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H. C. S. THOM

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H. C. S. THOM

Abstract

It is shown that the freeze distribution is a mixture of the distribution of freeze-date and the simple dichotomous distribution of freeze and freezeless years. This is applied both nonparametrically and assuming a normal distribution of freeze date to three stations at three different thresholds to obtain the probabilities of freeze before or after any date. The distribution of the freeze-free period is developed and application made to one of the stations to obtain probabilities of the freeze-free period being less than a given time interval. The expressions for the mean freeze-date and freeze-free period are also developed and estimates made for the stations treated.

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H. C. S. THOM

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The frequency distributions of tornado path width and length are developed using data series from Iowa and Kansas. From these, the distribution of path area is derived. Direction of path and annual frequency are discussed. It is found that all but about 1 percent of Iowa tornadoes had path directions toward the northeast and southeast quadrants. The annual frequency for a group of Iowa counties is found to have a negative binomial distribution indicating that the climatological series is formed from a Polya stochastic process. This resembles the situation for other types of storms where the events tend to cluster. A new map of annual frequency for the United States is presented for the period 1953–62, during which it is believed tornado observation was fairly stable. The expected value of tornado area is derived from the area distribution. From this and the annual frequency, the probability of a tornado striking a point is found.

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H. C. S. THOM

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Following previous work, climatological statistics and computational methods are presented for obtaining the quantiles of first one-inch 24-hour snowfall. These are employed in computing the .05, .10, .30, .90 quantiles for 164 United States and Alaskan first-order Weather Bureau stations.

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H. C. S. Thom

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Heating engineers sometimes have need for normal degree days for bases other than 65° F. Further analysis of the relationship between mean temperature and mean degree days for base 65° F. showed that the form of this relationship is independent of the base. This makes it possible to vary the base to any value and hence to compute degree-day normals for any base from normal temperature. Results are presented for selected stations for bases ranging from 35° to 70° F.

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H. C. S. THOM

Abstract

The probability function of degree days below the base 65° F. is derived from the temperature probability function. Standard statistical analysis is applied to this function to obtain the relationship between mean degree days and mean temperature. This relationship is modified for use with available data and applied in the conversion of a monthly normal temperature for Detroit to the corresponding degree day normal.

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H. C. S. THOM

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For later development of design snow loads, the water equivalent of snow on the ground appears to be the best meteorological variable for determining design values. The appropriate climatological series for this is the winter season maximum accumulated water equivalent series. Among many distributions investigated, the lognormal distribution provided the best fit to these climatological series. Distributions fitted to 140 stations provided data for preparing contour maps of the parameter estimates. In southern areas of the United States, where snow does not occur every year, the climatological series is a mixture of zeros and water equivalent, maxima. This requires the fitting of mixed distributions in these areas. A contour map is provided of the mixture parameter estimate. Methods for determining confidence intervals for quantiles from both distributions are developed.

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H. C. S. THOM

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Approximate convolution methods are developed for unmixed and mixed precipitation distributions. Results of applying these to monthly distributions to obtain the distributions of sums of various numbers of months are presented. These are compared to distributions fitted to the sums by employing the confidence intervals for the fitted distributions.

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H. C. S. THOM

Abstract

The general properties of the gamma distribution, which has several applications in meteorology, are discussed. A short review of the general properties of good statistical estimators is given. This is applied to the gamma distribution to show that the maximum likelihood estimators are jointly sufficient. A new, simple approximation of the likelihood solutions is given, and the efficiency of the fitting procedure is computed.

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H. C. S. THOM

Abstract

Equations are developed for obtaining mean monthly degree days above any base from mean monthly temperature and standard deviation of monthly average temperature. By the use of data for all months for twelve widely scattered stations and four bases it is shown that the truncation coefficient for degree days below any base with proper modification of the argument also applies for degree days above any base. This is also proved analytically, which leads to some further aspects of the universality of the truncation coefficient. Two formulas for the coefficient are also developed.

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