One effect which modifies the ice-water and ice-snow interface the is the small scale rough-ness. The assumption of negligible roughness at the interfaces at L-band due to the long wavelength is a strong simplification especially at the sea ice bottom. To investigate in this effect a small correction for the Fresnel reflection for rough surfaces from Choudhury et al. [1979] is introduced as
Rp,rough(θ) = Rp(θ) · exp(−4σ2(2π/λ)2· cos2θ), (5.8) with σ as standard deviation, R and Rrough as Fresnel reflection and modified Fresnel re-flection respectively and p as the polarization. The exponent of the cosine term of the incidence angle dependence is critically discussed in literature and also the standard devi-ation was found to not adequately represent roughness effects properly. It is suggested to use the autocorrelation of the roughness (correlation length) to improve the modification of the transmitted radiation through the rough interface [Mätzler, 2006, Choudhury et al., 1979]. However, as first approximation we are mainly interested in the characteristics of a surface roughness on the brightness temperatures. Figure 5.15 shows different combination for surface and bottom roughnesses for each dielectric model (rows) for three different ice thicknesses (columns) for a surface temperature of −20◦C at nadir. For dice= 50 cm, for the frazil and Vant models, the main sensitivity is found along the surface roughness axis because all effects emerging from the bottom roughness are hidden due to emission and absorption along the propagation path through the ice. Changes in the bottom roughness are still visible in the brightness temperatures for the weak absorbing columnar dielectric model. In case of thin ice at SIT=2 cm the Vant model shows a strong sensitivity to the bottom roughness because most radiation emerging from the water is reaching the surface as the absorption within the ice is small. The columnar model which also has a weak absorption shows higher brightness temperatures than the Vant model at small bottom
5.2. Revision of modeling
roughnesses at SIT=2 cm. In the frazil model the strong absorption is dominating and no sensitivity to bottom roughness is visible regardless of the ice thickness. In addition, the frazil ice model shows lower variability of brightness temperatures.
Figure 5.15 shows that the brightness temperatures using the frazil ice model and the Vant model (at higher bottom roughnesses) become smaller with increasing ice thickness.
The surface layer has the same temperature at all ice thicknesses, thus have the same trans-missivity through this layer independent of the ice thickness. However, the layers below are warmer at smaller ice thicknesses which increases the resulting brightness tempera-tures. Therefore, in case of rough sea ice bottom conditions, where most radiation from the water is penetrating through the water-ice boundary further ice growth can only lower the resulting brightness temperatures in this simulation. With the columnar ice we see an exception which needs further explanation. For the discretization of sea ice thicknesses, different intervals are chosen, but the 2 cm case should be an earlier ice development stage which can lead to the 10 cm and finally to the 50 cm case. This also means that the salinity of the bottom of the 2 cm case is very high due to the fast ice growth. High salinity at high temperatures, however lead to large brine volume fraction and thus to higher refractive indices and eventually to a higher transmissivity through this interface. The absorption and emission in the columnar model is so small that the increase of bottom roughness is the dominating effect for the resulting brightness temperatures. The Vant model seems not affected because its valid range of brine volume fraction is exceeded for such a saline warm sea ice case and returned refractive indices by the Vant model are somewhat smaller than expected.
In reality we expect the water to ice interface to be more structured rather than con-taining statistical roughness as shown in previous studies [Kovacs, 1996, Assur, 1960]. In addition, the structure will be oriented along the direction of the current, often called C-axis [Petrich and Eicken, 2010, Untersteiner, 1986]. It was also shown that this oriented structure can cause anisotropic effects in lower microwave frequencies [Golden and Ackley, 1981].
Most investigations the roughness of the sea ice surface focus on large scale roughness with respect to microwave emission either as deviation of orientation, i.e. the incidence angle, or even distribution of thicknesses Apinis and Peake [1976], Menashi et al. [1993], Stroeve et al. [2006]. For the small scale surface roughness only few in-situ measurements were taken [Paterson et al., 1991, Manninen, 1997, Drinkwater, 1989] even though it is an important quantity for SAR and other Radar based methods [Drinkwater and Crocker, 1988, Nghiem et al., 1995]. The small-scale roughness is quite variable for different ice types and is mainly within the range of 5 mm to 30 mm [Paterson et al., 1991, Nghiem et al., 1995].
When considering higher incidence angles the effect of surface roughness on Tb,V is
Figure 5.15: Brightness temperature for different combinations of bottom roughness and surface roughness for sea ice (without snow cover). Sea ice growth simulated with a CFDD based model.
5.2. Revision of modeling
much less than on Tb,H. Therefore, at high incidence angles, the polarization difference Q is also influenced by the surface roughness in addition to the influence from the snow cover as discussed (see Figures 4.16 and 4.20).