Temperature Gradient Metamorphism Research Articles

Analysis of local ice crystal growth in snow

ABSTRACTThe structural evolution of snow under metamorphism is one of the key challenges in snow modeling. The main driving forces for metamorphism are curvature differences and temperature gradients, inducing water vapor transport and corresponding crystal growth, which is detectable by the motion of the ice/air interface. To provide quantitative means for a microscopic validation of metamorphism models, a VTK-based image analysis method is developed to track the ice/air interface in time-lapseμCT experiments to measure local interface velocities under both, isothermal and temperature gradient conditions. Using estimates of local temperatures from microstructure-based finite element simulations, a quantitative comparison of measured interface velocities with theoretical expressions is facilitated. For isothermal metamorphism, the data are compared with a kinetics and a diffusion limited growth law. In both cases the data are largely scattered but consistently show a mean curvature dependency of the interface velocity. For temperature gradient metamorphism, we confirm that the main contribution stems from the temperature gradient induced vapor flux, accompanied by effects of mean curvature as a secondary process. The scatter and uncertainties are discussed in view of the present theoretical understanding, the experimental setup and complications such as mechanical deformations.

Tomography-based characterization of ice-air interface dynamics of temperature gradient snow metamorphism under advective conditions

Snow at or close to the surface commonly undergoes temperature gradient metamorphism under advective flow, which alters its microstructure and physical properties. A functional understanding of this process is essential for many disciplines, from modeling the effects of snow on regional and global climate to assessing avalanche formation. Time-lapse X-ray microtomography was applied to investigate the structural dynamics of temperature gradient snow metamorphism exposed to an advective airflow in controlled laboratory conditions. Experiments specifically analyzed sublimation and deposition of water vapor on the ice structure. In addition, an analysis of the ice-air interface dynamics was carried out using a macroscopic equivalent model of heat and water vapor transport through a snow layer. The results indicate that sublimation of the ice matrix dominated for flow rates < 10−6 m3 s−1 while during increased mass flow rates the water vapor deposition supplied by the advective flow counteracted sublimation. A flow rate dependence of water vapor deposition at the ice interface was observed, asymptotically approaching an average estimated maximum deposition rate on the whole sample of 1.05 · 10−4 kg m−3 s−1. The growth of microsized whisker-like crystals on larger ice crystals was detected on microscope photographs, leading to an increase of the specific surface area and thus suggest a change of the physical and optical properties of the snow. The estimated values of the curvature effect of the ice crystals and the interface kinetic coefficient are in good agreement with previously published values.

Evolution of the specific surface area of snow during high‐temperature gradient metamorphism

AbstractThe structural evolution of low‐density snow under a high‐temperature gradient over a short period usually takes place in the surface layers on clear, cold nights. In this paper, X‐ray computed microtomography (microCT) was combined with numerical simulations to investigate the temperature gradient metamorphism (TGM) on different types of snow. Precipitation particles (PP), small rounded particles (RGsr), and large rounded particles (RGlr) were each observed in high‐temperature gradients (100–500 K m−1) at a mean temperature of −4°C. The specific surface area (SSA) was used to characterize the TGM, which were influenced by both the magnitude of the temperature gradient and the initial snow structures. PP samples experienced a logarithmic decrease of SSA with time, and the depth hoar structures created under high TGM (500 K m−1) have higher SSA compared to those under lower TGM. Unlike previous observations, for initial rounded and connected structures, like RGlr samples, the SSA increased during TGM. Simulated normal vapor flux distributions for different snow types were used to help understand the structural evolution under TGM. Understanding the SSA increase is important in order to predict the enhanced uptake of chemical species by snow or increase in snow albedo.

Study of a temperature gradient metamorphism of snow from 3-D images: time evolution of microstructures, physical properties and their associated anisotropy

Abstract. We carried out a study to monitor the time evolution of microstructural and physical properties of snow during temperature gradient metamorphism: a snow slab was subjected to a constant temperature gradient in the vertical direction for 3 weeks in a cold room, and regularly sampled in order to obtain a series of three-dimensional (3-D) images using X-ray microtomography. A large set of properties was then computed from this series of 3-D images: density, specific surface area, correlation lengths, mean and Gaussian curvature distributions, air and ice tortuosities, effective thermal conductivity, and intrinsic permeability. Whenever possible, specific attention was paid to assess these properties along the vertical and horizontal directions, and an anisotropy coefficient defined as the ratio of the vertical over the horizontal values was deduced. The time evolution of these properties, as well as their anisotropy coefficients, was investigated, showing the development of a strong anisotropic behavior during the experiment. Most of the computed physical properties of snow were then compared with two analytical estimates (self-consistent estimates and dilute beds of spheroids) based on the snow density, and the size and anisotropy of the microstructure through the correlation lengths. These models, which require only basic microstructural information, offer rather good estimates of the properties and anisotropy coefficients for our experiment without any fitting parameters. Our results highlight the interplay between the microstructure and physical properties, showing that the physical properties of snow subjected to a temperature gradient cannot be described accurately using only isotropic parameters such as the density and require more refined information. Furthermore, this study constitutes a detailed database on the evolution of snow properties under a temperature gradient, which can be used as a guideline and a validation tool for snow metamorphism models at the micro- or macroscale.

Evolution of crystal orientation in snow during temperature gradient metamorphism

AbstractThe physical properties of snow are tied to its microstructure. Especially for the slow, plastic deformation of snow and firn, the crystal orientation is an important factor in addition to the geometry of the ice matrix. While micro-computed tomography measures the snow microstructure precisely, it gives no information about the orientation of the ice crystals. In this study, we applied a temperature gradient of 50 K m−1 to large blocks of undisturbed decomposed snow and sieved snow during 3 months. The mean temperature of the snow samples during the temperature gradient experiment was −20°C. Two closely spaced snow samples were taken before the experiment, then every week during the first month and afterwards every month. From each sampling, one sample was analyzed by micro-computed tomography and the other was used for thin sections. The orientation of the c-axis was measured in the thin sections using an automatic ice texture analyzer. Initial density was 30% higher in the sieved snow sample. Density and specific surface area evolved alike, while the fabric showed a different evolution between the two samples. The undisturbed snow evolved from a weak single-maximum fabric towards a weak girdle fabric, while the sieved sample showed no evolution. The undisturbed snow sample converged toward the sieved sample fabric after 6 weeks, but continued its evolution thereafter. We suggest that the main factor causing this different behavior is the difference in density and in pore size.

Vapor flux and recrystallization during dry snow metamorphism under a steady temperature gradient as observed by time-lapse micro-tomography

Abstract. Dry snow metamorphism under an external temperature gradient is the most common type of recrystallization of snow on the ground. The changes in snow microstructure modify the physical properties of snow, and therefore an understanding of this process is essential for many disciplines, from modeling the effects of snow on climate to assessing avalanche risk. We directly imaged the microstructural changes in snow during temperature gradient metamorphism (TGM) under a constant gradient of 50 K m−1, using in situ time-lapse X-ray micro-tomography. This novel and non-destructive technique directly reveals the amount of ice that sublimates and is deposited during metamorphism, in addition to the exact locations of these phase changes. We calculated the average time that an ice volume stayed in place before it sublimated and found a characteristic residence time of 2–3 days. This means that most of the ice changes its phase from solid to vapor and back many times in a seasonal snowpack where similar temperature conditions can be found. Consistent with such a short timescale, we observed a mass turnover of up to 60% of the total ice mass per day. The concept of hand-to-hand transport for the water vapor flux describes the observed changes very well. However, we did not find evidence for a macroscopic vapor diffusion enhancement. The picture of {temperature gradient metamorphism} produced by directly observing the changing microstructure sheds light on the micro-physical processes and could help to improve models that predict the physical properties of snow.

Anisotropic Thermal Conductivity Model for Dry Snow

Fabric tensors quantify the directional arrangement of a granular material's microstructure. In treating snow as such they are beneficial in characterizing morphologies that exhibit a distinct directional arrangement—like chains of grains in depth hoar and potentially other weak layers. Microstructural variables, including the directional arrangement of bonds, impact thermo-mechanical properties like strength, stiffness, and conductivity of the granular material. The conductivity model proposed here incorporates a fabric tensor, linking the textural arrangement of a granular assembly to a material property. In this work, dry dense snow was subject to temperature gradients (100 and 50 K/m) in a lab. The resulting morphology was driven by temperature gradient metamorphism. Underpinning the importance of microstructure, the observed heat transfer coefficient (EHC) increased in the direction of the applied gradient without appreciable changes in density. Periodic tomography yielded measurable microstructural data used to calculate a fabric tensor and the evolving conductivity tensor. Through the fabric tensor the analytical conduction model accounts for ~ 43% of the observed increase in EHC. The model also calculates a decrease in conductivity in the plane orthogonal to the temperature gradient due to a developing anisotropy. Snow metamorphism models parameterized by density alone cannot predict such directionally-dependent behavior because they are strictly valid for only isotropic materials.

Hourly simulations of the microwave brightness temperature of seasonal snow in Quebec, Canada, using a coupled snow evolution–emission model

To interpret the snowpack evolution, and in particular to estimate snow water equivalent (SWE), passive microwave remote sensing has proved to be a useful tool given its sensitivity to snow properties. However, the main uncertainties using existing SWE algorithms arise from snow metamorphism which evolves during the winter season, and changes the snow emissivity. To consider the evolution in snow emissivity a coupled snow evolution–emission model can be used to simulate the brightness temperature (T B) of the snowpack. During a dedicated campaign in the winter season, from November to April, of 2007–2008 two surface-based radiometers operating at 19 GHz and 37 GHz continuously measured the passive microwave radiation emitted through a seasonal snowpack in southern Quebec (Canada). This paper aims at modeling and interpreting this time series of T B over the whole season, with an hourly step, using a coupled multi-layer snow evolution–emission model. The thermodynamic snow evolution model, referred as to Crocus, was driven by local meteorological measurements. Results from this model provided, in turn, the input variables to run the Microwave Emission Model of Layered Snowpacks (MEMLS) in order to predict T B at 19 GHz and 37 GHz for both vertical (V) and horizontal (H) polarizations. The accuracy of T B predicted by the Crocus–MEMLS coupled model was evaluated using continuous measurements from the surface-based radiometers. The weather conditions observed during the winter season were diverse, including several warm periods with melting snow and rain-on-snow events, producing very complex variations in the time series of T B. To aid our analysis, we identified days with melting snow versus days with dry snow. The Crocus–MEMLS coupled model was able to accurately predict melt events with a success rate of 86%. The residual error was due to an overestimation of the duration of several melt events simulated by Crocus. This problem was explained by 1) a limitation of percolation, and 2) a very long-acting melt of lower layers due to geothermal flux. When the snowpack was completely dry, the global trend of T B during the season was characterized by a decrease of T B due to growth in the snow grain size. During most of the season, Crocus–MEMLS correctly predicted the evolution of T B resulting from temperature gradient metamorphism; the root mean square errors ranged between 2.8 K for the 19 GHz vertical polarization (19V) and 6.9 K for the 37 GHz horizontal polarization (37H). However, during dry periods near the end of the season, the values of T B were strongly overestimated. This overestimation was mainly due to a limitation of the growth of large snow grains in the wet snowpack simulated by Crocus. This effect was confirmed by estimating snow grain sizes from the observed T B and the coupled model. The estimated snow grain sizes were larger and more realistic than those initially predicted by the Crocus model.

Observation of temperature gradient metamorphism in snow by X-ray computed microtomography: measurement of microstructure parameters and simulation of linear elastic properties

AbstractThe process of temperature gradient metamorphism in snow strongly affects the microstructure and associated mechanical properties of the snow. The purpose of this study was to: (1) examine the temporal variations in three-dimensional snow microstructure under the influence of a strong temperature gradient for 6 days using X-ray computed microtomography (μCT); and (2) numerically simulate the linear elastic properties of snow from microtomographic data using a voxel-based finite-element technique. The temporal changes in the snow structure were analyzed in terms of density, specific surface area (SSA), thickness distribution of ice matrix and pores, structure model index and mean intercept length (MIL) fabric tensor. The structural indices and orthotropic elastic compliance matrix were computed over several sub-volumes within the reconstructed volume to account for statistical uncertainties. The mean density increased by about 14% on day 1 and no significant trend was observed thereafter. The SSA decreased by 22%, whereas both the ice and pore thickness distributions widened with time. The computed Young’s moduli were 1.5–4 times larger than previously published dynamic measurements and found to be significantly correlated with ice volume fraction and MIL fabric measures. The increasing trend in computed moduli during the experiment is consistent with the observed development of thicker vertical ice structures. Multiple linear regression models of elastic compliances using fabric tensor formulation and ice volume fraction could explain 89.9–93.0% of the variance. Our results suggest a strong dependence of elastic properties on both density and microstructural fabric.

Breeding snow: an instrumented sample holder for simultaneous tomographic and thermal studies

To study the recrystallization processes during temperature gradient metamorphism of snow, we developed a sample holder that allows applying well-defined and stable thermal gradients to a snow sample while it is scanned in an x-ray micro-tomograph. To this end, both the thermal insulation of the sample as well as image contrast and resolution of the tomography had to be optimized. We solved this conflict by using thin aluminum cylinders in combination with highly insulating foam. This design is light, does not corrupt image quality and provides very good thermal decoupling from the environment. The sample holder was instrumented to measure the effective conductivity of the snow sample and calibrated using five materials of known conductivity. Finite element simulations were consistent with the calibration measurements and gave insight into the internal temperature and heat flux fields. With this setup, geometric and thermal evolution of snow under realistic thermal boundary conditions like alternating temperature gradients can be measured.

Advances in seasonal snow water equivalent (SWE) retrieval using in situ passive microwave measurements over first‐year sea ice

Dramatic changes have occurred in the Arctic over the past three decades in response to an accelerated warming that will have a significant impact on the world's climate. Snow accumulation (measured as snow water equivalent, SWE) over sea ice plays a key role in the changes observed due to its effect on the surface energy balance that dictates the timing of sea‐ice freeze‐up and decay. Increased awareness of the role of snow in the Arctic system has triggered numerous studies that have attempted to characterize snow accumulation from space since the early 1980s, but none has successfully quantified SWE on a seasonal basis. This work presents the first seasonally valid SWE algorithm for first‐year sea ice based on in situ passive microwave radiometry. The in situ data were collected as a part of the Canadian Arctic Shelf Exchange Study (CASES) during the overwintering mission of the Canadian Coast Guard Ship (CCGS) Amundsen in 2003–2004. Previous work clearly demonstrated two different patterns of seasonal snow evolution, for which the algorithm presented in this paper accounts for. Our algorithm's results are valid for temperatures between −5 and −30°C and SWE in the range of 0–55 mm. Results show that the behaviour of the snow's thermophysical properties and brightness temperatures (T b) is quite different in the winter cooling period compared with that in the warming period, where temperature gradient metamorphism begins at a SWE value of 33 mm. The SWE algorithm successfully models this change with a high degree of correlation.

The temperature-gradient metamorphism of snow: vapour diffusion model and application to tomographic images

AbstractA simple physical model describing the temperature-gradient metamorphism of snow is presented. This model, based on Kelvin’s equation and Fick’s law, takes into account the local variation of the saturating vapour pressure with temperature. It can determine locally whether the ice is condensing or subliming, depending on both the pressure and temperature fields in the snow structure. This model can also explain the formation of facets that occurs during the metamorphism. Using X-ray microtomographic images of snow samples obtained under low to moderate temperature-gradient conditions, this model has been tested and compared to the reaction-limited model proposed in a previous work.

Rate of decrease of the specific surface area of dry snow: Isothermal and temperature gradient conditions

The specific surface area (SSA) of snow is the surface area available to gases per unit mass. It is an important variable for quantifying air‐snow exchange of chemical species, and it is closely related to other variables such as albedo. Snow SSA decreases during metamorphism, but few data are available to quantify its rate of decrease. We have performed laboratory experiments under isothermal and temperature gradient conditions during which the SSA of snow samples was monitored for several months. We have also monitored the SSA of snowfalls subjected to large temperature gradients at a field site in the central Alaskan taiga. The same snow layers were also monitored in a manipulated snowpack where the temperature gradient was greatly reduced. In all cases, the SSA decay follows a logarithmic equation with three adjustable variables that are parameterized using the initial snow SSA and the time‐averaged temperature of the snow. Two parameterizations of the three adjustable variables are found: One applies to the isothermal experiments and to the quasi‐isothermal cases studied in Alaska (equitemperature (ET) metamorphism), and the other is applicable to both the laboratory experiments performed under temperature gradients and to the natural snowpack in Alaska (temperature gradient (TG) metamorphism). Higher temperatures accelerate the decrease in SSA, and this decrease is faster under TG than ET conditions. We discuss the conditions of applicability of these parameterizations and use them to speculate on the effect of climate change on snow SSA. Depending on the climate regime, changes in the rate of decay of snow SSA and hence in snow albedo may produce either negative or positive feedbacks on climate change.

Tomography of temperature gradient metamorphism of snow and associated changes in heat conductivity

AbstractTemperature gradient metamorphism is one of the dominant processes changing the structure of natural dry snow. The structure of snow regulates the thermal and mechanical properties. Physical models and numerical simulations of the evolution of the snow cover require a thorough understanding of the interplay between structure and physical properties. The structure of snow and the heat conductivity were measured simultaneously without disturbance in a miniature snow breeder. The structure was measured by microtomography, and heat conductivity by measuring heat fluxes and temperatures. A temperature gradient from 25 to 100 K m−1 was applied to the snow. The snow density range of the samples varied from 150 to 500 kg m−3. The density in the observed volume remained constant during the experiments under temperature gradient conditions. The structure was analysed with respect to the size of typical ice structures and air pores, specific surface area, curvature and anisotropy of the ice matrix. The temporal changes in structure and heat conductivity are compared. The heat conductivity changed by as much as twice its initial value, caused by changes in structure and texture, but not due to changes in density. This shows the enormous importance of structure in the evolution of the heat conductivity. The observed changes are not in good agreement with the current understanding of the metamorphic process, because heat conductivity increased during temperature gradient metamorphism, instead of the expected decrease due to a shrinking of the bonds. We also observed a plateau in the evolution of the heat conductivity coefficient, which indicates a quasi‐steady state of the structural evolution with respect to thermophysical properties of snow. Copyright © 2004 John Wiley &amp; Sons, Ltd.

The principle of minimum entropy production and snow structure

AbstractAn essential problem in snow science is to predict the changing form of ice grains within a snow layer. Present theories are based on the idea that form changes are driven by mass diffusion induced by temperature gradients within the snow cover. This leads to the well-established theory of isothermal- and temperature-gradient metamorphism. Although diffusion theory treats mass transfer, it does not treat the influence of this mass transfer on the form — the curvature radius of the grains and bonds — directly. Empirical relations, based on observations, are additionally required to predict flat or rounded surfaces. In the following, we postulate that metamorphism, the change of ice surface curvature and size, is a process of thermodynamic optimization in which entropy production is minimized. That is, there exists an optimal surface curvature of the ice grains for a given thermodynamic state at which entropy production is stationary. This state is defined by differences in ice and air temperature and vapor pressure across the interfacial boundary layer. The optimal form corresponds to the state of least wasted work, the state of minimum entropy production. We show that temperature gradients produce a thermal non-equilibrium between the ice and air such that, depending on the temperature, flat surfaces are required to mimimize entropy production. When the temperatures of the ice and air are equal, larger curvature radii are found at low temperatures than at high temperatures. Thus, what is known as isothermal metamorphism corresponds to minimum entropy production at equilibrium temperatures, and so-called temperature-gradient metamorphism corresponds to minimum entropy production at none-quilibrium temperatures. The theory is in good agreement with general observations of crystal form development in dry seasonal alpine snow.

Snow crystal imaging using scanning electron microscopy: II. Metamorphosed snow

Abstract Low-temperature scanning electron microscopy (SEM) was used to observe metamorphosed snow crystals and grains obtained in the field. Metamorphosed snow was obtained from seasonal snowpacks in the Colorado Rocky Mountains and in Alaska. The snow samples obtained in snowpits were mounted on modified SEM stubs, frozen in liquid nitrogen, transported in Dewar flasks to the SEM facility, sputter coated with platinum, and imaged with an electron beam. Analysis of a representative set of snow samples revealed examples of metamorphosed stellar crystals, fine snow grains with sintering, rounded and faceted crystals, several types of depth hoar, rounded grains of melt metamorphism, and an ice lens. Some of the crystals exhibiting both rounding and facets indicated that both equitemperature and temperature gradient metamorphism influenced the snowpack. The SEM methods developed are operable in the field and can be used to quantify three-dimensionally size, shape and bonding characteristics of crystals. SEM appears to have direct application for better understanding of snow crystal metamorphism and snowpack processes, increasing knowledge of conditions leading to avalanche formation, and improving modelling of the transfer of microwave energy from the ground surface through the snowpack for eventual estimation of snow water equivalent.

Relocation of Major Ions in Snow along the Tundra-Taiga Ecotone

The chemistry of seasonal snowcovers north of Inuvik, Northwest Territories, Canada was stratified by biophysical landscape. In this region, deposition of ions in winter occurs largely through the redistribution of wind-blown snow with accumulations in forest-edges and valley sides 8 to 12 times that of the open tundra. While dominated by this snow redistribution, the loading of most ions, except for SO42−, does not scale exactly with that of snow, there being several mechanisms by which ion concentrations become relatively enriched or depleted in various landscape units. Vaporisation during temperature-gradient metamorphism in shallow-snow and uptake during either photochemical reactions or gaseous scavenging to well-exposed snow transformed concentrations of NO3−− by 50%. Dry deposition of aerosols to forested terrain and valley bottoms enriched Cl−, Na+, Mg2+, K+ and Ca2+ concentrations up to more than two-fold, however scavenging of aerosols to blowing snow particles contributed an additional 40% to the sea-salt enrichment and 20% to the Ca2+ enrichment in wind-blown treeline forests. It is concluded that central measurements of snow chemistry in the Arctic cannot be reliably extrapolated without reference to changes caused by over-winter physical and chemical metamorphic processes. Associating the physical/chemical changes with readily identifiable Arctic landscape units suggests a simple and robust method for spatial extrapolation.

Experimental investigation of optical snow properties

The authors have developed an experimental device in a cold laboratory with the purpose of measuring optical parameters of natural snow depending on grain-size, impurity content and density. Snow samples were prepared from homogeneous layers in order to measure the radiative properties of clearly identified snow types. The first part of this paper describes the working assumptions and the experimental device. In the second part, experiment results are described and discussed. We have compared albedo measurements of different natural snow types with theoretical values derived from physical optics, based on Mie scattering. The albedo evolution of three different snow types submitted to temperature-gradient metamorphism is analyzed.

Experimental investigation of optical snow properties

The authors have developed an experimental device in a cold laboratory with the purpose of measuring optical parameters of natural snow depending on grain-size, impurity content and density. Snow samples were prepared from homogeneous layers in order to measure the radiative properties of clearly identified snow types. The first part of this paper describes the working assumptions and the experimental device. In the second part, experiment results are described and discussed. We have compared albedo measurements of different natural snow types with theoretical values derived from physical optics, based on Mie scattering. The albedo evolution of three different snow types submitted to temperature-gradient metamorphism is analyzed.

Snowpack structure and avalanching, Craigieburn Range, New Zealand

Abstract A study of the seasonal development of the snowpack at 1700 m elevation in the Craigiebum Range, New Zealand, has revealed three phases of snowpack development. This phased development is considered in relation to snow avalanching. Analysis of a short period of continuous snowpack temperature gradient data has shown that temperature gradients exceed those generally required for recrystallisation processes, as evidenced by the common occurrence of temperature gradient forms in the snowpack. Partially metamorphosed new snow, especially clusters of rimed needles, and snow in the early stages of temperature gradient metamorphism, are weak in shear and frequently appear in avalanche sliding layers. Weak snowpack stratigraphies resemble those found for Northern Hemisphere inland-continental and coastal-maritime snow climates. Three categories of potential sliding layers for avalanche release are suggested. These are: (1) weaknesses in new snow stratigraphy, (2) weaknesses at old snow surfaces, and (3) ...