page_title: Millimeter cloud radar
section_title: The Doppler spectra
hierarchical_section_title: Millimeter cloud radar / The Doppler spectra
caption_attribution_description: English: The figure shows a radar Doppler spectrum.
context_page_description: Millimeter-wave cloud radars, also denominated cloud radars, are radar systems designed to monitor clouds with operating frequencies between 24 and 110 GHz. Accordingly, their wavelengths range from 1 mm to 1.11 cm, about ten times shorter than those used in conventional S band radars such as NEXRAD.
context_section_description: Usually numerous targets are present in the sample volume of the radar. Each of the individual targets produces a frequency shift according to its radial velocity. Measuring
  the returned power in any interval of the frequency shift allows the detection of the Doppler spectrum. This is illustrated in the Figure on the right, where a sketch of the Doppler spectrum is shown. The frequency is already converted into velocity in the x axis.
  From the Doppler spectrum the reflectivity  can be calculated using the expression:
  The integral of the spectral power  is called the 0-moment of the Doppler spectrum, which equals the reflectivity . Further, the first moment (8) and the second moment (9) of the Doppler spectrum can be calculated:
  The first moment of the Doppler spectrum is the mean Doppler velocity . It corresponds to the mean radial velocity in the sampled volume.
  The second moment is called the Doppler width . It corresponds to the variance of the Doppler spectrum. The Doppler width basically is a measure of the width of the spectrum of the detected velocities. It can also be a measure of the number of modes the targets size distribution has. A mono-modal distribution gives a small spectral width. A distribution that has several modes yields a lager spectral width, as illustrated in Figure 5. The spectral width is also influenced by turbulent motion of the targets in the sample volume: the spectral width increases with increasing turbulence.
  The expressions to calculate the Kurtosis and the Skewness are coming out of mathematical statistics several formulations are used. Some of them can be found in the quoted literature in Kurtosis section.
caption: Sketch of a Doppler spectrum. The spectral power 
    
      
        
          S
          (
          
            v
            
              d
            
          
          )
        
      
      {\textstyle S(v_{d})}
    
   is represented as a function of the Doppler velocity 
    
      
        
          
            v
            
              d
            
          
        
      
      {\textstyle v_{d}}
    
  . The parameters 
    
      
        
          
            v
            
              m
              i
              n
            
          
        
      
      {\textstyle v_{min}}
    
   and 
    
      
        
          
            v
            
              m
              a
              x
            
          
        
      
      {\textstyle v_{max}}
    
   denote the minimum and the maximum velocities, at which 
    
      
        
          S
          (
          
            v
            
              d
            
          
          )
          >
          0
        
      
      {\textstyle S(v_{d})>0}
    
  , and 
    
      
        
          d
          v
        
      
      {\textstyle dv}
    
   is the velocity resolution.
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