Measuring specific surface area of snow by near-infrared photography


Measuring specific surface area of snow by
near-infrared photography

Margret MATZL, Martin SCHNEEBELI
WSL Swiss Federal Institute for Snow and Avalanche Research, Flüelastrasse 11, CH-7260 Davos Dorf, Switzerland

E-mail: schneebeli@slf.ch

ABSTRACT. The specific surface area (SSA) is considered an essential microstructural parameter for the
characterization of snow. Photography in the near-infrared (NIR) spectrum is sensitive to the SSA.
We calculated the snow reflectance from calibrated NIR images of snow-pit walls and measured the
SSA of samples obtained at the same locations. This new method is used to map the snow stratigraphy.
The correlation between reflectance and SSA was found to be 90%. Calibrated NIR photography allows
quantitative determination of SSA and its spatial variation in a snow profile in two dimensions within an
uncertainty of 15%. In an image covering 0.5–1.0 m2, even layers of 1 mm thickness can be documented
and measured. Spatial maps of SSA are an important tool in initializing and validating physical and
chemical models of the snowpack.

1. INTRODUCTION

The specific surface area (SSA) is an essential microstructural
parameter for the characterization of sintered materials such
as snow (German, 1996). The SSA of snow changes during
isothermal and temperature-gradient metamorphism
(Schneebeli and Sokratov, 2004; Legagneux and Dominé,
2005) and determines the radiative properties of snow
(Warren, 1982; Leroux and others, 1998). The SSA is a
highly relevant parameter for the catalytic effect caused by
photochemical properties (Dominé and Shepson, 2002). It is
also likely that the permeability of snow (Albert and Perron,
2000) is determined by SSA, as German (1996) shows is true
for other sintered materials.

In this paper, SSA (mm–1) is defined as the ratio between
surface area and the volume of the ice phase.

Natural snowpacks consist of morphologically different
layers (Colbeck, 1991). The complexity of the stratigraphy
(Pielmeier and Schneebeli, 2003; Sturm and Benson, 2004)
usually precludes a detailed and exhaustive sampling of
snow to determine SSA. Current methods of determining
SSA, such as adsorption (Legagneux and others, 2002),
microtomography (Brzoska and others, 2001; Schneebeli
and Sokratov, 2004) and stereology (Matzl and Schneebeli,
2006), are restricted to relatively small snow samples and
confined to essentially point measurements. These methods
also require a cold laboratory, and are relatively time-
consuming. Thus, a method that could deliver spatial
information on natural snow profiles while requiring only
simple equipment would make the measurement of SSA
more accessible. Such a method could also be extremely
valuable in initializing and validating numerical simulations
of snowpack metamorphism (Brun and others, 1989;
Lehning and others, 2002).

Warren and Wiscombe (1980) used Mie theory to
describe the optical properties of snow in the near-infrared
(NIR) spectrum. Based on this theory, the reflectance
between wavelengths of 750 and 1400 nm is controlled
largely by snow grain size. The influence of snow density can
be neglected, as the interparticle distances between the
grains are still large compared with the wavelength. Accord-
ing to Dozier (1992), the grain-size effect dominates in the
NIR spectrum as long as the snow density is < 650 kg m–3.

Impurities influence the reflectance of snow only in the
visible spectrum, but not in the NIR spectrum (Warren and
Wiscombe, 1980; Leroux and others, 1999). As a conse-
quence, the dependence of snow reflectance on grain size is
used in remote sensing to map grain size in the surface snow
layer (Dozier and others, 1981; Nolin and Dozier, 2000).
Giddings and LaChapelle (1961) speculated that the most
appropriate definition of the optically relevant grain size of
snow could be derived from the volume : surface ratio, the
inverse ratio of the SSA. This speculation has yet to be verified
experimentally. Grenfell and Warren (1999) reviewed pre-
vious works on the importance of the volume : area ratio for
explaining optical properties of snow and clouds. But
Mitchell (2002) showed theoretically that the SSA could be
directly converted to an effective optical diameter. This
suggests that SSA provides a direct link between optical and
structural snow properties. Wiesmann and others (1998)
correlated scattering and absorption coefficients at micro-
wave frequencies to the correlation length of snow particles.
Mätzler (2002) showed that correlation length is equivalent
to SSA per total volume.

In a related but different problem, there is no simple way
to document the stratigraphy observed in a snow pit. The
translucent snow profile (Benson, 1962; Good and Krüsi,
1992) is perhaps the best-known attempt to map layer
features more quantitatively. The translucent profile delivers
a clear delineation of boundaries between layers, but the
transmitted light intensity cannot be interpreted in a unique
fashion, because transmissivity depends not only on grain
size but also on snow density (Zhou and others, 2003) and
section thickness. Experiments comparing NIR photographs
on film and translucent profiles showed the feasibility of
using an NIR photographic method (Haddon and others,
1997), but analogue photographs were cumbersome to
process quantitatively. Here we describe a new method
based on NIR digital photography that can be used to
determine the SSA and map the pit stratigraphy. The NIR
reflectance was compared with measured values of SSA for
precisely located snow samples. The correlation between
the two measurements was about 90%, with an uncertainty
of 3–15%, where the uncertainty increases with increasing
SSA. Based on this correlation function we have calculated
the SSA for the NIR images. The SSA can be mapped with a

Journal of Glaciology, Vol. 52, No. 179, 2006558

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spatial resolution of approximately 1 mm in an image
covering a profile wall with a size up to 1 m2. Even thin
layers, which can hardly be detected by traditional methods,
can thus be detected in the images.

2. METHOD
The correlation between SSA and snow reflectance required
an experimental design that allowed measurement of both
parameters for the same snow samples. The reflectance of a
snow profile wall was measured using digital photography in
the NIR spectrum (section 2.1). Subsequently, snow samples
containing specific layers were taken from the same snow
wall. The SSA of the snow samples was determined using
stereological methods (section 2.2) described by Matzl
(2006). The reflectance of these samples was calculated
from the NIR images. Reflectance and SSA were correlated
for easily distinguishable and preferably homogeneous
layers (section 2.3). Figure 1 illustrates the experimental
design. The correlation function was then used to calculate
the SSA for the whole NIR image of the snow-pit wall.

2.1. NIR photography
The camera used for the digital photographs was a Kodak
DCS420ir with a 20 mm Nikkor lens. A gelatine filter (Kodak
Wratten 87c) was placed over the charge-coupled device
(CCD). The wavelength of the detected light ranged from
840 to 940 nm. The distance between camera and profile
wall varied between 1.5 and 2.0 m, resulting in pit wall
photos varying from 0.5 to 1.0 m2. Before the photographs

were taken, the profile wall was cut carefully with a saw and
smoothed with a rounded-edge wooden board about 20 cm
in width.

To compensate for tilting or turning of the camera with
respect to the profile wall, a geometrical correction was
performed on the digital image. The correction required at
least three targets, inserted in the profile wall with a known
distance to each other and a known geometry (Fig. 1a). The
nearest-neighbour method was used to transform the target
coordinates in the digital image congruently with their
original geometry and distance.

The calibration targets were manufactured of Spectralon
greyscale standards with NIR reflectances of 50% and 99%.
Alongside the geometrical correction, these reflectance
values corrected illumination variations by interpolation
between the 50% targets and subtracting the interpolation
from the original image. The NIR reflectance, r, of the snow
was calibrated with regard to the pixel intensities of the
targets:

r ¼ a þ bi , ð1Þ
where i is the intensity of each pixel and a and b are
determined by a linear regression on the pixel intensities of
the greyscale standards. The coefficient of deviation of the
reflectance from the calibrated image measured at the white
targets is 2.6%.

After photographing the smoothed wall, a second image
of the profile wall was taken, including the inserted
containers of the snow samples (Fig. 1c). The comparison
of the two images allowed us to define the exact sample
coordinates in the first image. The reflectance signal was

Fig. 1. (a) NIR image of a snow-pit wall with four calibration targets (i) in the corners. The locations of the sample containers are marked with
a black frame. (b) Magnification of the NIR image at one sample location. The vertical distribution of the reflectance signal for this sample is
calculated based on the pixel intensity of the targets (i). (c) Image covering the same snow-pit wall with the inserted sample containers (ii).
The surface section of one sample is displayed (d) and also the corresponding measured specific surface area (SSA) values.

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calculated by averaging horizontally over the 65 mm width
of the image covering the sample location (Fig. 1b), thereby
producing a graph of SSA with height.

2.2. Measuring the SSA from surface sections
Samples with a volume of approximately 70 � 70 � 50 mm
were cast with dyed diethyl phthalate and frozen for

transport to the cold laboratory (www.slf.ch/schnee-
lawinen/Schneephysik/Downloads/CastingSnowPhthalate/
phthalatesamples-en.html). In the cold laboratory, vertical
surface sections were cut using a Leica Sliding Microtome,
and photographed. The resulting images had a resolution of
10 mm, a width of 10–25 mm and a height of 30–60 mm
(Fig. 1d). The SSA from the vertical surface sections was

Fig. 2. Surface section and NIR image of two snow samples and the derived density, specific surface area (SSA) and reflectance signals. For
sample 2 the absolute height of the surface section and the NIR image vary. The grey bands mark visually identified layers.

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measured using model-based stereology (Baddeley and
others, 1986; Matzl, 2006). Stereological estimations were
also used to determine the volume density of the snow
samples, which allowed the further calculation of snow
density. The snow type of the surface sections was deter-
mined visually according to the International Classification
of Snow (Colbeck and others, 1990).

For very fine new snow particles the resolution of the SSA
measurements leads to an underestimation of the SSA. We
experienced such an underestimation for SSA values higher
than approximately 55 mm–1. For the correlation in this
study we used snow types of explicit smaller SSA.

2.3. Correlation of reflectance and SSA
For each sample we visually identified discrete layers,
defined as zones of vertical homogeneity with lateral extent.
The mean SSA and the mean reflectance were calculated for
each layer. These values were used for correlating SSA and
reflectance. Samples with strongly inclined layers were
excluded.

3. RESULTS
Figure 2 gives an overview of all the measured parameters.
Density and SSA are stereological estimates from the
segmented surface section, while the reflectance is calcu-
lated from the NIR image. Corresponding layers are marked
for the SSA and the reflectance signal.

In total, 29 samples were obtained from field measure-
ments. For each sample, we identified between one and
three layers for which mean reflectance and SSA were
measured. Figure 3 shows the scatter plot of reflectance and
SSA for all layers. For a comparison with existing data we
choose values published by Warren and Wiscombe (1980),
Dozier (1992) and Sergent and others (1993) at 890 nm. We
transformed the optical sphere diameter, d, used in these
publications to SSA using:

SSAsphere ¼ 6=d : ð2Þ
To avoid an overweighting of the intermediate reflectance
class, we grouped our data in reflectance classes of 5%. Six
measurements per class were randomly selected. The
regression was calculated based on these stratified samples.

The scatter plot shows an exponentially growing relationship
between SSA and reflectance, r:

SSA ¼ Aer=t , ð3Þ

where A ¼ 0.017 � 0.009 mm–1 and t ¼ 12.222 � 0.842.
The correlation coefficient, R2, is 90.8% at a significance
level p < 0.002. The error increases with increasing SSA from
4% at an SSA of 5 mm–1 to about 15% for SSA values of
about 25 mm–1. Alternatively, a linear fit of the reflectance vs
square root of grain diameter was tried, based on the
simplified equation in Wiscombe and Warren (1980). In this
case the correlation coefficient, R2, is 89.5% at a signifi-
cance level p < 0.0001.

The scatter plot of density and SSA for the same snow
layers shows that we included snow types with a wide range
of densities and SSA values (Fig. 4). It can also be seen that
low-density snow covers the whole range of measured SSA,
and samples with a low SSA cover a wide range of densities.

Figures 5 and 6 show a quantitative two dimensional
(2-D) mapping based on Equations (1) and (3). Figure 5 also
shows a conventional hand profile. The photograph corres-
ponds with the hand profile. Note that the ice crust at a
height of 73 cm and the boundary at 36 cm are very distinct.
Not only layers are mapped but also gradual transitions (e.g.
that between 57 and 60 cm height). The SSA varies between
1 mm–1 for the lower parts of the profile and for the ice crust,
and 27 mm–1 for the upper parts of the profile.

Figure 6 shows an NIR image with inhomogeneous
illumination. The upper-left part of the profile is too bright.
However, it is still possible to recognize features such as the
melt crust in the upper third of the profile or the infiltration
zone below.

4. DISCUSSION
The SSA and reflectance of a wide range of snow types were
measured. An increasing reflectance is correlated with an
exponentially increasing SSA. We did not observe any
systematic difference between snow type and the fitted line.
This result supports the assumption of Giddings and
LaChapelle (1961) that SSA is the most important parameter
determining snow reflectance in the NIR spectrum.

The comparison with data published by Wiscombe and
Warren (1980), Dozier (1992) and Sergent and others (1993)
shows good agreement with our observations for SSA values

Fig. 3. Scatter plot of measured specific surface area (SSA) values vs
reflectance with a fit (solid line; Equation (3)). The dotted line
indicates the relationship between reflectance at 890 nm and SSA
based on published values by Wiscombe and Warren (1980),
Dozier (1992), and Sergent and others (1993).

Fig. 4. Scatter plot of SSA and density.

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below approximately 20 mm–1 (Fig. 3). There are three
possible explanations for the difference for SSA values
greater than 30 mm–1. (i) The calibration targets may have
had a lower reflectance than specified because of staining
caused by field use. However, post-calibration indicates that
this effect is not more than 2%. (ii) Our estimated average
wavelength (890 nm) is underestimated. Because the NIR
sensitivity of the camera CCD is unknown, this is a
reasonable explanation. Comparison with figure 9 in
Wiscombe and Warren (1980) shows that our curve is
steeper than expected for 890 nm. (iii) The measured light
intensity was not only reflectance but also light that passed
the snowpack from the snow surface, as the snow surface
behind the profile was not always completely shaded.
Because the snow samples showing a large SSA value were
mostly obtained close to the surface, such an influence
cannot be excluded.

The comparison between density and SSA (Fig. 4) shows a
loose correlation between these properties, as high SSA
values are usually related to low densities and vice versa. For
densities from approximately 150 to 300 kg m–3 a wider
range of SSA values can be observed. This makes a direct
correlation, as suggested by Narita (1971) and Legagneux
and others (2002), very uncertain in this density range. Snow
classes 1–3, which include new snow, partly decomposed
snow and rounded snow, are well discriminated by a
steadily decreasing surface area. Snow classes 4–8, which
indicate stronger metamorphism, are not well discriminated
and cover a larger range of SSA and reflectivity.

The correlation function between reflectance and SSA
was used to calculate the SSA for the NIR images. The
images of the snow profiles (Figs 5 and 6), especially when
combined with a manual profile, show that variations in the
SSA reflect the layering of a snow cover in great detail. The

method ‘visualizes’ layers well and shows the slight vertical
and horizontal structural variations that are otherwise
difficult to record by conventional field methods. Even very
small local differences in the SSA are visible (e.g. an
infiltration zone in Fig. 6).

This method could be improved in several ways. A
homogeneous and diffuse illumination of the profile wall is
essential, because the digital correction of an inhomo-
geneous illumination is not possible without losing the
context to absolute reflectance. We found that in the field
such heterogeneities in the illumination are not detectable
by eye. Figure 6 shows such uncontrolled reflections. The
upper-left part of the profile was too bright, which makes a
quantitative interpretation of this part difficult. The shading
for diffuse illumination must cover at least 0.5 m behind the
profile wall, and must extend over the side walls of the pit.
The method could also be improved by the use of a flat-field
correction. A second image, where a target of constant
colour brightness covers the whole profile wall, is subtracted
from the first image. This method even corrects for very local
illumination heterogeneities and may be used instead of the
digital interpolation between the reference targets, as was
used in this study.

We conclude that the current technique allows us to
visualize relative differences of SSA at a very high resolution.
The SSA on a 2-D image can be measured with an
uncertainty of about 15%. The proposed improvements
could significantly enhance this result.

The ability to measure SSA in two dimensions opens up
the possibility of linking micro- and macroscale measure-
ments of snow structure. SSA of individual layers as well as
the stratigraphy of the snow cover is crucial for physical and
chemical models. Because of the widespread use of SSA to
parameterize air permeability and thermal conductivity of

Fig. 5. SSA mapped for a snow-pit wall combined with a traditional hand profile. Larger boundaries are marked with a dotted line.

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sintered materials (German, 1996), it can be expected that
this should also be possible for snow. Such an extension of
the present work would be very useful in initializing and
calibrating numerical models that simulate the transport and
transformation processes occurring in a snow cover.

ACKNOWLEDGEMENTS
We thank the reviewers, M. Sturm and S. Warren, for
valuable comments and suggestions. The financial support
of the Swiss National Science Foundation (project
No. 200021-101884) is acknowledged.

ADDITIONAL MATERIAL
Additional material describing new digital cameras suitable
for NIR imaging and programs for image processing can be
requested from the corresponding author (M.S.).

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