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Supplementary: The Madden-Julian Oscillation in a Warmer World
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Chiung-Wen June Chang1*, Wan-Ling Tseng2, Huang-Hsiung Hsu2, Noel
Keenlyside3 and Ben-Jei Tsuang4
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1. Chinese Cultural University, Taipei, Taiwan
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2. Academia Sinica, Research Center for Environmental Changes, Taipei, Taiwan
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3. Geophysical Institute and Bjerknes Centre, University of Bergen, Bergen , Norway
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4. National Chung-Hsing University, Taichung, Taiwan
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Corresponding author: Chiung-Wen June Chang, Chinese Cultural University, Taipei,
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Taiwan
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e-mail: c.june.chang@gmail.com
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Key points
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
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One of the few models capable in reproducing realistic MJO key features is used for MJO
projection under global warming
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
Global warming enhances MJO, leading to high-frequency and faster east travelling events
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
Key changes in the MJO vertical structure lead to mutual reinforcement of thermodynamic
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and dynamic factors
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Table S1. The amplitude for MJO precipitation and 850 hPa zonal wind anomalies, the estimated
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vertical velocity w', and the dry static stability (∂𝑠̅/∂p). The dry static stability ∂𝑠̅/∂p is the value
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averaged from 850 hPa to 200 hPa. The MJO precipitation and 850 hPa zonal wind anomalies
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amplitude is calculated as the square root of the integral spectra from wave number 1-4, cycle
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20-90 days for each respective parameter in Fig. 1.
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The MJO variance is defined as the spectra band between eastward zonal wave numbers 1-4,
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and periods of 20-90 days. The MJO variance in precipitation increases significantly by 17.5% in
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FUTURE relative to PRESENT whereas the U850 amplitude increases by 4.4%. Following the
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weak temperature gradient thermodynamic balance Q'=w'*(∂𝑠̅/∂p) relationship as equation (1) in
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Maloney and Xie (2013), we get an estimation of w' amplitude increase of 1.6% from PRESENT
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to FUTURE (assuming MJO band precipitation anomalies are proportional to Q'). The amplitude
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change in w' (1.6%) predicted by this relationship agrees reasonably well with the U850'
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amplitude change (4.4%). Thus, the discrepancy between precipitation and wind variance
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changes in the FUTURE experiment can be explained by the compensation effect of the change
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in static stability.
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Figure S1. Mean state changes relative to the 20th Century climate. (a) SST (contours are the 20
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year mean in PRESENT with contour interval of 0.5°C from 28°C.) (b) 850 hPa zonal wind
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(contours mark the westerly zone as black in PRESENT and blue in FUTURE. Unit: m s-1). The
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changes are computed as the 20 year mean difference of FUTURE minus PRESENT.
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Figure S2. Simulated zonal averaged mean state over the warm pool region (50°E-180°E). (a)
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SST (b) precipitation (solid line) and intraseasonal precipitation variance (dash line), and (c)
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specific humidity at 925 hPa (solid line) and 500 hPa (dash line).
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Figure S3. The vertically integrated energy Q1 and moisture Q2 budgets from surface to 200 hPa
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in the eight MJO phases, where the brackets represent the mass-weighted vertical integral. <Q1>
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is plotted in solid line; <Q2> in dash line.
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Figure S4. Vertical temperature advection change relative to the 20th century climate.
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(a) Temperature advection of the mean potential temperature by the MJO vertical flow

). Contour is the value in the PRESENT experiment, shading plots the change relative to
p
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( w'
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PRESENT ( ( w'
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change ( w'CTL (
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( w' (
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
) , term a in Eq. 2). (b) Contribution from the background dry static stability
p

) , term b in Eq. 2). (c) Contribution from the MJO vertical flow change
p

)CTL , term c in Eq. 2)
p
We approximate the Q1 change from the vertical component w

in the thermodynamic
p
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equation of the atmospheric potential temperature, where w is vertical velocity (omega) with
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negative value upward;  is potential temperature. When decomposing w into w  w' ,  into
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   ' (the overbar and prime denote the background mean and intraseasonal anomalies
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

term is mainly dominated by w' . Similar to Eq. 1 in the text, the change
p
p
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respectively), w
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in temperature advection by MJO vertical motion, w'
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



( w' )  ( w'CTL  )  (w' ( )CTL )  (w' ( ))
p
p
p
p


  

 
a
b
c

, can be written as:
p
(2)
d
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Terms a-c in the Eq. 2 are shown as the shadings in Fig. S4 a-c, respectively; term d is a
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small fraction henceforth not shown. Under global warming, the upper troposphere temperature
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increases more quickly than the lower troposphere, the dry stability becomes greater in the upper
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troposphere. The enhanced MJO deep convective heating is mainly due to the atmospheric dry
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stability change (Fig. S4b). The fact that the enhanced MJO vertical velocity in the shallow
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convective phase 1-3 and phase 6-7 attributing to the heating is demonstrated in Fig. S4c.
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Figure S5. Symmetric outgoing long wave radiation (OLR) wavenumber-frequency spectra of (a)
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the PRESENT experiment (b) the FUTURE experiment and (c) the FUTURE minus PRESENT.
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Spectra were computed for all longitudes in the domain 15°S -15°N. Superimposed are the
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dispersion curves of the equatorial waves for the equivalent depths of 12, 25 and 50m (definition
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following [Wheeler and Kiladis, 1999]). Note that the spectral variance in MJO (power at 0.03-
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0.05 cycle per day and zonal wave number one) is enhanced in the FUTURE experiment, and
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that there is an overall enhancement of the equatorial Kelvin waves in tropical wave spectra in
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FUTURE relative to PRESENT.
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Reference
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Wheeler, M., and G. N. Kiladis (1999), Convectively coupled equatorial waves: Analysis of
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clouds and temperature in the wavenumber-frequency domain, Journal of the Atmospheric
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Sciences, 56(3), 374-399.
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