On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths

The single scattering albedo w_0l in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength l and droplet size r. This note shows that for water droplets at weakly absorbing wavelengths, the ratio w_0l(r)/w_0l(r0) of two single scattering albedo spectra is a linear function of w_0l(r). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum w_0l(r) via one known spectrum w_0l(r0). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.

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 analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.

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.

Improving EU biofuels policy? Greenhouse gas emissions, policy efficiency, and WTO compatibility

Both the EU’s Renewable Energy Directive (RED) and Article 7a of its Fuel Quality Directive (FQD) seek to reduce greenhouse gas (GHG) emissions from transport fuels. The RED mandates a 10% share of renewable energy in transport fuels by 2020, whilst the FQD requires a 6% reduction in GHG emissions (from a 2010 base) by the same date. In practice, it will mainly be biofuels that economic operators will use to meet these requirements, but the different approaches can lead to either the RED, or the FQD, acting as the binding constraint. A common set of environmental sustainability criteria apply to biofuels under both the RED and the FQD. In particular, biofuels have to demonstrate a 35% (later increasing to 50/60%) saving in life-cycle GHG emissions. This could be problematic in the World Trade Organization (WTO), as a non-compliant biofuel with a 34% emissions saving would probably be judged to be ‘like’ a compliant biofuel. A more economically rational way to reduce GHG emissions, and one that might attract greater public support, would be for the RED to reward emission reductions along the lines of the FQD. Moreover, this modification would probably make the provisions more acceptable in the WTO, as there would be a clearer link between policy measures and the objective of reductions in GHG emissions; and the combination of the revised RED and the FQD would lessen the commercial incentive to import biofuels with modest GHG emission savings, and thus reduce the risk of trade tension.

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

Effects of non-uniform crosswind fields on scintillometry measurements

The effects of a non-uniform wind field along the path of a scintillometer are investigated. Theoretical spectra are calculated for a range of scenarios where the crosswind varies in space or time and compared to the ‘ideal’ spectrum based on a constant uniform crosswind. It is verified that the refractive-index structure parameter relation with the scintillometer signal remains valid and invariant for both spatially and temporally-varying crosswinds. However, the spectral shape may change significantly preventing accurate estimation of the crosswind speed from the peak of the frequency spectrum and retrieval of the structure parameter from the plateau of the power spectrum. On comparison with experimental data, non-uniform crosswind conditions could be responsible for previously unexplained features sometimes seen in observed spectra. By accounting for the distribution of crosswind, theoretical spectra can be generated that closely replicate the observations, leading to a better understanding of the measurements. Spatial variability of wind speeds should be expected for paths other than those that are parallel to the surface and over flat, homogenous areas, whilst fluctuations in time are important for all sites.

An ultimatum bargaining experiment on trade union efficiency

We present an ultimatum wage bargaining experiment showing that a trade union facilitating non-binding communication among workers, raises wages by simultaneously increasing employers’ posted offers and toughening the bargaining position of employees, without reducing overall market efficiency.

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Model predictions of the occurrence of non-Maxwellian plasmas, and analysis of their effects on EISCAT data

The recent identification of non-thermal plasmas using EISCAT data has been made possible by their occurrence during large, short-lived flow bursts. For steady, yet rapid, ion convection the only available signature is the shape of the spectrum, which is unreliable because it is open to distortion by noise and sampling uncertainty and can be mimicked by other phenomena. Nevertheless, spectral shape does give an indication of the presence of non-thermal plasma, and the characteristic shape has been observed for long periods (of the order of an hour or more) in some experiments. To evaluate this type of event properly one needs to compare it to what would be expected theoretically. Predictions have been made using the coupled thermosphere-ionosphere model developed at University College London and the University of Sheffield to show where and when non-Maxwellian plasmas would be expected in the auroral zone. Geometrical and other factors then govern whether these are detectable by radar. The results are applicable to any incoherent scatter radar in this area, but the work presented here concentrates on predictions with regard to experiments on the EISCAT facility.

Non-Maxwellian ion velocity distributions observed using EISCAT

Recent observations from the EISCAT incoherent scatter radar have revealed bursts of poleward ion flow in the dayside auroral ionosphere which are consistent with the ionospheric signature of flux transfer events at the magnetopause. These bursts frequently contain ion drifts which exceed the neutral thermal speed and, because the neutral thermospheric wind is incapable of responding sufficiently rapidly, toroidal, non-Maxwellian ion velocity distributions are expected. The EISCAT observations are made with high time resolution (15 seconds) and at a large angle to the geomagnetic field (73.5°), allowing the non-Maxwellian nature of the distribution to be observed remotely for the first time. The observed features are also strongly suggestive of a toroidal distribution: characteristic spectral shape, increased scattered power (both consistent with reduced Landau damping and enhanced electric field fluctuations) and excessively high line-of-sight ion temperatures deduced if a Maxwellian distribution is assumed. These remote sensing observations allow the evolution of the distributions to be observed. They are found to be non-Maxwellian whenever the ion drift exceeds the neutral thermal speed, indicating that such distributions can exist over the time scale of the flow burst events (several minutes).

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

Detection of coherent airstreams using cluster analysis: application to an extratropical cyclone

Flow in geophysical fluids is commonly summarized by coherent streams, for example conveyor belt flows in extratropical cyclones or jet streaks in the upper troposphere. Typically, parcel trajectories are calculated from the flow field and subjective thresholds are used to distinguish coherent streams of interest. This methodology contribution develops a more objective approach to distinguish coherent airstreams within extratropical cyclones. Agglomerative clustering is applied to trajectories along with a method to identify the optimal number of cluster classes. The methodology is applied to trajectories associated with the low-level jets of a well-studied extratropical cyclone. For computational efficiency, a constraint that trajectories must pass through these jet regions is applied prior to clustering; the partitioning into different airstreams is then performed by the agglomerative clustering. It is demonstrated that the methodology can identify the salient flow structures of cyclones: the warm and cold conveyor belts. A test focusing on the airstreams terminating at the tip of the bent-back front further demonstrates the success of the method in that it can distinguish fine-scale flow structure such as descending sting jet airstreams.

How is the balance of a forecast ensemble affected by adaptive and non-adaptive localization schemes?

This paper investigates the effect on balance of a number of Schur product-type localization schemes which have been designed with the primary function of reducing spurious far-field correlations in forecast error statistics. The localization schemes studied comprise a non-adaptive scheme (where the moderation matrix is decomposed in a spectral basis), and two adaptive schemes, namely a simplified version of SENCORP (Smoothed ENsemble COrrelations Raised to a Power) and ECO-RAP (Ensemble COrrelations Raised to A Power). The paper shows, we believe for the first time, how the degree of balance (geostrophic and hydrostatic) implied by the error covariance matrices localized by these schemes can be diagnosed. Here it is considered that an effective localization scheme is one that reduces spurious correlations adequately but also minimizes disruption of balance (where the 'correct' degree of balance or imbalance is assumed to be possessed by the unlocalized ensemble). By varying free parameters that describe each scheme (e.g. the degree of truncation in the schemes that use the spectral basis, the 'order' of each scheme, and the degree of ensemble smoothing), it is found that a particular configuration of the ECO-RAP scheme is best suited to the convective-scale system studied. According to our diagnostics this ECO-RAP configuration still weakens geostrophic and hydrostatic balance, but overall this is less so than for other schemes.