Tropospheric Effect on Electromagnetically Measured Range: Prediction from Surface Weather Data


  • H. S. Hopfield


Knowledge of the height integral of atmospheric refractivity (n — 1), where n is the refractive index, is essential for prediction of atmospheric range effect at any elevation angle. Observed values of the height integral for the lower, nonionized atmosphere can be obtained from weather balloon ascent data. Year-long collections of data from widely separated locations were used to relate this integral to surface data. Although (n — 1) at any point in a dry atmosphere depends on both pressure and temperature (the ratio P/T), the height integral of the observed dry part of (n — 1) is a linear function of surface pressure only, not of temperature. This is theoretically correct since P/T is equivalent to density, and the integral of density with height yields surface pressure. By application of this finding, the equivalent height for a (theoretically justified) quartic (n — 1) model (dry part) should be found to vary directly as surface temperature; the value obtained (least-squares fit to observed data) is 40.1 km for surface T = 0°C with a height expansion coefficient of 0.149 km per surface degree C. This would reduce the equivalent height to zero near 0° Kelvin. This theoretical model matches observed height integrals with an rms error of a few millimeters out of 2.3 meters (far less than 1%). Agreement between stations is excellent. A study of the more variable but much smaller wet part is in progress. The wet part is significant at radio but not at optical frequencies.