This section describes the diagnostics developed by the US CLIVAR MJO Working Group for assessing the fidelity of the simulation of the boreal winter Madden-Julian Oscillation and the boreal summer intraseasonal oscillation in climate models. For brevity, the term MJO will be used throughout, and it includes the broader category of eastward (and northward) intraseasonal oscillations that occur on time scales of 30-70 days. The development of the diagnostics was a protracted procedure carried out by the MJOWG, with exhaustive sensitivity tests using observational data to assess the necessity (or not) for such issues as stratifying the analysis by season, domains for analysis, the need (or lack thereof) of using tapering or de-trending during spectral analysis, developing simple methods for assessing statistical significance etc.

   The information and discussion below are meant to provide a brief description of the diagnostics chosen and the specific steps used for their calculation, and in some cases the motivation for these choices and steps.  The diagnostics are categorized into two levels of increasing complexity:


   Level 1: These diagnostics are meant to provide a basic indication of the spatial and temporal intraseasonal variability that can be easily understood and/or calculated by the non-MJO expert. Ease of use dictated that the analytic procedures be as simple as possible and as similar as possible for summer and winter calculations. These diagnostics include assessing variance in preferred frequency bands, spectral analysis over key domains, univariate empirical orthogonal function (EOF) analysis of bandpass filtered data, statistical significance assessment of the EOFs, and lead-lag assessment of the dominant intraseasonal principal component (PC) time series. Variables include OLR, precipitation and zonal wind at 850 and 200 hPa.  See more specific discussion.



   Level 2: These diagnostics provide a more comprehensive diagnosis of the MJO through multivariate EOF analysis and frequency wave-number decomposition. Sensitivity tests indicated that the multivariate EOF analysis could be performed on data encompassing the full year, with little or no compromise in capturing the more complex intraseasonal variations that occur during the boreal summer (e.g., including the northward propagation of convection that occurs over the Asian monsoon domain). The dominant intraseasonal PC's are also used to generate composites at key portions of the MJO life-cycle (alternatively, they can be used in lag regression to assess the mechanisms of MJO variability), and coherence-squared and phase between the PC's are calculated to determine the fidelity of the eastward propagation. Multivariate EOF analysis is based on OLR and zonal wind at 850 and 200 hPa.  However, a number of other variables are included in life cycle composites and mean field descriptions.  See more specific discussion.



   Other: These diagnostics provide additional measures that have in some cases been found to play an important role in MJO simulation fidelity (e.g., mean state) or characterize the manner the MJO interacts with other important weather/climate processes (e.g., ENSO). See more specific discussion.



   General: For both level 1 and level 2 diagnostics, unfiltered anomalies are computed by subtracting the climatological daily (or pentad where appropriate) means calculated using all years of the data.  The 20-100 day filtering discussed below is based on applying an 201-points Lanczos filter.  In addition, while the EOF analysis is performed on 20-100 day filtered data, the statistical significance of the EOFs is assessed by projecting the unfiltered anomalies (with only the seasonal cycle removed) back on to the EOFs to ascertain the significance of spectral peaks at intraseasonal time scales against a red noise background. Note that when the EOF analysis is applied to models, one can calculate and examine the EOFs of the model data directly. Additionally, it recommended that the  bandpass filtered anomalies from the models be projected onto the observed modes of variability to assess how well the model simulates the observed MJO. For these diagnostics, the seasons have been defined as: 1) boreal summer is May through October, and 2) boreal winter is November through April. For some diagnostics, computations are performed for specific domains of interest. These domains are given in the Table 1 and were determined from examination of the VARIANCE MAPS to isolate regions where the observed variability is large. Finally, for spectra calculations, unless otherwise noted, no windowing/tapering or de-trending was applied.