New insights in remote sensing applications to obtain information about water bodies
Multi-year experience of applying ERS data at the Hydrology Department of the Lomonosov Moscow State University demonstrated their high information value and efficiency when addressing a variety of global and local hydrological tasks. They can be extremely useful in determining the status of water bodies of different scale, parameterizations of different river runoff characteristics in order to highlight the ranges of their change, corresponding to dangerous hydrological events, in assessing the impact of climate change on water resources and the nature of hydrological processes.
Gravity Recovery And Climate Experiment (GRACE) twin-satellites have been observing the mass transports of the Earth inferred by the monthly gravity field solutions in terms of spherical harmonic coefficients since 2002. In particular, GRACE temporal gravity field observations revolutionize the study of basin-scale hydrology, because gravity data reflect mass changes related to groundwater redis- tribution, ice melting, and precipitation accumulation over large regions. However, to use the GRACE data products de-striping/filtering is required. We apply the Mul- tichannel Singular Spectrum Analysis (MSSA) technique to filter GRACE data and separate its principal components (PCs) at different periodicities. Data averaging over the 15 largest river basins of Russia was performed. Spring 2013 can be char- acterized by the extremely large snow accumulation occurred in Russia. Melting of this snow induced large floods and abrupt increase of river levels. The excep- tional maxima are evident from GRACE observations, which can be compared to the hydrological models, such as GLDAS or WGHM, and ground observations. Long-periodic climate-related changes were separated into PC 2. It has been ob- served that there were mass increases in Siberia and decreases around the Caspian sea. Overall trend over Russia demonstrates mass increase until 2009, when it has a maximum, following by the decrease.
This translation of selected chapters from Mauriac’s Notebooks reveals the meaning of such terms as “an engaged writer”, “an engaged journalist,” faith and grace.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.