Regine Hock

Temperature index melt modelling in mountain areas

Temperature index or degree-day models rest upon a claimed relationship between snow or ice melt and air temperature usually expressed in the form of positive temperatures. Since air temperature generally is the most readily available data, such models have been the most widely used method of ice and snow melt computations for many purposes, such as hydrological modelling, ice dynamic modelling or climate sensitivity studies. Despite their simplicity, temperature-index models have proven to be powerful tools for melt modelling, often on a catchment scale outperforming energy balance models. However, two shortcomings are evident: (1) although working well over long time periods their accuracy decreases with increasing temporal resolution; (2) spatial variability cannot be modelled accurately as melt rates may vary substantially due to topographic effects such as shading, slope and aspect angles. These effects are particularly crucial in mountain areas. This paper provides an overview of temperature-index methods, including glacier environments, and discusses recent advances on distributed approaches attempting to account for topographic effects in complex terrain, while retaining scarcity of data input. In the light of an increasing demand for melt estimates with high spatial and temporal resolution, such approaches need further refinement and development.

A Reconciled Estimate of Glacier Contributions to Sea Level Rise: 2003 to 2009

Melting Away We assume the Greenland and Antarctica ice sheets are the main drivers of global sea-level rise, but how large is the contribution from other sources of glacial ice? Gardner et al. (p. 852) synthesize data from glacialogical inventories to find that glaciers in the Arctic, Canada, Alaska, coastal Greenland, the southern Andes, and high-mountain Asia contribute approximately as much melt water as the ice sheets themselves: 260 billion tons per year between 2003 and 2009, accounting for about 30% of the observed sea-level rise during that period. The contribution of glaciers to sea level rise is nearly as much as that of the Greenland and Antarctic Ice Sheets combined. Glaciers distinct from the Greenland and Antarctic Ice Sheets are losing large amounts of water to the world’s oceans. However, estimates of their contribution to sea level rise disagree. We provide a consensus estimate by standardizing existing, and creating new, mass-budget estimates from satellite gravimetry and altimetry and from local glaciological records. In many regions, local measurements are more negative than satellite-based estimates. All regions lost mass during 2003–2009, with the largest losses from Arctic Canada, Alaska, coastal Greenland, the southern Andes, and high-mountain Asia, but there was little loss from glaciers in Antarctica. Over this period, the global mass budget was –259 ± 28 gigatons per year, equivalent to the combined loss from both ice sheets and accounting for 29 ± 13% of the observed sea level rise.

A distributed temperature-index ice- and snowmelt model including potential direct solar radiation

Hourly melt and discharge of Storglaciaren, a small glacier in Sweden, were computed for two melt seasons, applying temperature-index methods to a 30 m resolution grid for the melt component. The classical degree-day method yielded a good simulation of the seasonal pattern of discharge, but the pronounced melt-induced daily discharge cycles were not captured. Modelled degree-day factors calculated for every hour and each gridcell from melt obtained from a distributed energy-balance model varied substantially, both diurnally and spatially. A new distributed temperature-index model is suggested, attempting to capture both the pronounced diurnal melt cycles and the spatial variations in melt due to the effects of surrounding topography. This is accomplished by including a radiation index in terms of potential clear-sky direct solar radiation, and thus, without the need for other data besides air temperature. This approach improved considerably the simulation of diurnal discharge fluctuations and yielded a more realistic spatial distribution of melt rates. The incorporation of measured global radiation to account for the reduction in direct solar radiation due to cloudiness did not lead to additional improvement in model performance.

The concept of glacier storage: a review

Glacier storage is a widely used term, applied to different processes and time-scales by different disciplines in hydrology and glaciology. We identify that storage occurs as ice, snow, and water associated with three time-scales. Long-term storage concerns storage of ice and firn as glaciers on time-scales of years to centuries and longer. This storage affects global sea level and long-term water balance of glacierized catchments and is especially important for water resources in arid and semiarid areas. Intermediate-term storage is applicable to processes such as storage and release of snow and water, in and on a glacier on a seasonal scale. This is also the most common definition in the literature implied by the term storage. Intermediate-term storage affects runoff characteristics in glacierized catchments and downstream river flow regimes. Short-term storage concerns diurnal effects of drainage through the glacier including routing through snow, firn and en- and subglacial pathways. In addition to these time-scale dependent processes there are also event-driven storage releases, termed singular storage releases, including drainage from glacier surges and drainage of glacier-dammed water. These events are associated with glaciers but do not exhibit cyclic response or have irregular occurrences. It is evident that glacier storage is not handled well by current conceptual or mathematical models and that, e.g. sub- and englacial storage are poorly constrained. Hence, holistic approaches to studying and modelling glacier storage are of major importance to fully integrate glaciers into the hydrological balance to be used for water resources and river flow predictions on all time-scales.

A distributed surface energy-balance model for complex topography and its application to Storglaciären, Sweden

A grid-based surface energy-balance mass-balance model has been developed to simulate snow- and ice melt in mountainous regions with an hourly resolution. The model is applied to Storglaciaren, a valley glacier in Sweden, using a 30 m resolution digital elevation model. Emphasis is directed towards computing the radiation components. These are modelled individually, considering the effects of slope angle, aspect and effective horizon. A new parameterization for snow albedo is suggested, modifying the albedo of the preceding hour as a function of time after snowfall, air temperature and cloudiness. The model is used to provide the meltwater input for discharge modelling and to assess the influence of the individual components on melt. Results are validated by means of observed melt rates, patterns of snow-line retreat and proglacial discharge. In general, simulations are in good agreement with observations. In particular, the diurnal and seasonal fluctuations of discharge are simulated remarkably well.

Determination of the seasonal mass balance of four Alpine glaciers since 1865

Alpine glaciers have suffered major losses of ice in the last century. We compute spatially distributed seasonal mass balances of four glaciers in the Swiss Alps (Grosser Aletschgletscher, Rhonegletscher, Griesgletscher and Silvrettagletscher) for the period 1865 to 2006. The mass balance model is forced by daily air temperature and precipitation data compiled from various long-term data series. The model is calibrated using ice volume changes derived from five to nine high-resolution digital elevation models, annual discharge data and a newly compiled data set of more than 4000 in situ measurements of mass balance covering different subperiods. The cumulative mass balances over the 142 year period vary between -35 and -97 m revealing a considerable mass loss. There is no significant trend in winter balances, whereas summer balances display important fluctuations. The rate of mass loss in the 1940s was higher than in the last decade. Our approach combines different types of field data with mass balance modeling to resolve decadal scale ice volume change observations to seasonal and spatially distributed mass balance series. The results contribute to a better understanding of the climatic forcing on Alpine glaciers in the last century.

Mountain glaciers and ice caps around Antarctica make a large sea‐level rise contribution

The Intergovernmental Panel on Climate Change (IPCC) estimates that the sum of all contributions to sea‐level rise for the period 1961–2004 was 1.1 ± 0.5 mm a−1, leaving 0.7 ± ...

Static mass-balance sensitivity of Arctic glaciers and ice caps using a degree-day approach

Abstract Future climate warming is predicted to be more pronounced in the Arctic where approximately two-thirds of all small glaciers on Earth are located. A simple mass-balance model was applied to 42 glaciers and ice caps north of 60° N to estimate mass-balance sensitivities to a hypothetical climate perturbation. The model is based on daily temperature and precipitation data from climate stations in the vicinity of each glacier and ice cap. A regression analysis was made using a degree-day approach where the annual sum of positive daily air temperatures was correlated to measured summer mass balance, and the total annual snow precipitation was correlated to measured winter mass balance. The net mass-balance sensitivity to a hypothetical temperature increase of +1 K ranged from -0.2 to -2.0 m a-1, and an assumed increase in precipitation of +10% changed the mass balance by <+0.1 to +0.4 m a-1, thus on average offsetting the effect of a temperature increase by approximately 20%. Maritime glaciers showed considerably higher mass-balance sensitivities than continental glaciers, in agreement with similar previous studies. The highest sensitivities were found in Iceland, exceeding those reported in previous studies. Extrapolating our results, glaciers and ice caps north of 60° N are estimated to contribute ∼0.6 mm a–1 K–1 to global sea-level rise. Our results highlight the value of long-term mass-balance records and meteorological records in remote areas.

100-year mass changes in the Swiss Alps linked to the Atlantic multidecadal oscillation

Thirty new 100-year records of glacier surface mass balance, accumulation and melt in the Swiss Alps are presented. The time series are based on a comprehensive set of field data and distributed modeling and provide insights into the glacier-climate linkage. Considerable mass loss over the 20th century is evident for all glaciers, but rates differ strongly. Glacier mass loss shows multidecadal variations and was particularly rapid in the 1940s and since the 1980s. Mass balance is significantly anticorrelated to the Atlantic Multidecadal Oscillation (AMO) index assumed to be linked to thermohaline ocean circulation. We show that North Atlantic variability had a recognizable impact on glacier changes in the Swiss Alps for at least 250 years. Citation: Huss, M., R. Hock, A. Bauder, and M. Funk (2010), 100-year mass changes in the Swiss Alps linked to the Atlantic Multidecadal Oscillation, Geophys. Res. Lett., 37, L10501, doi:.

Modelling the Response of Mountain Glacier Discharge to Climate Warming

Glaciers are characteristic features of mountain environments but are often not recognized for their strong influence on catchment runoff quantity and distribution. Such modification occurs with glacierization of only a few percent of the total catchment area, and affects adjacent lowlands far beyond the limits of mountain ranges. The main impact occurs because glaciers temporarily store water as snow and ice on many different time scales (Jansson et al. 2003), the release from storage being controlled by both climate and internal drainage mechanisms.