# NASA Team Sea Ice Algorithm

Donald J. Cavalieri
NASA Goddard Space Flight Center

Published 1992

### Algorithm Description

In 1985 the NASA Sea Ice Algorithm Working Group (NSAWG) reviewed the state of passive microwave sea ice algorithm development for the purpose of recommending an algorithm for deriving sea ice products from the new DMSP SSM/I. The NSAWG chose three candidate algorithms that had been developed and tested, and selected one of these for processing the SSM/I data. A description of each of the three candidate algorithms and the rationale for selecting the NASA Team algorithm are summarized in Swift and Cavalieri (1985).

The three SSM/I channels used in calculating sea ice concentration with the NASA algorithm are the 19.4-GHz horizontally (H) and vertically (V) polarized channels and the vertically polarized 37.0-GHz channel. This algorithm is functionally the same as the Nimbus 7 SMMR algorithm described by Cavalieri et al. (1984) and Gloersen and Cavalieri (1986). The SSM/I radiances from each of the three channels are first mapped onto polar stereographic grids (the so-called SSM/I grid). The gridded radiances are then used to calculate grids for the two independent variables used in the algorithm. These are the polarization (PR) and spectral gradient ratios (GR) defined by:

```
PR = [TB(19V)-TB(19H)]/[TB(19V)+TB(19H)]                      (1)

GR = [TB(37V)-TB(19V)]/[TB(37V)+TB(19V)]                      (2)
```

where TB is the observed brightness temperature at the indicated frequency and polarization. From these two parameters the first-year ice concentration (CF) and the multiyear ice concentration (CM) are calculated from the following equations:

```
CF = (a0 + a1PR + a2GR + a3PR * GR)/D	(3)
CM = (b0 + b1PR + b2GR + b3PR * GR)/D	(4)
where D = c0 + c1PR + C2GR + c3PR * GR      (5)
```

The total ice concentration (CT) is the sum of the first-year and multiyear concentrations

```                                          CT = CF + CM	(6)
```

The coefficients ai, bi, and ci (i = 0, 3) are functions of a set of nine TBs. These TBs, referred to as algorithm tie points, are observed SSM/I radiances over areas of known ice-free ocean, first-year (FY) sea ice, and multiyear (MY) ice for each of the three SSM/I channels. The algorithm tie points, as well as the coefficients in equations 3 to 5, are given in table 1 (p. 40). The reasons for dropping the FY and MY ice nomenclature and for calculating only CT for the Antarctic are discussed in the next section.

In addition to constraining the solutions to concentrations between 0% and 100%, the algorithm also sets the total ice concentration to 0% for those SSM/I grid cells with GR values greater than preset thresholds. This serves to reduce spurious ice concentrations caused by weather-related effects over ice-free ocean. This so-called weather filter is discussed below.

### SSM/I Tie Points

The selection of the SSM/I F8 tie points (table 1, p. 40) was based on an analysis of SSM/I TBs, PR-GR distributions, histograms of sea ice concentrations, and on comparisons with near simultaneous measurements from the Nimbus-7 SMMR during July and August 1987. The two sets of SSM/I tie points (one for the Northern Hemisphere and one for the Southern Hemisphere) represent a global set designed for mapping global ice concentrations. While this global set of tie points provides a uniform measure of sea ice concentration on the large scale, improved accuracy is obtained with the use of regionally selected tie points (Steffen and Schweiger 1991). Please note that tie points are the same for F8 and F11 data.

The ice-free (open water) tie points were chosen to be near minimum ice-free ocean TBs (corresponding to near maximum values of PR). By choosing near minimum TBs, the PR range between open water and FY ice is about an order of magnitude, permitting greater algorithm sensitivity for detecting changes in ice concentration. Although the Arctic and Antarctic open water tie points were selected independently, the TB difference for corresponding channels is no more than about 1 K (see table 1).

The ice tie point selection was more difficult, since the passive-microwave ice signatures depend on region and season. This is particularly true of Arctic MY ice. Even for a given region and season there is a certain amount of random variability for a given ice type. Thus, there is generally a range of TBs that could be used as tie points. The series of SSM/I aircraft underflights helped in this regard (Cavalieri et al. 1991). Mosaic patterns covering several SSM/I image pixels were flown in the central Arctic over a two-week period in March 1988. Although the mosaicked aircraft data did not provide radiometric coverage at the SSM/I frequencies and polarizations, it did provide a constraint on the ice concentrations, which were calculated from passive and active microwave imagery. This allowed adjustment of the ice tie-points within the range of allowable values to improve the accuracy to within a few percent (relative to the aircraft data).

The need for different ice type tie points for the Arctic and Antarctic results from the very different environmental conditions of the two polar regions. Indeed, the observed physical characteristics of Antarctic sea ice are different from those in the Arctic (Ackley et al. 1980, Wadhams et al. 1987), implying a corresponding difference in microwave radiance characteristics. In the Antarctic the two ice types distinguished by the algorithm are identified as ice type A and ice type B. Examination of table 1 shows significant differences between the Arctic first-year and Antarctic ice type A tie points and between the Arctic multiyear ice and Antarctic ice type B tie points. While ice temperature differences may explain some of the observed tie point differences for corresponding ice types, real emissivity differences are reflected in the polarization and spectral differences. In the Antarctic the radiometric distinction between first-year (seasonal) ice and multiyear (perennial) ice is lost. Unlike the Arctic, where the predominant source of negative gradient ratios is the volume scattering by the empty brine pockets in the freeboard portion of multiyear ice, in the Antarctic, the main source of volume scattering is from sources other than multiyear ice. One very likely source of volume scattering is the snow cover on the sea ice. Snow cover of sufficient depth and of sufficiently large grain size will mimic the microwave signature of multiyear ice.

### Weather Filter

A problem in mapping the polar sea ice covers in both hemispheres has been the false indication of sea ice over the open ocean and at the ice edge. These spurious sea ice concentrations result from the presence of atmospheric water vapor, nonprecipitating cloud liquid water, rain and sea surface roughening by surface winds. While these effects are relatively minor at polar latitudes in winter, they result in serious weather contamination problems at all latitudes in summer (Cavalieri et al. 1992).

This problem was addressed for sea ice concentrations derived from the Nimbus 7 SMMR data through the development of a weather filter (Gloersen and Cavalieri 1986). The filter is based on the polarization (PR18) and spectral gradient ratio (GR37/18) distribution of ice-free and ice-covered seas. If GR(37/18) is greater than 0.07, then the sea ice concentration is set to zero. While this eliminates most of the unwanted weather effects, it also eliminates sea ice concentrations less than about 12% in FY ice regions and 8% in MY ice regions. Applying GR(37/19) filters to SSM/I-derived sea ice concentration maps is less successful because the closer proximity of the 19.35 GHz SSM/I channels to the center of the 22.2 GHz atmospheric water-vapor line makes the 19.35 GHz channels more sensitive to changes in atmospheric water vapor, resulting in greater contamination problems.

A new composite weather filter has been developed (Cavalieri et al. 1994) and implemented in the NASA Team sea ice algorithm for routine processing of the SSM/I data for generating sea ice concentration maps. The new filter is a combination of the original SSM/I GR(37/19), which effectively eliminates most of the spurious concentration resulting from wind-roughening of the ocean surface, cloud liquid water, and rainfall with another GR filter based on the 22.2 GHz and 19.35 GHz channels. The rationale for using GR(22/19) is based partly on the sensitivity of the 22.2 GHz to water vapor and partly on the need to minimize the effect of ice temperature variations at the ice edge.

This new weather filter works as follows: If GR(37/19) is greater than 0.05 and/or GR(22/19) is greater than 0.045, the sea ice concentration is set to zero. These GR thresholds effectively eliminate most of the weather contamination, except for winds greater than about 30 m/s, cloud liquid water more than 24 cm, water vapor greater than 0.2 cm, and rain rates greater than 12 mm/hour. Except for a few case studies completed during the development of this filter, the extent to which it eliminates ice-edge concentrations in different regions of the Arctic and Antarctic for different seasons is unknown. Work is currently underway to determine the overall effectiveness of the new SSM/I weather filter.

### AlgorithmSensitivity and Sources of Error

Algorithm Sensitivity

The sensitivity of the algorithm to random errors has been described previously (Swift and Cavalieri 1985) for the SMMR version of the algorithm. The sensitivity analysis was redone using the SSM/I algorithm coefficients in table 1. The results are presented in tables 2 and 3 for the Arctic and Antarctic sets of tie points, respectively. The sensitivity coefficients given in table 2 (p.40) were calculated for regions of first year (FY) ice and multi-year (MY) ice in the Arctic at three different ice concentrations. This was repeated for the Antarctic with ice type regions labeled A and B. Each coefficient represents the uncertainty in concentration in units of percent per 1 K uncertainty in TB. The total root-summed-square (rss) sensitivity is also given for each concentration.

The coefficients given in tables 2 and 3 may be used to obtain an estimate of the error incurred by variations in the radiometric properties of the ice surface. For example, a random variation in ice emissivity of ñ.01 over 100% FY ice corresponds to a variation in TB of 2.5 K (assuming a value of 250 K for the physical temperature of the radiating portion of the ice), which in turn corresponds to an error of ñ4.5% (ñ.018 x 2.5) in total ice concentration, assuming all three channels are subject to this variation.

The sensitivity of the calculated ice concentrations to ice temperature variations is reduced through the use of radiance ratios PR and GR (Cavalieri et al. 1984, Swift and Cavalieri 1985). Except at the onset of melt, there is no apparent correlation between PR and the increasing TBs resulting from seasonal warming. This is not the case for GR, which is correlated with the seasonal variation in TB. An estimated error of ñ 0.005 in GR (Gloersen et al. 1992) corresponds to an uncertainty in total ice concentration of about ñ 1%, while the error in MY ice concentration is about ñ 9%. These estimated errors are consistent with the results obtained from previously published comparative studies (Cavalieri et al. 1991, Steffen and Schweiger 1991).

### Sources of Error

Errors in the derived sea ice concentrations arise from several sources. In order of importance, these are (1) the inability of the algorithm to discriminate among more than two radiometrically different sea ice types, (2) seasonal variations in sea ice emissivity, (3) nonseasonal variations in sea ice emissivity, (4) weather effects at concentrations greater than about 15%, and (5) random and systematic instrument error.

The largest source of error is the inability of the algorithm to discriminate among more than two radiometrically different sea ice types (including different surface conditions). The broad categories of radiometrically different sea ice types are new and young ice, FY ice, and MY ice types. Since the algorithm allows for both FY and MY ice types, the largest source of error in total ice concentration is caused by the presence of newly forming sea ice. New and young ice, most commonly found in leads and coastal polynyas during winter, are characterized by polarization differences intermediate between open water and thick FY ice (Cavalieri et al. 1986). PR for thin ice will vary in proportion to ice thickness (Grenfell and Comiso 1986) and will increase in proportion to the fraction of new ice filling the SSM/I field of view. For example, if we presume that an FOV contains 10% new ice (PR = 0.14) and 90% FY ice (PR = 0.03), then the increase in PR results in an underestimate of about 10% in total ice concentration. Larger areas of new ice within the sensor FOV will result in proportionally larger underestimates by the algorithm. Recently, a new thin ice algorithm has been developed (Cavalieri et al. 1994) which mitigates this problem in seasonal sea ice zones and also permits the mapping of new and young ice types.

Seasonal variations in sea ice emissivities can be extremely large. MY ice, for example, loses its characteristic microwave spectral signature (negative GR) during spring and summer and becomes indistinguishable from FY ice. Another condition resulting in large errors in total ice concentration is the formation of melt ponds on the ice surface, making the ponded region indistinguishable from open water. While the areal extent of ponding is not well known, unpublished data reported by Carsey (1982) show that for the summer of 1975, 20% or less of the Arctic ice pack was covered by ponds and that ponding reached maximum areal extent in early July. For an area of the Beaufort Sea (AIDJEX triangle) during August 1975, Campbell et at. (1984) report that the average ponding was 30%. The percent coverage of melt ponds varies spatially and temporally across the Arctic and the extent to which they influence summer ice concentrations remains uncertain.

Nonseasonal variations in sea ice emissivity include local variations, resulting from fluctuations in the physical and chemical properties of sea ice, and regional variations resulting from environmental differences. Regional and hemispheric variability may be considerable, as indicated by previous studies (Comiso 1983, Ackley 1979). Differences between Arctic and Antarctic sea ice microwave signatures noted above result in different sets of algorithm tie-points for each hemisphere. Algorithm errors can be reduced by using locally and seasonally chosen algorithm tie points.

While weather effects resulting from atmospheric water vapor, cloud liquid water, rain, and sea surface roughening by near-surface winds on the calculated sea ice concentrations are greatly reduced over open ocean at polar latitudes by the algorithm weather filter described previously, they may nevertheless contribute to the sea ice concentration error at concentrations greater than about 15%. Presuming that the atmospheric contribution is nearly zero over consolidated FY ice and that the contribution at the open water end results totally from atmospheric effects estimated to be up to 15%, then the error resulting from atmospheric effects for any intermediate concentration may be estimated by a linear interpolation. While the effects of weather on high total ice concentrations are small, there is the potential for significant reductions in multiyear ice concentrations (Maslanik 1992).

Finally, errors in ice concentration also result from random and systematic instrument errors. Except for the 85-GHz channels, over the two years of SSM/I operation, no instrument drifts are apparent. Based on prelaunch measurements and on observed radiances over relatively stable targets where temporal and spatial geophysical variability is small, the error for each of the three SSM/I channels used in the algorithm is less than 1 K, and the absolute accuracy is estimated at 3 K (Hollinger 1989). Assuming a 1-K level of random instrument noise in each channel, an upper limit to the rss uncertainty in the calculated concentrations, which depends on surface type and concentration, ranges from about 1% to 1.8% for total ice concentration and from 4.5% to 6% for MY ice concentration.

### Algorithm Accuracy

Several sea ice validation studies have been published involving the NASA Team Sea Ice algorithm. Some of these resulted from the NASA Sea Ice Validation Program for the DMSP SSM/I, while others were conducted independently. Please review the bibliography for pertinent references.

Table 1. Tie points for open water, first year ice and multiyear ice

 Data Tb (Kelvins)Northern Hemisphere Tb (Kelvins)Southern Hemisphere TB19VW 177.1 176.6 TB19VF 258.2 249.8 TB19VM 223.2 221.6 TB19HW 100.8 100.3 TB19HF 242.8 237.8 TB19HM 203.9 193.7 TB37VW 201.7 200.5 TB37VF 252.8 243.3 TB37VM 186.3 190.3

Table 2. Coefficients derived from tie points used to compute the first year
and multiyear ice fractions according to equations 3 and 4

 Coefficient Northern Hemisphere Southern Hemisphere a0 3290.2 3055.0 a1 -20761.2 -18592.6 a2 23934.0 20906.9 a3 47985.4 42554.5 b0 -790.9 -782.750 b1 13825.3 13453.5 b2 -33155.8 -33098.3 b3 -47771.9 -47334.6 c0 2035.3 2078.00 c1 9244.6 7423.28 c2 -5665.8 -3376.76 c3 -12875.1 -8722.03

Table 3. NASA SSM/I Algorithm Sensitivity Coefficients* for First-year and Multiyear Ice Regions of the Arctic at Different Concentrations

First-year Ice

Multiyear Ice

*Each coefficient represents the uncertainty in concentration in units of percent per 1-K uncertainty in brightness temperature.

Table 4. NASA SSM/I Algorithm Sensitivity Coefficients' for Ice Type A and Ice Type B Regions of the Antarctic at Different Concentrations

```
Ice Type A		Ice Type B
100%	50%	15%	100%	50%	15%
dCT	dCT	dCT	dCT	dCT	dCT
dTB19H 		1.2	0.9	0.9	1.2	0.8	0.6
dTB19V		0.3	0.1	0.5	0.3	0.1	0.4
dTB37V 		0.8	0.8	0.9	0.8	0.8	0.8
[(dTB)2]	1.5	1.2	1.3	1.5	1.1	1.1

```

*Each coefficient represents the uncertainty in concentration in units of percent per 1-K uncertainty in brightness temperature.