Various indices have been defined to characterize the phase and amplitude of the Madden-Julian oscillation (MJO). One widely used index is the outgoing longwave radiation (OLR) based MJO index (OMI), which is calculated using the spatial pattern of 30–96-day eastward-filtered OLR. The empirical orthogonal functions (EOFs) used to calculate the OMI in observations are prone to degeneracy and exhibit oscillations on the order of 10–20 days, despite initial filtering of the OLR. We propose a simple modification to the OMI that involves aligning the EOFs between neighboring days while retaining the spatial pattern described by the EOFs. This rotation method is implemented as a postprocessing procedure of the current OMI calculation and cleanly removes the spurious oscillations and degeneracy issues seen in the standard method. A similar rotation procedure can be implemented in calculations of other MJO indices.

中文翻译：

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改进 MJO 指数季节性变化经验正交函数基的轮换程序

已经定义了各种指标来表征 Madden-Julian 振荡 (MJO) 的相位和幅度。一种广泛使用的指数是基于出射长波辐射 (OLR) 的 MJO 指数 (OMI)，它是使用 30-96 天向东过滤的 OLR 的空间模式计算的。用于计算观察中 OMI 的经验正交函数 (EOF) 易于退化，并表现出大约 10-20 天的振荡，尽管对 OLR 进行了初始过滤。我们建议对 OMI 进行简单修改，包括在相邻天之间对齐 EOF，同时保留 EOF 描述的空间模式。这种旋转方法被实施为当前 OMI 计算的后处理过程，并干净地消除了标准方法中出现的虚假振荡和退化问题。