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The accuracies of algorithms used to compute quasi-geostrophic diagnostic parameters such as Hoskins' Q-vector and its divergence are evaluated. Analytically-determined height values are invoked at grid points representing three pressure surfaces, and finite difference approximations to third and lower order derivatives are compared with analytic values. Errors from these approximations are found to be virtually identical to those predicted by a mathematical analysis of the centered difference scheme. The magnitudes of finite difference errors are a function of wavelength, being acceptably small for waves sampled nine or more times per wavelength. Interpolation of grid point values from analytically determined observations at a typical array of rawinsonde stations produces diagnostic results that, while they contain many distortions owing mainly to data sparseness still contain significant portions of the signal, as determined by a two-dimensional spectral estimation technique using Fourier analysis. With reference to results from a previous case study, it is concluded that meaningful meteorological information was diagnosed at wavelengths of about 1250 km and larger. However, the results also suggest that it may not be appropriate to compute vertical motions per se for the smaller wavelengths because of interpolation-induced uncertainties in the diagnosed fields of geostrophic forcing. Appendices contain derivations of theoretical errors in second-order, centered difference estimations of first, second and third derivatives, and explain the procedures for obtaining spectral estimates in limited domains for two-dimensional fields.
Abstract
The accuracies of algorithms used to compute quasi-geostrophic diagnostic parameters such as Hoskins' Q-vector and its divergence are evaluated. Analytically-determined height values are invoked at grid points representing three pressure surfaces, and finite difference approximations to third and lower order derivatives are compared with analytic values. Errors from these approximations are found to be virtually identical to those predicted by a mathematical analysis of the centered difference scheme. The magnitudes of finite difference errors are a function of wavelength, being acceptably small for waves sampled nine or more times per wavelength. Interpolation of grid point values from analytically determined observations at a typical array of rawinsonde stations produces diagnostic results that, while they contain many distortions owing mainly to data sparseness still contain significant portions of the signal, as determined by a two-dimensional spectral estimation technique using Fourier analysis. With reference to results from a previous case study, it is concluded that meaningful meteorological information was diagnosed at wavelengths of about 1250 km and larger. However, the results also suggest that it may not be appropriate to compute vertical motions per se for the smaller wavelengths because of interpolation-induced uncertainties in the diagnosed fields of geostrophic forcing. Appendices contain derivations of theoretical errors in second-order, centered difference estimations of first, second and third derivatives, and explain the procedures for obtaining spectral estimates in limited domains for two-dimensional fields.
Abstract
Using reported height data at mandatory pressure levels, a version of Hoskins' Q-vector analysis is computed for two layers, producing contoured patterns of vertical motion and other diagnostics at two levels. This analysis, based on quasi-geostrophic theory, is applied to a severe convective storm episode (25–26 June 1982) in eastern Colorado that resulted in the development of a mesoscale convective complex. Convection developed in association with a polar air mass overlying the high plains and a weak short wave in the westerlies. LFM/MOS and quantitative precipitation guidance indicated eastern Wyoming and western Nebraska as the most threatened area, whereas the actual convection was most intense in Colorado, and the resulting convective complex propagated into Kansas, weakening as it did so. Another convective system developed in northeastern New Mexico, later propagated southeastward into the Texas panhandle and intensified. Q-vector diagnostics correctly indicated similar changes in the large-scale forcing at least 4 h before the observed changes in the convective systems occurred, whereas LFM-predicted vertical motions indicated the Kansas storms would dominate. When viewed in light of concurrent information such as satellite images and surface maps, the Q-vector diagnostics suggest how NMC and NSSFC guidance could have been modified in this case. Omega diagnostic patterns computed from 3-hourly soundings (A VE-SESAME V, 20 May 1979) indicate for the most part reasonable temporal continuity over a period of 6 to 12 h, thus lending some justification to their potential use as a forecasting aid. Further experience and development are necessary to determine the scheme's value under a variety of synoptic conditions. However, the fact that it currently runs on a microcomputer in only 13 min indicates that it may have potential as a real-time operational diagnostic aid for short range forecasting.
Abstract
Using reported height data at mandatory pressure levels, a version of Hoskins' Q-vector analysis is computed for two layers, producing contoured patterns of vertical motion and other diagnostics at two levels. This analysis, based on quasi-geostrophic theory, is applied to a severe convective storm episode (25–26 June 1982) in eastern Colorado that resulted in the development of a mesoscale convective complex. Convection developed in association with a polar air mass overlying the high plains and a weak short wave in the westerlies. LFM/MOS and quantitative precipitation guidance indicated eastern Wyoming and western Nebraska as the most threatened area, whereas the actual convection was most intense in Colorado, and the resulting convective complex propagated into Kansas, weakening as it did so. Another convective system developed in northeastern New Mexico, later propagated southeastward into the Texas panhandle and intensified. Q-vector diagnostics correctly indicated similar changes in the large-scale forcing at least 4 h before the observed changes in the convective systems occurred, whereas LFM-predicted vertical motions indicated the Kansas storms would dominate. When viewed in light of concurrent information such as satellite images and surface maps, the Q-vector diagnostics suggest how NMC and NSSFC guidance could have been modified in this case. Omega diagnostic patterns computed from 3-hourly soundings (A VE-SESAME V, 20 May 1979) indicate for the most part reasonable temporal continuity over a period of 6 to 12 h, thus lending some justification to their potential use as a forecasting aid. Further experience and development are necessary to determine the scheme's value under a variety of synoptic conditions. However, the fact that it currently runs on a microcomputer in only 13 min indicates that it may have potential as a real-time operational diagnostic aid for short range forecasting.
Abstract
Data collected at the National Severe Storms Laboratory reveal the mesogamma-scale (2.5–25 km) features of two severe thunderstorms that struck Oklahoma City within 1 h of each other. This paper discusses the surface, upper air and radar data obtained during the passage of the first tornadic storm (F). Companion papers deal with the second storm (G) which exhibited twin tornado cyclones (Parts II and III), and another discusses the environmental conditions which led to the demise of an earlier hailstorm (Part IV).
At the surface, the tornadic supercell storms were characterized by mesocyclonic sinks beneath the main updrafts with convergence values greater than 2 × 10−3 s−1 and vorticity about half as large. Lowest pressures preceded the mesocyclones by several kilometers and are believed to be dissociated from the wind centers because of the storms' rapid translational speeds (25–32 m s−1). Highest pressures were found near the rainy cores but not coincident. Middle-tropospheric air descended on the southwest (rear) flanks and produced accelerators in the cold air behind the gust fronts. Changes in characteristics of tornadoes associated with three tornado cyclones seem closely related to an evolving interaction between each updraft's mesocyclone and the downdraft-induced vorticity maxima.
Just ahead of Storm F, rawinsoundings indicated both dry adiabatic descent near the surface and ascent aloft. Boundary layer divergence associated with the former was caused by differential acceleration of surface layer air as the intense 1.5 hPa mesolow rapidly approached. Dry-adiabatic ascent aloft is believed to be driven by the quasi-steady updraft and is a feature similar to that found in several numerical simulation models. One balloon penetrated Storm F's anvil from 7.5 to 9.9 km some 35–40 km downwind of the main updraft and experienced 71 m s−1 winds in a 4 m s−1 “residual” updraft. A Richardson number of about 0.3 indicates such convective perturbations may feed from mean flow energy as opposed to residual buoyancy alone.
Abstract
Data collected at the National Severe Storms Laboratory reveal the mesogamma-scale (2.5–25 km) features of two severe thunderstorms that struck Oklahoma City within 1 h of each other. This paper discusses the surface, upper air and radar data obtained during the passage of the first tornadic storm (F). Companion papers deal with the second storm (G) which exhibited twin tornado cyclones (Parts II and III), and another discusses the environmental conditions which led to the demise of an earlier hailstorm (Part IV).
At the surface, the tornadic supercell storms were characterized by mesocyclonic sinks beneath the main updrafts with convergence values greater than 2 × 10−3 s−1 and vorticity about half as large. Lowest pressures preceded the mesocyclones by several kilometers and are believed to be dissociated from the wind centers because of the storms' rapid translational speeds (25–32 m s−1). Highest pressures were found near the rainy cores but not coincident. Middle-tropospheric air descended on the southwest (rear) flanks and produced accelerators in the cold air behind the gust fronts. Changes in characteristics of tornadoes associated with three tornado cyclones seem closely related to an evolving interaction between each updraft's mesocyclone and the downdraft-induced vorticity maxima.
Just ahead of Storm F, rawinsoundings indicated both dry adiabatic descent near the surface and ascent aloft. Boundary layer divergence associated with the former was caused by differential acceleration of surface layer air as the intense 1.5 hPa mesolow rapidly approached. Dry-adiabatic ascent aloft is believed to be driven by the quasi-steady updraft and is a feature similar to that found in several numerical simulation models. One balloon penetrated Storm F's anvil from 7.5 to 9.9 km some 35–40 km downwind of the main updraft and experienced 71 m s−1 winds in a 4 m s−1 “residual” updraft. A Richardson number of about 0.3 indicates such convective perturbations may feed from mean flow energy as opposed to residual buoyancy alone.
Abstract
National Severe Storms Laboratory radar film reveals twin hook echoes on the southeast flank of a tornadic thunderstorm (Storm G) that struck Oklahoma City on 30 April 1970. Only one mesocyclone is apparent in surface wind analyses (that associated with G's supercell updraft), but both tornado cyclones produced tornadoes. As the two hook echoes merged into one larger hook, damage diminished. Divergence (−2.6 × 10−3 s−1) shows an overall decrease in updraft strength during the merger. Maximum vorticity (1.3 × 10−3 s−1) overtook the developing hook echoes and increased slightly in response to an accelerating downdraft impulse from the storm's southwest flank. The multiple-tornado cyclones that developed along the accelerating gust front are believed due to vortex sheet rollup induced partly by the horizontal momentum of the downdraft air and partly by an unusual distribution of pressure-gradient forces behind the gust front. Merger of the two tornado cyclones is believed related to updraft propagation along convergent axes of maximum pressure gradients.
One tornado cyclone contained multiple tornadoes orbiting about its center. Analyzed maximum vorticity/convergence ratio, updraft radius estimated from radar signatures and inflow layer depth are used to approximate the ratio of updraft perimeter tangential velocity to mean updraft speed (swirl ratio) which in turn is used to estimate radius of turbulent vortex core (about which multiple vortices orbit). The relationship used to estimate core radii from swirl ratio is that published by Davies-Jones who used Ward's experimental results. For the observed tornado cyclone, independent radius estimates range from 0.68 to 0.84 km, and bracket the 0.7 km radius deduced from damage path characteristics. It is concluded that divergence and vorticity maxima analyzed from wind observations 11 km apart reflect the kinematic properties of the inflowing air that determine tornado character. Evolutions of convergence and vorticity centers for this and three other tornado cyclones suggest that a tornado cyclone's ability to produce vortices in the surface (friction) layer depends on ambient vorticity exceeding a threshold value 10−3 to 10−2 s−1 on a scale from 25 to 2.5 km.
Abstract
National Severe Storms Laboratory radar film reveals twin hook echoes on the southeast flank of a tornadic thunderstorm (Storm G) that struck Oklahoma City on 30 April 1970. Only one mesocyclone is apparent in surface wind analyses (that associated with G's supercell updraft), but both tornado cyclones produced tornadoes. As the two hook echoes merged into one larger hook, damage diminished. Divergence (−2.6 × 10−3 s−1) shows an overall decrease in updraft strength during the merger. Maximum vorticity (1.3 × 10−3 s−1) overtook the developing hook echoes and increased slightly in response to an accelerating downdraft impulse from the storm's southwest flank. The multiple-tornado cyclones that developed along the accelerating gust front are believed due to vortex sheet rollup induced partly by the horizontal momentum of the downdraft air and partly by an unusual distribution of pressure-gradient forces behind the gust front. Merger of the two tornado cyclones is believed related to updraft propagation along convergent axes of maximum pressure gradients.
One tornado cyclone contained multiple tornadoes orbiting about its center. Analyzed maximum vorticity/convergence ratio, updraft radius estimated from radar signatures and inflow layer depth are used to approximate the ratio of updraft perimeter tangential velocity to mean updraft speed (swirl ratio) which in turn is used to estimate radius of turbulent vortex core (about which multiple vortices orbit). The relationship used to estimate core radii from swirl ratio is that published by Davies-Jones who used Ward's experimental results. For the observed tornado cyclone, independent radius estimates range from 0.68 to 0.84 km, and bracket the 0.7 km radius deduced from damage path characteristics. It is concluded that divergence and vorticity maxima analyzed from wind observations 11 km apart reflect the kinematic properties of the inflowing air that determine tornado character. Evolutions of convergence and vorticity centers for this and three other tornado cyclones suggest that a tornado cyclone's ability to produce vortices in the surface (friction) layer depends on ambient vorticity exceeding a threshold value 10−3 to 10−2 s−1 on a scale from 25 to 2.5 km.
Abstract
Newspaper accounts and damage tracks surveyed by National Severe Storms Laboratory staff reveal characteristics of three tornadoes that struck the Oklahoma City area shortly after midnight on 30 April 1970. Few details emerge from surveying the first tornado (Storm F) except that its path crossed mostly open country and passed several kilometers northwest of Oklahoma City. Twin tornado cyclones (Mustang and Camelot), observed an hour later in Storm G, apparently produced multiple tornadoes that moved rapidly (80 m s−1) around the southern half of larger cyclonic circulations (hook echoes). Sporadic damage mostly at roof level suggests that the tornadoes often did not extend to the ground. Typically, debris was strewn in straight paths at an angle to the path of the tornado cyclone, suggesting tornado spin velocity less than speed of forward movement. Geometric relationship between a portion of one damage path and the path and forward speed of the tornado cyclone are the basis for estimating maximum winds at the ground to have been less than 160 m s−1. The nature of the structural damage suggests maximum winds were about 105 m s−1. It is concluded that the $6.3 million damage done by these storms was caused by relatively weak tornadoes (probably less than 25 m s−1 spin velocity) embedded within rapidly rotating tornado cyclones.
Abstract
Newspaper accounts and damage tracks surveyed by National Severe Storms Laboratory staff reveal characteristics of three tornadoes that struck the Oklahoma City area shortly after midnight on 30 April 1970. Few details emerge from surveying the first tornado (Storm F) except that its path crossed mostly open country and passed several kilometers northwest of Oklahoma City. Twin tornado cyclones (Mustang and Camelot), observed an hour later in Storm G, apparently produced multiple tornadoes that moved rapidly (80 m s−1) around the southern half of larger cyclonic circulations (hook echoes). Sporadic damage mostly at roof level suggests that the tornadoes often did not extend to the ground. Typically, debris was strewn in straight paths at an angle to the path of the tornado cyclone, suggesting tornado spin velocity less than speed of forward movement. Geometric relationship between a portion of one damage path and the path and forward speed of the tornado cyclone are the basis for estimating maximum winds at the ground to have been less than 160 m s−1. The nature of the structural damage suggests maximum winds were about 105 m s−1. It is concluded that the $6.3 million damage done by these storms was caused by relatively weak tornadoes (probably less than 25 m s−1 spin velocity) embedded within rapidly rotating tornado cyclones.
Abstract
This paper summarizes the development of a convergent weighted-averaging interpolation scheme which can be used to obtain any desired amount of detail in the analysis of a set of randomly spaced data. The scheme is based on the supposition that the two-dimensional distribution of an atmospheric variable can be represented by the summation of an infinite number of independent waves, i.e., a Fourier integral representation. The practical limitations of the scheme are that the data distribution be reasonably uniform and that the data be accurate. However, the effect of inaccuracies can be controlled by stopping the convergence scheme before the data errors are greatly amplified. The scheme has been tested in the analysis of 500-mb height data over the United States producing a result with details comparable to those obtainable by careful manual analysis. A test analysis of sea level pressure based on the data obtained at only the upper air network stations produced results with essentially the same features as the analysis produced at the National Meteorological Center. Further tests based on a regional sampling of stations reporting airways data demonstrate the applicability of the scheme to mesoscale wavelengths.
Abstract
This paper summarizes the development of a convergent weighted-averaging interpolation scheme which can be used to obtain any desired amount of detail in the analysis of a set of randomly spaced data. The scheme is based on the supposition that the two-dimensional distribution of an atmospheric variable can be represented by the summation of an infinite number of independent waves, i.e., a Fourier integral representation. The practical limitations of the scheme are that the data distribution be reasonably uniform and that the data be accurate. However, the effect of inaccuracies can be controlled by stopping the convergence scheme before the data errors are greatly amplified. The scheme has been tested in the analysis of 500-mb height data over the United States producing a result with details comparable to those obtainable by careful manual analysis. A test analysis of sea level pressure based on the data obtained at only the upper air network stations produced results with essentially the same features as the analysis produced at the National Meteorological Center. Further tests based on a regional sampling of stations reporting airways data demonstrate the applicability of the scheme to mesoscale wavelengths.
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Abstract
On 24 May 1968 a rawinsonde observation was obtained in the updraft of a growing cell on the south flank of a thunderstorm which was turning to the right of winds and later produced large hail and funnel clouds. Moist adiabatic ascent was indicated with maximum excess temperature of 10C at 500 mb. Winds above 4.5 km deviated as much as 64° from environmental winds measured 15 n mi upwind. Diversion of mid-tropospheric flow is attributed to horizontal accelerators produced mainly by excess hydrostatic pressure within the updraft. At 5 km, a 23 m sec−1 updraft deduced from a hydrostatically-calculated ascent rate is one-third less than that obtained from an entraining jet model and two-thirds less than the parcel theory estimate. Excess hydrostatic pressure is considered as a contributing factor in reducing bouyancy. Although ambient vorticity through an attitude of 7 km was mostly anticyclonic, cyclonic rotation in the southwest portion of the storm was observed by radar and corroborated by visual observation of the cloud base. Evaluation of the vorticity equation for parcels entering the updraft base shows one component of the tilting term was generating cyclonic vorticity at a rate sufficient to maintain a parent tornadic cyclone. Obstacle flow and cyclonic rotation suggest existence of a right-deflecting force on the updraft, but the data are insufficient for quantitative evaluation of this effect. Sounding processing techniques are briefly described in an appendix.
Abstract
On 24 May 1968 a rawinsonde observation was obtained in the updraft of a growing cell on the south flank of a thunderstorm which was turning to the right of winds and later produced large hail and funnel clouds. Moist adiabatic ascent was indicated with maximum excess temperature of 10C at 500 mb. Winds above 4.5 km deviated as much as 64° from environmental winds measured 15 n mi upwind. Diversion of mid-tropospheric flow is attributed to horizontal accelerators produced mainly by excess hydrostatic pressure within the updraft. At 5 km, a 23 m sec−1 updraft deduced from a hydrostatically-calculated ascent rate is one-third less than that obtained from an entraining jet model and two-thirds less than the parcel theory estimate. Excess hydrostatic pressure is considered as a contributing factor in reducing bouyancy. Although ambient vorticity through an attitude of 7 km was mostly anticyclonic, cyclonic rotation in the southwest portion of the storm was observed by radar and corroborated by visual observation of the cloud base. Evaluation of the vorticity equation for parcels entering the updraft base shows one component of the tilting term was generating cyclonic vorticity at a rate sufficient to maintain a parent tornadic cyclone. Obstacle flow and cyclonic rotation suggest existence of a right-deflecting force on the updraft, but the data are insufficient for quantitative evaluation of this effect. Sounding processing techniques are briefly described in an appendix.
