U.S. Dept. of Commerce / NOAA / OAR / PMEL / Publications

Rectification of the Madden-Julian Oscillation into the ENSO cycle

W. S. Kessler1 and R. Kleeman2

1Pacific Marine Environmental Laboratory, National Oceanic and Atmospheric Administration, Seattle, Washington, 98115
2Bureau of Meteorology Research Center, Melbourne, Australia
Current affiliation: Courant Institute for Mathematical Sciences, New York University, New York, New York

Journal of Climate, 13(20), 3560–3575 (2000).
Copyright ©2000 by the American Meteorological Society. Further electronic distribution is not allowed.

Appendix A

Significance of Correlations

In this paper, several lag correlation statistics with confidence ranges are presented. The 95% confidence ranges for these were estimated according to the procedure in Kessler et al. (1996), based on estimating the degrees of freedom from the independence timescale of Davis (1976). A correlation coefficient r with n degrees of freedom, may be transformed to a variable z ("Fisher's z"), such that r = tanh(z), which is approximately normally distributed with standard deviation = (n - 3)-½ (Panofsky and Brier 1968). For normally distributed correlations, Student's t-test is an appropriate test to reject the null hypothesis that the values are not significantly different from zero. In section 1, a lag correlation between 1-yr running mean SOI and OLR intraseasonal variance (Fig. 1) was cited. In this case the Davis (1976) independence timescale for the filtered variables was found to be 370 days, leading to the estimate of about 17.5 degrees of freedom for the 18-yr time series. The 95% confidence range on the lag correlation r (back-transformed from the normally distributed z) was found from a t-test table to be 0.48; therefore the 0.72 correlation cited in section 1 is significant above this level.

Appendix B

Phase Relation of Observed Intraseasonal Winds, Currents and Pressure Gradients

In section 3b(3) it was shown that, in the OGCM, phase relations between intraseasonal zonal currents at the surface and subsurface advected the background temperature so as to alternately strengthen and weaken the vertical temperature gradient at the different levels. The result of this was that upwelling speed w was positively correlated with dT/dz and therefore vertical advection provided a net SST cooling, averaged over one cycle of the MJO. In this appendix, we briefly examine available observations to determine if this is the case in nature. In particular we would like to know what the phase relation is between intraseasonal zonal winds and the zonal pressure gradient and zonal currents (surface and subsurface).

The data studied come from the TAO buoy array (see section 2c) at the equator, 165°E and nearby locations. Primary measured quantities are the winds at 4-m height, surface and subsurface temperature, and subsurface current measured by a downward-looking ADCP. The common period of these observations at 165°E was from March 1991 through December 1997. A few data gaps occurred during this period, the largest for about 4 months in early 1995. For almost two years of the record, currents above 30-m depth were missing, so the 30-m current was chosen as an indicator of "surface" current, while the 175-m current was chosen to represent the currents at thermocline level. The zonal pressure gradient was estimated from the centered difference of 20°C depth between buoys at 156°E and 180°. The derivative of 20°C depth (rather than dynamic height), was chosen as an indicator of zonal pressure gradient because the TAO moorings did not regularly measure salinity and the dynamic height calculation would have to be made with a mean temperature-salinity relation. Since salinity variability not well represented by the mean temperature-salinity has been noted to significantly affect such estimates of dynamic height from the TAO moorings in this region (Ji et al. 2000), 20°C depth was used instead. In fact, the two estimates of intraseasonal pressure gradients are highly correlated and either field leads to the same conclusion in this case.

All the fields were bandpass filtered with half-power limits of about 35-140 days to extract the intraseasonal signal, and lag correlations were found among them. 95% confidence ranges were found as in appendix A. For these bandpassed time series, the independence timescales were typically 5-10 days, resulting in hundreds of degrees of freedom and 95% confidence ranges for the correlations of about 0.15. All correlations cited here are above this standard.

The results show lag relations similar to those noted in the OGCM. The highest lag correlation is given:

From these values we can conclude that the phase relation noted in the OGCM is a realistic representation of the observed intraseasonal changes in the vertical profile of zonal current and pressure gradient at 0°, 165°E. In particular, the sequence described in section 3b(3), in which zonal winds spin up a surface current with a lag of 8-10 days, and also a zonal pressure gradient and oppositely directed thermocline-level current with a lag of 15 days, is realistic.

Return to previous section or go to next section

PMEL Outstanding Papers

PMEL Publications Search

PMEL Homepage