Bimodal representation of the tropical intraseasonal oscillation

The tropical intraseasonal oscillation (ISO) shows distinct variability centers and propagation patterns between boreal winter and summer. To accurately represent the state of the ISO at any particular time of a year, a bimodal ISO index was developed. It consists of Madden-Julian Oscillation (MJO) mode with predominant eastward propagation along the equator and Boreal Summer ISO (BSISO) mode with prominent northward propagation and large variability in off-equatorial monsoon trough regions. The spatial–temporal patterns of the MJO and BSISO modes are identified with the extended empirical orthogonal function analysis of 31?years (1979–2009) OLR data for the December–February and June–August period, respectively. The dominant mode of the ISO at any given time can be judged by the proportions of the OLR anomalies projected onto the two modes. The bimodal ISO index provides objective and quantitative measures on the annual and interannual variations of the predominant ISO modes. It is shown that from December to April the MJO mode dominates while from June to October the BSISO mode dominates. May and November are transitional months when the predominant mode changes from one to the other. It is also shown that the fractional variance reconstructed based on the bimodal index is significantly higher than the counterpart reconstructed based on the Wheeler and Hendon’s index. The bimodal ISO index provides a reliable real time monitoring skill, too. The method and results provide critical information in assessing models’ performance to reproduce the ISO and developing further research on predictability of the ISO and are also useful for a variety of scientific and practical purposes.     

Symmetropy of earthquake patterns: asymmetry and rotation in a disordered seismic source

We demonstrate that the idea of symmetropy can be used for quantification of earthquake patterns. The symmetropy can be considered as a measure of asymmetry. A pattern is richer in asymmetry when the symmetropy is smaller. The specific results of its applications are obtained as follows. In a discrete model of a seismic source with self-organized criticality, the spatial patterns of earthquakes during critical states and sub-critical states are distinguished by the behaviour of the symmetropy: sub-critical patterns show that the symmetropy is approximately a constant but this has various values during critical states. The critical patterns show asymmetric property without any asymmetric force from the outside and without asymmetric intracellular rule. We show that the emergence of asymmetric patterns is a generic feature of dynamic ruptures in our model. Such a generic asymmetry results from the model which is an inherently discrete system consisting of finite-sized cells. These cells may represent geometrical disordered fault zones. We further discuss rotational motions that generate seismic rotational waves. In micromorphic continuum theory, such rotations are attributed to dynamic ruptures in disordered systems. We note that the concept of disorder in this theory is expressed by a set of finite-sized microstructures and is consistent with the concept of disorder modelled in the present study. Thus, we suggest that the spatially asymmetric patterns of earthquakes might be related to the rotational motions, because both come from dynamic ruptures in a discrete fault zone without a well-defined continuum limit.     

An introduction to combined Fourier–wavelet transform and its application to convectively coupled equatorial waves

Convectively coupled equatorial waves (CCEWs) are major sources of tropical day-to-day variability. The majority of CCEWs-related studies for the past decade or so have based their analyses, in one form or another, on the Fourier-based space–time spectral analysis method developed by Wheeler and Kiladis (WK). Like other atmospheric and oceanic phenomena, however, CCEWs exhibit pronounced nonstationarity, which the conventional Fourier-based method has difficulty elucidating. The purpose of this study is to introduce an analysis method that is able to describe the time-varying spectral features of CCEWs. The method is based on a transform, referred to as the combined Fourier–wavelet transform (CFWT), defined as a combination of the Fourier transform in space (longitude) and wavelet transform in time, providing an instantaneous space–time spectrum at any given time. The elaboration made on how to display the CFWT spectrum in a manner analogous to the conventional method (i.e., as a function of zonal wavenumber and frequency) and how to estimate the background noise spectrum renders the method more practically feasible. As a practical example, this study analyzes 3-hourly cloud archive user service (CLAUS) cloudiness data for 23 years. The CFWT and WK methods exhibit a remarkable level of agreement in the distributions of climatological-mean space–time spectra over a wide range of space–time scales ranging in time from several hours to several tens of days, indicating the instantaneous CFWT spectrum provides a reasonable snapshot. The usefulness of the capability to localize space–time spectra in time is demonstrated through examinations of the annual cycle, interannual variability, and a case study.