Henning Löwe

Density, specific surface area, and correlation length of snow measured by high-resolution penetrometry

Precise measurements of snow structural parameters are crucial to understand the formation of snowpacks by deposition and metamorphism and to characterize the stratigraphy for many applications and remote sensing in particular. The area-wide acquisition of structural parameters at high spatial resolution from state-of-the-art methods is, however, still cumbersome, since the time required for a single profile is a serious practical limitation. As a remedy we have developed a statistical model to extract three major snow structural parameters: density, correlation length, and specific surface area (SSA) solely from the SnowMicroPen (SMP), a high-resolution penetrometer, which allows a meter profile to be measured with millimeter resolution in less than 1 min. The model was calibrated by combining SMP data with 3-D microstructural data from microcomputed tomography which was used to reconstruct full-depth snow profiles from different snow climates (Alpine, Arctic, and Antarctic). Density, correlation length, and SSA were derived from the SMP with a mean relative error of 10.6%, 16.4%, and 23.1%, respectively. For validation, we compared the density and SSA derived from the SMP to traditional measurements and near-infrared profiles. We demonstrate the potential of our method by the retrieval of a two-dimensional stratigraphy at Kohnen Station, Antarctica, from a 46 m long SMP transect. The result clearly reveals past depositional and metamorphic events, and our findings show that the SMP can be used as an objective, high-resolution tool to retrieve essential snow structural parameters efficiently in the field.

Radiosity Approach for the Shortwave Surface Radiation Balance in Complex Terrain

The influence of topography on the radiation balance in complex terrain has so far been investigated either with very simple or very sophisticated approaches that are limited, respectively, by an uncontrolled spatial representation of radiative fluxes or heavy computational efforts. To bridge this gap in complexity, this paper proposes the radiosity approach, well known in computer graphics, to study anisotropic reflections of radiation in complex terrain. To this end the radiosity equation is rederived in the context of three-dimensional radiative transfer. The discretized equation is solved by means of an adapted version of progressive refinement iteration. To systematically study terrain effects, the geometrical disorder provided by the topography is considered in its simplest approximation by Gaussian random fields. These model topographies capture the most important length scales of complex terrain, namely a typical elevation and a typical valley width via the variance and the correlation length of the field, respectively. The mean reflected radiation is computed as a function of these length scales and sun elevation, thereby explicitly addressing finite system sizes and grid resolutions. A comparison with an isotropic parameterization of terrain reflections reveals that mean values are similar whereas spatial distributions vary remarkably. It is also shown that the mean reflected radiation in real topography is reasonably well characterized by the Gaussian approximation. As a final application of the method, the effective albedo of a topography is shown to vary with sun elevation and domain-averaged albedo, leading to albedo differences up to 0.025.

Drifting snow sublimation: A high-resolution 3-D model with temperature and moisture feedbacks

The snow transport model of Alpine3D is augmented with a drifting snow sublimation routine. Contrary to other three-dimensional high-resolution snow transport models, Alpine3D now accounts for feedback mechanisms on the air temperature, humidity, and snow mass concentration in three dimensions. Results show that the negative feedbacks of sublimation on the snow mass concentration, temperature, and humidity are, in general, small but relevant on the slope scale. We analyzed the deposition on a leeward slope for simulations including sublimation and compared these to a reference simulation of the model without sublimation. Including sublimation, but neglecting sublimation feedbacks, leads to a reduction in deposition of approximately 12% on this slope. In a simulation including sublimation and its feedbacks, the reduction in snow deposition on the same slope was 10%. The feedbacks thus reduced the loss of snow due to sublimation by 2%. The sublimation process is therefore quite important for a leeward slope influenced by drifting snow. However, we also show that the spatial variability is large and that drifting snow sublimation will mainly affect small regions within a catchment. Averaged over our model domain (2.4 km(2)) in the Swiss Alps, drifting snow sublimation causes a reduction in deposition of 2.3% during a 43 h test period, which is comparable to the sublimation loss from the snow cover during the same time.

Simulation of seasonal snow-cover distribution for glacierized sites on Sonnblick, Austria, with the Alpine3D model

Abstract A detailed model of Alpine surface processes is used to simulate the amount of preferential deposition as well as redistribution of snow due to snowdrift for two alpine glaciers (Goldbergkees and Kleinfleißkees, Austrian Alps). The sequence of snow-cover modelling consists of the simulation of the wind field with a mesoscale atmospheric model, a three-dimensional finite-element drift module, an energy-balance module and a snowpack module. All modules with the exception of the wind-field model are integrated within the Alpine3D model frame. The drift module of Alpine3D distinguishes between saltation and suspension and is able to capture preferential deposition of snow precipitation and redistribution of previously deposited snow. Validation of the simulated snow depth is done using the spatially dense snow-probing dataset collected during a campaign in May 2003. Simulated snow depths agree with measurements during winter 2002/03 at locations with detailed snow-height monitoring, taking into account the high spatial variability of snow depth on the glacier. Moreover, comparison of snow accumulation from model results with detailed probing on 1 May 2003 for the total glacier area shows that Alpine3D is able to capture major patterns of spatial distribution of snow accumulation. For the first time, the Alpine3D approach of using high-resolution wind fields from a meteorological model and a physical description of snow transport could be validated for a very steep glacierized area and for a full accumulation season. The results show that drift is a dominant factor to be considered for detailed glacier mass balances. Another dominant factor not considered in this study may be snow redistribution due to avalanches.

Statistical properties of fresh snow roughness

We present results from a series of experiments in which fresh snow roughness was measured by means of digital photography and analyzed using the random field approach. The aim of the paper is to investigate the scaling properties of fresh-snow-covered surfaces and to capture key roughness length scales which can characterize the surface geometry and the size of the snow crystals. Results from our experiments show the following: (1) fresh snow roughness exhibits two distinguished scaling regimes, one at scales comparable with the crystals size and another one at larger scales; (2) we confirm that the large scales are built up during snowfall and their scaling behavior is consistent with that of Ballistic Deposition (BD) processes; and (3) we suggest that the crossover length scale separating the two scaling regimes effectively defines a representative length scale of the aggregated snow crystals on the surface. The definition of this length scale is independent of the difficulties associated with measuring snow grain sizes by means of standard microscopic analysis of disaggregated crystals. Furthermore it can be obtained from a low-cost and quick experimental procedure. Results from this study provide a plausible justification for the wide scatter of aerodynamic roughness length values encountered in the literature for fresh snow. Moreover, they provide insight on the key roughness length scales which should be used for the modeling of this parameter.

Granulation of snow: From tumbler experiments to discrete element simulations

It is well known that snow avalanches exhibit granulation phenomena, i.e., the formation of large and apparently stable snow granules during the flow. The size distribution of the granules has an influence on flow behavior which, in turn, affects runout distances and avalanche velocities. The underlying mechanisms of granule formation are notoriously difficult to investigate within large-scale field experiments, due to limitations in the scope for measuring temperatures, velocities, and size distributions. To address this issue we present experiments with a concrete tumbler, which provide an appropriate means to investigate granule formation of snow. In a set of experiments at constant rotation velocity with varying temperatures and water content, we demonstrate that temperature has a major impact on the formation of granules. The experiments showed that granules only formed when the snow temperature exceeded -1(degrees)C. No evolution in the granule size was observed at colder temperatures. Depending on the conditions, different granulation regimes are obtained, which are qualitatively classified according to their persistence and size distribution. The potential of granulation of snow in a tumbler is further demonstrated by showing that generic features of the experiments can be reproduced by cohesive discrete element simulations. The proposed discrete element model mimics the competition between cohesive forces, which promote aggregation, and impact forces, which induce fragmentation, and supports the interpretation of the granule regime classification obtained from the tumbler experiments. Generalizations, implications for flow dynamics, and experimental and model limitations as well as suggestions for future work are discussed.

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxters sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number z_{c} of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of z_{c} and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ν_{c}=z_{c}ϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Measuring the Elastic Modulus of Snow

The elastic modulus is the most fundamental mechanical property of snow. However literature values scatter by orders of magnitude and hitherto no cross-validated measurements exists. To this end we employ P-wave propagation experiments under controlled laboratory conditions on decimeter-sized snow specimen, prepared from artificial snow and subjected to isothermal sintering, to cover a considerable range of densities (170 − 370kgm−3). The P-wave modulus was estimated from wave propagation speeds in transverse isotropic media and compared to microstructure-based finite element (FE) calculations from X-ray tomography images. Heterogeneities and size differences between acoustic and FE sample volumes were characterized by SnowMicroPen measurements, yielding an elastic modulus as a by-product. The moduli (10 − 340MPa) from the acoustic and FE method are in very good agreement (R2=0.99) over the entire range of densities. A remaining bias (24 %) between both methods can be explained by layer heterogeneities which systematically reduce the estimates from the acoustic method.