The omega equation and potential vorticity

Two fundamental perspectives on the dynamics of midlatitude weather systems are provided by potential vorticity (PV) and the omega equation. The aim of this paper is to investigate the link between the two perspectives, which has so far received very little attention in the meteorological literature. It also aims to give a quantitative basis for discussion of quasi-geostrophic vertical motion in terms of components associated with system movement, maintaining a constant thermal structure, and with the development of that structure. The former links with the isentropic relative-flow analysis technique. Viewed in a moving frame of reference, the measured development of a system depends on the velocity of that frame of reference. The requirement that the development should be a minimum provides a quantitative method for determining the optimum system velocity. The component of vertical velocity associated with development is shown to satisfy an omega equation with forcing determined from the relative advection of interior PV and boundary temperature. The analysis carries through in the presence of diabatic heating provided the omega equation forcing is based on the interior PV and boundary thermal tendencies, including the heating effect. The analysis is shown to be possible also at the level of the semi-geostrophic approximation. The analysis technique is applied to a number of idealized problems that can be considered to be building blocks for midlatitude synoptic-scale dynamics. They focus on the influences of interior PV, boundary temperature, an interior boundary, baroclinic instability associated with two boundaries, and also diabatic heating. In each case, insights yielded by the new perspective are sought into the dynamical behaviour, especially that related to vertical motion. Copyright © 2003 Royal Meteorological Society

Eye-movements aid the control of locomotion

Eye-movements have long been considered a problem when trying to understand the visual control of locomotion. They transform the retinal image from a simple expanding pattern of moving texture elements (pure optic flow), into a complex combination of translation and rotation components (retinal flow). In this article we investigate whether there are measurable advantages to having an active free gaze, over a static gaze or tracking gaze, when steering along a winding path. We also examine patterns of free gaze behavior to determine preferred gaze strategies during active locomotion. Participants were asked to steer along a computer-simulated textured roadway with free gaze, fixed gaze, or gaze tracking the center of the roadway. Deviation of position from the center of the road was recorded along with their point of gaze. It was found that visually tracking the middle of the road produced smaller steering errors than for fixed gaze. Participants performed best at the steering task when allowed to sample naturally from the road ahead with free gaze. There was some variation in the gaze strategies used, but sampling was predominantly of areas proximal to the center of the road. These results diverge from traditional models of flow analysis.

Implications of the altitude of transient 630-nm dayside auroral emissions

The altitude from which transient 630-nm (“red line”) light is emitted in transient dayside auroral breakup events is discussed. Theoretically, the emissions should normally originate from approximately 250 to 550 km. Because the luminosity in dayside breakup events moves in a way that is consistent with newly opened field lines, they have been interpreted as the ionospheric signatures of transient reconnection at the dayside magnetopause. For this model the importance of these events for convection can be assessed from the rate of change of their area. The area derived from analysis of images from an all-sky camera and meridian scans from a photometer, however, depends on the square of the assumed emission altitude. From field line mapping, it is shown for both a westward and an eastward moving event, that the main 557.7-nm emission comes from the edge of the 630 nm transient, where a flux transfer event model would place the upward field-aligned current (on the poleward and equatorward edge, respectively). The observing geometry for the two cases presented is such that this is true, irrespective of the 630-nm emission altitude. From comparisons with the European incoherent scatter radar data for the westward (interplanetary magnetic field By > 0) event on January 12, 1988, the 630-nm emission appears to emanate from an altitude of 250 km, and to be accompanied by some 557.7-nm “green-line” emission. However, for a large, eastward moving event observed on January 9, 1989, there is evidence that the emission altitude is considerably greater and, in this case, the only 557.7-nm emission is that on the equatorward edge of the event, consistent with a higher altitude 630-nm excitation source. Assuming an emission altitude of 250 km for this event yields a reconnection voltage of >50 kV during the reconnection burst but a contribution to the convection voltage of >15 kV. However, from the motion of the event we infer that the luminosity peaks at an altitude in the range of 400 and 500 km, and for the top of this range the reconnection and average convection voltages would be increased to >200 kV and >60 kV, respectively. (These are all minimum estimates because the event extends in longitude beyond the field-of-view of the camera). Hence the higher-emission altitude has a highly significant implication, namely that the reconnection bursts which cause the dayside breakup events could explain most of the voltage placed across the magnetosphere and polar cap by the solar wind flow. Analysis of the plasma density and temperatures during the event on January 9, 1989, predicts the required thermal excitation of significant 630-nm intensities at altitudes of 400-500 km.

Calibration and sensitivity analysis of a river water quality model under unsteady flow conditions

Water quality models generally require a relatively large number of parameters to define their functional relationships, and since prior information on parameter values is limited, these are commonly defined by fitting the model to observed data. In this paper, the identifiability of water quality parameters and the associated uncertainty in model simulations are investigated. A modification to the water quality model `Quality Simulation Along River Systems' is presented in which an improved flow component is used within the existing water quality model framework. The performance of the model is evaluated in an application to the Bedford Ouse river, UK, using a Monte-Carlo analysis toolbox. The essential framework of the model proved to be sound, and calibration and validation performance was generally good. However some supposedly important water quality parameters associated with algal activity were found to be completely insensitive, and hence non-identifiable, within the model structure, while others (nitrification and sedimentation) had optimum values at or close to zero, indicating that those processes were not detectable from the data set examined. (C) 2003 Elsevier Science B.V. All rights reserved.

Sensitivity analysis of a cyanobacterial growth and movement model under two different flow regimes

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling cyanobacterial behaviour in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes, reservoirs and rivers. A new deterministic–mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including light, nutrients and temperature. A parameter sensitivity analysis using a one-at-a-time approach was carried out. There were two objectives of the sensitivity analysis presented in this paper: to identify the key parameters controlling the growth and movement patterns of cyanobacteria and to provide a means for model validation. The result of the analysis suggested that maximum growth rate and day length period were the most significant parameters in determining the population growth and colony depth, respectively.

A flow system for the on-line quantitative measurement of the retention of dosage forms on biological surfaces using spectroscopy and image analysis

Measuring the retention, or residence time, of dosage forms to biological tissue is commonly a qualitative measurement, where no real values to describe the retention can be recorded. The result of this is an assessment that is dependent upon a user's interpretation of visual observation. This research paper outlines the development of a methodology to quantitatively measure, both by image analysis and by spectrophotometric techniques, the retention of material to biological tissues, using the retention of polymer solutions to ocular tissue as an example. Both methods have been shown to be repeatable, with the spectrophotometric measurement generating data reliably and quickly for further analysis.