Published paper: Shingle 2.0: generalising self-consistent and automated domain discretisation for multi-scale geophysical models

I have published a new paper on automated spatial domain mesh discretisations in the Journal of Geoscientific Model Development.

The challenge: to generate a self-consistent domain discretisation approach for geophysical domains that is generalised such that it can be applied to a wide range of applications, with new domains efficiently prototyped and iterated on, and is fully described such that the process can be automated, is reproducible and easily shared. (a) shows a typical source Digital Elevation Map (DEM) dataset (that naturally lend themselves to structured grid generation) used to produce a regular grid of the Atlantic Ocean (e.g. under a format-native land mask) in (b), and a selection of unstructured mesh spatial discretisations: (c) Bounded by part of the Chilean coastline and a meridian. (d) North Sea. (e) Global oceans. (f) Grounding line of the Filchner-Ronne ice shelf ocean cavity up to the 65\degree S parallel, with surface geoid mesh \(\mathcal{T}_h\), full mesh \(\mathcal{T}\) with ice-ocean melt interface highlighted, and accompanied by ice sheet full discretisation. (g) Greenland ice sheet.


Shingle is a new approach to describing and generating spatial mesh discretisations for multi-scale geophysical domains. Its novel use of an extendable, hierarchical formal grammar and natural language basis for geophysical features achieves robust reproduction and enables consistent comparison between models. This is designed to support the increase in complexity as models include a greater range of spatial scales and future-proof simulation set-up.


The approaches taken to describe and develop spatial discretisations of the domains required for geophysical simulation models are commonly ad hoc, model or application specific and under-documented. This is particularly acute for simulation models that are flexible in their use of multi-scale, anisotropic, fully unstructured meshes where a relatively large number of heterogeneous parameters are required to constrain their full description. As a consequence, it can be difficult to reproduce simulations, ensure a provenance in model data handling and initialisation, and a challenge to conduct model intercomparisons rigorously.

This paper takes a novel approach to spatial discretisation, considering it much like a numerical simulation model problem of its own. It introduces a generalised, extensible, self- documenting approach to carefully describe, and necessarily fully, the constraints over the heterogeneous parameter space that determine how a domain is spatially discretised. This additionally provides a method to accurately record these constraints, using high-level natural language based abstractions, that enables full accounts of provenance, sharing and distribution. Together with this description, a generalised consistent approach to unstructured mesh generation for geophysical models is developed, that is automated, robust and repeatable, quick-to-draft, rigorously verified and consistent to the source data throughout. This interprets the description above to execute a self-consistent spatial discretisation process, which is automatically validated to expected discrete characteristics and metrics.

A selection of graphical highlights

Library schematic

A schematic illustrating the generalised approach to flexible unstructured mesh specification and generation for geophysical models. The hierarchy of automation (tenet 7) is highlighted, from a relatively simple high-level interaction: {Diamond GUI \(\leftrightarrow\) Shingle \(\rightarrow\) Mesh}, to complex low-level development communicating with the LibShingle library. Nomenclature defined in section 2 of the paper.

Approach for integration of generalised spatial domain discretisation into geophysical simulation models

Framework for generalised spatial domain discretisation for geophysical model simulations. A formal spatial domain constraint description (a model-independent grouping of high-level directives describing key geospatial boundaries and features, required spatial resolution and source datasets) for a specific study (e.g. the geography to include in a CMIP intercomparison study) is joined with specific constraints from a simulation model, depending on its internal numerical discretisations and field representations (e.g. following Gridspec (Balaji et al., 2007), or a UFL description (Alnæs et al., 2014)). These constraints are used by the interpreter Shingle to produce, in a robust, automated, repeatable process, a model-specific mesh spatial discretisation. Moreover, the latter description is further used to specify numerical simulation output representation (as CMIP uses Gridspec).