Prevailing-frequency approximation of the coupling ray theory along the SH and SV reference rays in a heterogeneous generally anisotropic medium which is approximately uniaxial

The behaviour of the actual polarization of an electromagnetic wave or elastic S–wave is described by the coupling ray theory, which represents the generalization of both the zero–order isotropic and anisotropic ray theories and provides continuous transition between them. The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. In a generally anisotropic or bianisotropic medium, the actual wave paths may be approximated by the anisotropic–ray–theory rays if these rays behave reasonably. In an approximately uniaxial (approximately transversely isotropic) anisotropic medium, we can define and trace the SH (ordinary) and SV (extraordinary) reference rays, and use them as reference rays for the prevailing–frequency approximation of the coupling ray theory. In both cases, i.e. for the anisotropic–ray–theory rays or the SH and SV reference rays, we have two sets of reference rays. We thus obtain two arrivals along each reference ray of the first set and have to select the correct one. Analogously, we obtain two arrivals along each reference ray of the second set and have to select the correct one. In this paper, we suggest the way of selecting the correct arrivals. We then demonstrate the accuracy of the resulting prevailing–frequency approximation of the coupling ray theory using elastic S waves along the SH and SV reference rays in four different approximately uniaxial (approximately transversely isotropic) velocity models.     

Remote sensing detection of atmospheric pollutants by differential absorption LIDAR 510M/SODAR PA2 mobile system

Summary Air pollution problem in the Czech Republic is very complex due to large number of factors as turbulent dispersion and chemical reactions concurring in the status of the PBL. For this 3D distribution of pollutants is a key information that cannot be given by conventional monitoring stations. Combined use of DIAL lidar and sodar can give access to such information. Case studies of air pollutants transport are presented using 3D concentration fields of NO₂ and ozone measured by lidar and meteorological conditions monitored by Doppler Sodar.     

Uncertainties in projected impacts of climate change on European agriculture and terrestrial ecosystems based on scenarios from regional climate models

The uncertainties and sources of variation in projected impacts of climate change on agriculture and terrestrial ecosystems depend not only on the emission scenarios and climate models used for projecting future climates, but also on the impact models used, and the local soil and climatic conditions of the managed or unmanaged ecosystems under study. We addressed these uncertainties by applying different impact models at site, regional and continental scales, and by separating the variation in simulated relative changes in ecosystem performance into the different sources of uncertainty and variation using analyses of variance. The crop and ecosystem models used output from a range of global and regional climate models (GCMs and RCMs) projecting climate change over Europe between 1961–1990 and 2071–2100 under the IPCC SRES scenarios. The projected impacts on productivity of crops and ecosystems included the direct effects of increased CO₂ concentration on photosynthesis. The variation in simulated results attributed to differences between the climate models were, in all cases, smaller than the variation attributed to either emission scenarios or local conditions. The methods used for applying the climate model outputs played a larger role than the choice of the GCM or RCM. The thermal suitability for grain maize cultivation in Europe was estimated to expand by 30–50% across all SRES emissions scenarios. Strong increases in net primary productivity (NPP) (35–54%) were projected in northern European ecosystems as a result of a longer growing season and higher CO₂ concentrations. Changing water balance dominated the projected responses of southern European ecosystems, with NPP declining or increasing only slightly relative to present-day conditions. Both site and continental scale models showed large increases in yield of rain-fed winter wheat for northern Europe, with smaller increases or even decreases in southern Europe. Site-based, regional and continental scale models showed large spatial variations in the response of nitrate leaching from winter wheat cultivation to projected climate change due to strong interactions with soils and climate. The variation in simulated impacts was smaller between scenarios based on RCMs nested within the same GCM than between scenarios based on different GCMs or between emission scenarios.     

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.     

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth’s topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth’s surface. It is based on an evolution of a surface, which approximates the Earth’s topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth’s surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth’s topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.     

Integral transformations of gradiometric data onto a GRACE type of observable

Integral transformations of gravitational gradients onto a Gravity Recovery And Climate Experiment (GRACE) type of observable are derived in this article. The gravitational gradients represent components of the gravitational tensor in the local north-oriented frame. The GRACE type of observable corresponds to a difference between two gravitational vectors as projected onto the line of sight between the two GRACE satellites. In total, three integral transformations relating vertical–vertical, vertical–horizontal and horizontal–horizontal gravitational gradients with the GRACE type of observable are provided. Spectral and closed forms of corresponding isotropic kernels are derived for each transformation. Special cases show that the integral transformations are general and relate gravitational gradients to many other quantities of the gravitational field, such as the gravitational vector, and its radial and tangential components. Correctness of the mathematical derivations is validated in a closed-loop simulation using synthetic data.