# Details of ENSO Risk Calculations

 Go to: ENSO Seasonal Climate Risks

Temperature and precipitation data were obtained from The National Centers for Environmental Information (NCEI) and consist of more than 120 years of monthly values for each of 344 US climate divisions. The extended Multivariate ENSO Index (MEI.ext) (linear average of three bimonthly values that cover the season in question) is used to classify ENSO events. For the period 1895 to 2005, it was obtained from our website for the extended MEI (http://www.esrl.noaa.gov/psd/enso/mei.ext/table.ext.html ). More recent values were calculated by regressing the regular bimonthly MEI (http://www.esrl.noaa.gov/psd/enso/mei/table.html ) against the extended version.

To calculate the relative risk of an extreme of a variable given the state of ENSO, the ENSO index was first sorted for each season for the 120 years available. Then, the top and bottom 24 years (i.e. the La Niña and El Niño cases) were examined with respect to the variable in question (temperature or precipitation). This variable was sorted as well for each climate division. Then, a contingency table was constructed for the number of years that were both El NiĆ±o and warm (or cold, or wet, or dry), or both La Niña and warm (or cold, or wet, or dry).

Cases Expected by Chance:
ENSO PhaseExtreme ColdNeutralExtreme Warm
El Niño4.814.44.8
Neutral14.443.214.4
La Niña4.814.44.8

For the top/bottom extreme ENSO cases, we would expect

(24/120) * (24/120) *120 = 4.8
or the 4 corners of the table above as the number of extreme warm/cold (wet/dry) cases that would match by chance. For each climate division, variable, and ENSO phase chosen, we plotted:

[(actual number of matches-4.8)/(matches expected by chance)]*100

In the case of increased risk plots, regions that show an increased risk of seven (+46%), eight (+67%), or nine or more (at least +88%) matches are significant at the 83.5%, 93.5%, and 97.9% level, respectively. Significance levels were assessed using the hypergeometric distribution similar to the procedure followed in Wolter et al. (1999), except that we now draw 24 samples without replacement from a population of 120 instead of 20 out of 100. They are colored in shades of green (for increased risk of wetness), of red (for increased risk of dryness, or warmth), and of blue (for increased risk of cold). Should the risk for both extremes of either precipitation or temperature be inflated to eight or more cases, the corresponding climate division would be shaded in grey. This is very rare. For decreased risk plots, decreased risks of only two (-58%), one (-79%), and zero (-100%) matches are significant at the 91.1%, 97.9%, and 99.8% level, respectively, and are colored in similar shades of green, red, or blue to complement the increased risk maps. For example, suppressed risks of dry seasons would be colored in green to indicate relative wetness, and so forth. If both extremes of either precipitation or temperature are suppressed to at most two matches, the corresponding climate divisions would be shaded in grey. This is more common than for the increased risk maps.

Since there are 344 climate divisions and 12 seasons, one would expect a certain number of chance occurrences where the number of matches is significantly higher or lower than the 4 expected. Field significance tests addressed this question and results (not shown) indicate that our results are indeed field significant for almost all seasons and variables. Interpretation of analysis