraphy need to be converted into metres water equivalent (m w.e.). This requires knowledge of snowpack density, a parameter difficult to determine with the crevasse stratigraphy method (Meier et al., 1997). However, in New Zealand, it has been found that snow density in the accumulation area at the end of the ablation season is

reasonably consistent at ~600 kg m^-3 (Chinn, 1994; Ruddell, 1995). On temperate maritime glaciers melt/refreeze processes dominate snow metamorphism and

densification, resulting in a strong elevation-depth-density relationship (Paterson, 1994).

Ruddell (1995) analysed density measurements from a variety of temperate glaciers finding that, in these environments, layer density (ρ) could be determined as a function of the age of the layer (depth) and the elevation (E) of the crevasse, where density of the first annual layer is defined by;

ρ_snow = 44.75 E^-0.557

and the second annual layer by;

ρ_firn = 5.234 E^-0.255

2.3.2 Data analysis

To determine the degree of spatial variability in net accumulation within the accumulation area of each glacier, each year, descriptive statistics and spatial variograms were used. A spatial variogram plots the distance between each measurement pair against the semi-variance (γ) of each measurement pair,

) 1 (

) 5 (

. 0

2

−

=

∑

n x γ x

where x is net accumulation at each measurement point, x mean net accumulation of the sample, and n the total number of measurements. This allows testing of the

hypothesis that points closer together will be more similar than those further apart, and thereby gauge the degree of spatial variability. To explore within-glacier difference, an analysis of variance (ANOVA) of net accumulation (and control variables) was

conducted between the three FJG snowfields.

A number of variables were investigated to see which exert control on the spatial distribution of net accumulation namely; elevation, distance from Alpine Fault, distance from Main Divide, slope, aspect, potential wind exposure and insolation. As already outlined, elevation is thought to be a primary control on snow accumulation and melt, due to its effect on temperature. The influence of orography, in particular, precipitation distribution, is represented by distance from the Alpine Fault, where initial, rapid, increases in topography occur, and distance from the Main Divide, the topographic maxima.

The effect of wind re-distribution/preferential deposition is assessed by the development of a wind exposure index, derived by calculating the average elevation of 90° wedges (100 m radius) for four main compass directions (NW, SW, SE and SE) similar to the methods of Anderton et al., (2004) and Winstral et al., (2002). This identified whether windward terrain was higher (positive index) or lower (negative index) than each

measurement point, providing information on the degree of sheltering or exposure each point had to wind from those sectors.

Potential terrain controls, slope and aspect, were derived from a 25 m digital elevation model in ArcMap GIS, and values were extracted for each measurement point. The amount of insolation received at each measurement point was calculated from the ArcMap solar radiation function. Incoming solar radiation per square metre (MJ m^-2) over the ablation season (1 November - 31 March) was calculated for each measurement point each year.

Once all variables had been extracted for each net accumulation measurement, Spearman's Rank correlation was conducted between net accumulation and the

variables. Due to its non-linear nature, aspect data was transformed into north-south and east-west scalars as per Copland (1998). The north-south scalar is the cosine of the aspect, resulting in 0°→1 and 180°→-1. The east-west scalar is the sine of the aspect, where 90°→1 and 270°→-1. Inter-relationships exist between some of the variables.

For example, there is a linear relationship between net solar radiation and aspect scalars, as aspect is an important component of net radiation calculations. Due to co-linearity between some parameters, an un-rotated Principle Component Analysis (PCA) was conducted (Copland, 1998), which was followed by multiple-regression of net

accumulation data with the new uncorrelated PC factors. Only PCs with an eigen value

>1 were carried forward for regression analysis, as only these PCs are regarded as statistically significant.

2.3.3 Ablation estimation

Annual net accumulation is the combined result of winter accumulation and summer ablation. In order to estimate the magnitude of summer ablation (1 Nov-31 Mar) a positive degree-day model was applied. Utilising parameters from Anderson et al.

(2006) and Cutler and Fitzharris (2005), hourly temperature data from Franz Josef and Mount Cook village AWS were used to estimate ablation season melting each year for both glaciers. Summer snowfall was estimated using a standard accumulation model (see Anderson et al., 2006; Purdie et al., 2011b). Combined, these data allow the summer balance to be calculated.