Particle trajectory calculations with a two‐step three‐time level semi‐Lagrangian scheme well suited for curved flows

Abstract

This study proposes a new two-step three-time level semi-Lagrangian scheme for calculation of particle trajectories. The scheme is intended to yield accurate determination of the particle departure position, particularly in the presence of significant flow curvature. Experiments were performed both for linear and non-linear idealized advection problems, with different flow curvatures. Results for simulations with the proposed scheme, and with three other semi-Lagrangian schemes, and with an Eulerian method are presented. In the linear advection problem the two-step three-time level scheme produced smaller root mean square errors and more accurate replication of the angular displacement of a Gaussian hill than the other schemes. In the non-linear advection experiments the proposed scheme produced, in general, equal or better conservation of domain-averaged quantities than the other semi-Lagrangian schemes, especially at large Courant numbers. In idealized frontogenesis simulations the scheme performed equally or better than the other schemes in the representation of sharp gradients in a scalar field. The two-step three-time level scheme has some computational overhead as compared with the other three semi-Lagrangian schemes. Nevertheless, the additional computational effort was shown to be worthwhile, due to the accuracy obtained by the scheme in the experiments with large time steps. The most remarkable feature of the scheme is its robustness, since it performs well both for small and large Courant numbers, in the presence of weak as well strong flow curvatures.

Semi-Lagrangian transport of oxygen isotopes in polythermal ice sheets: implementation and first results

“…A glacial index gi(t) is used to vary the air temperature and precipitation distribution by interpolating between the present and the last glacial maximum (LGM) conditions. This index is defined gi = 1 for conditions at the LGM and gi = 0 for present conditions (Forsstrom et al, 2003) and is based on data derived from the δ 18 O GRIP ice core record from Greenland and from the δD Vostok ice core record from Antarctica (Dansgaard et al, 1993;Johnsen et al, 1995;Petit et al, 1999). For the first 100 kyr BP the GRIP record is used and prior to that the Vostok ice core.…”

“…Air temperature is related to stable isotopic composition of precipitation as indicated by observations (e.g. Dansgaard, 1964;Gat, 1996;Jouzel et al, 1997;Gornitz, 2009). When assuming this relationship remains the same in the past, it is possible to reconstruct past temperatures from ice or sediment cores.…”