1High Predictability of Tropical Pacific Decadal Variability Dominated by2Oceanic Rossby Waves

3(Supplementary material)

45

Xian Wu1*, Stephen G. Yeager2, Clara Deser2, Antonietta Capotondi3,4, Andrew T. Wittenberg5,

6and Michael J. McPhaden6

7
8

1 Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, NJ

92 National Center for Atmospheric Research, Boulder, CO

103 Cooperative Institute for Research in Environmental Sciences, University of Colorado

11Boulder, Boulder, CO

124 National Oceanic and Atmospheric Administration /Physical Sciences Laboratory, Boulder,

13CO145 National Oceanic and Atmospheric Administration/Geophysical Fluid Dynamics Laboratory,

15

Princeton, NJ

166 National Oceanic and Atmospheric Administration /Pacific Marine Environmental Laboratory,

17Seattle, WA

181920212223242526*Corresponding author: Xian Wu, xw2794@princeton.edu

2728Fig. S1 As in Fig. 1 but for the second leading EOF mode and PC2.

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3536Fig. S2 TPDV simulation in the alternative observational datasets and the CESM1 freerunning preindustrial simulation. As in Fig. 1 in the main text, but for (top row) HadISST(1955–2022) and ORAS4 (1958–2019), and (bottom) 1801-yr control simulation of CESM1 under
the preindustrial forcing condition. The timeseries of standardized PC1 are only shown for the last
101 years (2100–2200). The year in the axis indicates the start year of any 10-year average window.
The numbers in the top-left corner of panels in the first column denote the percentage of total
variance explained by the leading EOF mode in each dataset.

373839Fig. S3 As in Fig. 2 in the main text, but for skill evaluation relative to observations (SST inERSSTv5, and ocean temperature in EN4).

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52Fig. S4 Definition of different metrics capturing subsurface ocean temperature variability inFOSI. (a) Climatology and (b) standard deviation of equatorial Pacific (3°S–3°N) subsurface
ocean temperature, (c) standard deviation of 10-yr low-pass filtered component, and (d) standard
deviation ratio of low-pass filtered component of total (non-detrended) annual mean temperature.
(e-h) as in a–d but for the zonally averaged (130°E–140°W) subsurface ocean temperature. Thecurves in a–h denote the climatological mixed layer depth (blue curves), thermocline depth(defined as the depth of maximum vertical temperature gradient; black curves), and isopycnal
depth where the potential density is equal to 25.5 kg m-3 (σ_θ=25.5 kg m-3; red curves). (i)Climatology and (j) standard deviation of annual mean isopycnal depth (σ_θ=25.5 kg m-3). (k)Climatology and (l) standard deviation of annual mean spiciness [°C; defined as temperature onthe isopycnal depth (σ_θ=25.5 kg m-3)]. The yellow and pink dots in l denote pathways wherespiciness standard deviations are largest at each latitude.

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Fig. S5 As in Fig. 3a, but for non-filtered annual mean fields.

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Fig. S6 As in Fig. 3, but using EN4 for isopycnal depth, ERSSTv5 for SST, and ERA5 forsurface wind stress curl.

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Fig. S7 As in Fig. 3, but using ORAS4 for isopycnal depth, HadISST for SST, and NOAA 20CRfor surface wind stress curl.

616263646566Fig. S8 STC climatology and anomalies associated with TPDV. (top left) Climatology of ocean
overturning streamfunction (Sv) zonally averaged across the Pacific Ocean as a function of depth(m) and latitude. Postive (negative) values of overturning streamfunction indicate clockwise (anticlockwise) orbit direction of the transport. (right) Anomalies during the negative TPDV phases(1962–1977; 1998–2014) and positive TPDV phase (1978–1997).

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69Fig. S9 As in Fig. 5, but for DPLE.

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Fig. S10 Pattern and timeseries associated with the (top row) first and (bottom row) second SVD
modes of the covariance of predicted tropical Pacific (20°S–20°N, 120°E–120°W) SST anomalies
in FY1–10 during 1955–2016, and global initial SST anomalies in Nov0 during 1954–2015. SVD1
explains 59% of the total squared covariance, while SVD2 explains 15%. The expansion
coefficients are correlated at a coefficient of 0.79 and 0.70 for SVD1 and SVD2, respectively. (leftcolumn) Regression maps of predicted SST at FY1–10 on the standardized Nov0 SST expansion
coefficient (blue curve). (middle column) Regression maps of initial SST at Nov0 on thestandardized FY1–10 SST expansion coefficient. (right column) Standardized time series of FY1–10 SST (black) and Nov0 SST (blue) expansion coefficients.

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85Fig. S11 Quadratically detrended SST anomalies during 1999–2008 in (a) ERSSTv5 and (b) the10-member ensemble-mean forecast initialized in November 1998 in DPLE_NoVolc using
traditional drift correction method (see Methods). (c) Isopycnal depth anomalies (m; σ_θ= 25.5 kgm-3) on November 1, 1998, in FOSI.

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Fig. S12 Evaluation of SST initial conditions in FOSI (top left) Correlation, (top right)
standardized Root Mean Square Error (RMSE), and (bottom right) RMSE maps of SST inNovember in FOSI compared to ERSSTv5 during 1954-2015.

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Fig. S13 As in Fig. 2a–e in the main text, but for skill evaluation for the global SST relative toFOSI.

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Fig. S14 As in Fig. 2a–e in the main text, but for skill evaluation for the global SST relative toERSSTv5.