APPENDIX C: DETERMINATION OF MICROSTRUCTURAL
VARIABLES BY PLANE SECTION STEREOLOGY
Independent variables measured for snow un-
amples of such variables are measures relating to
dergoing mechanical testing should represent fun-
chains of grains, the number of bonds per grain
damental states or conditions of the snow, includ-
and others.
ing relevant macroscopic and microscopic
Other problems arise because the assumptions
features. Examples of such state variables might
used to convert measurements from plain section
be temperature, density, mean grain size (and or
or thick section images into the desired microstruc-
grain size distribution), mean number and radial
tural parameters are often overly simplified and
cross-sectional area of grain bonds per grain, the
may contain free variables (Gubler 1978a,b; Alley
mean number and length of unsupported chains
1986). In addition, the lack of objective methods
of grains, the mean distance between grains, and
for identifying many structural features in snow
other physically measurable characteristics. While
using plane section and thick section stereology
determining macroscopic state variables can be
has been well recognized (Kry 1975a, Alley 1986,
done reliably, measuring microscopic variables
Dozier et al. 1987).
and determining their significance is problematic.
Stereological methods require relatively large
Attempts to define and determine state vari-
investments in time and effort to construct plane
ables using plane section and thick section stere-
section or thick section samples, obtain good qual-
ology have demonstrated the importance of snow
ity images, and analyze the results. Because of
microstructure on the response of snow to an ap-
these difficulties few experimental studies relat-
plied load (Kry 1975a,b; Gubler 1978a,b; Alley
ing stereological parameters to the deformational
1986; Good 1987; Dozier et al. 1987; Hansen and
behavior of snow have been published since the
Brown 1987; Hansen 1988; Edens and Brown 1991;
work of Voitkovsky et al. (1975) and Kry (1975a,b).
Brown and Edens 1991). However, there are two
Voitkovsky et al. (1975) presented a relationship
difficulties with using stereological methods that
between cohesive force and the number of
need to be taken into account when evaluating
intergrain contacts per unit volume, based on
their usefulness. First, the accuracy with which
about 50 tests in five distinct density categories
stereological methods can be used to determine
while Kry's (1975b) results were based on repeated
many of the parameters they are intended to rep-
experiments on only five snow samples. Gubler
resent is, in general, unknown. While bulk den-
(1978a,b) presented results for the tensile strength
sity and parameters related to the two-dimen-
in terms of microstructural variables from fewer
sional plane section can be determined, extending
than twenty tests, and changes in microstructure
these measures to a three-dimensional represen-
under large deformations have been examined in
tation of microstructural measures requires as-
two studies (Edens and Brown 1991, Brown and
sumptions about the geometry of the material
Edens 1991).
which cannot be rigorously tested (Alley 1986).
We consider it unlikely that microstructural
The accuracy of the determination of the average
measures truly represent those features that di-
number of grains per unit volume (Nv) strongly
rectly control deformational behavior. They may
depends on the grain shape. Errors of more than
eventually be used to derive indexes of deforma-
tional behavior, in the same manner as the index
result from only small variations in grain shape
parameters discussed in the main text in Estab-
(Dehoff and Rhines 1961), and seasonal snow con-
lishing Independent Variables or Index Properties for
sists of grains of complex and variable shapes.
Snow Microstructure, but the effort required to
Thus, estimates of Nv, and variables that depend
measure microstructural variables suggests that
upon values of Nv from plane section stereology
other more easily measured properties should be
should be considered inaccurate (Alley 1986). Ex-
sought.
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