Unraveling the optical shape of snow.

The reflection of sunlight off the snow is a major driver of the Earth's climate. This reflection is governed by the shape and arrangement of ice crystals at the micrometer scale, called snow microstructure. However, snow optical models overlook the complexity of this microstructure by using simple shapes, and mainly spheres. The use of these various shapes leads to large uncertainties in climate modeling, which could reach 1.2 K in global air temperature. Here, we accurately simulate light propagation in three-dimensional images of natural snow at the micrometer scale, revealing the optical shape of snow. This optical shape is neither spherical nor close to the other idealized shapes commonly used in models. Instead, it more closely approximates a collection of convex particles without symmetry. Besides providing a more realistic representation of snow in the visible and near-infrared spectral region (400 to 1400 nm), this breakthrough can be directly used in climate models, reducing by 3 the uncertainties in global air temperature related to the optical shape of snow.

Investigating the influence of freezing rate and frozen storage conditions on a model sponge cake using synchrotron X-rays micro-computed tomography.

Synchrotron X-rays micro-computed tomography was applied to visualize and quantify 3D ice crystal changes into a model sponge cake after freezing and subsequent frozen storage. Model sponge cake samples were submitted to two different freezing rates (fast: 17.2 °C min-1 and slow: 0.3 °C min-1), then stored at constant and fluctuating temperatures over a two weeks period. 3D images were acquired at frozen state thanks to a thermostated cell (CellStat) and processed using a grey level based segmentation method. Image analysis revealed that the ice volume fraction is conserved during storage but ice crystal size and location change whatever the freezing rate and the storage conditions. Maximum local thicknesses increase both inside (from 20 µm to 50 µm) and outside (from 47 µm to 70 µm) the matrix during the fourteen days storage period. Both specific surface areas between starch and ice (SSAice/starch) and between air and ice (SSAair/ice) also evolve with storage duration: SSAice/starch decreases up to - 30 % while SSAair/ice increases up to + 13 % depending on the freezing rates and the storage conditions. These results highlighted that, during storage, ice crystals evolve according to two different mechanisms depending on the freezing rate: fast freezing leads to a local redistribution of water both within the starch matrix and within the pores, while slow freezing results in both local redistribution within the starch matrix and water migration towards the pores. In addition, stable storage temperatures favor local water redistribution whereas water migration from the starch matrix towards the pores was greater in the case of fluctuating storage temperatures. This study shows that freezing and frozen storage conditions have a synergistic effect on the microstructure evolution of sponge cake due to recrystallization phenomena.

3D Characterization of Sponge Cake as Affected by Freezing Conditions Using Synchrotron X-ray Microtomography at Negative Temperature.

In this study, the microstructural evolution of a non-reactive porous model food (sponge cake) during freezing was investigated. Sponge cake samples were frozen at two different rates: slow freezing (0.3 °C min-1) and fast freezing (17.2 °C min-1). Synchrotron X-ray microtomography (µ-CT) and cryo-scanning electron microscopy (Cryo-SEM) were used to visualize and analyze the microstructure features. The samples were scanned before and after freezing using a specific thermostated cell (CellStat) combined with the synchrotron beamline. Cryo-SEM and 3D µ-CT image visualization allowed a qualitative analysis of the ice formation and location in the porous structure. An image analysis method based on grey level was used to segment the three phases of the frozen samples: air, ice and starch. Volume fractions of each phase, ice local thickness and shape characterization were determined and discussed according to the freezing rates.

Macroscopic modeling for heat and water vapor transfer in dry snow by homogenization.

Dry snow metamorphism, involved in several topics related to cryospheric sciences, is mainly linked to heat and water vapor transfers through snow including sublimation and deposition at the ice-pore interface. In this paper, the macroscopic equivalent modeling of heat and water vapor transfers through a snow layer was derived from the physics at the pore scale using the homogenization of multiple scale expansions. The microscopic phenomena under consideration are heat conduction, vapor diffusion, sublimation, and deposition. The obtained macroscopic equivalent model is described by two coupled transient diffusion equations including a source term arising from phase change at the pore scale. By dimensional analysis, it was shown that the influence of such source terms on the overall transfers can generally not be neglected, except typically under small temperature gradients. The precision and the robustness of the proposed macroscopic modeling were illustrated through 2D numerical simulations. Finally, the effective vapor diffusion tensor arising in the macroscopic modeling was computed on 3D images of snow. The self-consistent formula offers a good estimate of the effective diffusion coefficient with respect to the snow density, within an average relative error of 10%. Our results confirm recent work that the effective vapor diffusion is not enhanced in snow.

Adaptive estimation of normals and surface area for discrete 3-D objects: application to snow binary data from X-ray tomography.

Estimating the normal vector field on the boundary of discrete three-dimensional objects is essential for rendering and image measurement problems. Most of the existing algorithms do not provide an accurate determination of the normal vector field for shapes that present edges. Here, we propose a new and simple computational method in order to obtain accurate results on all types of shapes, whatever their local convexity degree. The presented method is based on the gradient vector field analysis of the object distance map. This vector field is adaptively filtered around each surface voxel using angle and symmetry criteria so that as many relevant contributions as possible are accounted for. This optimizes the smoothing of digitization effects while preserving relevant details of the processed numerical object. Thanks to the precise normal field obtained, a projection method can be proposed to immediately derive the surface area from a raw discrete object. An empirical justification of the validity of such an algorithm in the continuous limit is also provided. Some results on simulated data and snow images from X-ray tomography are presented, compared to the Marching Cubes and Convex Hull results, and discussed.