An approach to response-based reliability analysis of quasi-linear Errors-in-Variables models

The paper presents an approach to internal reliability analysis of observation systems known as Errors-in-Variables (EIV) models with parameters estimated by the method of least squares. Such problems are routinely treated by total least squares adjustment, or orthogonal regression. To create a suitable environment for derivations in the analysis, a general nonlinear form of such EIV models is assumed, based on a traditional adjustment method of condition equations with unknowns, also known as the Gauss–Helmert model. However, in order to apply the method of reliability analysis based on the approach to response assessment in systems with correlated observations, presented in the earlier work of this author, it was necessary to confine the considerations to a quasi-linear form of the Gauss–Helmert model, representing quasi-linear EIV models. This made it possible to obtain a linear disturbance/response relationship needed in that approach. Several specific cases of quasi-linear EIV models are discussed. The derived formulas are consistent with those already functioning for standard least squares adjustment problems. The analysis shows that, as could be expected, the average level of response-based reliability for such EIV models under investigation is lower than that for the corresponding standard linear models. For EIV models with homoscedastic and uncorrelated observations, the relationship between the average reliability indices for the independent and the dependent variables is formulated for multiple regression and coordinate transformations. Numerical examples for these two applications are provided to illustrate this analysis.     

Piping dynamics in mid‐altitude mountains under a temperate climate: Bieszczady Mountains,eastern Carpathians

Piping has been recognized as an important geomorphic, soil erosion and hydrologic process. It seems that it is far more widespread than it has often been supposed. However, our knowledge about piping dynamics and its quantification currently relies on a limited number of data for mainly loess‐derived areas and marl badlands. Therefore, this research aimed to recognize piping dynamics in mid‐altitude mountains under a temperate climate, where piping occurs in Cambisols, not previously considered as piping‐prone soils. It has been expressed by the estimation of erosion rates due to piping and elongation of pipes in the Bere?nica Wy?na catchment in the Bieszczady Mountains, eastern Carpathians (305 ha, 188 collapsed pipes). The research was based on the monitoring of selected piping systems (1971–1974, 2013–2016). Changes in soil loss vary significantly between different years (up to 27.36 t ha^?1 yr^?1), as well as between the mean short‐term erosion rate (up to 13.10 t ha^?1 yr^?1), and the long‐term (45 years) mean of 1.34 t ha^?1 yr^?1. The elongation of pipes also differs, from no changes to 36 m during one year. The mean total soil loss is 48.8 t ha^?1 in plots, whereas in the whole studied catchment it is 2.0 t ha^?1. Hence, piping is both spatially and temporally dependent. The magnitude of piping in the study area is at least three orders of magnitude higher than surface erosion rates (i.e. sheet and rill erosion) under similar land use (grasslands), and it is comparable to the magnitude of surface soil erosion on arable lands. It means that piping constitutes a significant environmental problem and, wherever it occurs, it is an important, or even the main, sediment source. Copyright © 2017 John Wiley & Sons, Ltd.     

Hydrodynamic Equilibrium for Sediment Transport and Bed Response to Wave Motion

An experimental and theoretical identification of hydrodynamic equilibrium for sediment transport and bed response to wave motion are considered. The comparison between calculations and the results of laboratory experiments indicates the linear relation between sediment transport rate and the thickness zm of bed layer in which sediments are in apparent rectilinear motion. This linear relationship allows to use the first order “upwind” numerical scheme of FDM ensuring an accurate solution of equation for changes in bed morphology. However, it is necessary to carry out a decomposition of the sediment transport into transport in onshore direction during wave crest and offshore direction during wave trough. Further, the shape of bed erosion in response to sediment transport coincides with the trapezoid envelope or with part of it, when some sediments still remain within it. Bed erosion area is equal to the one of a rectangle with thickness znm.     

Extending the double-difference location technique to mining applications part I: Numerical study

The location of the seismic event hypocenter is the very first task undertaken when studying any seismological problem. The accuracy of the solution can significantly influence consecutive stages of analysis, so there is a continuous demand for new, more efficient and accurate location algorithms. It is important to recognize that there is no single universal location algorithm which will perform equally well in any situation. The type of seismicity, the geometry of the recording seismic network, the size of the controlled area, tectonic complexity, are the most important factors influencing the performance of location algorithms. In this paper we propose a new location algorithm called the extended double difference (EDD) which combines the insensitivity of the double-difference (DD) algorithm to the velocity structure with the special demands imposed by mining: continuous change of network geometry and a very local recording capability of the network for dominating small induced events. The proposed method provides significantly better estimation of hypocenter depths and origin times compared to the classical and double-difference approaches, the price being greater sensitivity to the velocity structure than the DD approach. The efficiency of both algorithms for the epicentral coordinates is similar.     

CO 2 emission trading model with trading prices

In this paper we consider the buying/selling prices of carbon dioxide (CO₂) emission permits in trading models with uncertainty. Permission prices, although usually omitted from standard models, may significantly influence the trading market. We thus undertook to construct a more realistic trade model and to compare it with the standard one. To do this, we introduced several important changes to the standard model, namely, (1) a new optimized quality function; and (2) transactions with price negotiations between regions. We also enhanced the model using methods described in the literature to allow it to deal with reported emissions uncertainty. Additionally, we used an original method of simulating this kind of market based on a specialized evolutionary algorithm (EA).     

Diurnal atmospheric forcing and temporal variations of the nutation amplitudes

A 29-year time-series of four-times-daily atmospheric effective angular momentum (EAM) estimates is used to study the atmospheric influence on nutation. The most important atmospheric contributions are found for the prograde annual (77 μas), retrograde annual (53 as), prograde semiannual (45 as), and for the constant offset of the pole (δψsinɛ₀=−86 as, δɛ=77 as). Among them only the prograde semiannual component is driven mostly by the wind term of the EAM function, while in all other cases the pressure term is dominant. These are nonnegligible quantities which should be taken into account in the new theory of nutation. Comparison with the VLBI corrections to the IAU 1980 nutation model taking into account the ocean tide contribution yields good agreement for the prograde annual and semiannual nutations. We also investigated time variability of the atmospheric contribution to the nutation amplitudes by performing the sliding-window least-squares analysis of both the atmospheric excitation and VLBI nutation data. Almost all detected variations of atmospheric origin can be attributed to the pressure term, the biggest being the in-phase annual prograde component (about 30 as) and the retrograde one (as much as 100200 as). These variations, if physical, limit the precision of classical modeling of nutation to the level of 0.1 mas. Comparison with the VLBI data shows significant correlation for the retrograde annual nutation after 1989, while for the prograde annual term there is a high correlation in shape but the size of the atmospherically driven variations is about three times less than deduced from the VLBI data. This discrepancy in size can be attributed either to inaccuracy of the theoretical transfer function or the frequency-dependent ocean response to the pressure variations. Our comparison also yields a considerably better agreement with the VLBI nutation data when using the EAM function without the IB correction for ocean response, which indicates that this correction is not adequate for nearly diurnal variations. Received: 10 September 1997 / Accepted: 5 March 1998     

Investigation of superstructures in mullite by high resolution electron microscopy and electron diffraction

Superstructures in synthetic mullite, Al_4+2x Si_2?2x O_10?x , prepared using the zone melting technique, are studied by high resolution electron microscopy (HREM), electron diffraction, and in situ energy dispersive X-ray spectroscopy. For x=0.40 composition HREM images indicate only short-range order. Near x=0.5 composition mullite has an antiphase domain structure with antiphase boundaries (APB's) oriented parallel to (100). For higher Al-content the APB's run in non-rational orientations which are slightly inclined against the {601}-planes. We propose models for the superstructures in which oxygen vacancies are arranged in channels parallel to the crystal b-axis. The models are supported by a one-to-one match between observed and computer-simulated images. An Al-rich limit of x=2/3 for mullite is deduced on the basis of stereochemical considerations. Different ordering schemes for the tetrahedral cations are believed to result in the orientation change of the APB's near x=0.5 composition.     

Motion of salt water and associated fronts in tideless estuaries

The hydrodynamics of saline water in Polish estuaries are addressed in this paper. The phenomena are described on the basis of field data from several types of estuaries along the Polish Baltic Coast. Field measurements were made to reveal and to characterize the physical processes in these estuaries; this information was then used for analytic testing and verification of mathematical models. The results demonstrate the unsteady and changeable nature of both the flow conditions and the motion of salt water in tideless estuaries. The magnitudes and directions of the barotropic and baroclinic horizontal pressure gradients have a marked influence on the flow characteristics and motion of salt water in these tideless estuaries.