500 BULLETIN AMERICAN IV ITEOROLGGICAL SOCIETY [Vol. 29 Charts of Dielectric Constant or Kefractive Index of the Troposphere * ALBERT W. FRIEND Cruft Laboratory, Harvard University** ABSTRACT An index chart and seven sector charts are given for use in providing an easy conversion from radiosonde (RAOB) or similar tropospheric sounding data of the total atmospheric pressure (millibars) the temperature (°C) and the water vapor mixing ratio (grams per kilogram) to the dielectric constant or the radio frequency index of refraction of the atmosphere. Reference is made to 17 reports and papers which indicate possible applications of these data and variations thereof. URING THE PAST fifteen years there has nally placed vacuum-tube oscillator of a been a progressive increase in the real- satisfactory order of stability. The nominal D ization of the role played by the varia- operating frequency of approximately 12.8625 tions and stratifications of the dielectric Mcps was varied with respect to an extremely properties of the troposphere in the propaga- stable secondary standard of frequency. The tion of electromagnetic waves. Early in 1939, operation of the latter unit was repeatedly Mr. W. W. Mumford, of the Bell Telephone checked by comparison with the primary Laboratories wave-propagation group, men- standard of frequency of the National Bureau tioned, in correspondence with the author* of Standards, via the 5 Mcps standard fre- that they were computing the dielectric con- quency transmissions from station WWV. stant of the atmosphere by the expression The variations of frequency were deter- mined by means of standard General Radio (er - 1) • 106 = (p + 4800e/T) (157.5/T), (1) Company frequency deviation meters. The where p = total air pressure (millibars), deviations of frequency caused by changes of e = water vapor pressure (millibars) atmospheric conditions were measured to T = absolute temperature (degrees within about one part in five million. The Kelvin), and uniformity of conditions and the possible er = relative dielectric constant of the accuracy of measurement of the atmospheric air. parameters were limiting factors in attaining absolute verification of Equation (1). How- The accuracy of this equation was theoret- ever, the results checked quite well, in most ically checked in collaboration with Professors instances. Therefore it was assumed that R. C. Colwell and Maurice C. Holmes, of Equation (1) was reasonably accurate. It West Virginia University, at that time. was utilized and published in notes appended Laboratory experiments were also performed to the paper "Developments in Meteoro- to verify the equation. logical Sounding by Radio Waves,"1 in 1940 A chamber was constructed to provide vari- and in a second paper2 published in 1941. able pressure and humidity. Within this space an especially constructed air capacitor This equation was employed extensively was arranged in connection with an exter- during the latter part of the recent war in the computations of the variations of radar propagation conditions which are produced * The research reported in this document was made possible through support extended Cruft Laboratory, by atmospheric diffraction.3-4-5-6,7 This work Harvard University, jointly by the Navy Department (Office of Naval Research) and the Signal Corps, 1 A. W. Friend, "Developments in Meteorological U. S. Army under ONR contract N5-ORI-76, T. O. 1, Sounding by Radio Wave Echoes," Jour. Aero. Sci., 7: and was published as "Charts of Dielectric Constant 347-352, June 1940. or Refractive Index of the Troposphere," Albert W. 2 A. W. Friend, "Further Comparisons of Meteoro- Friend, Cruft Laboratory, Harvard University, Tech- logical Sounding by Radio Waves with Radiosonde nical Report No. 34, Contract N5-ORI-76, Task Order Data," Bulletin of the American Meteorological Society, No. 1, March 1948. This material was previously 22: 53-61, Feb. 1941. extracted from a thesis submitted in partial fulfillment 3 D. E. Kerr and P. Rubenstein, "An Introduction to of the requirements for the degree of Doctor of Science Microwave Propagation," M. I. T. Radiation Labora- in Communication Engineering, Albert W. Friend, tory, Report No. 4.O6, 16 September 1943. "Reflections of Vertically Propagated Electromagnetic 4 R. H. Burgoyne and I. Katz, "Low Altitude Meas- Waves from the Troposphere," Graduate School of urements in New England to Determine Refractive Engineering, Harvard University, August ,1947. Index," M. I. T. Radiation Laboratory, Report No. J+2, ** Now at Radio Corporation of America, RCA 22 February 1944. Laboratories Division, Princeton, New Jersey. 5 Weather Division, Headquarters Army Air Forces, Unauthenticated | Downloaded 10/07/21 10:27 AM UTC December, 1948] ARTICLES 501 was chiefly a broad and expansive extension tables, and nomographs which were plotted of the work begun by several groups of experi- for radar work during the war have been menters and theorists of the Bell Telephone found insufficiently precise for use in work Laboratories8-9'10'11'12-13 and by Mr. Ross A. which requires a rather accurate knowledge of Hull,14-15-16 of the American Radio Relay small differences of dielectric constant. The League, with the assistance of Professor charts are designed to eliminate these diffi- Charles F. Brooks, of the Blue Hill Meteoro- culties. logical Observatory of Harvard University, A revised relation which was found to be and many others,17 in the prewar period be- more suitable than Equation (2) for separa- tween 1933 and 1940. tion of the variables is The extensive use and investigations of Equation (1) leave little room for doubting (3) its validity and accuracy. However, a slightly more precise set of constants may be inserted This form is attained by use of the well- to yield known meteorological relation (er - 1) -106 = (p + 4815e/77)(158.3/T). (2) e = wp/{ 621 + w), (4) Comparisons of radio-wave echo and dif- where w is the water vapor mixing ratio, in fraction effects with radiosonde (RAOB) grams of water vapor per kilogram of dry air. records and the results of other soundings The mixing ratio may be obtained directly require the computations of many values of from the coded RAOB data, which are trans- mitted twice daily over the teletype network (er — 1)106 for each test. It becomes labori- from the RAOB stations of the United States ous to make these repeated calculations, so a Weather Bureau. set of charts has been plotted to eliminate nearly all of the arithmetical effort. Certain The inclusion of the pressure (p) in each term of Equation (3), by substitution of (4) ' 'Preliminary Instructions Manual Weather Forecasting for Radar Operators," Report No. 614, March 1944, in (2), makes it possible to plot a chart for the 60 pages. [Prepared by H. Wexler.] solution for (er — 1) • 106 at a fixed reference 6 Raymond Wexler, 'Critical Atmospheric Condi- tions for Super-refraction," Camp Evans Signal Labora- pressure, in terms of w and T. If a fixed tory, Technical Memorandum No. 163E, 22 January 1945, 6 pages. pressure of 1,000 millibars is assumed, the 7 P. M. Woodward and J. W. Head, Mathematics resultant charts may be used for finding the Group, T. R. E. Malvern, "Radio-Meteorological Tables," Telecommunications Research Establishment, dielectric constant at that pressure. It is a Report No. T-1724 (1944), 19 pages. s J. C. Schelleng, C. R. Burrows and E. B. Ferrell, simple matter to multiply that result by the "Ultra-Short-Wave Propagation," Proc. I. R. E., 21: true pressure of the air, in thousandths of 427-463, March 1933. 9 C. R. Englund, A. B. Crawford and W. W. Mum- millibars (pressure in millibars divided by ford, "Some Results of a Study of Ultra-Short-Wave Transmission Phenomena," Proc. I. R. E., 21: 464-492, 1,000), to obtain the desired value of dielectric March 1933. constant. w C. R. Englund, A. B. Crawford and W. W. Mum- ford, "Further Studies of Ultra-Short-Wave Trans- Equation (3) is plotted, as outlined above, mission Phenomena," The Bell System Technical Jour- nal, 14: 369-387, July 1935. in FIGURES 0 through 7. FIGURE 0 is an 11 C. R. Burrows, "Radio Propagation Over Plane index chart which combines the results of all Earth-Field Strength Curves," The Bell System Tech- nical Journal, 16: 45-75, January 1937. the computations on one small sheet. This 12 C. R. Burrows, A. Decino and L. E. Hunt, "Sta- bility of Two-Meter Waves," Proc. I. R. E., 26: 516- plot is subdivided into seven regions, to pro- 528, May 1938. vide sector charts numbered from (1) to (7) « C. R. Englund, A. B. Crawford and W. W. Mum- ford, "Ultra-Short-Wave Transmission and Atmos- These regions or sectors correspond with pheric Irregularities," The Bell System Technical Jour- nal, 17: 489-519, October 1938. FIGURES 1 through 7. They are expanded 14 Ross A. Hull, "Air-Mass Conditions and the Bend- chart sections of FIGURE 0, which may be ing of Ultra-High-Frequency Waves," QST, Vol. 19, No. 6, pp. 3-8, June 1935. utilized advantageously for a more precise 15 Ross A. Hull, "Air-Wave Bending of Ultra-High- determination of the dielectric constant at Frequency Waves," QST, Vol. 21, No. 5, pp. 16-18, 78-82, May 1937. any point in the troposphere. FIGURE 0 is 16 A. W. Friend, "A Summary and Interpretation of Ultra-Short-Wave Propagation Data Collected by constructed to act as an index or guide to the Late Ross A. Hull," Proc. I. R. E., 33: 358-373, indicate the correct sector chart (1 to 7) for June 1945. 17 For instance: A. H. Waynick, "Experiments on the the particular set of values of temperature Propagation of Ultra-Short Radio Waves," Proc. I. R. E., 28: 468-475, Oct. 1940. and water vapor mixing ratio.