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

Properties of singular vectors using convective available potential energy as final time norm

We study the feasibility of using the singular vector technique to create initial condition perturbations for short-range ensemble prediction systems (SREPS) focussing on predictability of severe local storms and in particular deep convection. For this a new final time semi-norm based on the convective available potential energy (CAPE) is introduced. We compare singular vectors using the CAPE-norm with SVs using the more common total energy (TE) norm for a 2-week summer period in 2007, which includes a case of mesoscale extreme rainfall in the south west of Finland. The CAPE singular vectors perturb the CAPE field by increasing the specific humidity and temperature of the parcel and increase the lapse rate above the parcel in the lower troposphere consistent with physical considerations. The CAPE-SVs are situated in the lower troposphere. This in contrast to TE-SVs with short optimization times which predominantly remain in the high troposphere. By examining the time evolution of the CAPE singular values we observe that the convective event in the south west of Finland is clearly associated with high CAPE singular values.

Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds

In this paper we extend the well-known Leinfelder–Simader theorem on the essential selfadjointness of singular Schrödinger operators to arbitrary complete Riemannian manifolds. This improves some earlier results of Shubin, Milatovic and others.

Reframing 'crisis' in fair trade coffee production: trajectories of agrarian change in Nicaragua

A focus on crisis provides a methodological window to understand how agrarian change shapes producer engagement in fair trade. This orientation challenges a seperation between the market and development, situating fair trade within global processes that incorporate agrarian histories of social change and conflict. Reframing crisis as a condition of agrarian life, rather than emphasizing its cyclical manifestation within the global economy, reveals how market-driven development encompasses the material conditions of peoples' existence in ambiguous and contradictory ways. Drawing on the case of coffee production in Nicaragua, experiences of crisis demonstrate that greater attention needs to be paid to the socioeconomic and political dimensions of development within regional commodity assemblages to address entrenched power relations and unequal access to land and resources. This questions moral certainties when examining the paradox of working in and against the market, and suggests that a better understanding of specific trajectories of development could improve fair trade's objective of enhancing producer livelihoods.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

The plume also rises: trajectories of pheromone plumes issuing from point sources in an orchard canopy at night

The trajectories of pheromone plumes in canopied habitats, such as orchards, have been little studied. We documented the capture of male navel orangeworm moths, Amyelois transitella, in female-baited traps positioned at 5 levels, from ground level to the canopy top, at approximately 6 m above ground, in almond orchards. Males were captured in similar proportions at all levels, suggesting that they do not favor a particular height during ranging flight. A 3-D sonic anemometer was used to establish patterns of wind flow and temperature at 6 heights from 2.08 to 6.65 m in an almond orchard with a 5 m high canopy, every 3 h over 72 h. The horizontal velocity of wind flow was highest above the canopy, where its directionality also was the most consistent. During the time of A. transitella mating (0300–0600), there was a net vertical displacement upward. Vertical buoyancy combined with only minor reductions in the distance that plumes will travel in the lower compared to the upper canopy suggest that the optimal height for release of pheromone from high-release-rate sources, such as aerosol dispensers (“puffers”), that are deployed at low densities (e.g., 3 per ha.) would be at mid or low in the canopy, thereby facilitating dispersion of disruptant throughout the canopy. Optimal placement of aerosol dispensers will vary with the behavioral ecology of the target pest; however, our results suggest that current protocols, which generally propose dispenser placement in the upper third of the canopy, should be reevaluated.

Instantaneous threat detection based on a semantic representation of activities, zones and trajectories

Threat detection is a challenging problem, because threats appear in many variations and differences to normal behaviour can be very subtle. In this paper, we consider threats on a parking lot, where theft of a truck’s cargo occurs. The threats range from explicit, e.g. a person attacking the truck driver, to implicit, e.g. somebody loitering and then fiddling with the exterior of the truck in order to open it. Our goal is a system that is able to recognize a threat instantaneously as they develop. Typical observables of the threats are a person’s activity, presence in a particular zone and the trajectory. The novelty of this paper is an encoding of these threat observables in a semantic, intermediate-level representation, based on low-level visual features that have no intrinsic semantic meaning themselves. The aim of this representation was to bridge the semantic gap between the low-level tracks and motion and the higher-level notion of threats. In our experiments, we demonstrate that our semantic representation is more descriptive for threat detection than directly using low-level features. We find that a person’s activities are the most important elements of this semantic representation, followed by the person’s trajectory. The proposed threat detection system is very accurate: 96.6 % of the tracks are correctly interpreted, when considering the temporal context.