Low-Frequency Modulation of the ENSO–Indian Monsoon Rainfall Relationship: Signal or Noise?

Running correlations between pairs of stochastic time series are typically characterized by low-frequency evolution. This simple result of sampling variability holds for climate time series but is not often recognized for being merely noise. As an example, this paper discusses the historical connection between El Nin o-Southern Oscillation (ENSO) and average Indian rainfall (AIR). Decades of strong correlation (0.8) alternate with decades of insignificant correlation, and it is shown that this decadal modulation could be due solely to stochastic processes. In fact, the specific relationship between ENSO and AIR is significantly less variable on decadal timescales than should be expected from sampling variability alone.