Presentations and representations of surface singular braid monoids

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands, then its two or respectively three dimensional representations are not faithful. We will also derive new presentations for the surface singular braid monoid, one with reduced the number of defining relations, and the other with reduced the number of its singular generators. We include surface singular braid formulations of all knotted surfaces in Yoshikawa's table.Comment: 15 pages, 3 figures, 1 tabl

A Comparison of Two Shallow Water Models with Non-Conforming Adaptive Grids: classical tests

In an effort to study the applicability of adaptive mesh refinement (AMR) techniques to atmospheric models an interpolation-based spectral element shallow water model on a cubed-sphere grid is compared to a block-structured finite volume method in latitude-longitude geometry. Both models utilize a non-conforming adaptation approach which doubles the resolution at fine-coarse mesh interfaces. The underlying AMR libraries are quad-tree based and ensure that neighboring regions can only differ by one refinement level. The models are compared via selected test cases from a standard test suite for the shallow water equations. They include the advection of a cosine bell, a steady-state geostrophic flow, a flow over an idealized mountain and a Rossby-Haurwitz wave. Both static and dynamics adaptations are evaluated which reveal the strengths and weaknesses of the AMR techniques. Overall, the AMR simulations show that both models successfully place static and dynamic adaptations in local regions without requiring a fine grid in the global domain. The adaptive grids reliably track features of interests without visible distortions or noise at mesh interfaces. Simple threshold adaptation criteria for the geopotential height and the relative vorticity are assessed.Comment: 25 pages, 11 figures, preprin

Spontaneous QBO‐like oscillations in an atmospheric model dynamical core

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/99691/1/grl50723.pd

Assessing adaptive mesh refinement (AMR) in a forced shallow-water model with moisture

Two forced shallow-water flow scenarios are explored in a 2D fourth-order finite-volume dynamical core with adaptive mesh refinement (AMR) to investigate AMR’s ability to track and resolve complex evolving features. Traditional shallow-water test cases are mainly characterized by large-scale smooth flows that do not effectively test the multiscale abilities of variable-resolution and AMR models to resolve sharp gradients and small-scale flow filaments. Therefore, adding forcing mechanisms to the shallow-water system to model key atmospheric processes adds complexity and creates small-scale phenomena. These can serve as foci for dynamic grid refinement while remaining simple enough to study the numerical design of a model’s dynamical core. The first shallow-water flow scenario represents a strengthening, tropical cyclone–like, vortex that is driven by a Betts–Miller-like convection scheme. The second shallow-water test is built upon a barotropically unstable jet with an added Kessler-like warm rain scheme that leads to precipitating frontal zones. The key feature of both tests is that there is significant sensitivity to the model grid while converging (structurally) at high resolution. Both test cases are investigated for a series of uniform resolutions and a variety of AMR tagging criteria. The AMR simulations demonstrate that grid refinement can resolve local features without requiring global high-resolution meshes. However, the results are sensitive to the refinement criteria. Criteria that trigger refinement early in a simulation reproduce the uniform-resolution reference solutions most reliably. In contrast, AMR criteria that delay refinement for several days require careful tuning of the AMR thresholds to improve results compared with uniform-resolution simulations

Drohnen als Partner im Luftraum

In unserem Beitrag fassen wir drei Themen einer jüngst veröffentlichten Studie zur Technikfolgenabschätzung ziviler Drohnen zusammen. Erstens legen wir dar, dass der Rechtsbegriff der Drohne unklar geregelt ist und dass eine technische Definition des Begriffs „Drohne“ der falsche Weg ist. Wir präsentieren eine alternative Einbindung des Drohnenbegriffs in das europäische Luftfahrtrecht. Zweitens beschreiben wir die Komplexität der technisch zu regelnden Aspekte, um eine Einbindung von Drohnen in das Luftraumsystem ohne direkten Sichtkontakt zu ermöglichen. Wir beschreiben das Problem der technischen Sicherheit und die Komponenten eines Verkehrsmanagementsystems für Drohnen. Drittens verdeutlichen wir, dass bei der Bewältigung der ethischen, rechtlichen und sozialen Herausforderungen von Drohnen eine Vollzugslücke besteht, insbesondere im Datenschutz

A proposed baroclinic wave test case for deep‐ and shallow‐atmosphere dynamical cores

Idealised studies of key dynamical features of the atmosphere provide insight into the behaviour of atmospheric models. A very important, well understood, aspect of midlatitude dynamics is baroclinic instability. This can be idealised by perturbing a vertically sheared basic state in geostrophic and hydrostatic balance. An unstable wave mode then results with exponential growth (due to linear dynamics) in time until, eventually, nonlinear effects dominate and the wave breaks. A new, unified, idealised baroclinic instability test case is proposed. This improves on previous ones in three ways. First, it is suitable for both deep‐ and shallow‐atmosphere models. Second, the constant surface pressure and zero surface geopotential of the basic state makes it particularly well‐suited for models employing a pressure‐ or height‐based vertical coordinate. Third, the wave triggering mechanism selectively perturbs the rotational component of the flow; this, together with a vertical tapering, significantly improves dynamic balance.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108108/1/qj2241.pd

Short‐term time step convergence in a climate model

This paper evaluates the numerical convergence of very short (1 h) simulations carried out with a spectral‐element (SE) configuration of the Community Atmosphere Model version 5 (CAM5). While the horizontal grid spacing is fixed at approximately 110 km, the process‐coupling time step is varied between 1800 and 1 s to reveal the convergence rate with respect to the temporal resolution. Special attention is paid to the behavior of the parameterized subgrid‐scale physics. First, a dynamical core test with reduced dynamics time steps is presented. The results demonstrate that the experimental setup is able to correctly assess the convergence rate of the discrete solutions to the adiabatic equations of atmospheric motion. Second, results from full‐physics CAM5 simulations with reduced physics and dynamics time steps are discussed. It is shown that the convergence rate is 0.4—considerably slower than the expected rate of 1.0. Sensitivity experiments indicate that, among the various subgrid‐scale physical parameterizations, the stratiform cloud schemes are associated with the largest time‐stepping errors, and are the primary cause of slow time step convergence. While the details of our findings are model specific, the general test procedure is applicable to any atmospheric general circulation model. The need for more accurate numerical treatments of physical parameterizations, especially the representation of stratiform clouds, is likely common in many models. The suggested test technique can help quantify the time‐stepping errors and identify the related model sensitivities.Key Points:Convergence is slow in CAM5Stratiform cloud parameterizations have large errorsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111268/1/jame20146.pd