3D imaging of snow microstructure for a better knowledge of snow properties and of their time evolution: 2 examples

3D imaging of snow microstructure for a better knowledge of snow properties and of their time evolution: 2 examples

62A062+62A101

F. Flin

, N. Calonne

, C. Geindreau

, B. Lesaffre

, X. Wang

,

C. Carmagnola

, S. Rolland du Roscoat

, P. Charrier

, S. Morin

, D. Coeurjolly

1

CEN, CNRM - GAME URA 1357, Meteo-France - CNRS, Grenoble, France

2

3S-R UMR 5521, CNRS - Universite Joseph Fourier - Grenoble INP, Grenoble, France

3

LIRIS UMR 5205, CNRS, Lyon, France

3D imaging of snow microstructure for a better knowledge of snow properties and of their time evolution: 2 examples

Computation of snow permeability from 3D images

Calonne et al. 62A101

Evolution of snow properties under temperature gradient conditions

Flin et al. 62A062

EXAMPLE 1

3D Image-based Numerical Computations of the Snow Permeability: Links to Specific Surface Area, Density, and

Microstructural Anisotropy (62A101)

N. Calonne

, C. Geindreau

, F. Flin

, S. Morin

, B. Lesaffre

, S. Rolland du Roscoat

, and P. Charrier

1

CEN, CNRM - GAME URA 1357, Meteo-France - CNRS, Grenoble, France

2

3S-R UMR 5521, CNRS - Universite Joseph Fourier - Grenoble INP, Grenoble, France

where K

is the normalized (dimensionless) permeability tensor

• Darcy’s law

• One of the main transport properties of snow

• Key variable for several applications (atmospheric-firn chemistry, snow metamorphism, …)

• Related to a characteristic length l (in m), often used for normalization:

 p



  q K

Intrinsic Permeability Tensor of Snow

Introduction Methods Results & Discussion Conclusions

- K : intrinsic permeability tensor (m

) - q : discharge per unit area (m s

)

- μ : dynamic viscosity of air (kg m

s

) - : pressure gradient (Pa m  _p

)

l

K

 K

• Strongly depends on snow density ρ

 K

versus ρ

 l : estimate of the snow grain size

Problems

• Co-existence of models (experimental fits, analytical laws, numerical computations, …) which provide different relationships of K

vs. ρ

• Challenging measurements: large scatter in K

vs. ρ

observed in experimental studies  Litterature data may differ from several orders of magnitude for the same density

• No or few studies about the anisotropy of K.

Jordan et al., 1999

Shimizu

Carman - Kozeny

Zermatten et al., 2011

Introduction Methods Results & Discussion Conclusions

Issues and Contributions

Our study: Numerical computations of the permeability tensor K from 3D snow microstructure provided by X-ray tomography.

Objectives

1. Study of the relationship between K, l and ρ

2. Understand the origin of the scatter observed in litterature:

 Comparisons to models

 Comparisons to experimental data 3. Study of the anisotropy of K

Introduction Methods Results & Discussion Conclusions

7

Examples of Snow Samples (out of 35)

Precipitation Particles

Decomposing and

Fragmented precipitation particles

Rounded

Grains Depth

Hoar

1 mm 1 mm

1 mm

Melt Forms

1 mm 1 mm

Introduction Methods Results & Discussion Conclusions

L

Snow layer

Macroscopic scale Microscopic scale

α a

a

a

   p

 q K

pore) ( a 

Condition

Separation of scales L >> l

l

Numerical Computation - Homogenisation

Auriault et al. 2009

Periodic homogenisation

K (micros., K

)

 p



  q K

Introduction Methods Results & Discussion Conclusions

 







 









zz zy

zx

yz yy

yx

xz xy

xx

K K

K

K K

K

K K

K

K

Solving a specific boundary problem arising from the homogenisation process, on a 3D image, by Geodict software.

L

Snow layer

Macroscopic scale Microscopic scale

α a

a

a

   p

 q K

air) ( a 

l

Auriault et al. 2009

Periodic homogenisation

K (micros., K

)

 p



  q K

REV

Numerical Computation - Homogenisation

Introduction Methods Results & Discussion Conclusions

Choice of the characteristic length  equivalent sphere radius r

(m)

• directly related to the specific surface area of snow SSA (m

kg

)

• can be measured experimentally (DUFISSS, ASSSAP,…) and numerically from 3D images

• in the followings, we define (dimensionless)

K

vs. Density – Characteristic Length

2

r

K

 K

ice

r



 

SSA

3 where ρ

is the ice density (kg m

)

Introduction Methods Results & Discussion Conclusions

K

vs. Density - General Evolution

 Dimensionless permeability decreases with increasing density

Vertical component

Horizontal component

Introduction Methods Results & Discussion Conclusions

K

vs. Density - Anisotropy

Anisotropy of K

= vertical component horizontal component

 Anisotropy range:

0.74 – 1.66

Vertical component

Horizontal component

Introduction Methods Results & Discussion Conclusions

K

vs. Density - Anisotropy

The coefficient of anisotropy is linked to the snow

microstructure

Vertical component

Horizontal component

Introduction Methods Results & Discussion Conclusions

Example of vertically-oriented sample: Depth Hoar

 p

Air flow velocity

 p

K

vs. Density - Regression Curve

Exponential regression on 35 mean values of K

:

) 013 . 0 exp(

94 .

2

2

r

K    

 Strong relationship between K, SSA and ρ

Introduction Methods Results & Discussion Conclusions

R² = 0.985

K

vs. Density - Comparison to Models

Introduction Methods Results & Discussion Conclusions

• good agreement between models and computations, in overall

• Shimizu (experimental

fit, 1970): due to the

definition of the grain

size estimates?

K

vs. Density - Comparison to Experimental Data

• Our computations are consistent with values from others studies

• experimental values are more scattered:

due to the difficulty of measurements?

Introduction Methods Results & Discussion Conclusions

• Permeability is strongly correlated with density and SSA (r

)

 l = r

can be good choice

• Anisotropy of K ranges between 0.74 - 1.66 and is linked to snow microstructure.

• In overall, our computations are consistent with models and datasets from litterature

• An average value of K can be reasonnably inferred from SSA and density, using the proposed regression equation:

Conclusion

Introduction Methods Results & Discussion Conclusions

) 013 . 0 exp(

94 .

2

2

r

K    

Discussion paper:

Calonne et al., TCD, 2012

EXAMPLE 2

3D Characterization of Snow Evolution

under Temperature Gradient Conditions (62A062)

F. Flin

, N. Calonne

, B. Lesaffre

, X. Wang

, C. Carmagnola

,

S. Rolland du Roscoat

, P. Charrier

, S. Morin

, D. Coeurjolly

, C. Geindreau

1

Meteo-France - CNRS, CNRM-GAME URA 1357, CEN, Grenoble, France

3S-R CNRS UMR 5521, Universite Joseph Fourier - Grenoble INP, Grenoble, France

3

LIRIS UMR 5205, CNRS, Lyon, France

t = 0 h t = 313 h t = 500 h

• Common metamorphism regime in natural conditions

• Complicated phenomena involving various physical processes (heat and mass transfer, facetting, …)

• Complicated impact on snow mechanical and physical properties

Snow Metamorphism under Temperature Gradient (TG)

Atmosphere, T



T

Ground, T

Introduction Methods Results & Discussion Conclusions

vapor

growth direction

Yosida et al., 1955

Colbeck 1983

• grain growth

• neck evolution

• facetting effects

• evolution of physical properties

• anisotropic behavior

• Relationship between physical properties (K, k

, …) and snow microstructure poorly understood (anisotropic effects)

Problems

• How quantifying the snow evolution?

• Little complete 3D datasets to fully quantify the snow evolution under TG metamorphism

Introduction Methods Results & Discussion Conclusions

Issues and Contributions

Our study: 3D characterization of the snow evolution submitted to TG from tomographic images.

Objectives

1. Obtain precise measurements to characterize the

morphological evolutions occurring under TG metamorphism 2. Study the relationship between microstructure and physical

parameters (anisotropy)

Introduction Methods Results & Discussion Conclusions

Cold-room Experiment

Insulating polystyrene plate Copper plate

Snow slab obtained by fresh snow sieving

Thermal regulation of the copper plates by a fluid

circulation

T = - 1 °C T = - 7 °C

|| T|| = 43 K m^-1 1 m

14 cm

Introduction Methods Results & Discussion Conclusions

Temperature conditions during 3 weeks

Density = 300 kg m

1.6 cm 5.35 cm

1. Sampling 4. Machining

3. Freezing 2. Impregnation

Numerical Computation - Acquisition of 3D Images

5. X-ray tomography 6. Image processing

1 mm

- Image size: 6 - 10 mm - Voxel size: 7 - 9 µm

Introduction Methods Results & Discussion Conclusions

Gaussian and Mean Curvatures, Related Histograms

Gaussian curvature:

1 2

1 1

.

G ^ R R ^[L

-2

]

1 2

1 1 1

C 2

R R

 

     

 

[L

]

Mean curvature:

convex 0 concave

Introduction Methods Results & Discussion Conclusions

• Idea: to measure the degree of convexity of the ice-air interface

• Methods:

Flin et al, Ann. Glaciol., 2004 Brzoska et al, PCI, 2007

 Curvature histograms:

Count the amount of values having the same curvature on the whole

surface

Microstructural Anisotropy and Related Histograms

• Idea: to measure the anisotropy of the normal field of the ice-air interface

• Method:

• compute outward unit normal vectors n (Flin et al., 2005)

• for each normal vector, compute angles between n and the x, y, z axes

• compute the proportion of normals corresponding to a particular angle

• draw the resulting histogram in a polar plot

• estimate the ratio h_max_z / h_max_horizontal

ice

α _x

Introduction Methods Results & Discussion Conclusions

x z

n

Computation of Physical Properties - Homogenisation

 







 









zz zy

zx

yz yy

yx

xz xy

xx

k k

k

k k

k

k k

k

k

Solving a specific boundary problem arising from the homogenisation process, on a 3D image, by Geodict software.

L

Snow layer

Macroscopic scale Microscopic scale

T







α

k

F

 T



 k

F

ice) air, ( α 

l

Auriault et al. 2009

Periodic homogenisation

k

(micros., k

, k

)

Example for the effective thermal conductivity k

Introduction Methods Results & Discussion Conclusions

REV

Specific Surface Area (SSA)

• SSA decreases during metamorphism

• a fast SSA decrease corresponds to a high TG

Introduction Methods Results & Discussion Conclusions

10 12 14 16 18 20 22 24 26 28 30

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Time (hours) S S A ( m

k g

)

This study Flin et al., 2004

Schneebeli et al., 2004

Isothermal conditions

~ -2°C

100 K m

~ -7°C

43 K m

~ -4°C

Histograms of Mean Curvature (C)

Introduction Methods Results & Discussion Conclusions

After 0 hours

~2 mm

Histograms of Mean Curvature (C)

Introduction Methods Results & Discussion Conclusions

After 73 hours

~2 mm

Histograms of Mean Curvature (C)

Introduction Methods Results & Discussion Conclusions

After 144 hours

~2 mm

Histograms of Mean Curvature (C)

Introduction Methods Results & Discussion Conclusions

After 217 hours

~2 mm

Histograms of Mean Curvature (C)

Introduction Methods Results & Discussion Conclusions

After 313 hours

~2 mm

Histograms of Mean Curvature (C)

Introduction Methods Results & Discussion Conclusions

After 409 hours

~2 mm

Histograms of Mean Curvature (C)

Introduction Methods Results & Discussion Conclusions

After 500 hours

~2 mm

Histograms of Mean Curvature (C)

Conclusions:

+ the peak is moving to 0  grains are growing + the peak is narrowing  grains are facetting

+ the negative part of the peak increases  concave shapes are created

Introduction Methods Results & Discussion Conclusions

After 500 hours

~2 mm

Histograms of Gaussian Curvature (G)

Introduction Methods Results & Discussion Conclusions

After 0 hours

~2 mm

Histograms of Gaussian Curvature (G)

Introduction Methods Results & Discussion Conclusions

After 73 hours

~2 mm

Histograms of Gaussian Curvature (G)

Introduction Methods Results & Discussion Conclusions

After 144 hours

~2 mm

Histograms of Gaussian Curvature (G)

Introduction Methods Results & Discussion Conclusions

After 217 hours

~2 mm

Histograms of Gaussian Curvature (G)

Introduction Methods Results & Discussion Conclusions

After 313 hours

~2 mm

Histograms of Gaussian Curvature (G)

Introduction Methods Results & Discussion Conclusions

After 409 hours

~2 mm

Histograms of Gaussian Curvature (G)

Introduction Methods Results & Discussion Conclusions

After 500 hours

~2 mm

Histograms of Gaussian Curvature (G)

Introduction Methods Results & Discussion Conclusions

After 500 hours Conclusions:

+ the 0-centered peak is increasing and narrowing  grains are facetting + the proportion of convex shapes is decreasing  grains are growing + the proportion of concave shapes is decreasing  necks are growing

~2 mm

Intrinsic Permeability from Numerical Computations

• Permeability increases with time

• Larger increase in z direction

Introduction Methods Results & Discussion Conclusions

Effective Thermal Conductivity from Num. Computations

Introduction Methods Results & Discussion Conclusions

• Thermal conductivity increases with time

• Larger increase in z direction Density = 300 kg m

In overall

Effective Thermal Conductivity from Num. Computations

Introduction Methods Results & Discussion Conclusions

• Thermal conductivity decreases with time

• Larger decrease in horizontal direction Density = 300 kg m

At the beginning

Stage 1 Stage 2

Effective Thermal Conductivity from Num. Computations

Introduction Methods Results & Discussion Conclusions

• Thermal conductivity decreases with time

• Larger decrease in horizontal direction Density = 300 kg m

At the beginning

Schneebeli et al. 2004

Stage 1 Stage 2

Anisotropy

Relationship between Microstructure and Properties

• All anisotropic coefficients increase with time

 highlights the link between microstructural and physical properties

Introduction Methods Results & Discussion Conclusions

Conclusions

• We presented some numerical tools to quantitatively monitor the geometrical and physical properties of snow under TG metamorphism

• Observations are qualitatively consistent with previous experiments described in the litterature

• Anisotropy of K and k

are linked to snow microstructural anisotropy Perspectives

• Use this dataset as guidelines or validation tools for microstructural metamorphism models

Conclusion

Introduction Methods Results & Discussion Conclusions

Acknowledgements:

H. Arakawa, F. Domine for datasets and discussions ESRF ID19 beamline, 3SR lab for tomographic acquisitions

French National Research Agency (DigitalSnow ANR-11-BS02-009) for funding

General Conclusion

Both approaches are particularly helpful for better snowpack modeling One property for many snow samples:

Obtain robust relationships between complex physical

properties (K, keff) and more basic properties (density, SSA)

Many properties for a particular sample undergoing

metamorphism: better

understanding of the physical

processed involved

3D Snow Imaging by X-ray Microtomography

1200 pixels

12 00 p ix el s

Energy 18-20 keV

1 pixel

=

4.92 to 10 microns

10 mm Room temperature experiments:

A cold cell is needed

REV

Precipitation Particles Facetted Crystals

REV

• Smallest volume from which a variable representative of the whole can be estimated

• Computation of K on volume at least equal to the REV

• REV estimated by calculating K on increasing volumes

Representative Elementary Volume (REV)

Curvature of a line in a 2D space

R R’

Osculating circles

C = 1/R

Gaussian curvature :

1 2

1 1

.

G ^ R R ^[L

-2

]

1 2

1 1 1

C 2

R R

 

     

 

[L

]

 Allows to distinguish the surfaces whose radii R1 and R2 are opposite:

detects necks and saddle points Mean curvature :

3D segmentation of geometrical grains

Curvature of a surface in a 3D space

 important quantity for interface physics