The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

Simulation of monsoon disturbances in the LMD GCM

The monsoon depressions that form over India during the summer are analyzed using simulations from the Laboratoire de Meteorologie Dynamique general circulation model. This type of synoptic system often occurs with a frequency of one to two per month and can produce a strong Indian rainfall. Two kinds of analyses are conducted in this study. The first one is a subjective analysis based on the evolution of the precipitation rate and the pattern of the sea level pressure. The second one is an objective analysis performed using the TRACK program, which identifies and tracks the minima in the sea level pressure anomaly held and computes the statistics for the distribution of systems. The analysis of a 9-yr control run, which simulates strong precipitation rates over the foothills of the Himalayas and over southern India but weak rates over central India, shows that the number of disturbances is coo low and that they almost never occur during August, when break conditions prevail. The generated disturbances more often move north, toward the foothills of the Himalayas. Another analysis is performed to study the effect of the Tibetan Plateau elevation on these disturbances with a 9-yr run carried out with a Tibetan Plateau at 50% of its current height. It is shown that this later integration simulates more frequent monsoon disturbances, which move rather northwestward, in agreement with the current observations. The comparison between the two runs shows that the June-July-August rainfall difference is in large part due to changes in the occurrence of the monsoon disturbances.

Ecological and life-history traits predict bee species responses to environmental disturbances

The ability to predict the responses of ecological communities and individual species to human-induced environmental change remains a key issue for ecologists and conservation managers alike. Responses are often variable among species within groups making general predictions difficult. One option is to include ecological trait information that might help to disentangle patterns of response and also provide greater understanding of how particular traits link whole clades to their environment. Although this ‘‘trait-guild” approach has been used for single disturbances, the importance of particular traits on general responses to multiple disturbances has not been explored. We used a mixed model analysis of 19 data sets from throughout the world to test the effect of ecological and life-history traits on the responses of bee species to different types of anthropogenic environmental change. These changes included habitat loss, fragmentation, agricultural intensification, pesticides and fire. Individual traits significantly affected bee species responses to different disturbances and several traits were broadly predictive among multiple disturbances. The location of nests – above vs. below ground – significantly affected response to habitat loss, agricultural intensification, tillage regime (within agriculture) and fire. Species that nested above ground were on average more negatively affected by isolation from natural habitat and intensive agricultural land use than were species nesting below ground. In contrast below-ground-nesting species were more negatively affected by tilling than were above-ground nesters. The response of different nesting guilds to fire depended on the time since the burn. Social bee species were more strongly affected by isolation from natural habitat and pesticides than were solitary bee species. Surprisingly, body size did not consistently affect species responses, despite its importance in determining many aspects of individuals’ interaction with their environment. Although synergistic interactions among traits remain to be explored, individual traits can be useful in predicting and understanding responses of related species to global change.

Disturbances in morning cortisol secretion in association with maternal postnatal depression predict subsequent depressive symptomatology in adolescents

Background: We have previously reported higher and more variable salivary morning cortisol in 13-year-old adolescents whose mothers were depressed in the postnatal period, compared with control group adolescents whose mothers did not develop postnatal depression (PND). This observation suggested a biological mechanism by which intrafamilial risk for depressive disorder may be transmitted. In the current article, we examined whether the cortisol disturbances observed at 13 years could predict depressive symptornatology in adolescents at 16 years of age. Methods: We measured self-reported depressive symptoms in 16-year-old adolescents who had (n = 48) or had not (n = 39) been exposed to postnatal maternal depression and examined their prediction by morning and evening cortisol indices obtained via 10 days of salivary collections at 13 years. Results: Elevated morning cortisol secretion at 13 years, and particularly the maximum level recorded over 10 days of collection, predicted elevated depressive symptoms at 16 years over and above 13-year depressive symptom levels and other possible confounding factors. Morning cortisol secretion mediated an association between maternal PND and symptornatology in 16-year-old offspring. Conclusions: Alterations in steroid secretion observed in association with maternal PND may provide a mechanism by which risk for depression is transmitted from mother to offspring.

On improving the performance in robust controllers for robot manipulators with parametric disturbances

This paper presents a new strategy for controlling rigid-robot manipulators in the presence of parametric uncertainties or un-modelled dynamics. The strategy combines an adaptation law with a well known robust controller proposed by Spong, which is derived using Lyapunov's direct method. Although the tracking problem of manipulators has been successfully solved with different strategies, there are some conditions under which their efficiency is limited. Specifically, their performance decreases when unknown loading masses or model disturbances are introduced. The aim of this work is to show that the proposed strategy performs better than existing algorithms, as verified with real-time experimental results with a Puma-560 robot. (c) 2006 Elsevier Ltd. All rights reserved.

Disturbances in early parenting of depressed mothers and cortisol secretion in offspring: A preliminary study

Background: Disturbances in cortisol secretion are associated with risk for psychiatric disorder, including depression. Animal research indicates that early care experiences influence hypothalamic-pituitary-adrenal (HPA) axis functioning in offspring. Similar effects are suggested in human development, but evidence of longitudinal associations between observed early parenting and offspring cortisol secretion is extremely limited. We studied associations between parenting disturbances occurring in the context of maternal postnatal depression (PND), and elevations in morning cortisol secretion in the adolescent offspring of PND mothers. Methods: We observed maternal parenting behaviour on four occasions through the first year and at five-year follow up in postnatally depressed (n = 29) and well (n = 20) mothers. Observations were coded for maternal sensitivity and withdrawal. Basal offspring salivary cortisol secretion was measured at 13-years, using collections over 10-days. Results: Postnatal, but not five-year, maternal withdrawal predicted elevated mean and maximum morning cortisol secretion in 13-year-old offspring. There were no significant associations between maternal sensitivity and offspring cortisol secretion. Limitations: The sample size was relatively small, and effects tended to be reduced to trend level when covariates were considered. The correlational nature of the study (albeit longitudinal) limits conclusions regarding causality. Conclusions: Individual differences in early maternal parenting behaviour may influence offspring cortisol secretion, and thereby risk for depression. Parenting interventions that facilitate active maternal engagement with the infant may be indicated for high risk populations.

Neural networks for identification of nonlinear systems under random piecewise polynomial disturbances

The problem of identification of a nonlinear dynamic system is considered. A two-layer neural network is used for the solution of the problem. Systems disturbed with unmeasurable noise are considered, although it is known that the disturbance is a random piecewise polynomial process. Absorption polynomials and nonquadratic loss functions are used to reduce the effect of this disturbance on the estimates of the optimal memory of the neural-network model.

Identification of linear systems in the presence of piecewise polynomial disturbances

The paper proposes a method of performing system identification of a linear system in the presence of bounded disturbances. The disturbances may be piecewise parabolic or periodic functions. The method is demonstrated effectively on two example systems with a range of disturbances.

Autoregressive conditional kurtosis

This article proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student’s t-density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising U.S. and U.K. stocks and bonds, and significant evidence in favor of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are proposed, and we show that the response of kurtosis to good and bad news is not significantly asymmetric.

Synoptic scale disturbances of the Indian Summer Monsoon as simulated in a high resolution climate model

Hamburg atmospheric general circulation model ECHAM3 at T106 resolution (1.125' lat.Aon.) has considerable skill in reproducing the observed seasonal reversal of mean sea level pressure, the location of the summer heat low as well as the position of the monsoon trough over the Indian subcontinent. The present-day climate and its seasonal cycle are realistically simulated by the model over this region. The model simulates the structure, intensity, frequency, movement and lifetime of monsoon depressions remarkably well. The number of monsoon depressions/storms simulated by the model in a year ranged from 5 to 12 with an average frequency of 8.4 yr-', not significantly different from the observed climatology. The model also simulates the interannual variability in the formation of depressions over the north Bay of Bengal during the summer monsoon season. In the warmer atmosphere under doubled CO2 conditions, the number of monsoon depressions/cyclonic storms forming in Indian seas in a year ranged from 5 to 11 with an average frequency of 7.6 yr-', not significantly different from those inferred in the control run of the model. However, under doubled CO2 conditions, fewer depressions formed in the month of June. Neither the lowest central pressure nor the maximum wind speed changes appreciably in monsoon depressions identified under simulated enhanced greenhouse conditions. The analysis suggests there will be no significant changes in the number and intensity of monsoon depressions in a warmer atmosphere.

Wave activity for large-amplitude disturbances described by the primitive equations on the sphere

Pseudomomentum and pseudoenergy are both measures of wave activity for disturbances in a fluid, relative to a notional background state. Together they give information on the propagation, growth, and decay of disturbances. Wave activity conservation laws are most readily derived for the primitive equations on the sphere by using isentropic coordinates. However, the intersection of isentropic surfaces with the ground (and associated potential temperature anomalies) is a crucial aspect of baroclinic wave evolution. A new expression is derived for pseudoenergy that is valid for large-amplitude disturbances spanning isentropic layers that may intersect the ground. The pseudoenergy of small-amplitude disturbances is also obtained by linearizing about a zonally symmetric background state. The new expression generalizes previous pseudoenergy results for quasigeostrophic disturbances on the β plane and complements existing large-amplitude results for pseudomomentum. The pseudomomentum and pseudoenergy diagnostics are applied to an extended winter from the European Centre for Medium-Range Weather Forecasts Interim Re-Analysis data. The time series identify distinct phenomena such as a baroclinic wave life cycle where the wave activity in boundary potential temperature saturates nonlinearly almost two days before the peak in wave activity near the tropopause. The coherent zonal propagation speed of disturbances at tropopause level, including distinct eastward, westward, and stationary phases, is shown to be dictated by the ratio of total hemispheric pseudoenergy to pseudomomentum. Variations in the lower-boundary contribution to pseudoenergy dominate changes in propagation speed; phases of westward progression are associated with stronger boundary potential temperature perturbations.

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

Time development of small disturbances to plane Couette Flow

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.