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An MJO Hovmoeller diagram displays the time evolution of the ensemble mean anomaly.  The longitude within the equatorial band (15S-15N) is shown on the x-axis. Time is shown on the y-axis.  The analyed data at the data time of each extended range forecast run is shown above the horizontal line.  The forecast mean ENS ensemble values are shown below the horizontal line.  Several MJO forecast products are available:

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The Wheeler-Hendon MJO index plot displays the time evolution, location and magnitude of the MJO predicted by ENS ensemble and described by a multivariate MJO index (Wheeler and Hendon 2004 Mon. Wea. Rev. vol. 132, 1917-1932).  The magnitude of the MJO is essentially proportional to the distance of the point from the centre of the diagram.

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Fig8.2.2.5: Wheeler-Hendon MJO diagram.  Time evolution of the MJO as predicted by the ENSensemble using zonal winds at 850hPa, 200hPa velocity potential and simulated OLR, all averaged between 15S and 15N.  Individual ensemble member values at day 1, 5, 10, 15 and 20 are represented respectively by red, pink, orange blue and green circles. The ensemble mean values (black triangles) are joined by a solid black line, and the analysis values of the preceding 30 days are joined by a grey line (with grey dots added every 5 days).  Points representing sequential values trace anti-clockwise trajectories around the origin,indicating systematic eastward propagation of the MJO.  Large amplitudes (outside of the circle) signify strong cycles of the MJO, while weak activity appears as rather random motion near the origin. The phases (broadly geographical regions) are numbered 1 to 8.  See Wheeler and Hendon 2004 Mon. Wea. Rev. vol. 132, 1917-1932 for details.

In the example in Fig8.2.2.5 there is initially a strong indication of a large amplitude MJO (red, Day1; pink, Day5) progressing eastwards but this is forecast to probably weaken and become less identifiable (Day15, blue) over the western Pacific, but the ENS ensemble spread becomes large by then implying large uncertainty with some members maintaining a strong signal (plots far from the centre of the diagram), others weak (plots towards the centre and inside the circle).  Compare with the Hovmoeller diagrams (Fig8.2.2.4) where:

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Individual values of these parameters for the different ENS ensemble members give varying intensities of MJO on the diagram and the spread becomes large.  Note also that by construction, the amplitude of the forecast ENS ensemble mean MJO on this diagram (as shown by black triangles) will tend to reduce, on average, at longer lead-times.

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