## 1. Introduction

Studying coastal storms involves, among other things, a mapping of the near-surface marine wind field. Obtaining high-density marine measurements via on-site observations would require a prohibitively large number of buoys; therefore, space-based radar methods are often used. Such radars provide useful wind speed estimates because, as the wind speed over the ocean surface increases, so does the radar backscatter from the wind-driven waves. Synthetic aperture radar (SAR) yields higher resolution in these backscatter images than do scatterometers (Beal et al. 2005). Thus, it is particularly well suited for the coastal zone where land echoes can contaminate the scatterometer measurements. In both SAR and scatterometer analyses, an empirical backscatter to wind speed relationship is used. For the horizontally polarized C-band (approximately 5 cm in wavelength) observations from the *Radarsat-1* satellite, the CMOD algorithm modified for horizontal–horizontal polarization (HH-pol) is used (Horstmann et al. 2000; Sikora et al. 2006). This algorithm has been refined through several versions, including CMOD4, CMOD-Ifr2, and CMOD5 (Stoffelen and Anderson 1997b; Quilfen et al. 2004; Hersbach et al. 2007).

In addition to radar parameters (look direction and incidence angle), these wind speed retrieval models require the following variables as input: normalized radar cross section and the wind direction. The wind direction can sometimes be derived from streaks in the SAR imagery (Horstmann et al. 2002), but is otherwise generally obtained from a numerical weather prediction model’s analysis. While high-resolution regional models are better able to resolve the flow along mountainous coasts, lower-resolution global model analyses are often all that is available. Wind directions from global analyses have been used with success in SAR wind speed retrieval (Monaldo et al. 2001; Horstmann et al. 2003) over the open ocean although they are subject to errors when synoptic features are not correctly positioned (Beal et al. 2005) or when a terrain-induced mesoscale flow is not resolved (Young et al. 2007). The current study extends this work by testing the SAR wind speed estimates resulting from using global model wind directions along the mountainous coast of the Gulf of Alaska. This region is particularly appropriate for such a study because the terrain-enhanced mesoscale meteorological phenomena in the area are characterized by strong horizontal and temporal gradients (see, e.g., Winstead et al. 2006). Such phenomena include coastal barrier jets (e.g., Overland and Bond 1995; Loescher et al. 2006), gap flow exit jets (e.g., Colle and Mass 2000; Beal et al. 2005), and orographic gravity waves (e.g., Li 2004; Beal et al. 2005). Thus, the Gulf of Alaska can serve as a “worst case” location to test the limits of the CMOD model functions. The fact that accurate winds can be retrieved in such a complex and dynamic environment greatly increases our confidence in the methods examined below. Comparison with past studies will be used to determine the change in SAR wind speed retrieval accuracy resulting from the mountain-induced errors in the global model’s wind direction analysis.

To quantify the accuracy of the CMOD4 and CMOD5 backscatter to wind speed models in this challenging regime, their output is compared with simultaneous wind speed observations recorded at three U.S. Navy Oceanographic Meteorological Automatic Device (NOMAD) buoys off the Alaskan coast near mountainous coastal terrain. For the Gulf of Alaska coastal region shown in Fig. 1a, the data for buoys 46082, 46083, and 46084 are available for download from the National Data Buoy Center’s Web site (available online at http://www.ndbc.noaa.gov). Figure 1b shows an example SAR image of this region, including the complex terrain induced flow features typical of this setting.

Because the anemometer on a NOMAD buoy measures the wind speed at a height of 5 m above the water surface and the CMOD algorithms yield a proxy for the neutral wind speed at 10 m, the buoy data must be converted to the 10-m level in order to be comparable. This conversion can be done either by assuming that the surface layer is neutrally stratified and using the log wind law, or by allowing for stratification and using the appropriate Monin–Obukhov similarity profile (Fairall et al. 1996). Once the buoy wind speeds are converted to the same altitude as the SAR estimates, the two speeds can be compared statistically, and the accuracy of CMOD4 and CMOD5 can be ascertained for the mountainous coastal Alaskan setting.

## 2. Data

A set of SAR images, dating from 1998 to 2005 and containing over 700 SAR–buoy collocations, was obtained using the C-band radar aboard the Canadian *Radarsat-1* satellite (these images and additional information are available online at http://fermi.jhuapl.edu/sar/stormwatch/web_wind). Each of these images was processed using the software currently in operation at the Johns Hopkins University Applied Physics Laboratory (JHU/APL), the National Oceanic and Atmospheric Administration’s National Environmental Satellite, Data, and Information Service (NOAA/NESDIS), and the Alaska Satellite Facility. This software, known as the JHU/APL ANSWRS (for APL/NOAA/SAR Wind Retrieval System), was developed with the specific objective of demonstrating the capability to process SAR images into wind speed in an operational setting (i.e., as an automated full-time system). The system works by ingesting a calibrated SAR image including the relevant radar parameters (incidence angle, look angle, etc.) as well as wind direction data from an independent source. These data are then resampled onto a rectangular latitude, longitude grid; corrected from HH-pol to vertical–vertical polarization (VV-pol; as discussed below); and then the image is converted into wind speed using either CMOD4 or CMOD5.^{1} The resampled wind speeds are then output as imagery (available online, e.g., http://fermi.jhuapl.edu/sar/stormwatch/web_wind/) and network common data form (netCDF) files. We now outline the specifics of how we used the ANSWRS system to generate the image data used in this study.

In keeping with the worst-case nature of our test, we did not do any filtering to eliminate the more challenging images with mesoscale variability or microscale gustiness (Horstmann et al. 2003). The specified range of incidence angles for ScanSAR Wide B imagery is 20°–49°. In keeping with the “worst case” design of this test, data were not rejected at the lower end of this incidence angle range although it is well known that *Radarsat-1* suffers from saturation effects, in particular in the near range, due to limited dynamic range. The resulting backscatter images are 1200 × 1200 pixels in size and cross-section averaging to 600 m was used.^{2} CMOD4 and CMOD5, both modified for HH polarization [see Horstmann et al. (2005) for a summary of both approaches], were then used to estimate wind speeds for each pixel (Horstmann et al. 2005). The HH-polarization issue is one that remains somewhat controversial within the literature with multiple approaches and values of *α* proposed by various authors (Monaldo et al. 2001; Wackermann et al. 2002). The operational system uses the value of *α* = 0.6 as this is the value that has been shown to best fit data from the Alaska Satellite Facility (Monaldo et al. 2001). Therefore, we also use *α* = 0.6 here. However, it is also true that *α* may have a larger value (e.g., Vachon and Dobson, 2000) and the polarization ratio may also depend on both the azimuth and the incidence angle (Mouche et al. 2005). Since the relationship between the incidence angle and the cross section is governed by this parameter, incorrect values of the parameter may introduce biases into the results. This issue is beyond the scope of this paper.

CMOD4 is capable of determining wind speeds from 0 to 25 m s^{−1}, while CMOD5 wind speeds extend to 35 m s^{−1} (Hersbach et al. 2007; Horstmann et al. 2005). This upper limit results from saturation and a decrease in backscatter at higher wind speeds (Donnelly et al. 1999; Hersbach et al. 2007). These algorithms also have a minimum backscatter requirement that limits the slowest wind speed deducible (Stoffelen and Anderson 1997a, b). For either CMOD algorithm to accurately estimate wind speeds from the SAR image backscatter, the wind direction must be known a priori (Beal et al. 2005). The required wind direction data were obtained from two sources: the U.S. Navy Operational Global Atmospheric Prediction System (NOGAPS) global numerical weather prediction model and the buoy measurements themselves. Each of these approaches has potential shortcomings; the buoy directions are more susceptible to local fluctuations in the wind field (Monaldo et al. 2001) but the model is subject to regional-scale errors when the analysis of a storm position is in error (Beal et al. 2005) or when a terrain-induced mesoscale flow is not resolved (Young et al. 2007). Moreover, the model is rather smooth as compared with the SAR resolution. Thus, the error analysis for the SAR wind speed retrieval is conducted in parallel for the two sources of wind direction.

The buoy data were downloaded from the National Data Buoy Center (NDBC) and so were subject to their quality control procedures (information available online at the NDBC Web site: http://www.ndbc.noaa.gov/handbook.pdf). The NDBC quality control procedures include an automated real-time check for gross errors and consistency followed by strict range and time continuity checks, comparison between duplicate sensors, and graphical checks by a human quality control officer. All three buoys were 6-m NOMAD buoys owned by the NDBC. The buoys measure air temperature and dewpoint temperature at 4 m above sea surface, wind speed and direction at 5 m above sea surface, sea temperature at 1 m below the surface, and pressure at sea level (information online at http://www.ndbc.noaa.gov/station_page.php?station=46082). Observations are available every 10 min. Thus, the maximum time difference between a SAR image and the corresponding buoy wind measurement is 5 min. NDBC states the wind accuracy of the “ARES” payload aboard the three buoys used here as 10° and 1 m s^{−1} or 10% of wind speed if that is greater (information online at http://www.ndbc.noaa.gov/rsa.shtml). NDBC uses the unit-vector technique to produce the 10-min-average wind directions used here.

## 3. Procedures

Because we compare the CMOD4 and CMOD5 wind speed estimates with the wind speeds measured by the buoys, only SAR images with temporally corresponding buoy data were analyzed. In preparation for the comparison, the SAR wind speed estimates were averaged over a rectangular area centered at the buoy location. This averaging was undertaken to reduce the gust-induced errors that even a 5-min time difference could incur. To determine the best averaging area a sensitivity study was conducted in which the averaging half-width was varied between 0 and 50 pixels, that is, an averaging area from 0.36 to 3672.36 km^{2}. As seen in Fig. 2, the results with the highest correlation to the observed wind speeds using data from all three buoys, without stability corrections, occurred at a half-width of 12 pixels, yielding an optimum square of 625 pixels (225 km^{2}) centered at the buoy. Correlation between SAR and buoy wind speeds is not particularly sensitive to the averaging half-width, that is, varying little for values from 5 to 20 pixels (i.e., 3–12 km). For the typical wind speed of about 8 m s^{−1} (Table 1), this spatial scale corresponds an advective time of 6.25–25 min. Thus, the lower bound closely approximates the 10-min-averaging period of the buoys, while the upper bound roughly corresponds to the spatial scales above which mesoscale variability is typically observed along the Alaskan coast (e.g., Winstead et al. 2006). Thus, the spatial averaging removes the turbulent gusts but not the mesoscale flow patterns. It is worth noting that 12 km is also the scale of the current Quick Scatterometer (QuikSCAT) pixels.

*z*

_{2}, based on the speed at another,

*z*

_{1}, is

**u**is the wind speed,

*z*is the altitude,

*z*

_{0}is the roughness length, Ψ is the diabatic wind profile that is a function of the nondimensional height, and the subscripts indicate the observing height (1) and the height the wind is being converted to (2) (Fairall et al. 1996). In this study the SAR–buoy comparisons are conducted by first using neutral stratification, that is, Ψ = 0, and then repeated using the stability correction. If any of the values were missing from the buoy datasets, that is, if one or more of the instruments failed, the Ψ values were set to zero, so the algorithm reverted to neutral stability and thus use of the log wind law. Only 7% of the data had to be handled this way. Once the buoy wind speed was converted to 10 m, it was compared with the CMOD4- and CMOD5-estimated wind speeds. It is worth nothing that for the vast majority of the cases the magnitude of the stability correction was less than 0.5 m s

^{−1}. The median correction was 0.1 m s

^{−1}with 90% of the corrections falling between −0.6 and 0.3 m s

^{−1}.

The accuracy of both of the CMOD functions was visualized using scatterplots and quantified using linear robust regression (Huber 1981) and other statistics described below. The plots depicting CMOD4 or the CMOD5 wind speed estimates versus buoy wind speed measurements also show this best-fit relationship. The accuracy of the CMOD speeds was quantified, in part, by using the slope, intercept, and *r* ^{2} values of this best-fit line. The *r* ^{2} value is the fraction of SAR wind speed estimates’ variance explained by the buoy-measured wind speed. The higher this value, the more useful the CMOD wind speed estimates. This quantity is not, however, a measure of the accuracy of the RAW SAR wind speed retrieval, but rather the accuracy that would result from correcting the CMOD estimates via the best-fit line. Thus, the slope and intercept of the best-fit line represent the correctable multiplicative and additive biases of the CMOD estimates. Standard errors of these two quantities, and the standard deviation of SAR–buoy wind speed differences, are also presented to complete the picture.

## 4. Results

The results of this SAR versus buoy wind speed comparison are presented first for CMOD4 and then for CMOD5. In both, the results are presented first without and then with the surface-layer stability correction. All results are presented for SAR wind speed retrievals using both NOGAPS wind directions and buoy wind directions. The results are listed for each of the three buoys as well as for the combined dataset (All Buoy). The Data Points value for each buoy is the number of times that the buoy provided time-matched observations within one of the SAR images. Only the numbers for All Buoy will be discussed in detail, although comments will be made whenever the results from one buoy stand out.

Table 1 gives the sample size, the mean of the buoy wind speed converted to 10 m (without the wind profile stability correction) and the SAR-derived wind speed (estimated at 10 m using CMOD4), and the difference between the mean SAR-derived wind speed and the mean buoy wind speed. Mean difference (bias) is 1.11 m s^{−1} when NOGAPS wind directions are used and 0.43 m s^{−1} when buoy wind directions are used. Thus, the bias is reduced somewhat by using the measured wind direction instead of that from the model analysis. Figure 3 shows the corresponding scatterplot of the CMOD4 speeds versus wind speeds for all buoys (without stability correction) along with the best-fit line. On the whole, the SAR-derived wind speed estimates correspond to the buoy measurements, but there is both a degree of general scatter and a few outliers. Both are expected from the intentionally challenging conditions of this test, an operational system using SAR data from a region with frequent intense mesoscale weather systems. Because a real-time operational system is being tested, there are occasional lapses in the availability of the NOGAPS wind direction field. The operational system assumes a uniform wind direction in such cases, resulting in scatter when the assumed wind direction did not match reality and in outliers during high–wind speed events under such conditions. Additional scatter and some outliers resulted from the existence of mesoscale flows not resolved by the NOGAPS wind analyses. Most of these flows were terrain driven (i.e., gap flow exit jets, barrier jets, and orographic gravity waves), while a few were the result of NOGAPS errors in the placement of wind shift lines associated with synoptic-scale fronts. As discussed in the introduction, these are precisely the error sources we hoped to incur by choosing the Gulf of Alaska as the site for this study.

Table 2 presents the linear robust regression results and statistics: the slope and the *y* intercept of the best-fit line. A perfect match would result in a slope (*a*) of 1.0 and intercept (*b*) of 0.0. Using NOGAPS wind directions yields a slope of 1.01 and an intercept of 0.74 m s^{−1}. Thus, the CMOD4 wind speed estimates are typically biased high relative to the buoy observations. The standard errors of these parameters are small: 0.02 for the slope and 0.16 for the intercept. Thus, for the combined dataset neither the slope nor the intercept differ from the perfect match values at the 95% confidence level. The standard deviation of the SAR wind speed from the best-fit line (i.e., the root-mean-square error that would be achieved after correcting the additive and multiplicative biases) is 2.12 m s^{−1}, and the *r* ^{2} value is 0.78. Results for the runs using buoy wind directions (see Table 2) were similar although the slope was slightly farther from 1.0, the bias was closer to zero, the standard deviation slightly smaller, and the *r* ^{2} slightly smaller. Thus, the use of buoy-observed wind directions instead of those from the NOGAPS analyses had a mixed impact on the statistics, causing minor improvements in some cases and minor degradations in others; only the bias changed by more than a few percent.

Previous studies have reported several physical and mathematical effects that could account for part of the observed biases. Kent et al. (1998) demonstrated that the difference between the large error variance for merchant ship observations and the small error variance for scatterometer observations led to a slow bias in the scatterometer winds. This effect would be small in the current study, however, because the error variances in the buoy observations are much less than those for merchant ship observations. Shankaranarayanan and Donelan (2001) examined the effect of unresolved wind speed fluctuations within a scatterometer footprint. They showed that this effect decreases with decreasing footprint size, becoming much smaller for SAR results than for those from the scatterometer. Their findings have interesting implications for the application of a scatterometer algorithm such as CMOD4 or CMOD5 to the much higher resolution SAR data, but these have not yet been fully explored.

The impact of stability correction on these CMOD4 results is examined next. Table 3 gives the buoy wind speed (converted to 10 m using the wind profile stability correction), the SAR wind speeds (estimated using CMOD4), and the difference between the mean SAR-derived speed and the mean stability-corrected buoy speed. For only 7% of the cases did the algorithm have to revert to neutral stability due to missing thermodynamic data. Figure 4 is the corresponding scatterplot of the buoy wind speeds with stability correction versus the SAR image CMOD4 speeds along with the best-fit line using the robust regression values shown in Table 4. The standard deviations and *r* ^{2} values are not significantly changed by the stability correction. Likewise, for all buoys the multiplicative and additional biases with the stability correction are nearly identical to those resulting without the stability correction. Once again, similar statistics for the first two buoys resulted for the runs using buoy wind directions, while the *r* ^{2} value of the third buoy remained lower than the other two. Thus, correcting for surface-layer stratification neither eliminated nor increased the statistical significance of the small departure of these biases from the ideal values of one and zero. This result might be expected given that CMOD-retrieved winds assume neutrality.

The calculations are repeated using CMOD5. Figure 5 shows the scatterplot of the All Buoy CMOD5 wind speeds versus the buoy wind speeds (without profile stability correction) along with the best-fit line. Table 5 presents the sample size, the mean of the buoy wind speed (without the wind profile stability correction) and the SAR-derived wind speed (estimated using CMOD5), and the difference between the mean SAR-derived wind speed and the mean buoy speed. As with CMOD4, the results are listed for each of the three buoys as well as for the combined dataset. The mean difference is 1.71 m s^{−1} when NOGAPS wind directions are used and decreases to 0.9 m s^{−1} when buoy wind directions are used. Table 6 presents the corresponding linear robust regression results and statistics. The slope is 1.10 and the intercept is 0.53 m s^{−1}. Thus, the CMOD5 wind speed estimates are typically biased somewhat higher relative to the buoy than are those from CMOD4. The standard errors of these parameters are small: 0.02 for the slope and 0.17 for the intercept. Thus, unlike CMOD4, CMOD5 exhibited both multiplicative and additive biases that were statistically significant at the 95% level. The SAR speed standard deviation from the best-fit line is from 2.22 m s^{−1}, a value very similar to that for CMOD4. The *r* ^{2} value is from 0.76, only slightly worse than the CMOD4 values. Compared with the CMOD4 results, CMOD5 has larger slopes, smaller intercepts, greater mean difference, and larger standard deviations. Because CMOD5 has greater multiplicative bias, higher speeds will be overestimated more than with CMOD4. Except for this latter effect, none of the differences are large, however.

Results for the runs using buoy wind directions (also in Table 6) were similar, with the exception of the *r* ^{2} value on buoy 46084, which was again markedly lower. The slope is 1.02 and the intercept 0.53 m s^{−1}, depending on the buoy. The standard errors of these parameters are small: 0.02 for the slope and 0.15 for the *y* intercept. The standard deviation is 1.90 m s^{−1} and the *r* ^{2} value is 0.76. Again, for the first two buoys, both wind directions from both sources were of similar utility for SAR wind speed retrieval, while for the third buoy the accuracy of the wind sensor remains doubtful.

As with CMOD4, stability correction has little impact on the CMOD5 biases. Table 7 gives the buoy wind speed (with the wind profile stability correction), the SAR wind speeds (estimated using CMOD5), and the difference between the mean SAR-derived speed and the mean corrected buoy speed. Figure 6 is the corresponding scatterplot of the SAR image CMOD5 wind speeds versus the buoy wind speeds with stability correction along with the best-fit line. Table 8 gives the linear robust regression results for this line. The standard deviations and *r* ^{2} values are not significantly changed by the stability correction. Likewise, for all buoys the multiplicative and additional biases with the stability correction are nearly identical to those obtained without the stability correction. Thus, for CMOD5, as with CMOD4, correcting for surface-layer stratification did not eliminate the departure of the biases from the perfect match values of 1.0 and 0.0.

As discussed above, the *r* ^{2} values for CMOD4 and CMOD5 vary somewhat depending on whether NOGAPS or buoy wind directions are used in the wind speed retrievals. These differences are small but sufficient to reverse the relative standings of the two retrieval algorithms. For this dataset, CMOD4 faired slightly better than did CMOD5 when NOGAPS wind directions were used, but the reverse was true when the buoy wind directions were used. This suggests that CMOD5 was more dependent on getting the wind direction right (i.e., it is more sensitive to wind direction) than was CMOD4.

Figure 7 shows the All Buoy histograms of the buoy speed, the CMOD4 wind speed estimate, and the CMOD5 wind speed estimate. These results were created without stability corrections. Despite the biases noticed above, the similarity in shape of these histograms shows how closely the range and distribution of the CMOD4 and CMOD5 wind speed estimates match those of the buoy wind speeds.

## 5. Discussion

The results presented above are best understood through comparison with previous studies of SAR wind speed retrieval accuracy. These prior studies differ from our analysis in a number of ways. First, there are differences in the geographic regions covered and, thus, in the range of wind speed, surface-layer stratification, and mesoscale variability encountered. Second, there are differences in the operating characteristics of SARs aboard different satellites. Third, there are differences in the source from which the wind directions were obtained. Fourth, there are differences in the source of the “truth” against which the SAR wind speed retrievals are tested. Pairwise comparison allows some separation of these effects and, thus, estimation of the effect of complex coastal orography on the accuracy of offshore SAR wind speed retrievals.

Working in the Gulf of Alaska and U.S. Atlantic Coast region, using NOGAPS wind directions, an alpha parameter of 0.6, and incidence angles ranging from 18 to 45 degrees, Monaldo et al. (2001) found the mean difference between SAR wind speeds using CMOD4 and buoy wind speeds to be 1.06 m s^{−1}, consistent with the mean differences in the procedure above. The standard deviation of the SAR wind speeds was found to be 1.83 m s^{−1}, which is the same order as those found in Tables 2 and 4. For incident angles ranging only from 25° to 45°, Monaldo et al. (2001) determined a multiplicative bias of 0.91 and an *r* ^{2} value of 0.9, again the same order as the results found herein, although the higher *r* ^{2} values suggest less scatter in this predominantly Atlantic dataset than in the waters along the mountainous Alaskan coast. Because Monaldo et al. (2001) differed from the current study primarily in location, this comparison suggests that the mountainous Alaskan coast increased the scatter (lower *r* ^{2}) without having a major impact on the additive and multiplicative biases of the CMOD4 algorithm.

Horstmann et al. (2003) used the European Remote Sensing (ERS) satellite *ERS-2* and a fixed incidence angle of 23° to compare SAR-derived wind speeds found using CMOD4 with speeds found using the *ERS-2* scatterometer as well as those from the European Centre for Medium-Range Weather Forecasts (ECMWF) model analyses and forecasts. The wind direction values required for the SAR wind speed retrievals were taken from the same source as the verifying wind speeds. Their study was global in scope, in contrast with the regional focus of the other studies discussed here. Thus, the images analyzed were primarily from the open ocean well away from mountainous coasts. Moreover, a filter was applied to eliminate those images with mesoscale or microscale structures. The SAR versus scatterometer comparisons on these “clean” data yielded results that were, for some statistics, better than those obtained by the more inclusive studies. While the *r* ^{2} of 0.9 was the same as that of Monaldo et al. (2001), the bias of 0.01 m s^{−1} and RMSE of 1.0 m s^{−1} were smaller than those found by the current study and Monaldo et al. (2001). These differences suggest that the CMOD4 retrieval model is better calibrated for uniform scenes in the open ocean than for near-coastal areas and regions with mesoscale variability and microscale gustiness. The Horstmann et al. (2003) statistics for SAR versus ECMWF model wind speeds were closer to those obtained in this study and that of Monaldo et al. (2001), presumably because the error in the model analyses and forecasts exceeded that in the *ERS-2* scatterometer wind speed retrievals.

Considering several coastal regions, mainly in the North and Baltic Seas, Koch and Feser (2006) compared SAR wind speeds derived using CMOD4 with those produced by the mesoscale numerical Regional Model (REMO). The wind direction values needed for CMOD4 were obtained from two sources: The first using the streak method, and the second using directions given by REMO. Both methods are of similar accuracy, yielding similar mean differences, standard deviations, and correlations. The mean differences were found to be −1.54 m s^{−1} using the streak method and −1.60 m s^{−1} using REMO wind directions and are of the same order of magnitude as those found in Tables 1 and 3, but larger than those found by Horstmann et al. (2003) using ECMWF model wind directions and predominantly noncoastal images. The standard deviations were 2.92 m s^{−1} using the streak method and 3.01 m s^{−1} using REMO wind directions. These values are slightly larger than those shown in Tables 2 and 4 and about twice those obtained by Horstmann et al. (2003). Koch and Feser (2006) found *r* ^{2} values of 0.80 and 0.79, similar results to those obtained in this study and smaller than those obtained in the other studies discussed here. The larger standard deviations and the smaller correlation presumably result from a combination of coastal effects and errors in the REMO model winds in the challenging coastal environment.

Taken together, these comparisons suggest that SAR wind speed retrievals are most accurate in those open-ocean images with no mesoscale variability or microscale gustiness. Increased wind speed variability, whether due to complex coastal flows or other causes, degrades either the accuracy of the SAR wind speed retrievals or the verifying model and observational data. Nonetheless, SAR wind speeds retrieved off of the mountainous coast of Alaska yield *r* ^{2} values 85% as great as those for “clean” open-ocean images, with standard deviations increasing from about 1 m s^{−1} for clean open-ocean image to about 2 m s^{−1} for the Alaskan coast. This difference in skill may result from two causes. First, the wind directions required by the SAR wind speed retrieval models are much harder to obtain with accuracy in the presence of complex terrain-induced mesoscale flows. Second, the difficulty in obtaining an exact match between SAR- and buoy-sampled air parcels has much greater consequences as the flow variability increases. This would cause the SAR–buoy differences to be larger near the coast Alaskan coast than in previous, open-ocean, studies in spite of the better temporal collocations used in this study.

## 6. Conclusions

This study compares SAR-based wind speed estimates with those from buoys off of the mountainous coast of the coastal Gulf of Alaska for approximately 700 cases across a 7-yr period. The results were used to evaluate the performance of CMOD4 and CMOD5 in this challenging environment and to ascertain the effect of the stability correction on the additive and multiplicative biases of the SAR-based wind speed estimates. The skill of the resulting SAR wind speed estimates was quantified using the correlation with buoy-measured wind speeds.

Application of the CMOD4 algorithm to the SAR images yielded wind speed estimates within an *r* ^{2} value of 0.78. The remaining unexplained variance in the SAR estimates is not related to surface-layer stability, as there was in fact a small decrease in accuracy when the buoy wind speeds were corrected for stability. Instead, the SAR–buoy disagreement has been related to the representativeness of the SAR and buoy data (Stoffelen and Anderson 1997a) and to errors in the wind direction values derived from the NOGAPS global model analyses (Hogan et al. 1991). The correlation between the two was maximized with an SAR-averaging half-width of 12 pixels (a 225 km^{2} averaging area). This averaging eliminates from the SAR image those gusts that are too small in scale to correlate with the buoy observations given the SAR–buoy time difference of up to 5 min. The contribution of wind direction error to the small disagreement between SAR and buoy wind speed estimates might be reduced by using the analyses of a numerical weather prediction model that better resolves the mountainous coastal terrain, but only if it does not also introduce spurious small-scale variations in wind direction (see, e.g., Mass et al. 2002).

The robust regression equation predicting CMOD4 SAR speed from buoy speed has an intercept of 0.74 m s^{−1} and a slope of 1.01, neither value representing a statistically significant bias at the 95% confidence level. Surface-layer stability did not account for these biases, even in this region adjacent to a mountainous coast, as the neutral and stability-corrected analyses were nearly identical. Thus, CMOD4 has considerable skill despite the “worst case” nature of this test.

While the CMOD5 results are similar to those for CMOD4, there are some minor but interesting differences. CMOD5 estimates had an *r* ^{2} value of 0.76 with buoy-observed wind speeds with a small decrease in accuracy when these buoy observations were corrected for stability. As with CMOD4, averaging with a 12-pixel half-width yielded the greatest SAR–buoy correlation.

The multiplicative bias noted for CMOD5 is somewhat greater than for CMOD4. The robust regression equation predicting SAR speed from buoy speed has an intercept of 0.53 m s^{−1} and a slope of 1.10, both values statistically significant at the 95% confidence level. CMOD5 had a multiplicative bias of 1.10 compared with the 1.01 value for CMOD4. As with CMOD4, surface-layer stability did not account for the biases. Thus, for the mountainous coast of the Gulf of Alaska, CMOD4 provided a slightly better estimate of 10-m wind speeds, as seen by the smaller multiplicative bias, and slightly higher *r* ^{2} values. Both algorithms, however, did very well, with standard deviations of only 2.12 m s^{−1} for CMOD4 and 2.22 m s^{−1} for CMOD5. Thus, despite the small biases, the wind speed histograms for these two algorithms were similar in shape to that of the buoy observations. One possible explanation for the CMOD5 multiplicative bias is that CMOD5 was tuned to the lowest level of a numerical model analysis rather than to 10-m observations. If this model level were higher than 10 m, CMOD5 would yield proportionately higher wind speeds as a result of the log wind law.

Future work should involve verification of these results in other potentially challenging regions, particularly those with different wind speed and stability regimes. Likewise, the buoy-to-buoy variation in the statistics warrants comparisons with more buoys along other mountainous coasts. Doing so would require systematic acquisition of far more SAR images than are currently available. Such access remains a political as well as a technical issue (Beal et al. 2005; Sikora et al. 2006).

## Acknowledgments

This research was funded by National Science Foundation Grants ATM-0240869 and ATM-0240269. The authors are grateful to Frank Monaldo and Don Thompson for numerous technical discussions and for access to the algorithms used to perform the analysis. We also thank Ken Loescher for help with data acquisition and Nels Shirer for constructive comments and advice on the language used.

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The *r* ^{2} values for SAR–buoy wind speed as a function of the averaging half-width used. The dashed line with diamond markers represents buoy 46082, the dotted line with square markers represents buoy 46083, the dotted–dashed line with triangular markers represents buoy 46084, and the solid line with asterisks represents data from All Buoy. The maximum for All Buoy is indicated by the arrow.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

The *r* ^{2} values for SAR–buoy wind speed as a function of the averaging half-width used. The dashed line with diamond markers represents buoy 46082, the dotted line with square markers represents buoy 46083, the dotted–dashed line with triangular markers represents buoy 46084, and the solid line with asterisks represents data from All Buoy. The maximum for All Buoy is indicated by the arrow.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

The *r* ^{2} values for SAR–buoy wind speed as a function of the averaging half-width used. The dashed line with diamond markers represents buoy 46082, the dotted line with square markers represents buoy 46083, the dotted–dashed line with triangular markers represents buoy 46084, and the solid line with asterisks represents data from All Buoy. The maximum for All Buoy is indicated by the arrow.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

Scatterplot of the wind speed for All Buoy (without stability correction) vs the SAR wind speed estimates (CMOD4 using NOGAPS wind directions) along with the gray line described by linear robust regression where buoy speed = 1.01 × SAR speed + 0.74 and the black line marking the ideal one-to-one relationship.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

Scatterplot of the wind speed for All Buoy (without stability correction) vs the SAR wind speed estimates (CMOD4 using NOGAPS wind directions) along with the gray line described by linear robust regression where buoy speed = 1.01 × SAR speed + 0.74 and the black line marking the ideal one-to-one relationship.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

Scatterplot of the wind speed for All Buoy (without stability correction) vs the SAR wind speed estimates (CMOD4 using NOGAPS wind directions) along with the gray line described by linear robust regression where buoy speed = 1.01 × SAR speed + 0.74 and the black line marking the ideal one-to-one relationship.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 3, but for wind speed for All Buoy (with stability correction). The gray line is buoy speed = 1.03 × SAR speed + 0.68.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 3, but for wind speed for All Buoy (with stability correction). The gray line is buoy speed = 1.03 × SAR speed + 0.68.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 3, but for wind speed for All Buoy (with stability correction). The gray line is buoy speed = 1.03 × SAR speed + 0.68.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 3, but for the SAR wind speed estimates (CMOD5 using NOGAPS wind directions). The gray line is buoy speed = 1.10 × SAR speed + 0.53.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 3, but for the SAR wind speed estimates (CMOD5 using NOGAPS wind directions). The gray line is buoy speed = 1.10 × SAR speed + 0.53.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 3, but for the SAR wind speed estimates (CMOD5 using NOGAPS wind directions). The gray line is buoy speed = 1.10 × SAR speed + 0.53.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 5, but wind speed for All Buoy (with stability correction). The gray line is buoy speed = 1.12 × SAR speed + 0.47.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 5, but wind speed for All Buoy (with stability correction). The gray line is buoy speed = 1.12 × SAR speed + 0.47.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

As in Fig. 5, but wind speed for All Buoy (with stability correction). The gray line is buoy speed = 1.12 × SAR speed + 0.47.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

(a) Histogram of All Buoy data speeds converted to 10-m height without the wind profile stability correction. The corresponding histograms of the (b) CMOD4 and (c) CMOD5 wind speed estimates from the SAR images.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

(a) Histogram of All Buoy data speeds converted to 10-m height without the wind profile stability correction. The corresponding histograms of the (b) CMOD4 and (c) CMOD5 wind speed estimates from the SAR images.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

(a) Histogram of All Buoy data speeds converted to 10-m height without the wind profile stability correction. The corresponding histograms of the (b) CMOD4 and (c) CMOD5 wind speed estimates from the SAR images.

Citation: Journal of Applied Meteorology and Climatology 47, 5; 10.1175/2007JAMC1716.1

The mean buoy speeds (converted to 10 m height without the wind profile stability correction) and SAR-derived speeds (estimated for 10 m using CMOD4). The method for wind direction retrieval is indicated as either the NOGAPS model (NG) or buoy instruments (BY).

Robust regression statistics for the relationship between buoy speeds (converted to 10 m height without the wind profile stability correction) and SAR-derived speeds (estimated for 10 m using CMOD4). Std err = standard error of parameter estimates. Std dev = standard deviation of SAR wind speeds relative to the best-fit line.