An enhanced temperature-index glacier melt model, incorporating incoming shortwave radiation and albedo, is presented. The model is an attempt to combine the high temporal resolution and accuracy of physically based melt models with the lower data requirements and computational simplicity of empirical melt models, represented by the ‘degree-day’ method and its variants. The model is run with both measured and modelled radiation data, to test its applicability to glaciers with differing data availability. Five automatic weather stations were established on Haut Glacier d’Arolla, Switzerland, between May and September 2001. Reference surface melt rates were calculated using a physically based energy-balance melt model. The performance of the enhanced temperature-index model was tested at each of the four validation stations by comparing predicted hourly melt rates with reference melt rates. Predictions made with three other temperature-index models were evaluated in the same way for comparison. The enhanced temperature-index model offers significant improvements over the other temperature-index models, and accounts for 90–95% of the variation in the reference melt rate. The improvement is lower, but still significant, when the model is forced by modelled shortwave radiation data, thus offering a better alternative to existing models that require only temperature data input.

ABSTRACT. Spatial and temporal variations in aerodynamic roughness length (z 0 ) on Haut Glacier d'Arolla, Switzerland, during the 1993 and 1994 ablation seasons are described, based on measurements of surface microtopography. The validity of the microtopographic z 0 measurements is established through comparison with independent vertical wind profile z 0 measurements over melting snow, slush and ice. The z 0 variations are explained through correlation and regression analyses, using independent measurements of meteorological and surface variables, and parameterizations are developed to calculate z 0 variations for use in surface energy-balance melt models. Several independent variables successfully explain snow z 0 variation through their correlation with increasing surface roughness, caused by ablation hollow formation, during snowmelt. Non-linear parameterizations based on either accumulated melt or accumulated daily maximum temperatures since the most recent snowfall explain over 80% of snow z 0 variation. The z 0 following a fresh snowfall on an ice surface is parameterized based on relationships with the underlying ice z 0 , snow depth and accumulated daily maximum temperatures. None of the independent variables were able to successfully explain ice z 0 variation. Although further comparative studies are needed, the results lend strong support to the microtopographic technique of measuring z 0 over melting glacier surfaces.

ABSTRACT. Extensive covers of supraglacial debris are often present in glacier ablation areas, and it is essential to assess exactly how the debris affects glacier melt rates. This paper presents a physically based energy-balance model for the surface of a debris-covered glacier. The model is driven by meteorological variables, and was developed using data collected at

ablation seasons, meteorological conditions were recorded on the lower and upper parts of the debris-covered ablation zone of Miage Glacier, Italy. In 2005, debris temperature and subdebris ice melt were also monitored at 25 points with debris thickness of 0.04-0.55 m, spread over 5 km 2 of the glacier. The radiative fluxes were directly measured, and near-closure of the surface energy balance is achieved, providing support for the bulk aerodynamic calculation of the turbulent fluxes. Surface-layer meteorology and energy fluxes are dominated by the pattern of incoming solar radiation which heats the debris, driving strong convection. Mean measured subdebris ice melt rates are 6-33 mm d −1 , and mean debris thermal conductivity is 0.96 W m −1 K −1 , displaying a weak positive relationship with debris thickness. Mean seasonal values of the net shortwave, net longwave, and debris heat fluxes show little variation between years, despite contrasting meteorological conditions, while the turbulent latent (evaporative) heat flux was more than twice as large in the wet summer of 2007 compared with 2005. The increase in energy output from the debris surface in response to increasing surface temperature means that subdebris ice melt rates are fairly insensitive to atmospheric temperature variations in contrast to debris-free glaciers. Improved knowledge of spatial patterns of debris thickness distribution and 2 m air temperature, and the controls on evaporation of rainwater from the surface, are needed for distributed physically based melt modeling of debris-covered glaciers.

Spatial and temporal variations of surface albedo on Haut Glacier d'Arolla, Switzerland, during the 1993 and 1994 ablation seasons are described. Correlation and regression analyses are used to explain the albedo variations in terms of independent meteorological and surface property variables. Parameterizations are developed which allow estimation of albedo variation in surface energy-balance models. Snow albedo is best estimated from accumulated daily maximum temperatures since snowfall. On``deep'' snow (!0.5 cm w.e. depth) a logarithmic function is used, while on``shallow'' snow (50.5 cm w.e. depth) an exponential function is used to enable the albedo to decay to the underlying ice or debris albedo. The transition from``deep'' to``shallow'' snow is calculated as a function of decreasing snow depth (combined r 2 0.65).This new parameterization performs better than earlier schemes because accumulated daily maximum temperatures since snowfall correlate strongly with snow grain-size and impurity concentration, the main physical controls on snow albedo. Ice albedo may be parameterized by its relationship to elevation (r 2 0.28), but this approach results in only a small improvement over the assumption of a constant mean ice albedo.