THE BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY

Entered as second class matter September 24, 1945, at the Post Office at Lancaster, Pennsylvania, under Act of Aug. 24, 1912. Acceptance for mailing at special rate ©f postage provided for in the Act of Feb. 28, 1925, embodied in paragraph 4, section 538, P. L. and R., authorized Sept. 24, 1945. Published monthly except July and August. PUBLICATION OFFICE. American Meteorological Society, Prince & Lemon Sts., Lancaster, Pa. EDITOR. Robert G. Stone, P.O. Box 2061, South Station, Arlington, Va. SECRETARY. Charles F. Brooks, American Meteorological Society, Milton 86, Mass. EXECUTIVE SECRETARY. Kenneth C. Spengler, 5 Joy St., Boston, Mass. TREASURER. Ralph W. Burhoe, Milton 86, Mass. Annual subscription, $3.50; single copies of this issue,

Vol. 28 January, 1947 No. 1

Over-water of 10-cm Electromagnetic Radiation R. B. MONTGOMERY

Woods Hole Oceanographic Institution,1 Woods Hole, Mass.

ABSTRACT

A simple presentation is made of the optics involved in the nearly horizontal propagation of short radio waves above the . The refraction produced by various types of atmospheric layers is discussed, especially the refraction in atmospheric layers close to a water surface and the resulting wide variation in possible range of communication between low-altitude terminals. A formula showing how the of air at radio wave lengths depends on moist-air variables is reproduced. A graph for the determination of potential refractive index is presented. As examples of over-water conditions, the vertical distributions of , dew point, and po- tential refractive index are shown for two psychrometric ascents by airplane to 1000 feet.

HE PURPOSE of this paper is to pre- The refraction phenomena here described sent an introduction to a meteorologi- affect the band of wave lengths, briefly Tcal problem which was actively in- designated ' '10-cmJ9 in the title, from about vestigated by various groups during the one centimeter up to several meters. At recent war. More complete accounts are longer wave lengths these phenomena be- being prepared for publication elsewhere, come negligible, and the ionosphere becomes particularly by the Radiation Laboratory, important. Massachusetts Institute of Technology.2 It is evident, from the new applications Mention of the wartime developments has of short-wave communication and radar be- already been made by Sheppard (1946). A ing developed, that there will be need for prewar study of atmospheric refraction of further meteorological study of low-level re- short-wave radiation has been presented by fraction. Friend (1945). 1. Refractive Index of Air

1 Contribution No. 361. The refractive index of air does not vary 2 Volume 13 of the Radiation Laboratory Series, significantly with wave length over the en- to be published by McGraw-Hill Book Company, has the title Propagation of short radio waves and was tire range from about one centimeter up written under the leadership of Donald E. Kerr. Chapter 3 of this book is " of the re- through all the radio bands. It depends on fraction problem" by R. A. Craig, I. Katz, R. B. the air density and on the ratio of water- Montgomery, and P. J. Rubenstein.

Unauthenticated | Downloaded 10/03/21 06:49 PM UTC vapor concentration to absolute temperature, pends very much on the water-vapor con- increasing with both of these. If the symbol centration. For , it depends somewhat n is used for refractive index, p for total den- on wave length, but practically not at all on sity, q for specific , and T for ,3 the second term on the right- absolute temperature, and if A and B are hand side of (1) or (2) becoming negligible. dimensional constants, the basic relation is The values for dry air given by the formula of the form (Friend, 1940, p. 352) above are also approximately correct for light in air having any concentration of n - 1 = Ap( 1 + Bq/T). (1) water vapor. In dry air, therefore, the re- The working equation adopted at the Radi- fractive index is approximately the same for 2 ation Laboratory has p and vapor light and for radio waves. In air of con- pressure e as independent variables; it is stant water-vapor concentration the gradient of refractive index is approximately the n- 1 = - V + same for both bands. In air of variable T (2) water-vapor concentration, however, the where gradients may be entirely different. These a = 79 X 10-6 C mb"1, b = 48000.^ qualitative relations may be useful if the In the , refractive index tends refraction of radio waves is compared with to decrease upward due to the normal lapse such phenomena as . of density, to decrease upward if there is a humidity lapse, and to decrease upward if 2. Propagation of Radiant Energy there is a temperature inversion. An atmos- The propagation of electromagnetic radi- phere of homogeneous air, namely, air in ation is affected not only by refraction, as which potential temperature and water-vapor well as by partial reflection from ground concentration are constant, forms a con- and water surfaces, but also by absorption, venient standard and has a vertical distribu- scattering, and diffraction. If these last tion of refractive index not very different effects were non-existent, the feasibility of from that found under average atmospheric radio communication between two given conditions. In homogeneous air the lapse points could be determined by tracing the rate of refractive index is positive, and its rays (wave normals) emanating from one magnitude is about 0.8 X 10"6 per hundred of the points; the density of these rays in feet. Rays directed nearly horizontally are the neighborhood of the other point would therefore refracted downward, but the curva- be an indication of the power received in ture is only about one sixth of the curvature communication between the two points. Al- of the earth (FIG. 1). The downward re- though the method of takes account of refraction only, it is nevertheless useful in providing a rough, preliminary guide to the energy distribution surrounding a given point of transmission. The ray from the transmitter to the is called the tangent ray (FIG. 2). Energy reaches the region above the tangent ray by direct radiation, but it penetrates the FIG. 1. Curvature of ray in homogenous air com- pared with curvature of earth's surface. region below the tangent ray and beyond the point of tangency by the process of fraction allows rays to reach somewhat be- diffraction. The latter region is known as yond the geometric horizon. Visible radia- the diffraction region. The efficiency of the tion is affected in the same manner; the process of diffraction decreases rapidly as and other objects are normally visible when the wave length decreases. In the absence they are slightly below the geometric horizon. of diffraction, the tangent ray beyond the For radio waves, the refractive index in

air is independent of wave length but de- 8 See, for instance, Shaw (1930, p. 54).

Unauthenticated | Downloaded 10/03/21 06:49 PM UTC point of tangency would form a sharp refractive index, not merely a substandard boundary between the illuminated region layer, is required in order to produce inferior and the earth's shadow. mirage; an inversion of refractive index for Short-wave communication deep into the visible light accompanies an inversion of diffraction region is usually very difficult. density, as may be seen from equation (1). Since the location of the tangent ray can Any atmospheric layer in which the lapse vary widely due to changes in gradient of rate of refractive index exceeds the value found in homogeneous air may be called superstandard, because its effect is apt to be to decrease the size of the shadow cast by the earth and, hence, to make communication between low-altitude terminals possible over ranges greater than those attainable FIG. 2. Tangent ray in relation to earth's surface. in a homogeneous atmosphere. It can re- sult from either an inversion of temperature refractive index, it serves to explain why (strictly, a less than adiabatic) communication between two fixed points may or a positive lapse of water-vapor concentra- be possible at some times and not at others. tion. Since the lapse of water-vapor con- Likewise, the tangent ray drawn for the centration is normally positive, a tempera- location of a radar set is a help toward ture inversion is normally a superstandard determining which targets can be detected. layer. Although the substandard tempera- ture inversion described above is sometimes 8. Types of Befracting Layers observed, it is much less frequent. In visible If homogeneous air is regarded as a wave lengths, since water vapor does not standard,4 any layer in which the lapse rate affect the refractive index, a temperature of refractive index is less than the value inversion is always a superstandard layer; found in homogeneous air may be called under suitable conditions this layer results substandard, because its effect if any, is apt in looming, the phenomenon in which objects to be to increase the size of the shadow below the geometric horizon become unusu- for a transmitter at a low elevation. A ally visible. substandard layer occurs in hydrostatically Two degrees of superstandard layer need stable air if there is an upward increase in to be distinguished. If the layer is only water-vapor concentration sufficiently great moderately superstandard, rays directed to overbalance the effect of the upward in- nearly horizontally have a curvature which, crease in potential temperature. A second although greater than the curvature of rays kind of substandard layer is that due to a in homogeneous air, is less than the curva- superadiabatic temperature lapse rate ac- ture of the surface of the earth; this may companying constant water-vapor concen- be called a type-1 superstandard layer. If tration. The second kind occurs in a shallow the lapse rate of refractive index is suffi- layer of air above warmer, dry ground. ciently great, the rays' curvature exceeds The very great temperature lapse rate the earth's curvature; this may be called above a hot surface produces the visible a type-2 superstandard layer. The critical effect of inferior mirage: on pavements and refractive-index lapse rate separating the desert sand an image of the sky is formed two types6 is equal to the earth's curvature, by upward refraction and looks like a patch or to the reciprocal of the radius, and there- of water surface.5 An actual inversion of fore has the value 4.8 X 10~® per hundred feet. 4 The "standard" vertical distribution defined in the book referred to above is somewhat different. It corresponds to a lapse rate of refractive index equal 6 When the lapse rate of refractive index has this to about 1.2 X 10"® (100 ft)"1 instead of about critical value, the "modified index of refraction" M, 0.8 X 10-s (100 ft)"1. explained elsewhere (footnote 2), is constant by defi- 5 Regarding visible mirage see, for instance, Shaw nition. An "inversion of modified index" or an (1930), Hurd (1937), or Humphreys, Physics of the "M-inversion" is the same as a type-2 superstandard Air, 3rd ed., p. 473. layer.

Unauthenticated | Downloaded 10/03/21 06:49 PM UTC If a type-2 superstandard layer exists next The concentration of rays within a type-2 to the ground or sea surface, any horizontal superstandard layer represents a guiding of ray in the layer does not reach the horizon energy, enabling communication far beyond but is refracted downward to the surface. the normal horizon. In general, this effect If the surface is water, the ray is partially increases in importance as wave length de- reflected, usually rather efficiently. By a creases. For a given type-2 layer, the process of successive upward reflections at operating range of a system with a wave the sea surface and downward length of 3 cm may be extended by a in the air, a ray is trapped between the sur- hundred miles or more, while the operation face and the level where it is horizontal. of an otherwise comparable system with a This process of successive deviations con- wave length of 2 m or 3 m may not be tinues as far as the layer exists. For a noticeably affected. transmitter located below the top of a type-2 layer, all rays are trapped which are emitted within a certain finite angle above and below 4. Conditions Close to a Water Surface the horizontal. The angle increases as the distance separating transmitter from top of FIGURE 3 shows refractive index for a layer increases, but it usually does not ex- pressure of 1,000 mb as a function of tem- ceed half a degree. Those rays that are perature and vapor pressure; it was con- not trapped, however, remain in the layer structed from equation (2). The diagram for only a comparatively short path. includes lines of vapor pressure over two

FIG. 3. Eefractive index of air at a pressure of 1,000 mb. "Vapor pressure over pure water and over sea water is shown by two bounding curves.

Unauthenticated | Downloaded 10/03/21 06:49 PM UTC kinds of water surface.7 The temperature A diagram having temperature and vapor of a water surface of given salinity deter- pressure as coordinates (FIG. 3) is useful, in mines both the air temperature and the the same way as is the Rossby diagram, as a vapor pressure at the surface; hence it de- characteristic diagram. Since Taylor (1917) termines the refractive index also. An used it in discussing mixing processes and important fact is that the refractive index fog formation, a diagram with these par- of air in immediate contact with a water ticular coordinates may suitably be called surface increases with temperature at all the Taylor characteristic diagram. If over- (except below — IOC). water soundings are plotted on it, such a If the air a short distance above the air- diagram aids in their interpretation. An- water surface is potentially colder than the other application is that it serves for plot- surface, its refractive index is seen to be ting rapidly repeated observations at a less than the refractive index at the sur- fixed point; the resulting scatter diagram face. In this case of cold air over warm shows the relation between the fluctuations water the surface layer of air is therefore in temperature and those in vapor pressure.8 always superstandard. 5. Potential Refractive Index, nP In the case of warm air over cold water the surface layer of air may be either The vertical distributions of temperature, superstandard or substandard depending on humidity, and refractive index in the lower the humidity of the air. Only if the up- atmosphere over land or water are greatly ward increase in potential temperature is influenced by turbulent mixing. For this counterbalanced by a sufficient inversion of reason, as well as others, it is sometimes vapor pressure can the layer be substandard. convenient to express each of the three The temperature of the air-water surface properties by means of a quantity which is determines a point on the diagram in FIG. (a) conservative during adiabatic changes 3. An isopleth of refractive index ex- of pressure and which is (b) equal, in a tends diagonally upward from this point. mixture, to the average by mass of its If the point representing the air a short values in the ingredients. Each such quan- distance above the surface lies to the left tity is, consequently, (c) constant through- of this line, the surface layer is super- out homogeneous air. standard; if it lies to the right, the sur- These desiderata are satisfied by po- face layer is substandard. tential temperature and by water-vapor con- Above a water surface a lapse of vapor centration. The vapor pressure of any pressure is more frequent than an inversion mixture is equal to the mean by mass of of vapor pressure. Therefore, for radio the vapor of the ingredients, if waves, the surface layer of air is more fre- all are at the same total pressure; conse- quently superstandard than substandard. quently both desiderata are satisfied by Furthermore, close to the surface the vapor- potential vapor pressure. When a chart pressure lapse is usually large, giving type- like FIG. 3 is used as a characteristic dia- 2 superstandard conditions. The conditions gram, the two variables plotted on it should affecting visible radiation are usually less be potential temperature and potential vapor pronounced: since humidity gradients are pressure. unimportant, abnormal refraction is caused Potential vapor pressure is defined in the by temperature gradients only, and large same way as potential temperature. The temperature gradients above a water surface potential vapor pressure of a sample of air are less frequent than large humidity gradi- is the vapor pressure that would result if ents. the sample were changed adiabatically and without change in composition) to a standard 7 The values of vapor pressure over water above freezing and over ice are from the "Smithsonian pressure. Likewise, the potential refractive meteorological tables" (1931). Values for super- cooled water are given by Harrison (1934). The vapor index, nP, may be defined as the refractive pressure over sea water of salinity 35 per mille is 98.12 per cent of its value over pure water (Sverdrup, 8 The author is preparing a paper explaining some Johnson, and Fleming, 1942, p. 115). uses of the Taylor characteristic diagram.

Unauthenticated | Downloaded 10/03/21 06:49 PM UTC index a substance would have if changed equal to 1,000 mb. The formula for it, if adiabatically to a standard pressure. It 0si is potential temperature and esi is po- satisfies the desiderata described above. tential vapor pressure (both in terms of Potential refractive index, like potential sea-level pressure), is temperature and potential vapor pressure, is constant in homogeneous air. It in- rcp - 1 = ( — 1000 mb + b —) • (3) creases upward in a substandard layer and \0b\ 0sl/ decreases upward in a superstandard layer. Numerical values of this form of potential In a type-2 superstandard layer the lapse refractive index may be read directly from rate of potential refractive index exceeds a diagram like that in FIG. 3 by entering about 4.0 X 10"6 per hundred feet (the with potential temperature and potential critical lapse rate of refractive index less vapor pressure. the lapse rate of refractive index in homo- 6. Examples geneous air).9 In work with measurements over the During 1943, 1944, and 1945 the Radia- ocean it is not convenient to compute po- tion Laboratory, with the collaboration of tential values by use pf a fixed standard various Federal departments, carried out pressure such as 1,000 mb, because such both radio-transmission measurements11 and values would not be directly comparable low-level atmospheric soundings of tempera- with actual values at the surface. For in- ture and wet-bulb temperature. The most stance, although at the surface the water successful soundings were made from air- temperature is the same as the air tempera- planes; the speed of the airplane has been ture, it is not the same as the potential allowed for in reducing the observations to temperature of the air referred to 1,000 mb true temperature and dew point of the un- unless the surface pressure happens to be disturbed air. Two examples are shown, in exactly 1,000 mb; there is ordinarily a dis- FIGS. 4 and 5. crepancy of a degree or two. In the first example (FIG. 4) the tem- Sea-level pressure, therefore, is chosen as perature of the water is intermediate be- the standard pressure for potential tem- tween the temperature and the dew point perature and potential vapor pressure in of the air. Consequently, eddy diffusion what follows. If temperature or vapor pres- carries heat downward to the water surface sure is measured at a known height above and carries the water vapor upward that is sea level, the potential value is obtained by evaporated from the surface. The inversion adding to the measured value the product of temperature and the large lapse of dew height times lapse rate, in homogeneous air, point in the lowest few hundred feet makes of temperature or of vapor pressure.10 the layer superstandard. In the lowest 150 Refractive index and potential refractive ft the lapse rate of potential refractive in- 6 index depend on sea-level pressure. This dex exceeds 4.0 X 10" per hundred feet and variable may, however, be eliminated for is therefore type-2 superstandard. The layer practical purposes, because the vertical from 150 ft to 400 ft is type-1 superstand- gradient is of primary concern rather than ard. Above 400 ft the air is approximately the absolute value. For potential refractive homogeneous. index one may use the refractive index of Experience has shown that the results of air having temperature equal to the po- psychrometric observations may conveniently tential temperature, vapor pressure equal be represented, in vertical distribution, by to the potential vapor pressure, and pressure temperature and dew point. This pair can be shown on the same graph, as in FIGS. 4 9 In FIGS. 4 and 5 the scales of height and po- tential refractive index are so related that a line and 5, and so can the water temperature. with slope minus one separates type-1 from type-2 lapse rates of potential refractive index. At the water surface the temperature is the 10 This method is not strictly precise because of same for air and water. If the water is the density difference between the fictitiously dis- placed parcel and the environment. For low-level soundings, however, the actual discrepancy is insig- 11 See chapter 4 of the book referred to above (foot- nificant. note 2).

Unauthenticated | Downloaded 10/03/21 06:49 PM UTC FIG. 4. Over-water airplane sounding number C77 on 26 July 1944 at 42°31'N, 70° 36'W, 5 miles southeast of Cape Ann, Massachusetts. Large open circles represent first ascent at 09h57m-10h07m, small solid circles represent repeat ascent at 10H09M-10H16M (time meridian 60°W). The dashed lines show the vertical variations of dew point and temperature in homogeneous air. Arrows indicate possible values at the air-water bound- ary. Surface wind was observed to be SSW force 1 Beaufort. Water temperature of 17-19C was measured from boat a few miles away. fresh, the dew point at the surface coincides tion and are expected to appear in the near exactly with the surface temperature. At a future.12 surface of salt water the dew point is about 7. Summary of Over-water Conditions 0.3C lower than the temperature, a differ- ence which is so small as to be unimportant When the air is potentially warmer than in most cases. Each curve drawn in the the water, a group of phenomena of widely illustrations is to be extended in imagination varying effect may occur: Anomalous dis- from 20 ft, the lowest point of the sounding, tributions of refractive index may extend down to the arrow representing the surface several hundred feet up from the surface. value. The arrow for water temperature is While superstandard layers are more fre- the termination of the curve for tempera- quent, substandard layers occur at times, ture; for practical purposes, it is the termi- and both may exist simultaneously at differ- nation of the curve for dew point also. ent heights. Because the anomalous layers In the second example (FIG. 5) the water are so thick, they affect the maximum range temperature is lower than the dew point, a attainable by use of 10-cm radiation between rarer occurrence than the situation in the two points at low elevation over the ocean. first example. Eddy diffusion carries both Conditions of the sort shown in FIGS. 4 and heat and water vapor downward, and water 5 have been observed to have a marked vapor condenses on the sea surface. The favorable and unfavorable effect, respec- distribution of potential refractive index be- tively, oh the transmission between two such low 150 ft is mostly substandard. points. Cross sections based on a few others of the When the air is potentially colder than many Radiation Laboratory- soundings have the water, a different phenomenon occurs, already been published by Craig, Katz, and 12 Some of these are included in the book referred Harney (1945). Nearly a hundred more to above (footnote 2). Subsequent to the preparation of the present paper, a large group of soundings soundings have been prepared for publica- have been published by Craig (1946).

Unauthenticated | Downloaded 10/03/21 06:49 PM UTC FIG. 5. Over-water airplane sounding number C103 on 14 August 1944 at 42°08^'N, 70°16'W, 5 miles north of Race Point, Cape Cod, Massachusetts. Large open circles repre- sent first ascent at 10h58m-llh08m, small solid circles represent repeat ascent at llh15m- llh20m. Surface wind was observed to be SSW force 3 Beaufort. Water temperature of 21C measured at same time on beach at Race Point.

not included in the examples. The super - of Electronics, Massachusetts Institute of adiabatic temperature lapse rate near the Technology, for certain information in- water surface is accompanied by a much cluded in this article and for his careful greater lapse rate of dew point (so that examination of the manuscript. both heat and water vapor are carried up- ward by eddy diffusion). A markedly super- REFERENCES

standard surface layer always results. It is, Craig, R. A., 1946: Measurements of temperature however, comparatively shallow. The thick- and humidity in the lowest 1000 feet of the atmosphere over Massachusetts Bay. Pap. ness of the type-2 superstandard surface phys. Ocean. Meteor., Mass. Inst. Tech and. layer may be between 5 ft and 50 ft and Woods Hole ocean. Instn., 10, no. 1, 48 pp. Craig, R. A., Isadore Katz, and P. J. Harney, 1945: the noticeably superadiabatic temperature Sea breeze cross sections from psychrometric measurements. Bull Amer. meteor. Soc., 26: lapse rate does not extend much above this 405-410. layer. Above the shallow superadiabatic Friend, A. W., 1940: Developments in meteorological sounding by radio waves. /. aero. Sci., 7: 347- and superstandard surface layer the air is 352. , 1945: A summary and interpretation of ultra- nearly homogeneous, because it is continu- short-wave propagation data collected by the ally mixed by convection due to the warm, late Ross A. Hull. Proc. Inst. Radio Engrs., 33* 358—373 underlying surface. When the potential Harrison, L. P., 1934: Tables (in millibars) of the "pressure of saturated aqueous vapor over water" temperature of the air is close to the water at temperatures from 0° to — 50°C. Mon. Wea. temperature and at least a light breeze is Rev., 62: 247-248. Hurd, W. E., 1937: Refraction and mirage. Hydro- blowing, conditions are not very different graphic Office, U. S. Navy, Pilot chart of the from those just described. The superstand- North Pacific Ocean, February 1937, verso. Shaw, Napier, 1930: Manual of meteorology, 3, "The ard surface layer in either case may increase physical processes of weather." Cambridge University Press, 445 pp. the radio range if the layer is both Sheppard, P. A., 1946: Radio meteorology: influence ' ' strong'1 enough and thick enough and if of the atmosphere on the propagation of ultra- short radio waves. Nature {London), 157: 860- the wave length of the radiation is suffi- 862. Smithsonian Institution, 1931: Smithsonian meteoro- ciently short and transmitter and receiver logical tables, fifth revised edition (Smith- are in the layer or not far above; otherwise son. misc. Coll., 86), 282 pp. Sverdrup, H. U., M. W. Johnson, and R. H. Fleming, it may be quite ineffective. 1942: The oceans, their physics, chemistry, and general biology. New York, Prentice-Hall, Acknowledgment.—The author is grateful 1087 pp. to Mr. Donald E. Kerr, Research Laboratory Taylor, G. I., 1917: The formation of fog and mist. Quart. J. R. meteor. Soc., 43: 241-268.

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