(SR-52) Normalize Meteorological Variates

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An excerpt from A Method for Transforming Temperature Distributions to Normality, US-DoC, NOAA, National Weather Service (Western Region), Technical Memorandum (NWS WR-122), 1977-06, 22 pages

ABSTRACT. A method of transforming and fitting temperature distributions to the normal curve using the gamma distribution is presented. At the same time, the worth of the programmable calculator is once again demonstrated. The concept of "base temperature" is introduced in the presentation: a concept which permits the gamma distribution to be used with non-positive as well as positive values. An actual temperature distribution is transformed to normality using steps contained in a program designed to normalize meteorological variates. The resultant normal curve is then used to determine cumulative temperature probabilities.
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  Most meteorological variates are not normally distributed. This is true in the case of temperature, whose distributions are often skewed.
  It is desirable to transform and fit skewed distributions, such as temperature, to the normal curve. This is because many useful statistical tests such as analysis of variance, hypothesis testing about the mean, etc., are valid only for normal distributions …
  How can temperature distributions be transformed to normality? One way is to use the gamma distribution to fit and transform the temperature distribution (Panofsky and Brier 1958). Unfortunately, the transforming process is usually tedious, involves complicated equations, and hard-to-read tables.
  Enter the programmable calculator! These electronic marvels make the process of "normalizing" temperatures virtually painless, especially if the calculator is designed to accept magnetic program cards.
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The program to normalize meteorological distributions consists of 435 steps … It is designed to run on a Texas Instruments SR-52 calculator. The program flowchart is shown in Figure 2 …
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APPENDIX
 ACTUAL SR-52 PROGRAM USED TO NORMALIZE METEOROLOGICAL VARIATES
  program 1 cards {x, s, skew, â,  ß}
  program 2 cards {Γ & i-Γ} …

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