[1] The inhomogeneous snow distribution found in alpine terrain is the result of wind and precipitation interacting with the (snow) surface over topography. We introduce and explain preferential deposition of precipitation as the deposition process without erosion of previously deposited snow and thus in absence of saltation. A numerical model is developed, describing the relevant processes of saltation, suspension, and preferential deposition. The model uses high-resolution wind fields calculated with a meteorological model, ARPS. The model is used to simulate a 120 h snow storm period over a steep alpine ridge, for which snow distribution measurements are available. The comparison to measurements shows that the model captures the larger-scale snow distribution patterns and predicts the total additional lee slope loading well. However, the spatial resolution of 25 m is still insufficient to capture the smaller-scale deposition features observed. The model suggests that the snow distribution on the ridge scale is primarily caused by preferential deposition and that this result is not sensitive to model parameters such as turbulent diffusivity, drift threshold, or concentration in the saltation layer.

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.

Key Points:• Statistical model relating micro-CT structure to SMP force for many snow data • New method to retrieve density, correlation length, and SSA in the field • Efficient retrieval of spatial variability and 2-D stratigraphy of snow Abstract 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.

Finding relevant microstructural parameters beyond density is a longstanding problem which hinders the formulation of accurate parameterizations of physical properties of snow. Towards a remedy, we address the effective thermal conductivity tensor of snow via anisotropic, second-order bounds. The bound provides an explicit expression for the thermal conductivity and predicts the relevance of a microstructural anisotropy parameter Q, which is given by an integral over the two-point correlation function and unambiguously defined for arbitrary snow structures. For validation we compiled a comprehensive data set of 167 snow samples. The set comprises individual samples of various snow types and entire time series of metamorphism experiments under isothermal and temperature gradient conditions. All samples were digitally reconstructed by micro-computed tomography to perform microstructure-based simulations of heat transport. The incorporation of anisotropy via Q considerably reduces the root mean square error over the usual density-based parameterization. The systematic quantification of anisotropy via the two-point correlation function suggests a generalizable route to incorporate microstructure into snowpack models. We indicate the inter-relation of the conductivity to other properties and outline a potential impact of Q on dielectric constant, permeability and adsorption rate of diffusing species in the pore space

Abstract:The snow cover in the Alps is heavily affected by climate change. Recent data show that at altitudes below 1200 m a.s.l. a time-continuous winter snow cover is becoming an exception rather than the rule. This would also change the timing and characteristics of river discharge in Alpine catchments. We present an assessment of future snow and runoff in two Alpine catchments, the larger Inn catchment (1945 km 2 ) and the smaller Dischma catchment (43 km 2 ), based on two common climate change scenario (IPCC A2 and B2 (IPCC, 2007)). [etc]. The changes in snow cover and discharge are predicted using Alpine3D, a model for the high-resolution simulation of Alpine surface processes, in particular snow, soil and vegetation processes. The predicted changes in snow and discharge are extreme. While the current climate still supports permanent snow and ice on the highest peaks at altitudes above 3000 m a.s.l., this zone would disappear under the future climate scenarios. The changes in snow cover could be summarized by approximately shifting the elevation zones down by 900 m. The corresponding changes in discharge are also severe: while the current climate scenario shows a significant contribution from snow melt until middle to late summer, the future climate scenarios would feature a much narrower snow melt discharge peak in spring. A further observation is that heavy precipitation events in the fall would change from mainly snow to mainly rain and would have a higher probability of producing flooding. Future work is needed to quantify the effect of model uncertainties on such predictions.

ABSTRACT. We investigated the morphological evolution of laboratory snow under isothermal conditions at −3,−9 and −19 • • C, using X-ray tomography. We employed a two-point density correlation function to measure spatial fluctuations of the density of the bicontinuous ice/vapor system at different length scales. Length scales were derived from the correlation function to distinguish between interfacial coarsening due to the minimization of surface energy on the smallest scales and anisotropic structural rearrangements due to gravity on larger scales. On the smallest scales our data suggest a crossover between T = −9 and −19 • • C from evaporation/condensation to surface diffusion as the dominant transport mechanism. Anomalous growth was found for the slope of the correlation function at the origin, and it was similar to those reported for the coarsening of fractal clusters. This is consistent with the observed persistence of dendritic structures throughout an entire year. The dynamics of large-scale morphology was characterized by the first zero-crossing of the correlation function which displays a nonmonotonic evolution with a pronounced anisotropy between the direction of gravity and horizontal directions. Since the correlation function naturally emerges in problems of scattering of radiation in snow, our results appear to be important for optical and remote-sensing methods.

Abstract. The snow microstructure, i.e., the spatial distribution of ice and pores, generally shows an anisotropy which is driven by gravity and temperature gradients and commonly determined from stereology or computer tomography. This structural anisotropy induces anisotropic mechanical, thermal, and dielectric properties. We present a method based on radio-wave birefringence to determine the depth-averaged, dielectric anisotropy of seasonal snow with radar instruments from space, air, or ground. For known snow depth and density, the birefringence allows determination of the dielectric anisotropy by measuring the copolar phase difference (CPD) between linearly polarized microwaves propagating obliquely through the snowpack. The dielectric and structural anisotropy are linked by MaxwellGarnett-type mixing formulas. The anisotropy evolution of a natural snowpack in Northern Finland was observed over four winters (2009)(2010)(2011)(2012)(2013) with the ground-based radar instrument "SnowScat". The radar measurements indicate horizontal structures for fresh snow and vertical structures in old snow which is confirmed by computer tomographic in situ measurements. The temporal evolution of the CPD agreed in ground-based data compared to space-borne measurements from the satellite TerraSAR-X. The presented dataset provides a valuable basis for the development of new snow metamorphism models which include the anisotropy of the snow microstructure.

ABSTRACT. We have investigated the isothermal densification of new snow under an external mechanical stress. New snow samples that mimic natural snow were made in the laboratory by sieving ice crystals grown in a snowmaker. This allowed us to assemble homogeneous initial samples with reproducible values of low density and high specific surface area (SSA). Laboratory creep experiments were conducted in an X-ray microtomograph at -208 8C for 2 days. We focused on the evolution of density and SSA as a function of constant stress at a single temperature. External mechanical stresses resembled natural overburden stresses of a snow sample at depths of $0-30 cm of new snow. We demonstrate that densification increases with higher external stress and lower initial densities. We find that the evolution of the SSA is independent of the density and follows a unique decay for all measurements of the present type of new snow. The results suggest that details of the SSA decrease can be investigated using carefully designed experiments of short duration which are convenient to conduct. Additionally, we calculated the strain evolution and identify transient creep behavior that does not follow the Andrade creep law of denser snow or polycrystalline ice.