A standard test case suite for two-dimensional linear transport on the sphere: results from a collection of state-of-the-art schemes

Abstract

Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude-longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate-chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent, <br><br> The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data-sets are made available to facilitate the process of model evaluation and scheme intercomparison

A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics

“…For the deformation flow tests we have used the two types of analytic flow fields, the density shapes, and the validation diagnostics suggested in , and used in a model intercomparison (Lauritzen et al, 2013). For the diagnostics this means that, in addition to the l 2 and l ∞ error norms and related convergence rates used for the simple solid body rotation tests above, we have calculated an additional set of diagnostics, briefly described below.…”

Online coupled regional meteorology chemistry models in Europe: current status and prospects

“…Lauritzen and Thuburn (2011) proposed a set of numerical tests to investigate whether a numerical transport scheme introduces unmixing or overshooting. Recently, a number of transport schemes in various models around the world were inter-compared using the recommended tests (Lauritzen et al, 2013). It is strongly recommended that the numerical schemes (including all filters/limiters) used in European models and models elsewhere are investigated via these tests.…”

A flux‐form conservative semi‐Lagrangian multitracer transport scheme (FF‐CSLAM) for icosahedral‐hexagonal grids

“…Further details of these scheme and SG11 could be found in Lauritzen et al . []. In comparison to the other advection schemes, FF‐CSLAM does the extra calculations corresponding to the search associated with finding the overlap area between the area swept through the edge and the underlining grid.…”

“…Transport schemes implemented on ico‐hex grid are selected from the collection of 19 state‐of‐the art schemes participated in Lauritzen et al . []. For the convergence test case with cosine bells, FF‐CSLAM shows better rate of convergence than ICON and SLFV‐SL, whereas SG‐11 shows better global error norms.…”