(This material justifies a statement in the post “Predict weather from ENSO?”)

The graphs above are like those in an earlier post, but show how Manilla monthly rainfall anomalies, rather than maximum temperature anomalies relate to the El Nino-Southern Oscillation (ENSO). Most people using ENSO  want to predict Australian regional rainfall.

In the second graph I have improved the match at peaks and troughs of smoothed Manilla monthly rainfall anomalies and NINO3.4 sea surface temperature anomaly data in two ways.
1. I converted the sea surface temperature anomaly (degrees C) into a model of resultant rainfall anomaly (mm) by multiplying by minus fifteen.
2. I added 3.7 mm of rainfall to the Manilla figures, and I lagged the data by two months.

To the eye, the over-all correspondence between actual and modelled rainfall is good, but not quite as good as in the temperature graphs. One form of mis-match is that two of the greatest rainfall deficits (“El Nino” Nov-06, Dec-09) are broader and shallower than in the model. (Perhaps an arithmetic measure of rainfall anomaly is not the best.)

The third graph shows how much Manilla rainfall, as adjusted, differs from the rainfall “predicted” by the NINO3.4 model. Dashed lines show limits of a good match at +/- 7.5 mm (corresponding to +/-0.5 degrees). The nature of each larger discrepancy is noted.

A good match demands lagging actual rainfall at Manilla by two months. That implies that peaks and troughs in Manilla rainfall anomalies happen two months before the matching anomalies of NINO3.4. I wonder if prediction is even practical if that is the case in other parts of Australia.

Notes
1. High frequency noise is reduced in the case of the Manilla monthly data by a Gaussian smoothing function of half-width six months.
2. On advice, I represent the El Nino – Southern Oscillation phenomenon (ENSO) by the NINO3.4 area anomalies from the OISSTv2 data set.
My enquiries about the best data to use are in this “weatherzone”  thread.
The ensemble of sea surface temperatures does not have much high-frequency noise. There is some, however, and I have used the same smoothing as used in the (formerly authoritative) Oceanic Nino Index (ONI), that is, a running mean of each three monthly values.

This was posted originally in a “weatherzone” forum, with the date 28 October 2011. It is posted here with the nominal date 16 November 2011.

(Note added: Updated to include 2013 here.)