On-sky measurements of atmospheric dispersion – I. Method validation

ABSTRACT Observations with ground-based telescopes are affected by differential atmospheric dispersion due to the wavelength-dependent index of refraction of the atmosphere. The usage of an atmospheric dispersion corrector (ADC) is fundamental to compensate this effect. Atmospheric dispersion correction residuals above the level of ∼100 milliarcseconds (mas) will affect astronomical observations, in particular radial velocity and flux losses. The design of an ADC is based on atmospheric models. To the best of our knowledge, those models have never been tested on-sky. In this paper, we present a new method to measure the atmospheric dispersion on-sky in the optical range. We require an accuracy better than 50 mas that is equal to the difference between atmospheric models. The method is based on the use of cross-dispersion spectrographs to determine the position of the centroid of the spatial profile at each wavelength of each spectral order. The method is validated using cross-dispersed spectroscopic data acquired with the slit spectrograph UVES. We measure an instrumental dispersion of $\rm 47 ~ mas$ in the blue arm, and 15 and 23 mas in the two ranges of the red arm. We also measure a 4 per cent deviation in the pixel scale from the value cited in UVES manual. The accuracy of the method is ∼17 mas in the range of 315–665 nm. At this level, we can compare and characterize different atmospheric dispersion models for better future ADC designs.

Stirling numbers and Gregory coefficients for the factorization of Hermite subdivision operators

In this paper we present a factorization framework for Hermite subdivision schemes refining function values and first derivatives, which satisfy a spectral condition of high order. In particular we show that spectral order $d$ allows for $d$ factorizations of the subdivision operator with respect to the Gregory operators: a new sequence of operators we define using Stirling numbers and Gregory coefficients. We further prove that the $d$th factorization provides a ‘convergence from contractivity’ method for showing $C^d$-convergence of the associated Hermite subdivision scheme. Gregory operators are derived by explicitly solving a recursion based on the Taylor operator and iterated vector scheme factorizations. The explicit expression of these operators allows one to compute the $d$th factorization directly from the mask of the Hermite scheme. In particular, it is not necessary to compute intermediate factorizations, which simplifies the procedures used up to now.

Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model

Explicit Runge–Kutta methods and implicit multistep methods utilizing a Newton–Krylov nonlinear solver are evaluated for a range of configurations of the shallow-water dynamical core of the spectral element community atmosphere model to evaluate their computational performance. These configurations are designed to explore the attributes of each method under different but relevant model usage scenarios including varied spectral order within an element, static regional refinement, and scaling to the largest problem sizes. This analysis is performed within the shallow-water dynamical core option of a full climate model code base to enable a wealth of simulations for study, with the aim of informing solver development within the more complete hydrostatic dynamical core used for climate research. The limitations and benefits to using explicit versus implicit methods, with different parameters and settings, are discussed in light of the trade-offs with Message Passing Interface (MPI) communication and memory and their inherent efficiency bottlenecks. Given the performance behavior across the configurations analyzed here, the recommendation for future work using the implicit solvers is conditional based on scale separation and the stiffness of the problem. For the regionally refined configurations, the implicit method has about the same efficiency as the explicit method, without considering efficiency gains from a preconditioner. The potential for improvement using a preconditioner is greatest for higher spectral order configurations, where more work is shifted to the linear solver. Initial simulations with OpenACC directives to utilize a Graphics Processing Unit (GPU) when performing function evaluations show improvements locally, and that overall gains are possible with adjustments to data exchanges.