Radar Baak-Saatter from the Sea Surface 





c'^ 



•(I) 



2 



= (4)^ (21) 



For small depression angles (k3 « k ), the effect of the 

 carrier-wave slope becomes comparable with the phase shift induced 

 by the vertical displacement, and the relations (20), (21) should be 

 modified to include additional terms dependent on k° . However, 

 this requires a more detailed investigation of the electromagnetic 

 and hydrodynamic interactions. ' 



Exanaples of Doppler spectra obtained by Ward [ 22] from the 

 sea echo of 21.840 MHz (14 m) waves at ranges near 3000 km are 

 shown in Fig. 11. The analysis was based on short records of one 

 minute duration, so that the continuum is poorly resolved statistically 

 and individual spectra vary strongly. However, there is some indi- 

 cation of two side-band structures appearing on either side of a 

 central Bragg peak. Theoretically, the Bragg line should lie at 

 0.48 Hz, which agrees well with the central peak of the first spectrum 

 shown, but is somewhat to the left of the main peaks in the other 

 cases. The displacement of the side lobes relative to the Bragg peak 

 is of the order 0.1 Hz expected for typical ocean-wave frequencies. 



The ratio of the side-band energy e^^ = J X^^' (<*>d) ^'^'d *° ^^^ 

 energy e^'' of the Bragg line is given according to Eqs. (18) and 

 (21) by 



e^^Ve"^ =4(k;)'(^') 



Ward estimates a depression angle of 12°, which yields 



e'2Ve^'\ = 0.036<(am])^) 



The observed ratios of order unity correspond to root mean square 

 wave heights of about 5 m, which appear rather high, but not im- 

 possible. 



More plausible estimates of the wave height may have 

 resulted from a more accurate determination of the scattering 

 function ratio T /T at small depression angles. Contamination 

 of the observed spectra by ionospheric Doppler shifts may be an 

 alternative explanation of the high ratios €^^^ /c^'^ . A spurious inter- 

 action between the Bragg line and the low frequency ionospheric 

 Doppler spectrum could also have been introduced in the present 

 experiment by the data analysis, since the Doppler spectra appear 

 to have been computed -- as is often done -- from the time series of 

 » Note added in proof: A detailed analysis has recently been carried 

 out by D. E. Barrick "Dependence of Second-Order Doppler Side 

 Bands in HF Sea Echo on Sea State," to appear in 1971 G-AP 

 Inter nat, Symp, Digest. 



385 



