Frequency difference (19-37)Tg (passive data).

The difference in the brightness temperatures for same polarization for the two frequencies 19 and 37GHz are plotted as (19-37)Tg^ and (19-37)Tgj^.

The difference in the value of the measured brightness temperature at the two frequencies is due to the different depths of penetration at the two frequencies, and to the ftequency dependence of the emission of the snowpack due to the change in dielectric constant with frequency.

The 19GHz data will include emission from subsurface layers whereas the 37GHz data is from the near surface material. The typical penetration depth of 19GHz and 37GHz radar into snowpack is given by Ulaby et al. (1986), and is of the approximate order of metres (m) for 19GHz and centimetres (cm) for 37GHz; with the actual values depending on various factors including the wetness of the snow and ice particle size, together with the layering details of the snowpack, the presence of inhomogenieties and impurities, and the temperature etc.

The emissivity of the snowpack layers is also frequency dependent as the dielectric constant of snow is largely dependent on the water content, and the dielectric constant of water is frequency dependent The values of the dielectric constant of water may be calculated from the Debye equation (Equation 3.10) as follows:

dielectric of water at 19.2 Ghz and 37 Ghz from Debye equation:

where f^ = 18.64 GHz, relaxation frequency of water molecules, and f is the operating frequency of the radar, giving:

Erfw(i9.2) - 2 0 , tan5f^(i9 2) = 1.5 for 19.2 GHz, and

Erfv,(37) = 8, tan^f^(37) = 2.5 for 37 GHz.

The measurements from the AIRSAR system are accurate to ~ldB for total power values from the JPL internal calibration for each campaign. The polarization stability is better than this (A. Freeman, personal communication). Using the power ratio classification method, taking the ratio for the retum power of the two linear co polar signals (VV/HH power) and the relative phase difference for these two polarization states (W -H H phase) therefore gives a greater accuracy.

The effect of the variation in the value of the local incidence angle due to the change of slope of the ice sheet should be taken into account. Details of the local surface slope of the ice sheet (mean slope, and estimated direction of the slope) may be gained using the slopes database derived from ERS-1 radar altimeter data for areas ~25*25km^ (J. Morley, personal communication). For the dry zone of the ice sheet the mean slope is negligible (-0®) but for the ablation zone at the edge of the ice sheet the surface slope may be as much as 8®. The particular geometry for the system and the imaged area should be considered. The local incidence angle may be calculated from the values of the flight direction of the imaging system and the viewing angle, together with the relative direction and value of the surface slope.

aeroplane ground track Ro> imaged area _azimuth direction and ideal direction of surface slope near

range

far range

Figure 3.12: Geometry of AIRSAR system showing effect of surface slope on calculation of local incidence angle, where Ro = slant range to near edge of image, R = slant range to imaged point P, 0 = incidence angle at point P and h = altitude.

Note that for the AIRS AR system, flying up or down the ice sheet in the direction of the main surface slope would keep the local incidence angle constant as the direction of the wave incident on the surface from the imaging radar (viewing to one side of the plane) is perpendicular to, and therefore unaffected by, the surface slope. Details of the AIRS AR flight direction and surface slope values for the images of each zone of the ice sheet are discussed in chapter 5.

The passive data as measured by the SSM/I are average values, taken over a large area (~25*25km^), and processed into the gridded data. The relative direction of the flight direction and that of the surface slope should be considered.

For the work undertaken in this thesis, the mean daily brightness temperature for each area is considered. This mean signal is taken from the average value of the 6 daily passes of the satellite, 3 day and 3 night (3 ascending and 3 descending passes). The effect of the surface slope is reduced by considering the mean value of these different passes. The local incidence angle for the ascending passes due to the surface slope is different to that of the descending passes, and the effect of the surface slope is masked by taking the average daily value of the data.

If data from a single pass are used, then, when using the inversion technique, the surface slope of the ice sheet should be taken into account The change in surface slope is greatest for the ablation zone (8°), resulting in a potential change in local incidence angle of ±8®. For the SSM/I system the local incidence angle may change from 53.2® by ±8® , giving a range of possible local incidence angles from 45.2® to 61.2®. If the local incidence angle is known, then the theoretical polarization ratio for a range of dielectrics may be computed for this specific value of incidence angle and the dielectric constant of the imaged surface may be inferred from the measured polarization ratio data. The % wetness content can then be calculated without introducing any additional errors from the surface slope.

If data of the surface slope are not available, the error in predicting the dielectric value of the surface will result in errors in the calculation of the % wetness content The theoretical

the water content may then be determined for each calculation as necessary.

Using information of the value and direction of the surface slope from the slopes database derived from altimeter data to determine the local incidence angle, and then computing the theoretical polarization ratio for the amended incidence angle avoids these errors for the inversion technique. This combines data from active radar and the passive system to produce information on % wetness content of a particular area of the ice sheet