Comment on gmd-2021-323

doi:10.5194/gmd-2021-323-rc2

Abstract

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (<a href="#bib1.bibx41">Hill etÂ al.</a>,Â <a href="#bib1.bibx41">2004</a>), TempestRemap (<a href="#bib1.bibx88">Ullrich and Taylor</a>,Â <a href="#bib1.bibx88">2015</a>), generalized moving least squares (GMLS) (<a href="#bib1.bibx87">Trask and Kuberry</a>,Â <a href="#bib1.bibx87">2020</a>) with post-processing filters, and WLS-ENOR (<a href="#bib1.bibx61">Li etÂ al.</a>,Â <a href="#bib1.bibx61">2020</a>). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

Highlights

Coupled multimodel simulations often involve high degrees of computationally complex workflows, and achieving consistently 15 accurate solutions is strongly dependent on the choice of spatiotemporal numerical algorithms used to resolve the interacting scales in physical models
The current work is motivated by a need for an intercomparison of remapping schemes, which led us to standardize several numerical metrics to uniformly 25 compare the properties of these algorithms that are routinely applied to problems in climate and weather system modeling
We argue that these metrics are broadly useful for evaluating key properties that determine the accuracy and stability of the solution transfers between model components, and can be applied to all remapping algorithms widely used in climate codes

Summary

Introduction

Coupled multimodel simulations often involve high degrees of computationally complex workflows, and achieving consistently 15 accurate solutions is strongly dependent on the choice of spatiotemporal numerical algorithms used to resolve the interacting scales in physical models. Rigorous spatial coupling between components in such systems involves field transformations and communication of data across multiresolution grids while preserving key attributes of interest such as global integrals and local features, which is usually referred to as the process of remapping ( “regridding” or just “interpolation”) (Van Leer, 1979; Dukowicz and Kodis, 1987; Jones, 1999). Such remap procedures are critical in ensuring the stability and accuracy of 20 scientific codes simulating multiphysics problems that typically occur in many different scientific domains. Examples include schemes developed for fluid-structure interaction (FSI) or heat transfer (such as MpCCI (Joppich and Kürschner, 2006) and preCICE (Bungartz et al, 2016)), moving mesh problems with arbitrary Lagrangian-Eulerian (ALE) methods (Dukowicz and Kodis, 1987; Dukowicz and Baumgardner, 2000), and general-purpose remap software such as MOAB (Tautges and Caceres, 2009; Mahadevan et al, 2020), PANG (Gander and Japhet, 2013), and Data Transfer Kit (DTK) (Slattery et al, 2013)

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Results

Conclusion