Climate-Years in the True Prairie: Temporal Fluctuations of Ecologically Critical Climate Conditions

The True Prairie (TP) is a large area in the central U.S. which was a tall grass prairie for thousands of years prior to its conversion to crop land. An analysis of climatically controlling factors indicated that the tall grass prairie is favored by the ratio of warm season precipitation to potential evapotranspiration exceeding 0.75 (west boundary), cold season precipitation less than 38 cm (south boundary), high cold-season frequency of thunderstorms (north boundary), and high drought frequencies (entire region). A `climate-year' approach was used to assess the temporal and spatial variability of these conditions during the 20thcentury. This analysis did not reveal any long-term trends in most climate-year types, although there were significant decadal-scale fluctuations, most notably a high frequency of drought-type years in the 1930s and 1950s. However, the well-documented upward trend in precipitation is manifested in an increasing frequency of one climate-year type characterized by above normal cold season precipitation in the southern border area of the TP.     

In-situ Formation of Light-Absorbing Organic Matter in Cloud Water

Current climate models seem to underestimate the flux of solar energy absorbed by the global troposphere. All of these models are constrained with the assumption that cloud droplets consist of pure water. Here we demonstrate in a simple laboratory experiment that aromatic hydroxy-acids which are found in continental fine aerosol can react with hydroxyl radicals under typical conditions prevalent in cloud water influenced by biomass burning. The reactions yield colored organic species which do absorb solar radiation. We also suggest that the products of such reactions may be humic-like substances whose presence in continental aerosol has been confirmed but their source mechanisms are still much sought after. We also attempt to give a first order estimate of the enhancement of water absorption at a visible wavelength under atmospheric conditions.     

Modelling of the OASIS Energy Flux Measurements Using Two Canopy Concepts

Two land surface schemes, SCAM and CSIRO9, were used to model the measured energy fluxes during the OASIS (Observations At Several Interacting Scales) field program. The measurements were taken at six sites along a 100 km rainfall gradient. Two types of simulations were conducted: (1) offline simulations forced with measured atmospheric input data at each of the six sites, and (2) regional simulations with the two land surface schemes coupled to the regional climate model DARLAM.The two land surface schemes employ two different canopy modelling concepts: in SCAM the vegetation is conceptually above the ground surface, while CSIRO9 employs the more commonly used `horizontally tiled' approach in which the vegetation cover is modelled by conceptually placing it beside bare ground. Both schemes utilize the same below-ground components (soil hydrological and thermal models) to reduce the comparison to canopy processes only. However, the ground heat flux, soil evaporation and evapotranspiration are parameterised by the two canopy treatments somewhat differently.Both canopy concepts reproduce the measured energy fluxes. SCAM has a slightly higher root-mean standard error in the model-measurement comparison for the ground heat flux. The mean surface radiative temperature simulated by SCAM is approximately 1K lower than in the CSIRO9 simulations. However, the soil and vegetation temperatures (which contribute to the radiative temperature) varied more in the CSIRO9 simulations. These larger variations are due to the absence of a representation of the aerodynamic interactions between vegetation and ground.     

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     

On the Spatial Distribution and Seasonal Variation of Lower-Troposphere Ozone over Europe

Surface ozone data from 25 Europeanlow-altitude sites and mountain sites located between79°N and 28°N were studied. The analysiscovered the time period March 1989–February 1993.Average summer and winter O₃ concentrations inthe boundary layer over the continent gave rise togradients that were strongest in the north-west tosouth-east direction and west-east direction, respectively. WintertimeO₃ ranged from 19 to 27 ppbover the continent, compared to about 32 ppb at thewestern border, while for summer the continentalO₃ values ranged between 39 and 56 ppb and theoceanic mixing ratios were around 37 ppb. In the lowerfree troposphere average wintertime O₃ mixingratios were around 38 ppb, with only an 8 ppbdifference between 28°N and 79°N. For summerthe average O₃ levels decreased from about 55 ppbover Central Europe to 32 ppb at 79°N. Inaddition, O₃ and O_x(= O₃ + NO₂)in polluted and clean air were compared. Theamplitudes of the seasonal ozone variations increasedin the north-west to south-east direction, while thetime of the annual maximum was shifted from spring (atthe northerly sites) to late summer (at sites inAustria and Hungary), which reflected the contributionof photochemical ozone production in the lower partsof the troposphere.     

RECOGNISING THE UNCERTAINTY IN THE QUANTIFICATION OF THE EFFECTS OF CLIMATE CHANGE ON HYDROLOGICAL RESPONSE

A widely used method of evaluating effects of climate change on flow regime is to perturb the climate inputs to a rainfall–runoff model and examine the effect on a statistic of the modelled flows. Such studies require four elements: a method of perturbing the climate, a rainfall–runoff model, a study catchment and a flow index. In practice the direction and magnitude of the estimated effects depend on each of the four elements, leading to concern over the usefulness and generality of the results. To investigate these uncertainties two climate scenarios and eight climate sensitivity tests have been applied to three UK catchments using two conceptual rainfall–runoff models in order to quantify effects of climate change on three flow indices representing mean runoff, flood magnitudes and low flows. The sensitivity tests were found to be useful to assess the suitability of the models to simulate flows outside the conditions experienced in their calibration. Both models gave internally consistent results but, on close examination, one model was found inappropriate for this application. Results show that the effect of climate change on flow varies between catchments and that different flow response indices can change in opposite directions, e.g. floods increased in magnitude while low flows reduced. Contrasting results were obtained from the two climate scenarios.