Processes controlling atmospheric dispersion through city centres

We develop a process-based model for the dispersion of a passive scalar in the turbulent flow around the buildings of a city centre. The street network model is based on dividing the airspace of the streets and intersections into boxes, within which the turbulence renders the air well mixed. Mean flow advection through the network of street and intersection boxes then mediates further lateral dispersion. At the same time turbulent mixing in the vertical detrains scalar from the streets and intersections into the turbulent boundary layer above the buildings. When the geometry is regular, the street network model has an analytical solution that describes the variation in concentration in a near-field downwind of a single source, where the majority of scalar lies below roof level. The power of the analytical solution is that it demonstrates how the concentration is determined by only three parameters. The plume direction parameter describes the branching of scalar at the street intersections and hence determines the direction of the plume centreline, which may be very different from the above-roof wind direction. The transmission parameter determines the distance travelled before the majority of scalar is detrained into the atmospheric boundary layer above roof level and conventional atmospheric turbulence takes over as the dominant mixing process. Finally, a normalised source strength multiplies this pattern of concentration. This analytical solution converges to a Gaussian plume after a large number of intersections have been traversed, providing theoretical justification for previous studies that have developed empirical fits to Gaussian plume models. The analytical solution is shown to compare well with very high-resolution simulations and with wind tunnel experiments, although re-entrainment of scalar previously detrained into the boundary layer above roofs, which is not accounted for in the analytical solution, is shown to become an important process further downwind from the source.

Modelling signatures of pulsed magnetopause reconnection in cusp ion dispersion signatures seen at middle altitudes

It is shown that the open magnetosphere model can reproduce both the down-going and the up-going magnetosheath ions seen in the cusp and mantle regions by the Polar satellite at middle altitudes. ?he pass studied shows a series of discontinuities in the ion dispersion, most of which are shown to arise from pulses of magnetopause reconnection rate. A total of 9 pulses are detected in an interval estimated to be about 30 min long, giving a mean repetition period of about 3 min: they vary in length between 0.5 min and 3.5 min and are separated by periods of much slower reconnection of duration 1-3 min. One step is not as predicted for reconnection rate pulses but is explained in terms of compressive motions caused by a pulse of solar wind dynamic pressure. The reconnection site is found to be 16 +/- 3 R-E from the ionosphere along the separatrix field line, placing it at low latitudes on the dayside magnetopause.

An analysis of the accuracy of magnetopause reconnection rate variations deduced from cusp ion dispersion characteristics

We present an analysis of the accuracy of the method introduced by Lockwood et al. (1994) for the determination of the magnetopause reconnection rate from the dispersion of precipitating ions in the ionospheric cusp region. Tests are made by applying the method to synthesised data. The simulated cusp ion precipitation data are produced by an analytic model of the evolution of newly-opened field lines, along which magnetosheath ions are firstly injected across the magnetopause and then dispersed as they propagate into the ionosphere. The rate at which these newly opened field lines are generated by reconnection can be varied. The derived reconnection rate estimates are then compared with the input variation to the model and the accuracy of the method assessed. Results are presented for steady-state reconnection, for continuous reconnection showing a sine-wave variation in rate and for reconnection which only occurs in square wave pulses. It is found that the method always yields the total flux reconnected (per unit length of the open-closed field-line boundary) to within an accuracy of better than 5%, but that pulses tend to be smoothed so that the peak reconnection rate within the pulse is underestimated and the pulse length is overestimated. This smoothing is reduced if the separation between energy channels of the instrument is reduced; however this also acts to increase the experimental uncertainty in the estimates, an effect which can be countered by improving the time resolution of the observations. The limited time resolution of the data is shown to set a minimum reconnection rate below which the method gives spurious short-period oscillations about the true value. Various examples of reconnection rate variations derived from cusp observations are discussed in the light of this analysis.

Low and middle altitude cusp particle signatures for general magnetopause reconnection rate variations: 1. Theory

We present predictions of the signatures of magnetosheath particle precipitation (in the regions classified as open low-latitude boundary layer, cusp, mantle and polar cap) for periods when the interplanetary magnetic field has a southward component. These are made using the “pulsating cusp” model of the effects of time-varying magnetic reconnection at the dayside magnetopause. Predictions are made for both low-altitude satellites in the topside ionosphere and for midaltitude spacecraft in the magnetosphere. Low-altitude cusp signatures, which show a continuous ion dispersion signature, reveal "quasi-steady reconnection" (one limit of the pulsating cusp model), which persists for a period of at least 10 min. We estimate that “quasi-steady” in this context corresponds to fluctuations in the reconnection rate of a factor of 2 or less. The other limit of the pulsating cusp model explains the instantaneous jumps in the precipitating ion spectrum that have been observed at low altitudes. Such jumps are produced by isolated pulses of reconnection: that is, they are separated by intervals when the reconnection rate is zero. These also generate convecting patches on the magnetopause in which the field lines thread the boundary via a rotational discontinuity separated by more extensive regions of tangential discontinuity. Predictions of the corresponding ion precipitation signatures seen by midaltitude spacecraft are presented. We resolve the apparent contradiction between estimates of the width of the injection region from midaltitude data and the concept of continuous entry of solar wind plasma along open field lines. In addition, we reevaluate the use of pitch angle-energy dispersion to estimate the injection distance.

Modelling the high-latitude ionosphere for time-varying plasma convection

The paper discusses how variations in the pattern of convective plasma flows should beincluded in self-consistent time-dependent models of the coupled ionosphere-thermosphere system. The author shows how these variations depend upon the mechanism by which the solar wind flow excites the convection. The modelling of these effects is not just of relevance to the polar ionosphere. This is because the influence of convection is not confined to high latitudes: the resultant heating and composition changes in the thermosphere are communicated to lower latitudes by the winds which are also greatly modified by the plasma convection. These thermospheric changes alter the global distribution of plasma by modulatingthe rates of the chemical reactions which areresponsible for the loss of plasma. Hence the modelling of these high-latitude processes is of relevanceto the design and operation of HF communication, radar and navigation systems worldwide.

Time-varying price discovery in the eighteenth century: empirical evidence from the London and Amsterdam stock markets

This paper examines the time-varying nature of price discovery in eighteenth century cross-listed stocks. Specifically, we investigate how quickly news is reflected in prices for two of the great moneyed com- panies, the Bank of England and the East India Company, over the period 1723 to 1794. These British companies were cross-listed on the London and Amsterdam stock exchange and news between the capitals flowed mainly via the use of boats that transported mail. We examine in detail the historical context sur- rounding the defining events of the period, and use these as a guide to how the data should be analysed. We show that both trading venues contributed to price discovery, and although the London venue was more important for these stocks, its importance varies over time.

Time varying price discovery

We show how multivariate GARCH models can be used to generate a time-varying “information share” (Hasbrouck, 1995) to represent the changing patterns of price discovery in closely related securities. We find that time-varying information shares can improve credit spread predictions.

Dynamic game soundtrack generation in response to a continously varying emotional trajectory

Dynamic soundtracking presents various practical and aesthetic challenges to composers working with games. This paper presents an implementation of a system addressing some of these challenges with an affectively-driven music generation algorithm based on a second order Markov-model. The system can respond in real-time to emotional trajectories derived from 2-dimensions of affect on the circumplex model (arousal and valence), which are mapped to five musical parameters. A transition matrix is employed to vary the generated output in continuous response to the affective state intended by the gameplay.

Assessing the accuracy and dispersion of real estate investment forecasts

Existing empirical evidence has frequently observed that professional forecasters are conservative and display herding behaviour. Whilst a large number of papers have considered equities as well as macroeconomic series, few have considered the accuracy of forecasts in alternative asset classes such as real estate. We consider the accuracy of forecasts for the UK commercial real estate market over the period 1999-2011. The results illustrate that forecasters display a tendency to under-estimate growth rates during strong market conditions and over-estimate when the market is performing poorly. This conservatism not only results in smoothed estimates but also implies that forecasters display herding behaviour. There is also a marked difference in the relative accuracy of capital and total returns versus rental figures. Whilst rental growth forecasts are relatively accurate, considerable inaccuracy is observed with respect to capital value and total returns.

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.

The longitudinal variation of equatorial waves due to propagation on a varying zonal flow

The general 1-D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behaviour are found, depending on the sign of the group velocity (cg) and a wave property, B. For B positive the wave energy and the wave number vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang (1988) occurs where cg goes to zero. However for B negative they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analysed in detail using the theory. For non-dispersive Kelvin waves, B reduces to 2, and analytic solution is possible. B is positive for all the waves considered, except for the westward moving mixed Rossby-gravity (WMRG) wave which can have negative as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic are not consistent with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher latitude wave activity.

High-precision measurements of the co-polar correlation coefficient: non-Gaussian errors and retrieval of the dispersion parameter µ in rainfall

The co-polar correlation coefficient (ρhv) has many applications, including hydrometeor classification, ground clutter and melting layer identification, interpretation of ice microphysics and the retrieval of rain drop size distributions (DSDs). However, we currently lack the quantitative error estimates that are necessary if these applications are to be fully exploited. Previous error estimates of ρhv rely on knowledge of the unknown "true" ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. We show that frequency distributions of ρhv estimates are in fact highly negatively skewed. A new variable: L = -log10(1 - ρhv) is defined, which does have Gaussian error statistics, and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, we demonstrate how the imperfect co-location of the horizontal and vertical polarisation sample volumes may be accounted for. The possibility of using L to estimate the dispersion parameter (µ) in the gamma drop size distribution is investigated. We find that including drop oscillations is essential for this application, otherwise there could be biases in retrieved µ of up to ~8. Preliminary results in rainfall are presented. In a convective rain case study, our estimates show µ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial beta-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(epsilon)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby-gravity, and inertio-gravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(e) approximation, and the dynamics of these interactions have been studied in the presence of the forcing. It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k = 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby-gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an ""accelerator"" for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating low-frequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

The impact of smoke from forest fires on the spectral dispersion of cloud droplet size distributions in the Amazonian region

In this paper, the main microphysical characteristics of clouds developing in polluted and clean conditions in the biomass-burning season of the Amazon region are examined, with special attention to the spectral dispersion of the cloud droplet size distribution and its potential impact on climate modeling applications. The dispersion effect has been shown to alter the climate cooling predicted by the so-called Twomey effect. In biomass-burning polluted conditions, high concentrations of low dispersed cloud droplets are found. Clean conditions revealed an opposite situation. The liquid water content (0.43 +/- 0.19 g m(-3)) is shown to be uncorrelated with the cloud drop number concentration, while the effective radius is found to be very much correlated with the relative dispersion of the size distribution (R(2) = 0.81). The results suggest that an increase in cloud condensation nuclei concentration from biomass-burning aerosols may lead to an additional effect caused by a decrease in relative dispersion. Since the dry season in the Amazonian region is vapor limiting, the dispersion effect of cloud droplet size distributions could be substantially larger than in other polluted regions.