Identifying the skeleton of the Madden-Julian oscillation in observational data

The Madden-Julian oscillation (MJO) skeleton model offers a theoretical prediction of the MJO's structure. Here, a method is described for identifying this structure in observational data. The method utilizes projections onto equatorial wave structures, and a main question is: Can this method isolate the MJO without using temporal filtering or empirical orthogonal functions? For the data projection, a wide range of data is incorporated: multiple variables (wind, geopotential height, water vapor, and, as a proxy for convective activity, outgoing longwave radiation), multiple pressure levels (850 and 200 hPa), and multiple latitudes (both equatorial and off-equatorial). Such a data variety is combined using a systematic method, and it allows for a distinction between the Kelvin and Rossby components of the MJO's structure. Results are illustrated for some well-known cases, and statistical measures are presented to quantify the variability of the MJO skeleton signal, MJOS(x, t), and its amplitude, MJOSA(t). The robustness of the methods is demonstrated through a suite of sensitivity studies, including tests with two projection methods. When the projection is based on the skeleton model's energy, as opposed to the standard L² energy, water vapor is seen to be of primary importance. Finally, a simple interpretation is given for the MJO skeleton structure: it is related to the wave response to a moving heat source. From either perspective, the methods here identify signals that project onto coupled convection-circulation patterns, and the results suggest that a large portion of the MJO's structure is consistent with such a coupled pattern.