Brian J. Hoskins

The Steady Linear Response of a Spherical Atmosphere to Thermal and Orographic Forcing

Abstract Motivated by some results from barotropic models, a linearized steady-state five-layer baroclinic model is used to study the response of a spherical atmosphere to thermal and orographic forcing. At low levels the significant perturbations are confined to the neighborhood of the source and for midlatitude thermal forcing these perturbations are crucially dependent on the vertical distribution of the source. In the upper troposphere the sources generate wavetrains which are very similar to those given by barotropic models. For a low-latitude source, long wavelengths propagate strongly polewards as well as eastwards. Shorter wavelengths are trapped equatorward of the poleward flank of the jet, resulting in a split of the wave-trains at this latitude. Using reasonable dissipation magnitudes, the easiest way to produce an appreciable response in middle and high latitudes is by subtropical forcing. These results suggest an explanation for the shapes of patterns described in observational studies. The t...

The Generation of Global Rotational Flow by Steady Idealized Tropical Divergence

Abstract Tropical convective heating is balanced on the large scale by the adiabatic cooling of ascent. The horizontal divergence of the wind above this heating may be viewed as driving the upper tropospheric rotational wind field. A vorticity equation model is used to diagnose this relationship. It is shown that because of the advection of vorticity by the divergent component of the flow, the Rossby wave source can be very different from the simple −fD source often used. In particular, an equatorial region of divergence situated in easterly winds can lead to a Rossby wave source in the subtropical westerlies where it is extremely effective. This part of the source can be relatively insensitive to the longitudinal position of the equatorial divergence. A divergence field which is asymmetric about the equator can lead to a quite symmetric Rossby wave source. For a steady frictionless flow the Rossby wave source averaged over regions within closed streamfunction or absolute vorticity contours is, under cert...

Eliassen-Palm Cross Sections for the Troposphere

Abstract “Eliassen-Palm (EP) cross sections” are meridional cross sections showing the Eliassen-Palm flux F by arrows and its divergence by contours. For large-scale, quasi-geostrophic motion F is defined to have φ and ρ components r0 cosφ[−u′v′, fv′θ′/θp] where φ is latitude, ρ pressure, θ potential temperature, r0 the radius of the earth, bars and primes denote zonal means and deviations and (u,v) is horizontal velocity. The theoretical reasons for using EP cross sections diagnostically are reviewed. The divergence of F reflects the magnitude of transient and irreversible eddy processes at each height and latitude, and is proportional to the northward flux of quasi-geostrophic (not Ertels) potential vorticity. It is a direct measure of the total forcing of the zonal-mean state by the eddies. The direction of F indicates the relative importance of the principal eddy fluxes of heat and momentum. If the eddy dynamics is Rossby wavelike, then F is also a measure of net wave propagation from one height and ...

Atmospheric Frontogenesis Models: Mathematical Formulation and Solution

Abstract The approximation of geostrophic balance across a front is studied. Making this approximation, an analytic approach is made to a frontogenesis model based on the classic horizontal deformation field. Kelvins circulation theorem suggests the introduction of a new independent variable in the cross-front direction. The problem is solved exactly for a Boussinesq, uniform potential vorticity fluid. Non-Boussinesq, non-uniform potential vorticity, latent heat, and surface friction effects are all studied. Using a two-region fluid we model the effects of confluence near the tropopause. A similar approach is made to the appearance of fronts in the finite-amplitude development of the simplest Eady wave; this is also solved analytically. Based on the surface fronts produced by these models, we give a general model of a strong surface front. There is a tendency to form discontinuities in a finite time.

On the existence of storm-tracks

Abstract Given that middle latitude weather systems transport heat in a manner such as to weaken the baroclinicity that is thought to be crucial to their growth, it is perhaps surprising that concentrated regions of such eddy activity, i.e. storm-tracks, are found in the Northern Hemisphere winter. The existence and possible self-maintenance of storm-tracks is investigated using a linear, stationary wave model with storm-track region forcings taken from data averaged over a number of winters. It is found that the direct thermal effect of the eddies does indeed act against the existence of the storm-track. Their vorticity fluxes lead to some reduction of this effect. It is argued that the mean diabatic heating in the storm-track region is an indirect eddy effect. This heating is found to maintain the mean maximum in baroclinicity in the region. Further, the mean low-level flow induced by the eddy effects is such as to enhance the warm western oceanic boundary currents that are crucial to the existence of t...

New Perspectives on the Northern Hemisphere Winter Storm Tracks

Abstract The aim of this paper is to explore the use of both an Eulerian and system-centered method of storm track diagnosis applied to a wide range of meteorological fields at multiple levels to provide a range of perspectives on the Northern Hemisphere winter transient motions and to give new insight into the storm track organization and behavior. The data used are primarily from the European Centre for Medium-Range Weather Forecasts reanalyses project extended with operational analyses to the period 1979–2000. This is supplemented by data from the National Centers for Environmental Prediction and Goddard Earth Observing System 1 reanalyses. The range of fields explored include the usual mean sea level pressure and the lower- and upper-tropospheric height, meridional wind, vorticity, and temperature, as well as the potential vorticity (PV) on a 330-K isentropic surface (PV330) and potential temperature on a PV = 2 PVU surface (θPV2). As well as reporting the primary analysis based on feature tracking, t...

Rossby Wave Propagation on a Realistic Longitudinally Varying Flow

Abstract The response of a barotropic model, linearized about a climatological 300-mb December–February time-mean flow to localized forcing, is considered. In order to aid the design of the experiments and interpretation of the results, a simplified analysis is made of the basic flow in terms of zonal wind, meridional vorticity gradient, and stationary wavenumber. From the analysis the possible existence of a strong waveguide in the Asian jet and weaker waveguides in the North Atlantic and Southern Hemisphere jets is deduced. The possibility of propagation into the equatorial east Pacific and Atlantic oceans and even across these regions is also suggested. These features are confirmed by barotropic model integrations for a variety of perturbation vorticity source positions and shapes. These integrations also show preferred propagation regions arching across North America, from Europe to the Arabian Gulf and, in the Southern Hemisphere, into the equatorial Indian Ocean and Indonesian regions. They also sho...

The shape, propagation and mean-flow interaction of large-scale weather systems

Abstract For a zonal average operator the Eliassen-Palm flux provides a diagnostic of both eddy behavior and the feedback of the eddies onto the mean flow. This paper addresses the diagnosis problem for other averaging operators and, in particular, for time averaging which has proved in recent years such a powerful means of viewing the three-dimensional tropospheric flow. The horizontal velocity correlation tensor gives a measure of the characteristic horizontal eddy shape at a point. It also implies the direction of the group velocity relative to the mean flow in cases where such a concept is valid. However the major emphasis here is on the mean-flow feedback of eddies. In this respect, the eddy vorticity flux is determined by derivatives of the components of the anisotropic part of the tensor. Making a reasonable approximation allows the eddy vorticity flux convergence to be written in terms of E = (v′2 − u′2¯, u′v′¯). A simple interpretation of the mean flow feedback of eddies is then possible. A sligh...

Training and operation of an integrated neuromorphic network based on metal-oxide memristors

Despite much progress in semiconductor integrated circuit technology, the extreme complexity of the human cerebral cortex, with its approximately 1014 synapses, makes the hardware implementation of neuromorphic networks with a comparable number of devices exceptionally challenging. To provide comparable complexity while operating much faster and with manageable power dissipation, networks based on circuits combining complementary metal-oxide-semiconductors (CMOSs) and adjustable two-terminal resistive devices (memristors) have been developed. In such circuits, the usual CMOS stack is augmented with one or several crossbar layers, with memristors at each crosspoint. There have recently been notable improvements in the fabrication of such memristive crossbars and their integration with CMOS circuits, including first demonstrations of their vertical integration. Separately, discrete memristors have been used as artificial synapses in neuromorphic networks. Very recently, such experiments have been extended to crossbar arrays of phase-change memristive devices. The adjustment of such devices, however, requires an additional transistor at each crosspoint, and hence these devices are much harder to scale than metal-oxide memristors, whose nonlinear current–voltage curves enable transistor-free operation. Here we report the experimental implementation of transistor-free metal-oxide memristor crossbars, with device variability sufficiently low to allow operation of integrated neural networks, in a simple network: a single-layer perceptron (an algorithm for linear classification). The network can be taught in situ using a coarse-grain variety of the delta rule algorithm to perform the perfect classification of 3 × 3-pixel black/white images into three classes (representing letters). This demonstration is an important step towards much larger and more complex memristive neuromorphic networks.

Subtropical Anticyclones and Summer Monsoons

The summer subtropical circulation in the lower troposphere is characterized by continental monsoon rains and anticyclones over the oceans. In winter, the subtropical circulation is more strongly dominated by the zonally averaged flow and its interactions with orography. Here, the mechanics of the summer and winter lowertropospheric subtropical circulation are explored through the use of a primitive equation model and comparison with observations. By prescribing in the model the heatings associated with several of the world’s monsoons, it is confirmed that the equatorward portion of each subtropical anticyclone may be viewed as the Kelvin wave response to the monsoon heating over the continent to the west. A poleward-flowing low-level jet into a monsoon (such as the Great Plains jet) is required for Sverdrup vorticity balance. This jet effectively closes off the subtropical anticyclone to the east and also transports moisture into the monsoon region. The low-level jet into North America induced by its monsoon heating is augmented by a remote response to the Asian monsoon heating. The Rossby wave response to the west of subtropical monsoon heating, interacting with the midlatitude westerlies, produces a region of adiabatic descent. It is demonstrated here that a local ‘‘diabatic enhancement’’ can lead to a strengthening of the descent. Longitudinal mountain chains act to block the westerly flow and also tend to produce descent in this region. Below the descent, Sverdrup vorticity balance implies equatorward flow that closes off the subtropical anticyclone to the west and induces cool upwelling in the ocean through Ekman transport. Feedbacks, involving, for example, sea surface temperatures, may further enhance the descent in these regions. The conclusion is that the Mediterranean-type climates of regions such as California and Chile may be induced remotely by the monsoon to the east. Hence it can be argued that the subtropical circulation in summer comprises a set of weakly interacting monsoon systems, each involving monsoon rains, a low-level poleward jet, a subtropical anticyclone to the east, and descent and equatorward flow to the west. In winter, it is demonstrated how the nonlinear interaction between the strong zonal-mean circulation, associated with the winter ‘‘Hadley cell,’’ and the mountains can define many of the large-scale features of the subtropical circulation. The blocking effect of the longitudinal mountain chains is shown to be very important. Subsequent diabatic effects, such as a local diabatic enhancement, would appear to be essential for producing the observed amplitude of these features.