Numerical prediction of atmospheric blocking-A case study

A series of numerical models have been used to investigate the predictability of atmospheric blocking for an episode selected from FGGE Special Observing Period I. Level II-b FGGE data have been used in the experiment. The blocking took place over the North Atlantic region and is a very characteristic example of high winter blocking. It is found that the very high resolution models developed at ECMWF, in a remarkable way manage to predict the blocking event in great detail, even beyond 1 week. Although models with much less resolution manage to predict the blocking phenomenon as such, the actual evolution differs very much from the observed and consequently the practical value is substantially reduced. Wind observations from the geostationary satellites are shown to have a substantial impact on the forecast beyond 5 days, as well as an extension of the integration domain to the whole globe. Quasi-geostrophic baroclinic models and, even more, barotropic models, are totally inadequate to predict blocking except in its initial phase. The prediction experiment illustrates clearly that efforts which have gone into the improvement of numerical prediction models in the last decades have been worth while.

Introduction and the problems of weather interpretation

Numerical forecasts of the atmosphere based on the fundamental dynamical and thermodynamical equations have now been carried for almost 30 years. The very first models which were used were drastic simplifications of the governing equations and permitting only the prediction of the geostrophic wind in the middle of the troposphere based on the conservation of absolute vorticity. Since then we have seen a remarkable development in models predicting the large-scale synoptic flow. Verification carried out at NMC Washington indicates an improvement of about 40% in 24h forecasts for the 500mb geopotential since the end of the 1950’s. The most advanced models of today use the equations of motion in their more original form (i.e. primitive equations) which are better suited to predicting the atmosphere at low latitudes as well as small scale systems. The model which we have developed at the Centre, for instance, will be able to predict weather systems from a scale of 500-1000 km and a vertical extension of a few hundred millibars up to global weather systems extending through the whole depth of the atmosphere. With a grid resolution of 1.5 and 15 vertical levels and covering the whole globe it is possible to describe rather accurately the thermodynamical processes associated with cyclone development. It is further possible to incorporate sub-grid-scale processes such as radiation, exchange of sensible heat, release of latent heat etc. in order to predict the development of new weather systems and the decay of old ones. Later in this introduction I will exemplify this by showing some results of forecasts by the Centre’s model.

A unified theory of balance in the extratropics

Many physical systems exhibit dynamics with vastly different time scales. Often the different motions interact only weakly and the slow dynamics is naturally constrained to a subspace of phase space, in the vicinity of a slow manifold. In geophysical fluid dynamics this reduction in phase space is called balance. Classically, balance is understood by way of the Rossby number R or the Froude number F; either R ≪ 1 or F ≪ 1. We examined the shallow-water equations and Boussinesq equations on an f -plane and determined a dimensionless parameter _, small values of which imply a time-scale separation. In terms of R and F, ∈= RF/√(R^2+R^2 ) We then developed a unified theory of (extratropical) balance based on _ that includes all cases of small R and/or small F. The leading-order systems are ensured to be Hamiltonian and turn out to be governed by the quasi-geostrophic potential-vorticity equation. However, the height field is not necessarily in geostrophic balance, so the leading-order dynamics are more general than in quasi-geostrophy. Thus the quasi-geostrophic potential-vorticity equation (as distinct from the quasi-geostrophic dynamics) is valid more generally than its traditional derivation would suggest. In the case of the Boussinesq equations, we have found that balanced dynamics generally implies hydrostatic balance without any assumption on the aspect ratio; only when the Froude number is not small and it is the Rossby number that guarantees a timescale separation must we impose the requirement of a small aspect ratio to ensure hydrostatic balance.

Classification and fault detection methods for fuel cell monitoring and quality control

In this paper, various types of fault detection methods for fuel cells are compared. For example, those that use a model based approach or a data driven approach or a combination of the two. The potential advantages and drawbacks of each method are discussed and comparisons between methods are made. In particular, classification algorithms are investigated, which separate a data set into classes or clusters based on some prior knowledge or measure of similarity. In particular, the application of classification methods to vectors of reconstructed currents by magnetic tomography or to vectors of magnetic field measurements directly is explored. Bases are simulated using the finite integration technique (FIT) and regularization techniques are employed to overcome ill-posedness. Fisher's linear discriminant is used to illustrate these concepts. Numerical experiments show that the ill-posedness of the magnetic tomography problem is a part of the classification problem on magnetic field measurements as well. This is independent of the particular working mode of the cell but influenced by the type of faulty behavior that is studied. The numerical results demonstrate the ill-posedness by the exponential decay behavior of the singular values for three examples of fault classes.

Ketamine, propofol, and the EEG: A neural field analysis of HCN1-mediated interactions

Ketamine and propofol are two well-known, powerful anesthetic agents, yet at first sight this appears to be their only commonality. Ketamine is a dissociative anesthetic agent, whose main mechanism of action is considered to be N-methyl-D-aspartate (NMDA) antagonism; whereas propofol is a general anesthetic agent, which is assumed to primarily potentiate currents gated by γ-aminobutyric acid type A (GABAA) receptors. However, several experimental observations suggest a closer relationship. First, the effect of ketamine on the electroencephalogram (EEG) is markedly changed in the presence of propofol: on its own ketamine increases θ (4–8 Hz) and decreases α (8–13 Hz) oscillations, whereas ketamine induces a significant shift to beta band frequencies (13–30 Hz) in the presence of propofol. Second, both ketamine and propofol cause inhibition of the inward pacemaker current Ih, by binding to the corresponding hyperpolarization-activated cyclic nucleotide-gated potassium channel 1 (HCN1) subunit. The resulting effect is a hyperpolarization of the neuron’s resting membrane potential. Third, the ability of both ketamine and propofol to induce hypnosis is reduced in HCN1-knockout mice. Here we show that one can theoretically understand the observed spectral changes of the EEG based on HCN1-mediated hyperpolarizations alone, without involving the supposed main mechanisms of action of these drugs through NMDA and GABAA, respectively. On the basis of our successful EEG model we conclude that ketamine and propofol should be antagonistic to each other in their interaction at HCN1 subunits. Such a prediction is in accord with the results of clinical experiment in which it is found that ketamine and propofol interact in an infra-additive manner with respect to the endpoints of hypnosis and immobility.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

The Empirical Forcing Function as a tool for the diagnosis of large-scale atmospheric anomalies

The time-mean quasi-geostrophic potential vorticity equation of the atmospheric flow on isobaric surfaces can explicitly include an atmospheric (internal) forcing term of the stationary-eddy flow. In fact, neglecting some non-linear terms in this equation, this forcing can be mathematically expressed as a single function, called Empirical Forcing Function (EFF), which is equal to the material derivative of the time-mean potential vorticity. Furthermore, the EFF can be decomposed as a sum of seven components, each one representing a forcing mechanism of different nature. These mechanisms include diabatic components associated with the radiative forcing, latent heat release and frictional dissipation, and components related to transient eddy transports of heat and momentum. All these factors quantify the role of the transient eddies in forcing the atmospheric circulation. In order to assess the relevance of the EFF in diagnosing large-scale anomalies in the atmospheric circulation, the relationship between the EFF and the occurrence of strong North Atlantic ridges over the Eastern North Atlantic is analyzed, which are often precursors of severe droughts over Western Iberia. For such events, the EFF pattern depicts a clear dipolar structure over the North Atlantic; cyclonic (anticyclonic) forcing of potential vorticity is found upstream (downstream) of the anomalously strong ridges. Results also show that the most significant components are related to the diabatic processes. Lastly, these results highlight the relevance of the EFF in diagnosing large-scale anomalies, also providing some insight into their interaction with different physical mechanisms.

Dependence of winter precipitation over Portugal on NAO and baroclinic wave activity

The relationship between winter (DJF) rainfall over Portugal and the variable large scale circulation is addressed. It is shown that the poles of the sea level pressure (SLP) field variability associated with rainfall variability are shifted about 15° northward with respect to those used in standard definitions of the North Atlantic Oscillation (NAO). It is suggested that the influence of NAO on rainfall dominantly arises from the associated advection of humidity from the Atlantic Ocean. Rainfall is also related to different aspects of baroclinic wave activity, the variability of the latter quantity in turn being largely dependent on the NAO. A negative NAO index (leading to increased westerly surface geostrophic winds into Portugal) is associated with an increased number of deep (ps<980 hPa) surface lows over the central North Atlantic and of intermediate (980

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

Carbon monoxide inhibition of Cav3.2 T-type Ca2+ channels reveals tonic modulation by thioredoxin

T-type Ca2+ channels play diverse roles in tissues such as sensory neurons, vascular smooth muscle, and cancers, where increased expression of the cytoprotective enzyme, heme oxygenase-1 (HO-1) is often found. Here, we report regulation of T-type Ca2+ channels by carbon monoxide (CO) a HO-1 by-product. CO (applied as CORM-2) caused a concentration-dependent, poorly reversible inhibition of all T-type channel isoforms (Cav3.1-3.3, IC50 ∼3 μM) expressed in HEK293 cells, and native T-type channels in NG108-15 cells and primary rat sensory neurons. No recognized CO-sensitive signaling pathway could account for the CO inhibition of Cav3.2. Instead, CO sensitivity was mediated by an extracellular redox-sensitive site, which was also highly sensitive to thioredoxin (Trx). Trx depletion (using auranofin, 2-5 μM) reduced Cav3.2 currents and their CO sensitivity by >50% but increased sensitivity to dithiothreitol ∼3-fold. By contrast, Cav3.1 and Cav3.3 channels, and their sensitivity to CO, were unaffected in identical experiments. Our data propose a novel signaling pathway in which Trx acts as a tonic, endogenous regulator of Cav3.2 channels, while HO-1-derived CO disrupts this regulation, causing channel inhibition. CO modulation of T-type channels has widespread implications for diverse physiological and pathophysiological mechanisms, such as excitability, contractility, and proliferation

Rossby number expansions, slaving principles, and balance dynamics

We consider the problem of constructing balance dynamics for rapidly rotating fluid systems. It is argued that the conventional Rossby number expansion—namely expanding all variables in a series in Rossby number—is secular for all but the simplest flows. In particular, the higher-order terms in the expansion grow exponentially on average, and for moderate values of the Rossby number the expansion is, at best, useful only for times of the order of the doubling times of the instabilities of the underlying quasi-geostrophic dynamics. Similar arguments apply in a wide class of problems involving a small parameter and sufficiently complex zeroth-order dynamics. A modified procedure is proposed which involves expanding only the fast modes of the system; this is equivalent to an asymptotic approximation of the slaving relation that relates the fast modes to the slow modes. The procedure is systematic and thus capable, at least in principle, of being carried to any order—unlike procedures based on truncations. We apply the procedure to construct higher-order balance approximations of the shallow-water equations. At the lowest order quasi-geostrophy emerges. At the next order the system incorporates gradient-wind balance, although the balance relations themselves involve only linear inversions and hence are easily applied. There is a large class of reduced systems associated with various choices for the slow variables, but the simplest ones appear to be those based on potential vorticity.

Atmospheric point discharge current measurements using a temperature-compensated logarithmic current amplifier

Measurements of atmospheric corona currents have been made for over 100 years to indicate the atmospheric electric field. Corona currents vary substantially, in polarity and in magnitude. The instrument described here uses a sharp point sensor connected to a temperature compensated bi-polar logarithmic current amplifier. Calibrations over a range of currents from ±10 fA to ±3 μA and across ±20 ◦C show it has an excellent logarithmic response over six orders of magnitude from 1 pA to 1 μA in both polarities for the range of atmospheric temperatures likely to be encountered in the southern UK. Comparison with atmospheric electric field measurements during disturbed weather confirms that bipolar electric fields induce corona currents of corresponding sign, with magnitudes ∼0.5 μA.

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted