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

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Beam Propagation Equation

WSR-88D Range Height Equation

The Range vs. Height diagram shown in Figure 11 is based on the WSR-88D Range Height Equation assuming standard refractive conditions. Equation (12) is the mathematical expression used to derive the height (h) curves in the diagram. For consistency, the height calculations generated by all WSR-88D algorithms use the following equation:

H = SR*sin PHI + (SR*SR)/(2*IR*RE)


    H = height of the beam centerline above radar level in km
    SR = slant range in km
    PHI = angle of elevation in degrees
    IR = refractive index, 1.21, and
    RE = radius of earth, 6371 km.

For product generation, the metric units (km) are converted to nm and kft as necessary. The height calculations for the VCP graphics (Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, and Figure 24) are based on this equation.

NOTE: This equation is used by the WSR-88D Radar Product Generator (RPG) to compute radar beam heights. AWIPS radar beam height readouts may not match these heights exactly because AWIPS uses a slightly different formula in its computations.

Next Page: WSR-88D Range Resolution