Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

Sensitivities of a cyclone detection and tracking algorithm: individual tracks and climatology

Northern Hemisphere cyclone activity is assessed by applying an algorithm for the detection and tracking of synoptic scale cyclones to mean sea level pressure data. The method, originally developed for the Southern Hemisphere, is adapted for application in the Northern Hemisphere winter season. NCEP-Reanalysis data from 1958/59 to 1997/98 are used as input. The sensitivities of the results to particular parameters of the algorithm are discussed for both case studies and from a climatological point of view. Results show that the choice of settings is of major relevance especially for the tracking of smaller scale and fast moving systems. With an appropriate setting the algorithm is capable of automatically tracking different types of cyclones at the same time: Both fast moving and developing systems over the large ocean basins and smaller scale cyclones over the Mediterranean basin can be assessed. The climatology of cyclone variables, e.g., cyclone track density, cyclone counts, intensification rates, propagation speeds and areas of cyclogenesis and -lysis gives detailed information on typical cyclone life cycles for different regions. The lowering of the spatial and temporal resolution of the input data from full resolution T62/06h to T42/12h decreases the cyclone track density and cyclone counts. Reducing the temporal resolution alone contributes to a decline in the number of fast moving systems, which is relevant for the cyclone track density. Lowering spatial resolution alone mainly reduces the number of weak cyclones.

Dynamical control of the mesosphere by orographic and non-orographic gravity wave drag during the extended northern winters of 2006 and 2009

A version of the Canadian Middle Atmosphere Model (CMAM) that is nudged toward reanalysis data up to 1 hPa is used to examine the impacts of parameterized orographic and non-orographic gravity wave drag (OGWD and NGWD) on the zonal-mean circulation of the mesosphere during the extended northern winters of 2006 and 2009 when there were two large stratospheric sudden warmings. The simulations are compared to Aura Microwave Limb Sounder (MLS) observations of mesospheric temperature, carbon monoxide (CO) and derived zonal winds. The control simulation, which uses both OGWD and NGWD, is shown to be in good agreement with MLS. The impacts of OGWD and NGWD are assessed using simulations in which those sources of wave drag are removed. In the absence of OGWD the mesospheric zonal winds in the months preceding the warmings are too strong, causing increased mesospheric NGWD, which drives excessive downwelling, resulting in overly large lower mesospheric values of CO prior to the warming. NGWD is found to be most important following the warmings when the underlying westerlies are too weak to allow much vertical propagation of the orographic gravity waves to the mesosphere. NGWD is primarily responsible for driving the circulation that results in the descent of CO from the thermosphere following the warmings. Zonal mean mesospheric winds and temperatures in all simulations are shown to be strongly constrained by (i.e. slaved to) the stratosphere. Finally, it is demonstrated that the responses to OGWD and NGWD are non-additive due to their dependence and influence on the background winds and temperatures.

Effects of spatial resolution in the simulation of daily and subdaily precipitation in the southwestern US

We evaluate the effects of spatial resolution on the ability of a regional climate model to reproduce observed extreme precipitation for a region in the Southwestern United States. A total of 73 National Climate Data Center observational sites spread throughout Arizona and New Mexico are compared with regional climate simulations at the spatial resolutions of 50 km and 10 km for a 31 year period from 1980 to 2010. We analyze mean, 3-hourly and 24-hourly extreme precipitation events using WRF regional model simulations driven by NCEP-2 reanalysis. The mean climatological spatial structure of precipitation in the Southwest is well represented by the 10 km resolution but missing in the coarse (50 km resolution) simulation. However, the fine grid has a larger positive bias in mean summer precipitation than the coarse-resolution grid. The large overestimation in the simulation is in part due to scale-dependent deficiencies in the Kain-Fritsch convective parameterization scheme that generate excessive precipitation and induce a slow eastward propagation of the moist convective summer systems in the high-resolution simulation. Despite this overestimation in the mean, the 10 km simulation captures individual extreme summer precipitation events better than the 50 km simulation. In winter, however, the two simulations appear to perform equally in simulating extremes.

Tracking the momentum flux of a CME and quantifying its influence on geomagnetically induced currents at Earth

We investigate a coronal mass ejection (CME) propagating toward Earth on 29 March 2011. This event is specifically chosen for its predominately northward directed magnetic field, so that the influence from the momentum flux onto Earth can be isolated. We focus our study on understanding how a small Earth-directed segment propagates. Mass images are created from the white-light cameras onboard STEREO which are also converted into mass height-time maps (mass J-maps). The mass tracks on these J-maps correspond to the sheath region between the CME and its associated shock front as detected by in situ measurements at L1. A time series of mass measurements from the STEREO COR-2A instrument is made along the Earth propagation direction. Qualitatively, this mass time series shows a remarkable resemblance to the L1 in situ density series. The in situ measurements are used as inputs into a three-dimensional (3-D) magnetospheric space weather simulation from the Community Coordinated Modeling Center. These simulations display a sudden compression of the magnetosphere from the large momentum flux at the leading edge of the CME, and predictions are made for the time derivative of the magnetic field (dB/dt) on the ground. The predicted dB/dt values were then compared with the observations from specific equatorially located ground stations and showed notable similarity. This study of the momentum of a CME from the Sun down to its influence on magnetic ground stations on Earth is presented as a preliminary proof of concept, such that future attempts may try to use remote sensing to create density and velocity time series as inputs to magnetospheric simulations.

On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

The Madden-Julian Oscillation and the diurnal cycle over the Maritime Continent: scale interactions and modelling

The Maritime Continent archipelago, situated on the equator at 95-165E, has the strongest land-based precipitation on Earth. The latent heat release associated with the rainfall affects the atmospheric circulation throughout the tropics and into the extra-tropics. The greatest source of variability in precipitation is the diurnal cycle. The archipelago is within the convective region of the Madden-Julian Oscillation (MJO), which provides the greatest variability on intra-seasonal time scales: large-scale (∼10^7 km^2) active and suppressed convective envelopes propagate slowly (∼5 m s^-1) eastwards between the Indian and Pacific Oceans. High-resolution satellite data show that a strong diurnal cycle is triggered to the east of the advancing MJO envelope, leading the active MJO by one-eighth of an MJO cycle (∼6 days). Where the diurnal cycle is strong its modulation accounts for 81% of the variability in MJO precipitation. Over land this determines the structure of the diagnosed MJO. This is consistent with the equatorial wave dynamics in existing theories of MJO propagation. The MJO also affects the speed of gravity waves propagating offshore from the Maritime Continent islands. This is largely consistent with changes in static stability during the MJO cycle. The MJO and its interaction with the diurnal cycle are investigated in HiGEM, a high-resolution coupled model. Unlike many models, HiGEM represents the MJO well with eastward-propagating variability on intra-seasonal time scales at the correct zonal wavenumber, although the inter-tropical convergence zone's precipitation peaks strongly at the wrong time, interrupting the MJO's spatial structure. However, the modelled diurnal cycle is too weak and its phase is too early over land. The modulation of the diurnal amplitude by the MJO is also too weak and accounts for only 51% of the variability in MJO precipitation. Implications for forecasting and possible causes of the model errors are discussed, and further modelling studies are proposed.

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.

Oscillations in the open solar magnetic flux with a period of 1.68 years: imprint on galactic cosmic rays and implications for heliospheric shielding

An understanding of how the heliosphere modulates galactic cosmic ray (GCR) fluxes and spectra is important, not only for studies of their origin, acceleration and propagation in our galaxy, but also for predicting their effects (on technology and on the Earth’s environment and organisms) and for interpreting abundances of cosmogenic isotopes in meteorites and terrestrial reservoirs. In contrast to the early interplanetary measurements, there is growing evidence for a dominant role in GCR shielding of the total open magnetic flux, which emerges from the solar atmosphere and enters the heliosphere. In this paper, we relate a strong 1.68- year oscillation in GCR fluxes to a corresponding oscillation in the open solar magnetic flux and infer cosmic-ray propagation paths confirming the predictions of theories in which drift is important in modulating the cosmic ray flux.

IMF control of cusp proton emission intensity and dayside convection: implications for component and anti-parallel reconnection

We study a brightening of the Lyman-alpha emission in the cusp which occurred in response to a short-lived southward turning of the interplanetary magnetic field (IMF) during a period of strongly enhanced solar wind plasma concentration. The cusp proton emission is detected using the SI-12 channel of the FUV imager on the IMAGE spacecraft. Analysis of the IMF observations recorded by the ACE and Wind spacecraft reveals that the assumption of a constant propagation lag from the upstream spacecraft to the Earth is not adequate for these high time-resolution studies. The variations of the southward IMF component observed by ACE and Wind allow for the calculation of the ACE-to-Earth lag as a function of time. Application of the derived propagation delays reveals that the intensity of the cusp emission varied systematically with the IMF clock angle, the relationship being particularly striking when the intensity is normalised to allow for the variation in the upstream solar wind proton concentration. The latitude of the cusp migrated equatorward while the lagged IMF pointed southward, confirming the lag calculation and indicating ongoing magnetopause reconnection. Dayside convection, as monitored by the SuperDARN network of radars, responded rapidly to the IMF changes but lagged behind the cusp proton emission response: this is shown to be as predicted by the model of flow excitation by Cowley and Lockwood (1992). We use the numerical cusp ion precipitation model of Lockwood and Davis (1996), along with modelled Lyman-_ emission efficiency and the SI-12 instrument response, to investigate the effect of the sheath field clock angle on the acceleration of ions on crossing the dayside magnetopause. This modelling reveals that the emission commences on each reconnected field line 2–2.5min after it is opened and peaks 3–5 min after it is opened. We discuss how comparison of the Lyman-alpha intensities with oxygen emissions observed simultaneously by the SI-13 channel of the FUV instrument offers an opportunity to test whether or not the clock angle dependence is consistent with the “component” or the “anti-parallel” reconnection hypothesis.

Coordinated Cluster and ground-based instrument observations of transient changes in the magnetopause boundary layer during an interval of predominantly northward IMF: relation to reconnection pulses and FTE signatures

We study a series of transient entries into the low-latitude boundary layer (LLBL) of all four Cluster spacecraft during an outbound pass through the mid-afternoon magnetopause ([X(GSM), Y(GSM), Z(GSM)] approximate to [2, 7, 9] R(E)). The events take place during an interval of northward IMF, as seen in the data from the ACE satellite and lagged by a propagation delay of 75 min that is well-defined by two separate studies: (1) the magnetospheric variations prior to the northward turning (Lockwood et al., 2001, this issue) and (2) the field clock angle seen by Cluster after it had emerged into the magnetosheath (Opgenoorth et al., 2001, this issue). With an additional lag of 16.5 min, the transient LLBL events cor-relate well with swings of the IMF clock angle (in GSM) to near 90degrees. Most of this additional lag is explained by ground-based observations, which reveal signatures of transient reconnection in the pre-noon sector that then take 10-15 min to propagate eastward to 15 MLT, where they are observed by Cluster. The eastward phase speed of these signatures agrees very well with the motion deduced by the cross-correlation of the signatures seen on the four Cluster spacecraft. The evidence that these events are reconnection pulses includes: transient erosion of the noon 630 nm (cusp/cleft) aurora to lower latitudes; transient and travelling enhancements of the flow into the polar cap, imaged by the AMIE technique; and poleward-moving events moving into the polar cap, seen by the EISCAT Svalbard Radar (ESR). A pass of the DMSP-F15 satellite reveals that the open field lines near noon have been opened for some time: the more recently opened field lines were found closer to dusk where the flow transient and the poleward-moving event intersected the satellite pass. The events at Cluster have ion and electron characteristics predicted and observed by Lockwood and Hapgood (1998) for a Flux Transfer Event (FTE), with allowance for magnetospheric ion reflection at Alfvenic disturbances in the magnetopause reconnection layer. Like FTEs, the events are about 1 R(E) in their direction of motion and show a rise in the magnetic field strength, but unlike FTEs, in general, they show no pressure excess in their core and hence, no characteristic bipolar signature in the boundary-normal component. However, most of the events were observed when the magnetic field was southward, i.e. on the edge of the interior magnetic cusp, or when the field was parallel to the magnetic equatorial plane. Only when the satellite begins to emerge from the exterior boundary (when the field was northward), do the events start to show a pressure excess in their core and the consequent bipolar signature. We identify the events as the first observations of FTEs at middle altitudes.

Coordinated Cluster, ground-based instrumentation and low-altitude satellite observations of transient poleward-moving events in the ionosphere and in the tail lobe

During the interval between 8:00-9:30 on 14 January 2001, the four Cluster spacecraft were moving from the central magnetospheric lobe, through the dusk sector mantle, on their way towards intersecting the magnetopause near 15:00 MLT and 15:00 UT. Throughout this interval, the EIS-CAT Svalbard Radar (ESR) at Longyearbyen observed a series of poleward-moving transient events of enhanced F-region plasma concentration ("polar cap patches"), with a repetition period of the order of 10 min. Allowing for the estimated solar wind propagation delay of 75 ( 5) min, the interplanetary magnetic field (IMF) had a southward component during most of the interval. The magnetic footprint of the Cluster spacecraft, mapped to the ionosphere using the Tsyganenko T96 model (with input conditions prevailing during this event), was to the east of the ESR beams. Around 09:05 UT, the DMSP-F12 satellite flew over the ESR and showed a sawtooth cusp ion dispersion signature that also extended into the electrons on the equatorward edge of the cusp, revealing a pulsed magnetopause reconnection. The consequent enhanced ionospheric flow events were imaged by the SuperDARN HF backscatter radars. The average convection patterns (derived using the AMIE technique on data from the magnetometers, the EISCAT and SuperDARN radars, and the DMSP satellites) show that the associated poleward-moving events also convected over the predicted footprint of the Cluster spacecraft. Cluster observed enhancements in the fluxes of both electrons and ions. These events were found to be essentially identical at all four spacecraft, indicating that they had a much larger spatial scale than the satellite separation of the order of 600 km. Some of the events show a correspondence between the lowest energy magnetosheath electrons detected by the PEACE instrument on Cluster (10-20 eV) and the topside ionospheric enhancements seen by the ESR (at 400-700 km). We suggest that a potential barrier at the magnetopause, which prevents the lowest energy electrons from entering the magnetosphere, is reduced when and where the boundary-normal magnetic field is enhanced and that the observed polar cap patches are produced by the consequent enhanced precipitation of the lowest energy electrons, making them and the low energy electron precipitation fossil remnants of the magnetopause reconnection rate pulses.

High-latitude particle precipitation and its relationship to magnetospheric source regions

Two central issues in magnetospheric research are understanding the mapping of the low-altitude ionosphere to the distant regions of the magnetsphere, and understanding the relationship between the small-scale features detected in the various regions of the ionosphere and the global properties of the magnetosphere. The high-latitude ionosphere, through its magnetic connection to the outer magnetosphere, provides an important view of magnetospheric boundaries and the physical processes occurring there. All physical manifestations of this magnetic connectivity (waves, particle precipitation, etc.), however, have non-zero propagation times during which they are convected by the large-scale magnetospheric electric field, with phenomena undergoing different convection distances depending on their propagation times. Identification of the ionospheric signatures of magnetospheric regions and phenomena, therefore, can be difficult. Considerable progress has recently been made in identifying these convection signatures in data from low- and high-altitude satellites. This work has allowed us to learn much about issues such as: the rates of magnetic reconnection, both at the dayside magnetopause and in the magnetotail; particle transport across the open magnetopause; and particle acceleration at the magnetopause and the magnetotail current sheets.

Excitation and decay of solar-wind driven flows in the magnetosphere-ionosphere system

Basic concepts of the form of high-latitude ionospheric flows and their excitation and decay are discussed in the light of recent high time-resolution measurements made by ground-based radars. It is first pointed out that it is in principle impossible to adequately parameterize these flows by any single quantity derived from concurrent interplanetary conditions. Rather, even at its simplest, the flow must be considered to consist of two basic time-dependent components. The first is the flow driven by magnetopause coupling processes alone, principally by dayside reconnection. These flows may indeed be reasonably parameterized in terms of concurrent near-Earth interplanetary conditions, principally by the interplanetary magnetic field (IMF) vector. The second is the flow driven by tail reconnection alone. As a first approximation these flows may also be parameterized in terms of interplanetary conditions, principally the north-south component of the IMF, but with a delay in the flow response of around 30-60 min relative to the IMF. A delay in the tail response of this order must be present due to the finite speed of information propagation in the system, and we show how "growth" and "decay" of the field and flow configuration then follow as natural consequences. To discuss the excitation and decay of the two reconnection-driven components of the flow we introduce that concept of a flow-free equilibrium configuration for a magnetosphere which contains a given (arbitrary) amount of open flux. Reconnection events act either to create or destroy open flux, thus causing departures of the system from the equilibrium configuration. Flow is then excited which moves the system back towards equilibrium with the changed amount of open flux. We estimate that the overall time scale associated with the excitation and decay of the flow is about 15 min. The response of the system to both impulsive (flux transfer event) and continuous reconnection is discussed in these terms.

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.