{'fraction_non_alphanumeric': 0.025906735751295335, 'fraction_numerical': 0.0, 'mean_word_length': 5.410788381742739, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The diabatic contour‐advective semi‐Lagrangian algorithms for the dynamical core of global models in terrain‐following isentropic and pressure vertical coordinates

Design, development and assessment of numerical algorithms based on Rossby–Ertel potential vorticity (PV) for the dynamical core of global models are of particular importance in atmospheric and oceanic modelling for improving representation of both balanced and unbalanced flows. The general circulation models are usually developed in various vertical coordinates and horizontal grids. The Diabatic Contour‐Advective Semi‐Lagrangian (DCASL) algorithm based on contour representation of an approximate form of PV is further developed by (a) inclusion of a form of arbitrary Lagrangian–Eulerian method for the hybrid σ – θ vertical coordinate, and (b) extension to the σ –p vertical coordinate with both Charney–Phillips (CP) and Lorenz (L) grids. Using a baroclinic instability test case, the working of DCASL in the newly developed σ – θ is compared with two other forms of DCASL in σ –p developed with CP and L grids. These comparisons show that the initialisation problem present in σ – θ vertical coordinate is removed and the solutions become close to the numerically convergent solutions of four other dynamical cores, within the range of their uncertainties, when the σ –p vertical coordinate is used. Results also show the usefulness of DCASL in σ –p, even though the prognostic variable representing vortical flow is less materially conservative than that of the σ – θ .