DLOC Principles of Meteorological Doppler Radar:
WSR-88D Fundamentals

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Simplified Radar Equation and Signal Attenuation

For the WSR-88D, the only variables that are not fixed are returned power (Pr), reflectivity (Z), attenuation factor (La), and range (R). The fixed variables are combined to create a new term which we will refer to as the radar constant, Cr. By combining the fixed variables into a radar constant, Equation (1) simplifies into

Equation 3.  Simplified Radar Equation.  Click for long description.

where Cr is the radar constant. Solving for Z, the above equation, Equation (3), becomes


Equation 4.  Simplified Radar Equation solved for Z.  Click for long description.

By knowing the returned power and range (based on timing), the above equation, Equation (4), estimates target reflectivity.


A radar pulse can lose power as it travels through the atmosphere and areas of precipitation (i.e., a process know as attenuation). The wavelength (i.e., ~ 10 cm) used by the WSR-88D is less vulnerable to attenuation than shorter wavelength weather radars. However even with the WSR-88D, significant attenuation is possible down radial of areas of heavy rain or hail. For Reflectivity (Z), attenuation results in an underestimate of the dBZ values down radial from the heavy rain or hail.

Differential Attenuation

Attenuation can occur in both the horizontal and vertical channels. When attenuation impacts both channels, its referred to as differential attenuation. For Differential Reflectivity (ZDR), differential attenuation results in an underestimate of the dB values down radial from the heavy rain or hail. The degree of attenuation between the channels can vary. Therefore, the impact on ZDR also varies (i.e., extent of the underestimate)

Attenuation and differential attenuation are sometimes visible in the base products. Even when not obvious in the base products, bi-products of attenuation and differential attenuation may be noticed in the derived products (especially in the dual-polarization precipitation estimation products).

Next Page: Reflectivity