Kinematical analysis of redundant drive wire mechanisms with velocity constraint

In this paper, we propose a new velocity constraint type for Redundant Drive Wire Mechanisms. The purpose of this paper is to demonstrate that the proposed velocity constraint module can fix the orientation of the movable part and to use the kinematical analysis method to obtain the moving direction of the movable part. First, we discuss the necessity of using this velocity constraint type and the possible applications of the proposed mechanism. Second, we derive the basic equations of a wire mechanism with this constraint type. Next, we present a method of motion analysis on active and passive constraint spaces, which is used to find the moving direction of a movable part. Finally, we apply the above analysis method on a wire mechanism with a velocity constraint module and on a wire mechanism with four double actuator modules. By evaluating the results, we prove the validity of the proposed constraint type.

Axonal velocity distributions in neural feld equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

Potential role of the quasi-biennial oscillation in the stratosphere-troposphere exchange as found in water vapor in general circulation model experiments

The tropical tropopause is considered to be the main region of upward transport of tropospheric air carrying water vapor and other tracers to the tropical stratosphere. The lower tropical stratosphere is also the region where the quasi-biennial oscillation (QBO) in the zonal wind is observed. The QBO is positioned in the region where the upward transport of tropospheric tracers to the overworld takes place. Hence the QBO can in principle modulate these transports by its secondary meridional circulation. This modulation is investigated in this study by an analysis of general circulation model (GCM) experiments with an assimilated QBO. The experiments show, first, that the temperature signal of the QBO modifies the specific humidity in the air transported upward and, second, that the secondary meridional circulation modulates the velocity of the upward transport. Thus during the eastward phase of the QBO the upward moving air is moister and the upward velocity is less than during the westward phase of the QBO. It was further found that the QBO period is too short to allow an equilibration of the moisture in the QBO region. This causes a QBO signal of the moisture which is considerably smaller than what could be obtained in the limiting case of indefinitely long QBO phases. This also allows a high sensitivity of the mean moisture over a QBO cycle to the El Niño-Southern Oscillation (ENSO) phenomena or major tropical volcanic eruptions. The interplay of sporadic volcanic eruptions, ENSO, and QBO can produce low-frequency variability in the water vapor content of the tropical stratosphere, which renders the isolation of the QBO signal in observational data of water vapor in the equatorial lower stratosphere difficult.

Transport in the middle atmosphere

An overview is provided of the current understanding of transport in the middle atmosphere. Over the past quarter century this subject has evolved from a basic recognition of the Brewer-Dobson circulation to a detailed appreciation of many key features of transport such as the stratospheric surf zone, mixing barriers and the dynamics of filamentation. Whilst the elegant theoretical framework for middle atmosphere transport that emerged roughly twenty years ago never fulfilled its promise, useful phenomenological models have been developed together with innovative diagnostic methods. These advances were made possible by the advent of plenty of satellite and aircraft observations of long-lived chemical species together with developments in data assimilation and numerical modeling, and have been driven in large measure by the problem of stratospheric ozone depletion. This review is primarily focused on the stratosphere, where both the interest and the knowledge are the greatest, but a few remarks are also made on the mesosphere.

O_3-N_2O correlations from the Atmospheric Chemistry Experiment: revisiting a diagnostic of transport and chemistry in the stratosphere

Our knowledge of stratospheric O3-N2O correlations is extended, and their potential for model-measurement comparison assessed, using data from the Atmospheric Chemistry Experiment (ACE) satellite and the Canadian Middle Atmosphere Model (CMAM). ACE provides the first comprehensive data set for the investigation of interhemispheric, interseasonal, and height-resolved differences of the O_3-N_2O correlation structure. By subsampling the CMAM data, the representativeness of the ACE data is evaluated. In the middle stratosphere, where the correlations are not compact and therefore mainly reflect the data sampling, joint probability density functions provide a detailed picture of key aspects of transport and mixing, but also trace polar ozone loss. CMAM captures these important features, but exhibits a displacement of the tropical pipe into the Southern Hemisphere (SH). Below about 21 km, the ACE data generally confirm the compactness of the correlations, although chemical ozone loss tends to destroy the compactness during late winter/spring, especially in the SH. This allows a quantitative comparison of the correlation slopes in the lower and lowermost stratosphere (LMS), which exhibit distinct seasonal cycles that reveal the different balances between diabatic descent and horizontal mixing in these two regions in the Northern Hemisphere (NH), reconciling differences found in aircraft measurements, and the strong role of chemical ozone loss in the SH. The seasonal cycles are qualitatively well reproduced by CMAM, although their amplitude is too weak in the NH LMS. The correlation slopes allow a "chemical" definition of the LMS, which is found to vary substantially in vertical extent with season.

Using transport diagnostics to understand chemistry climate model ozone simulations

We use observations of N2O and mean age to identify realistic transport in models in order to explain their ozone predictions. The results are applied to 15 chemistry climate models (CCMs) participating in the 2010 World Meteorological Organization ozone assessment. Comparison of the observed and simulated N2O, mean age and their compact correlation identifies models with fast or slow circulations and reveals details of model ascent and tropical isolation. This process‐oriented diagnostic is more useful than mean age alone because it identifies models with compensating transport deficiencies that produce fortuitous agreement with mean age. The diagnosed model transport behavior is related to a model’s ability to produce realistic lower stratosphere (LS) O3 profiles. Models with the greatest tropical transport problems compare poorly with O3 observations. Models with the most realistic LS transport agree more closely with LS observations and each other. We incorporate the results of the chemistry evaluations in the Stratospheric Processes and their Role in Climate (SPARC) CCMVal Report to explain the range of CCM predictions for the return‐to‐1980 dates for global (60°S–60°N) and Antarctic column ozone. Antarctic O3 return dates are generally correlated with vortex Cly levels, and vortex Cly is generally correlated with the model’s circulation, although model Cl chemistry and conservation problems also have a significant effect on return date. In both regions, models with good LS transport and chemistry produce a smaller range of predictions for the return‐to‐1980 ozone values. This study suggests that the current range of predicted return dates is unnecessarily broad due to identifiable model deficiencies.

Desert dust deposition on Mt. Elbrus, Caucasus Mountains, Russia in 2009-2012 as recorded in snow and shallow ice core: high-resolution "provenancing", transport patterns, physical properties and soluble ionic composition

A record of dust deposition events between 2009 and 2012 on Mt. Elbrus, Caucasus Mountains derived from a snow pit and a shallow ice core is presented for the first time for this region. A combination of isotopic analysis, SEVIRI red-green-blue composite imagery, MODIS atmospheric optical depth fields derived using the Deep Blue algorithm, air mass trajectories derived using the HYSPLIT model and analysis of meteorological data enabled identification of dust source regions with high temporal (hours) and spatial (cf. 20–100 km) resolution. Seventeen dust deposition events were detected; fourteen occurred in March–June, one in February and two in October. Four events originated in the Sahara, predominantly in north-eastern Libya and eastern Algeria. Thirteen events originated in the Middle East, in the Syrian Desert and northern Mesopotamia, from a mixture of natural and anthropogenic sources. Dust transportation from Sahara was associated with vigorous Saharan depressions, strong surface winds in the source region and mid-tropospheric south-westerly flow with daily winds speeds of 20–30 m s−1 at 700 hPa level and, although these events were less frequent, they resulted in higher dust concentrations in snow. Dust transportation from the Middle East was associated with weaker depressions forming over the source region, high pressure centered over or extending towards the Caspian Sea and a weaker southerly or south-easterly flow towards the Caucasus Mountains with daily wind speeds of 12–18 m s−1 at 700 hPa level. Higher concentrations of nitrates and ammonium characterise dust from the Middle East deposited on Mt. Elbrus in 2009 indicating contribution of anthropogenic sources. The modal values of particle size distributions ranged between 1.98 μm and 4.16 μm. Most samples were characterised by modal values of 2.0–2.8 μm with an average of 2.6 μm and there was no significant difference between dust from the Sahara and the Middle East.

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

A Lagrangian model of air-mass photochemistry and mixing using a trajectory ensemble: the Cambridge Tropospheric Trajectory model of Chemistry And Transport (CiTTyCAT) version 4.2

A Lagrangian model of photochemistry and mixing is described (CiTTyCAT, stemming from the Cambridge Tropospheric Trajectory model of Chemistry And Transport), which is suitable for transport and chemistry studies throughout the troposphere. Over the last five years, the model has been developed in parallel at several different institutions and here those developments have been incorporated into one "community" model and documented for the first time. The key photochemical developments include a new scheme for biogenic volatile organic compounds and updated emissions schemes. The key physical development is to evolve composition following an ensemble of trajectories within neighbouring air-masses, including a simple scheme for mixing between them via an evolving "background profile", both within the boundary layer and free troposphere. The model runs along trajectories pre-calculated using winds and temperature from meteorological analyses. In addition, boundary layer height and precipitation rates, output from the analysis model, are interpolated to trajectory points and used as inputs to the mixing and wet deposition schemes. The model is most suitable in regimes when the effects of small-scale turbulent mixing are slow relative to advection by the resolved winds so that coherent air-masses form with distinct composition and strong gradients between them. Such air-masses can persist for many days while stretching, folding and thinning. Lagrangian models offer a useful framework for picking apart the processes of air-mass evolution over inter-continental distances, without being hindered by the numerical diffusion inherent to global Eulerian models. The model, including different box and trajectory modes, is described and some output for each of the modes is presented for evaluation. The model is available for download from a Subversion-controlled repository by contacting the corresponding authors.

Quantification of chemical and physical processes influencing ozone during long-range transport using a trajectory ensemble

During long-range transport, many distinct processes – including photochemistry, deposition, emissions and mixing – contribute to the transformation of air mass composition. Partitioning the effects of different processes can be useful when considering the sensitivity of chemical transformation to, for example, a changing environment or anthropogenic influence. However, transformation is not observed directly, since mixing ratios are measured, and models must be used to relate changes to processes. Here, four cases from the ITCT-Lagrangian 2004 experiment are studied. In each case, aircraft intercepted a distinct air mass several times during transport over the North Atlantic, providing a unique dataset and quantifying the net changes in composition from all processes. A new framework is presented to deconstruct the change in O3 mixing ratio (Δ O3) into its component processes, which were not measured directly, taking into account the uncertainty in measurements, initial air mass variability and its time evolution. The results show that the net chemical processing (Δ O3chem) over the whole simulation is greater than net physical processing (Δ O3phys) in all cases. This is in part explained by cancellation effects associated with mixing. In contrast, each case is in a regime of either net photochemical destruction (lower tropospheric transport) or production (an upper tropospheric biomass burning case). However, physical processes influence O3 indirectly through addition or removal of precursor gases, so that changes to physical parameters in a model can have a larger effect on Δ O3chem than Δ O3phys. Despite its smaller magnitude, the physical processing distinguishes the lower tropospheric export cases, since the net photochemical O3 change is −5 ppbv per day in all three cases. Processing is quantified using a Lagrangian photochemical model with a novel method for simulating mixing through an ensemble of trajectories and a background profile that evolves with them. The model is able to simulate the magnitude and variability of the observations (of O3, CO, NOy and some hydrocarbons) and is consistent with the time-average OH following air-masses inferred from hydrocarbon measurements alone (by Arnold et al., 2007). Therefore, it is a useful new method to simulate air mass evolution and variability, and its sensitivity to process parameters.

On the nature of large-scale mixing in the stratosphere and mesosphere

Studies of tracer transport in the stratosphere have shown that adiabatic quasi-horizontal tracer evolution is controlled primarily by the large-scale low-frequency component of the flow. This behavior is consistent with the concept of chaotic advection, wherein the Eulerian velocity field is spatially coherent and temporally quasi-regular on timescales over which the Lagrangian evolution is chaotic. In this study, winds from a middle atmosphere general circulation model (the Canadian Middle Atmosphere Model) are used to compare and contrast the nature of tracer evolution in the stratosphere and mesosphere. It is found that the concept of chaotic advection is relevant in the stratosphere but not in the mesosphere. The explanation for this behavior is the increased strength of gravity wave activity in the mesosphere as compared with the stratosphere, which leads to shallower kinetic energy spectra on synoptic scales and a much shorter Eulerian correlation time. The shallower kinetic energy spectra imply that tracer evolution in the mesosphere is spectrally local, in contrast with the spectrally nonlocal regime that prevails in the stratosphere. This means that tracer advection calculations in the mesosphere are controlled primarily by the gravity wave spectrum and are intrinsically resolution dependent.

A closer look at chaotic advection in the stratosphere: part I: geometric structure

The relevance of chaotic advection to stratospheric mixing and transport is addressed in the context of (i) a numerical model of forced shallow-water flow on the sphere, and (ii) a middle-atmosphere general circulation model. It is argued that chaotic advection applies to both these models if there is suitable large-scale spatial structure in the velocity field and if the velocity field is temporally quasi-regular. This spatial structure is manifested in the form of “cat’s eyes” in the surf zone, such as are commonly seen in numerical simulations of Rossby wave critical layers; by analogy with the heteroclinic structure of a temporally aperiodic chaotic system the cat’s eyes may be thought of as an “organizing structure” for mixing and transport in the surf zone. When this organizing structure exists, Eulerian and Lagrangian autocorrelations of the velocity derivatives indicate that velocity derivatives decorrelate more rapidly along particle trajectories than at fixed spatial locations (i.e., the velocity field is temporally quasi-regular). This phenomenon is referred to as Lagrangian random strain.

On the group-velocity property for wave-activity conservation laws

The density and the flux of wave-activity conservation laws are generally required to satisfy the group-velocity property: under the WKB approximation (i.e., for nearly monochromatic small-amplitude waves in a slowly varying medium), the flux divided by the density equals the group velocity. It is shown that this property is automatically satisfied if, under the WKB approximation, the only source of rapid variations in the density and the flux lies in the wave phase. A particular form of the density, based on a self-adjoint operator, is proposed as a systematic choice for a density verifying this condition.

Chaotic mixing and transport in Rossby-wave critical layers

A simple, dynamically consistent model of mixing and transport in Rossby-wave critical layers is obtained from the well-known Stewartson–Warn–Warn (SWW) solution of Rossby-wave critical-layer theory. The SWW solution is thought to be a useful conceptual model of Rossby-wave breaking in the stratosphere. Chaotic advection in the model is a consequence of the interaction between a stationary and a transient Rossby wave. Mixing and transport are characterized separately with a number of quantitative diagnostics (e.g. mean-square dispersion, lobe dynamics, and spectral moments), and with particular emphasis on the dynamics of the tracer field itself. The parameter dependences of the diagnostics are examined: transport tends to increase monotonically with increasing perturbation amplitude whereas mixing does not. The robustness of the results is investigated by stochastically perturbing the transient-wave phase speed. The two-wave chaotic advection model is contrasted with a stochastic single-wave model. It is shown that the effects of chaotic advection cannot be captured by stochasticity alone.