Blackbody Function Research Articles

A model for inferring canopy and underlying soil temperatures from multi-directional measurements

Thermal emission is modeled from a canopy/soil surface, where the soil and the leaves are at different temperatures,T g andT c respectively. The temperatureT m corresponding to a radiometer reading is given by $$B_\lambda (T_m ) = \chi B_\lambda (T_g ) + (1 - \chi )B_\lambda (T_c ) ,$$ whereB λ denotes the Planck blackbody function at wavelength λ, χ specifies the fraction of the field of view occupied by the soil at a given view direction, and an emissivity of 1.0 is assumed for the plants and the soil. The dependence of the soil-fraction χ on the view direction and the structure is expressed by the viewing-geometry parameter, which allows for concise and simple formulation. We observe from our model that at large view zenith angles, only the plants are effectively seen (that is, χ tends to zero), and thereforeT c can be determined from observations at large zenith angles, to the extent that such observations are practical. Viewing from the zenith, χ = exp(-L hc), whereL hc is the projection of the canopy leaf-area (per unit surface area) on a horizontal plane. For off-zenith observations, the soil-fraction χ depends on the distribution in the azimuth of the projected areas of various leaf categories, in addition to the dependence on the sum total of these projections,L hc.L hc, rather than the leaf-area index, emerges as the parameter characterizing the optical thickness of the canopy. Inferring bothT c andT g from observations from the zenith and from large zenith angles is possible ifL hc is known from other measurements. Drooping of leaves under water-stress conditions affects the observed temperatureT m in a complicated way because a leaf-inclination change produces a change inL hc (for the same leaf area) and also a change in the dependence of χ on the view direction. Water stress can produce an increase of the soil-fraction χ and thus tends to produce an exaggerated increase in the observed temperature compared to the actual increase in canopy temperature. These effects are analyzed for a simulated soybean canopy.

Optical emission studies of atomic, molecular, and particulate carbon produced from a laser vaporization cluster source

We perform optical emission studies on the species generated by the laser vaporization of graphite into a pulsed helium flow. With short flow channels prior to free-jet expansion the emission at short downstream distances is dominated atomic carbon lines and three band systems of C2: d 3∏g–a 3∏u (Swan), C 1 ∏g–A 1∏u (Deslandres–d’Azambuja), and D 1∑+u –X 1∑+g (Mulliken). Partially rotationally resolved spectra of the Δv=−1 Swan bands are analyzed using a band contour approach to obtain rotational temperatures and rough vibrational distributions for C2 d 3∏g. The direct emission spectrum from the short-channel source becomes a weaker, structureless continuum when viewed at long downstream distances. Similar long-lived continua are induced by a low-fluence laser at 266, 355, or 532 nm when it crosses the expansion emanating from a source with a long flow channel. We attribute these continua to the incandescence of hot carbon particles, T=2500–4000 K. The continua are fit to a model in which the Planck blackbody function is modified by the particle emissivity to determine particle temperatures and obtain crude estimates of particle sizes. These data provide the first direct evidence that carbon particles are produced in a laser-vaporization cluster source.

Spectroscopic study of cylindrically converging shock waves

Cylindrically converging shock waves have been produced by detonating 20-cm-diam explosive shells in atmospheric air. Shadowgraphs were taken to monitor the production of waves. A spectroscopic measurement of temperature was made using a monochromator combined with a photomultiplier. The spectral radiant energy was compared with the blackbody function (Planck’s law). The dependence of temperature upon the initiation energy (the chemical energy of explosives) was also investigated. It was shown that temperature was approximately proportional to the square root of the initiation energy. The attained temperatures ranged from 13 000–34 000 K depending on the initiation energy. These are 3500–9500 K lower than those estimated from shock propagation speeds. The implosion pulse duration (the half-value width) of 2.0–2.5 μs was observed. A possibility of the further increase of temperature as well as some problems was suggested.

Spectra and time variability of GX 5-1

From a short observation of GX 5-1 with EXOSAT we have derived information on spectral and temporal behaviour in the energy range 1–20 keV. The source was found to be variable on time scales from 10 s to 1 h. Describing the spectrum one is forced to assume at least two spectral components. The best fit is reached using a spectrum composed of two blackbody functions with typical temperatures 1 keV and 2 keV, corresponding to apparent blackbody radii of 43 km and 11 km, respectively (for a distance of 10 kpc). With respect to the hot component there is evidence for variability in temperature as well as in apparent blackbody radius. No periodic variability has been found over the period range 0.25 s to 2000 s. There is no evidence for an iron emission line.

The empirical determination of line source functions, β L -values, and the microturbulent and convective velocity components as functions of depth in the photosphere-chromosphere transition region

An empirical method for determining line source functions, previously applied by us to the cores of infrared lines has now been extended to the whole line profile and was applied to centre-limb observations of sixteen lines of five infrared multiplets, mainly of high excitation potential (Table I). The present investigation was performed in two steps. In the first part of the paper approximate values are derived for the depth dependence of the four functions named in the title of this paper, where β L is the ratio between the actual and the LTE population of the lower level of the transitions involved. In the second part of the paper we use these empirically derived functions to compute the line profiles. From the remaining differences between observed and computed profiles, corrections are derived to the four functions. The main results are: (a) Convective velocities: see Table IV.(b)(Micro-)turbulent velocities: see Figure 8. Between τ 5 = 10-4 and 10-1: 〈υ τ 〉 ≈ 1.4 km s-1, which is an upper limit since an unknown contribution of macroscopic motions could not be separated, (c) Line source functions: see Figures 9, 15 and 16. The source functions are close to the black-body function for τ 5≳ 10-3, slight deviations occur in higher levels. The interesting behaviour of the Caii source function near τ 5 = 10-5 should be noted. (d) Non LTE-functions: first approximations for the functions log β L (τ 5) were derived empirically in the first part, and are shown in Figure 10; the second approximation shows them to be too large and the real values seem to be closer to one-half or one-third of these functions.

The compton-getting effect for cosmic-ray particles and photons and the Lorentz-invariance of distribution functions

The anisotropy introduced by the motion of an observer with velocity V through a particle or photon flux is derived from the Lorentz-invariance of distribution functions in phase space. The invariance of the black-body distribution function leads to a ≅1 + ( V/ c) cos θ dependence of the temperature of the 3°K thermal background radiation. For massive particles whose speed, ν, is much greater than V, the Compton-Getting anisotropy — ( d( lnƒ)/ d( ln p)) V/ν is added to the angular part of the distribution function, and the isotropic part is unchanged, to order V/ ν. The cosmic-ray proton spectrum at solar minimum is observed to have a region where the Compton-Getting anisotropy is zero. The Lorentz-invariance of the volume element in phase space, and the consequent invariance of distribution functions, is demonstrated in the Appendix.

A note on the Wien Displacement Law

It is pointed out that, when deriving the Wien Displacement Law in terms of wavelength as compared to wavenumber, the spectral points of maximum flux are not equivalent. It is shown that this results from(where B(T) is the Planck Blackbody Function), and because B(T) is implicitly a differential.

Source functions in the cores of infrared Fraunhofer lines

If the profiles of all Fraunhofer lines were formed according to the mechanism of pure absorption (the L.T.E.-hypothesis) the source functions Sλ(τ) deduced empirically from the central intensities of these lines should all be identical, and equal to the blackbody function Bλ(τ). In order to examine this hypothesis the source functions Sλ(τ) were deduced empirically according to a method applied earlier by us (De Jager and Neven, 1967a) for some twenty infrared lines for which accurate centre-limb observations were available (De Jager and Neven, 1967b). The lines belonged to five different multiplets.

Radiative Thermal Conductivity in Planetary Interiors

IT is customary to invoke radiative thermal conductivity as a mechanism for efficiently removing heat from the Earth's interior1. Clark2 derived the formula for radiative thermal conductivity in planetary conditions, where n is the refractive index, B is the blackbody function, γ is the radiation wavelength, α is the absorption coefficient and s is the backscattering coefficient. He used this relationship to estimate the radiative conductivity for a number of minerals by measuring α at room temperature and neglecting s (ref. 3).

An Infrared Band Ratio Technique for Temperature Determinations of Hot Gases

A band ratio technique is developed for determining the temperature of optically thin hot gases from the infrared spectrum. The technique is based on the temperature variation of the integrated intensity of combination and overtone bands and not the Planck blackbody function. The technique can be applied to any fundamental, overtone, or combination band pair of a radiating molecule. In particular, the R-branch of the 2.7-μ fundamental band and the 1.87-μ and 1.34-μ combination bands of hot water vapor are investigated as a specific example of the technique. Characteristic band area ratios which can be used to determine the temperature from measured emissivity or radiance spectra are given for H2O. A comparison between temperatures determined from the band ratio technique and temperatures determined by independent experimental methods shows good agreement.