1000 resultados para boundary
Resumo:
The one-dimensional variational assimilation of vertical temperature information in the presence of a boundary-layer capping inversion is studied. For an optimal analysis of the vertical temperature profile, an accurate representation of the background error covariances is essential. The background error covariances are highly flow-dependent due to the variability in the presence, structure and height of the boundary-layer capping inversion. Flow-dependent estimates of the background error covariances are shown by studying the spread in an ensemble of forecasts. A forecast of the temperature profile (used as a background state) may have a significant error in the position of the capping inversion with respect to observations. It is shown that the assimilation of observations may weaken the inversion structure in the analysis if only magnitude errors are accounted for as is the case for traditional data assimilation methods used for operational weather prediction. The positional error is treated explicitly here in a new data assimilation scheme to reduce positional error, in addition to the traditional framework to reduce magnitude error. The distribution of the positional error of the background inversion is estimated for use with the new scheme.
Resumo:
The interaction between ocean surface waves and the overlying wind leads to a transfer of momentum across the air–sea interface. Atmospheric and oceanic models typically allow for momentum transfer to be directed only downward, from the atmosphere to the ocean. Recent observations have suggested that momentum can also be transferred upward when long wavelength waves, characteristic of remotely generated swell, propagate faster than the wind speed. The effect of upward momentum transfer on the marine atmospheric boundary layer is investigated here using idealized models that solve the momentum budget above the ocean surface. A variant of the classical Ekman model that accounts for the wave-induced stress demonstrates that, although the momentum flux due to the waves penetrates only a small fraction of the depth of the boundary layer, the wind profile is profoundly changed through its whole depth. When the upward momentum transfer from surface waves sufficiently exceeds the downward turbulent momentum flux, then the near-surface wind accelerates, resulting in a low-level wave-driven wind jet. This increases the Coriolis force in the boundary layer, and so the wind turns in the opposite direction to the classical Ekman layer. Calculations of the wave-induced stress due to a wave spectrum representative of fast-moving swell demonstrate upward momentum transfer that is dominated by contributions from waves in the vicinity of the peak in the swell spectrum. This is in contrast to wind-driven waves whose wave-induced stress is dominated by very short wavelength waves. Hence the role of swell can be characterized by the inverse wave age based on the wave phase speed corresponding to the peak in the spectrum. For a spectrum of waves, the total momentum flux is found to reverse sign and become upward, from waves to wind, when the inverse wave age drops below the range 0.15–0.2, which agrees reasonably well with previously published oceanic observations.
Resumo:
We consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.
Resumo:
A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.
Resumo:
We report the characteristics of the three-dimensional, time evolving, atmospheric boundary layer that develops beneath an idealised, dry, baroclinic weather system. The boundary-layer structure is forced by thermal advection associated with the weather system. Large positive heat fluxes behind the cold front drive a vigorous convective boundary layer, whereas moderate negative heat fluxes in the warm sector between the cold and warm fronts generate shallow, stably stratified or neutral boundary layers. The forcing of the boundary-layer structure is quantified by forming an Eulerian mass budget integrated over the depth of the boundary layer. The mass budget indicates that tropospheric air is entrained into the boundary layer both in the vicinity of the high-pressure centre, and behind the cold front. It is then transported horizontally within the boundary layer and converges towards the cyclone's warm sector, whence it is ventilated out into the troposphere. This cycling of air is likely to be important for the ventilation of pollution out of the boundary layer, and for the transformation of the properties of large-scale air masses.
Resumo:
Midlatitude cyclones are important contributors to boundary layer ventilation. However, it is uncertain how efficient such systems are at transporting pollutants out of the boundary layer, and variations between cyclones are unexplained. In this study 15 idealized baroclinic life cycles, with a passive tracer included, are simulated to identify the relative importance of two transport processes: horizontal divergence and convergence within the boundary layer and large-scale advection by the warm conveyor belt. Results show that the amount of ventilation is insensitive to surface drag over a realistic range of values. This indicates that although boundary layer processes are necessary for ventilation they do not control the magnitude of ventilation. A diagnostic for the mass flux out of the boundary layer has been developed to identify the synoptic-scale variables controlling the strength of ascent in the warm conveyor belt. A very high level of correlation (R-2 values exceeding 0.98) is found between the diagnostic and the actual mass flux computed from the simulations. This demonstrates that the large-scale dynamics control the amount of ventilation, and the efficiency of midlatitude cyclones to ventilate the boundary layer can be estimated using the new mass flux diagnostic. We conclude that meteorological analyses, such as ERA-40, are sufficient to quantify boundary layer ventilation by the large-scale dynamics.
Resumo:
This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.
Resumo:
Europe is a densely populated region that is a significant global source of black carbon (BC) aerosol, but there is a lack of information regarding the physical properties and spatial/vertical distribution of rBC in the region. We present the first aircraft observations of sub-micron refractory BC (rBC) aerosol concentrations and physical properties measured by a single particle soot photometer (SP2) in the lower troposphere over Europe. The observations spanned a region roughly bounded by 50° to 60° N and from 15° W to 30° E. The measurements, made between April and September 2008, showed that average rBC mass concentrations ranged from about 300 ng m−3 near urban areas to approximately 50 ng m−3 in remote continental regions, lower than previous surface-based measurements. rBC represented between 0.5 and 3% of the sub-micron aerosol mass. Black carbon mass size distributions were log-normally distributed and peaked at approximately 180 nm, but shifted to smaller diameters (~160 nm) near source regions. rBC was correlated with carbon monoxide (CO) but had different ratios to CO depending on location and air mass. Light absorption coefficients were measured by particle soot absorption photometers on two separate aircraft and showed similar geographic patterns to rBC mass measured by the SP2. We summarize the rBC and light absorption measurements as a function of longitude and air mass age and also provide profiles of rBC mass concentrations and size distribution statistics. Our results will help evaluate model-predicted regional rBC concentrations and properties and determine regional and global climate impacts from rBC due to atmospheric heating and surface dimming.
Resumo:
The interaction of a terahertz beam with a sample containing a material boundary across the profile of the terahertz beam produces characteristic spectroscopic detail. A full vectorial model is presented to quantify boundary definition for a series of wedged geometries. As a result of this work, using simple geometric forms, we wish to be able to extend these ideas to characterize boundaries in more irregular samples, impacting most application areas of pulsed terahertz radiation.
Resumo:
We present a novel topology of the radial basis function (RBF) neural network, referred to as the boundary value constraints (BVC)-RBF, which is able to automatically satisfy a set of BVC. Unlike most existing neural networks whereby the model is identified via learning from observational data only, the proposed BVC-RBF offers a generic framework by taking into account both the deterministic prior knowledge and the stochastic data in an intelligent manner. Like a conventional RBF, the proposed BVC-RBF has a linear-in-the-parameter structure, such that it is advantageous that many of the existing algorithms for linear-in-the-parameters models are directly applicable. The BVC satisfaction properties of the proposed BVC-RBF are discussed. Finally, numerical examples based on the combined D-optimality-based orthogonal least squares algorithm are utilized to illustrate the performance of the proposed BVC-RBF for completeness.
Resumo:
The Boltzmann equation in presence of boundary and initial conditions, which describes the general case of carrier transport in microelectronic devices is analysed in terms of Monte Carlo theory. The classical Ensemble Monte Carlo algorithm which has been devised by merely phenomenological considerations of the initial and boundary carrier contributions is now derived in a formal way. The approach allows to suggest a set of event-biasing algorithms for statistical enhancement as an alternative of the population control technique, which is virtually the only algorithm currently used in particle simulators. The scheme of the self-consistent coupling of Boltzmann and Poisson equation is considered for the case of weighted particles. It is shown that particles survive the successive iteration steps.