Given evidence of a significant tendency to relatively cool and wet growing conditions over the Midwest during moderate and strong El Niño JAS periods , and of above median and 4th quartile temperatures during strong La Niña summer conditions, corn crops harvested immediately after warm and cold SST JAS seasons were tested for significant skewness. This yield analysis was conducted over a longer time period than that of the climate analysis, as Wright's S index is defined as early as 1872 and NASS corn yield records extend back to 1866. However, as the S index has numerous data gaps prior to 1881 only per acre yield values after the harvest of 1880 were used here. The post-warm phase yield values sampled from the 1881-1994 corn records were those harvested after 12 El Niño JAS periods meeting the "6+" S Index criteria during 1895-1994, as no JAS periods exhibiting S index values above the highest sextile were found during 1881-1895. The post-cold phase values sampled correspond to harvests after 7 strong La Niña seasons of occuring over 1895-1994, plus the harvest subsequent to JAS 1886. For comparison, corn yields after 18 JAS periods consistent with moderate and strong (i.e., mean JAS S values below the first sextile) La Niña conditions were also tested for skewness. In Table 1 these analyses are indicated by (6-), while the analyses for harvests after JAS periods marked by 1st decile S index conditions are indicated by (10-).

      The rainfall analysis for September-October-November (SON) periods shows that wetter than normal conditions over Texas can occur as early as that season , while Oklahoma, Kansas, and Nebraska may see abnormally wet conditions as early as December-January-February (DJF), assuming SSTA conditions above the highest sextile during those three month periods. Conversely, the temperature and precipitation of La Niña OND ,NDJ , and JFM periods imply shifts to warmer and drier winter conditions during cold SST conditions. These La Niña climate responses are, again, conditional on anomalously cold SST conditions. Post-planting precipitation during the dormant period of winter wheat growth can have an important effect of soil moisture during the vegetative period, and thus effect subsequent yield. In view of the evidence of above(below) normal winter-spring precipitation during the El Niño(La Niña) phase, the effects on winter wheat crops harvested subsequent to periods of mature ENSO conditions were analyzed. The post-warm phase yield values sampled were those harvested after 19 El Niño NDJ periods that occurred during the period of available NASS winter wheat yield records (1909-1994), while the post-cold phase yields correspond to harvests after 20 La Niña NDJ seasons that occurred over that same period.

      The historical records of per-acre yield of both corn and winter wheat show monotonic increasing trends beginning in the middle decades of the 20th century. Mjelde and Keplinger (1998) discuss numerous reasons for the increase in wheat productivity in the years following World War II, while Handler (1984) cites the introduction of hybrid corn and the use of nitrogen fertilizers as factors contributing to higher corn yields. Determining significant inter-annual fluctuations in yield about these long term trends requires a year-to-year estimate of the trend values themselves. To solve for long-term trends in per-acre yields, USDA-NASS historical statewide yield estimates were first subjected here to a 71 point low-pass Lanczos filter (Duchon, 1979). Using such a selective low pass filter and a cutoff period of 25 years, the long term trends solved for are essentially the yield records minus all spectral components with a period of less than 25 years. Using the yield (y) and resulting trend values (t) for a particular year, Percentage Departure from Trend (PDT) values are given by;

"Normal" yields for a specified year are approximated by the year's trend value, thus the PDT values estimate a year's percentage departure from normal. Near normal yields were defined as the 1/3 of all yield values closest to the long-term trend line. Threshold values separating above from near, and near from below normal yield values were solved for by determining constants bounding the ~ 1/3 of values in a PDT time series closest to 0.0 . The PDT constants separating these classes varied in magnitude from .06 to .09, depending upon each state's yield record. For a threshold value of .06 near normal yield for a given year was defined as being within +/- 6% of the year's long-term trend value, while above(below) normal yields were defined as those greater than(less than) 106%(94%) of trend. As a result, the total number of harvests were divided into above, near, and below normal classes of approximately equal number. The magnitudes of these thresholds can be compared with the value of .03 used by Handler (1984, 1990) and .10 used by Carlson et al. (1996).

      After separating historical yield values into above, near, and below normal classes, the distribution of yields harvested after seasonal periods of anomalous S index conditions were tested for evidence of significant skewness. As in the analysis of historical climate data, hypergeometric statistics were used to check whether the distribution of warm and cold phase harvests were significantly different from that expected from random sampling. When a significant incidence of above normal harvests was tested for, near and below normal yields were grouped into one class. When the sampling of below normal harvests was tested, near and above normal yields were grouped together, etc. As in the climate analysis, the statistical significance of drawing a sample of harvests of size S0 ( = S1 + S2) from the population of harvests with S1 elements is determined by the cumulative probability of drawing 0,1,2… S1-1 elements in a random sample. Thus, for example, the red diamonds in the figure below show that of 19 post-El Niño Kansas winter wheat harvests, 3 were below normal, 5 were near normal, while 11 were above normal. Selecting 19 harvests from an 86 year record consisting of 32 below, 25 near, and 29 above normal yields and sampling 11 above normal is significant at a 98.65% confidence level, thus a significant tendency to above normal yields conditional on warm (i.e. sixth sextile ) November-December-January S index values is evident.

(Top) USDA-NASS per acre historical yields for Kansas winter wheat and long term trend line. Dashed curves delimit above, near and below normal yield values. Diamond shaped data points mark harvests subsequent to NDJ periods exhibiting 6th sextile mean S index values, while triangles mark harvests after 1st sextile (6-) S index conditions. (Bottom) Percentage Departure from Trend values [(yield-trend)/trend] for Kansas winter wheat. (Right) Distribution of above, near, and below normal PDT values for post-El Niño and post-La Niña winter wheat harvests. Light blue bars indicate skewness significant at 90% confidence level or better, and annotation shows associated significance level.

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      In the figure below a tendency for El Niño (La Niña) summer climate conditions to enhance (suppress) corn yields is evident, and a similar effect on winter wheat yield is found after periods of warm (cold) November- December-January (NDJ) SST. However, the effects of both ENSO phases on winter wheat appear more consistent than the effects on corn yield. In Table 2 and in the figure below significant tendencies to below and above normal wheat yield effects are found in every state with the exception of post-warm phase Nebraska yields, which just miss significance at a 90% confidence level. In the corn yield analysis of Table 1 , comparable results are found only in Indiana and Illinois. Results in other states either fail to meet the criteria of 90% significance, or display a significant incidence of near or below normal trend values. As a result, the tendency to other than normal yield values after extreme ENSO periods appears stronger in the wheat yield results. With the exception of the post-warm phase Nebraska corn yields, the PDT values of the winter wheat yields are more dispersed than that of corn. This is particularly clear in comparing the effects on post-warm phase yields. Table 1 shows a significant incidence of above normal corn yields in Illinois, Indiana, and Minnesota, but the associated PDT values found above are relatively modest (<.2) when compared to the magnitude of post-warm phase wheat yield values in Kansas, Oklahoma, and Texas.

Percentage Departure from Trend values for post ENSO per-acre corn and winter wheat yields in the states indicated. Diamond (Triangle) corn PDT values correspond to harvests after July-August-September periods showing mean S index values in the highest (lowest) 17% of historical values. Those values reproduce the distribution of below, near, and above normal 6+ (6-) entries in Table 1. Diamond (Triangle) winter wheat PDT values correspond to harvests after November-December-January seasons showing mean S index values the highest (lowest) 17% of the historical distribution, and reproduce the distribution of below, near, and above normal 6+ and 6- entries in Table 2. Vertical lines mark near normal yield values for each state. Light blue bars indicate skewness significant at 90% confidence level or better, and bar annotation shows associated significance level.