Spectrally invariant approximation within atmospheric radiative transfer

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These ‘‘spectrally invariant relationships’’ are the consequence of wavelength independence of the extinction coefficient and scattering phase function in veg- etation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accu- rately describe the extinction and scattering properties of cloudy atmospheres. The validity of the as- sumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Formal theory building for the avalanche game: explaining counter-intuitive behaviour of a complex system using geometrical and human behavioural/physiological effects

In 'Avalanche', an object is lowered, players staying in contact throughout. Normally the task is easily accomplished. However, with larger groups counter-intuitive behaviours appear. The paper proposes a formal theory for the underlying causal mechanisms. The aim is to not only provide an explicit, testable hypothesis for the source of the observed modes of behaviour-but also to exemplify the contribution that formal theory building can make to understanding complex social phenomena. Mapping reveals the importance of geometry to the Avalanche game; each player has a pair of balancing loops, one involved in lowering the object, the other ensuring contact. For more players, sets of balancing loops interact and these can allow dominance by reinforcing loops, causing the system to chase upwards towards an ever-increasing goal. However, a series of other effects concerning human physiology and behaviour (HPB) is posited as playing a role. The hypothesis is therefore rigorously tested using simulation. For simplicity a 'One Degree of Freedom' case is examined, allowing all of the effects to be included whilst rendering the analysis more transparent. Formulation and experimentation with the model gives insight into the behaviours. Multi-dimensional rate/level analysis indicates that there is only a narrow region in which the system is able to move downwards. Model runs reproduce the single 'desired' mode of behaviour and all three of the observed 'problematic' ones. Sensitivity analysis gives further insight into the system's modes and their causes. Behaviour is seen to arise only when the geometric effects apply (number of players greater than degrees of freedom of object) in combination with a range of HPB effects. An analogy exists between the co-operative behaviour required here and various examples: conflicting strategic objectives in organizations; Prisoners' Dilemma and integrated bargaining situations. Additionally, the game may be relatable in more direct algebraic terms to situations involving companies in which the resulting behaviours are mediated by market regulations. Finally, comment is offered on the inadequacy of some forms of theory building and the case is made for formal theory building involving the use of models, analysis and plausible explanations to create deep understanding of social phenomena.

Realistic mean field forward predictions for the integration of co-registered EEG/fMRI

Brain activity can be measured non-invasively with functional imaging techniques. Each pixel in such an image represents a neural mass of about 105 to 107 neurons. Mean field models (MFMs) approximate their activity by averaging out neural variability while retaining salient underlying features, like neurotransmitter kinetics. However, MFMs incorporating the regional variability, realistic geometry and connectivity of cortex have so far appeared intractable. This lack of biological realism has led to a focus on gross temporal features of the EEG. We address these impediments and showcase a "proof of principle" forward prediction of co-registered EEG/fMRI for a full-size human cortex in a realistic head model with anatomical connectivity, see figure 1. MFMs usually assume homogeneous neural masses, isotropic long-range connectivity and simplistic signal expression to allow rapid computation with partial differential equations. But these approximations are insufficient in particular for the high spatial resolution obtained with fMRI, since different cortical areas vary in their architectonic and dynamical properties, have complex connectivity, and can contribute non-trivially to the measured signal. Our code instead supports the local variation of model parameters and freely chosen connectivity for many thousand triangulation nodes spanning a cortical surface extracted from structural MRI. This allows the introduction of realistic anatomical and physiological parameters for cortical areas and their connectivity, including both intra- and inter-area connections. Proper cortical folding and conduction through a realistic head model is then added to obtain accurate signal expression for a comparison to experimental data. To showcase the synergy of these computational developments, we predict simultaneously EEG and fMRI BOLD responses by adding an established model for neurovascular coupling and convolving "Balloon-Windkessel" hemodynamics. We also incorporate regional connectivity extracted from the CoCoMac database [1]. Importantly, these extensions can be easily adapted according to future insights and data. Furthermore, while our own simulation is based on one specific MFM [2], the computational framework is general and can be applied to models favored by the user. Finally, we provide a brief outlook on improving the integration of multi-modal imaging data through iterative fits of a single underlying MFM in this realistic simulation framework.

Comments on 'Balance and the slow quasimanifold: some explicit results'

The concept of slow vortical dynamics and its role in theoretical understanding is central to geophysical fluid dynamics. It leads, for example, to “potential vorticity thinking” (Hoskins et al. 1985). Mathematically, one imagines an invariant manifold within the phase space of solutions, called the slow manifold (Leith 1980; Lorenz 1980), to which the dynamics are constrained. Whether this slow manifold truly exists has been a major subject of inquiry over the past 20 years. It has become clear that an exact slow manifold is an exceptional case, restricted to steady or perhaps temporally periodic flows (Warn 1997). Thus the concept of a “fuzzy slow manifold” (Warn and Ménard 1986) has been suggested. The idea is that nearly slow dynamics will occur in a stochastic layer about the putative slow manifold. The natural question then is, how thick is this layer? In a recent paper, Ford et al. (2000) argue that Lighthill emission—the spontaneous emission of freely propagating acoustic waves by unsteady vortical flows—is applicable to the problem of balance, with the Mach number Ma replaced by the Froude number F, and that it is a fundamental mechanism for this fuzziness. They consider the rotating shallow-water equations and find emission of inertia–gravity waves at O(F2). This is rather surprising at first sight, because several studies of balanced dynamics with the rotating shallow-water equations have gone beyond second order in F, and found only an exponentially small unbalanced component (Warn and Ménard 1986; Lorenz and Krishnamurthy 1987; Bokhove and Shepherd 1996; Wirosoetisno and Shepherd 2000). We have no technical objection to the analysis of Ford et al. (2000), but wish to point out that it depends crucially on R 1, where R is the Rossby number. This condition requires the ratio of the characteristic length scale of the flow L to the Rossby deformation radius LR to go to zero in the limit F → 0. This is the low Froude number scaling of Charney (1963), which, while originally designed for the Tropics, has been argued to be also relevant to mesoscale dynamics (Riley et al. 1981). If L/LR is fixed, however, then F → 0 implies R → 0, which is the standard quasigeostrophic scaling of Charney (1948; see, e.g., Pedlosky 1987). In this limit there is reason to expect the fuzziness of the slow manifold to be “exponentially thin,” and balance to be much more accurate than is consistent with (algebraic) Lighthill emission.

The roles and competencies of HR managers in Slovenian multinational companies

Purpose – The HRM literature provides various typologies of the HR managers’ roles in organizations. The purpose of this paper is to examine how the roles and required competencies of HR managers in Slovenian multinational companies change when these companies enter the international arena. Design/methodology/approach – The authors explored the total population of 25 Slovenian multinational companies (MNCs) operating in Serbia. In these companies the authors conducted interviews with 16 expatriates working in branches in Serbia, sent questionnaires to the CEOs, and conducted a survey of 50 HR managers and interviews with 15 of them. The authors used a triangulation approach and analyzed the results by multivariate methods and content analysis. Findings – The authors found that the complexity of HR managers’ roles, and expectations of their competencies, increases with an increasing level of internationalization of companies. Orientation to people and conflict resolution are seen as elementary competencies needed in all stages of internationalization. The key competence is seen to be strategic thinking that, according to CEOs and expatriates, goes hand in hand with cultural sensitivity, openness to change and a comprehensive understanding of the international environment and business processes. Practical implications – These results can potentially be used for assessing the HRM roles and competencies in different stages of company internationalization, especially MNCs operating in the ex-communist states of Europe, and will help HR managers to support expatriates, CEOs and other employees working in branches abroad more efficiently. Originality/value – This study contributes to the review and evaluation of the quite limited research on HR managers’ roles and competencies in MNCs. It focuses on MNCs and outward internationalization in the Central and Eastern European region. It contributes to studies of the HR managers’ roles and competencies and is the first study to establish a set of roles and competencies for HR managers in Slovenian MNCs.

Typographic layout and first impressions: testing how changes in text layout influence reader's judgments of documents

This study explores how the typographic layout of information influences readers' impressions of magazine contents pages. Thirteen descriptors were used in a paired comparison procedure that assessed whether participants' rhetorical impressions of a set of six controlled documents change in relation to variations in layout. The combinations of layout attributes tested were derived from the structural attributes associated with three patterns of typographic differentiation (high, moderate, and low) described in a previous study (see Moys, 2014). The content and the range of stylistic attributes applied to the test material were controlled in order to focus on layout attributes. Triangulation of the quantitative and qualitative data indicates that, even within the experimental confines of limited stylistic differentiation, the layout attributes associated with patterns of high, moderate, and low typographic differentiation do influence readers' rhetorical judgments. In addition, the findings emphasize the importance of considering inter-relationships between clusters of typographic attributes rather than testing isolated variables.

Researching farmer behaviour in climate change adaptation and sustainable agriculture: lessons learned from five case studies

Understanding farmer behaviour is needed for local agricultural systems to produce food sustainably while facing multiple pressures. We synthesize existing literature to identify three fundamental questions that correspond to three distinct areas of knowledge necessary to understand farmer behaviour: 1) decision-making model; 2) cross-scale and cross-level pressures; and 3) temporal dynamics. We use this framework to compare five interdisciplinary case studies of agricultural systems in distinct geographical contexts across the globe. We find that these three areas of knowledge are important to understanding farmer behaviour, and can be used to guide the interdisciplinary design and interpretation of studies in the future. Most importantly, we find that these three areas need to be addressed simultaneously in order to understand farmer behaviour. We also identify three methodological challenges hindering this understanding: the suitability of theoretical frameworks, the trade-offs among methods and the limited timeframe of typical research projects. We propose that a triangulation research strategy that makes use of mixed methods, or collaborations between researchers across mixed disciplines, can be used to successfully address all three areas simultaneously and show how this has been achieved in the case studies. The framework facilitates interdisciplinary research on farmer behaviour by opening up spaces of structured dialogue on assumptions, research questions and methods employed in investigation.

Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

'Rules of engagement’: how experiential learning facilitates the formation of a public–private partnership in Russia

Purpose – The purpose of this paper is to investigate to what extent one can apply experiential learning theory (ELT) to the public-private partnership (PPP) setting in Russia and to draw insights regarding the learning cycle ' s nature. Additionally, the paper assesses whether the PPP case confirms Kolb ' s ELT. Design/methodology/approach – The case study draws upon primary data which the authors collected by interviewing informants including a PPP operator ' s managers, lawyers from Russian law firms and an expert from the National PPP Centre. The authors accomplished data source triangulation in order to ensure a high degree of research validity. Findings – Experiential learning has resulted in a successful and a relatively fast PPP project launch without the concessionary framework. The lessons learned include the need for effective stakeholder engagement; avoiding being stuck in bureaucracy such as collaboration with Federal Ministries and anti-trust agency; avoiding application for government funding as the approval process is tangled and lengthy; attracting strategic private investors; shaping positive public perception of a PPP project; and making continuous efforts in order to effectively mitigate the public acceptance risk. Originality/value – The paper contributes to ELT by incorporating the impact of social environment in the learning model. Additionally, the paper tests the applicability of ELT to learning in the complex organisational setting, i.e., a PPP.

Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.