Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation

The use of analytical solutions of the diffusion equation for footprint prediction is explored. Quantitative information about the footprint, i.e., the upwind area most likely to affect a downwind flux measurement at a given height z, is essential when flux measurements from different platforms, particularly airborne ones, are compared. Analytical predictions are evaluated against numerical Lagrangian trajectory simulations which are detailed in a companion paper (Leclerc and Thurtell, 1990). For neutral stability, the structurally simple solutions proposed by Gash (1986) are shown to be capable of satisfactory approximation to numerical simulations over a wide range of heights, zero displacements and roughness lengths. Until more sophisticated practical solutions become available, it is suggested that apparent limitations in the validity of some assumptions underlying the Gash solutions for the case of very large surface roughness (forests) and tentative application of the solutions to cases of small thermal instability be dealt with by semi-empirical adjustment of the ratio of horizontal wind to friction velocity. An upper limit of validity of these solutions for z has yet to be established.     

A mixed spectral finite-difference model for pollutant concentrations over a hill

Given incident logarithmic profiles of wind and pollutant concentration above a rough, absorbing surface, the three-dimensional distribution of pollutant concentration over a hill of gentle slope is determined from a linearized model. The model is applied in neutrally stratified flow, without chemistry, and is integrated using spectral methods in the horizontal and a finite-difference scheme in the vertical. This approach allows for flexibility in choosing a closure scheme and a variety of surface boundary conditions. This was not possible in the analytic approach of Padro (1987) who added pollutant concentration and flux to the MS3DJH/1 model of Walmsley et al. (1980). The present model requires as input the turbulent kinetic energy, E, dissipation, , and the perturbation vertical velocity, w, from the three-dimensional boundary-layer flow model of Beljaars et al. (1987), hereinafter referred to as MSFD, The latter model also supplies wind velocity perturbations at the upper boundary, as input to upper boundary conditions on the pollutant flux perturbations.The present study describes applications of the model to idealized terrain features: isolated two- and three-dimensional hills and ridges and an infinite series of ridges. (Application to real terrain, however, presents no difficulties.) Comparisons were made with different (though uniform) surface roughnesses. Tests were performed to examine the effect of upstream terrain features in the periodic domain and to illustrate the importance of the vertical resolution of the output for interpreting results from the sinusoidal terrain case.     

Calibration of Al/Si order variations in anorthite

New single crystal diffraction data for natural and heat-treated anorthite crystals (Angel et al. 1990) allow the determination of their states of Al/Si order in terms of a macroscopic order parameter,Q _OD , for the transition. Numerical values ofQ _OD obtained from estimates of site occupancies are shown to vary with the scalar spontaneous strain, _s , as _s Q _OD ² , and with the ratio of the sums of typeb (superlattice) reflections and typea (sublattice) reflections asI _b/I _a Q _OD ² . An empirical calibration for pure anorthite is obtained giving varies between 0.92 and 0.87 in samples equilibrated at T1300° C, but then falls off relatively rapidly with increasing temperature, reaching 0.7 near the melting point ( 1557° C). The observed temperature dependence does not conform to the predictions of the simplest single order parameter models; coupling ofQ _OD withQ of the transition is suspeeted.     

High-resolution spectroscopy of gamma-ray bursts

We report on results from the Goddard germanium Gamma-Ray Burst Spectrometer flown on the ISEE-3 spacecraft. Spectral and temporal studies of two events on 4 and 19 November, 1978 are presented. The power law spectral indices were found to be respectively –1.82 and –1.31, the latter being the hardest event thus far detected. Evidence for two lines in the 4 November event is presented — a broad feature at 420 keV and a narrower one at 740 keV. These are consistent with a common redshift if the parent lines are assumed to be the positron annihilation line (511 keV) and the first excited state of iron (847 keV). If this interpretation is correct, it is shown that additional lines from higher levels of iron and possibly other nuclei are expected and that they may represent a significant contribution to the total spectrum above 1 MeV.Paper presented at the Symposium on Cosmic-Ray Bursts, held at Toulouse, France, 26–29 November, 1979.     

Climate and paleoclimate: What we can learn about solar luminosity variations

The Earth's climate is not constant, and has experienced major changes in the past on all timescales. The causes of these changes, although still incompletely understood, vary according to the timescale considered. Some of the most important causal mechanisms include continental drift, changes in the Earth's orbital parameters, volcanic activity and solar variations. Solar variations have been invoked to explain climatic change on almost all timescales from 1 to 10⁹ yr. Unfortunately, even though the Sun is a prime candidate for explaining many changes in past climate, the use of past climate as a proxy for solar luminosity changes is fraught with difficulty. For example:

1. In many cases observed changes in climate can be adequately explained without recourse to solar variations as a causal factor. In fact, on the longest timescales the Earth's climate was remarkably similar to today in spite of a considerably lower solar output.
2. For most timescales of climatic change there are, as yet, no plausible theories giving similar timescale variations in solar activity, so that a vital link between cause and effect is missing.
3. There are considerable uncertainties in the record of past climates.
4. On short timescales many proposed solar activity-climate links have failed to stand up to rigorous statistical analysis.

This paper reviews past changes in climate and proposed causal mechanisms on timescales of from 1 to 10⁹ yr. The evidence for solar activity-climate links is discussed with special reference to the above points.     

On convection in stellar atmospheres far from local thermodynamic equilibrium

Non-thermal effects generated by sub-photospheric convection are considered. It is shown that convective cells are destroyed by shocks generated when convective velocities reach the speed of sound. Terminologically this process is given the name of sonic-boom-interrupted convection. An estimate is made on the dependence of convective velocities on stellar parameters. It is suggested that the process being investigated could explain why some stars do not belong to any branch of the theoretical Hertzsprung-Russell diagram.     

The spectra and light curves of two gamma-ray bursts

During the last half of 1977 the UCSD/MIT Hard X-Ray and Low Energy Gamma-Ray Experiment of HEAO-1 observed two of the three gamma-ray bursts detected by at least three satellites. The first of these bursts (20 October, 1977) had a fluence of (3.1±0.5)×10^–5 erg cm^–2 integrated over the energy range 0.135–2.05 MeV and over its duration of 38.7 s, placing it among the largest bursts observed. The second (10 November, 1977) had a fluence of (2.1±0.8)×10^–5 erg cm^–2 integrated over the energy range 0.125–3 MeV and over its duration of 2.8 s. The light curves of both bursts exhibit time fluctuations down to the limiting time resolution of the detectors (0.1 s). The spectrum of the 20 October, 1977 burst can be fitted with a power law (index –1.93±0.16), which is harder than other reported gamma-ray burst spectral fits. This burst was detected up to 2.05 MeV, and approximately half of its energy was emitted at photon energies above 0.5 MeV. The spectrum of the 10 November, 1977 burst is softer (index –2.4±0.7) and is similar to the spectrum of the 27 April, 1972 burst.Paper presented at the Symposium on Cosmic Gamma-Ray Bursts held at Toulouse, France, 26–29 November, 1979.     

Second species solutions with an 0(μ v ), 0<v<1, near-Moon passage

This paper illustrates the application of the theory for second species solutions with an 0( ^v ), 0<v<1, near-Moon passage to first species-second species bifurcations and to second species-second species bifurcations. It also corrects and improves the asymptotic approximations obtained in the author's previous work on this subject and it establishes a local form of Broucke's Principle for the types of bifurcations studied in this paper.This work was supported by the National Science Foundation under Grant MCS 7703591.     

The strength of the Sun's polar fields

The magnetic field strength within the polar caps of the Sun is an important parameter for both the solar activity cycle and for our understanding of the interplanetary magnetic field. Measurements of the line-of-sight component of the magnetic field generally yield 0.1 to 0.2 mT near times of sunspot minimum. In this paper we report measurements of the polar fields made at the Stanford Solar Observatory using the Fe i line 525.02 nm. We find that the average flux density poleward of 55° latitude is about 0.6 mT peaking to more than 1 mT at the pole and decreasing to 0.2 mT at the polar cap boundary. The total open flux through either polar cap thus becomes about 3 × 10¹⁴ Wb. We also show that observed magnetic field strengths vary as the line-of-sight component of nearly radial fields.     

The center-to-limb behavior of Ca i λ6573 and [Ca ii] λ7324

Center-to-limb measurements of the Ca i 6573 intercombination line and the Ca ii 7324 forbidden line are compared with synthetic profiles based on a simple representation of the non-LTE Ca-Ca⁺ ionization equilibrium. The effects of photoionizations from low lying excited states of neutral calcium are found to reduce the sensitivity of the 6573 center-to-limb behavior as a thermal structure diagnostic. The synthetic center-to-limb behavior is also sensitive to uncertainties in the nonthermal broadening. Nevertheless, the measured center-to-limb behavior of 6573 favors a cool photospheric model similar to the Vernazza, Avrett, and Loeser model M over hotter models based on the Ca ii K wings. The non-LTE calcium abundance obtained from the disk center equivalent widths of 6573 and 7324 using the best fit model is A _Ca2.1±0.2 × 10^-6 (by number relative to hydrogen). Applications of these lines as diagnostics of the Ca-Ca⁺ ionization equilibrium in other stars are briefly discussed.Visiting Astronomer, Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.