Cryospheric Sensing Using GNSS-R - GNSS Remote Sensing: Theory, Methods and Applications - page 254

Fig. 11.2 ( Left :) Example of lag-hologram for a time series of N = 128 1-s complex waveforms
in a GNSS-R Dry Snow experiment at Concordia Station (Antarctica). It corresponds to PRN
13, December 16, 2009, between 44.5 ı and 45.5 ı elevation. Here the frequency is given as
interferometric cycles per degree-elevation (conversion from Hz as in Eq. 11.17 ). The zero-
frequency corresponds to the reference field: the direct ray. According to Eq. 11.16 , frequencies
more negatives than 5.8 cycle/deg-el correspond to scattering off reflecting-elements below the

snow-air interface. Note different spectral content for different delay along the waveform. ( Right :)
Lag-hologram of a series of 128 synthesized complex waveforms the geometry of each of them
follow the geometry of the 128 real waveforms in the left panel (From Cardellach et al. ( 2012 ))

Eq. 11.5 for the range of elevations embedded in the time series of observations used
to produce the lag-hologram; and (2) taking its (numerical) derivative with respect
to the elevation angle. The study in Cardellach et al. ( 2012 ) used this approach to
identify a set of sub-surface reflecting layers at the experimental set, located at 10,
70, 130 and 240 m depth, with vertical resolution between 5 and 10 m. The vertical
resolution of the identified layers is mainly given by the length of the time series
used to generate the spectral analysis. Other secondary factors are the geometry (it
is function of the elevation angle).

11.2 Wet Snow Monitoring

11.2.1 Observations from Space-Borne GNSS-R

Snow and ice on the land are important components of climate systems and a critical
storage component in the hydrologic cycle as well. However, in situ observations of
snow distribution are sparse, and remotely sensed products are imprecise and only
available at a coarse spatial scale, e.g., the U.S. Snowpack Telemetry (SNOTEL)
network ( Serreze et al. 1999 ). As the ice thickness is related to the amplitude
of the reflected signal as a function of the incidence angle or relative amplitudes
between different polarizations ( Lowe et al. 2002 ), the snow/ice thickness can be
retrieved from the GPS reflected signals. Komjathy et al. ( 2000 ) has derived the
condition of sea and fresh-water ice as well as the freeze/thaw state of frozen ground
from aircraft experiments with GPS reflections over the Arctic sea ice and ice