A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

The 'child of Babylon' and the problem of paternity in Medieval French Alexander romances

A study of the use of hybrid physical appearance both to signal and to explore the disputed paternity of Alexander the Great throughout its vernacular French tradition. The article compares the 'child of Babylon' portent and Alexander's son Alior in the twelfth-century French "Roman d'Alexandre" poem cycle, and a fifteenth-century prose adaptation of it.

Problem-based learning approaches in meteorology

Problem-Based Learning, despite recent controversies about its effectiveness, is used extensively as a teaching method throughout higher education. In meteorology, there has been little attempt to incorporate Problem-Based Learning techniques into the curriculum. Motivated by a desire to enhance the reflective engagement of students within a current field course module, this project describes the implementation of two test Problem-Based Learning activities and testing and improvement using several different and complementary means of evaluation. By the end of a 2-year program of design, implementation, testing, and reflection and re-evaluation, two robust, engaging activities have been developed that provide an enhanced and diverse learning environment in the field course. The results suggest that Problem-Based Learning techniques would be a useful addition to the meteorology curriculum and suggestions for courses and activities that may benefit from this approach are included in the conclusions.

On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

Synoptic preconditions for extreme flooding during the summer Asian Monsoon in the Mumbai area

The summer monsoon season is an important hydrometeorological feature of the Indian subcontinent and it has significant socioeconomic impacts. This study is aimed at understanding the processes associated with the occurrence of catastrophic flood events. The study has two novel features that add to the existing body of knowledge about the South Asian Monsoon: 1) combine traditional hydrometeorological observations (rain gauge measurements) with unconventional data (media and state historical records of reported flooding) to produce value-added century-long time-series of potential flood events, and 2) identify the larger regional synoptic conditions leading to days with flood potential in the time-series. The promise of mining unconventional data to extend hydrometeorological records is demonstrated in this study. The synoptic evolution of flooding events in the western-central coast of India and the densely populated Mumbai area are shown to correspond to active monsoon periods with embedded low-pressure centers and have far upstream influence from the western edge of the Indian Ocean basin. The coastal processes along the Arabian Peninsula where the currents interact with the continental shelf are found to be key features of extremes during the South Asian Monsoon

Using synoptic type analysis to understand New Zealand climate during the Mid-Holocene

Diagnosing the climate of New Zealand from low-resolution General Circulation Models (GCMs) is notoriously difficult due to the interaction of the complex topography and the Southern Hemisphere (SH) mid-latitude westerly winds. Therefore, methods of downscaling synoptic scale model data for New Zealand are useful to help understand past climate. New Zealand also has a wealth of palaeoclimate-proxy data to which the downscaled model output can be compared, and to provide a qualitative method of assessing the capability of GCMs to represent, in this case, the climate 6000 yr ago in the Mid-Holocene. In this paper, a synoptic weather and climate regime classification system using Empirical Orthogonal Function (EOF) analysis of GCM and reanalysis data was used. The climate regimes are associated with surface air temperature and precipitation anomalies over New Zealand. From the analysis in this study, we find at 6000 BP that increased trough activity in summer and autumn led to increased precipitation, with an increased north-south pressure gradient ("zonal events") in winter and spring leading to drier conditions. Opposing effects of increased (decreased) temperature are also seen in spring (autumn) in the South Island, which are associated with the increased zonal (trough) events; however, the circulation induced changes in temperature are likely to have been of secondary importance to the insolation induced changes. Evidence from the palaeoclimate-proxy data suggests that the Mid-Holocene was characterized by increased westerly wind events in New Zealand, which agrees with the preference for trough and zonal regimes in the models.

The dependent variable problem in quantitative studies of Active Labour Market Programmes: uncovering hidden dynamics?

The question of what explains variation in expenditures on Active Labour Market Programs (ALMPs) has attracted significant scholarship in recent years. Significant insights have been gained with respect to the role of employers, unions and dual labour markets, openness, and partisanship. However, there remain significant disagreements with respects to key explanatory variables such the role of unions or the impact of partisanship. Qualitative studies have shown that there are both good conceptual reasons as well as historical evidence that different ALMPs are driven by different dynamics. There is little reason to believe that vastly different programs such as training and employment subsidies are driven by similar structural, interest group or indeed partisan dynamics. The question is therefore whether different ALMPs have the same correlation with different key explanatory variables identified in the literature? Using regression analysis, this paper shows that the explanatory variables identified by the literature have different relation to distinct ALMPs. This refinement adds significant analytical value and shows that disagreements are at least partly due to a dependent variable problem of ‘over-aggregation’.

Diagnosing and treating operational and implementation barriers in synoptic marketing planning

Strategic marketing planning is now widely adopted by business-to-business organizations. While marketing planning principles are well established, practitioners attempting to implement the process often find their progress impeded by a variety of barriers. These barriers are explored through a review of published evidence and case study analysis of several organizations. This analysis exposes three levels of barriers to effective business-to-business marketing planning, relating to (i) organizational infrastructure, (ii) the planning process and (iii) implementation. These barriers reflect the synoptic nature of planning in many organizations. The findings lead to the development of a practitioner-oriented diagnostic and treatment tool which guides managers through the marketing planning process. Although this diagnostic deals specifically with issues which are relevant to the marketing planner, its wider implications for strategic planning are also explored.

Synoptic versus orographic control on stationary convective banding

Quasi-stationary convective bands can cause large localised rainfall accumulations and are often anchored by topographic features. Here, the predictability of and mechanisms causing one such band are determined using ensembles of the Met Office Unified Model at convection-permitting resolution (1.5 km grid length). The band was stationary over the UK for 3 h and produced rainfall accumulations of up to 34 mm. The amount and location of the predicted rainfall was highly variable despite only small differences between the large-scale conditions of the ensemble members. Only three of 21 members of the control ensemble produced a stationary rain band; these three had the weakest upstream winds and hence lowest Froude number. Band formation was due to the superposition of two processes: lee-side convergence resulting from flow around an upstream obstacle and thermally forced convergence resulting from elevated heating over the upstream terrain. Both mechanisms were enhanced when the Froude number was lower. By increasing the terrain height (thus reducing the Froude number), the band became more predictable. An ensemble approach is required to successfully predict the possible occurrence of such quasi-stationary convective events because the rainfall variability is largely modulated by small variations of the large-scale flow. However, high-resolution models are required to accurately resolve the small-scale interactions of the flow with the topography upon which the band formation depends. Thus, although topography provides some predictability, the quasi-stationary convective bands anchored by it are likely to remain a forecasting challenge for many years to come.

Development of a wind gust model to estimate gust speeds and their return periods

Spatially dense observations of gust speeds are necessary for various applications, but their availability is limited in space and time. This work presents an approach to help to overcome this problem. The main objective is the generation of synthetic wind gust velocities. With this aim, theoretical wind and gust distributions are estimated from 10 yr of hourly observations collected at 123 synoptic weather stations provided by the German Weather Service. As pre-processing, an exposure correction is applied on measurements of the mean wind velocity to reduce the influence of local urban and topographic effects. The wind gust model is built as a transfer function between distribution parameters of wind and gust velocities. The aim of this procedure is to estimate the parameters of gusts at stations where only wind speed data is available. These parameters can be used to generate synthetic gusts, which can improve the accuracy of return periods at test sites with a lack of observations. The second objective is to determine return periods much longer than the nominal length of the original time series by considering extreme value statistics. Estimates for both local maximum return periods and average return periods for single historical events are provided. The comparison of maximum and average return periods shows that even storms with short average return periods may lead to local wind gusts with return periods of several decades. Despite uncertainties caused by the short length of the observational records, the method leads to consistent results, enabling a wide range of possible applications.

Antarctic ocean and sea ice response to ozone depletion: a two timescale problem

The response of the Southern Ocean to a repeating seasonal cycle of ozone loss is studied in two coupled climate models and found to comprise both fast and slow processes. The fast response is similar to the inter-annual signature of the Southern Annular Mode (SAM) on Sea Surface Temperature (SST), on to which the ozone-hole forcing projects in the summer. It comprises enhanced northward Ekman drift inducing negative summertime SST anomalies around Antarctica, earlier sea ice freeze-up the following winter, and northward expansion of the sea ice edge year-round. The enhanced northward Ekman drift, however, results in upwelling of warm waters from below the mixed layer in the region of seasonal sea ice. With sustained bursts of westerly winds induced by ozone-hole depletion, this warming from below eventually dominates over the cooling from anomalous Ekman drift. The resulting slow-timescale response (years to decades) leads to warming of SSTs around Antarctica and ultimately a reduction in sea-ice cover year-round. This two-timescale behavior - rapid cooling followed by slow but persistent warming - is found in the two coupled models analysed, one with an idealized geometry, the other a complex global climate model with realistic geometry. Processes that control the timescale of the transition from cooling to warming, and their uncertainties are described. Finally we discuss the implications of our results for rationalizing previous studies of the effect of the ozone-hole on SST and sea-ice extent. %Interannual variability in the Southern Annular Mode (SAM) and sea ice covary such that an increase and southward shift in the surface westerlies (a positive phase of the SAM) coincides with a cooling of Sea Surface Temperature (SST) around 70-50$^\circ$S and an expansion of the sea ice cover, as seen in observations and models alike. Yet, in modeling studies, the Southern Ocean warms and sea ice extent decreases in response to sustained, multi-decadal positive SAM-like wind anomalies driven by 20th century ozone depletion. Why does the Southern Ocean appear to have disparate responses to SAM-like variability on interannual and multidecadal timescales? Here it is demonstrated that the response of the Southern Ocean to ozone depletion has a fast and a slow response. The fast response is similar to the interannual variability signature of the SAM. It is dominated by an enhanced northward Ekman drift, which transports heat northward and causes negative SST anomalies in summertime, earlier sea ice freeze-up the following winter, and northward expansion of the sea ice edge year round. The enhanced northward Ekman drift causes a region of Ekman divergence around 70-50$^\circ$S, which results in upwelling of warmer waters from below the mixed layer. With sustained westerly wind enhancement in that latitudinal band, the warming due to the anomalous upwelling of warm waters eventually dominates over the cooling from the anomalous Ekman drift. Hence, the slow response ultimately results in a positive SST anomaly and a reduction in the sea ice cover year round. We demonstrate this behavior in two models: one with an idealized geometry and another, more detailed, global climate model. However, the models disagree on the timescale of transition from the fast (cooling) to the slow (warming) response. Processes that controls this transition and their uncertainties are discussed.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.