Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

Can we measure terrestrial photosynthesis from space directly, using spectral reflectance and fluorescence?

Attempts to estimate photosynthetic rate or gross primary productivity from remotely sensed absorbed solar radiation depend on knowledge of the light use efficiency (LUE). Early models assumed LUE to be constant, but now most researchers try to adjust it for variations in temperature and moisture stress. However, more exact methods are now required. Hyperspectral remote sensing offers the possibility of sensing the changes in the xanthophyll cycle, which is closely coupled to photosynthesis. Several studies have shown that an index (the photochemical reflectance index) based on the reflectance at 531 nm is strongly correlated with the LUE over hours, days and months. A second hyperspectral approach relies on the remote detection of fluorescence, which is a directly related to the efficiency of photosynthesis. We discuss the state of the art of the two approaches. Both have been demonstrated to be effective, but we specify seven conditions required before the methods can become operational.

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1

Cooled infrared filters and dichroics for the James Webb Space Telescope Mid-Infrared Instrument

The cooled infrared filters and dichroic beam splitters manufactured for the Mid-Infrared Instrument are key optical components for the selection and isolation of wavelengths in the study of astrophysical properties of stars, galaxies, and other planetary objects. We describe the spectral design and manufacture of the precision cooled filter coatings for the spectrometer (7 K) and imager (9 K). Details of the design methods used to achieve the spectral requirements, selection of thin film materials, deposition technique, and testing are presented together with the optical layout of the instrument. (C) 2008 Optical Society of America.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

Infrared filters for space-flight focal plane array applications

Infrared filters and coatings have been employed on many sensing radiometer instruments to measure the thermal emission profiles and concentrations of certian chemical constituents found in planetary atmospheres. The High Resolution Dynamics Limb Sounder ( HIRDLS) is an example of the most recent developments in limb-viewing radiometry by employing a cooled focal plane detector array to provide simultaneous multi-channel monitoring of emission from gas and aerosols over an altitude range between 8 - 70 km. The use of spectrally selective cooled detectors in focal plane arrays has simplified the optical layout of radiometers, greatly reducing the number of components in the optical train. this has inevitably led to increased demands for the enviromnetal durability of the focal plane filters because of the need to cut sub-millimeter sizes, whilst maintaining an optimal spectral performance. Additionally the remaining refractive optical elements require antireflection coatings which must cover the entire spectral range of the focal plane array channels, in this case 6 to 18µm, with a minimum of reflection and absorption. This paper describes the optical layout and spectral design requirements for filteriong in the HIRDLS instrument, and reports progress on the manufacturing and testing of the sub-millimetre sized cooled filters. We also report on the spectral and environmental performance of prototype wideband antireflection coatings which satisfy the requirements above.

Spectral characterisation of cooled filters for remote sensing

The improvements obtained on cooling atmospheric remote-sensing instruments for space flight applications has promoted research in characterization of the necessary optical filters. By modelling the effects of temperature on the dispersive spectrum of some constituent thin film materials, the cooled performance can be simulated and compared. multilayer filter designs with the measured spectra from actual filters. Two actual filters are discussed, for the 7µm region, one a composite cut-on/cut-off design of 13% HBW and the other an integral narrowband design of 4% HBW.

Exposure to space radiation of high-performance infrared multilayer-filters and materials technology experiments

Infrared multilayer interference filters have been used extensively in satellite radiometers for about 15 years. Filters manufactured by the University of Reading have been used in Nimbus 5, 6, and 7, TIROS N, and the Pioneer Venus orbiter. The ability of the filters to withstand the space environment in these applications is critical; if degradation takes place, the effects would range from worsening of signal-to-noise performance to complete system failure. An experiment on the LDEF will enable the filters, for the first time, to be subjected to authoritative spectral measurements following space exposure to ascertain their suitability for spacecraft use and to permit an understanding of degradation mechanisms.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

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.

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.

Terrestrial ecosystems from space: a review of earth observation products for macroecology applications

Aim Earth observation (EO) products are a valuable alternative to spectral vegetation indices. We discuss the availability of EO products for analysing patterns in macroecology, particularly related to vegetation, on a range of spatial and temporal scales. Location Global. Methods We discuss four groups of EO products: land cover/cover change, vegetation structure and ecosystem productivity, fire detection, and digital elevation models. We address important practical issues arising from their use, such as assumptions underlying product generation, product accuracy and product transferability between spatial scales. We investigate the potential of EO products for analysing terrestrial ecosystems. Results Land cover, productivity and fire products are generated from long-term data using standardized algorithms to improve reliability in detecting change of land surfaces. Their global coverage renders them useful for macroecology. Their spatial resolution (e.g. GLOBCOVER vegetation, 300 m; MODIS vegetation and fire, ≥ 500 m; ASTER digital elevation, 30 m) can be a limiting factor. Canopy structure and productivity products are based on physical approaches and thus are independent of biome-specific calibrations. Active fire locations are provided in near-real time, while burnt area products show actual area burnt by fire. EO products can be assimilated into ecosystem models, and their validation information can be employed to calculate uncertainties during subsequent modelling. Main conclusions Owing to their global coverage and long-term continuity, EO end products can significantly advance the field of macroecology. EO products allow analyses of spatial biodiversity, seasonal dynamics of biomass and productivity, and consequences of disturbances on regional to global scales. Remaining drawbacks include inter-operability between products from different sensors and accuracy issues due to differences between assumptions and models underlying the generation of different EO products. Our review explains the nature of EO products and how they relate to particular ecological variables across scales to encourage their wider use in ecological applications.

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).

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).