Coordinate Systems and Transforms in Space Physics: Terms, Definitions, Implementations, and Recommendations for Reproducibility

TL;DR

The paper addresses reproducibility gaps in space physics coordinate transforms caused by inconsistent definitions and implementations across online resources, software, and ephemerides. It quantifies differences by comparing ephemerides and transform results, finding angular disparities up to about $0.3^ imes$ and transform discrepancies of order $10^{-3}$ to $10^{-2}$ degrees across libraries. To remedy this, it proposes standards for acronym definitions, a reference-frame standard dataset, a centralized SPICE kernel database with DOIs, and explicit versioning/documentation practices to ensure reproducibility and intercomparison of data products. The practical impact is a concrete framework to reduce duplication of effort across missions, improve validation, and enable precise, auditable transformations between reference frames.

Abstract

In space physics, acronyms for coordinate systems (e.g., \texttt{GEI}, \texttt{GSM}) are commonly used; however, differences in their definitions and implementations can prevent reproducibility. In this work, we compare definitions in online resources, software packages, and frequently cited journal articles and show that implementation differences can lead to transformations between same-named coordinate systems and ephemerides values from different data providers to differ significantly. Based on these comparisons and results, and to enable reproducibility, we recommend that (a) a standard for acronyms and definitions for coordinate systems is developed; (b) a standards body develops a citable database of reference data needed for these transforms; (c) a central authority maintains the SPICE (Spacecraft, Planet, Instrument, C-matrix, Events) kernels used by space physics spacecraft missions to generate data products in different coordinate systems; and (d) software developers provide explicit comparisons of their implementations with the results of (b) and documentation on implementation choices. Additionally, we provide recommendations for scientists and metadata developers to ensure that sufficient information is provided to enable reproducibility if these recommendations are not implemented.

Figures (3)

• Figure 1: Comparison of ephemerides values for the Geotail spacecraft from SSCWeb and CDAWeb in four different reference systems. The top panel in each subplot displays the $X$, $Y$, and $Z$ values from each provider (on this scale, differences are not visible) and the average radial distance, $\overline{r}$, between the two providers. The bottom panel of each subplot shows relative differences in the position vector $\Delta\mathbf{r}$ and the angular difference in the position vectors, $\Delta\theta$.
• Figure 2: Comparison of ephemerides values for the MMS-2 spacecraft from (a)--(b) SSCWeb and CDAWeb; (c)--(d) SSCWeb and JPL Horizons in two different reference systems.
• Figure 3: Angles between $Z$ axes in select coordinate frames as computed by different software packages. In the top panels of each subplot, the notation $\angle (Z_A, Z_B)$ means the angle between the $Z$ axis of coordinate frame $A$ and the $Z$ axis of coordinate frame $B$ computed using geopack_08_dp. The middle panel of each subplot shows the difference between $\angle (Z_A, Z_B)$ computed using geopack_08_dp and that computed using the library indicated in the legend; the maximum of the absolute value of each line is shown in parentheses. The bottom panels show the maximum absolute differences in the middle panel.