Whistler mode wave growth and propagation in the prenoon magnetosphere

Pitch-angle scattering of electrons can limit the stably trapped particle flux in the magnetosphere and precipitate energetic electrons into the ionosphere. Whistler-mode waves generated by a temperature anisotropy can mediate this pitch-angle scattering over a wide range of radial distances and latitudes, but in order to correctly predict the phase-space diffusion, it is important to characterise the whistler-mode wave distributions that result from the instability. We use previously-published observations of number density, pitch-angle anisotropy and phase space density to model the plasma in the quiet pre-noon magnetosphere (defined as periods when AE<100nT). We investigate the global propagation and growth of whistler-mode waves by studying millions of growing ray paths and demonstrate that the wave distribution at any one location is a superposition of many waves at different points along their trajectories and with different histories. We show that for observed electron plasma properties, very few raypaths undergo magnetospheric reflection, most rays grow and decay within 30 degrees of the magnetic equator. The frequency range of the wave distribution at large L can be adequately described by the solutions of the local dispersion relation, but the range of wavenormal angle is different. The wave distribution is asymmetric with respect to the wavenormal angle. The numerical results suggest that it is important to determine the variation of magnetospheric parameters as a function of latitude, as well as local time and L-shell.

Heliospheric Observations of STEREO-Directed Coronal Mass Ejections in 2008 – 2010: Lessons for Future Observations of Earth-Directed CMEs

We present a study of coronal mass ejections (CMEs) which impacted one of the STEREO spacecraft between January 2008 and early 2010. We focus our study on 20 CMEs which were observed remotely by the Heliospheric Imagers (HIs) onboard the other STEREO spacecraft up to large heliocentric distances. We compare the predictions of the Fixed-Φ and Harmonic Mean (HM) fitting methods, which only differ by the assumed geometry of the CME. It is possible to use these techniques to determine from remote-sensing observations the CME direction of propagation, arrival time and final speed which are compared to in-situ measurements. We find evidence that for large viewing angles, the HM fitting method predicts the CME direction better. However, this may be due to the fact that only wide CMEs can be successfully observed when the CME propagates more than 100∘ from the observing spacecraft. Overall eight CMEs, originating from behind the limb as seen by one of the STEREO spacecraft can be tracked and their arrival time at the other STEREO spacecraft can be successfully predicted. This includes CMEs, such as the events on 4 December 2009 and 9 April 2010, which were viewed 130∘ away from their direction of propagation. Therefore, we predict that some Earth-directed CMEs will be observed by the HIs until early 2013, when the separation between Earth and one of the STEREO spacecraft will be similar to the separation of the two STEREO spacecraft in 2009 – 2010.

A self-similar expansion model for use in solar wind transient propogation studies

Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed φ fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed φ, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient’s speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient’s angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Propagation of the Madden-Julian Oscillation through the Maritime Continent and scale interaction with the diurnal cycle of precipitation

The convectively active part of the Madden-Julian Oscillation (MJO) propagates eastward through the warm pool, from the Indian Ocean through the Maritime Continent (the Indonesian archipelago) to the western Pacific. The Maritime Continent's complex topography means the exact nature of the MJO propagation through this region is unclear. Model simulations of the MJO are often poor over the region, leading to local errors in latent heat release and global errors in medium-range weather prediction and climate simulation. Using 14 northern winters of TRMM satellite data it is shown that, where the mean diurnal cycle of precipitation is strong, 80% of the MJO precipitation signal in the Maritime Continent is accounted for by changes in the amplitude of the diurnal cycle. Additionally, the relationship between outgoing long-wave radiation (OLR) and precipitation is weakened here, such that OLR is no longer a reliable proxy for precipitation. The canonical view of the MJO as the smooth eastward propagation of a large-scale precipitation envelope also breaks down over the islands of the Maritime Continent. Instead, a vanguard of precipitation (anomalies of 2.5 mm day^-1 over 10^6 km^2) jumps ahead of the main body by approximately 6 days or 2000 km. Hence, there can be enhanced precipitation over Sumatra, Borneo or New Guinea when the large-scale MJO envelope over the surrounding ocean is one of suppressed precipitation. This behaviour can be accommodated into existing MJO theories. Frictional and topographic moisture convergence and relatively clear skies ahead of the main convective envelope combine with the low thermal inertia of the islands, to allow a rapid response in the diurnal cycle which rectifies onto the lower-frequency MJO. Hence, accurate representations of the diurnal cycle and its scale interaction appear to be necessary for models to simulate the MJO successfully.

The role of the harmonic vector average in motion integration

The local speeds of object contours vary systematically with the cosine of the angle between the normal component of the local velocity and the global object motion direction. An array of Gabor elements whose speed changes with local spatial orientation in accordance with this pattern can appear to move as a single surface. The apparent direction of motion of plaids and Gabor arrays has variously been proposed to result from feature tracking, vector addition and vector averaging in addition to the geometrically correct global velocity as indicated by the intersection of constraints (IOC) solution. Here a new combination rule, the harmonic vector average (HVA), is introduced, as well as a new algorithm for computing the IOC solution. The vector sum can be discounted as an integration strategy as it increases with the number of elements. The vector average over local vectors that vary in direction always provides an underestimate of the true global speed. The HVA, however, provides the correct global speed and direction for an unbiased sample of local velocities with respect to the global motion direction, as is the case for a simple closed contour. The HVA over biased samples provides an aggregate velocity estimate that can still be combined through an IOC computation to give an accurate estimate of the global velocity, which is not true of the vector average. Psychophysical results for type II Gabor arrays show perceived direction and speed falls close to the IOC direction for Gabor arrays having a wide range of orientations but the IOC prediction fails as the mean orientation shifts away from the global motion direction and the orientation range narrows. In this case perceived velocity generally defaults to the HVA.

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.

Eastward propagation of a plasma convection enhancement following a southward turning of the interplanetary magnetic field

On October 27th 1984, high-latitude ionospheric convection was observed by the European incoherent scatter (EISCAT) radar. For a nine-hour period, simultaneous observations of the interplanetary magnetic field (IMF) were obtained sunward of the Earth's bow shock. During this period, the IMF abruptly turned southward, having previously been predominantly northward for approximately three hours, and a strong enhancement in convection was observed 11 ± 1 minutes later. Using the very high time resolution of the EISCAT data, it is shown that the convection enhancement propagated eastward, around the afternoon magnetic local time sector, at a speed of the order of 1 kms−1. These results are interpreted in terms of the effects of an onset of steady IMF-geomagnetic field merging and are the first to show how a new pattern of enhanced convection is established in the high latitude ionosphere.