Models for 2005
In considering the application of the ArcTIM for 2005, the model accounts for about 80% of the variance in ablation. The total ablation normalised by glacier area was 1.62 m (σ = 0.16), which agrees with but is slightly higher than the ranges of specific melt suggested for the glacier in preceding years (Hodson et al., 2005).
Clearly, from the only minor improvements made to the Tc model performance with additional variables, air temperature was the forcing meteorological variable in ablation at ML, as reported for the adjacent Austre Brøggerbreen (Hodson et al., 1998) but contrasting with previous energy balance considerations at ML where net shortwave radiation dominated ablation (Hodson et al., 2005; Arnold et al., 2006). Such a finding illustrates the interrelation between Ta and radiative fluxes, but also alludes to the potential interannual variability in energy balance considerations and validity of parameterisations within ArcTIM. Nonetheless, internal optimisation of a threshold melt value (the Tmelt model variant) may provide a fruitful manner by which to improve TIM performance.
The small improvement by the inclusion of a radiation component compares well to similar models, but is considerably lower than those implied in results presented elsewhere (e.g. Kustas et al., 1994; Pellicciotti et al., 2005). Moreover, contrary to Pellicciotti et al.'s (2005) assertion, the inclusion of a simplistic albedo parameterisation was not beneficial in this instance. Data presented in Tables 2 and 3 suggest that a more complex and rigorous parameterisation of I (and thereby albedo) will likely have limited effect on improving model performance and partly justifies the exclusion of topographic shadowing here.
The time-series of potential and observed runoff during 2005 illustrated results analogous to those documented by Konya et al. (2004) in comparing similar melt models: the additive approach to TIM model formulation appeared more suited to modelling glacier melt. The difference between the TIM formulations was small, with the modified version showing reductions in both peak and trough values; however, consistently diurnal amplitude of modelled melt exceeded that of Q. This was verified by an F-test showing significant difference between the variance of W and Q (F = 1.7, p < 0.001) despite the similarity in mean value. The daily under-prediction of melt was typically between 20:00 and 02:00 when shadowing across the glacier was greatest, which further implies that the influence of shadow was small and that there were factors involved in delaying runoff to the proglacial streams. The hydrological interpretation is that meltwater flowpaths regulate runoff, dampening the amplitude of the melt signal. This inference is emphasised by the difference in cumulative discharge series (Figure 6c) which, assuming the validity of the 2005 model run, suggests a period of storage and release within the glacier catchment, a process which has been documented previously (Hodson et al., 2005); however, this is not explored further here. Nonetheless, the apparent lag time between W and Q of ~3 h agrees with dye tracing experiments at ML which reveal transit times over and through the glacier of the order of 1–3 h (Irvine-Fynn et al., 2005).
The larger errors indicated in Figure 6a appeared more commonly linked to rain-free periods (cf. Figure 8) and were indicative of the overestimation and underestimation at the apexes of the diurnal cycle. Assuming rapid supraglacial runoff, this is suggestive of either changes in the threshold temperature triggering melt or variability in melt factors (a and b). In particular, the largest errors (DOY200) are seen following the cool period (DOY193-199) suggesting a potential link to thermal conditions where energy is required to raise ice temperatures prior to initiation of melting. Noticeably, the errors between DOY200 and DOY220 also exhibit a much more marked diurnal signal than at other times. Temporal variation in melt factors has been reported elsewhere (e.g. Singh and Kumar, 1996) but has seldom been explored. To examine the potential for such trends at ML, we consider melt factor a derived from Equation (1) assuming c ≠ 0 for Tcrit = 1.62 °C given the similarity in its value across the TIM variants (refer to Table 2).
For 2005, the elevation-averaged mean value of a was 0.28 mm h−1 °C−1, which compares well to the range of values reported from numerous locations (e.g. Hock, 2003; Zhang et al., 2006). However, using AWS2 as an example, a showed variation across the observation periods (Figure 9): the increase during the middle of the ablation season then decrease thereafter is analogous to the results reported by Zhang et al. (2006). For glacier ice, temporal changes in a may be attributable to changes in the distribution of supraglacial dust and cryoconite (Singh et al., 2000); in the instance of ML and other Arctic glaciers, redistribution of cryoconite impacting upon surface albedo is known to occur (Hodson et al., 2007; Irvine-Fynn et al., 2011b).
Figure 9. Plot showing the values of a for AWS2 plotted against time. Dashed lines indicate the time-window over which a is calculated from periodic ablation stake measurements
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Surface ice density provides an alternative mechanism enabling variations in a: rapid refreezing that occurs during the spring and very early melt season results in bubble-rich, low density ice, which may form atop the dense, bubble-free superimposed ice generated at the close of the ablation season and in early winter (Wadham et al., 2006). Ice ablation is therefore likely to be reduced early in the melt season, with refreezing occurring initially, followed by a period demanding greater energy to melt the denser surface layer of winter-formed superimposed ice. Following the ablation of the dense superimposed ice layer, melt rates may increase for ice which represents the previous summer surface. The lowered porosity resulting from the previous year's melt processes, subsurface melting in response to direct irradiance and the formation of a weathering crust layer resulting from impurities including cryoconite (e.g. Müller and Keeler, 1969) may accelerate ablation.
The presence of near-surface meltwater may also further increase melt rates and influence surface ice density. Not only does meltwater decrease albedo (e.g. Zuo and Oerlemans, 1996) but water in the liquid phase also requires less energy to raise its temperature such that a greater surface water volume may enhance ablation and enlarge void space between ice crystals. A variable water volume at the ice surface, particularly within the weathering crust (e.g. Larson, 1978), may also potentially contribute to changes in a throughout the season.
Critically, all the ice surface processes discussed above are likely to be linked to meteorological conditions, posing the question: do changes in a reflect variations in the energy balance? To assess this simply, despite the underestimation of ablation, we used the output from the adjusted EBM run (described in the Comparitive Models section) to estimate the ratio between radiative and turbulent energy fluxes for each centre-line stake for all ablation survey periods. Despite the scatter, and given the uncertainties associated with both data series, comparison between the ratio of energies and a showed a significant positive relationship (r2 = 0.31, p < 0.05; Figure 10). This result suggests that temporal (and spatial) variations in a may be described by changes in meteorology, which in turn controls ice surface characteristics.
Figure 10. Scatter plot showing relationship between a and the ratio of radiative to turbulent energy fluxes derived using an adjusted EBM
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Models for 2004
The relative failure of ArcTIM when applied for the 2004 datasets highlighted the weaknesses explored above. Table 2 illustrates the difference in optimised model parameters, and a marked contrast in spatial and temporal trends in a was evident between the two years (data not shown here). As detailed fully in Irvine-Fynn (2008), the meteorology of the two summer observation periods contrasted: statistically, at 99% confidence, significant annual differences existed in the mean and variance of Ta and wind speeds at both AWS2 and AWS4; during 2004, 63% of the monitoring period was significantly overcast compared to 50% of the 2005 summer; and multivariate analysis suggested low-pressure synoptic weather patterns were perhaps more important during 2004. Moreover, although directly comparable data are unavailable to validate the non-linear lapse rate observed in 2005 (Equation ((4))), mean lapse rates between AWS2 and AWS4 were −0.005 °C m−1 and −0.004 °C m−1 in 2004 and 2005, respectively, potentially reflecting contrasting meteorology or the changing prevalence of inversions. This lends credence to the suggestion that TIMs are sensitive to lapse rate values and demands longer-term analyses of lapse rates with respect to air temperatures (e.g. Gardner and Sharp, 2009; Gardner et al., 2009; Hodgkins et al., 2012). Such interannual contrasts in synoptic influences will certainly define the relationship between melt and Ta because clouds and inversions both have marked influence on longwave radiation fluxes (Zhang et al., 1996; Zhang et al., 1997). Moreover, varying proportions of radiative energies can result in variability in ice surface characteristics (e.g. ice temperature, albedo and roughness) which reduces ability to confidently replicate ice ablation using parameters defined from a single year's observations, irrespective of TIM model formulation.
The importance of glacier surface condition is perhaps best emphasised over the first half of the 2004 season where ArcTIM over-predicted potential runoff prior to DOY210 during which time temperatures were persistently > 5 °C. An explanation of this is offered by field observations in 2004 which indicated that the early season was characterised by considerable volumes of slush, as is common on glaciers in Svalbard (e.g. Hodgkins, 2001): statistically, the mean pre-season (May) snow depths were greater in 2004 than 2005 despite a similarity in cross-glacier variance (t = 4.06, p < 0.001; F = 1.19, p = 0.01) and sea-level air temperatures consistently > 0 °C commenced 10 days later than in 2005. The ‘melt rate’ of saturated slush is likely to be considerably different from that of glacier ice or snow, rendering predefined parameters a and b erroneous, as too is the use of ice density to convert melt to a w.e. Consequently, the model runs presented here emphasise how, for temporal transferability of melt models, incorporation of distinct firn, slush and snowpack elements within TIMs are beneficial (e.g. Hock, 1999; de Woul et al., 2006). Indeed, existing snowpack retention (e.g. Bøggild, 2000; Janssens and Huybrechts, 2000) and refreezing (e.g. Hinzman and Kane, 1991; Gardner and Sharp, 2009) schemes to reduce or delay water release early in the melt season from TIM or EBM-based models (e.g. Hanna et al., 2005; Rye et al., 2010) are advantageous for prediction of runoff, but may reciprocally impact on parameters used within a TIM context.