G. Daniel Dockery

Theoretical description of the parabolic approximation/Fourier split-step method of representing electromagnetic propagation in the troposphere

A theoretical foundation for the use of the parabolic wave equation/Fourier split-step method for modeling electromagnetic tropospheric propagation is presented. New procedures are used to derive a scalar Helmholtz equation and to subsequently transform to a rectangular coordinate system without requiring approximations. The assumptions associated with reducing the resulting exact Helmholtz equation to the parabolic wave equation that is used for computations are then described. A similar discussion of the error sources associated with the Fourier split-step solution technique is provided as well. These discussions provide an important indication of the applicability of the parabolic equation/split-step method to electromagnetic tropospheric propagation problems. A rigorous method of incorporating an impedance boundary at the Earths surface in the split-step algorithm is also presented for the first time. Finally, a few example calculations which demonstrate agreement with other propagation models are provided.

Propagation measurements and modeling atCband for over-the-water, line-of-sight propagation links in the Mid-Atlantic coast

Fade, radar, and propagation modeling results are described for two nearby over-the-water, line-of-sight, propagation links operating at 4.7 GHz in the Mid-Atlantic coast of the United States. During a 5 day “intense experimental period” in August 1989 a focused examination of the propagation mechanisms relating to time series fading was conducted. Cumulative fade distributions associated with both propagation paths are presented for the individual days and the overall 5-day period. During this period, helicopter measurements of the refractivity structures along the propagation paths, boat measurements of the refractivity structure near the ocean surface at the center of the paths, and radar measurements of the clear atmosphere and ocean backscatter were executed. The refractivity measurements were interfaced with a complex parabolic equation propagation model which incorporated the two-dimensional structure of the refractive index to yield normalized power density structures as a function of range and height for the geometry of the propagation links. These results were compared with the time series fade measurements and provided clear indications of the mechanisms for fading and nonfading events. Azimuthal and vertical radar scans employing a high-resolution radar at the NASA Wallops Flight Facility showed excellent correlation between strong backscatter returns from the ocean surface well beyond the standard horizon and ducting events as evidenced by signal fading along the propagation links.

Three years of C band signal measurements for overwater, line‐of‐sight links in the mid‐Atlantic coast: 2. Meteorological aspects of sustained deep fades

The morphology of deep and long-lived fades for line-of-sight, overwater propagation links in the mid-Atlantic coast are examined. Such events, known as sustained deep fades (SDF), are analyzed employing weather maps, in situ measurements from radiosondes, an instrumented helicopter, and sensors on coastal platforms. These events occurred exclusively from November through July over the 3 years in which fade statistics were amassed; no SDF events were observed during the months August, September, or October. The SDF events biased the 3-year fade statistics described in a companion paper. The results have demonstrated that synoptic weather conditions created by a sustained high-pressure system over the subtropical Atlantic and occasionally by a sustained low-pressure system whose center lies west of the coastal region result in a steady flow of warm, humid air at higher altitudes. When coupled with colder water conditions, such a flow results in a surface temperature inversion, an increase of water vapor pressure with altitude, and a positive lapse rate of the radio refractivity. This condition leads to severe subrefraction resulting in fades ranging from 20 to 60 dB for durations in excess of 2 hours and lasting as long as 2 days. Propagation modeling using a refractivity profile derived from sensors on board a helicopter during an SDF event predicted the same range of fades as were measured during that period.

Three years of C band signal measurements for overwater, line‐of‐sight links in the mid‐Atlantic coast: 1. Fade statistics

Three years of fade statistics are described for two overwater, line-of-sight propagation linksalong the mid-Atlantic coast of the United States operating at 4.7 GHz. Single-terminal, joint fade, and fade duration statistics derived from time series of received signal losses due to refractive and diffractive effects are described for combined-year, annual, and monthly cases. In particular, year-to-year and month-to-month variabilities in the statistics and also the efficacy of employing space diversity for the two links to mitigate fade margin requirements are examined. Sustained deep fade (SDF) events due to severe subrefraction during the 3-year period tended to dominate the statistics. Statistics have been culled in terms of contiguous month groupings during which SDF events occurred (November–July) and did not occur (August–October) over the 3-year period. Although the year-to-year variability in the annual fade statistics was relatively small, the year-to-year variability in the monthly statistics was large, especially during the April–July period, which separated the periods during which deep subrefractive fades were maximum and the periods during which they were nonexistent.

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

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 near-continuous 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%.