SECT. 4] OTHER ELECTROMAGNETKl RADIATION 473 



that reflectivity depends most sensitively on conductivity for grazing angle of 

 incidence. At this angle 



Arir = AalGx'2, 



that is. the percentage change of reflection coefficient is of the same order as 

 percentage change in conductivity. 



The percentage change in conductivity is given by 



Aa 0.19 JT _^ 



The numerical value, 0.19, is the activation energy for sea-water. Hence a 

 1°C change in temperature will result in a 2.4% change in the conductivity of 

 sea-water. A reflectivity change of 2.4% is readily observable without elaborate 

 instrumentation . 



B. Radar Reflection from the Sea-Surface 



Two types of sea waves are primarily responsible for the back scattering of 

 ultra-high frequencies (radar). First, there are the highest amplitude gravity 

 waves. These are obviously effective scatterers simply because most of the 

 wave energy is concentrated in these waves. Secondly, there are surface waves 

 whose wavelengths happen to be close to "resonance" with the incident radar 

 wavelength ; because radar wavelengths are short, usually in the vicinity of 

 3 cm, these waves will generally be capillary or very short gravity waves. 



Consider first the well-developed sea waves : the phase velocity of these 

 waves, providing a moving target, will generate a Doppler shift in the scattered 

 radiation. For example, a gravity wave of wavelength 22 meters with velocity 

 600 cm/sec will be responsible for a Doppler shift given by AF — 2AvjX — 

 1200/A. Hence 3-cm radar will be shifted in frequency approximately 400 c/s. 

 This frequency shift is readily detectable with present equipment. In general 

 this frequency shift will be broadened by 10 to 20% by the effect of the particle 

 velocity in these well-developed waves. 



The wavelengths of sea waves which "resonate" or give maximum back 

 scattering are obtained from the familiar optical grating formula. 



sin i3-f sin 6 = Xjd, 



where d is now interpreted as the scattering wavelength on the sea-surface. 

 For maximum back scattering at grazing incidence (sin ^ = sin ^= 1) the 

 relation between radar wavelength. A, and capillary wave, d, is X=2d. This 

 result may be interpreted as meaning that, of the broad spectrum of capillary 

 waves ever present, only those waves satisfying this "resonance" relationship 

 will be effective scatterers. For example, 3-cm radar will "resonate" with sea 

 waves of wavelength 1.5 cm. These are capillary waves whose velocity is 

 24 cm/sec ; this results in a frequency shift of 32 c/s. Hence the statement can 

 be made that 3-cm radar will always exhibit a Doppler modulation of 32 c/s in 

 sea return. 



