Linear response functions for a vibrational configuration interaction state

Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

Numerical model of solid phase transformations governed by nucleation and growth: microstructure development during isothermal crystallization

A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal histories and no restrictions are imposed on the time and the temperature dependences of the nucleation and growth rates. We also develop an algorithm which evaluates the corresponding emerging grain-size distribution. The algorithm is easy to implement and particularly flexible, making it possible to simulate several experimental conditions. Its simplicity and minimal computer requirements allow high accuracy for two- and three-dimensional growth simulations. The algorithm is applied to explore the grain morphology development during isothermal treatments for several nucleation regimes. In particular, thermal nucleation, preexisting nuclei, and the combination of both nucleation mechanisms are analyzed. For the first two cases, the universal grain-size distribution is obtained. The high accuracy of the model is stated from its comparison to analytical predictions. Finally, the validity of the Kolmogorov-Johnson-Mehl-Avrami model SSSR, is verified for all the cases studied

Anàlisi del camp d'ones internes en sistemes limnològics petits. Simulacions amb el POM

Aquí hem aplicat el Princeton Ocean Model als embassaments de Sau i Boadella, situats a Catalunya, Espanya. Les simulacions s'han realitzat a l'estació d'estiu, quan la columna d'aigua està estratificada de forma contínua, i sota un règim de brisa amb velocitats de fins a 4 m/s. Basant-nos en aquestes simulacions hem analitzat el camp d'ones internes i comparat els resultats numèrics amb dades experimentals disponibles. El model reprodueix adequadament tots els modes observats en l'espectre de la velocitat i temperatura mesurades i ajuda a identificar els diferents modes. Les simulacions mostren la importància dels modes rotacionals en el camp d'ones internes dels embassaments estratificats. En el període estudiat, el radi de Rossby per l'embassament de Sau és de l'ordre de 100 m, que és varies vegades més petit que la amplitud de l'àrea lacustre de l'embassament, i el número de Rossby és de l'ordre de 0.1, corroborant la importancia de l'efecte de Coriolis.

Numerical Response of Breeding Birds Following Experimental Selection Harvesting in Northern Hardwood Forests

Silvicultural treatments have been shown to alter the composition of species assemblages in numerous taxa. However, the intensity and persistence of these effects have rarely been documented. We used a before-after, control-impact (BACI) paired design, i.e., five pairs of 25-ha study plots, 1-control and 1-treated plot, to quantify changes in the density of eight forest bird species in response to selection harvesting over six breeding seasons, one year pre- and five years postharvest. Focal species included mature forest associates, i.e., Northern Parula (Setophaga americana) and Black-throated Green Warbler (Setophaga virens), forest generalists, i.e., Yellow-bellied Sapsucker (Sphyrapicus varius) and Swainson’s Thrush (Catharus ustulatus), early-seral specialists, i.e., Mourning Warbler (Geothlypis philadelphia) and Chestnut-sided Warbler (Setophaga pensylvanica), species associated with shrubby forest gaps, i.e., Black-throated Blue Warbler (Setophaga caerulescens), and mid-seral species, i.e., American Redstart (Setophaga ruticilla). As predicted, we found a negative numerical response to the treatment in the Black-throated Green Warbler, no treatment effect in the Yellow-bellied Sapsucker, and a positive treatment effect in early-seral specialists. We only detected a year effect in the Northern Parula and the American Redstart. There was evidence for a positive treatment effect on the Swainson’s Thrush when the regeneration started to reach the pole stage, i.e., fifth year postharvest. These findings suggest that selection harvesting has the potential to maintain diverse avian assemblages while allowing sustainable management of timber supply, but future studies should determine whether mature-forest associates can sustain second- and third-entry selection harvest treatments.

The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0wave propagation mechanism and the CRW interaction. The behaviour of the Charney modes and the first neutral branch, which rely on tropospheric PV gradients, are arguably more applicable to the atmosphere than modes of the Eady model where the positive PV gradient exists only at the tropopause

The counterpropagating Rossby wave perspective on Kelvin Helmholtz instability as a limiting case of a Rayleigh shear layer with zero width

The Kelvin Helmholtz (KH) problem, with zero stratification, is examined as a limiting case of the Rayleigh model of a single shear layer whose width tends to zero. The transition of the Rayleigh modal dispersion relation to the KH one, as well as the disappearance of the supermodal transient growth in the KH limit, are both rationalized from the counterpropagating Rossby wave perspective.

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.

The counter-propagating Rossby-wave perspective on baroclinic instability. Part IV: Nonlinear life cycles

Pairs of counter-propagating Rossby waves (CRWs) can be used to describe baroclinic instability in linearized primitive-equation dynamics, employing simple propagation and interaction mechanisms at only two locations in the meridional plane—the CRW ‘home-bases’. Here, it is shown how some CRW properties are remarkably robust as a growing baroclinic wave develops nonlinearly. For example, the phase difference between upper-level and lower-level waves in potential-vorticity contours, defined initially at the home-bases of the CRWs, remains almost constant throughout baroclinic wave life cycles, despite the occurrence of frontogenesis and Rossby-wave breaking. As the lower wave saturates nonlinearly the whole baroclinic wave changes phase speed from that of the normal mode to that of the self-induced phase speed of the upper CRW. On zonal jets without surface meridional shear, this must always act to slow the baroclinic wave. The direction of wave breaking when a basic state has surface meridional shear can be anticipated because the displacement structures of CRWs tend to be coherent along surfaces of constant basic-state angular velocity, U. This results in up-gradient horizontal momentum fluxes for baroclinically growing disturbances. The momentum flux acts to shift the jet meridionally in the direction of the increasing surface U, so that the upper CRW breaks in the same direction as occurred at low levels

On the impact of humidity observations in numerical weather prediction

The impact of humidity observations on forecast skill is explored by producing a series of global forecasts using initial data derived from the ERA-40 reanalyses system, in which all humidity data have been removed during the data assimilation. The new forecasts have been compared with the original ERA-40 analyses and forecasts made from them. Both sets of forecasts show virtually identical prediction skill in the extratropics and the tropics. Differences between the forecasts are small and undergo characteristic amplification rate. There are larger differences in temperature and geopotential in the tropics but the differences are small-scale and unstructured and have no noticeable effect on the skill of the wind forecasts. The results highlight the current very limited impact of the humidity observations, used to produce the initial state, on the forecasts.

African easterly wave variability and its relationship to Atlantic tropical cyclone activity

Automatic tracking of vorticity centers in European Centre for Medium-Range Weather Forecasts analyses has been used to develop a 20-yr climatology of African easterly wave activity. The tracking statistics at 600 and 850 mb confirm the complicated easterly wave structures present over the African continent. The rainy zone equatorward of 15 degreesN is dominated by 600-mb activity, and the much drier Saharan region poleward of 15 degreesN is more dominated by 850-mb activity. Over the Atlantic Ocean there is just one storm track with the 600- and 850-mb wave activity collocated. Based on growth/decay and genesis statistics, it appears that the 850-mb waves poleward of 15 degreesN over land generally do not get involved with the equatorward storm track over the ocean. Instead, there appears to be significant development of 850-mb activity at the West African coast in the rainy zone around (10 degreesN, 10 degreesW), which, it is proposed, is associated with latent heat release. Based on the tracking statistics, it has been shown that there is marked interannual variability in African easterly wave (AEW) activity. It is especially marked at the 850-mb level at the West African coast between about 10 degrees and 15 degreesN, where the coefficient of variation is 0.29. For the period between 1985 and 1998, a notable positive correlation is seen between this AEW activity and Atlantic tropical cyclone activity. This correlation is particularly strong for the postreanalysis period between 1994 and 1998. This result suggests that Atlantic tropical cyclone activity may be influenced by the number of AEWs leaving the West African coast, which have significant low-level amplitudes, and not simply by the total number of AEWs.