Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Boundary layer dynamics over London, UK, as observed using Doppler lidar during REPARTEE-II

Urban boundary layers (UBLs) can be highly complex due to the heterogeneous roughness and heating of the surface, particularly at night. Due to a general lack of observations, it is not clear whether canonical models of boundary layer mixing are appropriate in modelling air quality in urban areas. This paper reports Doppler lidar observations of turbulence profiles in the centre of London, UK, as part of the second REPARTEE campaign in autumn 2007. Lidar-measured standard deviation of vertical velocity averaged over 30 min intervals generally compared well with in situ sonic anemometer measurements at 190 m on the BT telecommunications Tower. During calm, nocturnal periods, the lidar underestimated turbulent mixing due mainly to limited sampling rate. Mixing height derived from the turbulence, and aerosol layer height from the backscatter profiles, showed similar diurnal cycles ranging from c. 300 to 800 m, increasing to c. 200 to 850 m under clear skies. The aerosol layer height was sometimes significantly different to the mixing height, particularly at night under clear skies. For convective and neutral cases, the scaled turbulence profiles resembled canonical results; this was less clear for the stable case. Lidar observations clearly showed enhanced mixing beneath stratocumulus clouds reaching down on occasion to approximately half daytime boundary layer depth. On one occasion the nocturnal turbulent structure was consistent with a nocturnal jet, suggesting a stable layer. Given the general agreement between observations and canonical turbulence profiles, mixing timescales were calculated for passive scalars released at street level to reach the BT Tower using existing models of turbulent mixing. It was estimated to take c. 10 min to diffuse up to 190 m, rising to between 20 and 50 min at night, depending on stability. Determination of mixing timescales is important when comparing to physico-chemical processes acting on pollutant species measured simultaneously at both the ground and at the BT Tower during the campaign. From the 3 week autumnal data-set there is evidence for occasional stable layers in central London, effectively decoupling surface emissions from air aloft.

Simultaneous observations of reconnection pulses at Cluster and their effects on the cusp aurora observed at the Chinese Yellow River station

While the Cluster spacecraft were located near the high-latitude magnetopause, between 1010 and 1040 UT on 16 January 2004, three typical flux transfer event (FTE) signatures were observed. During this interval, simultaneous and conjugated all‐sky camera measurements, recorded at Yellow River Station, Svalbard, are available at 630.0 and 557.7 nm that show poleward‐moving auroral forms (PMAFs), consistent with magnetic reconnection at the dayside magnetopause. Simultaneous FTEs seen at the magnetopause mainly move northward, but having duskward (eastward) and tailward velocity components, roughly consistent with the observed direction of motion of the PMAFs in all‐sky images. Between the PMAFs meridional keograms, extracted from the all‐sky images, show intervals of lower intensity aurora which migrate equatorward just before the PMAFs intensify. This is strong evidence for an equatorward eroding and poleward moving open‐closed boundary associated with a variable magnetopause reconnection rate under variable IMF conditions. From the durations of the PMAFs, we infer that the evolution time of FTEs is 5–11 minutes from its origin on the magnetopause to its addition to the polar cap.

Advances in continuously profiling the thermodynamic state of the boundary layer: integration of measurements and methods

This paper describes advances in ground-based thermodynamic profiling of the lower troposphere through sensor synergy. The well-documented integrated profiling technique (IPT), which uses a microwave profiler, a cloud radar, and a ceilometer to simultaneously retrieve vertical profiles of temperature, humidity, and liquid water content (LWC) of nonprecipitating clouds, is further developed toward an enhanced performance in the boundary layer and lower troposphere. For a more accurate temperature profile, this is accomplished by including an elevation scanning measurement modus of the microwave profiler. Height-dependent RMS accuracies of temperature (humidity) ranging from 0.3 to 0.9 K (0.5–0.8 g m−3) in the boundary layer are derived from retrieval simulations and confirmed experimentally with measurements at distinct heights taken during the 2005 International Lindenberg Campaign for Assessment of Humidity and Cloud Profiling Systems and its Impact on High-Resolution Modeling (LAUNCH) of the German Weather Service. Temperature inversions, especially of the lower boundary layer, are captured in a very satisfactory way by using the elevation scanning mode. To improve the quality of liquid water content measurements in clouds the authors incorporate a sophisticated target classification scheme developed within the European cloud observing network CloudNet. It allows the detailed discrimination between different types of backscatterers detected by cloud radar and ceilometer. Finally, to allow IPT application also to drizzling cases, an LWC profiling method is integrated. This technique classifies the detected hydrometeors into three different size classes using certain thresholds determined by radar reflectivity and/or ceilometer extinction profiles. By inclusion into IPT, the retrieved profiles are made consistent with the measurements of the microwave profiler and an LWC a priori profile. Results of IPT application to 13 days of the LAUNCH campaign are analyzed, and the importance of integrated profiling for model evaluation is underlined.

Moving feedback forward: theory to practice

There is substantial research interest in tutor feedback and students’ perception and use of such feedback. This paper considers some of the major issues raised in relation to tutor feedback and student learning. We explore some of the current feedback drivers, most notably the need for feedback to move away from simply a monologue from a tutor to a student to a valuable tutor–student dialogue. In relation to moving feedback forward the notions of self regulation, dialogue and social learning are explored and then considered in relation to how such theory can translate into practice. The paper proposes a framework (GOALS) as a tool through which tutors can move theory into practice with the aim of improving student learning from feedback.

Citation and peer review of data: moving towards formal data publication

This paper discusses many of the issues associated with formally publishing data in academia, focusing primarily on the structures that need to be put in place for peer review and formal citation of datasets. Data publication is becoming increasingly important to the scientific community, as it will provide a mechanism for those who create data to receive academic credit for their work and will allow the conclusions arising from an analysis to be more readily verifiable, thus promoting transparency in the scientific process. Peer review of data will also provide a mechanism for ensuring the quality of datasets, and we provide suggestions on the types of activities one expects to see in the peer review of data. A simple taxonomy of data publication methodologies is presented and evaluated, and the paper concludes with a discussion of dataset granularity, transience and semantics, along with a recommended human-readable citation syntax.

Determining the contribution of volcanic ash and boundary layer aerosol in backscatter lidar returns: a three‐component atmosphere approach

A solution of the lidar equation is discussed, that permits combining backscatter and depolarization measurements to quantitatively distinguish two different aerosol types with different depolarization properties. The method has been successfully applied to simultaneous observations of volcanic ash and boundary layer aerosol obtained in Exeter, United Kingdom, on 16 and 18 April 2010, permitting the contribution of the two aerosols to be quantified separately. First a subset of the atmospheric profiles is used where the two aerosol types belong to clearly distinguished layers, for the purpose of characterizing the ash in terms of lidar ratio and depolarization. These quantities are then used in a three‐component atmosphere solution scheme of the lidar equation applied to the full data set, in order to compute the optical properties of both aerosol types separately. On 16 April a thin ash layer, 100–400 m deep, is observed (average and maximum estimated ash optical depth: 0.11 and 0.2); it descends from ∼2800 to ∼1400 m altitude over a 6‐hour period. On 18 April a double ash layer, ∼400 m deep, is observed just above the morning boundary layer (average and maximum estimated ash optical depth: 0.19 and 0.27). In the afternoon the ash is entrained into the boundary layer, and the latter reaches a depth of ∼1800 m (average and maximum estimated ash optical depth: 0.1 and 0.15). An additional ash layer, with a very small optical depth, was observed on 18 April at an altitude of 3500–4000 m. By converting the lidar optical measurements using estimates of volcanic ash specific extinction, derived from other works, the observations seem to suggest approximate peak ash concentrations of ∼1500 and ∼1000 mg/m3,respectively, on the two observations dates.