K factor statistics for subrefraction in the mid‐Atlantic coast of the United States

Abstract

Abstract. Statistics of "equivalent K factor" are derived for the mid-Atlantic coast of the United States. These statistics are associated with subrefraction using 3 years of nearcontinuous line-of-sight link signal measurements at 4.7 GHz in the mid-Atlantic coast of the United States. Probabilities are derived for a family of threshold levels of K factors ranging from 0.6 to 1.0 which are sustained over durations exceeding 1-5 hours. An analytical model is derived that characterizes this family of curves with excellent accuracy. It is, for example, demonstrated that for 6% of the average year the K factor is smaller than 1 for durations greater than 1 hour in the mid-Atlantic coast of the United States. Caveats that should be considered in applying these results are reviewed. Monthly probabilities of K factor statistics reveal that the winter and early spring months dominate. For example, during February of year 1 and December of years 2 and 3 the K factors were smaller than 0.8 for periods exceeding 2 hours at the probabilities of 11.5%, 12.0%, and 11.5%, respectively. This result is consistent with the fact that cold water conditions and warm overlying moist air are more prevalent during the winter season. These conditions represent the correct meteorological ingredients for extreme subrefraction to occur. Annually, the K factor was smaller than 0.8 with durations greater than 1 hour at a probability of 3.2%. The bending effects of propagating rays may be partially accounted for by replacing the Earth's radius "a" by an effective radius "Ka," where K (hereinafter called the K factor) is a constant that may be smaller or greater than 1. This concept was first introduced by Schelling et al. [1933] and was expanded by Lagrone [1960], who showed 5 year averages of "K factor" isopleths for the winter and summer months throughout the United States. These contours were derived from averaged radiosonde measurements over the first 300 rn from the surface. The use of a K factor, such as K = 4/3, which is referred to as a "standard propagation condition," implies a particular rate of decrease of refractivity with height for all altitudes. For K = 4/3, this rate is approximately -40 N units 1425