Homogeneous Path Research Articles

On the water vapour absorption in the 8?13 ?m spectral region for different atmospheric conditions

Experimental measurements of the absorption coefficient of atmospheric water vapour, at wavelengths between 8 and 13 μm, are examined on the basis of atmospheric models describing the meteorological conditions of the observed atmospheres to obtain estimates of the foreign-broadening absorption coefficient for homogeneous paths. The results show that the variable contribution given by unresolved lines predominates on the continuum term due to wing effects of remote lines, even for rather high spectral resolutions. Associated with estimates of the self-broadening absorption coefficient, as proposed byRoberts et al. (1976), these data are applied to a wide set of atmospheric models, corresponding to various latitudes and seasons, indicating that the two components of the atmospheric absorption coefficient are closely related to the surface temperature. Because of the variable weights given by foreign- and self-broadening terms, the atmospheric absorption coefficient turns out to increase with the surface temperature with different rates at various wavelengths.

Perturbation of a homogeneous current path by a stub

Perturbation of a homogeneous current path by a stub

Experimental data for groundwave propagation over cylindrical surfaces

Experimental data for the fields of EM groundwaves propagating over cylindrical homogeneous paths and two-section mixed paths were obtained by microwave (4.765 GHz) modeling. The cylindrical surfaces, which have a radius of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20 \lambda_{0}</tex> , closely approximate spherical surfaces insofar as groundwave propagation is concerned. The model is a curved tank which was constructed as a stratified combination of Plexiglas over distilled water, giving a predictable highly inductive surface impedance. Aluminum foil laid on the Plexiglas produced a nearly perfectly conducting surface wherever needed for the mixed path cases. For both homogeneous and mixed paths the residue series theory agrees well with the experimental data in the shadow and penumbra regions, but the agreement becomes poorer as the observation point moves into the illuminated region where an excess number of residue terms is needed. The results show that a groundwave which crosses an abrupt boundary rapidly acquires the characteristic properties of the second medium at small heights above the surface, and that the equivalent integral solution for mixed paths is therefore adequate close to the surface. This is especially useful near the boundary where the residue series converges poorly. It is concluded that if the constitutive electrical parameters of the earth are precisely known and constant, the theory can be reliably applied to LF and VLF groundwave propagation over the earth where the constraints are even less severe.

Aperture-averaging effects for weak scintillations*

A laser beam propagating through the lower atmosphere will be distorted by variations of the refractive index along the propagation path causing random fluctuations in the received signal flux. If the receiver aperture is finite (i.e., not a point), these fluctuations will in some sense be averaged. An aperture-averaging factor has been defined to specify this effect. Theoretical predictions of this factor in the region of weak fluctuations have existed in the literature for some time. Earlier experimental work, however, failed to show agreement with these calculations. Measurements of the aperture-averaging factor were made during the summer of 1972 near Boulder, Colo., over a horizontal (statistically homogeneous) path at distances of 200–1600 m. Good agreement with the theoretical calculations was observed in the region of weak fluctuations (i.e., at the shorter path lengths). Data in the region of strong fluctuations (i.e., at the longer path lengths) are inconclusive.

Method to Apply Homogeneous-Path Transmittance Models to Inhomogeneous Atmospheres

Abstract An accurate approximation to calculate atmospheric profiles of transmittance in instrumental spectral intervals is presented. The approximation assumes a known transmittance model; i.e., that the transmittance in the spectral interval of the instrument is known as a function of quantity of absorber, temperature, and total pressure in homogeneous paths. An inhomogeneous atmosphere is treated as a sequence of homogeneous layers. One applies the model by successively rescaling the quantity of absorber. The method is exact for monochromatic radiation. It avoids the computation of mean line strengths, and it is computationally fast. As an example, transmittance profiles are computed for two spectral intervals in which water vapor is the chief absorber. The results are in excellent agreement with the “exact” point-by-point calculation.

Height‐gain experimental data for groundwave propagation: 1, Homogeneous paths

Experimental height‐gain data for the magnitude of electromagnetic groundwaves propagating over flat homogeneous paths were obtained by microwave (4.765 GHz) modeling. The experimental results were compared with height‐gain theory, and the limitations of the theory were established in terms of surface impedance, height of the receiving point, and antenna separation distance. Earlier experimental studies of this problem have not been entirely conclusive due to an inadequate knowledge of the surface impedance and the influence of the surface upon the antenna impedance. Here, extensive corrective measures were taken to eliminate or account for these effects.It is concluded that the theory for the total field is remarkably accurate as the height above or distance along the surface is varied, even at distances as close as 2λ0 from the source. Furthermore, the question as to the choice between the various forms of numerical distance seems academic. The restriction on height above the surface is eliminated, and the restriction upon the magnitude of the surface impedance is relaxed depending upon the presence of a significant trapped surface wave.Part 2 is a companion paper which relates the homogeneous path height‐gain to mixed‐path experimental measurements versus height and distance.

Height‐gain experimental data for groundwave propagation: 2, Heterogeneous paths

Analytical as well as experimental height‐gain studies for mixed‐path groundwave propagation are virtually nonexistent. Therefore, it was shown how the theoretical height‐gain for a homogeneous path relates to heterogeneous‐path experimental measurements versus height and distance. The results show that the magnitude of a groundwave field which crosses an abrupt boundary rapidly acquires the characteristic properties of the second medium, and the field over a heterogeneous surface attenuates at essentially the same rate as the field on the surface. The groundwave which has crossed an abrupt boundary can be predicted for small heights above the surface by simply multiplying the well‐established mixed‐path theory for antennas located on the surface by appropriate homogeneous‐path height‐gain factors corresponding to the local surface impedance, provided the field is predominantly a surface wave.

Foreign-Gas-Broadening Effects in the 15 μm CO2 Bands

The effects of N2, O2 Ar, and He on the absorption of radiation by the 15 μm perpendicular CO2 bands are reported. The investigation was carried out at medium resolution and at gas pressures less than 1 atm. The results of the study are presented in the form of a band-averaged broadening coefficient for N2, band-averaged broadening factors for O2 Ar, and He, and wavelength dependent broadening coefficients for N2, O2 Ar, and He. Comparisons are made with other experimental and theoretical results. In addition transmittances were calculated for homogeneous paths using some of the molecular parameters determined in the study and compared with measured transmittances. The agreement was reasonably satisfactory and revised values for the intensities of some of the 15 μm bands are presented.

A NONLINEAR LEAST‐SQUARES METHOD FOR SEISMIC REFRACTION MAPPING—PART I: ALGORITHM AND PROCEDURE

An iterative inversion method (Reframap) based on the kinematic properties of critically refracted waves is developed. The method is based on ray tracing and assumes homogeneous and isotropic media and ray paths confined to a vertical plane through each source‐detector pair. Unlike the earlier Profile or Time‐Term Methods, no restrictions are imposed on interface topography except that it be continuous almost everywhere (in the mathematical sense). As in the preexisting methods, more observations than unknowns are assumed. The algorithm and procedure, on which the Reframap Method is based, generate apparent dips for each source detector pair at the noncritical interfaces from the slope of a least‐squares line approximation to the interface functional in the neighborhood of each refraction point. In turn, the dip and path along the critical refractor is, at every iteration, pairwise approximated by a line through the critical refracting points. The incidence angles are computed recursively by Snell’s law. The solution of the overdetermined, nonlinear multiple refractor time‐distance system of simultaneous equations is sought by Marquardt’s algorithm for least‐squares estimation of critical refractor velocity and vertical thickness under each element.

Current research on infrared radiation from rocket exhaust

Infrared radiation heating from rocket exhausts has been of particular interest to NASA in connection with large vehicles of the Saturn class. These vehicles are equipped mainly with two types of rocket engines: the J-2 model for which H 2O is the only radiating species, and the F-1 model for which H 2O, CO 2, CO and carbon particles are the radiating specie. A computer program has been developed to calculate infrared radiant heat transfer from inhomogeneous mixtures of these gases. This program uses a band model to express the absorption coefficients of the gases. The band model parameters necessary for these calculations are the mean line strength S, the mean line half-width γ, the mean line spacing d, averaged over 25 cm −1 increments. Analytical and experimental programs are in progress to complete the determination of these parameters at long path lengths and to include the effects of foreign gases on these parameters. A tentative set of γ's, 1/ d's, S/ d's has been determined, using data and analytical expressions coming principally from the literature. A modified Curtis-Godson approximation is used in the radiative heat transfer calculation and effectively substitutes a hypothetical homogeneous path for the inhomogeneous path. This approximation has been used successfully in predicting atmospheric radiative transmission. This modified Curtis-Godson approximation is experimentally shown to be applicable for strong temperature and concentration gradients for certain wavelengths in the H 2O and CO 2 infrared spectrums.

Use of the Curtis–Godson Approximation in Calculations of Radiant Heating by Inhomogeneous Hot Gases

Calculations of radiant heating by inhomogeneous hot gases require knowledge of spectral transmittances of inhomogeneous optical paths. Determination of these transmittances is a difficult problem that can be attacked by means of the Curtis-Godson approximation, which replaces each inhomogeneous optical path with a hypothetical homogeneous path that has the same transmittance. The authors have tested the accuracy of the Curtis-Godson approximation experimentally. Infrared spectral transmittances of inhomogeneous hot samples of H(2)O and CO(2) were measured. Each inhomogeneous hot gas specimen consisted of two or three homogeneous zones in series. The transmittance of each zone was measured, as was the transmittance of the entire multizone assembly. The measured transmittance of each inhomogeneous path was compared with a transmittance calculated from the homogeneous zonal transmittances, using the Curtis-Godson approximation in conjunction with a random band model. The measured and calculate inhomogeneous transmittances concurred to within about 0.02. The error appeared to be due more to the band model theory than to the Curtis-Godson approximation.

Atmospheric Transmission in the CO_2 Bands Between 12 μ and 18 μ

Calculations have been made of high-resolution transmission in the CO2 absorption bands between 12 μ and 18 μ by direct integration across the bands, for both homogeneous and atmospheric slant paths. Mixed Doppler-Lorentz broadening has been used at pressures lower than 100 mb. A method to eliminate the Curtis-Godson approximation has been developed and applied to the slant-path calculations. Comparisons have been made with previous theoretical and experimental data, and reasons for the discrepancies are discussed.

Transmission of the atmosphere of Mars in the region of 2 μ

The random Elsasser band model is used to compute the transmission of the atmospheres of Earth and Mars for the 2-μ bands of carbon dioxide. This band model is shown to give good agreement with measurements of spectral transmission for homogeneous paths of CO 2 and also for nonhomogeneous paths through the Earth's atmosphere when the Curtis-Godson approximation is used. The 2-μ bands of CO 2 are strong in the atmospheres of both Earth and Mars and, at a given temperature, their absorption is a function only of the product mp. Comparison of calculated values for transmission of sunlight through both atmospheres indicates that mp ♂ = 500 ± 100 meter-atm mbar where m is the amount of CO 2 in one air mass and p♂ is the “effective” surface pressure. For m♂ = 60 to 85 meter-atm, the above value of mp♂ leads to p s♂ = 7.1 ± 2.2 mbar for the surface pressure of the Martian atmosphere.

Spectral emissivity calculations for the parallel bands of carbon dioxide at 4·3 microns

The quasi-statistical band model is used to compute spectral emissivities for homogeneous paths of CO 2. Emissivities are presented for temperatures from 150 to 600°K, covering the temperature range encountered in planetary atmospheres where carbon dioxide adsorption is expected to be significant. These emissivities can be used to calculate atmospheric transmission. The present results are compared with both experimental measurements and other theoretical calculations. Spectrally, the agreement with observed values of absorption is seen to be somewhat better than in previous calculations.

Spectral Band Absorptance of Radiation Traversing Two or More Cells in Series

Theoretical equations are derived for the spectral band absorptance of radiation which traverses two or more cells in series. The amount of absorbing gas, pressure, and temperature of each cell may be chosen independently. Limiting expressions are obtained when the absorptance of all of the cells can be represented by either the weak line or the strong line approximation as well as when some of the cells can be represented by the weak line approximation while the remainder can be represented by the strong line approximation. Some of the results apply to any spectral band, while other results apply only to particular band models or to nonoverlapping spectral lines. The dependence of the absorptance on the various parameters is illustrated by numerous examples. The conditions for the validity of the usual interpolation procedure for obtaining the equivalent parameters for a homogeneous path are derived.

Transmittance of Carbon Dioxide and Water Vapor Over Stratospheric Slant Paths

The transmittance of carbon dioxide and water vapor over stratospheric slant paths has been calculated for various initial altitudes and angles of the path. The results are based on previously published transmittance tables for homogeneous paths. The slant path transmittance is obtained from the homogeneous path results by the use of theoretical conversion equations. The variation of slant path transmittance with altitude and with angle from the horizontal is illustrated. The influence of different stratospheric water vapor amounts on the transmittance is also considered. The results are compared with experimental measurements.

Spectral Band Absorptance for Atmospheric Slant Paths

A number of equations are derived for the absorptance along a slant path. The absorptances of slant and homogeneous paths are compared. Various combinations of assumptions are made in the derivation of these equations as to the variation of the temperature and absorber concentration along the path, the extent and nature of the overlapping of the spectral lines, the variation of the intensity and half-width from line to line, the shape of the spectral lines, and the extent of the frequency interval considered. The particular assumptions applicable to each result are clearly stated. A general method is developed for obtaining slant path absorptances from homogeneous path data when either the weak or strong line approximation is valid. A combination of the weak and strong line results gives new general expressions for the relationship of slant and homogeneous path absorptance. These results are correct in both of the weak and strong line limits and in addition provide a good approximation for all values of the parameters.