The geopotential value <Emphasis Type="Italic">W</Emphasis><Subscript>0</Subscript> for specifying the relativistic atomic time scale and a global vertical reference system

The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W ₀. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W ₀ have been investigated. The rounded value W ₀ = 62636856.0 ± 0.5) m ² s ⁻² has already been adopted by the International Astronomical Union for the definition of the constant L _G = W ₀/c ² = 6.969290134 × 10⁻¹⁰ (where c is the speed of light), which is required for the realization of the relativistic atomic time scale. The constant L _G , based on the above value of W ₀, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W ₀ is used to specify a global vertical reference system (GVRS). W ₀ ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W ₀, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J ₂) as primary constants (parameters), then the ellipsoidal parameters (a,α) can be computed and adopted as derived parameters. The scale of the International Terrestrial Reference Frame 2000 (ITRF2000) has also been specified with the use of W ₀ to be consistent with the geocentric coordinate time. As an example of using W ₀ for a GVRS realization, the geopotential difference between the adopted W ₀ and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.     

The Phobos gravitational field modeled on the basis of its topography

The parameters of the best-fitting ellipsoid have been derived using the latest spherical harmonics of the Phobos topography (Duxbury, 1989) by solution of non-linear overdetermined inverse problem. The lengths of the equatorial axes of the ellipsoid have been determined (a = 12.9 km, b = 11.4 km). They are nearly the same as established by Duxbury (ibid.) on the basis of the linearized relationship between the squared lengths of ellipsoidal axes and the topography coefficients C ₂₀ and C _22. The length of the polar axis (c = 9.1 km) differs of about 20% from Duxbury's value. Supposing mass homogeneity of Phobos, the Stokes parameters of the external gravitational field have been derived up to those of the sixth degree and order. The large irregularities in the Phobos figure cause the values of the Duxbury's potential coefficients be fairly inaccurate except the harmonics C ₂₀, C ₃₂, S ₄₃ and S ₅₁, i.e. linearized relationship between gravity and topography cannot be applied for Phobos. Finally, positions of the centre of figure and the directions of the principal axes of inertia have been established.     

Spatio-temporal regression kriging model of mean daily temperature for Croatia

High resolution gridded mean daily temperature datasets are valuable for research and applications in agronomy, meteorology, hydrology, ecology, and many other disciplines depending on weather or climate. The gridded datasets and the models used for their estimation are being constantly improved as there is always a need for more accurate datasets as well as for datasets with a higher spatial and temporal resolution. We developed a spatio-temporal regression kriging model for Croatia at 1 km spatial resolution by adapting the spatio-temporal regression kriging model developed for global land areas. A geometrical temperature trend, digital elevation model, and topographic wetness index were used as covariates together with measurements from the Croatian national meteorological network for the year 2008. This model performed better than the global model and previously developed models for Croatia, based on MODIS land surface temperature images. The R2 was 97.8% and RMSE was 1.2 °C for leave-one-out and 5-fold cross-validation. The proposed national model still has a high level of uncertainty at higher altitudes leaving it suitable for agricultural areas that are dominant in lower and medium altitudes.     

Reconstruction of missing data in remote sensing images using conditional stochastic optimization with global geometric constraints

This paper addresses the issue of missing data reconstruction for partially sampled, two-dimensional, rectangular grid images of differentiable random fields. We introduce a stochastic gradient–curvature (GC) reconstruction method, which is based on the concept of a random field model defined by means of local interactions (constraints). The GC reconstruction method aims to match the gradient and curvature constraints for the entire grid with those of the sample using conditional Monte Carlo simulations that honor the sample values. The GC reconstruction method does not assume a parametric form for the underlying probability distribution of the data. It is also computationally efficient and requires minimal user input, properties that make it suitable for automated processing of large data sets (e.g. remotely sensed images). The GC reconstruction performance is compared with established classification and interpolation methods for both synthetic and real world data. The impact of various factors such as domain size, degree of thinning, discretization, initialization, correlation properties, and noise on GC reconstruction performance are investigated by means of simulated random field realizations. An assessment of GC reconstruction performance on real data is conducted by removing randomly selected and contiguous groups of points from satellite rainfall data and an image of the lunar surface.     

Secular Love numbers of the major planets

Secular Love numbers of the major planets have been determined by solving the first (Dirichlet's) boundary — value problem for the level ellipsoid as the boundary surface. It has been demonstrated that the rotational distortions are responsible for the actual figure of the bodies above. The 6th degree Stokes zonal parameter for Uranus and for Neptune have been predicted.     

Apatite fission track and (U-Th)/He thermochronology of the Rochovce granite (Slovakia) – implications for the thermal evolution of the Western Carpathian-Pannonian region

The thermal evolution of the only known Alpine (Cretaceous) granite in the Western Carpathians (Rochovce granite) is studied by low-temperature thermochronological methods. Our apatite fission track and apatite (U-Th)/He ages range from 17.5 ± 1.1 to 12.9 ± 0.9 Ma, and 12.9 ± 1.8 to 11.3 ± 0.8 Ma, respectively. The data thus show that the Rochovce granite records a thermal event in the Middle to early Late Miocene, which was likely related to mantle upwelling, volcanic activity, and increased heat flow. During the thermal maximum between ~17 and 8 Ma, the granite was heated to temperatures ? 60 °C. Increase of cooling rates at ~12 Ma recorded by the apatic fission track and (U-Th)/He data is primarily related to the cessation of the heating event and relaxation of the isotherms associated with the termination of the Neogene volcanic activity. This contradicts the accepted concept, which stipulates that the internal parts of the Western Carpathians were not thermally affected during the Cenozoic period. The Miocene thermal event was not restricted to the investigated part of the Western Carpathians, but had regional character and affected several basement areas in the Western Carpathians, the Pannonian basin and the margin of the Eastern Alps.     

A model for Doppler peak spectral shift for low grazing angle sea scatter

A model is formulated for Doppler spectral characteristics of radar sea scatter for low grazing angles, and is compared with previous radar measurements reported in the literature. The Doppler model is based upon the two-scale model for radar scatter, with scatterer motions hypothesized as due to the orbital wave velocity of the large-scale waves, Stokes and wind drift currents, and the phase velocity of the small-scale Bragg scatterers. Expressions for Doppler shifts due to these motions are derived, and are given as a function of wave height, wave period, and wind speed. Although this model appears to account for the peak Doppler shift of the sea-scatter Doppler spectrum for vertical polarization, it is insufficient to describe horizontally and cross-polarized data, which have larger mean Doppler shifts. However, these two cases are found to scale very closely with the nearly simultaneous vertically polarized data for the variety of environmental conditions reported. Implications of the extension of these results to higher-angle remote-sensing applications are discussed.