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.

A wind tunnel model for quantifying fluxes in the urban boundary layer

Transport of pollution and heatout of streets into the boundary layer above is not currently understood and so fluxes cannot be quantified. Scalar concentration within the street is determined by the flux out of it and so quantifying fluxes for turbulent flow over a rough urban surface is essential. We have developed a naphthalene sublimation technique to measure transfer from a two-dimensional street canyon in a wind tunnel for the case of flow perpendicular to the street. The street was coated with naphthalene, which sublimes at room temperature, so that the vapour represented the scalar source. The transfer velocity wT relates the flux out of the canyon to the concentration within it and is shown to be linearly related to windspeed above the street. The dimensionless transfer coefficient wT/Uδ represents the ventilation efficiency of the canyon (here, wT is a transfer velocity,Uδ is the wind speed at the boundary-layer top). Observed values are between 1.5 and 2.7 ×10-3 and, for the case where H/W→0 (ratio of buildingheight to street width), values are in the same range as estimates of transfer from a flat plate, giving confidence that the technique yields accurate values for street canyon scalar transfer. wT/Uδ varies with aspect ratio (H/W), reaching a maximum in the wake interference regime (0.3 < H/W < 0.65). However, when upstream roughness is increased, the maximum in wT/Uδ reduces, suggesting that street ventilation is less sensitive to H/W when the flow is in equilibrium with the urban surface. The results suggest that using naphthalene sublimation with wind-tunnel models of urban surfaces can provide a direct measure of area-averaged scalar fluxes.

Structure of the planetary boundary layer over southeast England: modeling and measurements

The Weather Research and Forecasting model was applied to analyze variations in the planetary boundary layer (PBL) structure over Southeast England including central and suburban London. The parameterizations and predictive skills of two nonlocal mixing PBL schemes, YSU and ACM2, and two local mixing PBL schemes, MYJ and MYNN2, were evaluated over a variety of stability conditions, with model predictions at a 3 km grid spacing. The PBL height predictions, which are critical for scaling turbulence and diffusion in meteorological and air quality models, show significant intra-scheme variance (> 20%), and the reasons are presented. ACM2 diagnoses the PBL height thermodynamically using the bulk Richardson number method, which leads to a good agreement with the lidar data for both unstable and stable conditions. The modeled vertical profiles in the PBL, such as wind speed, turbulent kinetic energy (TKE), and heat flux, exhibit large spreads across the PBL schemes. The TKE predicted by MYJ were found to be too small and show much less diurnal variation as compared with observations over London. MYNN2 produces better TKE predictions at low levels than MYJ, but its turbulent length scale increases with height in the upper part of the strongly convective PBL, where it should decrease. The local PBL schemes considerably underestimate the entrainment heat fluxes for convective cases. The nonlocal PBL schemes exhibit stronger mixing in the mean wind fields under convective conditions than the local PBL schemes and agree better with large-eddy simulation (LES) studies.

Observations of urban boundary layer structure during a strong urban heat island event

It has long been known that the urban surface energy balance is different to that of a rural surface, and that heating of the urban surface after sunset gives rise to the Urban Heat Island (UHI). Less well known is how flow and turbulence structure above the urban surface are changed during different phases of the urban boundary layer (UBL). This paper presents new observations above both an urban and rural surface and investigates how much UBL structure deviates from classical behaviour. A 5-day, low wind, cloudless, high pressure period over London, UK, was chosen for analysis, during which there was a strong UHI. Boundary layer evolution for both sites was determined by the diurnal cycle in sensible heat flux, with an extended decay period of approximately 4 h for the convective UBL. This is referred to as the “Urban Convective Island” as the surrounding rural area was already stable at this time. Mixing height magnitude depended on the combination of regional temperature profiles and surface temperature. Given the daytime UHI intensity of 1.5∘C, combined with multiple inversions in the temperature profile, urban and rural mixing heights underwent opposite trends over the period, resulting in a factor of three height difference by the fifth day. Nocturnal jets undergoing inertial oscillations were observed aloft in the urban wind profile as soon as the rural boundary layer became stable: clear jet maxima over the urban surface only emerged once the UBL had become stable. This was due to mixing during the Urban Convective Island reducing shear. Analysis of turbulent moments (variance, skewness and kurtosis) showed “upside-down” boundary layer characteristics on some mornings during initial rapid growth of the convective UBL. During the “Urban Convective Island” phase, turbulence structure still resembled a classical convective boundary layer but with some influence from shear aloft, depending on jet strength. These results demonstrate that appropriate choice of Doppler lidar scan patterns can give detailed profiles of UBL flow. Insights drawn from the observations have implications for accuracy of boundary conditions when simulating urban flow and dispersion, as the UBL is clearly the result of processes driven not only by local surface conditions but also regional atmospheric structure.

Progress in observing and modelling the urban boundary layer

The urban boundary layer (UBL) is the part of the atmosphere in which most of the planet’s population now lives, and is one of the most complex and least understood microclimates. Given potential climate change impacts and the requirement to develop cities sustainably, the need for sound modelling and observational tools becomes pressing. This review paper considers progress made in studies of the UBL in terms of a conceptual framework spanning microscale to mesoscale determinants of UBL structure and evolution. Considerable progress in observing and modelling the urban surface energy balance has been made. The urban roughness sub-layer is an important region requiring attention as assumptions about atmospheric turbulence break down in this layer and it may dominate coupling of the surface to the UBL due to its considerable depth. The upper 90% of the UBL (mixed and residual layers) remains under-researched but new remote sensing methods and high resolution modelling tools now permit rapid progress. Surface heterogeneity dominates from neighbourhood to regional scales and should be more strongly considered in future studies. Specific research priorities include humidity within the UBL, high-rise urban canopies and the development of long-term, spatially extensive measurement networks coupled strongly to model development.

Motion of the dayside polar cap boundary during substorm cycles: II. Generation of poleward-moving events and polar cap patches by pulses in the magnetopause reconnection rate

Using data from the EISCAT (European Incoherent Scatter) VHF and CUTLASS (Co-operative UK Twin- Located Auroral Sounding System) HF radars, we study the formation of ionospheric polar cap patches and their relationship to the magnetopause reconnection pulses identified in the companion paper by Lockwood et al. (2005). It is shown that the poleward-moving, high-concentration plasma patches observed in the ionosphere by EISCAT on 23 November 1999, as reported by Davies et al. (2002), were often associated with corresponding reconnection rate pulses. However, not all such pulses generated a patch and only within a limited MLT range (11:00–12:00 MLT) did a patch result from a reconnection pulse. Three proposed mechanisms for the production of patches, and of the concentration minima that separate them, are analysed and evaluated: (1) concentration enhancement within the patches by cusp/cleft precipitation; (2) plasma depletion in the minima between the patches by fast plasma flows; and (3) intermittent injection of photoionisation-enhanced plasma into the polar cap. We devise a test to distinguish between the effects of these mechanisms. Some of the events repeat too frequently to apply the test. Others have sufficiently long repeat periods and mechanism (3) is shown to be the only explanation of three of the longer-lived patches seen on this day. However, effect (2) also appears to contribute to some events. We conclude that plasma concentration gradients on the edges of the larger patches arise mainly from local time variations in the subauroral plasma, via the mechanism proposed by Lockwood et al. (2000).

Motion of the dayside polar cap boundary during substorm cycles: I. Observations of pulses in the magnetopause reconnection rate

Using data from the EISCAT (European Incoherent Scatter) VHF radar and DMSP (Defense Meteorological Satellite Program) spacecraft passes, we study the motion of the dayside open-closed field line boundary during two substorm cycles. The satellite data show that the motions of ion and electron temperature boundaries in EISCAT data, as reported by Moen et al. (2004), are not localised around the radar; rather, they reflect motions of the open-closed field line boundary at all MLT throughout the dayside auroral ionosphere. The boundary is shown to erode equatorward when the IMF points southward, consistent with the effect of magnetopause reconnection. During the substorm expansion and recovery phases, the dayside boundary returns poleward, whether the IMF points northward or southward. However, the poleward retreat was much faster during the substorm for which the IMF had returned to northward than for the substorm for which the IMF remained southward – even though the former substorm is much the weaker of the two. These poleward retreats are consistent with the destruction of open flux at the tail current sheet. Application of a new analysis of the peak ion energies at the equatorward edge of the cleft/cusp/mantle dispersion seen by the DMSP satellites identifies the dayside reconnection merging gap to extend in MLT from about 9.5 to 15.5 h for most of the interval. Analysis of the boundary motion, and of the convection velocities seen near the boundary by EISCAT, allows calculation of the reconnection rate (mapped down to the ionosphere) from the flow component normal to the boundary in its own rest frame. This reconnection rate is not, in general, significantly different from zero before 06:45 UT (MLT<9.5 h) – indicating that the X line footprint expands over the EISCAT field-of-view to earlier MLT only occasionally and briefly. Between 06:45 UT and 12:45UT (9.5

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.

Ionospheric ion and electron heating at the poleward boundary of a poleward expanding substorm-disturbed region

We present observations of a poleward propagating substorm-disturbed region which was observed by the European Incoherent SCATter (EISCAT) radar and the Svalbard International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometers in the postmidnight sector. The expansion of the disturbance was launched by a substorm intensification which started similar to 25 min after the initial onset, and similar to 10 min before the disturbance arrived over Svalbard. In association with the magnetic disturbance, a poleward expanding enduring enhancement in the F region electron temperature was observed, indicative of soft electron precipitation, with a narrow band of enhanced ion temperature straddling its poleward edge, indicative of fast ion flows and ion-neutral collisional heating. This electron temperature boundary was coincident with the poleward propagating electrojet current system detected by the high-latitude IMAGE magnetometer stations and is taken to be a proxy for the observation of a substorm auroral bulge. The electron temperature boundary is inferred to have a width comparable or less than one radar range gate (similar to 60 km transverse to the magnetic field), while the region of high ion temperature was found to be approximately three gates wide, extending approximately two gates (similar to 120 km) poleward of the electron temperature boundary, and approximately one gate (similar to 60 km) equatorward. The two-beam radar line-of-sight velocity data are found to be consistent with the existence of a layer of high-speed flow in the boundary, peaking at values similar to1.5-3 km s(-1), roughly consistent with the ion temperature data. The flow is directed either east or west along the boundary depending on the direction of the flow in the poleward region. We infer that the flow is deflected along and around the boundary of the substorm-disturbed region due to the high conductivity of the latter. Variations in the flow poleward of the boundary produced no discernible magnetic effects on the ground, confirming the low conductivity of the preboundary ionosphere.

Meteorological forcing data for urban outdoor thermal comfort models from a coupled convective boundary layer and surface energy balance scheme

Site-specific meteorological forcing appropriate for applications such as urban outdoor thermal comfort simulations can be obtained using a newly coupled scheme that combines a simple slab convective boundary layer (CBL) model and urban land surface model (ULSM) (here two ULSMs are considered). The former simulates daytime CBL height, air temperature and humidity, and the latter estimates urban surface energy and water balance fluxes accounting for changes in land surface cover. The coupled models are tested at a suburban site and two rural sites, one irrigated and one unirrigated grass, in Sacramento, U.S.A. All the variables modelled compare well to measurements (e.g. coefficient of determination = 0.97 and root mean square error = 1.5 °C for air temperature). The current version is applicable to daytime conditions and needs initial state conditions for the CBL model in the appropriate range to obtain the required performance. The coupled model allows routine observations from distant sites (e.g. rural, airport) to be used to predict air temperature and relative humidity in an urban area of interest. This simple model, which can be rapidly applied, could provide urban data for applications such as air quality forecasting and building energy modelling, in addition to outdoor thermal comfort.

The low-latitude boundary layer: Application of ISTP advances to past data

The destruction of the four Cluster craft was a major loss to the planned ISTP effort, of which studies of the magnetopause and low-latitude boundary layer (LLBL) were an important part. While awaiting the re-flight mission, Cluster-II, we have been applying advances in our understanding made using other ISTP craft (like Polar and Wind) and using ground-based facilities (in particular the EISCAT incoherent scatter radars and the SuperDARN HF coherent radars) to measurements of the LLBL made in 1984 and 1985 by the AMPTE-UKS and -IRM spacecraft pair. In particular, one unexplained result of the AMPTE mission was that the electron characteristics could, in nearly all cases, order independent measurements near the magnetopause, such as the magnetic field, ion temperatures and the plasma flow. Studies of the cusp have shown that the precipitation is ordered by the time-elapsed since the field line was opened by reconnection. This insight has allowed us to reanalyse the AMPTE data and show that the ordering by the transition parameter is also due to the variation of time elapsed since reconnection, with the important implication that reconnection usually coats most of the dayside magnetopause with at least some newly-opened field lines. In addition, we can use the electron characteristics to isolate features like RDs, slow-mode shocks and slow-mode expansion fans. The ion characteristics can be used to compute the reconnection rate. We here retrospectively apply these new techniques, developed in the ISTP era, to a much-studied flux transfer event observed by the AMPTE satellites. As a result, we gain new understanding of its cause and structure.

Identifying the Open-Closed Field Line Boundary

Of all the various definitions of the polar cap boundary that have been used in the past, the most physically meaningful and significant is the boundary between open and closed field lines. Locating this boundary is very important as it defines which regions and phenomena are on open field lines and which are on closed. This usually has fundamental implications for the mechanisms invoked. Unfortunately, the open-closed boundary is usually very difficult to identify, particularly where it maps to an active reconnection site. This paper looks at the topological reconnection classes that can take place, both at the magnetopause and in the cross-tail current sheet and discusses the implications for identifying the open-closed boundary when reconnection is giving velocity filter dispersion of signatures. On the dayside, it is shown that the dayside boundary plasma sheet and low-latitude boundary layer precipitations are well explained as being on open field lines, energetic ions being present because of reflection of central plasma sheet ions off the two Alfvén waves launched by the reconnection site (the outer one of which is the magnetopause). This also explains otherwise anomalous features of the dayside convection pattern in the cusp region. On the nightside, similar considerations place the open-closed boundary somewhat poleward of the velocity-dispersed ion structures which are a signature of the plasma sheet boundary layer ion flows in the tail.

A Summary of the NATO ASI on Polar Cap Boundary Phenomena

The polar cap boundary is a subject of central importance to current magnetosphere-ionosphere research and its applications in “space weather” activities. The problems are that it has a number of definitions, and that the most physically meaningful definition (namely the open-closed field line boundary) is very difficult to identify in observations. New understanding of the importance of the structure and dynamics of the boundary region made the time right for a meeting reviewing our knowledge in this area. The Advanced Study Institute (ASI) on Svalbard in June 1997 discussed the boundary on both the dayside and the nightside, mapping magnetically to the dayside magnetopause and to tail plasma sheet/lobe interface, respectively. We held a “brainstorming” session, in which different ideas which arose from the presented papers were discussed and developed, and a summary session, in which session convenors gave a personal view of progress that has been made and problems which still need solving. Both were designed as ways of promoting further discussion. This paper attempts to distil some of the themes that emerged from these discussions.

Ion populations on open field lines within the dayside low-latitude boundary layer: theory and observations during a transient event

We analyze of ion populations observed by the NOAA-12 satellite within dayside auroral transients. The data are matched with an open magnetopause model which allows for the transmission of magnetosheath ions across one or both of the two Alfvén waves which emanate from the magnetopause reconnection site. It also allows for reflection and acceleration of ions of magnetospheric origin by these waves. From the good agreement found between the model and the observations, we propose that the events and the low-latitude boundary precipitation are both on open field lines.