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     

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

The twin perspective 4 point (twin P4P) problem – also called the combined three dimensional resection-intersection problem – is the problem of finding the position of a scene object from 4 correspondence points and a scene stereopair. While the perspective centers of the left and right scene image are positioned by means of a double three dimensional resection, the position of the scene object imaged on the left and right photograph is determined by a three dimensional intersection based upon given resected perspective centers. Here we present a new algorithm solving the twin P4P problem by means of M?bius barycentric coordinates. In the first algorithmic step we determine the distances between the perspective centers and the unknown intersected point by solving a linear system of equations. Typically, area elements of the left and right image build up the linear equation system. The second algorithmic step allows for the computation of the M?bius barycentric coordinates of the unknown intersected point which are thirdly converted into three dimensional object space coordinates {X,Y,Z} of the intersected point. Typically, this three-step algorithm based upon M?bius barycentric coordinates takes advantage of the primary double resection problem from which only distances from four correspondence points to the left and right perspective centre are needed. No orientation parameters and no coordinates of the left and right perspective center have to be made available. Received 1 May 1996; Accepted 13 September 1996     

Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution

Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same degree as that of the original spherical Poisson kernel. Received: 4 June 1996 / Accepted: 7 April 1997     

The spacetime gravitational field of a deformable body

The high-resolution analysis of orbit perturbations of terrestrial artificial satellites has documented that the eigengravitation of a massive body like the Earth changes in time, namely with periodic and aperiodic constituents. For the space-time variation of the gravitational field the action of internal and external volume as well as surface forces on a deformable massive body are responsible. Free of any assumption on the symmetry of the constitution of the deformable body we review the incremental spatial (“Eulerian”) and material (“Lagrangean”) gravitational field equations, in particular the source terms (two constituents: the divergence of the displacement field as well as the projection of the displacement field onto the gradient of the reference mass density function) and the `jump conditions' at the boundary surface of the body as well as at internal interfaces both in linear approximation. A spherical harmonic expansion in terms of multipoles of the incremental Eulerian gravitational potential is presented. Three types of spherical multipoles are identified, namely the dilatation multipoles, the transport displacement multipoles and those multipoles which are generated by mass condensation onto the boundary reference surface or internal interfaces. The degree-one term has been identified as non-zero, thus as a “dipole moment” being responsible for the varying position of the deformable body's mass centre. Finally, for those deformable bodies which enjoy a spherically symmetric constitution, emphasis is on the functional relation between Green functions, namely between Fourier-/ Laplace-transformed volume versus surface Love-Shida functions (h(r),l(r) versus h ^′(r),l ^′(r)) and Love functions k(r) versus k ^′(r). The functional relation is numerically tested for an active tidal force/potential and an active loading force/potential, proving an excellent agreement with experimental results. Received: December 1995 / Accepted: 1 February 1997     

Non-linear climate feedback analysis in an atmospheric general circulation model

 A method is described for evaluating the ‘partial derivatives’ of globally averaged top-of-atmosphere (TOA) radiation changes with respect to basic climate model physical parameters. This method is used to analyse feedbacks in the Australian Bureau of Meteorology Research Centre general circulation model. The parameters considered are surface temperature, water vapour, lapse rate and cloud cover. The climate forcing which produces the changes is a globally uniform sea surface temperature (SST) perturbation. The first and second order differentials of model parameters with respect to the forcing (i.e. SST changes) are estimated from quadratic least square fitting. Except for total cloud cover, variables are found to be strong functions of global SST. Strongly non-linear variations of lapse rate and high cloud amount and height appear to relate to the non-linear response in penetrative convection. Globally averaged TOA radiation differentials with respect to model parameters are also evaluated. With the exception of total cloud contributions, a high correlation is generally found to exist, on the global mean level, between TOA radiation and the respective parameter perturbations. The largest non-linear terms contributing to radiative changes are those due to lapse rate and high cloud. The contributions of linear and non-linear terms to the overall radiative response from a 4 K SST perturbation are assessed. Significant non-linear responses are found to be associated with lapse rate, water vapour and cloud changes. Although the exact magnitude of these responses is likely to be a function of the particular model as well as the imposed SST perturbation pattern, the present experiments flag these as processes which cannot properly be understood from linear theory in the evaluation of climate change sensitivity. Received: 16 January 1997/Accepted: 9 May 1997     

Column Amounts of ClONO2, HCl, HNO3, and HF from Ground-Based FTIR Measurements Made Near Kiruna, Sweden, in Late Winter 1994

During SESAME phase I ground-based FTIR measurements were performed atEsrange near Kiruna, Sweden, from 28 January to 26 March 1994. Zenith columnamounts of ClONO₂, HCl, HF, HNO₃,O₃, N₂O, CH₄, and CFC-12 werederived from solar absorption spectra. Time series of ClONO₂and HCl indicate a chlorine activation at the end of January and around 1March. On 1 March a very low amount of HCl of 2.09times; 10¹⁵molec. cm^-2 was detected, probably caused by a second chlorineactivation phase starting from an already decreased amount of HCl. The ratioof column amounts of HCl to ClONO₂ decreased inside the vortexfrom about 1 in January to 0.4 in late March compared to values of about 2outside the vortex. Although the Arctic stratosphere was rather warm in winter1993/94 and PSCs occurred seldom, chlorine partitioning into its reservoirspecies HCl and ClONO₂ changed during that winter andClONO₂ is the major chlorine reservoir at the end of thewinter as in cold winters like 1991/92 and 1994/95.     

Reactive Nitrogen Compounds at Spitsbergen in the Norwegian Arctic

Simultaneousindependent measurements of NO_y and NO_x(NO_x= NO + NO₂) by high-sensitivitychemiluminescence systems and of PAN (peroxyacetylnitrate) and PPN (peroxypropionyl nitrate) by GC-ECDwere made at Spitsbergen in the Norwegian Arcticduring the first half year of 1994. The average mixingratio of the sum of PAN and PPN (denoted PANs)increased from around 150 pptv in early winter to amaximum of around 500 pptv in late March, whereasepisodic peak values reached 800 pptv. This occurredsimultaneously with a maximum in ozone which increasedto 45–50 ppbv in March–April. The average NO_xmixing ratio was 27 pptv and did not show any cyclethrough the period. The NO_y mixing ratio showeda maximum in late March, while the difference betweenNO_y and PAN decreased during spring. This is anindication of the dominance of PAN in the NO_ybudget in the Arctic, but possible changes in theefficiency of the NO_y converter could alsocontribute to this. Although most PAN in theArctic is believed to be due to long range transport,the observations indicate local loss and formationrates of up to 1–2 pptv h^-1 in April–May.Measurements of carbonyl compounds suggest thatacetaldehyde was the dominant, local precursor ofPAN.Now at 1.     

Non-stationary Markov chains for modelling daily sunshine at São Paulo, Brazil

Summary Non-stationary, four-state Markov chains were used to model the sunshine daily ratios at São Paulo, Brazil. Fourier series were used to account for the periodic seasonal variations in the transition probabilities. All the regressions and tests, based on Generalized Linear Models, were made through the software GLIM. Significant seasonal variations were detected in the conditional probabilities, especially for the extreme categories of overcast and clear days. The fitted model provided a concise summary of the daily data, useful for short-range (1 day) sunshine predictions and simulations.With 6 Figures     

SENSITIVITY OF MALARIA, SCHISTOSOMIASIS AND DENGUE TO GLOBAL WARMING

Global assessment of the potential impacts of anthropogenically-induced climate change on vector-borne diseases suggests an increase in extent of the geographical areas susceptible to transmission of malarial Plasmodium parasites, dengue Flavivirus and Schistosoma worms. The transmission potential of the three associated vector-borne diseases studied is highly sensitive to climate changes on the periphery of the currently endemic areas and at higher altitudes within such areas. Our findings vis-à-vis the present endemic areas indicate that the increase in the epidemic potential of malaria and dengue transmission may be estimated at 12–27% and 31–47%, respectively, while in contrast, schistosomiasis transmission potential may be expected to exhibit a 11–17% decrease.     

Climatic and environmental reconstructions based on fossil assemblages from middle devensian (Weichselian) deposits of the river Thames at south kensington, central London, UK

Fossiliferous silts within the Late Pleistocene Kempton Park Gravel, of the River Thames Valley, were exposed in 1980 during foundation works for the Ismaili Centre in South Kensington, London. The results of a multidisciplinary study of the geomorphology, sediments, fossil plants, vertebrates, molluscs, ostracods and insects are reported. The silts were deposited under two distinct climatic regimes; a lower unit accumulated when the climate was arctic and an upper when the temperatures were at least as warm as those of the present day. Both these units occupy the same channel system and are separated from one another by less than a metre of sediment, implying that the climatic change was probably sudden and intense. The strongest evidence for this climatic difference comes from a study of the Coleoptera, which show an almost complete replacement of the arctic element in the fauna by a suite of temperate species. Palaeotemperature reconstructions using the Mutual Climatic Range method, based on the coleopteran assemblages from the lower unit, suggest that the mean temperature of the warmest month was 9±2 °C and that of the coldest month −22±10 °C. For the upper unit the mean temperature of the warmest month had risen to about 17 °C and that of the coldest month to about −4 °C. The episode represented by the lower unit, with its arctic climate, had not previously been recognized in the Thames Valley. The fauna from the upper, temperate, unit is very similar to that from other sites in the Kempton Park Gravel, such as that from Isleworth, 10 km upriver, which, like the upper unit at the Ismaili Centre, was characterized by the virtual absence of trees. It would appear that in such cases this treelessness does not indicate cold conditions, equivalent to those of the modern tundra, but may instead result from a combination of ecological and temporal factors. The value of multidisciplinary studies in reaching such conclusions is emphasized.The temperate episode described here is correlated with the thermal maximum at the early part of the Upton Warren Interstadial Complex. An earlier suggestion, based on amino acid epimerization ratios, that the Upton Warren Interstadial correlates with Oxygen Isotope Sub-stage 5a is not supported by the data, which show no evidence of the forested environments that characterized this period in both Britain and the adjacent Continent. It is thought that the temperate deposits at the Ismaili Centre belong to the Middle (Pleniglacial), rather than the Early, Devensian (Weichselian) and are equivalent to Oxygen Isotope Stage 3.