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.

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 vertical structure of oceanic Rossby waves: a comparison of high-resolution model data to theoretical vertical structures

Tests of the new Rossby wave theories that have been developed over the past decade to account for discrepancies between theoretical wave speeds and those observed by satellite altimeters have focused primarily on the surface signature of such waves. It appears, however, that the surface signature of the waves acts only as a rather weak constraint, and that information on the vertical structure of the waves is required to better discriminate between competing theories. Due to the lack of 3-D observations, this paper uses high-resolution model data to construct realistic vertical structures of Rossby waves and compares these to structures predicted by theory. The meridional velocity of a section at 24° S in the Atlantic Ocean is pre-processed using the Radon transform to select the dominant westward signal. Normalized profiles are then constructed using three complementary methods based respectively on: (1) averaging vertical profiles of velocity, (2) diagnosing the amplitude of the Radon transform of the westward propagating signal at different depths, and (3) EOF analysis. These profiles are compared to profiles calculated using four different Rossby wave theories: standard linear theory (SLT), SLT plus mean flow, SLT plus topographic effects, and theory including mean flow and topographic effects. Our results support the classical theoretical assumption that westward propagating signals have a well-defined vertical modal structure associated with a phase speed independent of depth, in contrast with the conclusions of a recent study using the same model but for different locations in the North Atlantic. The model structures are in general surface intensified, with a sign reversal at depth in some regions, notably occurring at shallower depths in the East Atlantic. SLT provides a good fit to the model structures in the top 300 m, but grossly overestimates the sign reversal at depth. The addition of mean flow slightly improves the latter issue, but is too surface intensified. SLT plus topography rectifies the overestimation of the sign reversal, but overestimates the amplitude of the structure for much of the layer above the sign reversal. Combining the effects of mean flow and topography provided the best fit for the mean model profiles, although small errors at the surface and mid-depths are carried over from the individual effects of mean flow and topography respectively. Across the section the best fitting theory varies between SLT plus topography and topography with mean flow, with, in general, SLT plus topography performing better in the east where the sign reversal is less pronounced. None of the theories could accurately reproduce the deeper sign reversals in the west. All theories performed badly at the boundaries. The generalization of this method to other latitudes, oceans, models and baroclinic modes would provide greater insight into the variability in the ocean, while better observational data would allow verification of the model findings.

Estimating the potential yield of small wind turbines in urban areas: a case study for Greater London, UK

To optimise the placement of small wind turbines in urban areas a detailed understanding of the spatial variability of the wind resource is required. At present, due to a lack of observations, the NOABL wind speed database is frequently used to estimate the wind resource at a potential site. However, recent work has shown that this tends to overestimate the wind speed in urban areas. This paper suggests a method for adjusting the predictions of the NOABL in urban areas by considering the impact of the underlying surface on a neighbourhood scale. In which, the nature of the surface is characterised on a 1 km2 resolution using an urban morphology database. The model was then used to estimate the variability of the annual mean wind speed across Greater London at a height typical of current small wind turbine installations. Initial validation of the results suggests that the predicted wind speeds are considerably more accurate than the NOABL values. The derived wind map therefore currently provides the best opportunity to identify the neighbourhoods in Greater London at which small wind turbines yield their highest energy production. The model does not consider street scale processes, however previously derived scaling factors can be applied to relate the neighbourhood wind speed to a value at a specific rooftop site. The results showed that the wind speed predicted across London is relatively low, exceeding 4 ms-1 at only 27% of the neighbourhoods in the city. Of these sites less than 10% are within 10 km of the city centre, with the majority over 20 km from the city centre. Consequently, it is predicted that small wind turbines tend to perform better towards the outskirts of the city, therefore for cities which fit the Burgess concentric ring model, such as Greater London, ‘distance from city centre’ is a useful parameter for siting small wind turbines. However, there are a number of neighbourhoods close to the city centre at which the wind speed is relatively high and these sites can only been identified with a detailed representation of the urban surface, such as that developed in this study.

High-speed Keck spectroscopy of flares and oscillations in AE Aquarii

Using high-time-resolution (72 ms) spectroscopy of AE Aqr obtained with LRIS on Keck II we have determined the spectrum and spectral evolution of a small flare. Continuum and integrated line fluxes in the flare spectrum are measured, and the evolution of the flare is parametrized for future comparison with detailed models of the flares. We find that the velocities of the flaring components are consistent with those previously reported for AE Aqr by Welsh, Horne & Gomer and Horne. The characteristics of the 33-s oscillations are investigated: we derive the oscillation amplitude spectrum, and from that determine the spectrum of the heated regions on the rotating white dwarf. Blackbody fits to the major and minor pulse spectra and an analysis of the emission-line oscillation properties highlight the shortfalls in the simple hotspot model for the oscillations.

High speed keck spectroscopy of flickering in AM Her

We present fast (72 ms) spectroscopy of AM Her obtained at an intermediate brightness state just before a rise to high state. Interesting features in the line behaviour of AM Her are noted and the variability spectrum is presented and compared to that of SS Cyg.

Nature of vegetation and building morphology characteristics across a city: influence on shadow patterns and mean radiant temperatures in London

Vegetation and building morphology characteristics are investigated at 19 sites on a north-south LiDAR transect across the megacity of London. Local maxima of mean building height and building plan area density at the city centre are evident. Surprisingly, the mean vegetation height (zv3) is also found to be highest in the city centre. From the LiDAR data various morphological parameters are derived as well as shadow patterns. Continuous images of the effects of buildings and of buildings plus vegetationon sky view factor (Ψ) are derived. A general reduction of Ψ is found, indicating the importance of including vegetation when deriving Ψ in urban areas. The contribution of vegetation to the shadowing at ground level is higher during summer than in autumn. Using these 3D data the influence on urban climate and mean radiant temperature (T mrt ) is calculated with SOLWEIG. The results from these simulations highlight that vegetation can be most effective at reducing heat stress within dense urban environments in summer. The daytime average T mrt is found to be lowest in the densest urban environments due to shadowing; foremost from buildings but also from trees. It is clearly shown that this method could be used to quantify the influence of vegetation on T mrt within the urban environment. The results presented in this paper highlight a number of possible climate sensitive planning practices for urban areas at the local scale (i.e. 102- 5 × 103 m).

The influence of vegetation and building morphology on shadow patterns and mean radiant temperatures in urban areas: model development and evaluation

The solar and longwave environmental irradiance geometry (SOLWEIG) model simulates spatial variations of 3-D radiation fluxes and mean radiant temperature (T mrt) as well as shadow patterns in complex urban settings. In this paper, a new vegetation scheme is included in SOLWEIG and evaluated. The new shadow casting algorithm for complex vegetation structures makes it possible to obtain continuous images of shadow patterns and sky view factors taking both buildings and vegetation into account. For the calculation of 3-D radiation fluxes and T mrt, SOLWEIG only requires a limited number of inputs, such as global shortwave radiation, air temperature, relative humidity, geographical information (latitude, longitude and elevation) and urban geometry represented by high-resolution ground and building digital elevation models (DEM). Trees and bushes are represented by separate DEMs. The model is evaluated using 5 days of integral radiation measurements at two sites within a square surrounded by low-rise buildings and vegetation in Göteborg, Sweden (57°N). There is good agreement between modelled and observed values of T mrt, with an overall correspondence of R 2 = 0.91 (p < 0.01, RMSE = 3.1 K). A small overestimation of T mrt is found at locations shadowed by vegetation. Given this good performance a number of suggestions for future development are identified for applications which include for human comfort, building design, planning and evaluation of instrument exposure.

In situ and remote-sensing measurements of the mean microphysical and optical properties of industrial pollution aerosol during ADRIEX

We present a summary of the principal physical and optical properties of aerosol particles using the FAAM BAE-146 instrumented aircraft during ADRIEX between 27 August and 6 September 2004, augmented by sunphotometer, lidar and satellite retrievals. Observations of anthropogenic aerosol, principally from industrial sources, were concentrated over the northern Adriatic Sea and over the Po Valley close to the aerosol sources. An additional flight was also carried out over the Black Sea to compare east and west European pollution. Measurements show the single-scattering albedo of dry aerosol particles to vary considerably between 0.89 and 0.97 at a wavelength of 0.55 μm, with a campaign mean within the polluted lower free troposphere of 0.92. Although aerosol concentrations varied significantly from day to day and during individual days, the shape of the aerosol size distribution was relatively consistent through the experiment, with no detectable change observed over land and over sea. There is evidence to suggest that the pollution aerosol within the marine boundary layer was younger than that in the elevated layer. Trends in the aerosol volume distribution show consistency with multiple-site AERONET radiometric observations. The aerosol optical depths derived from aircraft measurements show a consistent bias to lower values than both the AERONET and lidar ground-based radiometric observations, differences which can be explained by local variations in the aerosol column loading and by some aircraft instrumental artefacts. Retrievals of the aerosol optical depth and fine-mode (<0.5 μm radius) fraction contribution to the optical depth using MODIS data from the Terra and Aqua satellites show a reasonable level of agreement with the AERONET and aircraft measurements.

The stochastic component in choice and regression to the mean

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate the point in the context of a social comparison experiment.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.

Reconstruction of geomagnetic activity and near-Earth interplanetary conditions over the past 167 yr - Part 4: Near-Earth solar wind speed, IMF, and open solar flux

In the concluding paper of this tetralogy, we here use the different geomagnetic activity indices to reconstruct the near-Earth interplanetary magnetic field (IMF) and solar wind flow speed, as well as the open solar flux (OSF) from 1845 to the present day. The differences in how the various indices vary with near-Earth interplanetary parameters, which are here exploited to separate the effects of the IMF and solar wind speed, are shown to be statistically significant at the 93% level or above. Reconstructions are made using four combinations of different indices, compiled using different data and different algorithms, and the results are almost identical for all parameters. The correction to the aa index required is discussed by comparison with the Ap index from a more extensive network of mid-latitude stations. Data from the Helsinki magnetometer station is used to extend the aa index back to 1845 and the results confirmed by comparison with the nearby St Petersburg observatory. The optimum variations, using all available long-term geomagnetic indices, of the near-Earth IMF and solar wind speed, and of the open solar flux, are presented; all with ±2sigma� uncertainties computed using the Monte Carlo technique outlined in the earlier papers. The open solar flux variation derived is shown to be very similar indeed to that obtained using the method of Lockwood et al. (1999).

Evidence for solar wind modulation of lightning

The response of lightning rates over Europe to arrival of high speed solar wind streams at Earth is investigated using a superposed epoch analysis. Fast solar wind stream arrival is determined from modulation of the solar wind V y component, measured by the Advanced Composition Explorer spacecraft. Lightning rate changes around these event times are determined from the very low frequency arrival time difference (ATD) system of the UK Met Office. Arrival of high speed streams at Earth is found to be preceded by a decrease in total solar irradiance and an increase in sunspot number and Mg II emissions. These are consistent with the high speed stream's source being co-located with an active region appearing on the Eastern solar limb and rotating at the 27 d period of the Sun. Arrival of the high speed stream at Earth also coincides with a small (~1%) but rapid decrease in galactic cosmic ray flux, a moderate (~6%) increase in lower energy solar energetic protons (SEPs), and a substantial, statistically significant increase in lightning rates. These changes persist for around 40 d in all three quantities. The lightning rate increase is corroborated by an increase in the total number of thunder days observed by UK Met stations, again persisting for around 40 d after the arrival of a high speed solar wind stream. This result appears to contradict earlier studies that found an anti-correlation between sunspot number and thunder days over solar cycle timescales. The increase in lightning rates and thunder days that we observe coincides with an increased flux of SEPs which, while not being detected at ground level, nevertheless penetrate the atmosphere to tropospheric altitudes. This effect could be further amplified by an increase in mean lightning stroke intensity that brings more strokes above the detection threshold of the ATD system. In order to remove any potential seasonal bias the analysis was repeated for daily solar wind triggers occurring during the summer months (June to August). Though this reduced the number of solar wind triggers to 32, the response in both lightning and thunder day data remained statistically significant. This modulation of lightning by regular and predictable solar wind events may be beneficial to medium range forecasting of hazardous weather.

Evaluation of high-resolution surface wind products at global and regional scales

High resolution surface wind fields covering the global ocean, estimated from remotely sensed wind data and ECMWF wind analyses, have been available since 2005 with a spatial resolution of 0.25 degrees in longitude and latitude, and a temporal resolution of 6h. Their quality is investigated through various comparisons with surface wind vectors from 190 buoys moored in various oceanic basins, from research vessels and from QuikSCAT scatterometer data taken during 2005-2006. The NCEP/NCAR and NCDC blended wind products are also considered. The comparisons performed during January-December 2005 show that speeds and directions compare well to in-situ observations, including from moored buoys and ships, as well as to the remotely sensed data. The root-mean-squared differences of the wind speed and direction for the new blended wind data are lower than 2m/s and 30 degrees, respectively. These values are similar to those estimated in the comparisons of hourly buoy measurements and QuickSCAT near real time retrievals. At global scale, it is found that the new products compare well with the wind speed and wind vector components observed by QuikSCAT. No significant dependencies on the QuikSCAT wind speed or on the oceanic region considered are evident.Evaluation of high-resolution surface wind products at global and regional scales

How well can we measure the ocean’s mean dynamic topography from space?

Recent gravity missions have produced a dramatic improvement in our ability to measure the ocean’s mean dynamic topography (MDT) from space. To fully exploit this oceanic observation, however, we must quantify its error. To establish a baseline, we first assess the error budget for an MDT calculated using a 3rd generation GOCE geoid and the CLS01 mean sea surface (MSS). With these products, we can resolve MDT spatial scales down to 250 km with an accuracy of 1.7 cm, with the MSS and geoid making similar contributions to the total error. For spatial scales within the range 133–250 km the error is 3.0 cm, with the geoid making the greatest contribution. For the smallest resolvable spatial scales (80–133 km) the total error is 16.4 cm, with geoid error accounting for almost all of this. Relative to this baseline, the most recent versions of the geoid and MSS fields reduce the long and short-wavelength errors by 0.9 and 3.2 cm, respectively, but they have little impact in the medium-wavelength band. The newer MSS is responsible for most of the long-wavelength improvement, while for the short-wavelength component it is the geoid. We find that while the formal geoid errors have reasonable global mean values they fail capture the regional variations in error magnitude, which depend on the steepness of the sea floor topography.