A generalization of Szebehely's equation for three dimensions

Szebehely's equation for the potential generating a prescribed family of orbits in two dimensions is generalized for three-dimensional orbits. A simultaneous system of first-order linear partial differential equations is derived for the determination of the potential in the three-dimensional case. Solutions of this system are found in several cases including Kepler's problem too.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.This paper is dedicated to Professor Victor Szebehely on the occasion of his 60th birthday.     

Mercury enrichments in core sediments in Hugli–Matla–Bidyadhari estuarine complex,north-eastern part of the Bay of Bengal and their ecotoxicological significance

Mercury concentrations (Hg_T) in fine-grained fraction (<63 μm) of core sediments of the Hugli–Matla–Bidyadhari estuarine complex, India were analyzed. Results revealed a wide range of spatial variations (<4–93 ng g⁻¹ dry weight) with a definite enhancement level at the lower stretch of the estuarine complex infested with mangrove plants, which might act as a sink to Hg_T. An elevated concentration of Hg was encountered in surface/subsurface layer of the core in majority of the cases resulting from physical, biogenic and postdepositional diagenetic processes that remobilized and resuspended the metal from deeper sediments. A strong positive correlation was observed between the Hg and clay fraction content of the sediments, while the correlations of Hg with Al, Fe and Mn were poor. Based on the index of geoaccumulation (I _geo) and effects range-low (ER-L) value, it is considered that the sediments are less polluted and thus there is less chance of ecotoxicological risk to organisms living in sediments.     

LOLAS: an optical turbulence profiler in the atmospheric boundary layer with extreme altitude resolution

We report the development and first results of an instrument called Low Layer SCIDAR (Scintillation Detection and Ranging) (LOLAS) which is aimed at the measurement of optical-turbulence profiles in the atmospheric boundary layer with high altitude resolution. The method is based on the Generalized SCIDAR (GS) concept, but unlike the GS instruments which need a 1-m or larger telescope, LOLAS is implemented on a dedicated 40-cm telescope, making it an independent instrument. The system is designed for widely separated double-star targets, which enables the high altitude resolution. Using a 200-arcsec-separation double star, we have obtained turbulence profiles with unprecedented 12-m resolution. The system incorporates necessary novel algorithms for autoguiding, autofocus and image stabilization. The results presented here were obtained at Mauna Kea Observatory. They show LOLAS capabilities but cannot be considered as representative of the site. A forthcoming paper will be devoted to the site characterization. The instrument was built as part of the Ground Layer Turbulence Monitoring Campaign on Mauna Kea for Gemini Observatory.     

Energy balance of simple elastodynamic sources

Complete relations are derived for energy and energy flux of elastic waves generated by an isotropic and double-couple source in a perfectly elastic, homogeneous, isotropic, and unbounded medium. In the energy balance of elastodynamic sources near-field waves play an essential role, transforming static energy into wave energy, andvice versa. For explosive and dislocation sources, the sources surface radiates a positive wave energy that is partially distributed to the medium transforming into static energy. For implosive and antidislocation sources, the source surface generates elastic waves, but it does not necessarily imply that it also radiates a positive wave energy. The energy transported by waves can originate in gradual transformation of the static-to-wave energy during propagation of waves through a stressed medium.On leave from Geophysical Institute, Czech Academy of Sciences, Boní II/1401, 41 31, Praha 4 Czech Republic     

Selection of regional historical rainfall time series as input to urban drainage simulations at ungauged locations

It has become established practice during the past 20 years to use high-resolution historical rainfall time series as input to hydrological model packages for detailed simulation of urban drainage systems. However, sufficiently long rain series are rarely available from the exact catchment in question and simulations are hence often based on available rain series from other locations. Extreme rainfall properties of importance to the performance of urban storm drainage systems vary significantly even in regions with only minor physiographic differences. Part of this variation can be explained by regional variations of the mean annual rainfall and the remaining statistical residue can be interpreted as statistical uncertainty.In Denmark, more than 75 high-resolution rain gauges are installed across a total area of 43,000 m. About 40 gauges had sufficiently long records to be included in a comprehensive national investigation where newly developed statistical regionalisation procedures were used to model the regional variation of extreme rainfalls. On this basis, a spreadsheet model was made available for estimation of extreme design rainfalls and the associated uncertainty at any location in the country. Statistics were furthermore computed to classify historical rainfall time series according to the developed regional model, and this makes it possible to assess the uncertainty related with using different historical rain series for simulations at ungauged locations.This research indicates that use of historical point rainfall data at ungauged locations introduces a significant uncertainty that is largely overlooked in today's practice. The engineering recommendation is to select historical rain series based on an evaluation of the local physiographic characteristics (e.g., the mean annual rainfall) and a (pre-defined) desired safety level of the simulations.     

An Overview of Thunderstorm-Related Research on the Atmospheric Electric Field, Schumann Resonances, Sprites, and the Ionosphere at Sopron, Hungary

This paper gives a resume of the papers written in English which (a) describe some of the recording instruments in use at the Nagycenk Observatory (NCK) since the International Geophysical Year (IGY 1957–1958) and up to the present time, (b) summarise the most important and different types of observations associated with thunderstorms which have been made there, and (c) discuss their various geophysical interpretations. The paper describes the main results which have been obtained in four areas of thunderstorm associated atmospheric and geospace science within the context of Earth system science. These relate to the following parameters of atmospheric electricity: the vertical electric potential gradient just above the Earth’s surface and the air–Earth current as well as the point discharge current, Schumann resonance (SR) signals of the Earth-ionosphere cavity at 8, 14 and 20 Hz, transient luminous events (TLEs), and some aspects of the behaviour of the ionosphere. Deductions from these data sets are concerned with the global lightning activity and the conductivity of the air, with diurnal, seasonal, annual and long-term variations of the SR amplitudes and resonant frequencies in terms of migrating thunderstorm centres, with transient SR excitations and with sprites and other TLEs, and with ionospheric disturbances. The paper closes with some thoughts on future research directions based on the observations at NCK and Sopron and the results achieved since the IGY.     

Evidence from the Trent terrace archive, Lincolnshire, UK, for lowland glaciation of Britain during the Middle and Late Pleistocene

The late Middle Pleistocene fluvial terrace sequence of the lower Trent system, Lincolnshire (eastern England), provides an excellent record of environmental change, including evidence for the last two interglacial episodes. It also provides important stratigraphical evidence for the timing and extent of three separate glaciations. Two of these, the Anglian and Devensian, are well-established correlatives of Marine Isotope Stages (MIS) 12 and 2 respectively; the third is a hitherto un-named post-Anglian-pre-Devensian glaciation in eastern England that has been the subject of much previous speculation, but can now be attributed with some confidence to MIS 8. Crucially, the recognition of MIS 7 interglacial deposits within the Balderton-Southrey terrace of the proto-Trent indicates that the underlying Wragby Till, which is ascribed to this additional glaciation, was emplaced no later than MIS 8. The oldest terrace preserved within the lower Trent staircase, the Eagle Moor-Martin Terrace, is considered to be a complex glacial outwash terrace related to the Wragby Till glaciation. It is suggested that deposits representing MIS 11-9, which are conspicuously absent throughout the Trent system, were removed by this glaciation. This is a departure from previous interpretations, which have suggested MIS 10 or MIS 6 as the most likely stages in which an extensive post-Anglian-pre-Devensian lowland glaciation might have occurred in Britain. However, the widespread preservation of undisrupted post-MIS 8 fluvial sequences throughout the Trent valley and in neighbouring systems, within which MIS 7 interglacial deposits have now been recognized at a number of localities, indicates that ice sheets are unlikely to have advanced further into this catchment during MIS 6 than during the Devensian (MIS 2). Recognition of a British glaciation during MIS 8 corresponds with widespread evidence in Europe, which suggests that glacial deposits classified as ‘Saalian’ represent both MIS 8 and MIS 6; in many areas, distinguishing these remains controversial, as confident correlation with either stage is often only possible where glacial sediments interdigitate with well-constrained fluvial records.