3D Growth Rates from TomographicImages: Local … · 1Météo-France -CNRS, CNRM -GAME UMR 3589 /...
1
local growth (and sublimation) rates local fluxes j = r . ρ ice at the interface r Binary image – interface in blue Distance map Φ : proportional to the distance of the background (pores) F. Flin F. Flin 1 1 , N. Calonne , N. Calonne 1, 2, 3 1, 2, 3 , R. Denis , R. Denis 4 4 , R. Caneill , R. Caneill 1 1 , B. Lesaffre , B. Lesaffre 1 1 , A. Dufour , A. Dufour 1 1 , , A. Philip A. Philip 1 1 , J. Roulle , J. Roulle 1 1 , S. Rolland du Roscoat , S. Rolland du Roscoat 2 2 , C. Geindreau , C. Geindreau 2 2 1 M M é é t t é é o o - - France France - - CNRS, CNRM CNRS, CNRM - - GAME UMR 3589 / CEN, Saint Martin d'H GAME UMR 3589 / CEN, Saint Martin d'H è è res, France res, France 2 CNRS CNRS - - UJF UJF - - G G - - INP, Laboratoire 3SR UMR 5521, Grenoble, France INP, Laboratoire 3SR UMR 5521, Grenoble, France 3 now now at at WSL, Institute for Snow and Avalanche WSL, Institute for Snow and Avalanche Research Research SLF, Davos, SLF, Davos, Switzerland Switzerland 4 Universit Universit é é Savoie Mt. Blanc Savoie Mt. Blanc - - CNRS, LAMA UMR 5127, Le CNRS, LAMA UMR 5127, Le - - Bourget Bourget - - du du - - Lac, France Lac, France 3D Growth Rates from 3D Growth Rates from Tomographic Tomographic Images: Local Measurements Images: Local Measurements for a Better Understanding of Snow Metamorphism for a Better Understanding of Snow Metamorphism - - Application to Isothermal Metamorphism and Comparison with a Ph Application to Isothermal Metamorphism and Comparison with a Ph ase ase - - Field Model Field Model - - Once deposited on the ground, snow forms a complex porous material whose microstructure constantly transforms over time. These evolutions, which strongly impact the physical and mechanical properties of snow (e.g. Srivastava et al, 2010; Löwe et al, 2013; Calonne et al, 2014) need to be considered in details for an accurate snowpack modeling. However, some of the physical mechanisms involved in metamorphism are still poorly understood. To address this problem, several investigations combining X-ray tomography and 3D micro-modeling have been carried out (e.g. Flin et al, 2003; Kaempfer and Plapp, 2009; Pinzer et al, 2012) but precise comparisons between experimentation and modeling remain difficult. One of the difficulties comes from the lack of high resolution time-lapse series for experiments occurring with very well-defined boundary conditions, and from which precise measurements of the interfacial growth rates can be done. Using CellDyM, a recently developed cryogenic cell (Calonne et al, 2015), we conducted in situ time-lapse tomographic experiments on several snow and ice samples under various conditions (isothermal metamorphism at -7°C, temperature gradient metamorphism at -2°C under a TG of 18 K/m, air bubble migration in a single crystal at -4°C under a TG of 45 K/m). The non-destructive nature of X-ray microtomography yielded series of 8 micron resolution images that were acquired with time steps ranging from 2 to 12 hours. An image analysis method was then developed to estimate the normal growth rates on each point of the ice-air interface and applied to the series obtained. Here, we focus on isothermal metamorphism at -7°C, where the results obtained and their comparison to those of existing models (e.g. Flin et al, 2003; Bretin et al, 2015) give interesting outlooks for the understanding of the physical mechanisms involved. 1. Introduction 1. Introduction 2. 2. CellDyM CellDyM : a Cryogenic Cell for Time : a Cryogenic Cell for Time - - Lapse Tomography at Room Lapse Tomography at Room - - Temperature Temperature 3. A Simple Method to Measure Normal Growth Rates from 3D Time 3. A Simple Method to Measure Normal Growth Rates from 3D Time - - Lapse Images Lapse Images 4. Preliminary Results: Is Sublimation 4. Preliminary Results: Is Sublimation - - Deposition Deposition a a Dominant Mechanism at Dominant Mechanism at - - 7 7 ° ° C? Which Value for C? Which Value for α α α α α α eff eff ? ? Results: 3D time-lapse series with : - high spatial and temporal resolution - well-defined thermal conditions Metamorphism under isothermal conditions at -7°C Conclusions: -A simple method has been developed to measure normal growth rates from time-lapse 3D images. It gives consistent results and can be used to better understand snow metamorphism. -This method has been applied to snow to analyze the physical mechanisms occuring under isothermal metamorphism at -7°C. The obtained results have also been compared to an approach based on phase-field modeling: the sublimation-deposition appears as a possible mechanism with an effective accomodation coefficient about 10 -3 but contributions of other mechanisms (vapor diffusion, grain boundary, mechanical effects…) seem difficult to neglect. -Further analyses on larger datasets are now in progress. Continous problem Ice Vapor t = t0 t = t0 + 1 Ice Vapor Vapor Image binaire 5 5 5 5 5 5 5 5 5 7 5 5 5 7 7 7 10 10 15 10 10 10 11 11 14 14 5 5 5 5 Vapor Image binaire 5 5 5 5 5 5 5 5 5 7 5 5 5 7 7 7 10 10 15 10 10 10 11 11 14 14 5 5 5 5 Vapor The (signed) distance of the red interface from the blue one is directly given by the distance map Φ as follows: d = (5 - Φ) / 5 (pixels) DigitalSnow DigitalSnow Initial State Step 1 Step 2 Snow sample 1 cm 1 cm 131 voxels ~ 1 mm Acknowledgments: F. Dominé, M. Dumont, F. Karmous, F. Lahoucine, J-M. Panel, P. Puglièse and G. Vian for their help with the cryo-cell development; E. Ando, J. Desrues and P. Charrier for tomography at 3SR; E. Bretin, J.-O. Lachaud, E. Oudet and T. Roussillon for their implication in the phase-filed model. Funding: ANR DigitalSnow (ANR-11-BS02-009-03); 3SR is part of the Labex Tec 21 (ANR-11-LABX-0030), CEN is part of the Labex OSUG@2020 (ANR-10-LABX-56) References: Bretin, E., R. Denis, F. Flin, J.-O. Lachaud, E. Oudet, T. Roussillon (2015), Discrete-Continuous approach for deformable partitions, Technical Report 4 of ANR DigitalSnow Project. Calonne, N., F. Flin, C. Geindreau, B. Lesaffre and S. Rolland du Roscoat (2014), The Cryosphere, 8(6), 2255–2274, doi:10.5194/tc-8-2255-2014. Calonne, N., F. Flin, B. Lesaffre, A. Dufour, J. Roulle, P. Puglièse, A. Philip, F. Lahoucine, C. Geindreau, J.-M. Panel, S. Rolland du Roscoat and P. Charrier (2015), Geophys. Res. Lett., 42, doi: 10.1002/2015GL063541. Flin, F., J.-B. Brzoska, B. Lesaffre, C. Coléou and R. A. Pieritz (2003), J. Phys. D. Appl. Phys., 36, A49-A54, doi: 10.1088/0022-3727/36/10A/310. Flin, F. and J.-B. Brzoska (2008), Ann. Glaciol., 49, 17–21, doi:10.3189/172756408787814834. Kämpfer, T. U. and M. Plapp (2009), Phase-field modeling of dry snow metamorphism, Phys. Rev. E, 79 (3), 031502, doi:10.1103/PhysRevE.79.031502. Krol, Q., H. Löwe, Analysis of local ice crystal growth in snow, J. Glaciol, 15J181, in press. Löwe, H., F. Riche and M. Schneebeli (2013), The Cryosphere, 7(5), 1473–1480, doi:10.5194/tc-7-1473-2013. Pinzer, B., M. Schneebeli and T. Kämpfer (2012), The Cryosphere, 6, 1141–1155. Srivastava, P., P. Mahajan, P. Satyawali and V. Kumar (2010), Ann. Glaciol., 51, 73–82. C13C-0818 [email protected] [email protected] 1mm t = 0 hour t = 28 hours z z z z: direction of gravity convex concave convex concave Based on the following principles: -thermal regulation using 2 Peltier modules at top and base of the sample -thermal insulation from room temperature using a vacuum chamber -an amovible conductive sample holder that protects specimens during their installation into the cell ~5.5 m m Approach 1: Growth rates measurements Binary image – interface in blue In red: new position of the interface linear regression Sublimation-deposition model (see e.g., Flin et al, 2003; Krol and Löwe, in press): j = αk (C mean - C) 3D images with curvature fields Enlarged views Vertical cross-section Interface velocity estimated between 0 and 28 h α growth_rates = 5.10 -4 Approach 2: Phase-field model α phase-field = 7.10 -3 z x deposition: +5.10 -10 m s -1 sublimation: -5.10 -10 m s -1 y C mean = 7.4 mm -1 C mean = 6.3 mm -1 Experiment t = 0 hour t = 28 hours Phase-field model t adjusted = 13 hours t adjusted = 28 hours Similar structure 200 voxels ~ 2 mm Large scatter in the measurements + 38 mm -1 -38 mm -1
Transcript of 3D Growth Rates from TomographicImages: Local … · 1Météo-France -CNRS, CNRM -GAME UMR 3589 /...
�local growth (and sublimation) rates�local fluxes j = r . ρice at the interface
rBinary image – interface in blueDistance map Φ : proportional to the distance of the background (pores)
F. FlinF. Flin11, N. Calonne, N. Calonne1, 2, 31, 2, 3, R. Denis, R. Denis44, R. Caneill, R. Caneill11, B. Lesaffre, B. Lesaffre11, A. Dufour, A. Dufour11,,
A. PhilipA. Philip11, J. Roulle, J. Roulle11, S. Rolland du Roscoat, S. Rolland du Roscoat22, C. Geindreau, C. Geindreau22
11 MMééttééoo--France France -- CNRS, CNRM CNRS, CNRM -- GAME UMR 3589 / CEN, Saint Martin d'HGAME UMR 3589 / CEN, Saint Martin d'Hèères, Franceres, France22 CNRS CNRS -- UJF UJF -- GG--INP, Laboratoire 3SR UMR 5521, Grenoble, FranceINP, Laboratoire 3SR UMR 5521, Grenoble, France
33 nownow atat WSL, Institute for Snow and Avalanche WSL, Institute for Snow and Avalanche ResearchResearch SLF, Davos, SLF, Davos, SwitzerlandSwitzerland44 UniversitUniversitéé Savoie Mt. Blanc Savoie Mt. Blanc -- CNRS, LAMA UMR 5127, LeCNRS, LAMA UMR 5127, Le--BourgetBourget--dudu--Lac, FranceLac, France
3D Growth Rates from 3D Growth Rates from TomographicTomographic Images: Local MeasurementsImages: Local Measurements
for a Better Understanding of Snow Metamorphismfor a Better Understanding of Snow Metamorphism-- Application to Isothermal Metamorphism and Comparison with a PhApplication to Isothermal Metamorphism and Comparison with a Phasease--Field Model Field Model --
Once deposited on the ground, snow forms a complex porous material whose microstructure constantly transforms over time. These evolutions, which strongly impact the physical and
mechanical properties of snow (e.g. Srivastava et al, 2010; Löwe et al, 2013; Calonne et al, 2014) need to be considered in details for an accurate snowpack modeling. However, some of the
physical mechanisms involved in metamorphism are still poorly understood.
To address this problem, several investigations combining X-ray tomography and 3D micro-modeling have been carried out (e.g. Flin et al, 2003; Kaempfer and Plapp, 2009; Pinzer et al, 2012)
but precise comparisons between experimentation and modeling remain difficult. One of the difficulties comes from the lack of high resolution time-lapse series for experiments occurring
with very well-defined boundary conditions, and from which precise measurements of the interfacial growth rates can be done.
Using CellDyM, a recently developed cryogenic cell (Calonne et al, 2015), we conducted in situ time-lapse tomographic experiments on several snow and ice samples under various
conditions (isothermal metamorphism at -7°C, temperature gradient metamorphism at -2°C under a TG of 18 K/m, air bubble migration in a single crystal at -4°C under a TG of 45 K/m). The
non-destructive nature of X-ray microtomography yielded series of 8 micron resolution images that were acquired with time steps ranging from 2 to 12 hours. An image analysis method was
then developed to estimate the normal growth rates on each point of the ice-air interface and applied to the series obtained.
Here, we focus on isothermal metamorphism at -7°C, where the results obtained and their comparison to those of existing models (e.g. Flin et al, 2003; Bretin et al, 2015) give interesting
outlooks for the understanding of the physical mechanisms involved.
1. Introduction1. Introduction
2. 2. CellDyMCellDyM: a Cryogenic Cell for Time: a Cryogenic Cell for Time--Lapse Tomography at RoomLapse Tomography at Room--TemperatureTemperature
3. A Simple Method to Measure Normal Growth Rates from 3D Time3. A Simple Method to Measure Normal Growth Rates from 3D Time--Lapse ImagesLapse Images
4. Preliminary Results: Is Sublimation4. Preliminary Results: Is Sublimation--Deposition Deposition aa Dominant Mechanism at Dominant Mechanism at --77°°C? Which Value for C? Which Value for ααααααααeffeff??
�Results: 3D time-lapse series with :
- high spatial and temporal resolution
- well-defined thermal conditions
Metamorphism under isothermal conditions at -7°C
Conclusions:-A simple method has been developed to measure normal growth rates
from time-lapse 3D images. It gives consistent results and can be used
to better understand snow metamorphism.
-This method has been applied to snow to analyze the physical
mechanisms occuring under isothermal metamorphism at -7°C.
The obtained results have also been compared to an approach based
on phase-field modeling: the sublimation-deposition appears as a
possible mechanism with an effective accomodation coefficient about
10-3 but contributions of other mechanisms (vapor diffusion, grain
boundary, mechanical effects…) seem difficult to neglect.
-Further analyses on larger datasets are now in progress.
Continous problem
Ice
Vaport = t0
t = t0 + 1
Ice
Vapor Vapor
Image binaire
5 5
5 5 5
5
5
5
5
7
5
55
7
7
7
1010 15
1010
10
11
11 1414
5
5 5
5Vapor
Image binaire
5 5
5 5 5
5
5
5
5
7
5
55
7
7
7
1010 15
1010
10
11
11 1414
5
5 5
5Vapor
The (signed) distance of the red interface from the blue one is directly given by the distance map Φ as follows:
d = (5 - Φ) / 5 (pixels)
DigitalSnowDigitalSnow
Initial State Step 1 Step 2
Snow sample
1 cm
1 cm
131
voxels
~ 1 mm
Acknowledgments:
F. Dominé, M. Dumont, F. Karmous, F. Lahoucine, J-M. Panel, P. Puglièse and G. Vian for their help with the cryo-cell development; E. Ando, J. Desrues and P. Charrier for tomography at 3SR; E. Bretin, J.-O. Lachaud, E. Oudet and T. Roussillon for their implication in the phase-filed model.
Funding: ANR DigitalSnow (ANR-11-BS02-009-03); 3SR is part of the Labex Tec 21 (ANR-11-LABX-0030), CEN is part of the Labex OSUG@2020 (ANR-10-LABX-56)
References:
Bretin, E., R. Denis, F. Flin, J.-O. Lachaud, E. Oudet, T. Roussillon (2015), Discrete-Continuous approach for deformable partitions, Technical
Report 4 of ANR DigitalSnow Project.
Calonne, N., F. Flin, C. Geindreau, B. Lesaffre and S. Rolland du Roscoat (2014), The Cryosphere, 8(6), 2255–2274, doi:10.5194/tc-8-2255-2014.
Calonne, N., F. Flin, B. Lesaffre, A. Dufour, J. Roulle, P. Puglièse, A. Philip, F. Lahoucine, C. Geindreau, J.-M. Panel, S. Rolland du Roscoat and P.
Charrier (2015), Geophys. Res. Lett., 42, doi: 10.1002/2015GL063541.
Flin, F., J.-B. Brzoska, B. Lesaffre, C. Coléou and R. A. Pieritz (2003), J. Phys. D. Appl. Phys., 36, A49-A54, doi: 10.1088/0022-3727/36/10A/310.
Flin, F. and J.-B. Brzoska (2008), Ann. Glaciol., 49, 17–21, doi:10.3189/172756408787814834.
Kämpfer, T. U. and M. Plapp (2009), Phase-field modeling of dry snow metamorphism, Phys. Rev. E, 79 (3), 031502,
doi:10.1103/PhysRevE.79.031502.
Krol, Q., H. Löwe, Analysis of local ice crystal growth in snow, J. Glaciol, 15J181, in press.
Löwe, H., F. Riche and M. Schneebeli (2013), The Cryosphere, 7(5), 1473–1480, doi:10.5194/tc-7-1473-2013.
Pinzer, B., M. Schneebeli and T. Kämpfer (2012), The Cryosphere, 6, 1141–1155.
Srivastava, P., P. Mahajan, P. Satyawali and V. Kumar (2010), Ann. Glaciol., 51, 73–82.
C13C-0818
[email protected]@meteo.fr
1mm
t = 0 hour t = 28 hours
z
z z
z: direction of gravity
conv
ex
conc
ave
conv
ex
conc
ave
Based on the following principles:
-thermal regulation using 2 Peltier modules at top and base of the sample
-thermal insulation from room temperature using a vacuum chamber
-an amovible conductive sample holder that protects specimens during
their installation into the cell
~5.5 mm
Approach 1: Growth rates measurements
Binary image – interface in blueIn red: new position of the interface
linear regression
Sublimation-deposition model (see e.g., Flin et al, 2003; Krol and Löwe, in press):
j = αk (Cmean- C)
3D images with curvature fields
Enlarged views
Vertical cross-section
Interface velocityestimated between 0 and 28 h
� αgrowth_rates = 5.10-4
Approach 2: Phase-field model
� αphase-field = 7.10-3
z
x
deposition: +5.10 -10 m s -1
sublimation: -5.10 -10 m s -1y
Cmean= 7.4 mm-1
Cmean= 6.3 mm-1
Experiment
t = 0 hour t = 28 hours
Phase-fieldmodel
tadjusted = 13 hours tadjusted = 28 hours
Similar structure
200
voxels
~ 2 mm
Large scatterin the measurements + 38 mm -1
-38 mm -1
