Research ArticleATMOSPHERIC SCIENCE

Phase coherence between precipitation in South America and Rossby waves

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Science Advances  19 Dec 2018:
Vol. 4, no. 12, eaau3191
DOI: 10.1126/sciadv.aau3191
  • Fig. 1 Precipitation regimes in austral summer in South America.

    Geopotential height (GPH) at 250 hPa and precipitation anomalies [with respect to the NDJF (November to February) climatology] for times when (A) and (C) precipitation in SESA is above its 90% percentile and (B) and (D) when precipitation in SEBRA is above its 90% percentile. For the calculation of the percentiles, only time steps with precipitation larger than 0.01 mm/day are considered. The reference regions SESA and SEBRA serve as a proxy for the South American precipitation dipole in this study, and the GPH in southern South America serves as a proxy for Rossby wave activity. The size and position of the GPH reference region are chosen, such that it roughly covers one-half of the spatial wavelength.

  • Fig. 2 Data and model EOF analysis.

    (A and B) First and second EOFs of the precipitation data. NDJF precipitation anomalies were used to calculate these EOFs, which account for 9% of the total precipitation variability. A plot of the eigenvalue spectrum can be found in fig. S1. (C and D) First and second EOFs of the data generated by the conceptual model introduced in this article.

  • Fig. 3 First CEOF of the NDJF precipitation anomalies.

    (A) Spatial phase θ0(λ, ϕ) and (B) spatial amplitude S0(λ, ϕ) of the first CEOF component. (C and D) Temporal phase and temporal amplitude of the 2008/2009 season. Only one season is shown to representatively show the qualitative behavior of these measures. The other seasons exhibit a similar behavior. (See Materials and Methods for a detailed account of CEOF analysis.)

  • Fig. 4 Phase embedding.

    (A) Example of a processed observable (SEBRA), its derivative, and the Hilbert transform of the derivative for the 2002/2003 NDJF season. (B) Example of the embedding of a processed observable (SEBRA) via Hilbert transform, for three consecutive seasons 2002/2003, 2003/2004, and 2004/2005.

  • Fig. 5 Phase difference time series.

    (A) The gray shaded area marks the 5 and 95% percentiles of phase difference time series from the 250 AR2 surrogates of the time series computed with maximum likelihood estimates of the AR2 parameters. (B) Zoomed in view of (A).

  • Fig. 6 Phase difference histograms.

    (A to C) Histograms H(x, y) of phase difference of all reference time series. The empirical distributions of the observables are significantly different from iAAFT surrogates at a significance level α < 0.0001 due to a KS test. (D) Temporal evolution of the dispersion parameter κ of a MLE fitted von Mises distribution to the phase differences for each season.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/12/eaau3191/DC1

    Fig. S1. Eigenvalue spectrum of the PCA performed with precipitation anomalies from MERRA2 shown in Fig. 2.

    Fig. S2. Spatial phase of the first CEOF of the conceptual model.

    Fig. S3. SSA of all three investigated observables.

    Fig. S4. Phase difference time series results analogous to Fig. 5.

    Fig. S5. Phase difference time series results analogous to Fig. 5.

    Fig. S6. Phase difference histogram results analogous to Fig. 6.

    Fig. S7. Phase difference time series results analogous to Fig. 5.

    Fig. S8. Phase difference histogram results analogous to Fig. 6.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Eigenvalue spectrum of the PCA performed with precipitation anomalies from MERRA2 shown in Fig. 2.
    • Fig. S2. Spatial phase of the first CEOF of the conceptual model.
    • Fig. S3. SSA of all three investigated observables.
    • Fig. S4. Phase difference time series results analogous to Fig. 5.
    • Fig. S5. Phase difference time series results analogous to Fig. 5.
    • Fig. S6. Phase difference histogram results analogous to Fig. 6.
    • Fig. S7. Phase difference time series results analogous to Fig. 5.
    • Fig. S8. Phase difference histogram results analogous to Fig. 6.

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