Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Human frontal lobes are not relatively large

One of the most pervasive assumptions about human brain evolution is that it involved relative enlargement of the frontal lobes. We show that this assumption is without foundation. Analysis of five independent data sets using correctly scaled measures and phylogenetic methods reveals that the size of human frontal lobes, and of specific frontal regions, is as expected relative to the size of other brain structures. Recent claims for relative enlargement of human frontal white matter volume, and for relative enlargement shared by all great apes, seem to be mistaken. Furthermore, using a recently developed method for detecting shifts in evolutionary rates, we find that the rate of change in relative frontal cortex volume along the phylogenetic branch leading to humans was unremarkable and that other branches showed significantly faster rates of change. Although absolute and proportional frontal region size increased rapidly in humans, this change was tightly correlated with corresponding size increases in other areas andwhole brain size, and with decreases in frontal neuron densities. The search for the neural basis of human cognitive uniqueness should therefore focus less on the frontal lobes in isolation and more on distributed neural networks.

The vertical structure of oceanic Rossby waves: a comparison of high-resolution model data to theoretical vertical structures

Tests of the new Rossby wave theories that have been developed over the past decade to account for discrepancies between theoretical wave speeds and those observed by satellite altimeters have focused primarily on the surface signature of such waves. It appears, however, that the surface signature of the waves acts only as a rather weak constraint, and that information on the vertical structure of the waves is required to better discriminate between competing theories. Due to the lack of 3-D observations, this paper uses high-resolution model data to construct realistic vertical structures of Rossby waves and compares these to structures predicted by theory. The meridional velocity of a section at 24° S in the Atlantic Ocean is pre-processed using the Radon transform to select the dominant westward signal. Normalized profiles are then constructed using three complementary methods based respectively on: (1) averaging vertical profiles of velocity, (2) diagnosing the amplitude of the Radon transform of the westward propagating signal at different depths, and (3) EOF analysis. These profiles are compared to profiles calculated using four different Rossby wave theories: standard linear theory (SLT), SLT plus mean flow, SLT plus topographic effects, and theory including mean flow and topographic effects. Our results support the classical theoretical assumption that westward propagating signals have a well-defined vertical modal structure associated with a phase speed independent of depth, in contrast with the conclusions of a recent study using the same model but for different locations in the North Atlantic. The model structures are in general surface intensified, with a sign reversal at depth in some regions, notably occurring at shallower depths in the East Atlantic. SLT provides a good fit to the model structures in the top 300 m, but grossly overestimates the sign reversal at depth. The addition of mean flow slightly improves the latter issue, but is too surface intensified. SLT plus topography rectifies the overestimation of the sign reversal, but overestimates the amplitude of the structure for much of the layer above the sign reversal. Combining the effects of mean flow and topography provided the best fit for the mean model profiles, although small errors at the surface and mid-depths are carried over from the individual effects of mean flow and topography respectively. Across the section the best fitting theory varies between SLT plus topography and topography with mean flow, with, in general, SLT plus topography performing better in the east where the sign reversal is less pronounced. None of the theories could accurately reproduce the deeper sign reversals in the west. All theories performed badly at the boundaries. The generalization of this method to other latitudes, oceans, models and baroclinic modes would provide greater insight into the variability in the ocean, while better observational data would allow verification of the model findings.

Interpretation of ageostrophic winds and implications for jet stream maintenance

The use of ageostrophic flow to infer the presence of vertical circulations in the entrances and exits of the climatological jet streams is questioned. Problems of interpretation arise because of the use of different definitions of geostrophy in theoretical studies and in analyses of atmospheric data. The nature and role of the ageostrophic flow based on constant and variable Coriolis parameter definitions of geostrophy vary. In the latter the geostrophic divergence cannot be neglected, so the vertical motion is not associated solely with the ageostrophic flow. Evidence is presented suggesting that ageostrophic flow in the climatological jet streams is primarily determined by the kinematic requirements of wave retrogression rather than by a forcing process. These requirements are largely met by the rotational flow, with the divergent circulations present being geostrophically forced, and so playing a secondary, restoring role.

Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

Low-cost momentum strategies

This paper analyses the impact of trading costs on the profitability of momentum strategies in the United Kingdom and concludes that losers are more expensive to trade than winners. The observed asymmetry in the costs of trading winners and losers crucially relates to the high cost of selling loser stocks with small size and low trading volume. Since transaction costs severely impact net momentum profits, the paper defines a new low-cost relative-strength strategy by shortlisting from all winner and loser stocks those with the lowest total transaction costs. While the study severely questions the profitability of standard momentum strategies, it concludes that there is still room for momentum-based return enhancement, should asset managers decide to adopt low-cost relative-strength strategies.

Mixing length controls on high resolution simulations of convective storms

We perform simulations of several convective events over the southern UK with the Met Office Unified Model (UM) at horizontal grid lengths ranging from 1.5 km to 200 m. Comparing the simulated storms on these days with the Met Office rainfall radar network allows us to apply a statistical approach to evaluate the properties and evolution of the simulated storms over a range of conditions. Here we present results comparing the storm morphology in the model and reality which show that the simulated storms become smaller as grid length decreases and that the grid length that fits the observations best changes with the size of the observed cells. We investigate the sensitivity of storm morphology in the model to the mixing length used in the subgrid turbulence scheme. As the subgrid mixing length is decreased, the number of small storms with high area-averaged rain rates increases. We show that by changing the mixing length we can produce a lower resolution simulation that produces similar morphologies to a higher resolution simulation.

The physics of orographic gravity wave drag

The drag and momentum fluxes produced by gravity waves generated in flow over orography are reviewed, focusing on adiabatic conditions without phase transitions or radiation effects, and steady mean incoming flow. The orographic gravity wave drag is first introduced in its simplest possible form, for inviscid, linearized, non-rotating flow with the Boussinesq and hydrostatic approximations, and constant wind and static stability. Subsequently, the contributions made by previous authors (primarily using theory and numerical simulations) to elucidate how the drag is affected by additional physical processes are surveyed. These include the effect of orography anisotropy, vertical wind shear, total and partial critical levels, vertical wave reflection and resonance, non-hydrostatic effects and trapped lee waves, rotation and nonlinearity. Frictional and boundary layer effects are also briefly mentioned. A better understanding of all of these aspects is important for guiding the improvement of drag parametrization schemes.

Synoptic versus orographic control on stationary convective banding

Quasi-stationary convective bands can cause large localised rainfall accumulations and are often anchored by topographic features. Here, the predictability of and mechanisms causing one such band are determined using ensembles of the Met Office Unified Model at convection-permitting resolution (1.5 km grid length). The band was stationary over the UK for 3 h and produced rainfall accumulations of up to 34 mm. The amount and location of the predicted rainfall was highly variable despite only small differences between the large-scale conditions of the ensemble members. Only three of 21 members of the control ensemble produced a stationary rain band; these three had the weakest upstream winds and hence lowest Froude number. Band formation was due to the superposition of two processes: lee-side convergence resulting from flow around an upstream obstacle and thermally forced convergence resulting from elevated heating over the upstream terrain. Both mechanisms were enhanced when the Froude number was lower. By increasing the terrain height (thus reducing the Froude number), the band became more predictable. An ensemble approach is required to successfully predict the possible occurrence of such quasi-stationary convective events because the rainfall variability is largely modulated by small variations of the large-scale flow. However, high-resolution models are required to accurately resolve the small-scale interactions of the flow with the topography upon which the band formation depends. Thus, although topography provides some predictability, the quasi-stationary convective bands anchored by it are likely to remain a forecasting challenge for many years to come.

How body mass and lifestyle affect juvenile biomass production in placental mammals

In mammals, the mass-specific rate of biomass production during gestation and lactation, here called maternal productivity, has been shown to vary with body size and lifestyle. Metabolic theory predicts that post-weaning growth of offspring, here termed juvenile productivity, should be higher than maternal productivity, and juveniles of smaller species should be more productive than those of larger species. Furthermore because juveniles generally have similar lifestyles to their mothers, across species juvenile and maternal productivities should be correlated. We evaluated these predictions with data from 270 species of placental mammals in 14 taxonomic/lifestyle groups. All three predictions were supported. Lagomorphs, perissodactyls and artiodactyls were very productive both as juveniles and as mothers as expected from the abundance and reliability of their foods. Primates and bats were unproductive as juveniles and as mothers, as expected as an indirect consequence of their low predation risk and consequent low mortality. Our results point the way to a mechanistic explanation for the suite of correlated life-history traits that has been called the slow–fast continuum.

Investigation of Petasis and Ugi reactions in series in an automated microreactor system

Petasis and Ugi reactions are used successively without intermediate purification, effectively accomplishing a six-component reaction. The examined reactions are transferred from traditional batch reactors to an automated continuous flow microreactor setup, where optimization and kinetic analyses are performed, proposed mechanisms evaluated, and rate-limiting steps determined.

Scalable and fault tolerant failure detection and consensus

Future extreme-scale high-performance computing systems will be required to work under frequent component failures. The MPI Forum's User Level Failure Mitigation proposal has introduced an operation, MPI_Comm_shrink, to synchronize the alive processes on the list of failed processes, so that applications can continue to execute even in the presence of failures by adopting algorithm-based fault tolerance techniques. This MPI_Comm_shrink operation requires a fault tolerant failure detection and consensus algorithm. This paper presents and compares two novel failure detection and consensus algorithms. The proposed algorithms are based on Gossip protocols and are inherently fault-tolerant and scalable. The proposed algorithms were implemented and tested using the Extreme-scale Simulator. The results show that in both algorithms the number of Gossip cycles to achieve global consensus scales logarithmically with system size. The second algorithm also shows better scalability in terms of memory and network bandwidth usage and a perfect synchronization in achieving global consensus.

Comparison of terrain following and cut cell grids using a non-hydrostatic model

Terrain following coordinates are widely used in operational models but the cut cell method has been proposed as an alternative that can more accurately represent atmospheric dynamics over steep orography. Because the type of grid is usually chosen during model implementation, it becomes necessary to use different models to compare the accuracy of different grids. In contrast, here a C-grid finite volume model enables a like-for-like comparison of terrain following and cut cell grids. A series of standard two-dimensional tests using idealised terrain are performed: tracer advection in a prescribed horizontal velocity field, a test starting from resting initial conditions, and orographically induced gravity waves described by nonhydrostatic dynamics. In addition, three new tests are formulated: a more challenging resting atmosphere case, and two new advection tests having a velocity field that is everywhere tangential to the terrain following coordinate surfaces. These new tests present a challenge on cut cell grids. The results of the advection tests demonstrate that accuracy depends primarily upon alignment of the flow with the grid rather than grid orthogonality. A resting atmosphere is well-maintained on all grids. In the gravity waves test, results on all grids are in good agreement with existing results from the literature, although terrain following velocity fields lead to errors on cut cell grids. Due to semi-implicit timestepping and an upwind-biased, explicit advection scheme, there are no timestep restrictions associated with small cut cells. We do not find the significant advantages of cut cells or smoothed coordinates that other authors find.