A new empirical multi-parameter SSM/I retrieval algorithm based on the neural network approach which retrieves wind speed, columnar water vapor, columnar liquid water, and sea surface temperature simultaneously using only SSM/I brightness temperatures is compared with existing global SSM/I retrieval algorithms. In terms of wind speed retrieval accuracy, the new algorithm systematically outperforms all algorithms considered under all weather conditions where retrievals are possible with an algorithm rms error of 1.0 m/s under clear, and 1.3 m/s under clear plus cloudy conditions. It also generates high wind speeds with acceptable accuracy. This improvement in accuracy is coupled with increased areal coverage with obvious benefits for operational applications. In terms of columnar water vapor and columnar liquid water, the new algorithm reproduces the results of existing algorithms closely. SST retrievals are less accurate and have low spatial resolution; however, by including SST as an additional output, the accuracy in retrieving wind speed is improved especially at high wind speeds. The new algorithm has been tested and accepted for operational use at the NWS's National Centers for Environmental Prediction. This algorithm produces a positive impact on forecast winds through data assimilation into NCEP's numerical weather prediction models.
 
 

We evaluate an empirical neural network (NN) algorithm which simultaneously retrieves several geophysical parameters over the ocean from brightness temperature (BT) measurements acquired by the Special Sensor Microwave Imager (SSM/I) (Hollinger et al., 1987) with primary emphasis on retrieving wind speed. This NN-based algorithm (OMBNN3) which retrieves wind speed, columnar water vapor, and columnar liquid water (see http://polar.ncep.noaa.gov/marine.meteorology/marine.winds/) has been recently developed and is described elsewhere (Krasnopolsky et al., 1996, 1997, 1999). Here we present a comparison of this algorithm with other global SSM/I wind speed, W (m/s), columnar water vapor, V (mm), and cloud liquid water, L (mm), retrieval algorithms. We also examine different BT retrieval flags and their relation to different forms of atmospheric moisture, an important topic which is usually bypassed in studies of this type. We also present various cross sections of wind speed retrieval error analysis.

In Section 2, we describe existing global SSM/I retrieval algorithms which were used in this study. In Section 3, our new multi-parameter empirical approach and the NN-based SSM/I retrieval algorithm, OMBNN3 (the corresponding FORTRAN code is available upon request at: Vladimir.Krasnopolsky@noaa.gov), are briefly described. In Section 4, we compare OMBNN3 with existing algorithms and perform error analyses using different retrieval flags. Finally, we discuss some operational applications of the geophysical fields which are retrieved by the new algorithm⁽²⁾ and present a recent example.
 
 

For comparison we have selected: (i) the original global operational (cal/val) wind speed retrieval algorithm developed by Goodberlet et al. (1989) (GSW); (ii) the current operational algorithm (GSWP) which is the same as the GSW algorithm but corrected for water vapor (Petty, 1993); (iii) a physically-based (PB) retrieval algorithm (F. Wentz, 1997).

The GSW empirical wind speed retrieval algorithm, which is based on multiple linear regression, uses a simple linear combination of four SSM/I brightness temperatures to approximate the SSM/I wind speed transfer function (TF):
 

W_GSW = 147.9 + 1.0969 T19V - 0.4555 T22V - 1.76 T37V + 0.786 T37H (1)
 

Because the actual SSM/I TF is nonlinear, several attempts have been made to improve the performance of the GSW algorithm using nonlinear approaches. The nonlinear water vapor correction, V, introduced by Petty (1993) is another type of linear regression which provides a nonlinear approximation for the transfer function with respect to SSM/I brightness temperatures. Nonlinear functions of BT, introduced in the linear regression in this case, represent the nonlinear behavior of the TF more closely:

     (2)
 

Here W_GSW is given by (1) and the terms (-2.13 + 0.2198V - 0.4008×10^-2 V²) represent a nonlinear function which corrects the linear TF (1) for the contribution of water vapor in the atmosphere. Due to this correction, the GSWP algorithm (2) takes into account the co-variability of columnar water vapor which was unaccounted for in (1). Since they retrieve wind speed only, both (1) and (2) are single-parameter algorithms. They can be represented as
 

w = f (T) (3)
 

where w is wind speed, T is a vector of SSM/I BTs, and f is the transfer function. SSM/I algorithms which retrieve columnar water vapor (e.g., Alishouse et al., 1990; Petty, 1993) and liquid water (Weng and Grody, 1994; Weng et al., 1997) are likewise single-parameter algorithms (3).

The PB retrieval algorithm (Wentz, 1997) numerically inverts a physically-based forward model. Therefore, it requires a physically-based forward model as a necessary prerequisite which is not required for the empirical algorithms described above, and, as a consequence, the PB algorithm requires a considerable amount of empirical data for its development (a significantly larger amount than the number of matchups normally used to develop competing empirical algorithms). Since PB algorithms do not produce an explicit transfer function, they require that a forward model to be inverted for each satellite measurement. Symbolically, they can be represented as,
 

g = f (T, T_s) (4)
 

where g = {W, V, L}, and T_s is sea surface temperature (SST). Compared with empirical algorithms (1) and (2), the PB algorithm requires an additional input, T_s (e.g., SST climatology) (see Wentz, 1997 for a detailed description). An important advantage of the PB algorithm which distinguishes it from the empirical algorithms above is its ability to retrieve several parameters simultaneously, in this case g = {W, V, L}: wind speed, columnar water vapor and columnar liquid water.
 
 

The NN algorithm presented here is a multi-parameter NN algorithm called OMBNN3 (Krasnopolsky et al., 1996, 1997). It contains three new elements. First, it is a multi-parameter retrieval algorithm. The co-variability of related atmospheric and surface parameters which can be extracted from the same set of brightness temperatures is taken into account: wind speed, columnar water vapor, columnar liquid water, and SST are retrieved simultaneously,
 

g = f_NN(T) (5)
 

where g = {W, V, L, T_s} is now a vector of simultaneously retrieved parameters, W is wind speed, V is columnar water vapor, L is columnar liquid water, and T_s is SST. T_S is an output here rather than an additional input as is required in the case of physically-based retrieval algorithms (Wentz, 1997). This empirical multi-parameter algorithm retrieves several physical parameters simultaneously which to a significant extent determines the state of the atmosphere and the ocean surface in a given area. Single-parameter retrieval algorithms (3) produce retrievals (e.g., wind speed) which do not correspond to any particular atmospheric state (e.g., specific amounts of columnar water vapor and liquid water) or ocean surface state (a specific value of SST). These retrievals correspond to some unknown "mean" atmospheric and surface states which can not be specified without additional information. Thus, single-parameter retrieval algorithms effectively average over an ensemble of atmospheric and surface states for all of the related geophysical parameters except for the one which is retrieved. This averaging gives rise to additional "artificial" errors in this single retrieved parameter which do not arise in the multi-parameter approach. If w is the wind speed retrieved by a single-parameter algorithm (1-2) and W is the wind speed retrieved by the corresponding multi-parameter algorithm (5), then this "artificial" systematic error (bias) can be estimated as,

The horizontal bar above the symbols on the left-hand side implies averaging over V, L, and T_S which are not known for single-parameter algorithms, b_i and _i² are the biases and variances of these geophysical parameters, and the c_ij are correlation coefficients between these parameters; _i, _i, and _ij are coefficients which are described in Krasnopolsky et al. (1999). Similar estimates can be obtained for additional "artificial" variances (random errors). It is clear from (6) that the multi-parameter wind speed retrievals, W, compared with single-parameter retrievals, w, do not contain additional "artificial" systematic (bias) or random errors. Avoiding these additional errors is an important advantage of the multi-parameter approach.

Second, a method of NN training which enhances learning at high wind speeds was used (Krasnopolsky et al., 1996). In preparation for training the NN, the weights, , in the error function were generated using the following formula,

where p(W) is the observed wind speed probability distribution and C is a normalization constant. This choice of weights allows us to assign higher values to the tails of the distribution and effectively produces a distribution which is approximately uniform. By introducing the square root in the denominator, we have restricted the rate of increase in the weights which reduces noise-like influences at the highest wind speeds.

Third, an extensive new buoy/SSM/I matchup database containing raw matchup data sets for the F8, F10, and F11 SSM/I sensors (provided by the Naval Research Laboratory, Washington, D.C.) and augmented with additional matchup data for high latitudes containing a significant number of high wind speed events (up to 26 m/s) from European Ocean Weather Stations MIKE and LIMA (provided by D. Kilham, Bristol University) , was used in developing this algorithm ( > 15,000 matchups overall). Both buoy and Ocean Weather Station data include wind speed and SST; however, they do not include columnar water vapor and columnar liquid water. These two parameters were also required for training and validation of the new algorithm. Because collocated buoy/radiosonde/SSMI data were not available for developing this algorithm, we obtained columnar water vapor and columnar liquid water using cal/val (Alishouse et al., 1990), and Weng and Grody (1994) algorithms. Such single-parameter empirical algorithms, of course, only generate proxies for the "true" data. These single-parameter retrievals may be biased and do contain significant random errors which affect NN training and allow only an approximate separation of the V- and L-signals from the other components. However, as shown below (Table 1 and Fig. 2), even such an approximate separation of signals allows us to reduce the random and systematic errors in wind speed and reduce the dependence of the wind speed bias on V and L. Because the Weng and Grody (1994) algorithm for cloud liquid water utilizes the 85 GHz channel, and this channel was not available from F8 during the time of creating the matchup database, all comparisons which involve cloud liquid water have been performed on a subset which includes only F10 and F11 BTs (> 12,000 matchups). The OMBNN3 algorithm uses five SSM/I channels: 19 GHz and 37 GHz (horizontal and vertical polarizations) and 22 GHz (vertical polarization).

From a mathematical point of view, the multi-parameter retrieval algorithm (5) corresponds to a continuous mapping. It maps a vector of SSM/I BTs, T, onto a vector of retrieved geophysical parameters, g. NNs are well suited for performing a wide variety of continuous mappings (Chen and Chen, 1995). The architecture of the NN which we use for developing the OMBNN3 algorithm is presented in Fig. 1. The NN which represents this algorithm has n = 5 inputs, m = 4 outputs, and one hidden layer with k = 12 neurons. This NN can also be written explicitly as,

where the matrix W_ji and the vector B_j represent weights and biases in the neurons of the hidden layer; w_qj  and the b_q  represent weights and biases in the neurons of the output layer; and a_q and b_q are scaling parameters.

4.1 Wind speed

SSM/I wind speed retrieval algorithms are usually used together with so-called retrieval flags which are based on various BT criteria. These retrieval flags serve as delimiters for BT over the ranges of applicability for a given algorithm. They also are used to indicate reliability and accuracy of retrieved wind speed. At least two different sets of retrieval flags have been developed for SSM/I wind speed retrievals, and they are presented in Table1 below:
 

Table 1. Two sets of retrieval flags used for SSM/I wind speed retrievals: RF (Goodberlet et al., 1989) and SF (Stogryn et al., 1994)
 

RF	Criteria	SF	Criteria
0	T37V - T37H > 50 K T19H < 165 K	0	T37V - T37H > 50 K
1	T37V - T37H < 50 K T19H > 165 K	1	T37V - T37H 50 K T19V < T37V T19H 185 T37H 210 K
2	T37V - T37H < 37 K	2	Everything else
3	T37V - T37H < 30 K

The first set of criteria was developed by Goodberlet et al. (1989) and is closely related to the linear regression algorithm they developed. This set consists of four retrieval flags (RF0, ..., RF3). The second set was developed by Stogryn et al. (1994) for use with NN algorithms and consists of three flags (SF0, ..., SF2). These two sets of flags are similar but not identical. For obvious reasons we have adopted Stogryn's retrieval flags in our algorithm development. We excluded BTs which corresponded to flag SF2 (the "very cloudy" case) from consideration because, under these conditions, according to Stogryn, "wind speed effects on brightness temperatures are so overshadowed by atmospheric attenuation that retrievals should not be attempted". As a result, we have performed our algorithm development work, validation and comparisons only for "clear" (SF0) and for "cloudy" (SF1) conditions.

For wind speed, high quality ground truth observations, including buoy and ocean weather station wind speed measurements, are available to create matchups with the SSM/I brightness temperatures. Evaluating the different algorithms was performed by comparing them with ground truth observations. Table 2 shows the summary wind speed statistics for clear (SF0) and clear + cloudy (SF0 + SF1) conditions. This table compares four algorithms, GSW, GSWP, PB, and OMBNN3 using all available matchups (> 15,000) for three SSM/I instruments F8, F10, and F11. The table presents wind speed bias, RMS algorithm error, total RMSE, and RMSE for high wind speeds ( W > 15 m/s). Additional analyses have been performed to estimate the algorithm error itself (Wentz, 1997; Krasnopolsky, 1997). The sensor and observation errors were estimated separately and removed from the total RMSE. The residual, after removing the sensor and observation errors, corresponds to the algorithm error per se. In terms of algorithm error, the improved performance of the OMBNN3 algorithm (RMS errors of 1 m/s for clear-, and 1.3 m/s for clear+cloudy conditions) becomes even more apparent. Table 2 also shows that the NN algorithm provides significant improvement in retrieval accuracy at high wind speeds.
 

Table 2. Error budget (m/s) for different SSM/I wind speed algorithms for clear, and clear+cloudy (in parentheses) cases, and separately for higher wind speeds.
 

Algorithm	Bias	Algorithm RMSE	Total RMSE	W > 15 m/s RMSE
GSW1	-0.2 (-0.5)	1.4 (1.8)	1.8 (2.1)	(2.7)
GSWP2	-0.1 (-0.3)	1.3 (1.6)	1.7 (1.9)	(2.6)
PB3	0.1 (-0.1)	1.3 (1.8)	1.7 (2.1)	(2.6)
OMBNN34	-0.1 (-0.2)	1.0 (1.3)	1.5 (1.7)	(2.3)

¹Goodberlet et al., 1989; ²Petty, 1993; ³Wentz, 1997; ⁴Krasnopolsky et al., 1996
 

Figure 2. Systematic (wind speed bias - upper row) and random (standard deviation (SD) of wind speed error - lower row) errors in wind speed retrieved by four different algorithms as functions of columnar water vapor, V, (a and b); columnar liquid water, L, (c and d); and SST (e and f). Solid line - OMBNN3, dotted line - GSWP, dashed line - GSW, and dash-dotted line the Wentz (1997) algorithm.
 

As mentioned earlier, one of the advantages of the OMBNN3 algorithm is its ability to retrieve not only wind speed but also three other parameters: columnar water vapor V, columnar liquid water L, and SST simultaneously. The accuracies of these additional retrievals are discussed below. Here we show how simultaneous retrievals of the entire vector of related geophysical parameters (5) improves the accuracy of the wind speed retrievals by taking into account the co-variability of these parameters. Fig. 2 shows the systematic and random errors (bias and SD) in wind speed retrieval as functions of V,L, and SST for the GSW, GSWP, PB, and OMBNN3 algorithms. These statistics were calculated using more than 12,000 matchups. Including the nonlinear water vapor correction in GSWP reduces the bias and its dependence on water vapor concentration (and partly on SST which is closely related to water vapor); however, it does not reduce the dependence on liquid water concentration. The OMBNN3 and PB algorithms, which both employ the simultaneous multi-parameter retrieval approach, reduce the bias, and the dependence of the bias, on both water vapor and cloud liquid water concentrations. The PB algorithm does not retrieve SST but requires SST as an input parameter. The OMBNN3 algorithm also demonstrates the best performance with respect to SST co-variability. The random errors for the OMBNN3 algorithm are significantly smaller and demonstrate weaker dependencies on the related atmospheric and surface (SST) parameters than do the errors for the other algorithms.

Figure 3. (a) Number of matchups corresponding to different       Figure 4. Same as for Fig. 3 but only for
retrieval flags. Wind speed bias (b), RMSE (c), and standard                      wind speeds > 15 m/s.
deviation (SD) of wind speed differences (differences
between buoy and SSM/I wind speeds) for different retrieval
flags, and for two different retrieval algorithms, GSWP
(dashed line) and OMBNN3 (solid line).
 

We have selected two algorithms, GSWP (currently used operationally by Fleet Numerical Meteorological and Oceanographic Center) and OMBNN3 (currently used operationally at National Centers for Environmental Prediction) which demonstrate the best overall performance in accordance with Table 2. Next, we perform a more detailed comparison and error analysis for these two algorithms. Fig 3 shows such a comparison for different retrieval flags (for both SF and RF, see Table 1). Panel (a) shows the number of matchups for different flags (matchups corresponding to SF2 were eliminated from the database at the start). Panels (b), (c), and (d) show wind speed bias, RMSE, and standard deviation (SD) of the error for different flags. Fig. 4 shows a similar comparison for high wind speeds (W > 15 m/s). Flags RF0 and SF0 are similar (SF0 includes a small portion of RF1 in addition to RF0) both in terms of the number of matchups included, and the corresponding statistics. The SF1 flag includes the rest of RF1 and portions of RF2 and RF3 which do not overlap SF2 (the overlapping portions are not included).

Using a much more limited data set, Krasnopolsky et al. (1995) demonstrated that BT retrieval flags are closely related to the amount of cloud liquid water in the atmosphere. Fig. 5 further supports this conclusion for a much larger data set. This figure shows mean amounts of water vapor (V) and cloud liquid water (L) for each retrieval flag. There is a strong correlation between the retrieval flags and L. Retrieval flags RF2 and RF3 clearly correspond to higher levels of L than does RF1. RF retrieval flags are more discriminative from this point of view than the SF flags. However, Figs. 3 and 4 show that OMBNN3, which outperforms GSWP under all conditions, demonstrates much better performance than GSWP especially at SF1, RF2, and RF3 when the amount of cloud liquid water increases significantly. Thus, we conclude that the SF flags are well suited for use with the NN algorithms. Of considerable significance operationally is the fact that the OMBNN3 algorithm has extended the retrieval domain from clear (SF0 or RF0), to clear plus cloudy (SF0 + SF1) conditions, yielding an increase in areal coverage of 15% globally. This result is particularly important for obtaining more complete coverage of synoptic weather systems such as extratropical cyclones which are typically characterized by higher levels of moisture and wind speed. In such areas (Fig. 6 below) the increase in areal coverage can exceed the global average increase significantly.
 

4.2 Columnar water vapor, liquid water, and SST
 

Because radiosonde observations which are collocated with buoy and SSM/I measurements are not available, we have used simulated data for V and L for training the OMBNN3 algorithm. Values of V generated by the cal/val algorithm (Alishouse et al., 1990) and values of L from the algorithm developed by Weng and Grody (1994) (WG) were used. Thus, we do not consider OMBNN3 as a new algorithm for retrieving V and L but rather consider them as ancillary parameters which improve the accuracy of the wind speed retrievals. We have performed comparisons for V obtained from the cal/val, PB, Petty [1993] with the OMBNN3 algorithm. OMBNN3 agrees well with the other algorithms for V, with an RMS difference of less than 2 mm. We also compared values of L obtained from the WG and OMBNN3 algorithms. These algorithms also compare favorably, yielding an RMS difference of less than 0.02 mm. When new collocated buoy/radiosonde/SSM/I data become available, the NN algorithm will be retrained to produce improved retrievals for V and L.

SST is also an ancillary parameter which improves the retrieval accuracy of wind speed. Because the dependence of SSM/I BTs on SST is weak in the 19- to 37 GHz band, the accuracy and resolution of retrieved SSTs is low compared with SSTs retrieved from other instruments such as the Advanced Very High Resolution Radiometer.
 

4.3 Operational data validation
 

OMBNN3 has been carefully evaluated using operational data from the F10, F11, F13 and F14 SSM/I instruments since mid-1997. Positive impact has been demonstrated from the assimilation of wind speed and columnar water vapor retrieved by the NN algorithm into an operational numerical weather prediction (NWP) model (Yu et al., 1997). The wind speed, columnar water vapor and columnar liquid water fields retrieved by OMBNN3, taken together, depict significant information concerning weather patterns over the ocean (Gemmill and Krasnopolsky, 1999). Comparisons of these fields with other satellite and surface observations, and with various subjective (manual, human generated) and objective (computer generated using NWP models) analyses, show that the new algorithm generates high wind speeds (> 20 m/s) in areas where they occur. It is clear that this algorithm effectively separates the wind speed, columnar water vapor, and columnar liquid water signals contained in the SSM/I brightness temperatures. The multi-parameter retrievals, in addition to characterizing the instantaneous state of the atmosphere, preserve the correct physical relationships between the retrieved parameters. For example, there is a relation between areas with higher amounts of cloud liquid water and higher wind speeds , but they are not necessarily identical. The areas with the highest wind speeds do not usually correspond to the areas with the highest amounts of liquid water and vice versa. Higher amounts of columnar liquid water are related to areas of water vapor convergence which are closely associated with active fronts. Fronts and cyclonic patterns can be seen in both the SSM/I wind speed and columnar liquid water fields, and their locations are well supported by subjective and objective analyses. Conversely, the structure of the water vapor field differs from both wind speed and liquid water, and its higher values in this case are related to a moist air mass which most likely originates in the subtropics (see Gemmill and Krasnopolsky,1999) .

Fig 6. shows an example of cross validation performed during a synoptically active period in the Eastern North Pacific on March 21, 1999. A series of six panels is shown: (a) SSM/I ocean surface winds speed, (b) SSM/I columnar water vapor, (c) SSM/I columnar liquid water, (d) ocean surface wind data from buoys and ship, (e) ERS2 scatterometer wind vector data, and (f) a sea level pressure analysis available from the NCEP Global Data Analysis System. The satellite data were acquired within a ± 3 hour window about the analysis time. The SSM/I data are a composite from three DMSP satellites (F11, F13 and F14), which together provide almost complete coverage of the region. There is an intense, low pressure system in the NE Pacific centered at 37 N and 131 W, with a central pressure of 983 mb. The SSM/I wind speed data show a broad area of strong winds that exceed gale force ( > 17 m/s) especially on the southern and western sides of the system. A swath of ERS-2 wind vector data shows a similar wind speed pattern south of the storm, with wind speeds again well above gale force. This area of high wind speed corresponds closely to the area of high sea level pressure gradients seen in the objective analysis (Fig. 6f). Both the SSM/I and ERS-2 data show the center of the storm itself. The SSM/I data suggest that the center is located near the area of wind speed minimum (7.5 m/s) just north of the sea level pressure minimum (Fig. 6f). The ERS-2 wind vectors locate the circulation center in about the same area. The buoy and ship wind data depict the general wind circulation pattern around the storm, but are much too sparse to identify details of the system. Two ships reporting winds above gale force, one near 38N, 126 W in front of the storm, agrees with the SSM/I wind speed pattern, and the other near 37 N, 132 W behind the storm, agrees with the SSM/I and ERS-2 wind patterns. The water vapor and liquid water patterns show that the storm is well mixed, i.e., with no strongly contrasting air masses. Higher values of water vapor occur at lower latitudes, with the highest values of liquid water being associated with the storm front approaching from the west.

After evaluating many cases in different oceanic regions, we find the overall agreement between the SSM/I derived parameter fields and those obtained from other sources to be excellent.

A new empirical, multi-parameter SSM/I retrieval algorithm based on the neural network approach (OMBNN3) is compared with other global SSM/I retrieval algorithms. This algorithm simultaneously retrieves wind speed, columnar water vapor, columnar liquid water, and SST using only SSM/I brightness temperatures. The accuracy of the wind speed retrievals from the new OMBNN3 algorithm (algorithm RMS error 1.0 m/s under clear, and 1.3 m/s under clear plus cloudy conditions) is systematically higher than the accuracy of wind speed retrievals for the other algorithms tested, for all SSM/I instruments. This improvement is valid under all weather conditions and for all wind speeds where retrievals are possible. The OMBNN3 algorithm has extended the areal coverage by 15% globally and even higher in areas of increased meteorological activity (storms and fronts) which have higher levels of moisture and wind speed .

The new algorithm successfully separates the wind speed, columnar water vapor, columnar liquid water, and SST signals contained in the SSM/I brightness temperatures. Multi-parameter retrievals preserve the correct physical relationships between the retrieved parameters by partitioning the variance among the variables in an appropriate manner. The simultaneous retrieval of related atmospheric and surface parameters is also beneficial when cloudy and very cloudy weather conditions are present. Because the brightness temperature retrieval flags which we use are essentially statistical (based on global statistics), they are not highly sensitive to local conditions. In some cases this may lead to degraded retrievals; therefore, any additional information about related local atmospheric and surface conditions which can be derived from the same brightness temperatures may improve these brightness temperature retrieval flags. Local atmospheric and surface parameters (V, L, and SST), which the OMBNN3 algorithm now produces simultaneously with wind speed, help to describe the instantaneous state of the atmosphere more completely, and, therefore may help to improve the retrieval flags and to further improve the accuracy of retrievals under cloudy conditions.

OMBNN3 represents a new generic approach for developing multi-parameter empirical retrieval algorithms based on the NN technique. This approach may find use in many other remote sensing applications as well.
 
 

We thank D.B. Rao for his thorough and critical review of this paper. Also, we want to thank those who provided us with expanded collocated SSM/I - buoy data sets; Gene Poe of the Naval Research Laboratory for providing a preliminary raw version of the new NRL matchup database, David Kilham of Bristol University for providing us with additional matchup data for high latitudes, and Michael McPhaden and Linda Magnum for providing information concerning TOGA-TAO buoys. Without this comprehensive data set, our results could not have been extended through high wind speeds.

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1. OMB Contribution No. ¹⁵⁹

^2. Since April 1998, OMBNN3 has been running as the operational SSM/I retrieval algorithm in the data assimilation system at the National Centers for Environmental Prediction.