Provided with a 6 GHz radar bandwidth, the best (theoretical) range resolution of RAASTI is 25 mm (in vacuo). However, RAASTI is an instrument that measures the time separation between returns. Hence, the refractive index is used to estimate the velocity of propagation of the EM waves in the media, in order to map time to distance. The velocity of propagation in a medium as a function of the refractive index is given by:
v= c
3.3. SENSITIVITY OF SNOW THICKNESS ESTIMATES TO ERRORS IN REFRACTIVE INDEX 57
0
1
2
3
4
5
6
7
8
9
10
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Snow wetness per volume (%)
Refractive index (n
ws)
@ 2GHz
@ 5GHz
@ 8GHz
Figure 3.13: Refractive index at the frequencies 2, 5, and 8 GHz as a function of increasing snow water content. The values demonstrate that equation 3.8 will remain satised even with increasing snow wetness, hence the reection from the snow/ice interface can be expected to be stronger. However, this ignores the increasing power losses of the EM radiation in a wet snow pack, which is further explored in the text.
Knowledge of the refractive index is imperative to accurately deriving the snow layer thickness, hence it is necessary to gauge the sensitivity of the radar to errors in estimates of the refractive index.
In dry snow, the density of the snowpack is considered the dominating factor affecting the refractive index (Hallikainen et al., 1986; Galley et al., 2009). An average snow density value of300kgm−3 results in a refractive index of 1.24 (calculated afterGalley et al., 2009). Table 3.3
summarises the percentage error in distance as a function of increasing error in density.
However, as snow over sea ice in Antarctica is frequently wet, similar calculations (using equations for refractive index provided byGalley et al.[2009]) are also provided here for the average snow and sea ice conditions. As wet snow will be a dispersive media, table 3.4 summarises the calculated refractive index for wet snow as a function of the frequencies: 2, 5, and 8 GHz. (Average snow wetness of 0.65% (Massom et al., 2001)is combined with a nominal snow density of300kgm−3 is used in calculating the values in the table.) Fortunately, as the results in table 3.4 show, wetness
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 4 5 6 7
Snow wetness per volume (%)
Absorption Length (l a ) (m) @ 2GHz @ 5GHz @ 8GHz
Figure 3.14: The absorption length (or the penetration depth) of the EM radiation at 2, 5 and 8 GHz as a function of increasing snow wetness. The large difference in penetration depth over the frequency range indicates that it is likely that a wet snow pack degrades the range resolution of the radar by preventing reection of the higher frequencies.
does not have a strong dispersive effect on the refractive index over these frequencies. However, as the last row of table 3.3 however shows there is increasing error made in distance calculations under wet snow conditions.
The values in table 3.3 demonstrate that the error in refractive index due to even a 90% error in density is small. This can explained by the relatively large and dominating factor of the propagation velocity6, combined with the relatively thin snow thickness over sea ice7, resulting in
a high tolerance for error in density measurements when the snow thickness is relatively shallow. This has important implications for the many layered (and hence of variable density) snow pack present on sea ice in Antarctica, i.e. it may not always be necessary to quantify the density of each layer.
The measurement of the density and wetness of the snow pack is subject to commission and ommission errors. A commission error may be committed when, due to the heterogeneous nature of the snow pack, density measurement of each layer in the snow may not be feasible (for example,
6Similar results are mentioned byMarshall et al.[2008b]. 7Taken here to be 1 m, as a conservative estimate.
3.4. BACKSCATTERING COEFFICIENT ESTIMATION 59
thin crusty layers with the largest density are ignored), and/or wetness measurements with the required vertical resolution into the snow prole are not made. The values in tables 3.3 and 3.4 demonstrate that sampling every layer in the snow pack is not necessary under dry snow conditions, however, in cases where a wet snow pack is expected, accurate knowledge of density becomes more important in conversion of radar delay time to thickness. In addition, the advantage of regional-scale remote sensing of snow thickness would be compromised if the values in these tables showed that the density and wetness estimates of the snow pack needed to be known with high accuracy in order to avoide large errors in snow thickness estimates. The values in table 3.3 show that for a dry snow pack a 90% error in density contributes approximately a 20% error to snow thickness (for example, if the snow thickness is 20 cm, this is gives a 4 cm error in snow thickness, which is just above RAASTI’s vertical range resolution), consequently there is some tolerance to ommission error in in-situ sampling of snow density. Notably, under wet snow conditions density estimates become more important, and if it is suspected that the snow to be studied will have liquid water content, then more regular sampling of snow density may be required.
It should also be noted that the effect of wetness coupled with an increase in salinity within the snow is not considered. The change in refractive index according to changes in salinity are being studied in depth (Goldsetzer et al., 2009). Under these conditions, dispersion and additional power loss of the EM signal do occur (Marshall and Koh, 2008a). This could further contribute to ambiguity in interface identication, and further work in this area is necessary.
ρ= 300kgm−3 ρ ρ+ 33% ρ−33% ρ+ 50% ρ−50% ρ+ 90% ρ−90%
nds 1.24 1.32 1.16 1.36 1.12 1.47 1.02
error in distance (%) 0 6.64 6.50 10.1 9.79 18.4 17.4
nws(5GHz) 1.26 1.34 1.18 1.38 1.14 1.48 1.05
error in distance (%) 0 6.06 6.72 8.95 10.5 15.2 20.2 Table 3.3: Error in snow pack thickness calculations as a function of error in density for dry snow (nds) and wet snow (nws). (Refractive index calculated after Galley et al.,2009.)