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Calculating Sea Ice Concentration from ESMR

Variations in the brightness temperature (TB) observed over the surface of the Earth are caused by variations in the emissivity of the surface material and variations in physical temperature according to the equation:

TB = epsilonT          [1]

This equation is valid for the TB of a uniform surface type with emissivity epsilon and physical temperature T. Within the ice pack, the TB of a pixel area derives from various sources, including atmospheric contributors as well as the water and ice within the field of view. The TB of ice with uniform emissivity is approximated as:

TB = CW epsilonW TW + CI epsilonI TI + TA          [2]


epsilonW = Emissivity of open water
TW = Surface physical temperature of open water
CW = Areal percentage of open water
epsilonI = Emissivity of sea ice
TI = Surface physical temperature of sea ice
CI = Areal percentage of sea ice
TA = Sum of atmospheric and other above-surface contributions, including direct upwelling radiation from the atmosphere, downwelling radiation reflected by the surface, and radiation from space reflected by the surface. Atmospheric opacity in the polar regions is negligible.

Recognizing that CW + CI = 1, the ice concentration CI, can be determined from Equation [2] as:

CI = TB - T0 / epsilonI Teff - T0          [3]


T0 = epsilonW TW + TA, the measured TB of the water
Teff = TI + TA / epsilonI, the effective surface physical temperature.

In the polar regions, the atmospheric contribution to the effective temperature is small because the atmospheric humidity and the water vapor content are very low; therefore, Teff is equal to TI. The appropriate value for TI is the temperature at the top of the sea ice below the snow cover, because most of the observed radiation emanates from a thin top layer of saline ice. In the absence of real-time physical temperature data, TI is estimated from climatological surface air temperatures in Equation [4] below. The temperature at the top surface of the sea ice is calculated as lying between the surface air temperature Tair -- estimated by mean monthly climatological values -- and the temperature of the water underneath the ice:

TI = Tair + f(Tf - Tair)          [4]


Tf = Freezing point of sea water, 271.2 K

f = Empirical parameter determined from the observed TB data, by adjusting f until the values of CI are consistently about 100% during winter. A value of f = 0.25 was used in the Antarctic atlas (Zwally et al. 1983) through examination of the July 1974 data over the Southern Ocean. Later examination of the Northern Hemisphere data showed that f = 0.25 is also appropriate for the Arctic. This value of 0.25 agrees with the overall average of surface measurements made at Pond Inlet in the Canadian Archipelago (R. Ramseier, personal communication). In reality, the magnitude of f varies spatially with the thickness of the ice and snow cover, but f = 0.25 appears to be a reasonable average value.

Analysis of TBs from the open-ocean area in the vicinity of the ice pack allowed determination of T0 for use in Equation [1]. Specifically, the four-year average TB over ice-free areas of the north polar region was calculated from the ESMR observations as 138.3 K. This is the value inserted for T0. Of the 138.3 K, approximately 120 K derives from the water, and the remainder derives from the atmosphere. In the Antarctic, the similarly calculated T0 is 135 K. The 3.3 K difference between hemispheres is caused predominantly by actual differences in the average signature of ice-free ocean in the two hemispheres. It could also be caused in part by variations in the sensitivity of the instrument with temperature. The satellite is exposed to solar heating as it approaches the north polar region but not in the south polar region.

The ice concentration parameter is generated from Equation [2] using T0 = 138.3 K, Teff = TI (calculated from Equation [3]), and epsilonI = 0.92. The emissivity value of 0.92 is estimated from radiative equations appropriate for first-year sea ice, and is confirmed empirically for first-year ice by examination of ESMR data; however, many regions of the Arctic contain significant amounts of multiyear ice, which has an emissivity of approximately 0.84 instead of 0.92; hence, the gridded data can be interpreted directly as ice concentrations only in those grid squares containing open water and first-year sea ice; otherwise, the data should be interpreted using a nomogram in which both ice concentration, C, and multiyear ice fraction, FMY are represented as variables. The crucial element in the generation of the nomogram is the proper placement of the concentration values on the right-hand scale, corresponding to a field of view with exclusively multiyear ice and open water. The right-hand scale on the nomogram was constructed by recognizing that the concentrations CI calculated with a first-year ice emissivity were determined by:

C1 = TB - T0 / 0.92TI - T0          [5]

Where T0 = 183.3 K.

For multiyear ice, the equation is:

CMY = TB - T0 / 0.84TI - T0     = CI[(0.92TI - T0) / (0.84TI - T0)]          [6]

Inserting 248 K as an appropriate overall value for TI, Equation [6] reduces to CMY = 1.283 CI, which is the conversion used in creating the nomogram. In the Arctic atlas, the ice concentration maps and nomograms are color-coded, with, for instance, the boundary between light pink and deep brown occurring at 78% concentration for first-year ice. During periods of surface melting, first-year and multiyear ice are indistinguishable by passive microwave measurements (Parkinson et al. 1987), and the appropriate scale for both ice types is the scale on the left of the nomogram.


Differences between wet and dry first-year ice, which are about 3%, are neglected in the nomogram. The values on tape are termed "pseudo ice concentrations."

This nomogram should be used to interpret pseudo ice concentrations gridded on the magnetic tapes. A given gridded value is associated with a unique ice concentration only if the multiyear ice fraction FMY is known. For instance, in seasonal sea ice regions with only first-year ice, FMY = 0. The appropriate scale is shown on the left of the nomogram, so that the gridded values are indeed the calculated ice concentrations. By contrast, in locations where the observed ice field is all multiyear ice (FMY = 1), then the appropriate scale is on the right-hand side of the nomogram, and the ice concentrations are derived by multiplying the gridded values by 1.283. If no information is known about the multiyear ice fraction, then the nomoram provides the appropriate range of ice concentrations for each gridded value, with the range extending from the gridded value on the left-hand scale to the value horizontally opposite it on the right-hand scale. For instance, a gridded value of 52% indicates an ice concentration anywhere from 52% (if there is no multiyear ice) to 67% (if the ice is all multiyear ice). The nomogram can also be used in an inverted manner to determine the multiyear ice fraction, if there is independent knowledge (or an estimate) of the total ice concentration. This method was done for the Arctic atlas in several cases where the total ice concentration approaches 100%.