The response of a uniform horizontal temperature gradient to heating

The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.

An overview of Earth's global electric circuit and atmospheric conductivity

The Earth’s global atmospheric electric circuit depends on the upper and lower atmospheric boundaries formed by the ionosphere and the planetary surface. Thunderstorms and electrified rain clouds drive a DC current (∼1 kA) around the circuit, with the current carried by molecular cluster ions; lightning phenomena drive the AC global circuit. The Earth’s near-surface conductivity ranges from 10−7 S m−1 (for poorly conducting rocks) to 10−2 S m−1 (for clay or wet limestone), with a mean value of 3.2 S m−1 for the ocean. Air conductivity inside a thundercloud, and in fair weather regions, depends on location (especially geomagnetic latitude), aerosol pollution and height, and varies from ∼10−14 S m−1 just above the surface to 10−7 S m−1 in the ionosphere at ∼80 km altitude. Ionospheric conductivity is a tensor quantity due to the geomagnetic field, and is determined by parameters such as electron density and electron–neutral particle collision frequency. In the current source regions, point discharge (coronal) currents play an important role below electrified clouds; the solar wind-magnetosphere dynamo and the unipolar dynamo due to the terrestrial rotating dipole moment also apply atmospheric potential differences. Detailed measurements made near the Earth’s surface show that Ohm’s law relates the vertical electric field and current density to air conductivity. Stratospheric balloon measurements launched from Antarctica confirm that the downward current density is ∼1 pA m−2 under fair weather conditions. Fortuitously, a Solar Energetic Particle (SEP) event arrived at Earth during one such balloon flight, changing the observed atmospheric conductivity and electric fields markedly. Recent modelling considers lightning discharge effects on the ionosphere’s electric potential (∼+250 kV with respect to the Earth’s surface) and hence on the fair weather potential gradient (typically ∼130 V m−1 close to the Earth’s surface. We conclude that cloud-to-ground (CG) lightning discharges make only a small contribution to the ionospheric potential, and that sprites (namely, upward lightning above energetic thunderstorms) only affect the global circuit in a miniscule way. We also investigate the effects of mesoscale convective systems on the global circuit.

Projected gradient approach to the numerical solution of the SCoTLASS

The SCoTLASS problem-principal component analysis modified so that the components satisfy the Least Absolute Shrinkage and Selection Operator (LASSO) constraint-is reformulated as a dynamical system on the unit sphere. The LASSO inequality constraint is tackled by exterior penalty function. A globally convergent algorithm is developed based on the projected gradient approach. The algorithm is illustrated numerically and discussed on a well-known data set. (c) 2004 Elsevier B.V. All rights reserved.

Suprathermal electron evolution in a Parker spiral magnetic field

Suprathermal electrons (>70 eV) form a small fraction of the total solar wind electron density but serve as valuable tracers of heliospheric magnetic field topology. Their usefulness as tracers of magnetic loops with both feet rooted on the Sun, however, most likely fades as the loops expand beyond some distance owing to scattering. As a first step toward quantifying that distance, we construct an observationally constrained model for the evolution of the suprathermal electron pitch-angle distributions on open field lines. We begin with a near-Sun isotropic distribution moving antisunward along a Parker spiral magnetic field while conserving magnetic moment, resulting in a field-aligned strahl within a few solar radii. Past this point, the distribution undergoes little evolution with heliocentric distance. We then add constant (with heliocentric distance, energy, and pitch angle) ad-hoc pitch-angle scattering. Close to the Sun, pitch-angle focusing still dominates, again resulting in a narrow strahl. Farther from the Sun, however, pitch-angle scattering dominates because focusing is effectively weakened by the increasing angle between the magnetic field direction and intensity gradient, a result of the spiral field. We determine the amount of scattering required to match Ulysses observations of strahl width in the fast solar wind, providing an important tool for inferring the large-scale properties and topologies of field lines in the interplanetary medium. Although the pitch-angle scattering term is independent of energy, time-of-flight effects in the spiral geometry result in an energy dependence of the strahl width that is in the observed sense although weaker in magnitude.

An overview of Earth’s global electric circuit and atmospheric conductivity

The Earth’s global atmospheric electric circuit depends on the upper and lower atmospheric boundaries formed by the ionosphere and the planetary surface. Thunderstorms and electrified rain clouds drive a DC current (∼1 kA) around the circuit, with the current carried by molecular cluster ions; lightning phenomena drive the AC global circuit. The Earth’s near-surface conductivity ranges from 10−7 S m−1 (for poorly conducting rocks) to 10−2 S m−1 (for clay or wet limestone), with a mean value of 3.2 S m−1 for the ocean. Air conductivity inside a thundercloud, and in fair weather regions, depends on location (especially geomagnetic latitude), aerosol pollution and height, and varies from ∼10−14 S m−1 just above the surface to 10−7 S m−1 in the ionosphere at ∼80 km altitude. Ionospheric conductivity is a tensor quantity due to the geomagnetic field, and is determined by parameters such as electron density and electron–neutral particle collision frequency. In the current source regions, point discharge (coronal) currents play an important role below electrified clouds; the solar wind-magnetosphere dynamo and the unipolar dynamo due to the terrestrial rotating dipole moment also apply atmospheric potential differences. Detailed measurements made near the Earth’s surface show that Ohm’s law relates the vertical electric field and current density to air conductivity. Stratospheric balloon measurements launched from Antarctica confirm that the downward current density is ∼1 pA m−2 under fair weather conditions. Fortuitously, a Solar Energetic Particle (SEP) event arrived at Earth during one such balloon flight, changing the observed atmospheric conductivity and electric fields markedly. Recent modelling considers lightning discharge effects on the ionosphere’s electric potential (∼+250 kV with respect to the Earth’s surface) and hence on the fair weather potential gradient (typically ∼130 V m−1 close to the Earth’s surface. We conclude that cloud-to-ground (CG) lightning discharges make only a small contribution to the ionospheric potential, and that sprites (namely, upward lightning above energetic thunderstorms) only affect the global circuit in a miniscule way. We also investigate the effects of mesoscale convective systems on the global circuit.

Force constants and dipole‐moment derivatives of molecules from perturbed Hartree–Fock calculations

General expressions for the force constants and dipole‐moment derivatives of molecules are derived, and the problems arising in their practical application are reviewed. Great emphasis is placed on the use of the Hartree–Fock function as an approximate wavefunction, and a number of its properties are discussed and re‐emphasised. The main content of this paper is the development of a perturbed Hartree–Fock theory that makes possible the direct calculation of force constants and dipole‐moment derivatives from SCF–MO wavefunctions. Essentially the theory yields ∂ϕi / ∂RJα, the derivative of an MO with respect to a nuclear coordinate.

Force constants and dipole moment derivatives of molecules from perturbed Hartree-Fock calculations II. Applications to limited basis set SCF-MO wavefunctions

The perturbed Hartree–Fock theory developed in the preceding paper is applied to LiH, BH, and HF, using limited basis‐set SCF–MO wavefunctions derived by previous workers. The calculated values for the force constant ke and the dipole‐moment derivative μ(1) are (experimental values in parentheses): LiH, ke  =  1.618(1.026)mdyn/Å,μ(1)  =  −18.77(−2.0±0.3)D/ÅBH,ke  =  5.199(3.032)mdyn/Å,μ(1)  =  −1.03(−)D/Å;HF,ke  =  12.90(9.651)mdyn/Å,μ(1)  =  −2.15(+1.50)D/Å. The values of the force on the proton were calculated exactly and according to the Hellmann–Feynman theorem in each case, and the discrepancies show that none of the wavefunctions used are close to the Hartree–Fock limit, so that the large errors in ke and μ(1) are not surprising. However no difficulties arose in the perturbed Hartree–Fock calculation, so that the application of the theory to more accurate wavefunctions appears quite feasible.

Determination of the vibrational transition moment ratio for the Coriolis interacting v9 and v10 fundamentals of allene

Comparison between observed and calculated infrared band contours has been made to determine the vibrational transition moment ratio |M10/M9| for the Coriolis interacting ν9 and ν10 perpendicular fundamentals of allene-h4. The ratio obtained is appreciably lower than that of a previous estimate and the result obtained by integrated band intensity measurements of Overend and Crawford. From the best estimate of the ratio, the dipole moment derivatives of the two bands are determined; the value for the weaker band ν9 is subject to a large uncertainty.