paper.md

title	tags	authors	affiliations	date	bibliography
Xgcm: A Python Package for Analyzing Data from General Circulation Models	Python finite volume fluid dynamics ocean modeling climate modeling	name orcid affiliation Ryan Abernathey 0000-0001-5999-4917 1 name orcid affiliation Julius Busecke 0000-0001-8571-865X 2 name orcid affiliation Anderson Banihirwe 0000-0001-6583-571X 3 name orcid affiliation Ci Zhang 0000-0001-8584-8569 1, 4 name orcid affiliation Timothy Smith 0000-0003-4463-6126 5 name orcid affiliation Deepak Cherian 0000-0002-6861-8734 3 name orcid affiliation Aurélien Ponte 0000-0002-0252-6028 6	name index Lamont Doherty Earth Observatory of Columbia University 1 name index Princeton University 2 name index National Center for Atmospheric Research, Boulder, USA 3 name index Tsinghua University 4 name index The Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin 5 name index Univ. Brest, CNRS, IRD, Ifremer, Laboratoire d’Océanographie Physique et Spatiale (LOPS), IUEM, Brest, France 6	15 February 2020	paper.bib

Summary

Xgcm is a python package whose goal is to enable scientists to analyze finite-volume datasets easily, efficiently, and accurately. Finite volume methods are used throughout science and engineering to discretize and solve partial differential equations, especially in computational fluid dynamics. Xgcm is not an equation solver--rather, it is a package aimed at analyzing the output of such simulations, i.e. "post-processsing." Post-processing is important because large-scale simulations are often run once on supercomputer, producing massive datasets ripe for exploration and discovery. Many common simulation codes use legacy Fortran, and their internal routines are inaccessible in interactive, post-processing workflows using python. Xgcm enables users to recreate the finite-volume operations used internally by a simulation within python post-processing code, allowing users to easily compute quantities such as divergence, curl, etc. in a numerically faithful way. Xgcm was inspired by the General Circulation Models (GCMs) of weather, ocean, and climate science, but could be utilized for other domains, such as plasma physics or astrophysical modeling, which use similar numerical grids.

Statement of Need

The Python package Xarray [@hoyer2017xarray] is, in many ways, an ideal tool for analyzing GCM data, providing file I/O, convenient indexing and grouping, coordinate-aware data transformations, and (via Dask, @rocklin2015dask) parallel, out-of-core array computation. However, GCM data provides a challenge to Xarray's data model: most finite-volume GCMs use Arakawa Grids [@ARAKAWA1977173], in which different variables are offset (a.k.a. staggered) from one another and situated at different locations with respect to the cell center and edge points. An example, illustrated in Fig. 1, is the C-grid geometry, which places scalars (such as temperature) at the cell center and vector components (such as velocity) at the cell faces.

Xarray has no concept of a grid cell center, face, etc. in its data model. Xgcm augments xarray with an understanding of these staggered grids and provides the associated operators for interpolating and differencing variables from one grid position to another while keeping track of their coordinates. Xgcm also includes an understanding of grid "metrics," the distance / area / volume measures which characterize the grid-cell geometry. By combining the primitive interpolation / difference operators with the metrics, Xgcm can perform finite-volume integrals and derivatives in a manner consistent with simulation internals. Xgcm therefore can serve as a foundation for advanced GCM analytics, such as tracer, momentum, vorticity, and energy budgets. Xgcm supports orthogonal curvilinear grids, including complex, multiply-connected grid topologies such as the cubed-sphere.

Scientific Applications

Since xgcm was developed by oceanographers, its main applications have been in ocean GCM analysis. Xgcm is most frequently used to compute finite-volume budgets for quantities like heat, salinity, or chemical concentration.

Some published results include:

• Analysis of kinematic simulations of tracer mixing in the global ocean [@busecke_ocean_2019].
• Analysis of simulations of the southern ocean phytoplankton ecosystem [@uchida2019contribution].
• Analysis of the momentum budget in the equatorial undercurrent [@busecke_ocean_2019].
• Diagnostics of temporal variability the global ocean heat budget in the ECCOv4 state estimate [@tesdal_abernathey_2020].

Xgcm also provides the computational backbone for several downstream tools, including OceanSpy [@almansi_et_al_2019], a Python package for ocean model data analysis and visualization and ECCOv4-py [@eccov4py], a tool used for to postprocess and analyze output from the ECCOv4 state estimate [@forgetECCOv4], a global ocean model constrained to 25 years of observational data. The finite volume grid on which the ECCOv4 solution lives is made up of 13 connected tiles (see Fig. 1, [@forgetECCOv4]) which, due to the orientation of some of the tiles, can make standard computations challenging. For example, computing meridional heat transport requires realigning the vector components of the horizontal heat fluxes on some grid tiles. Notably, the generic differencing and interpolation operations in xgcm make computations like this

1. intuitive and transparent within the ECCOv4-py code, and
2. computationally flexible because of integration with Xarray and Dask.

We welcome reports of applications in other domains.

Acknowledgements

Some Xgcm development has been support by NSF award OAC-1835778 and the Gordon and Betty Moore Foundation. However, much of the development occurred outside the context of any funded project.

References