Estimation of the friction velocity in stably stratified boundary-layer flows over hills

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.

Climate and human influences on global biomass burning over the past two millennia

Large, well-documented wildfires have recently generated worldwide attention, and raised concerns about the impacts of humans and climate change on wildfire regimes. However, comparatively little is known about the patterns and driving forces of global fire activity before the twentieth century. Here we compile sedimentary charcoal records spanning six continents to document trends in both natural and anthropogenic biomass burning for the past two millennia. We find that global biomass burning declined from AD 1 to 1750, before rising sharply between 1750 and 1870. Global burning then declined abruptly after 1870. The early decline in biomass burning occurred in concert with a global cooling trend and despite a rise in the human population. We suggest the subsequent rise was linked to increasing human influences, such as population growth and land-use changes. Our compilation suggests that the final decline occurred despite increasing air temperatures and population. We attribute this reduction in the amount of biomass burned over the past 150 years to the global expansion of intensive grazing, agriculture and fire management.

Predictability of biomass burning in response to climate changes

Climate is an important control on biomass burning, but the sensitivity of fire to changes in temperature and moisture balance has not been quantified. We analyze sedimentary charcoal records to show that the changes in fire regime over the past 21,000 yrs are predictable from changes in regional climates. Analyses of paleo- fire data show that fire increases monotonically with changes in temperature and peaks at intermediate moisture levels, and that temperature is quantitatively the most important driver of changes in biomass burning over the past 21,000 yrs. Given that a similar relationship between climate drivers and fire emerges from analyses of the interannual variability in biomass burning shown by remote-sensing observations of month-by-month burnt area between 1996 and 2008, our results signal a serious cause for concern in the face of continuing global warming.

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.

Global biomass burning: a synthesis and review of Holocene paleofire records and their controls.

We synthesize existing sedimentary charcoal records to reconstruct Holocene fire history at regional, continental and global scales. The reconstructions are compared with the two potential controls of burning at these broad scales – changes in climate and human activities – to assess their relative importance on trends in biomass burning. Here we consider several hypotheses that have been advanced to explain the Holocene record of fire, including climate, human activities and synergies between the two. Our results suggest that 1) episodes of high fire activity were relatively common in the early Holocene and were consistent with climate changes despite low global temperatures and low levels of biomass burning globally; 2) there is little evidence from the paleofire record to support the Early Anthropocene Hypothesis of human modification of the global carbon cycle; 3) there was a nearly-global increase in fire activity from 3 to 2 ka that is difficult to explain with either climate or humans, but the widespread and synchronous nature of the increase suggests at least a partial climate forcing; and 4) burning during the past century generally decreased but was spatially variable; it declined sharply in many areas, but there were also large increases (e.g., Australia and parts of Europe). Our analysis does not exclude an important role for human activities on global biomass burning during the Holocene, but instead provides evidence for a pervasive influence of climate across multiple spatial and temporal scales.

Coupled Kelvin-wave and mirage-wave instabilities in semigeostrophic dynamics

A weak instability mode, associated with phase-locked counterpropagating coastal Kelvin waves in horizontal anticyclonic shear, is found in the semigeostrophic (SG) equations for stratified flow in a channel. This SG instability mode approximates a similar mode found in the Euler equations in the limit in which particle-trajectory slopes are much smaller than f/N, where f is the Coriolis frequency and N > f the buoyancy frequency. Though weak under normal parameter conditions, this instability mode is of theoretical interest because its existence accounts for the failure of an Arnol’d-type stability theorem for the SG equations. In the opposite limit, in which the particle motion is purely vertical, the Euler equations allow only buoyancy oscillations with no horizontal coupling. The SG equations, on the other hand, allow a physically spurious coastal “mirage wave,” so called because its velocity field vanishes despite a nonvanishing disturbance pressure field. Counterpropagating pairs of these waves can phase-lock to form a spurious “mirage-wave instability.” Closer examination shows that the mirage wave arises from failure of the SG approximations to be self-consistent for trajectory slopes f/N.

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.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Climatic control of the biomass-burning decline in the Americas after AD 1500

The significance and cause of the decline in biomass burning across the Americas after AD 1500 is a topic of considerable debate. We synthesized charcoal records (a proxy for biomass burning) from the Americas and from the remainder of the globe over the past 2000 years, and compared these with paleoclimatic records and population reconstructions. A distinct post-AD 1500 decrease in biomass burning is evident, not only in the Americas, but also globally, and both are similar in duration and timing to ‘Little Ice Age’ climate change. There is temporal and spatial variability in the expression of the biomass-burning decline across the Americas but, at a regional–continental scale, ‘Little Ice Age’ climate change was likely more important than indigenous population collapse in driving this decline.

Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

Vertical distribution and radiative effects of mineral dust and biomass burning aerosol over West Africa during DABEX

This paper presents measurements of the vertical distribution of aerosol extinction coefficient over West Africa during the Dust and Biomass-burning Aerosol Experiment (DABEX)/African Monsoon Multidisciplinary Analysis dry season Special Observing Period Zero (AMMA-SOP0). In situ aircraft measurements from the UK FAAM aircraft have been compared with two ground-based lidars (POLIS and ARM MPL) and an airborne lidar on an ultralight aircraft. In general, mineral dust was observed at low altitudes (up to 2 km), and a mixture of biomass burning aerosol and dust was observed at altitudes of 2–5 km. The study exposes difficulties associated with spatial and temporal variability when intercomparing aircraft and ground measurements. Averaging over many profiles provided a better means of assessing consistent errors and biases associated with in situ sampling instruments and retrievals of lidar ratios. Shortwave radiative transfer calculations and a 3-year simulation with the HadGEM2-A climate model show that the radiative effect of biomass burning aerosol was somewhat sensitive to the vertical distribution of aerosol. In particular, when the observed low-level dust layer was included in the model, the absorption of solar radiation by the biomass burning aerosols increased by 10%. We conclude that this absorption enhancement was caused by the dust reflecting solar radiation up into the biomass burning aerosol layer. This result illustrates that the radiative forcing of anthropogenic absorbing aerosol can be sensitive to the presence of natural aerosol species.

Optimization of a sea ice model using basinwide observations of Arctic sea ice thickness, extent, and velocity

A stand-alone sea ice model is tuned and validated using satellite-derived, basinwide observations of sea ice thickness, extent, and velocity from the years 1993 to 2001. This is the first time that basin-scale measurements of sea ice thickness have been used for this purpose. The model is based on the CICE sea ice model code developed at the Los Alamos National Laboratory, with some minor modifications, and forcing consists of 40-yr ECMWF Re-Analysis (ERA-40) and Polar Exchange at the Sea Surface (POLES) data. Three parameters are varied in the tuning process: Ca, the air–ice drag coefficient; P*, the ice strength parameter; and α, the broadband albedo of cold bare ice, with the aim being to determine the subset of this three-dimensional parameter space that gives the best simultaneous agreement with observations with this forcing set. It is found that observations of sea ice extent and velocity alone are not sufficient to unambiguously tune the model, and that sea ice thickness measurements are necessary to locate a unique subset of parameter space in which simultaneous agreement is achieved with all three observational datasets.