Radar Beam Refraction

The WSR-88D, like other weather radars, calculates the height of the radar beam centerline assuming a standard atmosphere. If the atmosphere deviates from standard refractive conditions, the radar beam also deviates from its assumed or normal propagation path. In other words, it refracts or bends just like a beam of light propagating through different media and can either subrefract or superrefract. Figure 10 is an illustration of the various beam propagation paths. Figure 11 is a Range vs. Height graph of beam centerline heights under standard refractive conditions.

Figure 10: Beam propagation paths for various atmospheric reflective index conditions.

The beam is assumed to refract a certain amount in the standard atmosphere. If it refracts less than normal, this is called subrefraction. The beam will be higher than the radar calculation and, hence, target height will be underestimated. Using 110 nm range and 1.5° elevation as an example, Fig. 11 indicates the beam centerline height is ~ 26,000 ft. Under subrefractive conditions, echo tops at 26,000 ft would be overshot by the radar beam and go undetected. The echo tops would be detected on a lower elevation slice.

Figure 11: Beam centerline height for various ranges as a function of elevation angle assuming standard refractive conditions. These curves are derived from the WSR-88D Beam Height Equation, Equation (12)

Subrefraction occurs when the atmospheric temperature lapse rate approaches dry adiabatic, and when moisture increases with height. The classic scenario is an "inverted-V" sounding with a moist layer aloft which, in the United States, occurs most frequently in the west, especially in the summer. In addition to underestimated echo heights, this phenomenon tends to reduce ground clutter in the lowest elevation cuts.

Superrefraction

The opposite situation, superrefraction, occurs when the radar beam refracts more than standard. The beam will be lower than calculated and target height will be overestimated. The classic situation is a temperature inversion, either at the surface or aloft, and can be caused by terrestrial radiation, subsidence, thunderstorm outflows, cold advection behind a front, etc. Besides overestimated echo heights, superrefraction increases ground clutter in the lowest elevation cuts and is the cause of what we normally refer to as anomalous propagation or AP echoes.

As an example, using 90 nm range and 1.5° elevation, Figure 11 indicates the beam centerline height is ~ 19,000 ft. Under superrefractive conditions, echo tops at 19,000 ft would be undershot by the radar beam. The echo tops would be detected on a higher elevation slice.

Ducting is a special superrefractive condition such that the radar "beam" gets trapped or "ducted" within a stable layer or temperature inversion. This causes the beam to bend downward more than normal, but the beam rarely comes in contact with the ground. Operationally, this is an extreme case of superrefraction which can result in the detection of targets well beyond the operating R_max.

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