On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

Scenario and modelling uncertainty in global mean temperature change derived from emission-driven global climate models

We compare future changes in global mean temperature in response to different future scenarios which, for the first time, arise from emission-driven rather than concentration-driven perturbed parameter ensemble of a global climate model (GCM). These new GCM simulations sample uncertainties in atmospheric feedbacks, land carbon cycle, ocean physics and aerosol sulphur cycle processes. We find broader ranges of projected temperature responses arising when considering emission rather than concentration-driven simulations (with 10–90th percentile ranges of 1.7 K for the aggressive mitigation scenario, up to 3.9 K for the high-end, business as usual scenario). A small minority of simulations resulting from combinations of strong atmospheric feedbacks and carbon cycle responses show temperature increases in excess of 9 K (RCP8.5) and even under aggressive mitigation (RCP2.6) temperatures in excess of 4 K. While the simulations point to much larger temperature ranges for emission-driven experiments, they do not change existing expectations (based on previous concentration-driven experiments) on the timescales over which different sources of uncertainty are important. The new simulations sample a range of future atmospheric concentrations for each emission scenario. Both in the case of SRES A1B and the Representative Concentration Pathways (RCPs), the concentration scenarios used to drive GCM ensembles, lies towards the lower end of our simulated distribution. This design decision (a legacy of previous assessments) is likely to lead concentration-driven experiments to under-sample strong feedback responses in future projections. Our ensemble of emission-driven simulations span the global temperature response of the CMIP5 emission-driven simulations, except at the low end. Combinations of low climate sensitivity and low carbon cycle feedbacks lead to a number of CMIP5 responses to lie below our ensemble range. The ensemble simulates a number of high-end responses which lie above the CMIP5 carbon cycle range. These high-end simulations can be linked to sampling a number of stronger carbon cycle feedbacks and to sampling climate sensitivities above 4.5 K. This latter aspect highlights the priority in identifying real-world climate-sensitivity constraints which, if achieved, would lead to reductions on the upper bound of projected global mean temperature change. The ensembles of simulations presented here provides a framework to explore relationships between present-day observables and future changes, while the large spread of future-projected changes highlights the ongoing need for such work.

Evaluation of a photosynthesis-based biogenic isoprene emission scheme in JULES and simulation of isoprene emissions under present-day climate conditions

We have incorporated a semi-mechanistic isoprene emission module into the JULES land-surface scheme, as a first step towards a modelling tool that can be applied for studies of vegetation – atmospheric chemistry interactions, including chemistry-climate feedbacks. Here, we evaluate the coupled model against local above-canopy isoprene emission flux measurements from six flux tower sites as well as satellite-derived estimates of isoprene emission over tropical South America and east and south Asia. The model simulates diurnal variability well: correlation coefficients are significant (at the 95 % level) for all flux tower sites. The model reproduces day-to-day variability with significant correlations (at the 95 % confidence level) at four of the six flux tower sites. At the UMBS site, a complete set of seasonal observations is available for two years (2000 and 2002). The model reproduces the seasonal pattern of emission during 2002, but does less well in the year 2000. The model overestimates observed emissions at all sites, which is partially because it does not include isoprene loss through the canopy. Comparison with the satellite-derived isoprene-emission estimates suggests that the model simulates the main spatial patterns, seasonal and inter-annual variability over tropical regions. The model yields a global annual isoprene emission of 535 ± 9 TgC yr−1 during the 1990s, 78 % of which from forested areas.

Further evidence for variable synchrotron emission in XTE J1118+480 in outburst

We present simultaneous multicolor infrared and optical photometry of the black hole X-ray transient XTE J1118+480 during its short 2005 January outburst, supported by simultaneous X-ray observations. The variability is dominated by short timescales, ~10 s, although a weak superhump also appears to be present in the optical. The optical rapid variations, at least, are well correlated with those in X-rays. Infrared JHKs photometry, as in the previous outburst, exhibits especially large-amplitude variability. The spectral energy distribution (SED) of the variable infrared component can be fitted with a power law of slope α=-0.78+/-0.07, where F_ν~ν^α. There is no compelling evidence for evolution in the slope over five nights, during which time the source brightness decayed along almost the same track as seen in variations within the nights. We conclude that both short-term variability and longer timescale fading are dominated by a single component of constant spectral shape. We cannot fit the SED of the IR variability with a credible thermal component, either optically thick or thin. This IR SED is, however, approximately consistent with optically thin synchrotron emission from a jet. These observations therefore provide indirect evidence to support jet-dominated models for XTE J1118+480 and also provide a direct measurement of the slope of the optically thin emission, which is impossible, based on the average spectral energy distribution alone.

A GCSS model intercomparison for a tropical squall line observed during toga-coare. II: Intercomparison of single-column models and a cloud-resolving model

This paper presents single-column model (SCM) simulations of a tropical squall-line case observed during the Coupled Ocean-Atmosphere Response Experiment of the Tropical Ocean/Global Atmosphere Programme. This case-study was part of an international model intercomparison project organized by Working Group 4 ‘Precipitating Convective Cloud Systems’ of the GEWEX (Global Energy and Water-cycle Experiment) Cloud System Study. Eight SCM groups using different deep-convection parametrizations participated in this project. The SCMs were forced by temperature and moisture tendencies that had been computed from a reference cloud-resolving model (CRM) simulation using open boundary conditions. The comparison of the SCM results with the reference CRM simulation provided insight into the ability of current convection and cloud schemes to represent organized convection. The CRM results enabled a detailed evaluation of the SCMs in terms of the thermodynamic structure and the convective mass flux of the system, the latter being closely related to the surface convective precipitation. It is shown that the SCMs could reproduce reasonably well the time evolution of the surface convective and stratiform precipitation, the convective mass flux, and the thermodynamic structure of the squall-line system. The thermodynamic structure simulated by the SCMs depended on how the models partitioned the precipitation between convective and stratiform. However, structural differences persisted in the thermodynamic profiles simulated by the SCMs and the CRM. These differences could be attributed to the fact that the total mass flux used to compute the SCM forcing differed from the convective mass flux. The SCMs could not adequately represent these organized mesoscale circulations and the microphysicallradiative forcing associated with the stratiform region. This issue is generally known as the ‘scale-interaction’ problem that can only be properly addressed in fully three-dimensional simulations. Sensitivity simulations run by several groups showed that the time evolution of the surface convective precipitation was considerably smoothed when the convective closure was based on convective available potential energy instead of moisture convergence. Finally, additional SCM simulations without using a convection parametrization indicated that the impact of a convection parametrization in forced SCM runs was more visible in the moisture profiles than in the temperature profiles because convective transport was particularly important in the moisture budget.

Changes of the equilibrium line altitude since the Little Ice Age in the Nepalese Himalayas

Changes of the equilibrium-line altitude (ELA) since the end of the Little Ice Age (LIA) in eastern Nepal have been studied using glacier inventory data. The toe-to-headwall altitude ratios (THARs) for individual glaciers were calculated for 1992, and used to estimate the ELA in 1959 and at the end of the LIA. THAR for debris-free glaciers is found to be smaller than for debris-covered glaciers. The ELAs for debris-covered glaciers are higher than those for debris-free glaciers in eastern Nepal. There is considerable variation in the reconstructed change in ELA (ΔELA) between glaciers within specific regions and between regions. This is not related to climate gradients, but results from differences in glacier aspect: southeast- and south-facing glaciers show larger ΔELAs in eastern Nepal than north- or west-facing glaciers. The data suggest that the rate of ELA rise may have accelerated in the last few decades. The limited number of climate records from Nepal, and analyses using a simple ELA–climate model, suggest that the higher rate of the ΔELA between 1959 and 1992 is a result of increased warming that occurred after the 1970s at higher altitudes in Nepal.

Self-consistent wave-particle interactions in dispersive scale long-period field-line-resonances

Using 1D Vlasov drift-kinetic computer simulations, it is shown that electron trapping in long period standing shear Alfven waves (SAWs) provides an efficient energy sink for wave energy that is much more effective than Landau damping. It is also suggested that the plasma environment of low altitude auroral-zone geomagnetic field lines is more suited to electron acceleration by inertial or kinetic scale Alfven waves. This is due to the self-consistent response of the electron distribution function to SAWs, which must accommodate the low altitude large-scale current system in standing waves. We characterize these effects in terms of the relative magnitude of the wave phase and electron thermal velocities. While particle trapping is shown to be significant across a wide range of plasma temperatures and wave frequencies, we find that electron beam formation in long period waves is more effective in relatively cold plasma.

Field line resonances as a trigger and a tracer for substorm onset

In this paper, we show that periodic auroral arc structures are seen at the location of one particular auroral substorm onset for the 15 min preceding onset, suggesting that field line resonances should be considered a strong candidate for triggering substorm onset. Irrespective of whether this field line resonance is coincidentally or causally linked to this substorm onset, the characteristics of the field line resonance can be used to remote sense the characteristics of the geomagnetic field line that supports substorm onset. In this instance, the eigenfrequency of this resonance is around 12 mHz. Interestingly, however, there is no evidence of this field line resonance in a seven satellite major Time History of Events and Macroscale Interactions during Substorms (THEMIS)-GOES conjunction, ranging from geosynchronous orbit to ~30 RE. However, using space-based cross-phase measurements of the local field line eigenfrequency at the inner THEMIS locations, we find that the local field line eigenfrequency is 6–10 mHz. Hence, we can reliably say that this 12 mHz Field Line Resonance (FLR) must lie inside of THEMIS locations. Our conclusion is that a high-m field line resonance can both represent a strong candidate for a trigger for substorm onset, as first proposed by Samson et al. (1992), and that its characteristics can provide invaluable information as to where substorm onset occurs in the magnetosphere.

Methane in the atmosphere of the transiting hot Neptune GJ436b?

We present an analysis of seven primary transit observations of the hot Neptune GJ436b at 3.6, 4.5, and 8 μm obtained with the Infrared Array Camera on the Spitzer Space Telescope. After correcting for systematic effects, we fitted the light curves using the Markov Chain Monte Carlo technique. Combining these new data with the EPOXI, Hubble Space Telescope, and ground-based V, I, H, and Ks published observations, the range 0.5-10 μm can be covered. Due to the low level of activity of GJ436, the effect of starspots on the combination of transits at different epochs is negligible at the accuracy of the data set. Representative climate models were calculated by using a three-dimensional, pseudospectral general circulation model with idealized thermal forcing. Simulated transit spectra of GJ436b were generated using line-by-line radiative transfer models including the opacities of the molecular species expected to be present in such a planetary atmosphere. A new, ab-initio-calculated, line list for hot ammonia has been used for the first time. The photometric data observed at multiple wavelengths can be interpreted with methane being the dominant absorption after molecular hydrogen, possibly with minor contributions from ammonia, water, and other molecules. No clear evidence of carbon monoxide and carbon dioxide is found from transit photometry. We discuss this result in the light of a recent paper where photochemical disequilibrium is hypothesized to interpret secondary transit photometric data. We show that the emission photometric data are not incompatible with the presence of abundant methane, but further spectroscopic data are desirable to confirm this scenario.

Plasma structure within poleward-moving cusp/cleft auroral transients: EISCAT Svalbard radar observations and an explanation in terms of large local time extent of events

We report high-resolution observations of the southward-IMF cusp/cleft ionosphere made on December 16th 1998 by the EISCAT (European incoherent scatter) Svalbard radar (ESR), and compare them with observations of dayside auroral luminosity, as seen at a wavelength of 630 nm by a meridian scanning photometer at Ny Alesund, and of plasma flows, as seen by the CUTLASS (co-operative UK twin location auroral sounding system) Finland HF radar. The optical data reveal a series of poleward-moving transient red-line (630 nm) enhancements, events that have been associated with bursts in the rate of magnetopause reconnection generating new open flux. The combined observations at this time have strong similarities to predictions of the effects of soft electron precipitation modulated by pulsed reconnection, as made by Davis and Lockwood (1996); however, the effects of rapid zonal flow in the ionosphere, caused by the magnetic curvature force on the newly opened field lines, are found to be a significant additional factor. In particular, it is shown how enhanced plasma loss rates induced by the rapid convection can explain two outstanding anomalies of the 630 nm transients, namely how minima in luminosity form between the poleward-moving events and how events can re-brighten as they move poleward. The observations show how cusp/cleft aurora and transient poleward-moving auroral forms appear in the ESR data and the conditions which cause enhanced 630 nm emission in the transients: they are an important first step in enabling the ESR to identify these features away from the winter solstice when supporting auroral observations are not available.

Temporal and spatial variability of auroral forms in the 10–14 MLT sector: Relationship to plasma convection and solar wind-magnetosphere coupling

Ground-based observations of dayside auroral forms and magnetic perturbations in the arctic sectors of Svalbard and Greenland, in combination with the high-resolution measurements of ionospheric ion drift and temperature by the EISCAT radar, are used to study temporal/spatial structures of cusp-type auroral forms in relation to convection. Large-scale patterns of equivalent convection in the dayside polar ionosphere are derived from the magnetic observations in Greenland and Svalbard. This information is used to estimate the ionospheric convection pattern in the vicinity of the cusp/cleft aurora. The reported observations, covering the period 0700-1130 UT, on January 11, 1993, are separated into four intervals according to the observed characteristics of the aurora and ionospheric convection. The morphology and intensity of the aurora are very different in quiet and disturbed intervals. A latitudinally narrow zone of intense and dynamical 630.0 nm emission equatorward of 75 degrees MLAT, was observed during periods of enhanced antisunward convection in the cusp region. This (type 1 cusp aurora) is considered to be the signature of plasma entry via magnetopause reconnection at low magnetopause latitudes, i.e. the low-latitude boundary layer (LLB I,). Another zone of weak 630.0 nm emission (type 2 cusp aurora) was observed to extend up to high latitudes (similar to 79 degrees MLAT) during relatively quiet magnetic conditions, when indications of reverse (sunward) convection was observed in the dayside polar cap. This is postulated to be a signature of merging between a northward directed IMF (B-z > 0) and the geomagnetic field poleward of the cusp. The coexistence of type 1 and 2 auroras was observed under intermediate circumstances. The optical observations from Svalbard and Greenland were also used to determine the temporal and spatial evolution of type 1 auroral forms, i.e. poleward-moving auroral events occurring in the vicinity of a rotational convection reversal in the early post-noon sector. Each event appeared as a local brightening at the equatorward boundary of the pre-existing type 1 cusp aurora, followed by poleward and eastward expansions of luminosity. The auroral events were associated with poleward-moving surges of enhanced ionospheric convection and F-layer ion temperature as observed by the EISCAT radar in Tromso. The EISCAT ion flow data in combination with the auroral observations show strong evidence for plasma flow across the open/closed field line boundary.

Location and characteristics of the reconnection X line deduced from low-altitude satellite and ground-based observations: 2. Defense Meteorological Satellite Program and European Incoherent Scatter data

We present an analysis of a cusp ion step, observed by the Defense Meteorological Satellite Program (DMSP) F10 spacecraft, between two poleward moving events of enhanced ionospheric electron temperature, observed by the European Incoherent Scatter (EISCAT) radar. From the ions detected by the satellite, the variation of the reconnection rate is computed for assumed distances along the open-closed field line separatrix from the satellite to the X line, do. Comparison with the onset times of the associated ionospheric events allows this distance to be estimated, but with an uncertainty due to the determination of the low-energy cutoff of the ion velocity distribution function, ƒ(ν). Nevertheless, the reconnection site is shown to be on the dayside magnetopause, consistent with the reconnection model of the cusp during southward interplanetary magnetic field (IMF). Analysis of the time series of distribution function at constant energies, ƒ(ts), shows that the best estimate of the distance do is 14.5±2 RE. This is consistent with various magnetopause observations of the signatures of reconnection for southward IMF. The ion precipitation is used to reconstruct the field-parallel part of the Cowley D ion distribution function injected into the open low-latitude boundary layer in the vicinity of the X line. From this reconstruction, the field-aligned component of the magnetosheath flow is found to be only −55±65 km s−1 near the X line, which means either that the reconnection X line is near the stagnation region at the nose of the magnetosphere, or that it is closely aligned with the magnetosheath flow streamline which is orthogonal to the magnetosheath field, or both. In addition, the sheath Alfvén speed at the X line is found to be 220±45 km s−1, and the speed with which newly opened field lines are ejected from the X line is 165±30 km s−1. We show that the inferred magnetic field, plasma density, and temperature of the sheath near the X line are consistent with a near-subsolar reconnection site and confirm that the magnetosheath field makes a large angle (>58°) with the X line.

Location and characteristics of the reconnection X line deduced from low-altitude satellite and ground-based observations: 1. Theory

A method for estimating both the Alfvén speed and the field-aligned flow of the magnetosheath at the magnetopause reconnection site is presented. The method employs low-altitude cusp ion observations and requires the identification of a feature in the cusp ion spectra near the low-energy cutoff which will often be present for a low-latitude dayside reconnection site. The appearance of these features in data of limited temporal, energy, and pitch angle resolution is illustrated by using model calculations of cusp ion distribution functions. These are based on the theory of ion acceleration at the dayside magnetopause and allow for the effects on the spectrum of flight times of ions precipitating down newly opened field lines. In addition, the variation of the reconnection rate can be evaluated, and comparison with ground-based observations of the corresponding sequence of transient events allows the field-aligned distance from the ionosphere to the reconnection site to be estimated.

Flow-aligned jets in the magnetospheric cusp: Results from the Geospace Environment Modeling Pilot Program

The extended flight of the Airborne Ionospheric Observatory during the Geospace Environment Modeling (GEM) Pilot program on January 16, 1990, allowed continuous all-sky monitoring of the two-dimensional ionospheric footprint of the northward interplanetary magnetic field (IMF) cusp in several wavelengths. Especially important in determining the locus of magnetosheath electron precipitation was the 630.0-nm red line emission. The most striking morphological change in the images was the transient appearance of zonally elongated regions of enhanced 630.0-nm emission which resembled “rays” emanating from the centroid of the precipitation. The appearance of these rays was strongly correlated with the Y component of the IMF: when the magnitude of By was large compared to Bz, the rays appeared; otherwise, the distribution was relatively unstructured. Late in the flight the field of view of the imager included the field of view of flow measurements from the European incoherent scatter radar (EISCAT). The rays visible in 630.0-nm emission exactly aligned with the position of strong flow jets observed by EISCAT. We attribute this correspondence to the requirement of quasi-neutrality; namely, the soft electrons have their largest precipitating fluxes where the bulk of the ions precipitate. The ions, in regions of strong convective flow, are spread out farther along the flow path than in regions of weaker flow. The occurrence and direction of these flow bursts are controlled by the IMF in a manner consistent with newly opened flux tubes; i.e., when |By| > |Bz|, tension in the reconnected field lines produce east-west flow regions downstream of the ionospheric projection of the x line. We interpret the optical rays (flow bursts), which typically last between 5 and 15 min, as evidence of periods of enhanced dayside (or lobe) reconnection when |By| > |Bz|. The length of the reconnection pulse is difficult to determine, however, since strong zonal flows would be expected to persist until the tension force in the field line has decayed, even if the duration of the enhanced reconnection was relatively short.

The characteristics of the magnetopause reconnection X-line deduced from low-altitude satellite observations of cusp ions

We present an analysis of a “quasi-steady” cusp ion dispersion signature observed at low altitudes. We reconstruct the field-parallel part of the Cowley-D ion distribution function, injected into the open LLBL in the vicinity of the reconnection X-line. From this we find the field-parallel magnetosheath flow at the X-line was only 20 ± 60 km s−1, placing the reconnection site close to the flow streamline which is perpendicular to the magnetosheath field. Using interplanetary data and assuming the subsolar magnetopause is in pressure balance, we derive a wealth of information about the X-line, including: the density, flow, magnetic field and Alfvén speed of the magnetosheath; the magnetic shear across the X-line; the de-Hoffman Teller speed with which field lines emerge from the X-line; the magnetospheric field; and the ion transmission factor across the magnetopause. The results indicate that some heating takes place near the X-line as the ions cross the magnetopause, and that sheath densities may be reduced in a plasma depletion layer. We also compute the reconnection rate. Despite its quasi-steady appearance on an ion spectrogram, this cusp is found to reveal a large pulse of enhanced reconnection rate.