Geoscience Reference
In-Depth Information
sensitivity of DT
B
to changes in SWE. This result holds for ideal snow and demonstrates
the possibility that the saturation value is not globally fixed. For example, with an
uncertainty of 2 K in observed brightness temperature difference and a SWE error
threshold of 10 mm for the uniform snowpack in Fig.
1
, the saturation SWE rises to
195 mm, equivalent to 108 cm depth.
However, in real situations, this is non-trivial to determine, as simulating the radiative
transfer of actual snow profiles leads to additional uncertainty in DT
B
ð
SWE
Þ
which must
also be considered. Given an optimistic assessment of our ability to simulate radiative
transfer in snow and observational uncertainties, this saturation threshold will be assumed
to limit the utility of passive microwave measurements to snowpacks of\180 mm SWE or
under 1 metre in depth.
Davenport et al. (
2012
) showed clearly that the functional form of DT
B
ð
SWE
Þ
depends
on the microstructural properties of the snow. The physical basis of DT
B
's sensitivity to
microstructural properties can be explored by assuming that the snow is a collection of
spheres in each other's far fields, for which the single scattering properties can be cal-
culated from Mie theory. In particular, the single scattering albedo is actually a function of
the size parameter x
¼
2pr
k
where r is the radius of the scatterer and k the wavelength.
Single scattering properties for non-spherical grains have also been determined (Teschl
et al.
2010
), although radiative transfer models (RTMs) generally assume sphericity.
Critically, it is the ratio of scatterer size to wavelength, which determines the single
scattering parameters, and so the retrieved signal is strongly affected by the size of the
scatterer as well as the wavelength of the light. Figure
2
shows the brightness temperature
differences assessed for snow with scatterer diameters ranging from 0.2 to 1.0 mm in
0.2 mm increments, and Table
2
shows how the Chang sensitivity depends strongly on this
value. Grains of 0.2 mm diameter are typical of fresh snowfall and 1.0 mm of moderate-
sized depth hoar at the bottom of snow layers, although larger and smaller sizes do occur.
From Fig.
2
and Table
2
, it can be seen that the saturation value of the signal will also
depend on the properties of the snow.
The Mie approach provides useful physical insight about scattering of radiation in snow,
but any observations of the structure of real snowpacks show that snow is a complex,
porous medium and as such these microstructural parameters are accounted for in a number
of ways, such as specific surface area (SSA), optical grain size and correlation length. The
optical grain size approximation comes from modelling the snow as a collection of spheres
in each other's far fields, with the optical grain size defined as the spherical grain size
required to reproduce the optical properties of the real snow. This size can vary with
wavelength and with grain shape (Macke et al.
1996
).
Grenfell and Warren (
1999
) found that if the optical properties of non-spherical snow
were modelled using spheres, then spheres with the same SSA best matched the optical
properties of the snow, for which the diameter can be determined from other properties
using;
D
q
¼
6M
qS
ð
3
Þ
where M is the total snow mass in a selected volume, q the snow density and S the total
ice-air interface area.
Correlation length is defined as the gradient of the spatial autocorrelation at a dis-
placement of zero, and like specific surface area is defined independently of grain shape. It
can be calculated from mean intercept lengths, by numerical analysis of the autocorrelation
