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A Critical Evaluation of Correlation Methods in Climatology and HydrologyThe sampling properties of three types of correlation coefficients are examined critically with reference to the practical problem of selecting a statistic optimally suited to correlation analyses in climatology and hydrology. Reasons are presented for concluding (1) that undue concern has been given the problem of nonnormality of underlying frequency distributions, and (ii) that application of significance tests and determinations of confidence limits for the productmoment coefficient, r, are quite adequately achieved through simple use of the standard error of r. It is suggested that the growing tendency in climatology and hydrology to employ unnecessarily elaborate methods stems jointly from characteristic emphasis upon theoretical refinements found 1n most statistics references and from neglect on the part of users of statistics to examine the numerical magnitudes of these refinements in relation to basic dataprecision and to desired precision of inference. The properties of a tetrachoric and a rank correlation coefficient are discussed, and it is concluded that in many geophysical applications, especially in cases of moderate sample sizes, the Spearman rankdifference coefficient should be regarded as the preferred correlation statistic. Em . pirical comparison of these three coefficients are presented for a sample of precipitation data taken from a region (Arizona) where nonnormality of precipitation frequency .distributions .. is known to be extreme. The rank difference coefficient is found to lie within one standard error of r for eleven of fourteen cases in this sample. The tetrachoric coefficient is found to be a much poorer estimate of r, yet in thirteen of fourteen cases it yields (on an approximation basis) the same inferences as does r with regard to existence of correlation.

Characteristics of Summer Radar Echoes in Arizona, 1956This report describes an investigation of the radar data obtained during the summer of 1956. Descriptions of the evaluation and analysis techniques, of the basic data and of the findings of this study are given in considerable detail. For the convenience of the more casual reader, all discussion and a summary of the findings are contained in sections VI and VII.

Distribution of Relative Humidity and Dew Point in the Southwestern United StatesThis report consists of three basic parts. In the first, average monthly values of relative humidity are presented for between one and four hours of the day at 126 weather observing stations in the southwestern United States, including all of Arizona, New Mexico, Colorado, Utah, and Nevada, and parts of California, Texas, Idaho, and Wyoming. The nature, accuracy, and import of these data are discussed briefly. It is shown that the month with lowest average humidities varies systematically from March in central Texas to August in northern Nevada, antedating the westward movement of the Atlantic high pressure system, with its moist unstable air. In the second section, the distribution of dew point over the Southwest is discussed. High values are found on the windward sides of most of the larger mountain ranges, near bodies of water, and in heavily irrigated farmland; low values are concentrated at higher elevations and in the dry desert regions bounded by the Sierra Nevada Mountains to the west and the Rocky Mountains to the east. Hourly data for Arizona indicate that the diurnal variation of dew point is small, with a tendency for the lowest values to occur in the midafternoon in dry regions and in the early morning in moist regions, i.e., those with a surface snow cover or with considerable crop irrigation. The final section outlines a method of estimating the mean relative humidity from the mean temperature. Ordinary linear regression techniques are used, with a correction added to account for the systematic geographical distribution of regression errors.

Doppler Radar Observations of a HailstormA severe hailstorm, occurring on 10 August 1966, passed over a zenith pointing, Xband, pulsedDoppler radar located on a mountain in southeastern Arizona. An analysis was made of measurements of radar reflectivity, mean Doppler velocity, variance of the Doppler spectrum and calculated updraft velocity. The vertical air motions and characteristics of the hydrometeors within the storm were highly variable over distances of a few hundred meters to a few kilometers. The storm consisted of a series of updraft cores containing a number of discrete volumes, 1 to 2 km in diameter, of rapidly rising air with smaller accompanying eddies. The updraft cores were separated by regions of weak updrafts or downdrafts. For the most part, the highest reflectivitives were outside the updraft cores. It is visualized that the hailstone growth was initiated within the updraft, not as a continuous process, but rather as pockets of hailstones within the fast rising distinct volumes. This process could account for the layers of clear and opaque ice within large stones by allowing them to pass through several rising volumes. It might also account for brief bursts of hail and short hailstreaks observed at the ground.

Doppler Radar Observations of a Mountain HailstormBy means of an Xband, vertically pointing Doppler radar observations were made of a thunderstorm on 20 August 1973 producing hail about 6 mm in diameter. The observations confirm earlier ones showing a highly variable internal structure. Updrafts are composed of high velocity "eddies" having diameters of about a few 100 m to a kilometer. It is speculated that such hailstorm features as the size and layering of ice type and the sporadic nature of hail showers are explained by the highly variable character of each updraft region and the sequence, at periods of 3 to 4 minutes, of updraft formation.

Observed Doppler Spectra of HailObservations of Doppler spectra from particles 610 m above the ground were obtained by means of a vertically pointing Xband radar during a period when large hail was falling at the ground. It was found that the variance of the Doppler spectrum was a fairly good indicator of maximum hailstone sizes. Calculations of iceparticle size spectra were made on the basis of assumptions of particle shape, composition and fall speed. The many assumptions needed to bring calculated icesphere spectra into approximate conformity with observations indicates the complexity of this procedure and the need for at least one more independent observation of the properties of the hailstones. Measurements of depolarization might yield an independent estimate of particle shape. It is concluded that the pronounced minima in the backscattering curves of large ice spheres should serve as an independent indicator of the speed of vertical air motions.

Wind Gradients and Variance of Doppler SpectraAn Xband pulsedDoppler radar having its beam fixed at an elevation angle of 3 deg, was used to measure radial velocity spectra in a light shower. Observations were made at intervals of 152 m between radar ranges of 7 and 18 km. It was found that the mean Doppler velocity, variance of the Doppler spectrum and radar reflectivity varied markedly over distances of the order of 100 m. The observed variance was below about 1 m2 sec2 in 80 percent of the observations, but in about 4 percent of the cases, it exceeded 3m2 sec2. An analysis of ~V/~r, the radial gradient of the mean Doppler velocity yielded a nearly Gaussian curve having a mean of 0.2 x 103 sec1 and a standard deviation of 5.9 x 103 sec1. The largest value observed was 3 X 10 2 sec1. The effects of the radial gradient of the radial wind apparently can explain about 25 percent of the observed variance of the Doppler spectrum.