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Ralph J. Donaldson Jr.

Abstract

The storm which spawned the devastating Union City, Okla., tornado of 24 May 1973 was observed by Doppler Plan Shear Indicator (PSI). The PSI, an analog device for display of velocity gradients, had been temporarily mated to the 10 cm Doppler radar operated by the National Severe Storms Laboratory. The first PSI picture showed intense shear at 8–9 km altitude, 45 min before the earliest tornado damage. About 40 min before the tornado struck, a vortex pattern with cyclonic rotation was recognizable at 5–8 km, but the wind field in the storm below 4 km was quite uniform. The base of the flow disturbance as well as the vortex descended and intensified during this early period prior to tornado touchdown. Vortex diameter was as large as 5 km when initially detected but decreased to less than 1 km at the surface when the tornado was on the ground. Maximum tangential speeds of the vortex were generally 10–25 m s−1, with the higher values measured just before and during the period of surface damage. Shears as large as 0.1 s−1 were measured. The vortex was tilted toward the left of the storm direction of travel, at an angle of about 30° from vertical. While the tornado was in progress the vortex was a highly organized, intense singularity in an otherwise smooth wind field near the ground; but in the upper third of the storm, at heights of 10–14 km, the disturbance was greatly enlarged, disorganized and unstable.

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Ralph J. Donaldson Jr.

Abstract

A Doppler radar technique is proposed for remote estimation of hurricane structure by sampling the kinematic properties of the hurricane wind field in a relatively small circular area outside the radius of maximum winds. This technique uses Fourier analysis of the pattern of Doppler velocities measured in a horizontal circle surrounding the radar, following guidelines developed by Browning and Wexler. Two indices, potential-vortex fit (PVF) and radial confluence, are developed as measures of the degree of conformity of the wind field sampled by radar to an idealized Rankine axisymmetric cyclone circulation. The PVF index reveals the extent to which the sampled wind held fits a potential-vortex flow regime, wherein both curvature and speed of the tangential wind component are inversely proportional to distance from a circulation center. The confluence of the radial wind component provides an independent estimate of the curvature of the tangential component.

These two indices were measured in Hurricane Gloria (1985) during a period of more than 3 h following its landfall. Values of PVF indicated a weakened circulation during the first half of this period, followed in the latter half by a progressive and rapid decay of the circulation, consistent with other observations. The magnitudes of the radial confluence index, on the other hand, evidently were adversely affected by significant contamination by asymmetries in the hurricane circulation throughout most of the observational period. However, trends in both indices provided an early indication of the deterioration of Hurricane Gloria. Accordingly, it appears worthwhile to seek further evidence of the potential value of this technique as an aid in monitoring hurricane severity.

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Ralph J. Donaldson Jr.

Abstract

Measurement errors caused by antenna main-lobe and side-lobe distortion are computed for seven model thunderstorm reflectivity distributions observed over various ranges by model antenna beams with half-power widths of one and two degrees. Errors in echo top height measured by the two-degree beam, somewhat larger than the one-degree beam errors, rarely exceed ±5000 ft at ranges up to 25 n mi. In very intense storms, however, and at ranges of 50 mi or more, the measured echo top may be displayed at least 20,000 ft above the actual storm top. In extreme situations the displayed echo top may be double the true storm top. Measured maximum reflectivity may decrease with range by a much as 8 db at 50 mi. However, the reflectivity measured at 30,000 ft, roughly midway between maximum reflectivity and storm top, is largely independent of range out to 150 mi. The detectability of a hole surrounded by intense precipitation may be dependent on reduced radar sensitivity. A fairly accurate estimate of hole size is not possible unless its edges are sharp and its actual width exceeds twice the half-power antenna beam width.

Several methods are considered for correcting antenna beam distortion of echo tops. None of them are versatile enough to be used with confidence in all cases. The most promising one for sharp-edged reflectivity structures is a nomogram technique suggested by Probert-Jones, wherein side-lobe errors are eliminated by suitable reduction in radar sensitivity.

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Ralph J. Donaldson Jr.

Abstract

The measured reflectivity of a distributed target is given by the integration of reflectivity over the radar antenna radiation pattern. Assuming a Gaussian form for the main antenna lobe and fairly simple exponential and Gaussian distributions of true reflectivity, the measured reflectivity is computed as a function of sharpness of reflectivity relative to antenna beam size. The resolving power of the radar antenna for measurement of a single reflectivity feature to a specified accuracy, or for discrimination between two identical features, is also a function of relative sharpness of the target reflectivity field. Relative sharpness is defined by the product of reflectivity gradient, range, and half-power beam radius (exponential case) or of derivative of reflectivity gradient, range squared, and half-power beam radius squared (Gaussian case). Relative sharpness is also a determining factor of the size of the area in which side-lobe errors may be considered negligible. A method is developed for recovery of the gross structure of true reflectivity from measurements. The intersection of the true reflectivity distribution, so derived, with a standard equivalent reflectivity factor of 0.1 mm6 m−3 is suggested as an objective estimate of cloud tops measured by radar.

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Ralph J. Donaldson Jr.

Abstract

The frequency of hail occurrence in New England thunderstorms during 1956 and 1957 was directly related to the maximum heights and maximum reflectivity factors of the thunderstorm echoes measured by CPS-9 radar. Hail frequencies in excess of 33 per cent occurred in storms with echo heights above 46,000 to 49,000 ft, with little dependence on reflectivity. Higher hail frequencies were found with even greater echo heights and were also strongly related to large values of radar reflectivity factor.

The over-all frequency of hail reported in all thunderstorms was 20.6 per cent, considerably larger than the value of somewhat less than five per cent computed for the region by Shands. The discrepancy is believed to reflect a difference in definition of thunderstorm area, and an observer bias in favor of the larger, hail-producing storms which was evident in the present study.

Storms that produced large tornadoes and destructive winds and hail were characterized by significantly greater than average echo heights but not by unusually high echo reflectivities at low altitude. Five storms that resulted in large tornadoes had maximum echo heights during their lifetime of 47,000 ft to 57,000 ft. In two tornado-bearing storms, limited evidence was obtained for extremely large values of radar reflectivity factor at high altitudes with a pronounced maximum around 20,000 ft.

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Ralph J. Donaldson Jr.

Abstract

Vertical profiles of radar reflectivity have been measured in the cores of New England thunderstorms and correlated with surface weather conditions reported by an extensive network of cooperating observers. Although the reflectivity differences between hailstorms and rain-thunderstorms are slight at low altitudes, they are significant in the middle and upper portions of the storms. Tornado-producing thunderstorms reveal even more striking anomalies in high-altitude reflectivity. The maximum reflectivity of the profile, the height of the maximum, and the reflectivity ratio (maximum aloft to surface) all increase with the severity of thunderstorm weather. The experience of 233 profiles measured during two years is the basis for an estimate of hail and tornado probability as a function of reflectivity at an altitude of 30,000 ft and the profile shape parameters. These indices provided tornado warning times of one to nearly three hours in two multi-tornado squall lines.

The extremely high values of reflectivity observed aloft in a few thunderstorms are interpreted as indications of large hail, having diameters in excess of the radar wavelength of 3.2 cm and in concentrations of 10 g per m3 or more, occurring in the very small core region and in a limited height range about 20,000 ft. The persistence of large reflectivity ratios in unusually severe thunderstorms provides evidence for the storage of hailstones near the altitude of updraft maximum in a convection cell, followed by a gradual release of particles as a new cell becomes active and begins to grow and store a new supply of hailstones.

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Ralph J. Donaldson Jr.

Abstract

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Ralph J. Donaldson Jr.

Abstract

The depth to which a liquid-water cloud may be detected has been computed as a function of liquid-water content for radars at wavelengths of 0.86, 1.25 and 3.2 cm, with use of Atlas' relationship for Z versus liquid-water content, and with account being taken of attenuation. An estimation is made of the effect of attenuation on calibration error; the resultant error in liquid-water content places a limit on the depth to which the liquid-water concentration in a cloud may be measured to a given accuracy by radar means. For the two shorter wavelengths and for relatively high liquid-water concentrations, error considerations, and not detectability, limit the measurement. The 0.86-cm radar is superior to the other two in cloud detectability for nearly all commonly encountered values of liquid-water content. For cases where an attenuation correction is desirable, a relatively simple method of making this correction is developed.

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Ralph J. Donaldson Jr.

Abstract

A survey of thunderstorms observed during 1956 by CPS-9 radar from Blue Hill (Milton, Massachusetts) revealed a high frequency of hail occurrence (as reported by a regional network of cooperative observers) in storms in which the radar echo attained high altitudes and large values of radar reflectivity factor. Hail frequencies are related to these criteria, and to the single criterion of maximum echo height, since a correlation was noted between echo height and radar reflectivity factor in all convective storms, Most of the observed damaging windstorms and tornadoes were associated with parent echoes extending above 40,000 ft and the most severe tornadoes occurred along or above the curve of 50 per cent hail frequency and had maximum echo heights above 47,000 ft.

In one tornado situation, the echo heights of several neighboring storms increased and decreased nearly in phase with one another, and the wind damage and hail at the ground occurred during the periods of rapid increase of echo height. This suggests the possibility of control of a group of storms by a meso-scale system. The median of a number of observations of the variation with height of radar reflectivity factor shows a steady decrease with height in a thunderstorm. The decrease is slow up to about 20,000 ft but more rapid at higher altitudes. Just before the appearance of the tornado, however, the radar reflectivity factor in the tornado storm increased substantially with height up to 20,000 ft.

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Ralph J. Donaldson Jr.

Abstract

A scanning Doppler radar has capability for measurement of the tangential shear of radial velocity or gradient of the radial component of velocity in a direction normal to the radial vector. Tangential shear of sufficient magnitude in a horizontal direction reveals one term of the expression for vorticity in a horizontal plane. A vortex is reasonably well identified by Doppler radar if the shear is sufficiently steady during the time required for half a revolution of a vortex, and is further confirmed by extension of the shear pattern throughout a depth greater than its diameter, and by invariance of the character of the shear with respect to a change in viewing angle. A vortex in solid rotation has a characteristically uniform signature on a Doppler velocity display which may, however, be smoothed down according to the resolution limitations of the antenna beam. Sharp velocity peaks are rounded down to roughly half the magnitude of the velocity interval encompassed within the half-power antenna beamwidth.

An illustration of a persistent vortex at altitudes of 1–4 km in a severe thunderstorm revealed a solidly rotating core averaging 600 m in radius with vorticities as high as 0.06 sec−1, surrounded by a much larger area of considerably smaller vorticity. During a 30-min period, an echo hole was found at a height of 1.5–2 km in the center of the vortex, with a structure quite similar in shape to the echo-free vault which has occurred on a larger scale in several tornadic storms in the Great Plains.

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