Isomap nonlinear dimensionality reduction and bimodality of Asian monsoon convection

It is known that the empirical orthogonal function method is unable to detect possible nonlinear structure in climate data. Here, isometric feature mapping (Isomap), as a tool for nonlinear dimensionality reduction, is applied to 1958–2001 ERA-40 sea-level pressure anomalies to study nonlinearity of the Asian summer monsoon intraseasonal variability. Using the leading two Isomap time series, the probability density function is shown to be bimodal. A two-dimensional bivariate Gaussian mixture model is then applied to identify the monsoon phases, the obtained regimes representing enhanced and suppressed phases, respectively. The relationship with the large-scale seasonal mean monsoon indicates that the frequency of monsoon regime occurrence is significantly perturbed in agreement with conceptual ideas, with preference for enhanced convection on intraseasonal time scales during large-scale strong monsoons. Trend analysis suggests a shift in concentration of monsoon convection, with less emphasis on South Asia and more on the East China Sea.

A normative method to analyse workarounds in a healthcare environment: motivations, consequences, and constraints

Healthcare information systems have the potential to enhance productivity, lower costs, and reduce medication errors by automating business processes. However, various issues such as system complexity and system abilities in a relation to user requirements as well as rapid changes in business needs have an impact on the use of these systems. In many cases failure of a system to meet business process needs has pushed users to develop alternative work processes (workarounds) to fill this gap. Some research has been undertaken on why users are motivated to perform and create workarounds. However, very little research has assessed the consequences on patient safety. Moreover, the impact of performing these workarounds on the organisation and how to quantify risks and benefits is not well analysed. Generally, there is a lack of rigorous understanding and qualitative and quantitative studies on healthcare IS workarounds and their outcomes. This project applies A Normative Approach for Modelling Workarounds to develop A Model of Motivation, Constraints, and Consequences. It aims to understand the phenomenon in-depth and provide guidelines to organisations on how to deal with workarounds. Finally the method is demonstrated on a case study example and its relative merits discussed.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part I: gravity wave forcing

Parameterization schemes for the drag due to atmospheric gravity waves are discussed and compared in the context of a simple one-dimensional model of the quasi-biennial oscillation (QBO). A number of fundamental issues are examined in detail, with the goal of providing a better understanding of the mechanism by which gravity wave drag can produce an equatorial zonal wind oscillation. The gravity wave–driven QBOs are compared with those obtained from a parameterization of equatorial planetary waves. In all gravity wave cases, it is seen that the inclusion of vertical diffusion is crucial for the descent of the shear zones and the development of the QBO. An important difference between the schemes for the two types of waves is that in the case of equatorial planetary waves, vertical diffusion is needed only at the lowest levels, while for the gravity wave drag schemes it must be included at all levels. The question of whether there is downward propagation of influence in the simulated QBOs is addressed. In the gravity wave drag schemes, the evolution of the wind at a given level depends on the wind above, as well as on the wind below. This is in contrast to the parameterization for the equatorial planetary waves in which there is downward propagation of phase only. The stability of a zero-wind initial state is examined, and it is determined that a small perturbation to such a state will amplify with time to the extent that a zonal wind oscillation is permitted.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.

The troposphere-to-stratosphere transition in kinetic energy spectra and nonlinear spectral fluxes as seen in ECMWF analyses

Global horizontal wavenumber kinetic energy spectra and spectral fluxes of rotational kinetic energy and enstrophy are computed for a range of vertical levels using a T799 ECMWF operational analysis. Above 250 hPa, the kinetic energy spectra exhibit a distinct break between steep and shallow spectral ranges, reminiscent of dual power-law spectra seen in aircraft data and high-resolution general circulation models. The break separates a large-scale ‘‘balanced’’ regime in which rotational flow strongly dominates divergent flow and a mesoscale ‘‘unbalanced’’ regime where divergent energy is comparable to or larger than rotational energy. Between 230 and 100 hPa, the spectral break shifts to larger scales (from n 5 60 to n 5 20, where n is spherical harmonic index) as the balanced component of the flow preferentially decays. The location of the break remains fairly stable throughout the stratosphere. The spectral break in the analysis occurs at somewhat larger scales than the break seen in aircraft data. Nonlinear spectral fluxes defined for the rotational component of the flow maximize between about 300 and 200 hPa. Large-scale turbulence thus centers on the extratropical tropopause region, within which there are two distinct mechanisms of upscale energy transfer: eddy–eddy interactions sourcing the transient energy peak in synoptic scales, and zonal mean–eddy interactions forcing the zonal flow. A well-defined downscale enstrophy flux is clearly evident at these altitudes. In the stratosphere, the transient energy peak moves to planetary scales and zonal mean–eddy interactions become dominant.

Energetics of a symmetric circulation including momentum constraints

A theory of available potential energy (APE) for symmetric circulations, which includes momentum constraints, is presented. The theory is a generalization of the classical theory of APE, which includes only thermal constraints on the circulation. Physically, centrifugal potential energy is included along with gravitational potential energy. The generalization relies on the Hamiltonian structure of the conservative dynamics, although (as with classical APE) it still defines the energetics in a nonconservative framework. It follows that the theory is exact at finite amplitude, has a local form, and can be applied to a variety of fluid models. It is applied here to the f -plane Boussinesq equations. It is shown that, by including momentum constraints, the APE of a symmetrically stable flow is zero, while the energetics of a mechanically driven symmetric circulation properly reflect its causality.

Modeling the effects of anesthesia on the electroencephalogram

Changes to the electroencephalogram (EEG) observed during general anesthesia are modeled with a physiological mean field theory of electrocortical activity. To this end a parametrization of the postsynaptic impulse response is introduced which takes into account pharmacological effects of anesthetic agents on neuronal ligand-gated ionic channels. Parameter sets for this improved theory are then identified which respect known anatomical constraints and predict mean firing rates and power spectra typically encountered in human subjects. Through parallelized simulations of the eight nonlinear, two-dimensional partial differential equations on a grid representing an entire human cortex, it is demonstrated that linear approximations are sufficient for the prediction of a range of quantitative EEG variables. More than 70 000 plausible parameter sets are finally selected and subjected to a simulated induction with the stereotypical inhaled general anesthetic isoflurane. Thereby 86 parameter sets are identified that exhibit a strong “biphasic” rise in total power, a feature often observed in experiments. A sensitivity study suggests that this “biphasic” behavior is distinguishable even at low agent concentrations. Finally, our results are briefly compared with previous work by other groups and an outlook on future fits to experimental data is provided.

Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

On nonlinear symmetric stability and the nonlinear saturation of symmetric instability

A nonlinear symmetric stability theorem is derived in the context of the f-plane Boussinesq equations, recovering an earlier result of Xu within a more general framework. The theorem applies to symmetric disturbances to a baroclinic basic flow, the disturbances having arbitrary structure and magnitude. The criteria for nonlinear stability are virtually identical to those for linear stability. As in Xu, the nonlinear stability theorem can be used to obtain rigorous upper bounds on the saturation amplitude of symmetric instabilities. In a simple example, the bounds are found to compare favorably with heuristic parcel-based estimates in both the hydrostatic and non-hydrostatic limits.

Nonlinear symmetric stability of planetary atmospheres

The energy–Casimir method is applied to the problem of symmetric stability in the context of a compressible, hydrostatic planetary atmosphere with a general equation of state. Formal stability criteria for symmetric disturbances to a zonally symmetric baroclinic flow are obtained. In the special case of a perfect gas the results of Stevens (1983) are recovered. Finite-amplitude stability conditions are also obtained that provide an upper bound on a certain positive-definite measure of disturbance amplitude.

Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established.

Nonlinear stability of Eady's model

A nonlinear stability theorem is established for Eady's model of baroclinic flow. In particular, the Eady basic state is shown to be nonlinearly stable (for arbitrary shear) provided (Δz)/(Δy) > 2(5)^1/2f/(πN),where Δz is the height of the domain, Δy the channel width, f the Coriolis parameter, and N the buoyancy frequency. When this criterion is satisfied, explicit bounds can be derived on the disturbance potential enstrophy, the disturbance energy, and the disturbance available potential energy on the rigid lids, which are expressed in terms of the initial disturbance fields. The disturbances are completely general (with nonzero potential vorticity) and are not assumed to be of small amplitude. The results may be regarded as an extension of Arnol'd's second nonlinear stability theorem to continuously stratified quasigeostrophic baroclinic flow.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

Nonlinear saturation of baroclinic instability: part III: bounds on the energy

Rigorous upper bounds are derived on the saturation amplitude of baroclinic instability in the two-layer model. The bounds apply to the eddy energy and are obtained by appealing to a finite amplitude conservation law for the disturbance pseudoenergy. These bounds are to be distinguished from those derived in Part I of this study, which employed a pseudomomentum conservation law and provided bounds on the eddy potential enstrophy. The bounds apply to conservative (inviscid, unforced) flow, as well as to forced-dissipative flow when the dissipation is proportional to the potential vorticity. Bounds on the eddy energy are worked out for a general class of unstable westerly jets. In the special case of the Phillips model of baroclinic instability, and in the limit of infinitesimal initial eddy amplitude, the bound states that the eddy energy cannot exceed ϵβ2/6F where ϵ = (U − Ucrit)/Ucrit is the relative supercriticality. This bound captures the essential dynamical scalings (i.e., the dependence on ϵ, β, and F) of the saturation amplitudes predicted by weakly nonlinear theory, as well as exhibiting remarkable quantitative agreement with those predictions, and is also consistent with heuristic baroclinic adjustment estimates.