Transcript Quantitative interpretation of SMP signals

Quantitative interpretation of
SMP signals
H.P. Marshall
BSU, CRREL
M. Schneebeli
SLF
J. Johnson
CRREL
Snow Characterization Workshop, April 13-15, 2009
Emperical Relationships
• Textural Index [Schneebeli, Pielmeier,
Johnson, 1999, CRST]
TI=1.45+5.72 CV
• SMP hardness
shows good
agreement hand
hardness profiles
• Serial section
shows similar
boundaries and
texture index
trend makes
sense
Emperical Relationships
• Density [Pielmeier, 2003; Stahli et al, J Glac, 2003]
Rho=55.6 * ln(mR)+317.4 [kg/m^3]
[Marshall, 2005]
Emperical Relationships
Thermal conductivity [Stahli et al, J Glac, 2003; Dadic,
Schneebeli, Lehning, Hutterli, Ohmura, in press JGR ]
parameterization of thermal conductivity
using penetration hardness
summit snow profile - top 0.5 m
NIP
SnowMicroPen
Summit Temperature
100 mm depth
300 mm depth
Temperature measured
Temperature simulated 1 mm layer resolution
Temperature simulated 100 mm layer resolution
Summit temperature simulation
simulation
layer thickness
100 mm
1 mm
Hardness analysis
• Spatial variability [e.g. Kronholm,
2003,…]
• Temporal variability [Birkeland et al,
2004, Annals…]
• Weak layer thickness [Lutz et al, 2005,
CRST]
But SMP has detailed
microstructural signal
Similar features can be found in nearby profiles,
and coincide with layer boundaries from manual
profiles and radar measurements
[Marshall, Schneebeli, Koh, 2007, CRST]
Snow under rapid loading
behaves nearly linear elastically
Mechanical Properties
• Physics-based model [Schneebeli &
Johnson, 98, Annals; Johnson and
Schneebeli, 99, CRST]
• Further improvements [Sturm et al, 04
(Manali); Marshall and Johnson, in review,
JGR]
SnowMicroPenetrometer (SMP)
• Micro-scale
measurements
(resolution = 0.004
mm)
• Deflection and rupture
of individual elements
measured
f p  f n cos  f  sin 
f p  f n cos   sin  
N
Fp   f p , n
n 1
(Johnson and Schneebeli, 1999)
Basic structural element
[Johnson and Schneebeli, 99, CRST]
Multiple structural elements
simultaneously engaged with SMP tip
Simulated signal shows similar
structure to field measurements
Retrieval of microstructural properties
2
V

r
z
T
L 3
3
N
N
N
f 
f
n 1
n
N
2

f
f
f r   
Fm  N e  N a Pc   2   
2
2
2  L  L 
Fm z
 N
 fn
n 1
Micromechanical properties
k
f

Emicro
 micro
k

L
f
 2
L
• Mechanical properties are very sensitive to
errors in basic microstructural properties
Improvement to physical theory
• Removed assumption of uniform random
distribution of elements [Sturm et al, Manali, 2004]
   r  d1    r  d 2 
  r  d n 
  
    

FT  f rn   Fn  f rn 1  
n 1
   r    r

 r

N
Use typical parameters, generate
Monte-Carlo, check results
Used Monte-Carlo to simulate signals,
applied theory, and made modifications to
improve accuracy
• Overlapping ruptures
• Solve exactly for delta
• Remove increase in
force during rupture
(digitization)
• Include all force values
in calculation
   d n 
FT   f n 

 

n 0
Ne
Ne

 f d
n 0
Ne
f
n 0
n
n
n
 FT
Correction for overlapping ruptures
Accuracy of retrieving L
Accuracy of retrieving f
Accuracy of retrieving delta
Real data is noisy, includes force
variations not due to ruptures
• Rupture force threshold [Johnson and Schneebeli, 99]
• Rupture slope threshold [Kronholm et al]
• Air signals typically have ruptures ~0.01N
Resulting microstructural parameters are
sensitive to snow type
Application to 4 snow types
Application to 8 snow types
Basic statistics
Emperical Models
Basic microstructural parameters
Derived micromechanical parameters
Scaling to macroscale
Scaling Elastic Modulus
Scaling Compressive strength
Macro scale mechanical
properties important for
modeling stress on slope
Comparison SMP and
traditional stability tests
[Pielmeier and Marshall, ISSW 2008]
SMP profile near failure
interface
Classification of stability based on
SMP analysis
88% total accuracy, 87% stable accuracy,
89% unstable accuracy
Accuracy of classification
Testing changes in strength
with increased load
SMP Orientation
P
SM
1
2
3
I
II
Pit Layout
III
[Lutz et al, ISSW 2008]
26°-28°
0.3
0.2
0.1
S (N/mm2)
0.4
Weak Layer: Micro-Strength S
[ n = 100 ]
[ n = 100 ]
[ n = 100 ]
I
II
III
Column
• Strength estimates agree with stability tests
• Decrease in strength with increasing load
Conclusions
• Major sources of error in micromechanical analysis corrected
• Retrieval of parameters from simulated
signals accurate over wide range of
parameters
• Analysis applied to field studies show
stability can be classified based on
parameters with 88% accuracy
• Provides new rapid method for studying
spatial variability of snowpack stability