The GRAPE aerosol retrieval algorithm

The aerosol component of the Oxford-Rutherford Aerosol and Cloud (ORAC) combined cloud and aerosol retrieval scheme is described and the theoretical performance of the algorithm is analysed. ORAC is an optimal estimation retrieval scheme for deriving cloud and aerosol properties from measurements made by imaging satellite radiometers and, when applied to cloud free radiances, provides estimates of aerosol optical depth at a wavelength of 550 nm, aerosol effective radius and surface reflectance at 550 nm. The aerosol retrieval component of ORAC has several incarnations – this paper addresses the version which operates in conjunction with the cloud retrieval component of ORAC (described by Watts et al., 1998), as applied in producing the Global Retrieval of ATSR Cloud Parameters and Evaluation (GRAPE) data-set.

Generalized beta generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

A 3D cloud-construction algorithm for the EarthCARE satellite mission

This article presents and assesses an algorithm that constructs 3D distributions of cloud from passive satellite imagery and collocated 2D nadir profiles of cloud properties inferred synergistically from lidar, cloud radar and imager data. It effectively widens the active–passive retrieved cross-section (RXS) of cloud properties, thereby enabling computation of radiative fluxes and radiances that can be compared with measured values in an attempt to perform radiative closure experiments that aim to assess the RXS. For this introductory study, A-train data were used to verify the scene-construction algorithm and only 1D radiative transfer calculations were performed. The construction algorithm fills off-RXS recipient pixels by computing sums of squared differences (a cost function F) between their spectral radiances and those of potential donor pixels/columns on the RXS. Of the RXS pixels with F lower than a certain value, the one with the smallest Euclidean distance to the recipient pixel is designated as the donor, and its retrieved cloud properties and other attributes such as 1D radiative heating rates are consigned to the recipient. It is shown that both the RXS itself and Moderate Resolution Imaging Spectroradiometer (MODIS) imagery can be reconstructed extremely well using just visible and thermal infrared channels. Suitable donors usually lie within 10 km of the recipient. RXSs and their associated radiative heating profiles are reconstructed best for extensive planar clouds and less reliably for broken convective clouds. Domain-average 1D broadband radiative fluxes at the top of theatmosphere(TOA)for (21 km)2 domains constructed from MODIS, CloudSat andCloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) data agree well with coincidental values derived from Clouds and the Earth’s Radiant Energy System (CERES) radiances: differences betweenmodelled and measured reflected shortwave fluxes are within±10Wm−2 for∼35% of the several hundred domains constructed for eight orbits. Correspondingly, for outgoing longwave radiation∼65% are within ±10Wm−2.

"Oft expectation fails": a time-series analysis of construction starts in the London office market

Expectations of future market conditions are generally acknowledged to be crucial for the development decision and hence for shaping the built environment. This empirical study of the Central London office market from 1987 to 2009 tests for evidence of adaptive and naive expectations. Applying VAR models and a recursive OLS regression with one-step forecasts, we find evidence of adaptive and naïve, rather than rational expectations of developers. Although the magnitude of the errors and the length of time lags vary over time and development cycles, the results confirm that developers’ decisions are explained to a large extent by contemporaneous and past conditions in both London submarkets. The corollary of this finding is that developers may be able to generate excess profits by exploiting market inefficiencies but this may be hindered in practice by the long periods necessary for planning and construction of the asset. More generally, the results of this study suggest that real estate cycles are largely generated endogenously rather than being the result of unexpected exogenous shocks.

The accuracy of valuations: expectation and reality

The relationship between valuations and the subsequent sale price continues to be a matter of both theoretical and practical interest. This paper reports the analysis of over 700 property sales made during the 1974/90 period. Initial results imply an average under-valuation of 7% and a standard error of 18% across the sample. A number of techniques are applied to the data set using other variables such as the region, the type of property and the return from the market to explain the difference between the valuation and the subsequent sale price. The analysis reduces the unexplained error; the bias is fully accounted for and the standard error is reduced to 15.3%. This model finds that about 6% of valuations over-estimated the sale price by more than 20% and about 9% of the valuations under-estimated the sale prices by more than 20%. The results suggest that valuations are marginally more accurate than might be expected, both from consideration of theoretical considerations and from comparison with the equivalent valuation in equity markets.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Expectation versus provision in the management and use of urban open space

This paper discusses the implications of the shifting cultural significance of public open space in urban areas. In particular, it focuses on the increasing dysfunction between people's expectations of that space and its actual provision and management. In doing so, the paper applies Lefebvre's ideas of spatiality to the evident paradigm shift from 'public' to 'private' culture, with its associated commodification of previously public space. While developing the construct of paradigm shift, the paper recognises that the former political notions inherent in the provision of public space remain in evidence. So whereas public parks were formerly seen as spaces of confrontation between the 'rationality' of public order as the 'irrationality' of individual leisure pursuits, they are now increasingly seen, particularly 'out of hours', as the domain of the dispossessed, to be defined and policed as 'dangerous'. Where once people were welcomed into public open spaces as a means of 'educating' them in good, acceptable, leisure practices, therefore, they are now increasingly excluded, but for the same ostensible reasons. Building on survey work undertaken in Reading, Berkshire, the paper illustrates how communities can become separated from 'their' space, leaving them with the overriding impression that they have been 'short-changed' in terms of both the provision and the management of urban open space. Rather than the intimacy of local space for local people, therefore, the paper argues that parks have become externalised places, increasingly responding to commercial definitions of culture and what is 'public'. Central urban open spaces are therefore increasingly becoming sites of stratification, signification of a consumer-constructed citizenship and valorisation of public life as a legitimate element of the market surface of town and city centres.

An improvement in clear-air turbulence forecasting based on spontaneous imbalance theory: the ULTURB algorithm

Recent research has shown that Lighthill–Ford spontaneous gravity wave generation theory, when applied to numerical model data, can help predict areas of clear-air turbulence. It is hypothesized that this is the case because spontaneously generated atmospheric gravity waves may initiate turbulence by locally modifying the stability and wind shear. As an improvement on the original research, this paper describes the creation of an ‘operational’ algorithm (ULTURB) with three modifications to the original method: (1) extending the altitude range for which the method is effective downward to the top of the boundary layer, (2) adding turbulent kinetic energy production from the environment to the locally produced turbulent kinetic energy production, and, (3) transforming turbulent kinetic energy dissipation to eddy dissipation rate, the turbulence metric becoming the worldwide ‘standard’. In a comparison of ULTURB with the original method and with the Graphical Turbulence Guidance second version (GTG2) automated procedure for forecasting mid- and upper-level aircraft turbulence ULTURB performed better for all turbulence intensities. Since ULTURB, unlike GTG2, is founded on a self-consistent dynamical theory, it may offer forecasters better insight into the causes of the clear-air turbulence and may ultimately enhance its predictability.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

Robust control system design for generalized state-space systems

Robustness in multi-variable control system design requires that the solution to the design problem be insensitive to perturbations in the system data. In this paper we discuss measures of robustness for generalized state-space, or descriptor, systems and describe algorithmic techniques for optimizing robustness for various applications.

A simple analysis of thermodynamic properties for classical plasmas: I. theory

By eliminating the short range negative divergence of the Debye–Hückel pair distribution function, but retaining the exponential charge screening known to operate at large interparticle separation, the thermodynamic properties of one-component plasmas of point ions or charged hard spheres can be well represented even in the strong coupling regime. Predicted electrostatic free energies agree within 5% of simulation data for typical Coulomb interactions up to a factor of 10 times the average kinetic energy. Here, this idea is extended to the general case of a uniform ionic mixture, comprising an arbitrary number of components, embedded in a rigid neutralizing background. The new theory is implemented in two ways: (i) by an unambiguous iterative algorithm that requires numerical methods and breaks the symmetry of cross correlation functions; and (ii) by invoking generalized matrix inverses that maintain symmetry and yield completely analytic solutions, but which are not uniquely determined. The extreme computational simplicity of the theory is attractive when considering applications to complex inhomogeneous fluids of charged particles.