DOI: 10.5061/dryad.sxksn03dw
title: Data and code from: Propagation of the Madden–Julian oscillation as a deterministic chaotic phenomenon

description: The Madden–Julian oscillation (MJO), a gigantic weather system marked by
 eastward travel of cumulus cloud clusters over the Indo-Pacific, often
 causes severe weather and climate events worldwide. Despite its frequent
 realization, the physics and predictability characteristics of MJO
 propagation are not well understood. We here reveal the chaoticity of MJO
 propagation, using 4,000-member ensemble global cloud-system-resolving
 simulations of two MJOs. Against previous linearized thinking, multiple
 regimes supporting MJO propagation emerge under a single atmosphere-ocean
 background, depending critically on the equatorial asymmetry of
 climatological sea surface temperature. Selection of the bifurcated
 regimes results from the stochastic modulation of moisture transport via
 westward-propagating equatorial waves, fostered or inhibited by
 tropical-extratropical interplay. Tracking the nonlinear processes we
 found gives metrics for predicting the timing of MJO propagation.
description: # Data and code from: Propagation of the Madden–Julian oscillation as a
 deterministic chaotic phenomenon Dataset DOI:
 [10.5061/dryad.sxksn03dw](10.5061/dryad.sxksn03dw) ## Description of the
 data and file structure This dataset contains the simulation data,
 observational data, and scripts for creating the figures in Takasuka et
 al. (2025). It also provides NCL (NCAR command language) scripts for
 plotting the figures.  ### Files and variables #### File:
 Takasuka_etal_2025_Science.tar.gz **Description:** All the data have the
 netCDF format. Variable information has been provided in the metadata of
 the files, so we do not repeat the details here. The directory structure
 is as follows. — NICAM This directory stores the three types of data.  1\)
 Atmospheric data composited for the Nov-1, Dec-1, and Dec-2 regimes. They
 exist at the directories of [Nov, Dec]/[Nov-1, Dec-1, Dec-2]/[case, com].
 The directories of “case” and “com” store the 2d/3d variables for each
 case and composites categorized into the regimes, respectively. In “case”
 and “com”, there are some directories with different data contents. *
 [none]: default anomalies * raw: raw values of the data * ranom: anomalies
 from 11-day running mean * ranom2: anomalies from 15-day running mean *
 rmean2: 15-day running mean * hbudget: Anomalous budget terms of moist
 static energy 2\) Phase composite OLR data using the MJO index (“K12com”
 directory) 3\) Data file describing the number of MJO events on each date
 when the eastward propagation is completed (“others” directory) — OBS\
 This directory stores the ERA5 reanalysis data (“ERA5” directory), SST,
 and OLR data (“others” directory). The “others” directory includes the two
 types of data: climatology and raw values. — Drawscript\ This directory
 stores NCL (NCAR Command Language; version 6.6.2) scripts needed to create
 all the figures in the main text and supplementary materials. The names of
 the files (XX of “XX.ncl”) correspond to the names of the figures. More
 detailed descriptions are as follows: * Figure1AB.ncl: Script for
 Time-longitude digagrams of MJO convection for November and December in
 2018 (hereafter, denoted as Nov-MJO and Dec-MJO). * Figure1CD.ncl: Script
 for the histogram of the timing of MJO propagation in NICAM ensemble
 simulations. * Figure1EFG.ncl: Script for time-logitude diagrams of CWV
 and OLR related to the representative MJO regimes. * Figure2A.ncl: Script
 for maps of the OLR evolution associated with the two regimes simulated in
 NICAM ensemble simulations. * Figure2B.ncl: Same as Figure2A.ncl, but for
 the meridional-vertical sections of circulations. * Figure2C.ncl: Script
 for the map of the climatology and ensemble mean of observed and simulated
 OLR, respectively. * Figure2D.ncl: Script for the map of observed SSTs. *
 Figure3A.ncl: Script for the histogram of the timing of MJO propagation in
 Dec-MJO control and sensitivity experiments. * Figure3BC.ncl: Same as
 Figure3A.ncl, but for Nov-MJO control and sensitivity experiments. *
 Figure4A.ncl: Script for the map of upper-tropospheric dynamics (QGPV and
 Q-vector), water vapor, and lower-troposphericy eddy kinetic energy before
 the observed Dec-MJO propagation. * Figure4B.ncl: Same as Figure4A.ncl,
 but for the NICAM simulation. * Figure4C.ncl: Script for the map of
 upper-tropospheric extratropical Rossby waves before the observed Dec-MJO
 propagation. * Figure4D.ncl: Same as Figure4C.ncl, but for the NICAM
 simulation. * Figure4E.ncl: Script for the map of differences in
 background upper-tropospheric QGPV and Rossby-wave refractive index
 between the two different Dec-MJO propagation regimes. * Figure4F.ncl:
 Script for the zonal-vertical section of the differences in MJO
 circulations between the two different Dec-MJO propagation regimes. *
 figureS1.ncl: Script for the phase composite of MJO convection. *
 figureS2ac.ncl: Script for the maps of observed OLR evolution associated
 with Nov-MJO and Dec-MJO propagation. * figureS2bd.ncl: Same as
 figureS2ac.ncl, but for the NICAM simulations. * figureS3ab.ncl: Script
 for the comparisons of MSE budgets in the simulated Dec-MJO propagation. *
 figureS3cd.ncl: Script for the maps of surface heat fluxes, OLR, and
 background winds for the second regime of Dec-MJO propagation in the NICAM
 simulations. * figureS4.ncl: Script for the EKE budget analysis for the
 westward-propagating synoptic-scale wave in the observations, Dec- 1 and
 Dec-2 regimes. #### File: Takasuka_etal_2025_Science_Part2.tar.gz
 **Description:** All the data have the netCDF format. The directory
 structure is as follows. — data/OBS\ This directory stores the three
 files. * ex.200.day.clima.1979-2022.nc  * ey.200.day.clima.1979-2022.nc *
 uwnd.200.day.clima.1979-2022.nc The former two files include the daily
 climatology of x- and y-components of 200-hPa E vector (m^2^/s^2^), and
 the last file includes that of 200-hPa zonal winds (m/s). — scripts\ This
 directory stores NCL (NCAR Command Language; version 6.6.2) scripts needed
 to create all the figures in the main text and supplementary materials.
 The names of the files (XX of “XX.ncl”) corresponds to the names of the
 figures. More detailed descriptions are as follows: * Figure1CD.ncl:
 Updated script of the Figure1CD.ncl in Takasuka_etal_2025_Science.tar.gz.
 * Figure2B.ncl: Updated script of the Figure2B.ncl in
 Takasuka_etal_2025_Science.tar.gz. * Figure4A-D.ncl: Scripts for the
 decomposition of the Figure4A.ncl and Figure4B.ncl in
 Takasuka_etal_2025_Science.tar.gz. * Figure5A-D.ncl: Same as Figure 4C,
 4D, 4E, 4F.ncl in Takasuka_etal_2025_Science.tar.gz. * Figure6AB.ncl:
 Scripts for the map of the climatological upper-tropospheric zonal winds
 during Nov-MJO and Dec-MJO propagation and its difference. * Figure6C.ncl:
 Script for the map of the difference in climatological upper-tropospheric
 E vectors and zonal winds between Nov-MJO and Dec-MJO periods. *
 figureS2bde.ncl: Updated scripts of the figureS2*.ncl in
 Takasuka_etal_2025_Science.tar.gz. * figureS5.ncl: Script for comparisons
 of composite OLR anomalies averaged over the Indian Ocean during the
 initial phase of MJO convection between the Dec-1, Dec-2 and Nov-1
 regimes. * figureS6.ncl: Script for the tropical-extratropical dynamic
 evolution for observed Nov-MJO and/or the Nov-1 regime.