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| Wind Erosion & Water Conservation Unit |
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The climate analysis method used here tests for significant skewness in cumulative rainfall and mean temperatures during seasonal periods consistent with El Niño and La Niña SST conditions. A skewed sample of seasonal data is defined here as one whose distribution of values above or below the historical median, or in the highest and lowest 25% of the historical distribution, is inconsistent with random sampling at a specified confidence level. |
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Wright's (1989) S index is used to identify seasonal periods consistent with both ENSO phases. The S index provides a continuous historical record (1881-1986) of SST anomalies averaged over an irregular region of the equatorial Pacific extending from the dateline to 90W and 6N to 10 S. The index was extended here by regressing it against Niño 3.4 SSTA values during the 1950-1986 period, and using the resulting regression coefficients and Nino 3.4 values during 1987-1997 to infer S values over that 11 year period. |
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The state of seasonal climate over the continental U.S. was determined through the use of U.S. Climate Division Data (Guttman and Quayle,1996). Climate Division precipitation (temperature) data is reported as monthly totals (averages) over each of the continental United State's 344 climate divisions. The data used in Mauget and Upchurch (1998) includes 132 climate divisions covering a major portion of the Great Plains and Midwest, and extends over the 103 year period between Jan. 1895 and Dec. 1997. Before analysis, each climate division's rainfall (temperature) data was converted to seasonal values by summing (averaging) the monthly data values over consecutive and overlapping three month periods (January-February-March=JFM, February-March-April=FMA, ...December-January-February=DJF, etc.). These values were then ranked from the smallest seasonal value over the 103 year period of record (1) to the largest (102,103), and the resulting order statistics were then used to determine lower quartile, median, and upper quartile thresholds in the manner suggested by Wilks (1995). This process was repeated for each climate division over each three month seasonal time window. |
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In testing for ENSO-related skewness in a climate division's seasonal rainfall and temperature data, seasons of moderate and strong El Niño conditions were identified as those 3 month periods during which the average S index value was above the highest sextile (+.84° C) of the distribution of historical (1895-1997) S index values . Conversely, 3 month periods during which the average S value was below the lowest sextile (-.64° C) marked seasons of moderate and strong La Niña conditions. Periods of strong El Niño (La Niña) forcing were identified as those seasons during which the average S value was above (below) the lowest (highest) decile of historical values, +1.09° C (-.84° C). Extreme sextile and decile thresholds are used here to define extreme SST conditions because the S index is somewhat skewed towards positive values and is not normally distributed. For notational purposes these quantiles will at times be indicated by 10+, 6+, 6-, and 10-, with 10- indicating the lowest (coldest) decile, etc. Unless otherwise stated, the skewness tests found here were conducted on samples of climate division data consistent with periods of moderate and strong; i.e., 6+ and 6-, El Niño and La Niña conditions. |
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The thresholds of eastern equatorial Pacific SSTA are more likely to be exceeded during the northern winter months than during spring or summer periods , thus the size of the ENSO-specific samples of seasonal climate varies by season. As the sample size during northern winter seasons (18-25) is not negligible compared to the size of the population from which it is drawn (102,103), hypergeometric probability distributions (Mendenhall et al., 1990) were used to calculate null statistics. The hypergeometric probability function assumes a population of finite size (P) divided into two groups of separate characteristics (P = N1 + N2), and returns the probability of drawing a sample of size S0 from that population with a certain composition of the two types (S0 = S1 + S2). The statistical significance of drawing a sample with S1 elements is determined by the cumulative probability of drawing 0,1,2… (S1)-1 elements in a random sample of size S0. For example, assuming a population of 102 November-December-January seasons evenly divided above and below a climate division's median precipitation or temperature value, the cumulative probability of 15 or fewer seasons being above median in a random sample of 25 is 90.7%. Thus drawing a sample of 25 from such a population and gathering 16 above median values is significant at a 90.7% confidence level. Because of the discontinuous nature of the hypergeometric cumulative probability distribution, approximate 90% confidence levels were used to identify significant skewness about median and extreme quartile values. In no instance is the minimum threshold of these local confidence levels less than 85%, while in some cases local confidence levels for skewness about the median exceed 90%. |
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In the skewness analyses of climate found here climate divisions are shaded where it was found that the seasonal rainfall or temperature during the indicated seasons was significantly skewed about the division's 1895-1997 seasonal median value. If results indicated significant skewness about the median, then an additional test was conducted to determine whether the sampled seasons held a significant incidence of values in the lowest and highest 25% of historical values. Annotated climate divisions indicate those that showed a significant incidence of climate conditions below the lowest quartile or above the highest quartile. Climate divisions that are both shaded and annotated allow for a complete breakdown of how seasonal climate during anomalous ENSO conditions fell within the long-term quartile distribution. For example, in the July-August-September (JAS) rainfall analysis the shading of Nebraska's westernmost climate division shows that of the 13 seasons indicated, 12 were above the 103 year median for July-August-September rainfall. The annotation (0/6) shows that none of those 13 seasons resulted in rainfall in the first (driest) 25%, while 6 seasons resulted in rainfall in the highest (wettest) 25%. Twelve seasons were above the median while 6 were above the highest quartile, thus 6 JAS periods fell in the 50th - 75th percentile. As 1 season was below the median but not below the first (driest) quartile, that season fell in the 25th - 50th percentile. As a result, those 13 El Niño seasons resulted in 0-1-6-6 instances occurring in the 1st-2nd-3rd-4th 25% of that climate division's historical distribution of JAS seasonal rainfall values. |
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