How a Tornado Can Be Below the Radar Beam

The radar beam of the 88D inherently rises with height as range increases. In the first place, to avoid strong ground returns, the radar's rotating antenna is tilted at a slight upwards angle (the minimum tilt is 0.5 degrees). Thus it naturally gains altitude with range. If this were the only limitation, the beam would rise geometrically with respect to the surface (which would be considered flat). That is, the center line height of the lowest beam segment would be governed by Height=(tangent of 0.5 degrees)X(distance from radar). However, this is not quite the whole story, since 1) the earth's surface is curved, and 2) the radar beam is a little less curved. Thus the 88D's actual beam propagates at 4/3 the surface curvature. Needless to say, this can make it very pesky to find the exact height of the beam. (The actual equation, for anyone interested, is Height={slant range squared + 2X[(4/3 earth raduis)X(slant range)X(sin of 0.5 degrees)]} divided by {2X(4/3 earth raduis)}.)

If you bothered to make this height calculation for the location of the tornado in question, which was occurring at a range of about 77.5 nautical miles (about 144 kilometers) from the radar, you would have found that the center line height of the of the beam was 8500 to 8600 feet - about 1.62 statute miles - above the ground. Thus it is quite possible for intense rotations to exist below the height of the radar beam.

That's one of the main reasons we need spotters!