Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

Magnetosheath Interaction with the High Latitude Magnetopause

We present both statistical and case studies of magnetosheath interaction with the high-latitude magnetopause on the basis of Interball-1 and other ISTP spacecraft data. We discuss those data along with recently published results on the topology of cusp-magnetosheath transition and the roles of nonlinear disturbances in mass and energy transfer across the high-latitude magnetopause. For sunward dipole tilts, a cusp throat is magnetically open for direct interaction with the incident flow that results in the creation of a turbulent boundary layer (TBL) over an indented magnetopause and downstream of the cusp. For antisunward tilts, the cusp throat is closed by a smooth magnetopause; demagnetized ‘plasma balls’ (with scale ∼ few R_E, an occurrence rate of ∼25% and trapped energetic particles) present a major magnetosheath plasma channel just inside the cusp. The flow interacts with the ‘plasma balls’ via reflected waves, which trigger a chaotization of up to 40% of the upstream kinetic energy. These waves propagate upstream of the TBL and initiate amplification of the existing magnetosheath waves and their cascade-like decays during downstream passage throughout the TBL. The most striking feature of the nonlinear interaction is the appearance of magnetosonic jets, accelerated up to an Alfvenic Mach number of 3. The characteristic impulsive local momentum loss is followed by decelerated Alfvenic flows and modulated by the TBL waves; momentum balance is conserved only on time scales of the Alfvenic flows (1/f_A ∼12 min). Wave trains at f_A∼1.3 mHz are capable of synchronizing interactions throughout the outer and inner boundary layers. The sonic/Alfvenic flows, bounded by current sheets, control the TBL spectral shape and result in non-Gaussian statistical characteristics of the disturbances, indicating the fluctuation intermittency. We suggest that the multi-scale TBL processes play at least a comparable role to that of macro-reconnection (remote from or in the cusp) in solar wind energy transformation and population of the magnetosphere by the magnetosheath plasma. Secondary micro-reconnection constitutes a necessary chain at the small-scale (∼ion gyroradius) edge of the TBL cascades. The thick TBL transforms the flow energy, including deceleration and heating of the flow in the open throat, ‘plasma ball’ and the region downstream of the cusp.     

The Magnetospheric cusps: A Summary

The polar cusps of the magnetosphere are key regions for the transfer of mass, momentum, and energy from the solar wind into the magnetosphere. Understaning these key regions and the dynamical interactions that occur there are fundamentally important to determining the physical nature of the magnetosphere. In this paper we try to summarize many of the conclusions reached in the papers of this special issue emphasizing the present concepts and definition of the cusp, what variations could be temporal structures and what could be spatial structures. We address the need for further measurements and the role of present and planned projects to address these needs.     

High-Altitude CUSP: The Extremely Dynamic Region in Geospace

The high-altitude dayside cusps (both northern and southern) are extremely dynamic regions in geospace. Large diamagnetic cavities with significant fluctuations of the local magnetic field strength have been observed there. These cusp diamagnetic cavities are always there day after day and are as large as 6 R_E Associated with these cavities are charged particles with energies from 20 keV up to 10 MeV. The intensities of the cusp energetic ions have been observed to increase by as much as four orders of the magnitude when compared with regions adjacent to the cusp which includes the magnetosheath. Their seed populations are a mixture of ionospheric and solar wind particles. The measured energetic ion fluxes in the high-altitude cusp are higher than that in both the regions upstream and downstream from the bow shock. Turbulent electric fields with an amplitude of about 10 mV/m are also present in the cusp, and a cusp resonant acceleration mechanism is suggested. The observations indicate that the dayside high-altitude cusp is a key region for transferring the solar wind mass, momentum, and energy into the Earth’s magnetosphere.     

Relief-rejuvenation and topographic length scales in a fluvial drainage basin, Napf area, Central Switzerland

This paper explores how, and to what extent, a phase of relief-rejuvenation modifies the mode of surface erosion in an approximately 63 km² drainage basin located at the northern border of the Swiss Alps (Luzern area). In the study area, the retreat of the Alpine glaciers at the end of the Last Glacial Maximum (LGM) caused base level to lower by approximately 80 m. The fluvial system adapted to the lowered base level by headward erosion. This is indicated by knickzones in the longitudinal stream profiles and by the continuous upstream narrowing of the width of the valley floor towards these knickzones. In the headwaters above these knickzones, processes are still to a significant extent controlled by the higher base level of the LGM. There, frequent exposure of bedrock in channels and especially on hillslopes implies that sediment flux is to a large extent limited by weathering rates. In the knickzones, however, exposure of bedrock in channels implies that sediment flux is supply-limited, and that erosion rates are controlled by stream power.The morphometric analysis reveals the existence of length scales in the topography that result from distinct geomorphic processes. Along the tributaries where the upstream sizes of the drainage basins exceed 100,000–200,000 m², the mode of sediment transport and erosion changes from predominantly hillslope processes (i.e., landsliding, creep of regolith, rock avalanches and to some extent debris flows) to processes in channels (fluvial processes and debris flows). This length scale reflects the minimum size of the contributing area for channelized processes to take over in the geomorphic development (i.e., threshold size of drainage basin). This threshold size depends on the ratio between production rates of sediment on hillslopes, and export rates of sediment by processes in channels. Consequently, in the headwaters, erosion rates and sediment flux, and hence landscape evolution rates, are to a large extent limited by weathering processes. In contrast, in the lower portion of the drainage basin that adjusts to the lowered base-level, rates of channelized erosion and relief formation are controlled mainly by stream power. Hence, this paper shows that base-level lowering, headward erosion and establishment of knickzones separate drainage basins in two segments with different controls on rates of surface erosion, sediment flux and relief formation.     

Tetrahedral Plots of the Phase Relations for Basalts

The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.     

Assessing quality of volunteer crowdsourcing contributions: lessons from the Cropland Capture game

Volunteered geographic information (VGI) is the assembly of spatial information based on public input. While VGI has proliferated in recent years, assessing the quality of volunteer-contributed data has proven challenging, leading some to question the efficiency of such programs. In this paper, we compare several quality metrics for individual volunteers’ contributions. The data were the product of the ‘Cropland Capture’ game, in which several thousand volunteers assessed 165,000 images for the presence of cropland over the course of 6 months. We compared agreement between volunteer ratings and an image's majority classification with volunteer self-agreement on repeated images and expert evaluations. We also examined the impact of experience and learning on performance. Volunteer self-agreement was nearly always higher than agreement with majority classifications, and much greater than agreement with expert validations although these metrics were all positively correlated. Volunteer quality showed a broad trend toward improvement with experience, but the highest accuracies were achieved by a handful of moderately active contributors, not the most active volunteers. Our results emphasize the importance of a universal set of expert-validated tasks as a gold standard for evaluating VGI quality.