Meso-gamma scale forecasts using the nonhydrostatic model LM

Summary ?The nonhydrostatic model LM was developed for small scale operational predictions. Advances in computer development will give the possibility of operational models of a rather fine scale, which will cover the meso-gamma scale. The LM is currently applied at a scale of 7 km and an increase of the operational resolution to 2.5 km is planned for the next few years. Predictions of such high resolution require to abandon the hydrostatic assumption, which is used with most current operational weather prediction models. The LM was designed to cover all resolutions from 50 m to 50 km with an efficiency making it suitable for operational use. It is a fully elastic model, using second order centred finite differences. The time integration is done using the Klemp–Wilhelmson method, treating the slow modes by a larger time step than the fast modes. The vertical propagation of the fast waves is done implicitly. After describing the design of the LM, this paper gives examples of model predictions at the meso-γ scale. Some results of the current operational application at the resolution 7 km are presented. Deficiencies in the localisation of model generated precipitation are investigated using an idealised bell shaped mountain and applying different resolutions. In this way the convergence to the correct solution can be investigated. From these results it is concluded, that orographic filtering is necessary and the effect of such filtering on precipitation forecasts is investigated. Finally, the prediction of a squall line over northern Germany is shown in order to demonstrate the potential of the model in forecasting the meso-γ scale. Received May 15, 2001; revised September 21, 2001     

The climatic impacts of land surface change and carbon management, and the implications for climate-change mitigation policy

Strategies to mitigate anthropogenic climate change recognize that carbon sequestration in the terrestrial biosphere can reduce the build-up of carbon dioxide in the Earth’s atmosphere. However, climate mitigation policies do not generally incorporate the effects of these changes in the land surface on the surface albedo, the fluxes of sensible and latent heat to the atmosphere, and the distribution of energy within the climate system. Changes in these components of the surface energy budget can affect the local, regional, and global climate. Given the goal of mitigating climate change, it is important to consider all of the effects of changes in terrestrial vegetation and to work toward a better understanding of the full climate system. Acknowledging the importance of land surface change as a component of climate change makes it more challenging to create a system of credits and debits wherein emission or sequestration of carbon in the biosphere is equated with emission of carbon from fossil fuels. Recognition of the complexity of human-caused changes in climate does not, however, weaken the importance of actions that would seek to minimize our disturbance of the Earth’s environmental system and that would reduce societal and ecological vulnerability to environmental change and variability.     

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     

地震前兆观测仪器标定问题的探讨

标定工作，在地震前兆观测仪器的研究，使用及所得数据的处理中均已成为一个不可少的环节，但缺少有关标定问题的基石性研究和讨论。本文就标定的定义、种类、目的、要求、存在的问题等做一粗线的讨论，以期今后加强这一工作的深入研究。     

丽江7.0级地震地下流体异常特征

通过对１９９６年２月３日云南丽江Ｍｓ７．０地震前震中周围水位、水氡、水汞、泉点宏观等地下流体共７１个台项观测资料的异常及综合特征分析，初步认为震前异常数量较多，异常时间分布具有整体性、同步性、集中性的特点，但异常主要集中在短期阶段，临震异常不突出；突间分布具有集中性和非均匀性，孕震区至远场影响区的异常比例最高，震源区内为相对“盲区”，且突出而肯定的宏观异常极少；异常的时空演变特征复杂，总体没有规律     

丽江大研镇震灾分布和地脉动测量结果之间的相关性

丽江７．０级地震后，大研镇被毁建筑物的地理分布呈显４条条带，伤亡人员的地理分布和上述条带重合。９１个短周期地脉动测点的观测资料表明，分布在上述条带内的大多数测点，其卓越周期大于０．３Ｓ；条带外的测点，其卓越周期一般在０．１Ｓ左右。作认为卓越周期和烈度异常之间良好的相关性，是因为地脉动卓越周期和地方震的频谱之间存在良好的相关性。