A Lagrangian vertical coordinate version of the ENDGame dynamical core. Part I: Formulation, remapping strategies, and robustness

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.Previous work provides evidence that Lagrangian conservation and related properties of a numerical model dynamical core can be improved by the use of a Lagrangian or quasi-Lagrangian vertical coordinate (LVC). Most previous model developments based on this idea have made the hydrostatic approximation. Here the LVC is implemented in a nonhydrostatic compressible Euler equation dynamical core using almost identical numerical methods to ENDGame, the operational dynamical core of the Met Office atmospheric Unified Model. This enables a clean comparison of LVCand height-coordinate versions of the dynamical core using numerical methods that are as similar as possible. Since Lagrangian surfaces distort over time, model level heights are continually reset to certain ‘target levels’ and the values of model fields are remapped onto their new locations. Different choices for these target levels are discussed, along with remapping strategies that focus on different conservation or balance properties. Sample results from a baroclinic instability test case are presented. The LVC formulation is found to be rather less robust than the height-coordinate version; some reasons for this are discussed.We are grateful to Nigel Wood for pointing out the computational mode of the LVC vertical discretization. We also thank two anonymous reviewers for their constructive comments on an earlier version of this paper. This work was funded by the Natural Environment Research Council under grant NE/H006834/1

A Lagrangian vertical coordinate version of the ENDGame dynamical core. Part II: Evaluation of Lagrangian conservation properties.

This is the author accepted manuscript.Final version available from Wiley via the DOI in this record.A baroclinic instability test case is used to compare the Lagrangian conservation properties of three versions of a semi‐implicit semi‐Lagrangian dynamical core: one using a height based vertical coordinate and two using a Lagrangian vertical coordinate. The Lagrangian coordinate versions differ in the choice of target levels to which model levels are reset after each step—the first uses the initial model level heights while the second uses quasi‐Lagrangian target levels. A range of diagnostics related to Lagrangian conservation are computed, including global entropy, unavailable energy, cross‐isentrope mass flux, and consistency of potential temperature and potential vorticity with passive tracers and parcel trajectories. The global entropy, unavailable energy, and cross‐isentrope fluxes do not suggest any clear advantage or disadvantage from the use of a Lagrangian vertical coordinate, though the cross‐isentrope flux reveals a flaw in the formulation of the remapping of potential temperature in the Lagrangian coordinate model at the top boundary. The use of a Lagrangian vertical coordinate with quasi‐Lagrangian target levels improves the consistency among potential temperature as a dynamical variable, potential temperature as a tracer and potential temperature on Lagrangian particle trajectories. It also improves consistency between a potential vorticity tracer and potential vorticity on Lagrangian particle trajectories. However, it degrades the consistency between model and tracer potential vorticity, as well as between model potential vorticity and potential vorticity on Lagrangian trajectories. This degradation appears to be related to the slopes of model levels, which are greater in the version with quasi‐Lagrangian target levels.This work was funded by the Natural Environment Research Council under grant NE/H006834/

Double K-shell photoionization of low-Z atoms and He-like ions

We report on the investigation of the photon energy dependence of double 1s photoionization of light atoms and compare the cross sections for hollow atom and He-like ion production. Measurements of the Kα hypersatellite x-ray spectra of Mg, Al, and Si were carried out using the Fribourg high-resolution x-ray spectrometer installed at the ID21 and ID26 beam lines at the ESRF. The double-to-single photoionization cross section ratios were derived as a function of the incident photon beam energy and compared to convergent close-coupling (CCC) calculations for He-like ions. The dynamical electron-electron scattering contribution to the DPI cross-sections was found to be more important for neutral atoms than for the He isoelectronic serie

Potential Energy Surface Reconstruction and Lifetime Determination of Molecular Double-Core-Hole States in the Hard X-Ray Regime

A combination of resonant inelastic x-ray scattering and resonant Auger spectroscopy provides complementary information on the dynamic response of resonantly excited molecules. This is exemplified for CH3I, for which we reconstruct the potential energy surface of the dissociative I 3d−2 double- core-hole state and determine its lifetime. The proposed method holds a strong potential for monitoring the hard x-ray induced electron and nuclear dynamic response of core-excited molecules containing heavy elements, where ab initio calculations of potential energy surfaces and lifetimes remain challenging