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.

Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence

We study two-dimensional (2D) turbulence in a doubly periodic domain driven by a monoscale-like forcing and damped by various dissipation mechanisms of the form νμ(−Δ)μ. By “monoscale-like” we mean that the forcing is applied over a finite range of wavenumbers kmin≤k≤kmax, and that the ratio of enstrophy injection η≥0 to energy injection ε≥0 is bounded by kmin2ε≤η≤kmax2ε. Such a forcing is frequently considered in theoretical and numerical studies of 2D turbulence. It is shown that for μ≥0 the asymptotic behaviour satisfies ∥u∥12≤kmax2∥u∥2, where ∥u∥2 and ∥u∥12 are the energy and enstrophy, respectively. If the condition of monoscale-like forcing holds only in a time-mean sense, then the inequality holds in the time mean. It is also shown that for Navier–Stokes turbulence (μ=1), the time-mean enstrophy dissipation rate is bounded from above by 2ν1kmax2. These results place strong constraints on the spectral distribution of energy and enstrophy and of their dissipation, and thereby on the existence of energy and enstrophy cascades, in such systems. In particular, the classical dual cascade picture is shown to be invalid for forced 2D Navier–Stokes turbulence (μ=1) when it is forced in this manner. Inclusion of Ekman drag (μ=0) along with molecular viscosity permits a dual cascade, but is incompatible with the log-modified −3 power law for the energy spectrum in the enstrophy-cascading inertial range. In order to achieve the latter, it is necessary to invoke an inverse viscosity (μ<0). These constraints on permissible power laws apply for any spectrally localized forcing, not just for monoscale-like forcing.

Centrality and spectral radius in dynamic communication networks

We explore the influence of the choice of attenuation factor on Katz centrality indices for evolving communication networks. For given snapshots of a network observed over a period of time, recently developed communicability indices aim to identify best broadcasters and listeners in the network. In this article, we looked into the sensitivity of communicability indices on the attenuation factor constraint, in relation to spectral radius (the largest eigenvalue) of the network at any point in time and its computation in the case of large networks. We proposed relaxed communicability measures where the spectral radius bound on attenuation factor is relaxed and the adjacency matrix is normalised in order to maintain the convergence of the measure. Using a vitality based measure of both standard and relaxed communicability indices we looked at the ways of establishing the most important individuals for broadcasting and receiving of messages related to community bridging roles. We illustrated our findings with two examples of real-life networks, MIT reality mining data set of daily communications between 106 individuals during one year and UK Twitter mentions network, direct messages on Twitter between 12.4k individuals during one week.

Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere

Nonlinear spectral transfers of kinetic energy and enstrophy, and stationary-transient interaction, are studied using global FGGE data for January 1979. It is found that the spectral transfers arise primarily from a combination, in roughly equal measure, of pure transient and mixed stationary-transient interactions. The pure transient interactions are associated with a transient eddy field which is approximately locally homogeneous and isotropic, and they appear to be consistently understood within the context of two-dimensional homogeneous turbulence. Theory based on spatial wale separation concepts suggests that the mixed interactions may be understood physically, to a first approximation, as a process of shear-induced spectral transfer of transient enstrophy along lines of constant zonal wavenumber. This essentially conservative enstrophy transfer generally involves highly nonlocal stationary-transient energy conversions. The observational analysis demonstrates that the shear-induced transient enstrophy transfer is mainly associated with intermediate-scale (zonal wavenumber m > 3) transients and is primarily to smaller (meridional) scales, so that the transient flow acts as a source of stationary energy. In quantitative terms, this transient-eddy rectification corresponds to a forcing timescale in the stationary energy budget which is of the same order of magnitude as most estimates of the damping timescale in simple stationary-wave models (5 to 15 days). Moreover, the nonlinear interactions involved are highly nonlocal and cover a wide range of transient scales of motion.

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Modeling ocean primary production: sensitivity to spectral resolution of attenuation and absorption of light

Modeling the vertical penetration of photosynthetically active radiation (PAR) through the ocean, and its utilization by phytoplankton, is fundamental to simulating marine primary production. The variation of attenuation and absorption of light with wavelength suggests that photosynthesis should be modeled at high spectral resolution, but this is computationally expensive. To model primary production in global 3d models, a balance between computer time and accuracy is necessary. We investigate the effects of varying the spectral resolution of the underwater light field and the photosynthetic efficiency of phytoplankton (α∗), on primary production using a 1d coupled ecosystem ocean turbulence model. The model is applied at three sites in the Atlantic Ocean (CIS (∼60°N), PAP (∼50°N) and ESTOC (∼30°N)) to include the effect of different meteorological forcing and parameter sets. We also investigate three different methods for modeling α∗ – as a fixed constant, varying with both wavelength and chlorophyll concentration [Bricaud, A., Morel, A., Babin, M., Allali, K., Claustre, H., 1998. Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters. Analysis and implications for bio-optical models. J. Geophys. Res. 103, 31033–31044], and using a non-spectral parameterization [Anderson, T.R., 1993. A spectrally averaged model of light penetration and photosynthesis. Limnol. Oceanogr. 38, 1403–1419]. After selecting the appropriate ecosystem parameters for each of the three sites we vary the spectral resolution of light and α∗ from 1 to 61 wavebands and study the results in conjunction with the three different α∗ estimation methods. The results show modeled estimates of ocean primary productivity are highly sensitive to the degree of spectral resolution and α∗. For accurate simulations of primary production and chlorophyll distribution we recommend a spectral resolution of at least six wavebands if α∗ is a function of wavelength and chlorophyll, and three wavebands if α∗ is a fixed value.

CP-OQAM-OFDM based SC-FDMA: adjustable user bandwidth and space-time coding

The discrete Fourier transmission spread OFDM DFTS-OFDM) based single-carrier frequency division multiple access (SC-FDMA) has been widely adopted due to its lower peak-to-average power ratio (PAPR) of transmit signals compared with OFDM. However, the offset modulation, which has lower PAPR than general modulation, cannot be directly applied into the existing SC-FDMA. When pulse-shaping filters are employed to further reduce the envelope fluctuation of transmit signals of SC-FDMA, the spectral efficiency degrades as well. In order to overcome such limitations of conventional SC-FDMA, this paper for the first time investigated cyclic prefixed OQAMOFDM (CP-OQAM-OFDM) based SC-FDMA transmission with adjustable user bandwidth and space-time coding. Firstly, we propose CP-OQAM-OFDM transmission with unequally-spaced subbands. We then apply it to SC-FDMA transmission and propose a SC-FDMA scheme with the following features: a) the transmit signal of each user is offset modulated single-carrier with frequency-domain pulse-shaping; b) the bandwidth of each user is adjustable; c) the spectral efficiency does not decrease with increasing roll-off factors. To combat both inter-symbolinterference and multiple access interference in frequencyselective fading channels, a joint linear minimum mean square error frequency domain equalization using a prior information with low complexity is developed. Subsequently, we construct space-time codes for the proposed SC-FDMA. Simulation results confirm the powerfulness of the proposed CP-OQAM-OFDM scheme (i.e., effective yet with low complexity).

A review of measurement-based assessments of the aerosol direct radiative effect and forcing

Aerosols affect the Earth's energy budget directly by scattering and absorbing radiation and indirectly by acting as cloud condensation nuclei and, thereby, affecting cloud properties. However, large uncertainties exist in current estimates of aerosol forcing because of incomplete knowledge concerning the distribution and the physical and chemical properties of aerosols as well as aerosol-cloud interactions. In recent years, a great deal of effort has gone into improving measurements and datasets. It is thus feasible to shift the estimates of aerosol forcing from largely model-based to increasingly measurement-based. Our goal is to assess current observational capabilities and identify uncertainties in the aerosol direct forcing through comparisons of different methods with independent sources of uncertainties. Here we assess the aerosol optical depth (τ), direct radiative effect (DRE) by natural and anthropogenic aerosols, and direct climate forcing (DCF) by anthropogenic aerosols, focusing on satellite and ground-based measurements supplemented by global chemical transport model (CTM) simulations. The multi-spectral MODIS measures global distributions of aerosol optical depth (τ) on a daily scale, with a high accuracy of ±0.03±0.05τ over ocean. The annual average τ is about 0.14 over global ocean, of which about 21%±7% is contributed by human activities, as estimated by MODIS fine-mode fraction. The multi-angle MISR derives an annual average AOD of 0.23 over global land with an uncertainty of ~20% or ±0.05. These high-accuracy aerosol products and broadband flux measurements from CERES make it feasible to obtain observational constraints for the aerosol direct effect, especially over global the ocean. A number of measurement-based approaches estimate the clear-sky DRE (on solar radiation) at the top-of-atmosphere (TOA) to be about -5.5±0.2 Wm-2 (median ± standard error from various methods) over the global ocean. Accounting for thin cirrus contamination of the satellite derived aerosol field will reduce the TOA DRE to -5.0 Wm-2. Because of a lack of measurements of aerosol absorption and difficulty in characterizing land surface reflection, estimates of DRE over land and at the ocean surface are currently realized through a combination of satellite retrievals, surface measurements, and model simulations, and are less constrained. Over the oceans the surface DRE is estimated to be -8.8±0.7 Wm-2. Over land, an integration of satellite retrievals and model simulations derives a DRE of -4.9±0.7 Wm-2 and -11.8±1.9 Wm-2 at the TOA and surface, respectively. CTM simulations derive a wide range of DRE estimates that on average are smaller than the measurement-based DRE by about 30-40%, even after accounting for thin cirrus and cloud contamination. A number of issues remain. Current estimates of the aerosol direct effect over land are poorly constrained. Uncertainties of DRE estimates are also larger on regional scales than on a global scale and large discrepancies exist between different approaches. The characterization of aerosol absorption and vertical distribution remains challenging. The aerosol direct effect in the thermal infrared range and in cloudy conditions remains relatively unexplored and quite uncertain, because of a lack of global systematic aerosol vertical profile measurements. A coordinated research strategy needs to be developed for integration and assimilation of satellite measurements into models to constrain model simulations. Enhanced measurement capabilities in the next few years and high-level scientific cooperation will further advance our knowledge.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Synergistic angular and spectral estimation of aerosol properties using CHRIS/PROBA-1 and simulated Sentinel-3~data

A method has been developed to estimate Aerosol Optical Depth (AOD), Fine Mode Fraction (FMF) and Single Scattering Albedo (SSA) over land surfaces using simulated Sentinel-3 data. The method uses inversion of a coupled surface/atmosphere radiative transfer model, and includes a general physical model of angular surface reflectance. An iterative process is used to determine the optimum value of the aerosol properties providing the best fit of the corrected reflectance values for a number of view angles and wavelengths with those provided by the physical model. A method of estimating AOD using only angular retrieval has previously been demonstrated on data from the ENVISAT and PROBA-1 satellite instruments, and is extended here to the synergistic spectral and angular sampling of Sentinel-3 and the additional aerosol properties. The method is tested using hyperspectral, multi-angle Compact High Resolution Imaging Spectrometer (CHRIS) images. The values obtained from these CHRIS observations are validated using ground based sun-photometer measurements. Results from 22 image sets using the synergistic retrieval and improved aerosol models show an RMSE of 0.06 in AOD, reduced to 0.03 over vegetated targets.

Derivation of an urban materials spectral library through emittance and reflectance spectroscopy

Recent advances in thermal infrared remote sensing include the increased availability of airborne hyperspectral imagers (such as the Hyperspectral Thermal Emission Spectrometer, HyTES, or the Telops HyperCam and the Specim aisaOWL), and it is planned that an increased number spectral bands in the long-wave infrared (LWIR) region will soon be measured from space at reasonably high spatial resolution (by imagers such as HyspIRI). Detailed LWIR emissivity spectra are required to best interpret the observations from such systems. This includes the highly heterogeneous urban environment, whose construction materials are not yet particularly well represented in spectral libraries. Here, we present a new online spectral library of urban construction materials including LWIR emissivity spectra of 74 samples of impervious surfaces derived using measurements made by a portable Fourier Transform InfraRed (FTIR) spectrometer. FTIR emissivity measurements need to be carefully made, else they are prone to a series of errors relating to instrumental setup and radiometric calibration, which here relies on external blackbody sources. The performance of the laboratory-based emissivity measurement approach applied here, that in future can also be deployed in the field (e.g. to examine urban materials in situ), is evaluated herein. Our spectral library also contains matching short-wave (VIS–SWIR) reflectance spectra observed for each urban sample. This allows us to examine which characteristic (LWIR and) spectral signatures may in future best allow for the identification and discrimination of the various urban construction materials, that often overlap with respect to their chemical/mineralogical constituents. Hyperspectral or even strongly multi-spectral LWIR information appears especially useful, given that many urban materials are composed of minerals exhibiting notable reststrahlen/absorption effects in this spectral region. The final spectra and interpretations are included in the London Urban Micromet data Archive (LUMA; http://LondonClimate.info/LUMA/SLUM.html).

New opportunities for secure communication networks using shaped femtosecond laser pulses inducing filamentation processes in the atmosphere

The current study discusses new opportunities for secure ground to satellite communications using shaped femtosecond pulses that induce spatial hole burning in the atmosphere for efficient communications with data encoded within super-continua generated by femtosecond pulses. Refractive index variation across the different layers in the atmosphere may be modelled using assumptions that the upper strata of the atmosphere and troposphere behaving as layered composite amorphous dielectric networks composed of resistors and capacitors with different time constants across each layer. Input-output expressions of the dynamics of the networks in the frequency domain provide the transmission characteristics of the propagation medium. Femtosecond pulse shaping may be used to optimize the pulse phase-front and spectral composition across the different layers in the atmosphere. A generic procedure based on evolutionary algorithms to perform the pulse shaping is proposed. In contrast to alternative procedures that would require ab initio modelling and calculations of the propagation constant for the pulse through the atmosphere, the proposed approach is adaptive, compensating for refractive index variations along the column of air between the transmitter and receiver.

(Re)shaping the South Bank: the (post)politics of sustainable place-making

While the private sector has long been in the vanguard of shaping and managing urban environs, under the New Labour government business actors were also heralded as key agents in the delivery of sustainable places. Policy interventions, such as Business Improvement Districts (BIDs), saw business-led local partnerships positioned as key drivers in the production of economically, socially and environmentally sustainable urban communities. This research considers how one business-led body, South Bank Employer’s Group (SBEG), has inserted itself into, and influenced, local (re)development trajectories. Interview, observational and archival data are used to explore how, in a neighbourhood noted for its turbulent and conflictual development past, SBEG has led on a series of regeneration programmes that it asserts will create a “better South Bank for all”. A belief in consensual solutions underscored New Labour’s urban agenda and cast regeneration as a politically neutral process in which different stakeholders can reach mutually beneficial solutions (Southern, 2001). For authors such as Mouffe (2005), the search for consensus represents a move towards a ‘post-political’ approach to governing in which the (necessarily) antagonistic nature of the political is denied. The research utilises writings on the ‘post-political’ condition to frame an empirical exploration of regeneration at the neighbourhood level. It shows how SBEG has brokered a consensual vision of regeneration with the aim of overriding past disagreements about local development. While this may be seen as an attempt to enact what Honig (1993: 3) calls the ‘erasure of resistance from political orderings’ by assuming control of regeneration agendas (see also Baeten, 2009), the research shows that ‘resistances’ to SBEG’s activities continue to be expressed in a series of ways. These resistances suggest that, while increasingly ‘post-political’ in character, local place shaping continues to evidence what Massey (2005: 10) calls the ‘space of loose ends and missing links’ from which political activity can, at least potentially, emerge.