A 3D stochastic cloud model for investigating the radiative properties of inhomogeneous cirrus clouds

(From author). Comments: First 3D stochastic/fractal model of cirrus; first detailed analysis & explanation of power spectra of ice water content, including first observations of 50-km scale break and mixing-induced steepening of spectrum; first demonstration of the potential effect of wind shear on radiative fluxes by changing fall-streak orientation. Has spawned work on the effect of 3D photon transport on the radiative effects of cirrus clouds.

Femtosecond evolution of spatially inhomogeneous carrier excitations: part 2: stochastic approach and GRID implementation

We present a stochastic approach for solving the quantum-kinetic equation introduced in Part I. A Monte Carlo method based on backward time evolution of the numerical trajectories is developed. The computational complexity and the stochastic error are investigated numerically. Variance reduction techniques are applied, which demonstrate a clear advantage with respect to the approaches based on symmetry transformation. Parallel implementation is realized on a GRID infrastructure.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Inhomogeneous two-dimensional turbulence in the atmosphere

Faced with the strongly nonlinear and apparently random behaviour of the energy-containing scales in the atmosphere, geophysical fluid dynamicists have attempted to understand the synoptic-scale atmospheric flow within the context of two-dimensional homogeneous turbulence theory (e.g. FJØRTOFT [1]; LEITH [2]). However atmospheric observations (BOER and SHEPHERD [3] and Fig.1) show that the synoptic-scale transient flow evolves in the presence of a planetary-scale, quasi-stationary background flow which is approximately zonal (east-west). Classical homogeneous 2-D turbulence theory is therefore not strictly applicable to the transient flow. One is led instead to study 2-D turbulence in the presence of a large-scale (barotropically stable) zonal jet inhomogeneity.

A finite element-spherical harmonics model for radiative transfer in inhomogeneous clouds. Part II. some applications

EVENT has been used to examine the effects of 3D cloud structure, distribution, and inhomogeneity on the scattering of visible solar radiation and the resulting 3D radiation field. Large eddy simulation and aircraft measurements are used to create realistic cloud fields which are continuous or broken with smooth or uneven tops. The values, patterns and variance in the resulting downwelling and upwelling radiation from incident visible solar radiation at different angles are then examined and compared to measurements. The results from EVENT confirm that 3D cloud structure is important in determining the visible radiation field, and that these results are strongly influenced by the solar zenith angle. The results match those from other models using visible solar radiation, and are supported by aircraft measurements of visible radiation, providing confidence in the new model.

A sodar for profiling in a spatially inhomogeneous urban environment

The urban boundary layer, above the canopy, is still poorly understood. One of the challenges is obtaining data by sampling more than a few meters above the rooftops, given the spatial and temporal inhomogeneities in both horizontal and vertical. Sodars are generally useful tools for ground-based remote sensing of winds and turbulence, but rely on horizontal homogeneity (as do lidars) in building up 3-component wind vectors from sampling three or more spatially separated volumes. The time taken for sound to travel to a typical range of 200 m and back is also a limitation. A sodar of radically different design is investigated, aimed at addressing these problems. It has a single vertical transmitted sound pulse. Doppler shifted signals are received from a number of volumes around the periphery of the transmitted beam with microphones which each having tight angular sensitivity at zenith angles slightly off-vertical. The spatial spread of sampled volumes is therefore smaller. By having more receiver microphones than a conventional sodar, the effect of smaller zenith angle is offset. More rapid profiling is also possible with a single vertical transmitted beam, instead of the usual multiple beams.A prototype design is described, together with initial field measurements. It is found that the beam forming using a single dish antenna and the drift of the sound pulse downwind both give rise to reduced performance compared with expectations. It is concluded that, while the new sodar works in principle, the compromises arising in the design mean that the expected advantages have not been realized

The role of nonhydrostatic dynamics in controlling development of a surface ocean front

Numerical studies of surface ocean fronts forced by inhomogeneous buoyancy loss show nonhydrostatic convective plumes coexisting with baroclinic eddies. The character of the vertical overturning depends sensitively on the treatment of the vertical momentum equation in the model. It is less well known how the frontal evolution over scales of O(10 km) is affected by these dynamics. Here, we compare highly resolved numerical experiments using nonhydrostatic and hydrostatic models and the convective-adjustment parametrization. The impact of nonhydrostatic processes on average cross-frontal transfer is weak compared to the effect of the O(1 km) scale baroclinic motions. For water-mass distribution and formation rate nonhydrostatic dynamics have similar influence to the baroclinic eddies although adequate resolution of the gradients in forcing fluxes is more important. The overall implication is that including nonhydrostatic surface frontal dynamics in ocean general circulation models will have only a minor effect on scales of O(1 km) and greater.

Chlorophyll-a in the rivers of eastern England

Chlorophyll-a concentration variations are described for two major river basins in England, the Humber and the Thames and related to catchment characteristics and nutrient concentrations across a range of rural, agricultural and urban/industrial settings. For all the rivers there are strong seasonal variations, with concentrations peaking in the spring and summer time when biological activity is at its highest. However, there are large variations in the magnitude of the seasonal effects across the rivers. For the spring-summer low-flow periods, average concentrations of chlorophyll-a correlate with soluble reactive phosphor-us (SRP). Chlorophyll-a is also correlated with particulate nitrogen (PN), organic carbon (POC) and suspended sediments. However, the strongest relationships are with catchment area and flow, where two straight line relationships are observed. The results indicate the importance of residence times for determining planktonic growth within the rivers. This is also indicated by the lack of chlorophyll-a response to lowering of SRP concentrations in several of the rivers in the area due to phosphorus stripping of effluents at major sewage treatment works. A key control on chlorophyll-a concentration may be the input of canal and reservoir waters during the growing period: this too relates to issues of residence times. However, there may well be a complex series of factors influencing residence time across the catchments due to features such as inhomogeneous flow within the catchments, a fractal distribution of stream channels that leads to a distribution of residence times and differences in planktonic inoculation sources. Industrial pollution on the Aire and Calder seems to have affected the relationship of chlorophyll-a with PN and POC. The results are discussed in relation to the Water Framework Directive. (c) 2006 Elsevier B.V. All rights reserved.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.