Intercomparison of Stratospheric Chemistry Models under Polar Vortex Conditions

Several stratospheric chemistry modules from box, 2-D or 3-D models, have been intercompared. The intercomparison was focused on the ozone loss and associated reactive species under the conditions found in the cold, wintertime Arctic and Antarctic vortices. Comparisons of both gas phase and heterogeneous chemistry modules show excellent agreement between the models under constrained conditions for photolysis and the microphysics of polar stratospheric clouds. While the mean integral ozone loss ranges from 4–80% for different 30–50 days long air parcel trajectories, the mean scatter of model results around these values is only about ±1.5%. In a case study, where the models employed their standard photolysis and microphysical schemes, the variation around the mean percentage ozone loss increases to about ±7%. This increased scatter of model results is mainly due to the different treatment of the PSC microphysics and heterogeneous chemistry in the models, whereby the most unrealistic assumptions about PSC processes consequently lead to the least representative ozone chemistry. Furthermore, for this case study the model results for the ozone mixing ratios at different altitudes were compared with a measured ozone profile to investigate the extent to which models reproduce the stratospheric ozone losses. It was found that mainly in the height range of strong ozone depletion all models underestimate the ozone loss by about a factor of two. This finding corroborates earlier studies and implies a general deficiency in our understanding of the stratospheric ozone loss chemistry rather than a specific problem related to a particular model simulation.     

Understanding Climatic Impacts, Vulnerabilities, and Adaptation in the United States: Building a Capacity for Assessment

Based on the experience of the U.S. National Assessment, we propose a program of research and analysis to advance capability for assessment of climate impacts, vulnerabilities, and adaptation options. We identify specific priorities for scientific research on the responses of ecological and socioeconomic systems to climate and other stresses; for improvement in the climatic inputs to impact assessments; and for further development of assessment methods to improve their practical utility to decision-makers. Finally, we propose a new institutional model for assessment, based principally on regional efforts that integrate observations, research, data, applications, and assessment on climate and linked environmental-change issues. The proposed program will require effective collaboration between scientists, resource managers, and other stakeholders, all of whose expertise is needed to define and prioritize key regional issues, characterize relevant uncertainties, and assess potential responses. While both scientifically and organizationally challenging, such an integrated program holds the best promise of advancing our capacity to manage resources and the economy adaptively under a changing climate.     

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     

Climate Dangers and Atoll Countries

Climate change-induced sea-level rise, sea-surface warming, and increased frequency and intensity of extreme weather events puts the long-term ability of humans to inhabit atolls at risk. We argue that this risk constitutes a dangerous level of climatic change to atoll countries by potentially undermining their national sovereignty. We outline the novel challenges this presents to both climate change research and policy. For research, the challenge is to identify the critical thresholds of change beyond which atoll social-ecological systems may collapse. We explain how thresholds may be behaviorally driven as well as ecologically driven through the role of expectations in resource management. The challenge for the international policy process, centred on the UN Framework Convention on Climate Change (UNFCCC), is to recognize the particular vulnerability of atoll countries by operationalising international norms of justice, sovereignty, and human and national security in the regime.     

Comparison of the Langrangian Footprint

We compare flux and concentration footprint estimates of athree-dimensional Lagrangian stochastic dispersion modelapplying backward trajectories with the results of ananalytical footprint model by Kormann and Meixner.The comparison is performed for varying stability regimesof the surface layer as well as for different measurementheights. In general, excellent correspondence is found.     

The parallel sum of matrices and its application in geodetic adjustments

Summary . It is well known that for the comparison and combination of geodetic networks their heterogeneous datum definitions are well to be considered. Various algorithms have been developed for this purpose. As an alternative concept to deal with hybrid datum problems, the operator parallel sum of matrices is introduced in this paper. To begin with, a definition is given and some basic properties are explained. To demonstrate the usefulness of the operator, two practical applications are given. The first deals with the estimation of parameters describing the deformation of two networks which are to be compared to each other. The second one treats the estimation of parameters representing the heterogeneous datum definitions of two networks which are to be merged into a hybrid network. It will be shown that – regardless of the datum definitions of the preadjusted individual networks – the parallel sum of matrices can be used to simplify the algorithms applied for the estimation of those parameters. Received 15 December 1995; Accepted 24 September 1996     

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     

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