Brian F. Jewett and Robert B. Wilhelmson
[1]
Department of Atmospheric Sciences and
National Center for Supercomputing Applications (NCSA)
University of Illinois at Urbana-Champaign
1. INTRODUCTION
Forecasting the initiation and mature structure of severe thunderstorms remains a formidable challenge. Earlier research into the underlying processes responsible for multicell and supercell evolution has successfully revealed much about the relationship between the in-situ thermodynamic and shear profiles and the subsequent character of the convection (e.g. Weisman and Klemp, 1982, hereafter WK82). At the same time, it is acknowledged that mesoscale phenomena are often crucial in determining not only the location and nature of thunderstorm initiation but also in some cases the mature structure and longevity of the convection.
Cloud models are often initialized with simple perturbations (thermal bubbles, line thermals, etc.) upon base state fields which are functions of height only. Use of this method of initialization emphasizes the mature structure over the manner of convective initiation and the early thunderstorm structure. It also assumes the mature structure is not significantly dependent on the method of initialization. However, McPherson and Droegemeier (1991, hereafter MC91) and Droegemeier and Levit (1993) have described sometimes surprising sensitivity to the initial perturbations used to start their modeled convection.
Severe convection is often associated with synoptic and mesoscale features, but the degree to which the local vertical profiles of buoyancy and shear uniquely determine the mature structure is not as clear. Doswell (1987) notes that large scale flows are responsible for the local thermodynamic environment, while mesoscale phenomena provide lift for initiation. We seek to better understand the role of mesoscale (horizontally variable) forcing and want a model of squall line initiation which is realistic and which may have a lasting influence on the storm's mature structure.
We are investigating the development and evolution of potentially severe squall line thunderstorms. The mesoscale forcing is associated with a cold front as part of a growing baroclinic wave. We seek to
* realistically model initiation of convective lines
* produce desired (moderately unstable) profiles
of temperature and moisture at time of initiation
* examine the role of mesoscale forcing on the early
and mature structure of squall lines
2. MESOSCALE ENVIRONMENT
Earlier studies of frontal convection have often been carried out in highly idealized environments including the use of constant vertical stratification and constant, high relative humidity. In keeping with our emphasis on severe convection, we seek along-front environments associated with observed severe thunderstorms, including the presence of a realistic tropopause, near-neutral conditions near the ground, gradual drying with height, a curved hodograph and a slightly stable layer to delay convective initiation until the desired potential instability has developed.
We first select the desired thermodynamic profiles for the leading edge of the front. Our motivation to choose these conditions first is based on prior studies by WK82 and others relating mature thunderstorm structure to the vertical profiles of potential temperature [[theta]], mixing ratio qv and wind immediately prior to initiation of deep convection. To extend these studies in the context of frontal forcing, we must first reach these selected vertical profiles with the evolving frontal system.
The chosen sounding (not shown) is characterized by a surface (first model layer) temperature of 25.0 deg. C, dewpoint 20.1 deg. C, and mixing ratio of 14.8 g kg-1. The convective available potential energy (CAPE) is 2480 J kg-1, and the convective inhibition to be overcome (CIN) is 54 J kg-1.
To prepare appropriate forcing for convection, we develop a two-dimensional (2D) cold front by modeling shear-type frontogenesis at high (under 2 km) horizontal resolution using the nested-grid COMMAS (COllaborative Model for Multiscale Atmospheric Simulation) cloud model (Wicker and Wilhelmson, 1995). The computational grid is 18 km high and 4000 km wide. The vertical resolution is fixed at 250 m, while the horizontal resolution is 16.0, 5.3, and 1.8 km for the coarse and first and second nested grids. An initial sounding is chosen, along with a unidirectional base-state east-west wind (U) increasing linearly 20 m s-1 from the model surface to the tropopause, and decreasing aloft. The most unstable mode is determined numerically. Two nested grids are employed and the 3-grid system is run until the frontal solution approaches "collapse", after which the model damping is increased to slow the collapse and the system is run another 12 hours. Water vapor, until collapse+12 hours diagnosed from a chosen relative humidity profile (function of height only), is then allowed to fully evolve for 3 hours. The along-front sounding is retrieved at this "verification" time (15 hours past collapse), and the conditions compared to the desired sounding. Incremental changes are made to the initial [[theta]] field and the integration is repeated until the potential temperature profile is acceptable. Moisture is also iteratively altered, but only over the last 3-hour period to save computation time.
Figure 1. Actual along-front skew-T/log-P (left) and hodograph (right) from our 2D simulation. The skew-T/log-P shows the temperature (solid), dewpoint (dashed) and parcel profiles. Each hodograph circle represents 10 m s-1.
The final sounding and hodograph (at collapse+15 hours) are shown in Fig. 1. Compared to the desired sounding, the maximum [[theta]] and qv "errors" are 0.3 deg.C and 0.10 g kg-1, the CAPE is 2483 J kg-1 and CIN is 59.5 J kg-1. The bulk Richardson number is 93, putting this environment in the multicell regime. The 2D simulations (not shown) have frontal updrafts of 23 cm s-1.
3. THREE DIMENSIONAL RESULTS
To move to three dimensions (3D), we first extract the innermost nested grid from the 2D simulations. The move from 2D to 3D was chosen to be 20 minutes after the (collapse+15 hour) verification time, which was only 6 minutes prior to convective initiation in the 2D simulation. The 2D fields (with along-front velocity also predicted) are then expanded to 3D and perturbations are added to allow 3D structures to develop. The innermost grid is run in 3D rather than all three nested grids because the nested grid solver cannot place nested grids all the way to the north/south (N/S) boundaries. Without this capability the broader structure of the front on the lower-resolution grids begins to corrupt the fine-scale structure on the innermost grid where inflow is present (e.g. at the south boundary) when we move to three dimensions. Our primary 3D simulation grid is 102x80x73, for a domain of 181x142 km in the horizontal and 18 km in the vertical.
Our experiments are designed to determine the difference between simulations with and without the presence of the front. To allow the "isolated" simulations (i.e., those without the front present) to also take on a line orientation, we applied a N/S line of thermals to the initial 3D fields of both the isolated experiments and those with the front present. Each bubble was 5 grid points in horizontal radius (about 9 km) with a vertical radius of 1400 m and was centered at the lowest grid point (z=125 m). The bubble edges just overlapped in the horizontal, as in MC91. This size allows 8 thermals in the N/S direction.
We are using periodic N/S boundaries (for all model variables) to simulate a long, straight front and squall line. The meridional temperature gradient assumed in the 2D simulations are omitted in 3D, consistent with periodicity. Although periodicity directly enforces a scale on the moist convection, previous simulations with purely random initial perturbations (over the entire horizontal domain) suggested an evolving line of approximately 8 storms in the model domain, so we feel the use of 8 initial perturbations is appropriate for this case.
Given these boundary conditions, we first carried out simulations for 75 minutes with only one thermal "bubble" modeled, since the periodic boundaries make this equivalent to explicitly simulating a line of thermals. These runs allowed us to estimate the effect of the front over a range of perturbation values without running the full model domain in each case. For the isolated simulations, we needed a sounding profile with which to initialize the otherwise horizontally homogeneous conditions. We chose two: at the location of maximum frontal updraft and also at the location of lowest pressure, which was two grids points (3.6 km) farther east. The maximum updraft over the duration of these runs (75 min.) is listed for the frontal case and for the two isolated runs below in Table 1.
Table 1. Single-thermal experiments - max. updraft (m s-1) over
75 minutes
Perturbation Frontal run Isolated run Isolated run
(deg.C) at Pmin at Wmax
0.25 27.75 0.12 0.12
0.50 28.17 0.20 0.18
0.75 27.99 0.31 0.31
1.00 28.00 0.44 20.10
1.50 30.05 19.20 26.18
2.00 31.86 23.07 25.69
4.00 31.08 30.74 28.18
6.00 36.59 33.64 33.50
These simulations demonstrate that for small thermal disturbances no convection develops at all in the isolated cases. For these cases the frontal updraft and sloping ascent of moist air is nonetheless sufficient to initiate convection. We acknowledge that mimicking a three-dimensional process with a one-dimensional sounding is difficult; clouds in the frontal cases first form several grid points west of the maximum frontal updraft. But this is also of interest because 3D models initialized with single soundings are missing the horizontal structures appropriate to (and formed simultaneously with) these vertical profiles of buoyancy and shear.
The frontal simulations were characterized by an initial peak updraft (larger for larger perturbation magnitudes), a gradual leveling off and then a steep decrease in intensity. The isolated simulations generally increased in updraft strength with time (Fig. 2). The isolated time series composite in Fig. 2 appears to have less data because for the first three simulations (perturbation magnitudes below 1 deg.C) no thunderstorm formed.
Notable in Fig. 2 is the indication of greater variation among runs for the isolated simulations vs. the frontal ones. The primary scatter among the frontal runs is in the time at which the peak updraft is realized, generally later for weaker initial perturbation magnitude. After this peak the individual runs have similar behavior. For the isolated simulations there are differences in not just timing but also in evolution. Some simulations have a dual peak followed by decline while others are clearly intensifying with time.
Figure 2. Time series data from 3D single-thermal simulations with frontal structure present (left) and absent (right). Each curve represents a run with a different initial perturbation magnitude.
Periodicity combined with a regular line of initial perturbations restricts considerably the nature of the evolving convection. We seek experiments in which the convective behavior is less restricted but which still allows meaningful comparisons between the forced and isolated paradigms. A pair of simulations were carried out. Thermal bubbles were used, here employing a line of 8 disturbances in the full 142-km north-south model domain. An initial perturbation magnitude of 2.0deg.C was used, larger than needed for convective initiation in the frontal case but large enough to assure initiation without the front. In addition, a weak (0.25 deg.C) random perturbation was superimposed to allow more of a 3D character to the convection. The resulting convection was stronger early on for the frontal case (Fig. 3), which then weakened to at or under 20 m s-1.
Fig. 3: Time series of peak updraft (m s-1) for the full-domain 3D simulations. The frontal experiment is denoted by solid line, while the isolated experiment is dashed.
The isolated convection, as in the single-thermal experiments discussed above, maintained larger vertical velocity towards the end of the simulation (2.5 hours) but is characterized by a less fully-formed anvil than the frontal storms (Fig. 4). The presence of the front in this case has not helped but rather resulted in weaker convection, as the low-level gust front (not shown) becomes established farther ahead of the line compared to the isolated case.
Figure 4. View (towards the northwest) of the cloud+rainwater fields at 2.5 hours for the frontal (left) and isolated (right) cases. For the frontal case, the 297 K potential temperature surface is also displayed to show the approximate location of the front.
4. SUMMARY AND CONCLUSIONS
We are investigating forced convection and the role of mesoscale processes (here a cold front) on the initiation and mature structure of convection. Consistent with our emphasis on potentially severe thunderstorms, we have emphasized the evolution of along-frontal buoyancy profiles consistent with observed severe convection.
These simulations are in the multicell regime, consistent with the larger bulk Richardson number associated with the modest shear found at the leading edge of the front. For the multicell storms shown here the presence of the front was necessary for convective initiation when weakly forced. For larger forcing the front was not of apparent benefit to the convection; the isolated non-frontal simulations were generally stronger for a longer period of time. As a method of convective modeling, the single-sounding approach would have exaggerated the convective strength in this case.
Single-thermal experiments indicate significant sensitivity to the initial perturbation magnitude for the isolated convective runs. This sensitivity, also noted by MC91 in their isolated thunderstorm simulations, is not found in our simulations with frontal forcing present. This may indicate that in some cases the suggested sensitivity is an indication more of an underspecified initial state - the absence of the mesoscale forcing and features commonly accompanying severe weather.
5. FUTURE WORK
We will next focus on the supercell range of shear and buoyancy. Experiments with greater base-state (east-west) cross-frontal shear along with reduced CAPE are planned to move our simulations toward lower bulk Richardson numbers. These simulations will be discussed at the conference. 3D simulations with the N/S temperature (and stability) gradients included are planned. In addition, we will move toward higher horizontal and especially vertical resolution, since frontal updrafts have been observed to reach 3-5 m s-1 (Shapiro et al., 1985), vs. the 20-40 cm s-1 we have found.
6. ACKNOWLEDGMENTS
Our modeling research is being supported by NSF through ATM 92-14098. The simulations were carried out on the Pittsburgh Supercomputing Center C90. Additional computing and other support was provided by NCSA. The assistance of Crystal Shaw in visualizing the 3D simulations is appreciated. Discussions with William Skamarock of NCAR and Bruce Lee of the University of Illinois have been very helpful.
7. REFERENCES
Doswell, C. A. III, 1987: The distinction between large-scale and mesoscale contribution to severe convection: a case study example. Wea. Forecasting, 2, 3-16.
Droegemeier, K. K., and J. J. Levit, 1993: The sensitivity of numerically-simulated storm evolution to initial conditions. Preprints, 17th Conf. on Severe Local Storms, St. Louis, Amer. Meteor. Soc., 431-435.
McPherson, R. A., and K. K. Droegemeier, 1991: Numerical predictability experiments of the 20 May 1977 Del City, OK supercell storm. Preprints, 9th Conf. on Numerical Weather Prediction, Denver, Amer. Meteor. Soc., 734-738.
Shapiro, M. A., T. Hampel, D. Rotzoll and F. Mosher, 1985: The frontal hydraulic head: a micro-[[alpha]] (~ 1 km) triggering mechanism for mesoconvective weather systems. Mon Wea. Rev., 113, 1166-1183.
Wicker, L. J., and R. B. WIlhelmson, 1995: Simulation and analysis of tornado development and decay within a three-dimensional supercell thunderstorm. J. Atmos. Sci., 52, 2675-2703.
Weisman, M. L., and J. B. Klemp, 1982: The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Wea. Rev., 110, 504-520.