Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

Wautier, Antoine; Geindreau, Christian; Flin, Frédéric

doi:10.5194/tc-11-1465-2017

Cited by 13 publications

(27 citation statements)

References 56 publications

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“…Up to now, many studies have focused on retrieving the single-scattering properties of individual ice crystals with "idealized" shapes (e.g. Xie et al, 2006;Picard et al, 2009;Liou et al, 2011;Räisänen et al, 2015;Dang et al, 2016) and on using these calculations to infer the effect of crystal shapes on snow optical properties. Several studies have already shown that the effect of shape is more pronounced on bidirectional reflectance (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Understanding and modelling the variations in snow directional reflectance with snow microstructure are essential to correctly interpret satellite data (Schaepman-Strub et al, 2006). Moreover, the sensitivity of snow directional reflectance to crystal shapes at least for high absorptive wavelengths (Xie et al, 2006;Dumont et al, 2010;Krol and Löwe, 2016a) makes snow directional reflectance a good candidate to provide an objective measurement of snow morphology. This characterization is often performed using the grain types defined in Fierz et al (2009).…”

Section: Introductionmentioning

confidence: 99%

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Experimental and model-based investigation of the links between snow bidirectional reflectance and snow microstructure

et al. 2021

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Abstract. Snow stands out from materials at the Earth’s surface owing to its unique optical properties. Snow optical properties are sensitive to the snow microstructure, triggering potent climate feedbacks. The impacts of snow microstructure on its optical properties such as reflectance are, to date, only partially understood. However, precise modelling of snow reflectance, particularly bidirectional reflectance, are required in many problems, e.g. to correctly process satellite data over snow-covered areas. This study presents a dataset that combines bidirectional reflectance measurements over 500–2500 nm and the X-ray tomography of the snow microstructure for three snow samples of two different morphological types. The dataset is used to evaluate the stereological approach from Malinka (2014) that relates snow optical properties to the chord length distribution in the snow microstructure. The mean chord length and specific surface area (SSA) retrieved with this approach from the albedo spectrum and those measured by the X-ray tomography are in excellent agreement. The analysis of the 3D images has shown that the random chords of the ice phase obey the gamma distribution with the shape parameter m taking the value approximately equal to or a little greater than 2. For weak and intermediate absorption (high and medium albedo), the simulated bidirectional reflectances reproduce the measured ones accurately but tend to slightly overestimate the anisotropy of the radiation. For such absorptions the use of the exponential law for the ice chord length distribution instead of the one measured with the X-ray tomography does not affect the simulated reflectance. In contrast, under high absorption (albedo of a few percent), snow microstructure and especially facet orientation at the surface play a significant role in the reflectance, particularly at oblique viewing and incidence.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Experimental and model-based investigation of the links between snow bidirectional reflectance and snow microstructure

et al. 2021

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“…Still, in situ studies of snow mostly consist of following time lapse metamorphism for different types of snow [16] and with controlled thermal gradients or other particular conditions [17,18]. The ultimate goal is usually to compute snow effective properties [19] or model snow behavior [20,21,22]. Moreover, curvature change is a key feature of snow metamorphism and its investigation reveals underlying processes at work [23,24].…”

Section: Introductionmentioning

confidence: 99%

In situ X-ray tomography densification of firn: The role of mechanics and diffusion processes

Burr¹,

Lhuissier²,

Martín³

et al. 2019

Acta Materialia

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One of the most efficient proxy methods for paleoclimatology consists of obtaining data previously preserved within polar ice cores. Models for past climate reconstruction are based in particular on the characterization of entrapped gases in ice closed pores. Improving the temporal accuracy of these models requires a better understanding of firn densification mechanisms. In particular, the interplay between viscoplastic deformation and diffusion processes for pore closure is not well understood. In this work, we describe the first in situ laboratory densification experiments on polar firn retrieved from Antarctica with live characterization by X-ray tomography. Our in situ tests allow for the first time to approximately access the process of pore closure in ice, which takes thousands of years to occur in Antarctica, from visualizations and quantitative analyses of short time laboratory experiments. The parameters of pore separation and closure and the microstructural changes that accompany them are monitored. We show that densification of polar

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“…The CLD p (i) (l) of phase i denotes the probability p (i) (l)dl of finding a random chord of length between l and l + dl in phase i (Torquato, 2002), thus 5 giving us information on the thicknesses of the elements constituting the considered phase. In the case of snow, which is known to be an anisotropic material with an orthotropic axis corresponding to the vertical (z) direction (see Calonne et al, 2011Calonne et al, , 2012Löwe et al, 2013;Calonne et al, 2014b, a;Wautier et al, 2015;Srivastava et al, 2016;Wautier et al, 2017), the CLD measured along a particular line depends on its direction. Assuming that the anisotropy is small, we consider the statistical characteristics of a sample in the three Cartesian directions.…”

Section: Chord Length Distributionmentioning

confidence: 99%

Experimental and model-based investigation of the links between snow bidirectional reﬂectance and snow microstructure

Dumont¹,

Flin²,

Malinka³

et al. 2021

Preprint

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Abstract. Snow stands out from materials at the Earth's surface owing to its unique optical properties. Snow optical properties are sensitive to the snow microstructure, triggering potent climate feedbacks. The impacts of snow microstructure on its optical properties such as reflectance are, to date, only partially understood. However, precise modelling of snow reflectance, particularly bidirectional one, are required in many problems, e.g. to process correctly satellite data over snow-covered areas. This study presents a dataset that combines bidirectional reflectance measurements over 500–2500 nm and the X-ray tomography of the snow microstructure for three snow samples of two different morphological types. The dataset is used to evaluate the stereological approach from Malinka (2014) that relates snow optical properties to the chord length distribution in the snow microstructure. The mean chord length and SSA retrieved with this approach from the albedo spectrum and those measured by the X-ray tomography are in excellent agreement. The analysis of the 3D images has shown that the random chords of the ice phase obey the gamma distribution with the shape parameter m taking the value approximately equal or a little greater than 2. For weak and intermediate absorption (high and medium albedo), the simulated bidirectional reflectances reproduce the measured ones accurately but tend to slightly overestimate the anisotropy of the radiation. For such absorptions the use of the exponential law for the ice chord length distribution instead of the one measured with the X-ray tomography does not affect the simulated reflectance. In contrast, under high absorption (albedo of a few percent), snow microstructure and especially facet orientation at the surface, plays a significant role for the reflectance, particularly at oblique viewing and incidence.

show abstract

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

Cited by 13 publications

References 56 publications

Experimental and model-based investigation of the links between snow bidirectional reflectance and snow microstructure

Experimental and model-based investigation of the links between snow bidirectional reflectance and snow microstructure

In situ X-ray tomography densification of firn: The role of mechanics and diffusion processes

Experimental and model-based investigation of the links between snow bidirectional reﬂectance and snow microstructure

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