The Emerging States of Madden-Julian Oscillation Convection Initiation

In light of recent results indicating that a build-up of lower-tropospheric moisture due to advection over the Western Indian Ocean precedes the initiation of MJO convection, here we propose an approach for detecting the local time changes of atmospheric states prior to the initiation. Permutation entropy (PE), a measure of randomness capable of detecting dynamical changes in a temporal process (Bandt and Pompe 2002; Cao et al., 2004), is used to characterize the complex time evolution of perturbation kinetic energy (PKE) at 850- and 200-hPa, specific humidity integrated from surface to 750 hPa (IWV), and temperature at 750-hPa globally between 45 S and 45 N in ECMWF Interim reanalysis. Since permutation entropy is based on rank statistics, it is unaffected by signal amplitude. This makes it ideal for detecting dynamical changes across both tropical and extratropical regions.

Phase indices of MJO convective activities from 1984 to 2005 are created based on the temporal evolution of a pair of MJO modes obtained via the Nonlinear Laplacian Spectral Analysis applied to infrared brightness temperature averaged over the tropical belt (Tung et al., 2014). PKE-, IWV-, and temperature-based PE time series computed within a ~10-day window are compared with the phase indices to identify the typical dynamical configuration of states and changes which occur when nascent MJO convection is in the Western Indian Ocean. A statistical testing framework reveals the spatial patterns of the emerging states. First, to remove serial correlations from the data, temporal averages of PE at each grid point are computed between state transitions into and out of each phase. Then, the Wilcoxon rank-sum test (which assumes independence among observations) determines locations where mean PE during the initiative phases tends to differ from other phases.

Major results show that, around the time of MJO convection initiation, PKE, IWV, and temperature fields undergo significant dynamical changes toward organized activities in the northern hemisphere centered around 25 N and disorganized activities in the southern hemisphere around 25 S. The initiative dynamical changes in lower-level PKE correspond to organized envelopes of activities in the North Pacific, Gulf of Mexico, and Caribbean Sea and disorganized signals centered on the continental land masses Australia, South America, and Africa which extend zonally into the surrounding ocean basins. By contrast, upper-level PKE exhibits enhanced organization in the northern Indian Ocean and enhanced disorganization in southern Africa and the southwestern Indian Ocean. Dynamical changes in lower-tropospheric moisture dynamics involve increased organized activities over the western North Pacific and the eastern US/Caribbean Sea with disorganization over the Australian and South American land masses. Changes in temperature are similar with organized envelopes in the western North Pacific and the eastern US/Caribbean Sea/westernAtlantic. A swath of disorganized activity extends globally through the southern extratropics with greatest intensity over South America and the southeast coast of Africa. These kinematic and thermodynamic changes over the northern and southern extratropics strongly indicate extratropical forcing at the initiation. Finally, upon examining the PE time series during the TOGA-COARE period in 1992-1993, it appears that IWV and temperature change more gradually into MJO initiation, riding on a sinusoidal background corresponding to the annual cycle, whereas PKE tends to shift from one regime to another. Qualitatively similar observations are found during the DYNAMO period in 2011-2012.

References:

Bandt, C., and B. Pompe, 2002. Permutation Entropy: A Natural Complexity Measure for Time Series. Physical Review Letters, 88(17):174102, doi: 10.1103/Phys- RevLett.88.174102.

Cao, Y., W.-w. Tung, J. Gao, V. Protopopescu, and L. Hively, 2004. Detecting dynamical changes in time series using the permutation entropy. Physical Review E, 70(4):046217, doi: 10.1103/PhysRevE.70.046217.

Tung, W.-w., D. Giannakis, and A. J. Majda, 2014. Symmetric and antisymmetric signals in MJO deep convection. Part I. Basic modes. J. Atmos. Sci., doi:10.1175/JAS-D-13-0122.1.