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The TOPEX CD of Geophysical Data Records includes estimates of 1 Hz s^{0} values and of wind speeds derived from s^{0}. Wind speed is calculated from an algorithm obtained by AVISO (1996) by fitting a table, given by Witter & Chelton (1991), of wind speed:s^{0} values from Geosat data. To adjust for differences in observed values of s^{0 }from Geosat and from TOPEX Kuband, 0.63 dB is subtracted from the TOPEX value before entering the algorithm. The wind speed written to the CD is rounded to the nearest 0.1 m/s.
Recently, improvements to the algorithm have been sort by including the altimeter estimates of significant wave height (Hs) as well as s^{0}; for example by Gourrion et al. (2000) who derive algorithms for wind speed from an analysis of altimeter and scatterometer crossovers. Gommenginger et al. (in press) compare values from a range of algorithms against buoy wind speeds and conclude that Gourrion et al's algorithm derived using a multilayer percepton (MLP) network design (see Annex A below) gives the 'best overall results for a twoparameter algorithm'.
This note compares colocated wind speeds from US NDBC buoys and from the TOPEX B transmitter (operational since February 1999) from the AVISO (1996) algorithm with s^{0}  0.63 (i.e. the wind speed on the CD but not rounded to 0.1 m/s) and from the Gourrion et a/. (2000) MLP algorithm with the Kuband estimates of s^{0} and Hs (neither adjusted).
The derivation of the data set of 992 pairs of US NDBC buoy and TOPEX data are described in Cotton (2001). The criteria for "coincident" altimeter and buoy data were 50 km and 30 minutes; for each event, the single altimeter 1 Hz data record closest to the buoy location was used. Buoy speeds were adjusted, when necessary, to that at 10 m above the sea surface.
Figure 1 shows the buoy wind speeds plotted against those from TOPEX using the oneparameter algorithm with s^{0} reduced by 0.63 dB, together with the line obtained by orthogonal distance regression (assuming both buoy and TOPEX winds have errors of equal magnitude).
The regression equation is:
U(TOPEX) = 1.135 U(buoy)  0.721 (1)
The residual standard deviation is 0.89 m/s, and slope and intercept are significantly different from 1 and 0 respectively. 95% confidence limits are included in Table 1 (below). (Using the wind speeds on the TOPEX CDROM, specified to 0.1 m/s, gives slope and intercepts of 1.136 and 0.725 respectively.)
Figure 2 shows the buoy wind speeds plotted against those from TOPEX using the twoparameter MLP algorithm with TOPEX s^{0} and Hs. The regression equation is:
U(MLP) = 1.073 U(buoy)  0.539 (2)
with residual standard deviation of 0.83 m/s. Again, both slope and intercept are significant, but closer to 1 and 0 than in Equation 1.
However, the plotted data do not appear to be distributed quite linearly; the low wind speeds do not seem to fit. So regressions were carried out fitting only data pairs with both buoy and MLP wind speeds greater or equal to a cutoff ranging from 2.5 m/s to 10 m/s. Results are included in Table 1, and show that with increasing cutoff the slope decreases towards 1 and the intercept approaches 0. For cutoff at 5 m/s the 95% confidence limits of slope and intercept cover 1 and 0 respectively, and the residual standard deviation is reduced to 0.74 m/s.
The regression of the 197 pairs with both buoy and TOPEX MLP values less than 5 m/s is shown in Figure 3. The regression equation is:
U(MLP) = 1.203 U(buoy)  1.090 (3)
But note the scatter in the figure and the rather wide confidence limits given in Table 1. (Some of this scatter may be because of relatively large variations over 50 km and 0.5 hr when winds are light, or because of the high sensitivity of U to s^{0} at low U.)
The above analyses use uncalibrated TOPEX Hs values. Regressing TOPEX and buoy Hs (Figure 4) gives:
Hs(TOPEX) = 0.9638 Hs(buoy) + 0.0650 (4)
i.e
Hs(buoy) = 1.038 Hs(TOPEX)  0.0674 (5)
Using TOPEX Hs corrected by Equation 5 in the MLP algorithm, instead of the unadjusted values, makes very little difference to the results. For example, the slope and intercept of U(MLP) on U(buoy) of all the 992 data pairs become 1.070 and 0.521, compared to 1.073 and 0.539 in Equation 2.
The good agreement between wind speeds from US NDBC buoys and those from TOPEX obtained from the MLP algorithm of Gourrion et al (2000) using Transmitter B s^{0} and Hs values indicates that for wind speeds above 5 m/s no calibration is required.
At wind speeds less than 5 m/s the situation is not so clear  see Figure 3. Equation 3 suggests that the algorithm underestimates the true (buoy) wind speed, increasingly so with decreasing wind speed, but the use of equation 3 would result in no estimated speed less than 0.9 m/s. Further research is clearly needed if altimeter measurements of low wind speeds are to be better resolved; meanwhile no large errors will result if, as for higher wind speeds, no calibrations are applied to the values from the MLP algorithm.
Note that if the MLP algorithm is used with data from Geosat or ERS altimeters then the s^{0} value entered into it should be the measured value plus 0.63 dB.
AVISO 1996
AVISO User Handbook: Merged TOPEX/POSEIDON Products
AVINT02101CN, Edition 3.0, July 1996. CNES, Toulouse.
Cotton
P. D. 2001
TOPEX B Side Altimeter Wind Speed and Significant Wave Height
Calibration (19992001).
Satellite Observing Systems Unpublished note.
Gommenginger C. P., Srokosz M. A., Challenor P. G. &
Cotton P. D. [In press]
Development and validation of altimeter wind speed algorithms
using an extended collocated buoy/Topex dataset.
IEEE TGRS.
Gourrion, J., Vandemark D., Bailey S. & Chapron B. 2000
Satellite altimeter models for surface wind speed developed using
ocean satellite crossovers.
Ifremer Tech. Report No. IFREMERDROOS200002.

Eq. 
Number 
Intercept/ 
95%ile 
range 
Res. s.d. 
U(s^{0}):buoy 
1 
992 
0.7206 
0.9461 
0.4950 
0.894 



1.1355 
1,0461 
1.09951 

U(s^{0},Hs):buoy 
2 
992 
0.5386 
0.7415 
0.3357 
0.833 
1.0728 
1.0461 
1.0995 

U(s^{0},Hs):buoy >2.5 
900 
0.3709 
0.6053 
0.1366 
0.795 

1.0536 
1.0241 
1.0832 

U(s^{0},Hs):buoy >5.0 
684 
0.1728 
0.4960 
0.1505 
0.741 

1.0320 
0.9950 
1.0690 

U(s^{0},Hs):buoy >7.5 

375 
0.1592 
0.7460 
0.4276 
0.734 



1.0270 
0.9689 
1.0851 

U(s^{0},Hs):buoy >10.0 

113 
0.1047 
1.2364 
1.4459 
0.769 



1.0079 
0.8977 
1.1182 

U(s^{0},Hs):buoy <5.0 
3 
197 
1.0900 
1.6609 
0.5191 
0.729 



1.2034 
1.0346 
1.3722 

Hs:buoy 
4 
992 
0.0650 
0.0348 
0.0952 
0.172 



0.9638 
0.9499 
0.9777 

where
and
where
and
where
Then wind speed (in metre/sec) is given by:
where
and