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# Annular modes of variability in the atmospheres of Mars and Titan

## Abstract

Annular modes explain much of the internal variability of Earth’s atmosphere but have never been identified as influential on other planets. Using data assimilation datasets for Mars and a general circulation model for Titan, we demonstrate that annular modes are prominent in the atmospheres of both worlds, capturing a larger fraction of their respective variabilities than Earth’s. One mode describes latitudinal shifts of the jet on Mars, as on Earth, and vertical shifts of the jet on Titan. Another describes pulses of mid-latitude eddy kinetic energy on all three worlds, albeit with somewhat different characteristics. We demonstrate that this latter mode has predictive power for regional dust activity on Mars, revealing its usefulness for understanding Martian weather. The similarity of annular variability in dynamically diverse worlds suggests its ubiquity across the Solar System, potentially extending to exoplanets.

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## Data availability

The Mars Analysis Correction Data Assimilation is available at https://catalogue.ceda.ac.uk/uuid/01c44fb05fbd6e428efbd57969a11177. The Ensemble Mars Atmospheric Reanalysis System is available at ftp://ftp.pasda.psu.edu/pub/commons/meteorology/greybush/emars-1p0/data/. ERA-Interim data are available at https://www.ecmwf.int. The Mars Dust Activity Database is available at https://doi.org/10.7910/DVN/F8R2JX. Titan Atmospheric Model results are archived on Zenodo at https://doi.org/10.5281/zenodo.4780576.

## Code availability

The source code for TAM is currently not publicly available. EOF analysis was done in part with the Climate Data Toolbox for MATLAB (https://github.com/chadagreene/CDT). Scripts used in the generation of figures can be obtained from the corresponding author upon request.

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## Author information

Authors

### Contributions

J.M.B. conceived the work. J.M.B. performed the analysis and wrote the manuscript, with contributions from J.M.L. J.M.L. ran the TAM simulations.

### Corresponding author

Correspondence to J. Michael Battalio.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 The spatial signature of the first non-dipolar annular mode in anomalous zonal-mean zonal wind on Mars for both reanalysis datasets.

(a–l) As in Fig. 1, but for the first non-dipolar U-AM.

### Extended Data Fig. 2 Polar plots of the regression of the first three EOFs onto the anomalous surface pressure from EMARS in the northern hemisphere.

(a, c, e) results performed using weighting of $$\sqrt {cos\phi }$$. (b, d, f) results using cosϕ. The individual panel titles indicate the percent of variance explained in each EOF. Topography is shown in 2000 m increments with the 0 m contour dot-dashed in gray and negative contours dashed. Regressions are only shown exceeding 99% confidence.

### Extended Data Fig. 3 Polar plots of the regression of the Martian U-AM onto the anomalous surface pressure (a–d) and the regression of the Martian EKE-AM onto the anomalous, vertically (mass) integrated EKE (e–h).

(a, c, e, g) MACDA. (b, d, f, h) EMARS. Topography is shown in 2000 m increments with the 0 m contour dot-dashed in gray and negative contours dashed. Regressions are only shown exceeding 99% confidence.

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Battalio, J.M., Lora, J.M. Annular modes of variability in the atmospheres of Mars and Titan. Nat Astron 5, 1139–1147 (2021). https://doi.org/10.1038/s41550-021-01447-4

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• DOI: https://doi.org/10.1038/s41550-021-01447-4