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Physical geodesy applies potential theory to study the Earth’s gravitational field in space outside and up to a few km inside the Earth’s mass. Among various tools offered by this theory, boundary-value problems are particularly popular for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the nineteenth century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable; the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice. [ABSTRACT FROM AUTHOR]

Relict vegetation of water-splashed petrifying rocks with calcareous tufa formation dominated by the fern Adiantum capillus-veneris and wetland bryophytes (phytosociological class Adiantetea) was investigated in Georgia, Caucasus biodiversity hotspot. The study brings the first phytosociological data on this scarce community in the Caucasus based on a novel dataset of vegetation plot records. A classification analysis revealed two main vegetation communities. They are represented by the Caucasian community recorded in the Mtkvari River valley inside the Tbilisi city (E Georgia) and the Colchic community developed under the humid, warm-temperate climate of Colchis (W Georgia), one of the key refugia of Tertiary flora across W Eurasia. To compare newly recorded vegetation types and so far described associations of the Adiantetea class, we used a broader dataset of the analogous communities reported from Europe and surroundings. It associated the Caucasian community with the pan-Mediterranean association Eucladio-Adiantetum. It was characterized by subhalophytes (e.g. Samolus valerandi), Eucladium verticillatum as a dominant bryophyte, and the absence of relict or endemic vascular plant species. The Colchic community represented a previously undescribed community. Therefore, we designated a new association Saxifrago cymbalariae-Adiantetum capilli-veneris delineated by the characteristic species of the Colchic-Caucasian territory (e.g. Hedera colchica, Saxifraga cymbalaria) and Palustriella commutata as the dominant bryophyte. Both associations belong to the Mediterranean-Atlantic alliance Adiantion. Described communities require conservation attention for their rarity, refugial character and presence of relict and endemic species. Modifications of the hydrological regime and construction activities are among their most important potential threats. [ABSTRACT FROM AUTHOR]

Physical heights is one of the most important topics in physical geodesy. Their original concept, introduced in the 19-th century, defined physical heights as lengths of plumblines of the Earth's gravity field between the geoid and points of interest. There are orthometric heights of surface points, that have been traditionally estimated by spirit levelling and measured gravity; however, the knowledge of the density distribution of topographic masses (masses between the geoid and Earth's surface) is required that significantly affects their determinability. This was also the main reason why a new type of physical heights was proposed in the mid of the 20-th century. Normal heights approximate orthometric heights in a sense that the Earth's gravity field is replaced by the normal gravity field, an analytic model based on the theory of an equipotential ellipsoid. This height system has been introduced since that time in different countries in Europe and beyond. Contrary to the classical height system based on orthometric heights, its counterpart based on normal heights may have slightly different definitions. Moreover, normal heights are often defined as heights of points above the quasigeoid. This contribution reviews alternative definitions of normal heights and respective height systems. It is argued that both orthometric and normal heights refer to the geoid. In the case physical heights are estimated by satellite positioning, normal heights must be computed through the height anomaly estimated at each point of interest, whether it is below, at or above the Earth's surface. On the contrary, orthometric heights of all points along the same plumbline, be it below, at or above the Earth's surface, are estimated by introducing one value of the geoid height. Normal heights of surface points can be estimated by spirit levelling easier than orthometric heights as no topographic mass density hypothesis is required; however, one has to keep in mind the gravity field approximation used both for their definition and realization. [ABSTRACT FROM AUTHOR]

The aim of the study was to evaluate treatment protocols for improvement of clinical and bacteriological cure rate of non-severe clinical mastitis (CM) and selective dry cow therapy (SDCT). Mastitis management based on on-farm commercial culture system MicroMastTM and data analysis were implemented into two dairy herds. Quarters with evidence of Gram-positive agents were treated using benzyl penicillin or amoxicillin and/or by amoxicillin with clavulanic acid. In herd A, 31 quarters of non-severe CM were recorded. Of them, Streptococcus uberis was isolated in 16 (51.6%), non-aureus staphylococci (NAS) in 8 (25.8%), E. coli in 5 (16.1%) and no growth in 2 (6.5%) cases. Bacteriological cure was observed in 24/29 (82.8%) quarters. Antimicrobial consumption was reduced from 3.56 to 2.33 doses per case. Under the SDCT protocol, 28 quarters (13.2%) of 53 cows dried-off were included, achieving a reduction by 86.8% on the quarter level. In herd B, 23 quarters of non-severe CM were recorded. Of them, S. uberis and Escherichia coli were identified equally in 8 (34.8%) samples and NAS in 2 (8.7%) samples and with no growth in 5 (21.7%) cases. Bacteriological cure was achieved in 17/18 quarters (94.4%). Antimicrobial consumption was reduced from 4.45 to 1.83 doses per case. Only 5 (1.7%) quarters of 72 cows were included for SDCT with reduction in consumption of antimicrobials by 98.3% on the quarter level. In summary, innovated treatment protocols based on results of on-farm culture enabled a significant reduction of antimicrobial consumption and improvement of bacteriological cure rate in conditions of practise. [ABSTRACT FROM AUTHOR]

The gravitational field of the Earth reflects Earth's surface mass redistribution and its inner structure and dynamics. Satellite gravimetry techniques have been used to observe the Earth's external gravitational field and its temporal variations on a global scale. The global gravitational models from satellite gravimetry, typically in terms of spherical harmonic coefficients, are crucial in geodetic, geodynamic, geophysical, hydrological, glaciological, oceanographic, and many other geoscience applications. In this paper, we provide a comprehensive overview of theoretical definitions describing relationships between the spherical harmonic coefficients and different satellite gravimetry observables such as orbital perturbations in terms of satellite positions, velocities, and accelerations; satellite-to-satellite range rates; and gravitational gradients. Products and applications of the Earth's static global gravitational models are presented and discussed in the context of determination of the gravimetric geoid and physical heights, gravimetric and isostatic crustal thickness, bathymetric depths, glacier bedrock relief, sediment thickness, geostrophic and eddy currents, Earth's inertia tensor and dipole, precession and nutation parameters of the Earth's rotation, and prediction of the satellite orbital geometry. Furthermore, applications and advances of the Earth's time-variable gravitational models for monitoring large earthquakes, hydrological mass transport, Earth's rotation parameters, and vertical crustal motions (due to the glacial isostatic adjustment and other phenomena) are presented. Finally, future trends and prospects in the satellite gravimetry are discussed. • A comprehensive mathematical foundations of satellite gravimetry is presented. • A complete progress for applications of satellite gravimetry products is shown. • An overview for future satellite gravimetry missions and trend is given. [ABSTRACT FROM AUTHOR]