Spherical integral formulas for upward/downward continuation of gravitational gradients onto gravitational gradients

New integral formulas for upward/downward continuation of gravitational gradients onto gravitational gradients are derived in this article. They provide more options for continuation of gravitational gradient combinations and extend available mathematical apparatus formulated for this purpose up to now. The starting point represents the analytical solution of the spherical gradiometric boundary value problem in the spatial domain. Applying corresponding differential operators on the analytical solution of the spherical gradiometric boundary value problem, a total of 18 integral formulas are provided. Spatial and spectral forms of isotropic kernels are given and their behaviour for parameters of a GOCE-like satellite is investigated. Correctness of the new integral formulas and the isotropic kernels is tested in a closed-loop simulation. The derived integral formulas and the isotropic kernels form a theoretical basis for validation purposes and geophysical applications of satellite gradiometric data as provided currently by the GOCE mission. They also extend the well-known Meissl scheme.     

Third-order geomorphometric variables (derivatives): definition,computation and utilization of changes of curvatures

Third-order geomorphometric variables (based on third derivatives of the altitudinal field) have been neglected in geomorphometry, but their application to the delimitation of surface objects will lead to their increasing significance in future. New techniques of computation, presented and evaluated here, facilitate their use. This paper summarizes recent knowledge concerning definition, computation and geomorphologic interpretation of these variables. Formulae defining various third-order variables are unified based on the physical definition of slope gradient. Methods for their computation are compared from the point of view of method error and error generated by digital elevation model (DEM) inaccuracy. For exact mathematical test surfaces, the most natural and simple variant of the method of central differences (CD2) shows a method error 2–3 times smaller than the other methods used recently in geomorphometry. However, success in coping with DEM inaccuracy depends (for a given grid mesh) on the number and weighting of points from which the derivative is computed. This was tested for surfaces with varying degrees of random error. Here least squares-based methods are the most effective for mixed derivatives (especially for finer grids and less accurate DEMs), while a variant of the CD method, that repeats numerical evaluation of first derivatives (CD1), is the most successful for derivatives in cardinal directions. The CD2 method is generally the most successful for coarser grids where the method error is dominant.

Utilization of third-order variables is documented from examples of terrain feature (ridge, valley and edge) extraction and from a first statistical test of the hypothesis that real segments of the land surface have a tendency to a constant value of some morphometric variable. For detection of (sharp) ridges and valleys, it is shown that the rate of change of tangential curvature is inadequate: rate of change of normal curvature is also required. A basic confirmation of the constant-value tendency is provided.     

How a Sphagnum fuscum‐dominated bog changed into a calcareous fen: the unique Holocene history of a Slovak spring‐fed mire

In general, mires develop by autogenic succession from more groundwater‐fed to more rainwater‐fed. This study from a calcareous mire in the West Carpathians (Slovakia) describes a similar development in the Early Holocene, followed by a reverse development in the Middle and Late Holocene. Pollen, macrofossil and testate amoeba analyses show that the site started as a minerotrophic open fen woodland. After 10 700 cal a BP autogenic succession led to the accumulation of at least 1 m of Sphagnum fuscum peat. Around 9000 cal a BP, as climate could no longer sustain a stable water regime, the bog desiccated and a fire broke out. The fire removed part of the peat layer and as a consequence relative water levels rose, leading to the establishment of a wet minerotrophic swamp carr with Thelypteris palustris, Equisetum sp. and Alnus sp. with extremely slow peat accumulation. After 600 cal a BP, rapid peat accumulation with calcareous tufa formation resumed as a result of anthropogenic deforestation and hydrological changes in the catchment and resulting increased groundwater discharge. At present the mire still hosts a wealth of relict and endangered plant and animal species typical of calcareous fens and fen meadows. Copyright © 2011 John Wiley & Sons, Ltd.     

Local Recovery of Sub-Crustal Stress Due to Mantle Convection from Satellite-to-Satellite Tracking Data

Two integral transformations between the stress function, differentiation of which gives the meridian and prime vertical components of the sub-crustal stress due to mantle convection, and the satellite-to-satellite tracking (SST) data are presented in this article. In the first one, the SST data are the disturbing potential differences between twin-satellites and in the second one the line-of-sight (LOS) gravity disturbances. It is shown that the corresponding integral kernels are well-behaving and therefore suitable for inversion and recovery of the stress function from the SST data. Recovery of the stress function and the stress components is also tested in numerical experiments using simulated SST data. Numerical studies over the Himalayas show that inverting the disturbing potential differences leads to a smoother stress function than from inverting LOS gravity disturbances. Application of the presented integral formulae allows for recovery of the stress from the satellite mission GRACE and its planned successor.     

Elementary forms for land surface segmentation: The theoretical basis of terrain analysis and geomorphological mapping

Land surface morphology is fundamental to geomorphological mapping and many GIS applications. Review and comparison of various approaches to segmentation of the land surface reveals common features, and permits development of a broad theoretical basis for segmentation and for characterization of segments and their boundaries. Within the context of defining landform units that maximise internal homogeneity and external differences, this paper introduces the concept of elementary forms (segments, units) defined by constant values of fundamental morphometric properties and limited by discontinuities of the properties. The basic system of form-defining properties represents altitude and its derivatives, constant values of which provide elementary forms with various types of homogeneity. Every geometric type of elementary form can be characterized by a defining function, which is a specific case of the general polynomial fitted function. Various types of boundary discontinuity and their connections and transformations into other types of morphological unit boundaries are analysed.The wealth of types of elementary forms and their boundaries is potentially unbounded and thus is sufficient to cover the real variety of landforms. Elementary forms in the basic set proposed here have clear potential for genetic and dynamic interpretation. A brief worked example documents the possibility of analytical computation of various models of ideal elementary forms for particular segments of landform. Ideal elementary forms can be considered as attractors, to which the affinity of surface segments can be measured by multivariate statistical methods. The use of the concept of elementary forms in landscape segmentation is promising and it could be adapted for elementary segmentation of various other spatial fields.     

High-frequency QPO modulation in neutron-star and black-hole sources

After twelve years have past since the discovery of the first high-frequency quasi-periodic oscillation in Sco X-1, an enormous progress has been made on the observational side and on the field of data analysis. Equal amount of effort has been devoted also to the theoretical aspect of the QPO problem. However, so far no model is able to sufficiently fully explain the mechanism of QPO production. There are two aspects: the question of the QPO origin; and the question of its modulation. In this article, I am focusing solely on the second issue – I discuss ways of how the outgoing flux can be modulated at a level sufficient to match the observational rms amplitudes. Some more space is devoted to my own work in the field.     

Motion of dust in mean motion resonances with planets

Effect of stellar electromagnetic radiation on the motion of spherical dust particle in mean motion orbital resonances with a planet is investigated. Planar circular restricted three-body problem with the Poynting–Robertson (P–R) effect yields monotonic secular evolution of eccentricity when the particle is trapped in the resonance. Planar elliptic restricted three-body problem with the P–R effect enables nonmonotonous secular evolution of eccentricity and the evolution of eccentricity is qualitatively consistent with the published results for the complicated case of interaction of electromagnetic radiation with nonspherical dust grain. Thus, it is sufficient to allow either nonzero eccentricity of the planet or nonsphericity of the grain and the orbital evolutions in the resonances are qualitatively equal for the two cases. This holds both for exterior and interior mean motion orbital resonances. Evolutions of argument of perihelion in the planar circular and elliptical restricted three-body problems are shown. Numerical integrations show that an analytic expression for the secular time derivative of the particle’s argument of perihelion does not exist, if only dependence on semimajor axis, eccentricity and argument of perihelion is admitted. Connection between the shift of perihelion and oscillations in secular eccentricity is presented for the planar elliptic restricted three-body problem with the P–R effect. Period of the oscillations corresponds to the period of one revolution of perihelion. Change of optical properties of the spherical grain with the heliocentric distance is also considered. The change of the optical properties: (i) does not have any significant influence on the secular evolution of eccentricity, (ii) causes that the shift of perihelion is mainly in the same direction/orientation as the particle motion around the Sun. The statements hold both for circular and noncircular planetary orbits.     

Analysis of thunderstorm and lightning activity associated with sprites observed during the EuroSprite campaigns: Two case studies

During the summers of 2003 to 2006 sprites were observed over thunderstorms in France by cameras on mountain tops in Southern France. The observations were part of a larger coordinated effort, the EuroSprite campaigns, with data collected simultaneously from other sources including the French radar network for precipitation structure, Meteosat with images of cloud top temperature and the Météorage network for detection of cloud-to-ground (CG) flash activity. In this paper two storms are analyzed, each producing 27 sprite events. Both storms were identified as Mesoscale Convective Systems (MCS) with a trailing stratiform configuration (ST) and reaching a maximum cloud area of ~ 120,000 km². Most of the sprites were produced while the stratiform area was clearly developed and during periods of substantial increase of rainfall in regions with radar reflectivity between 30 and 40 dBZ. The sprite-producing periods followed a maximum in the CG lightning activity and were characterized by a low CG flash rate with a high proportion of + CG flashes, typically around 50%. All sprites were associated with + CGs except one which was observed after a − CG as detected by the Météorage network. This − CG was estimated to have − 800 C km charge moment change. The peak current of sprite-producing + CG (SP + CG) flashes was twice the average value of + CGs and close to 60 kA with little variation between the periods of sprite activity. The SP + CG flashes were further characterized by short time intervals before a subsequent CG flash (median value < 0.5 s) and with clusters of several CG flashes which suggest that SP + CG flashes often are part of multi-CG flash processes. One case of a lightning process associated with a sprite consisted of 7 CG flashes.     

Field Test of Enhanced Remedial Amendment Delivery Using a Shear‐Thinning Fluid

Heterogeneity of hydraulic properties in aquifers may lead to contaminants residing in lower‐permeability zones where it is difficult to deliver remediation amendments using conventional injection processes. The focus of this study is to examine use of a shear‐thinning fluid (STF) to improve the uniformity of remedial amendment distribution within a heterogeneous aquifer. Previous studies have demonstrated the significant potential of STFs for improving remedial amendment delivery in heterogeneous aquifers, but quantitative evaluation of these improvements from field applications is lacking. A field‐scale test was conducted that compares data from successive injection of a tracer in water followed by injection of a tracer in an STF to evaluate the impact of the STF on tracer distribution uniformity in the presence of permeability contrasts within the targeted injection zone. Data from tracer breakthrough at multiple depth‐discrete monitoring intervals and electrical resistivity tomography (ERT) showed that inclusion of STF in the injection solution improved the distribution of the injected fluid within the targeted treatment zone. One improvement was a reduction in the movement of injected fluids through high‐permeability pathways, as evidenced by slower breakthrough of tracer at monitoring locations where breakthrough in baseline tracer‐only injection data was faster. In addition, STF‐amended injection solutions arrived faster and to a greater extent in monitoring locations within low‐permeability zones. ERT data showed that the STF injection covered a higher percentage of a two‐dimensional cross section within the injection interval between the injection well and a monitoring well about 3 m away.     

The environmental significance of the remobilisation of ancient mass movements in the Atbara–Tekeze headwaters, Northern Ethiopia

Old landslides are prominent features in the landscape around Hagere Selam, Tigray Highlands, Ethiopia. The available evidence suggests their Late Pleistocene to Middle Holocene age and conditions of soil humidity. The affected geological layers, often silicified lacustrine deposits prone to sliding, rest upon or above the water holding Amba Aradam sandstone aquifer.Three examples of present-day (remobilisation of old) mass movements are illustrated and discussed. The aims of the study were to unravel the environmental conditions of the present-day remobilisation of ancient flows, as well as those of first-time landslides. The first two mass movements discussed are slumps, located in areas with vigorous regeneration of (grassy) vegetation. Their activation is thought to be the consequence of an increase in infiltration capacity of the soils under regenerating vegetation. One of these slumps had a horizontal movement of the order of 10–20 m in 1 day.The other case is the remobilisation of the May Ntebteb debris flow below the Amba Aradam sandstone cliff. The debris flow presently creeps downslope at a rate of 3–6 cm year⁻¹. Palynological evidence from tufa shows that the reactivation of the flow started 70 years ago. Shear resistance measurements indicate the danger for continuous or prefailure creep. From the soil mechanics point of view, the reactivation of the debris flow is due to the combination of two factors: (1) the reduction of flow confining pressures as a result of gully incision over the last hundred years, and (2) the increase of seepage pressure as a consequence of the cumulative effect of this incision and the increase in infiltration rates on the lobe since grazing and woodcutting have been prohibited 8 years ago. The role of such exclosures as possible landslide triggers is discussed.From the geomorphological point of view, the ancient movements and their present-day reactivation cannot be compared: the ancient movements led to the development of debris flows, whereas the reactivations relate to the dissection of these mass movement deposits.