Variational Analysis of Temperature and Moisture Advection in a Severe Storm Environment

Transcription

1 August 1977 M. J. McFarland and Y. K. Sasaki 421 Variational Analysis of Temperature and Moisture Advection in a Severe Storm Environment By Marshall J. McFarland National Weather Service, Environmental Studies Service Center, College Station, Texas and Yoshi K. Sasaki Department of Meteorology, University of Oklahoma, Norman, Oklahoma (Manuscript received 25 December 1976, in revised form 18 May 1977) Abstract Horizontal wind components, potential temperature, and mixing ratio fields associated with a severe storm environment in the south central U.S, were objectively analyzed from synoptic upper air observations with a non-homogeneous, anisotropic weighting function. The grid dimensions of the area of study were near 125 kilometers horizontally and 50 millibars vertically at 18 pressure levels. Each data field was filtered and the vertical motion field was then analyzed using variational methods to insure that the three-component wind field satisfied mass continuity. The local time change of potential temperature and mixing ratio was determined in order to correlate the temperature and moisture advection patterns with severe storm development. A three-dimensional advection equation was used to produce advective forecasts of the potential temperature and mixing ratio fields. The case study discussed in this article is 26 May 1973, when a tornado producing squall line moved through eastern Oklahoma. The synoptic situation which preceded squall line development was cyclogenesis and frontogenesis in the lee-of-the-mountain trough, which produced a well-defined surface dry line (or dew point front) and a pronounced mid-level dry air intrusion. Results indicated that the mid-level dry air intrusion was also characterized by warm air, with a lapse rate approaching the dry adiabatic. The advection of this warm air produced a well-defined upward motion pattern. A corresponding downward motion pattern apparently comprising a deep vertical circulation in the warm air sector of the low pressure system was detected. The squall line that subsequently developed was aligned closely with the axes of the maximum dry and warm advection above the 850 mb surface. Below the 850 mb surface, the squall line coincided with the axis of maximum moisture advection. 1. Introduction Cyclogenesis and frontogenesis in the lee-ofthe-mountains pressure trough provide a favored synoptic situation for severe thunderstorm development in the Great Plains during the spring months. The pre-existing lee trough has a pronounced warm-core structure through the lowest several kilometers of the atmosphere. As a consequence of the subsidence which produces the warming, this thermal ridge is also characterized by a very low moisture content. As the system develops dynamically in response to the approach of mid-level trough, the warm, dry air is advected eastward and northward in advance of the developing low pressure center. The surface location of the sharp boundary of this warm, dry air mass with the cooler, moister maritime air mass is known variously as the dew point front, Marfa front, or the dry line. The advection of the warm, dry air mass over the denser maritime air mass constitutes the dry intrusion. Both the dew point front and the dry intrusion are well-known as indicators and locators for severe thunderstorm activity (Miller, 1972; Tegtmeier, 1974). The temperature and moisture advection patterns of the dry intrusion were analyzed with the variational analysis method (Sasaki, 1970a, 1970b; McFarland, 1975) to relate the mesoscale advection patterns to the severe thunderstorm environment. Although the dry line and dry intrusion are present with all occurrences of cyclogenesis and frontogenesis in the lee trough, the associated advection patterns must exist on a sufficiently

2 422 Journal of the Meteorological Society of Japan Vol. 55, No. 4 large scale to be resolvable in an analysis based on data acquired from the synoptic upper air reporting stations. The analysis results presented in this paper were obtained from a case study, 26 May 1973, when a tornadic squall line developed in Oklahoma in conjunction with a clearly delineated dry air intrusion. For the data base of the 26/1200Z May 1973 synoptic upper air reports from 25 reporting stations in the south-central United States, an objective analysis was performed to assign the meteorological variables to 15 * 14 * 18 grid points. The assigned fields were then simultaneously filtered in the three spatial dimensions using a variational filter with filter weights determined by the minimum resolvable wavelengths, both horizontally and vertically. The vertical motion, omega, was calculated using the kinematic method in variational form to insure that mass continuity was satisfied. The advection pattern changes using the adjusted omega field were determined from a four dimensional variational formalism with the conservation equations for potential temperature and mixing ratio as weak constraints. The results indicated that the mid-level dry variables to grid points of a 15 * 14 horizontal grid with approximate 125 km grid spacing at each pressure level. The weighting function used was a anisotropic exponential function, W, modified from Barnes (1973), where V is the absolute value of wind speed at observation point, V is a scale maximum wind, r2 is the distance squared from the observation point to the grid point, k is the scale response parameter, * is the anisotropy parameter, and is the angle defined by the wind direction * and the direction from the grid point to the observation point. A small value of the scale response parameter k allows short wavelengths in the analyzed data field; a larger value of k suppresses these short wavelengths. The larger anisotropy term allows a greater weight to upwind/downwind observations than for crosswind observations (see also Endlich and Mancuso, 1968 for anisotropic weighting). After the objective analysis, which was accomplished with one pass for each pressure level, the data fields were each smoothed using a variational filter (Wagner, 1971), air intrusion was also characterized by warm air, with a lapse rate approaching the dry adiabatic. The advection of this warm air produced a welldefined upward motion pattern. A corresponding downward motion pattern apparently comprising (2) a deep vertical circulation in the warm air sector where J is the adjustment functional; *, *h, and of the low pressure system was detected. The are the weak constraint weights applied to *p the axis of the squall line that subsequently developed observational terms and to the first derivative was aligned closely with the axes of the maximum filter terms horizontally and vertically; u is the dry and warm advection above the 850 mb surface. Below the 850 mb surface, the squall line unfiltered interpolated grid point value and u is the filtered value. The Euler-Lagrange equation axis coincided with the axis of maximum moisture derived from (2) is, advection. The thunderstorm development apparently represented an indirect circulation, with moist, cooler air rising convectively through dry, warmer air; a negative buoyancy was indicated (3) at cloud base levels. The presence of the dry, which was solved for u by relaxation techniques warm air strongly suggests that detrainment cooling will produce a downward momentum transport sponse of variational filters is known, the weak in finite difference form. Since the filtering re- and enhance the development of severe activity. constraint weights were specified in the horizontal and vertical dimensions, based on original observational data density, to achieve a 2. Data objective analysis and filtering simultaneous The 26/1200Z May 1973 upper air observation three dimensional smoothing. from the synoptic upper air network were used 3. Vertical motion computation for inputs of horizontal wind components, potential temperature, and mixing ratio at each 50 mb The vertical motion field was derived from the increment from 950 mb to 100 mb. An objective horizontal wind components using the kinematic analysis was accomplished to assign values of the method expressed in variational form to insure (1)

3 August 1977 M. J. McFarland and Y. K. Sasaki 423 that mass continuity is satisfied over the grid (O'Brien, 1970; McGinley, 1973). The variational formalism used was (4) where J is the adjustment functional; * is the weak constraint weight applied to the filtered horizontal wind components, and * is the Lagrange multiplier applied as a strong constraint to mass continuity. The formalism did not include vertical motion induced by wind flow over sloping terrain; the presence of a very strong inversion (apparent in Figs. 4 and 5), indicated that the terrain would have negligible effect on the vertical motion fields above the inversion surface. The terrain induced vertical motions assume significance when the inversion breaks, but while the inversion is present the surface layers are effectively decoupled from processes above the inversion. The resulting Euler-Lagrange equations were (5a) (5b) (5c) (5d) Eqs. (5a) and (5b) show that the relationship between the "true" fields of u and * and the observed u and * fields is a function of the Lagrange multiplier, *, which is independent of pressure from (5c). * was obtained by the elimination of u and * from (5d) to form (6) The unknown vertical motion, *, was eliminated through integration over pressure, with specified boundary conditions of zero vertical motion at 100 mb (assumed top of atmosphere) and at 950 mb, although a terrain-induced vertical motion could be calculated and used on the lower boundary condition. In finite difference form, * was determined through relaxation techniques and was used to adjust the values of u and * to the "true" values, which provided the vertical motion Fig. 1 Horizontal grid for the numerical analysis. The grid spacing is approximately 125km horizontally. The grid extends 18 pressure levels vertically at 50 mb intervals. Section A-A' is the location of the cross section for display of numerical results. field. In finite difference form, the Lagrange multiplier was determined through relaxation techniques with a convergent iterative process to account for the inexactness of finite differencing. The correction to a wind component at a grid point is based analytically on the wind components at the same grid, but in finite differencing form, the correction is based on the wind components at neighboring grid points. The variations are small, but important when strong constraint formalisms are used. The gradients of the Lagrange multiplier were used to adjust the horizontal wind components to values that satisfied mass continuity. The vertical motion field was obtained through integration (trapezoidal rule) of the horizontal divergence at each pressure level. The boundary conditions for the vertical motion were set at zero at 100 mb and 950 mb, the top and bottom levels in the analysis. The final 11 * 10 horizontal grid for the advection analysis is shown in Fig. 1, which also contains the location of the vertical cross section used in the study. 4. Synoptic situation As indicated in Fig. 2, the synoptic situation for the southern Great Plains at 26/1200Z May 1973 was dominated by cyclogenesis in the lee trough. The thermal ridge of the warm-core low

4 424 Journal of the Meteorological Society of Japan Vol. 55, No. 4 has flattened with the northeastward advection of the warm air. The thermal ridge extended through the 700 mb surface coincident with the pronounced weakening with height of the low height Fig. 2 NMC Analysis, 850 mb, 26/1200Z May Fig. 5 Temperature profiles for Abilene, Texas (ABI), Greater Southwest Airport, TX (GSW), and Tinker AFB, OK (TIK) 26/ 1200Z May The horizontal and vertical uniformity of the dry intrusion is evident. Fig. 3 NMC Analysis, 700 mb, 26/1200Z May center, as shown in Fig. 3. The very rapid warm air advection through central Oklahoma was indicated by the Tinker AFB, OK (TIK) temperature and dew point profile changes, shown in Fig. 4. At 1200Z the dry line location was in western Texas; the surface dew points in the dry air were as low as -5C. The dry intrusion was characterized by its uniformity over a several hundred kilometer distance and by a lapse rate approaching the dry adiabatic, as indicated in Fig. 5. A low level jet developed in conjunction with the dry intrusion; 45 knot winds were reported at the inversion base at Tinker AFB, OK at 26/1200Z. The reported wind profiles to 500 mb are listed in Table 1. Fig. 4 Tinker AFB, OK (TIK) temperature and dew point profiles, 26/0000Z and 26/1200Z May The coordinates are Skew T-log p. The dry intrusion is pronounced at 26/ 1200Z as a result of very rapid advective processes.

5 August 1977 M. J. McFarland and Y. K. Sasaki Temperature advection and vertical motion It is well known that the large scale upward vertical motion is produced by differential Fig. 6a 800 mb omega (10-3 mb sec-1) at 26/1200Z May An axis of upward vertical motion extended through central Kansas and eastern Oklahoma. vorticity advection and warm air advection; normally the vorticity term predominates. However, Pfeffer (1962) suggested that thermal advection in the lower troposphere is the dominant term in determining vertical motion fields for smaller scale (meso-scale) phenomena, and Morris (1972) related the vertical motion field of a warmcore trough to the thermal advection patterns. Accordingly, one would expect to find a strong upward motion pattern associated with the maximum warm air advection. For the case study, the axis of upward motion coincided closely with the axis of maximum warm air advection, as shown in Fig. 6. This common axis was also the axis of the squall line that subsequently developed. In cross-section along A-A' (Fig. 1), the lower tropospheric thermally-produced upward vertical motion pattern is evident. As shown in Fig. 7, this pattern and a corresponding downward vertical motion pattern apparently comprising a deep mesoscale circulation were pronounced. The existency of this vertical circulation would tend to contribute to the near dryadiabatic lapse rates in the dry intrusion, shown in Fig. 4. Fig. 6b 850 mb potential temperature advection at 26/1200Z May The warm air advection axis coincided with the upward vertical motion axis of Fig. 6a. The temperature advection was calculated from at t=26/1200z May 1973 where the wind components were from the mass continuity satisfied motion field. The horizontal advection terms were generally dominant. Fig. 7 Cross section of vertical motion, *(10-3 mb sec-1) 26/1200Z May 1973.

6 426 Journal of the Meteorological Society of Japan Vol. 55, No. 4 It should be noted that the upward vertical motion axis occurred several hours before the squall line developed; consequently the vertical motion patterns are not associated with convective circulations. A subsequent investigation by Liles (1976) of a central Oklahoma tornadic squall line of 8 June 1974 using similar numerical techniques also showed the existence of a welldeveloped vertical motion axis that coincided with the orientation of the squall line. Even though Liles used a 09/00Z June 1974 data base when the tornadic storms were occurring, he concluded that the vertical motion pattern was thermally induced. The thunderstorms were occurring along a small fraction of the total length of the vertical motion axis and the lower tropospheric thermal advection patterns supported the vertical motions. 6. Advective forecasts The potential temperature and mixing ratio fields were advectively forecast for periods up to eight hours using the existing mass continuity satisfied wind field in an effort to determine the relative advective patterns associated with the storm environment. The fields of * (potential temperature) and * (mixing ratio) at all time steps were determined with linear advection in the form This equation, a linear elliptic type partial differential equation with variable coefficients, was the primary analysis equation for the advection of temperature; a similar equation was developed to forecast the mixing ratio fields. The time and space grids are the same as the case of (7). The coefficients *l/*, *1 /*, *2/* and *3/* are chosen on the basis of the scale response of the filter (Wagner, 1971). The short term advective forecasts of potential temperature and mixing ratio indicated continued warm and dry air advection associated with the dry intrusion and continued low level moisture advection beneath the dry intrusion. These results, indicated physically by examination of Fig. 4, are of primary significance in relating the storm scale processes to the environmental advection fields. 7. Severe thunderstorm development through the warm, dry intrusion The initial condition at 26/1200Z May 1973 and the advective forecasts from the variational model indicated that at the time and location of squall line development, the low-level moist air was overlain by a deep layer of warm, very dry with ten minute time steps and zero curvature of on the spatial boundaries at each step. In order * to suppress the high frequency noise, the forecast scheme was restarted every two hours, forward at the first two steps, and then centered (Magata and Nishida, 1971). Then the adjustment, by using a variational low-pass filter for the advective forecasts (in * only), was made. The lowpass filter is described by the following equation; the first variation of the functional J vanishes: (7) The resulting Euler-Lagrange equation for * was (8) (9) Fig. 8 ATS III, 26/1819Z May The location of the dry intrusion is approximated by the clear area, indicated by A. The cloudiness B is associated with a southeastward moving cold front from a surface low pressure center in Kansas. The cloudiness C is stratiform beneath the dry intrusion. There is no thunderstorm activity in Oklahoma at this time.

7 August 1977 M. J. McFarland and Y. K. Sasaki 427 Fig. 9 ATS III, 26/1858Z May The first reported thunderstorm reported by weather radar are indicated at D. Fig. 11 ATS III, 26/2110Z May The squall line E is now producing funnel clouds and tornadoes along its entire length. Fig. 10 ATS III, 26/2031Z May The thunderstorm activity has developed southward as a well-defined squall line E. The first of the numerous tornadoes with this squall line was reported at 2052Z with the thunderstorm in Kansas just north of the Oklahoma border. Tornadoes were also reported at 2051Z with the frontal line thunderstorms G in Kansas. air. The presence of the thunderstorms indicated an indirect circulation; cool and moist air from below the inversion was rising convectively through the overlying warmer air. At cloud base, the thunderstorm updraft air would be negative- Fig. 12 ATS III, 26/2201Z May A tornado at Keefeton, OK near F, resulted in five fatalities at 2200Z. Large tornadoes were reported at 2200Z at G with the frontal line activity. ly buoyant with respect to the mesoscale environmental conditions. The existence of this indirect circulation is supported by an examination of the ATS III imagery for 26/1200Z May 1973 in conjunction with the variational model results. Five selected frames with brief descriptions are. included as Figs. 8 through 12. Fig. 8 depicts the pre-thunderstorm environ-

8 428 Journal of the Meteorological Society of Japan Vol. 55, No. 4 ment. The warm, dry air of the dry intrusion extends eastward over the stratus in eastern Oklahoma (apparent also in Fig 4, the Tinker AFB sounding) from the surface position to the west of the stratus boundary. The initial thunderstorm development occurred on the western boundary of the moist air. This is a preferred location for squall line thunderstorm development (Tegtmeier, 1974) which is in basic agreement with Schaefer's model (1974) of the relation of the surface dryline to the inversion marking the lower boundary of the dry intrusion. As the thunderstorms developed, the warm, dry air continued to move toward the east, as shown in Figs. 8 through 10. This eastward advection was indicated also in the forecasts from the variational advective model. The mesoscale environment of the severe thunderstorms shown in Figs. 11 and 12 appeared to be a low level moist layer (below 850 mb), capped by an inversion marking the boundary between the moist air and the much warmer dry intrusion, which extended at least through the 700 mb level. The mesoscale environment thus indicated an indirect convective circulation below the 700 mb level; cool, moist air rising convectively through warmer dry air. As the thunderstorms develop to severe levels, they significantly modify their mesoscale environment in the vicinity of the storm and in the area downwind from the storm, since the storms typically translate at a rate less than that of the environmental winds. The scale interactions which exist at the levels of the dry air intrusion immediately upwind of the storm may be a significant factor in the development of the storm to severe levels. The variational advection forecast results indicated that the intrusion was very dry, with consequently a virtually unlimited capacity for evaporation, and warm, with a near neutral lapse rate. Thus, evaporation of cloud material into the dry air would produce a strong subsidence of the cooler air, especially since with a dry adiabatic descent, the equilibrium level may be several hundred millibars below the original level of cooling. As surface heating warms the cooler layer beneath the inversion, this subsiding air may reach the surface. A major effect of the warm, dry intrusion in the severe storm environment is to facilitate a detrainment of the storm air into the mesoscale environmental air, as opposed to the entrainment of environmental air into the storm. The zone where rapid evaporative cooling occurs will protect the storm updrafts from the dry environmental air, which perhaps is necessary for development to severe levels. Recent research on severe storms support detrainment into the dry intrusion (Davies-Jones, 1974; Marwitz, 1972a, 1972b; Foote and Fankhauser, 1973). Davies-Jones observed that soundings in severe storm updrafts indicated that the cores of strong updrafts were undiluted by the environmental air. He also observed that the sounding balloons rose almost vertically in the storm in spite of pronounced environmental shear. A negative buoyance at cloud base was observed from aircraft measurements by Marwitz. Based on time-section analyses of two storms, Marwitz inferred that the descending air to the southwest (the windward side) of the thunderstorms had subsided from above the cloud base. He suggested that this mid-tropospheric air is directed downward as a result of evaporative cooling and deflection; this subsiding air reaching the surface layers could intensify the gust front. Foote and Fankhauser (1973) state that negatively buoyant inflow air is a fairly general observation for large, persistent storms and conclude that dynamic forcing drives the low-level inflow into the storm. Correlations of the surface conditions, as indicative of the low-level inflow, with squall line thunderstorm development have been good. Sasaki (1973) concluded that intense surface moisture convergence coincided with squall line development and local severe weather areas and that a local downward momentum transport is very important to squall line formation. The role of the dry air intrusion to severe storm development is as yet speculative. The scale interactions are difficult to parameterize, describe and model; the measurements made of several thunderstorms may sample either the mesoscale unaltered environmental conditions, the thunderstorm scale conditions, or the interacting zones. Some conclusions may be drawn, however. The warm, dry intrusion facilitates detrainment with a resulting downward transport of modified air and deflection of environmental air. This mechanism provides for a protection of the storm interior from the dry air and the environmental shear through the dry layer. The subsiding air provides for a downward momentum transport and will serve to intensify the gust front. Another significant factor not directly commented upon is that the inversion layer marking the lower boundary of the dry intrusion serves to cap the potential

9 August 1977 M. J. McFarland and Y. K. Sasaki 429 instability of the moist air below. Acknowledgments This research was conducted at the University of Oklahoma under National Aeronautics and Space Administration Contract NAS , a part of SKYLAB Experiment Project Number 582 Severe Storm Environment, and also, the National Science Foundation under the Global Atmospheric Research Program, Grant OCD The authors gratefully acknowledge the assistance to Ms. Anita Cameron, Ms. Jaye Barry and Ms. Debbie Killian for the preparation of this manuscript. References Davies-Jones, R. P., 1974: Discussion of measurements inside high-speed thunderstorm updrafts. J. Appl. Meteor., 13, Endlich, R. M. and R. C. Mancuso, 1968: Objective analysis of environmental conditions associated with severe thunderstorms and tornadoes. Mon. Wea. Rev., 96, Foote, G. B. and J. C. Fankhauser, 1973: Airflow and moisture budget beneath a northeast Colorado hailstorm. J. Appl. Meteor., 13, Liles, C. A., 1976: Variational optimization analyses of the 8 June 1974 severe storms in Oklahoma. Master's Thesis, Texas A&M University, 85 pp. Magata, M. and K. Nishida, 1971: On the computational errors in the numerical experiment. J. Meteor. Soc. Japan, 49, Marwitz, J. D., 1972a: The structure and motion of severe hailstorms, Part I: Supercell storms. J. Appl. Meteor., 11, b: The structure and motion of severe hailstorms, Part III: Severely sheared storms. J. Appl. Meteor, 11, McFarland, M. J., 1975: Variational optimization analysis of temperature and moisture advection in a severe storm environment. University of Oklahoma, WEAT Report No. 16, 86 pp. Miller, R. C., 1972: Notes on analysis and severestorm forecast procedures of the Air Force Global Weather Central. AWS Technical Report 200 (Rev). Morris, R. M., 1972: The trowal, an important feature of frontal analysis. Meteor. Magazine, 101, O'Brien, J. J., 1970: Alternative solutions to the classical vertical velocity problem. J. Appl. Meteor., 9, Pfeffer, R. L., 1962: Results of recent research in meteorology at the Lamont Geological Observation. Proc., International Symposium on Numerical Weather Prediction in Tokyo. Meteorological Society of Japan, Nov. 7-13, 1960, Sasaki, Y. K., 1970a: Some basic formalism in numerical variational analysis. Mon. Wea. Rev., 98, b: Numerical variational analysis formulated under the constraints as determined by longwave equations and a low-pass filter. Mon. Wea. Rev., 98, : Mechanism of squall-line formation as suggested from variational analysis of hourly surface observations. Preprints, Eighth Conf. on Severe Local Storms, Oct , American Meteorological Society, 8 pp. Schaefer, J. T., 1974: The life cycle of the dryline. J. Appl. Meteor., 13, Tegtmeier, S. A., 1974: The role of the surface, subsynoptic low pressure system in severe weather forecasting. Master's Thesis, University of Oklahoma, 66 pp. Wagner, K. K., 1971: Variational analysis using observational and low-pass filtering constraints. Master's Thesis, University of Oklahoma, 39 pp.

10 430 Journal of the Meteorological Society of Japan Vol. 55, No. 4 M. J. McFarland National Weather Service Y. K. Sasaki University of Oklahoma