With increased interest in sea ice and its effects on the global climate, efficient methods are required to monitor both its extent and exchange processes. Satellite-mounted, microwave radiometers, such SSMI, AMSR and AMSU, are an ideal tool for the task because they can see through cloud cover, and they have frequent, global coverage. A passive microwave instrument detects objects through emitted radiation since different substance have different emission spectra. To detect sea ice more efficiently, there is a need to model these emission processes. The interaction of sea ice with electromagnetic radiation in the microwave range is still not well understood. In general is collected information limited because of the large-scale variability due to the emissivity of sea ice.
General Satellite microwave data (and visible, infrared data depending on the conditions) collected from sensors assumes that ocean surface is a binary (ice covered or ice free) and observations are used to quantify the radiative flux. During the melt seasons in spring and summer, sea ice surface temperature goes above freezing. Thus, passive microwave measurements are able to detect rising brightness temperatures, as the emissivity increases to almost that of a blackbody, and as liquid starts to form around the ice crystals, but when melting continues, slush forms and then melt ponds and the brightness temperature goes down to that of ice free water. Because the emissivity of sea ice changes over time and often in short time spans, data and algorithms used to interpret findings are crucial.
Effective permittivity As established in the previous section, the most important quantity in radiative transfer calculations of sea ice is the relative permittivity. Sea ice is a complex composite composed of pure ice and included pockets of air and highly saline brine. The electro-magnetic properties of such a mixture will be different from, and normally somewhere in between (though not always—see, for instance, metamaterial), those of its constituents. Since it is not just the relative composition that is important, but also the geometry, the calculation of effective permittivities introduces a high level of uncertainty. Vant et al.
have performed actual measurements of sea ice relative permittivities at frequencies between 0.1 and 4.0 GHz which they have encapsulated in the following formula:
ϵ ∗ = a V b + b {\displaystyle \epsilon ^{*}=aV_{b}+b}
where ϵ ∗ {\displaystyle \epsilon ^{*}} is the real or imaginary effective relative permittivity, Vb is the relative brine volume—see sea ice growth processes—and a and b are constants. This empirical model shows some agreement with dielectric mixture models based on Maxwell's equations in the low frequency limit, such as this formula from Sihvola and Kong
ϵ e f f = ϵ 1 + V b ϵ 1 ( ϵ 2 − ϵ 1 ) / ( ϵ 1 + P ( ϵ 2 − ϵ 1 ) 1 − P V b ( ϵ 2 − ϵ 1 ) / [ ϵ 1 + P ( ϵ 2 − ϵ 1 ) ] {\displaystyle \epsilon _{eff}=\epsilon _{1}+{\frac {V_{b}\epsilon _{1}(\epsilon _{2}-\epsilon _{1})/(\epsilon _{1}+P(\epsilon _{2}-\epsilon 1)}{1-PV_{b}(\epsilon _{2}-\epsilon _{1})/\left[\epsilon _{1}+P(\epsilon _{2}-\epsilon _{1})\right]}}}
where ϵ 1 {\displaystyle \epsilon _{1}} is the relative permittivity of the background material (pure ice), ϵ 2 {\displaystyle \epsilon _{2}} is the relative permittivity of the inclusion material (brine) and P is a depolarization factor based on the geometry of the brine inclusions. Brine inclusions are frequently modelled as vertically oriented needles for which the depolarization factor is P=0.5 in the vertical direction and P=0. in the horizontal. The two formulas, while they correlate strongly, disagree in both relative and absolute magnitudes.
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