Several summer/growing season (MaySeptember) parameters were combined to produce an integrated summer severity index for Goodland, Kansas, so as to observe any trend(s) of severity over the last 75 years. The period of record was from 19201994. This study is based upon a similar winter severity index produced for Goodland, Kansas and Pittsburgh, Pennsylvania (Nouhan 1992).
In deriving a total index value for each winter season for the Goodland winter study, each parameter was individually normalized to produce subindex values with each scaled on a 100point system. The mildest occurrence of a parameter was given a near zero value and the most severe a near 100 value. All scaled subindex values were then combined with their respective weighting factors to produce a total index value for a given winter season (Nouhan 1992).
A similar approach was used in this project, except parameters related to summer and the growing season, were selected. The chosen parameters with their weighting factors are 1) Summer (S) mean (June, July, and August temperatures combined) 40 percent, 2) Averaged May/September (MS) mean temperatures for each season 10 percent, 3) Extremes (high temperature) index (E) 25 percent, and 4) Growing season (MaySept) rainfall (R) 25 percent. The following points were considered in the selection and weighting of the above parameters: A) Data availability, B) Public impact, and C) Impact on the agricultural community (Goodland's economy is mainly agriculturally based).
Departures from the normal summer mean temperature directly relate to energy demands due to airconditioning use. Crop growth and stress factors are also directly related to this parameter.
Averaged May/Sept mean temperatures were included mainly as a longevity factor to the growing season (defined as May 1Sept 30 for the purpose of this study).
The Extremes index in this study simply incorporates the number of days with maximum temperature > 90 deg F and > 100 deg F for each season. This index is a good proxy to measure human and crop stress as well as crop water consumption (i.e., irrigation use). Days over 100 deg F were weighted two and a half more times than days over 90 deg F because of much higher heat stress 100+ deg F heat places on outdoor human activities. Also, since 100+ deg F heat at Goodland normally occurs with low relative humidities, much higher evapotranspiration rates can be expected from crops. For the Extremes index, 90+ deg F days were assigned 2 points while 100+ deg F days were assigned 5 points each. The total number of points was then tallied for each season. A graduated point scheme based on interim values between 90 and 110 deg F would have been more desirable, but much more labor intensive, since Local Climate Data from the National Climate Data Center does not list the number of occurrences for any interim values (i.e., number of days > 95 deg F and etc.).
Dew point and overnight low temperatures were other possible parameters for this study. Goodland, however, rarely experiences dew points and overnight low temperatures >65 deg F due to its high plains location at 3760 ft above MSL and its close proximity to the Rocky Mountain rain shadow. In fact, high temperatures >95 deg F are normally accompanied by a reduction in dew point to below 60 deg F and occasionally below 50 deg F. Consequently, dew point and overnight low temperatures were not chosen for this location. Growing season rainfall, the last parameter selected for this study, was exclusively chosen as a summer crop (mainly corn at Goodland) stress proxy.
First, the mean for each parameter was calculated. Second, the standard deviation (s) for each parameter was computed to show relative variability and skewness.
Since no parameter in this study was exactly normally distributed, a splitsplit standard deviation procedure was employed to include unique aspects of each individual parameter distribution. This method is a proxy to, and much less rigorous than employing an incomplete gamma distribution (Wilks 1995) on each parameter. In using the split standard deviation technique, the extreme highest and lowest values of each parameter were assumed to be +3s and 3s respectively (despite actual calculations based on true s values derived in step 2). The difference between the mean and extreme endpoint values of each parameter (Table 1a and 1b) were then divided by 3, resulting in two approximate s values per parameter, one for above (s+) and the other for below (s) the mean (end of Table 1b). Endpoints were then assigned Z values (similar to those found in a normal distribution table) as close to +3s and 3s as possible based on the precision of rounding for each respective parameter unit. The result of this step was to help later calibrate the most extreme endpoints of every parameter as close as possible to subindex values of zero or 100. This maximizes the range of the overall summer severity index between opposing extreme seasons.
An important exception to this procedure was the E parameter. The distribution of this particular parameter was skewed far enough to the right (with the left tail somewhat bounded by zero), that if one were to use the actual s value calculated from step 2, the lowest value of E would only be around 2s below the mean. Consequently, using the s and s+ values for E, the 1923, 1934 and 1936 seasons were assigned Z values (see step 4) greater than 3.0, but less than 4.0 above (or below) the mean respectively. The assigned Z values for these seasons were approximately based on the numerical ranking of each respective seasonal E value divided by the total range of E from the entire record. Since the median (Ott 1977) of the E distribution was significantly less than the mean, values of s for above the mean were assigned increasingly larger increments to reflect each seasons relative position within the distribution.
Next, a statistical "Z" score (Ott 1977) for all data values was derived using the appropriate mean and s for each parameter. The equation used was:

(1) 
where x represents a value from any of the four parameters and s represents the corresponding s or s+ for the respective parameter (including incremental s+ values for E). Note, that "Z" values derived in this step from the split standard deviation approach used in step 3 are close but not the same as theoretical normal curve Z values. Lastly, this pseudonormal distribution was used in this study because there was 75 years of data for each parameter. Locations with less than 30 years of data should calculate t values (from Student's t distribution) and then proceed with the rest of the procedure using t values in place of Z (Ott 1977).
Signs of Z for each parameter were determined by how each contributes toward higher final index values. Positive departures of S, E, and MS are associated with severe summers, so, the sign of Z for these parameters correctly reflect their contribution. Conversely, negative departures of R contribute to greater summer severity at Goodland. Therefore, the opposite sign of Z for this parameter must be taken to properly account for a positive contribution toward the final index.
Next, the fraction (Zp) of the area under the normal curve right (+Z) or left (Z) of the mean for each data point were found. This was done by taking the fractional value listed for each Z from a normal curve statistics table (Ott 1977). Zp values derived from a negative Z must be preceded by a negative sign to reflect the proper contribution toward the final index.
Next, the individual subindices (ix) were computed for each parameter using the following equation, where x represents any of the four parameters:

(2) 

If Z exceeds (is less than) 3s (3s) but is less (greater) than or equal to 4s (4s), then equation 3 must be used:

(3) 

In equation (3) xx.x denotes a subindex of 99.6 (0.4) and the constant 0.5 is multiplied by Z3 (Z+3). These equations were formulated too essentially to adjust Zp values closer to the mean (flatten the normal curve somewhat).
Equation (2) was used for all except for 5 parameter values. The remaining values exceeded +3s, requiring equation 3. Note that both equations linearly smooth the total area under the normal curve right of each individual Z value. Individual indices could have been computed by multiplying the result of .50 + or  Zp by 100. However, the resulting index values obtained would have varied too greatly between 1s and +1s, because index values near 1s would be too high and those near 1s values too low (Table 2). In order to expand the rapidly changing portion of the index scale over a greater range of Z, a linear smoothing term was included in the first term of the numerator in both equations (2) and (3). This smoothing term provided a linear value simply based on an input Z value. The 16.5 Z constant in equation (2) kept the smoothing term from rising (falling) above 99.5 (0.5) for inputs of < +3s (> 3s) and also kept the smoothing term always less (more) than the Normal Curve (NC) term (second term of numerator in both equations (2) and (3)) for +Z (Z) values. The smoothing term in equation (3) simply increments the max (min) subindex value of 99.6 (0.4) from equation 2 by 0.1 (0.1) for each 0.25s above (below) +3.0s (3.0s).
Inclusion of the smoothing term in equation (2) expanded the range where ix undergoes the most rapid change from 0.0s to +1.0s (1.0s) to 0.0s to +2.0s (2.0s) and further linearized ix values up (down) to +2.5s (2.5s) compared to straight NC values. A close examination of Tables 3a & b (Table 3a) shows that the smoothed ix values differ the most from NC values between +1.0s and +1.5s and between 1.0s and 1.5s (i.e., greatest smoothing intervals). Both values are the same at Z=0 and begin to approach each other again beyond +2.5s and 2.5s.
The term "affected" in this description is defined as causing lower than expected crop yields.^{1}
____________
^{1} Note, percentages were derived after consulting with an HMT on staff at Goodland who also is a local farmer. These percentages are only approximations.
Next, the individual indices were combined with the appropriate weighting factors to compute the total index (T) for each summer season. The equation used for this step was:

(4) 
Lastly, the final index (I) was computed by applying a linear correction, if necessary, to center the mean close to 50.0 and to center the total range of T values equidistant from the 0 and 100 scale endpoints. This step would likely be required to correct any errors resulting from using the split standard deviation technique. For this particular study, however, errors from each parameter cancelled each other out, resulting in the mean of all T values very nearly at 50, and the extreme seasons nearly equidistant to the 0 and 100 scale endpoints respectively. Subsequently, no correction was necessary at this time.

(5) 
A correction factor may need to be employed in the future at Goodland if this study is extended to include additional seasons which significantly alter the means of parameters or increases the skew of their distributions. Also, the use of this procedure on data sets from other locations will likely generate a correction factor (Nouhan 1992, 1995).
Given a large sample size (> 30 years) and the subsequent conservative nature of the means, these steps should only need to be reaccomplished every 10 years (i.e., when NCDC publishes new decade means). Interim years can be calculated using original means and s+/s values.
Individual parameter values (including overall means and s values), final index values, and five year running mean index values (5RM) are given in Table 1. Table 2 gives straight normal curve (NC) values along with smoothed subindex values (ix) for 0.5 increment values of Z.
The qualitative summer rating threshold scheme is shown in Table 3a, including the distribution of all seasons within this scheme. Each rating was determined by successive thresholds of standard deviations (s) above and below the combined parameter mean (I). For instance, if I was within + 0.4s of the mean (0s, I=50), an individual summer would be considered "average". Physical implications of the qualitative terms are given in Table 3b.
Decadal means are listed in Table 4. Tables 5a, 5b, 5c, and 5d gives the 10 most oppressive and dismal summers by final index, the 10 coolest and warmest summers, the 10 wettest and driest growing seasons (May September), and the ten wettest and driest summers (JuneAugust). Lastly, Figure 1 shows the graphs of the final index vs. the five year running mean.
The five year running mean (5RM) data (centered on the current year) in Figure 1 indicates that summer severity at Goodland was in the "average" category during the 1920s reaching a low of 39.5 during 1928. Subsequently, the 5RM index rose dramatically through the "oppressive" category during the early 1930s and into the "very oppressive" category during the mid 1930s as indicated by an amazing record maximum value of 83.2 in the summer of 1936. After remaining in the "very oppressive" category through 1938, the 5RM decreased sharply through 1939 and the early 1940s reaching 38.0 (moderate category) in 1943. The 5RM then remained in the normal category through 1948 only to reach another minimum of 34.4 in 1949. Afterwards, the index suddenly spiked back into the "oppressive" category during the early 1950s as indicated by a maximum value of 77.1 in 1954. Subsequently, the 5RM has remained in the "average" or "moderate" categories reaching low values of 33.3 in 1973 and a record low value of 28.8 (nearly into the dismal category) in 1991.
Figure 1. Final index vs five year running mean.
Two periods of oppressive summer severity are highlighted by this study. The first period, extending from 1931 through 1939; often referred to as the "dust bowl" by the local populace, is one of the best examples of U.S. regional climate fluctuation this century. The second period extended from 1952 through 1956 and was shorter and not quite as severe. Outside of these two periods, with the exception of the 1963 and 1964 seasons, no consecutive oppressive summers could be documented from the Goodland record.
When anomalous midtropospheric ridging occurs through summer over the Rockies and high Plains, greater sunshine, lower relative humidities, and above normal surface temperatures result over the Goodland area (Namias 1982). This is especially true when below normal antecedent ground moisture is carried over from the previous spring (Namias 1982, Erikson 1983). Conversely, anomalous troughing over the Rockies and high plains is associated with cooler than normal temperatures and above normal rainfall at Goodland.
The occurrence of many oppressive severe summers in the 1930s and to a lesser extent in the 1950s may be linked with the reoccurrence of certain patterns of Pacific midlatitude and tropical sea surface temperature anomalies. Investigation in this area is beyond the scope of his study, but is worthy of further research (assuming reliable sea surface temperature data exists for these periods) by those who can employ more powerful statistical techniques.
Several summer/growing season parameters were normalized (approximately) and transformed into subindex values for each summer season for a 75year climate series at Goodland, Kansas. The subindices were then linearly combined to calculate a total index for each summer season based on a weighting scheme that considers the public and agricultural impact of each parameter. Lastly, final corrected indices were qualitatively rated from very dismal too extremely oppressive based on the number of standard deviations the average of combined parameters was from the mean.
Five year running mean data generated from the final indices showed that summer severity conservatively averaged "very oppressive" during the mid and late 1930s and "oppressive" during the mid 1950s. Outside these periods, the fiveyear running mean remained in the average and moderate categories.
I would like to thank Roy Freiburger, HMT, John Kwiatkowski, Goodland SOO, for the general review and Preston Leftwich, Central Region Science Officer, for the statistical review of the paper.
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