Charles Fierz

A physical SNOWPACK model for the Swiss avalanche warning Part III: meteorological forcing, thin layer formation and evaluation

Abstract The development of the seasonal snow cover is entirely driven by atmospheric forcing. SNOWPACK uses measured snow depths to determine snow precipitation rates via the calculated settling rates. This requires a rigid data control algorithm. A new statistical model is used to estimate fresh snow density as a function of the measured atmospheric conditions. A statistical model is also derived for the snow albedo, which is necessary to determine the absorbed radiation. The surface sensible and latent heat flux parameterizations are derived from Monin–Obukhov similarity and include a formulation for wind pumping. The formulations will also adapt to drifting snow conditions. The new suggestion is consistent with the observation of different roughness lengths for scalars and momentum over snow. An accurate formulation, especially for the latent heat exchange, is crucial because latent heat exchange determines the formation of surface hoar, a very important weak layer. We also account for the effect of wind pumping on the thermal conductivity in the uppermost snow layers. The surface energy and mass exchange formulations are evaluated by looking at the formation of the important thin layers surface hoar and melt–freeze crusts in SNOWPACK. Those layers are well simulated. In addition, the complete snow profile development is modeled successfully for the parameters grain type, temperature, density, grain size and liquid water content. An overall score between 0 and 1 is used to describe the profile agreement with observations and an average score of over 0.8 is reached.

A physical SNOWPACK model for the Swiss avalanche warning Part II. Snow microstructure

The snow cover model SNOWPACK includes a detailed model of snow microstructure and metamorphism. In SNOWPACK, the complex texture of snow is described using the four primary microstructure parameters: grain size, bond size, dendricity and sphericity. For each parameter, rate equations are developed that predict the development in time as a function of the environmental conditions. The rate equations are based on theoretical considerations such as mixture theory and on empirical relations. With a classification scheme, the conventional snow grain types are predicted on the basis of those parameters. The approach to link the bulk constitutive properties, viscosity and thermal conductivity to microstructure parameters is novel to the field of snow cover modeling. Expanding on existing knowledge on microstructure-based viscosity and thermal conductivity, a complete description of those quantities applicable to the seasonal snow cover is presented. This includes the strong coupling between physical processes in snow: The bond size, which changes not only through metamorphic processes but also through the process of pressure sintering (included in our viscosity formulation), is at the same time the single most important parameter for snow viscosity and thermal conductivity. Laboratory results are used to illustrate the performance of the formulations presented. The numerical implementation is treated in the companion paper Part I. A more complete evaluation for the entire model is found in the companion paper Part III.

Micrometeorological and morphological observations of surface hoar dynamics on a mountain snow cover

The formation, growth, and destruction of surface hoar crystals is an important feature of mountain snow covers as buried surface hoar layers are a frequent weak layer leading to unstable snowpacks. The energy and mass exchange associated with surface hoar dynamics is further an important part of land-atmosphere interaction over snow. A quantitative prediction of surface hoar evolution based on local environmental conditions is, however, difficult. We carried out measurements of crystal hoar size and total surface mass changes in the period between January and March 2007 on the Weissfluhjoch study plot of the WSL Institute for Snow and Avalanche Research SLF, located above Davos, Switzerland, at 2540 m above sea level. For the first time, a direct comparison between eddy correlation measurements of latent heat flux and lysimeter-like measurements of surface mass change has been made. Results show that the growth of surface hoar crystals is very well correlated with deposition of water vapor during clear-sky nights as measured by two eddy correlation systems placed close to the ground. By analyzing local meteorological data, we confirm that low to moderate wind speed, humid air, and clear-sky nights are the necessary ingredients for the occurrence of significant vapor fluxes toward the surface and thus for the growth of surface hoar. We also confirm that surface hoar crystals tend to preserve during daytime, when strong sublimation occurs, although their size significantly reduces. Despite the complexities associated with mountain terrain and snow surfaces, such as nonequilibrium boundary layers and stratification effects, the hoar formation could be predicted by the snow cover model SNOWPACK, which uses a bulk Monin-Obukhov (MO) parameterization for the turbulent heat fluxes. On the basis of the comparison between direct observations and model predictions, we suggest that neutral stability conditions in the MO formulation provide the most stable and least flawed prediction for surface hoar formation.

Evaluation of snow-surface energy balance models in alpine terrain

Abstract The increasing complexity of snow-cover models demands high-quality forcing data. In complex alpine terrain, both short and long wave incoming radiation components are expected to be influenced by small-scale topographic effects, i.e. shading and multiple scattering as well as long-wave irradiance from the surroundings. Not only should the latter be included in distributed energy balance models, but, because of their increasing resolution, also in meteorological models of the next generation. The energy balance at the snow-cover surface is calculated by means of different distributed energy balance models over a region of a few square kilometres, the spatial resolution being 25 m. The models include topographical effects on the radiation components of the energy balance. The region of interest is located in the Eastern Swiss Alps, around study sites of the Swiss Federal Institute for Snow and Avalanche Research SLF, Davos. The primary forcing data are taken from automatic weather stations located within the study area. To assess performance and differences of the models, two approaches are taken. First, model outputs are compared to measurements of both incoming radiation and snow surface temperature measured at automatic weather stations located on either level or inclined terrain within the region. Second, the models are used to calculate snowmelt at the beginning of the ablation period. The results are compared with changes of the snow water equivalent as measured in various spots of the modelled region, including all aspects on one elevation range. In view of the above comparison, the necessity to include small-scale topographic influences on the energy balance at the snow-cover surface as well as to consider snow surface properties and internal processes within the snow cover will be discussed. The possible implications for hydrological and meteorological models of the next generation will be addressed too.

Snow mechanics and avalanche formation: field experiments on the dynamic response of the snow cover

Knowledge about snow mechanics and snow avalanche formation forms the basis of any hazard mitigation measures. The crucial point is the snow stability. The most relevant mechanical properties - the compressive, tensile and shear strength of the individual snow layers within the snow cover - vary substantially in space and time. Among other things the strength of the snow layers depends strongly on the state of stress and the strain rate. The evaluation of the stability of the snow cover is hence a difficult task involving many extrapolations.To gain insight in the release mechanism of slab avalanches triggered by skiers, the skiers impact is measured with a load cell at different depths within the snow cover and for different snow conditions. The study focused on the effects of the dynamic loading and of the damping by snow compaction. In accordance with earlier finite-element (FE) calculations the results show the importance of the depth of the weak layer or interface and the snow conditions, especially the sublayering.In order to directly measure the impact force and to study the snow properties in more detail, a new instrument, called rammrutsch was developed. It combines the properties of the rutschblock with the defined impact properties of the rammsonde. The mechanical properties are determined using (i) the impact energy of the rammrutsch and (ii) the deformations of the snow cover measured with accelerometers and digital image processing of video sequences. The new method is well suited to detect and to measure the mechanical processes and properties of the fracturing layers. The duration of one test is around 10 minutes and the method seems appropriate for determining the spatial variability of the snow cover. A series of experiments in a forest opening showed a clear difference in the snow stability between sites below trees and ones in the free field of the opening.

An objective snow profile comparison method and its application to SNOWPACK

Abstract With the increasing use of numerical models predicting the snow cover status, the need for a simple and standardized evaluation procedure arises. We present such a method that compares numerical model profiles with snow pit profiles and provides a quantitative statistical agreement–disagreement measure. The method can also be used to compare several model profiles with each other. The first step of the method is the mapping of the model profile layers onto the layers of the observed profile. This mapping is necessary to adjust for deviating total snow depth and shifted positions of the layers. Following the mapping, the individual profile parameters such as grain type, grain size, liquid water content, temperature and density are compared. The result of the comparison is a score between 0 (profiles show no agreement) and 1 (profiles are identical) for each parameter. The parameter scores can be combined to give an overall profile score between 0 and 1. The method facilitates evaluation studies and allows to quantify improvements made in the modeling of processes in the snow cover. This is illustrated by analyzing a simulated profile at an IMIS (German: Interkantonales Mess-und Informations System) automatic snow and weather station with an observed, detailed snow pit profiles from the Swiss Alps. The agreement score for the parameter grain type increased from 0.3 to 0.7 after introducing an additional grain type in the simulation. In addition, the scores were calculated for two observation stations in the Swiss Alps for a whole winter season and it was detected that for most of the winter an overall agreement score between SNOWPACK simulation and snow pit profile of approximately 0.8 is reached. The temperature regime is modeled best and most difficulties are encountered with grain type. An important result is further that the energy balance processes at the beginning of the spring melt season has to be improved.

A model for kinetic grain growth

Abstract Snow-cover models are used in many applications in today’s snow and ice research. Descriptions of changes in size and shape are a major problem in modelling the snow cover. Empirical models for kinetic growth under temperature gradients have been developed, as well as more complicated models based upon microstructure. In this work a simple; physically based model is derived which depends on one adjustable geometric factor only Snow texture is described as a body-centred cubic lattice containing source and sink grains. The latter grow as plates due to water-vapour transport in the layer as well as between the layers. The model was implemented in a research version of the one-dimensional snow-cover model SNOWPACK. Model outputs are compared to experiments done in the cold laboratory where sieved snow is subjected to temperature gradients. Disaggregated snow samples are analyzed by digital image processing, by sieving and by visual characterization. In order to determine grain-size as objectively as possible, these various methods are evaluated for compatibility. The new model simulates very well kinetic grain growth for densities of 100–200 kg m−3 and temperature gradients up to –200 Km−1. The model will be incorporated in the operational version of SNOWPACK.

Assessment of the microstructure-based snow-cover model SNOWPACK: thermal and mechanical properties

Abstract It is well known that snow texture affects many properties of the snowpack. For example, new snow, layers of either small rounded grains or larger faceted and cup-shaped crystals, as well as wet snow, all show different viscous behaviors. The most direct approach to include such effects in snow-cover models is to formulate processes and properties in terms of microstructure parameters such as grain and bond size, coordination number, bond neck length, etc. Such an approach was taken for the Swiss snow-cover model SNOWPACK. Because the interdependence of properties and processes is inherent to a microstructure-based formalism, great care must be taken to properly adjust the parameters involved. Using both laboratory and field experiments, it is shown how a consistent set of parameters may be found to account for growth processes, as well as for conductivity and viscosity.

Modeling snow instability with the snow-cover model SNOWPACK

Abstract SNOWPACK has been in operational use for five consecutive winters on approximately 100 automatic weather stations in the Swiss Alps. It calculates snow precipitation, snowdrift and the layered structure of the snow cover. An analysis routine has been implemented that gives a stability estimation for a model profile. We distinguish between slab instability and direct action or deformation-rate instability. Slab instability relies on a static force balance within the snowpack (stability index) and may be used to assess stability for both natural and skier-triggered slab avalanches. We heuristically improve the slab index by adding a term of overload correction for all grain types and scaling the stability index with the bond size. Deformation-rate instability means that the load of the snow cover increases faster than the snow gains strength. An index is formulated based on the snow deformation rate. It may be associated with large snowfall events and wet-snow situations as they occur in catastrophic situations, or with the effect of a sudden increase in temperature. The results of both stability indices are compared to the fore-casted avalanche danger. The indices are able to recognize cases of avalanching. It is shown that the inclusion of several locations, for which the indices are calculated, improves the correlation between stability indices and avalanche danger. A sufficient number of profiles could bridge the gap between snow-cover characteristics at a point and avalanche danger.

Quantifying grain-shape changes in snow subjected to large temperature gradients

Abstract Snow-cover models are used in many applications in today’s snow and ice research. Although physically based models allow the evolution of the internal structure of the snow cover to be followed very closely a quantitative and objective description of the layer texture’s evolution in snow subjected to large temperature gradients is still required, in order to both improve and verify existing snow-cover models. Based on experiments done in the cold laboratory as well as on field observations on snow subjected to kinetic-growth metamorphism, we present new results on the quantification of texture-related parameters. Problems such as linking objective laboratory work to pragmatic field observations and finding a reproducible method to measure shape-related parameters are discussed. Finally a new shape parameter is proposed, zero curvature, which differentiates well between depth hoar, faceted crystals and snow types with rounded grains. It also shows a pronounced dependence on temperature gradient.