The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation II-the topographic-isostatic geoid

In Part I we focussed on a convergent representation of the gravitational potential generated bytopographic masses on top of the equipotential surface atMean Sea Level, thegeoid, and by those masses which compensate topography. Topographic masses have also been condensated, namely represented by a single layer. Part II extends the computation of the gravitational field of topographic-isostatic masses by a detailed analysis of itsforce field in terms ofvector-spherical harmonic functions. In addition, the discontinuous mass-condensated topographic gravitational force vector (head force) is given. Once we identify theMoho discontinuity asone interface of isostatically compensated topographical masses, we have computed the topographic potential and the gravitational potential which is generated by isostatically compensated masses atMean Sea Level, the geoid, and illustrated by various figures of geoidal undulations. In comparison to a data oriented global geoid computation ofJ. Engels (1991) the conclusion can be made that the assumption of aconstant crustal mass density, the basic condition for isostatic modeling, does not apply. Insteaddensity variations in the crust, e.g. betweenoceanic and continental crust densities, have to be introduced in order to match the global real geoid and its topographic-isostatic model. The performed analysis documents that thestandard isostatic models based upon aconstant crustal density areunreal.     

A comparison of the photospheric and interplanetary magnetic fields during the flight of Mariner IV

The polarity of the interplanetary magnetic field observed by the Mariner IV spacecraft is compared to the polarity of the photospheric magnetic field observed with the solar magnetograph at Mt. Wilson Observatory. Unlike the results obtained from observations during the flight of IMP-I, these polarities are not well correlated when the photospheric polarity is determined from data along a narrow latitudinal strip. It is suggested that the structure of the interplanetary field is often related to major features in the photospheric field that are observed over a broad range of solar latitudes.     

Time–space continuity of daily maps of fractional snow cover and albedo from MODIS

Using reflectance values from the seven MODIS “land” bands with 250 or 500 m resolution, along with a corresponding cloud product, we estimate the fraction of each 500 m pixel that snow covers, along with the albedo of that snow. The daily products have data gaps and errors because of cloud cover and sensor viewing geometry. Rather than make users interpolate and filter these patchy daily maps without completely understanding the retrieval algorithm and instrument properties, we use the daily time series to improve the estimate of the measured snow properties for a particular day. We use a combination of noise filtering, snow/cloud discrimination, and interpolation and smoothing to produce our best estimate of the daily snow cover and albedo. We consider two modes: one is the “predictive” mode, whereby we estimate the snow-covered area and albedo on that day using only the data up to that day; the other is the “retrospective” mode, whereby we reconstruct the history of the snow properties for a previous period.     

Tropospheric Ozone in a Global-Scale Three-Dimensional Lagrangian Model and Its Response to NOX Emission Controls

A three-dimensional Lagrangian tropospheric chemistry modelis used toinvestigate the impact of human activities on the tropospheric distributionofozone and hydroxyl radicals. The model describes the behaviour of 50 speciesincluding methane, carbon monoxide, oxides of nitrogen, sulphur dioxide andnineorganic compounds emitted from human activities and a range of other sources.Thechemical mechanism involves about 100 chemical reactions of which 16 arephotochemical reactions whose diurnal dependence is treated in full. The modelutilises a five minute chemistry time step and a three hour advection timestepfor the 50,000 air parcels. Meteorological data for the winds, temperatures,clouds and so on are taken from the UK Meteorological Office global model for1994 onwards. The impacts of a 50% reduction in European NO_Xemissions onglobal ozone concentrations are assessed. Surface ozoneconcentrations decrease in summertime and rise in wintertime, but to differentextents.     

Comparing flow regime,channel hydraulics,and biological communities to infer flow–ecology relationships in the Mara River of Kenya and Tanzania

Abstract

Equatorial rivers of East Africa exhibit unusually complex seasonal and inter-annual flow regimes, and aquatic and adjacent terrestrial organisms have adapted to cope with this flow variability. This study examined the annual flow regime over the past 40 years for three gauging stations on the Mara River in Kenya and Tanzania, which is of international importance because it is the only perennial river traversing the Mara-Serengeti ecoregion. Select environmental flow components were quantified and converted to ecologically relevant hydraulic variables. Vegetation, macroinvertebrates, and fish were collected and identified at target study sites during low and high flows. The results were compared with available knowledge of the life histories and flow sensitivities of the riverine communities to infer flow–ecology relationships. Management implications are discussed, including the need to preserve a dynamic environmental flow regime to protect ecosystems in the region. The results for the Mara may serve as a useful model for river basins of the wider equatorial East Africa region.

Editor Z.W. Kundzewicz; Guest editor M. Acreman     

Concentration and Diffusion of Nutrients in the Interpore–Bottom Water System of the Ob River Estuary

Oceanology - On cruise 76 in 2019, the R/V Akademik Mstislav Keldysh completed the Gulf of Ob–Kara Sea slope transect. Samples of bottom water and two sediment layers 1 cm thick were obtained...     

Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates

 The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of M?bius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex generated by the unknown point and the four known points. Substitution of M?bius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4. contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gau? (1842), A. Schreiber (1908) and A.␣Ansermet (1910). Received: 05 March 1996; Accepted: 15 October 1996     

Solving the problem of shock wave attenuation in an obstacle during a contact explosion of a high-energy material charge

A problem of estimation of shock wave attenuation in an obstacle under an explosion of a high-energy material (explosive) charge on its surface is considered. An algorithm for its solution is proposed using the analytical and semiempirical dependences generally recognized in explosion physics.     

Evolution and Spectrum of the Radio Emission of Tycho’s Supernova Remnant

The radio spectrum of Tycho’s Supernova Remnant is constructed at frequencies 12.6–143 000 MHz for epoch 2010.3, taking into account the secular decrease in the radio flux density of the remnant at the rate d = ?(0.46 ± 0.03)%/year:

$$S_\nu ^{3C10} (t = 2010.3) = (43.1 \pm 1.8 Jy)(\nu [GHz])^{ - (0.592 \pm 0.019) + (0.041 \pm 0.012)\log (\nu [GHz])} .$$

The spectrum has positive curvature. The presence of a low-frequency turnover in the spectrum of the radio source 3C10 with its maximum at 7.7 MHz is predicted, due to absorption in the interstellar medium in the direction toward the source.