Simulations of baroclinic waves and cold fronts have been carried out for many years. Early work concentrated on dry frontogenesis and frontal collapse (Williams, 1967; Orlanski and Ross, 1977), and this has remained an active area of research (Gall et al., 1987; Snyder et al., 1993). Moist two-dimensional frontogenesis associated with shear deformation has been studied recently (e.g. Bénard et al., 1992), usually initialized with the semi-geostrophic solution. These simulations were often characterized by limited domain height (8-10 km), constant vertical stratification and simplified vertical moisture profiles. A range of realistic frontal convective phenomena was modeled, including wide rainbands and the narrow cold-frontal rainband, with maximum vertical velocities of a few meters per second. Greater realism was found in the three-dimensional Eady-wave simulations of Zhang and Cho (1995).

Idealized simulations of deep convection along fronts have been carried out by Ross and Orlanski (1978) and later Crook (1987; "C87"). In these studies the base-state zonal wind and meridional jet structure were specified and the cross-frontal temperature structure was specified consistent with thermal wind balance. C87 studied the long-term behavior of the frontal convection, which had a lifetime of nearly 12 hours and regenerated every 20 hours.

We are studying the initiation and evolution of intense cold-frontal thunderstorms. Realistic forcing to the convection is sought here in the form of a cold front developed as part of a growing baroclinic wave. Because our emphasis is on deep, sustained frontal thunderstorms, we require along-front conditions similar to those found prior to observed deep convection, including a modest potential temperature "cap", a sharp tropopause, and substantial instability. The wave cyclone development is based on the Eady model while allowing non-constant static stability and vertical shear.

Mesoscale phenomena such as fronts, drylines and jet streaks are more often than not present when deep convection occurs. Their critical role in providing lower-tropospheric lift is well documented. Given a realistic and somewhat multifaceted initial state, the continuing role of the front on the convection is being investigated.

2. METHODOLOGY

The nested grid COMMAS (COllaborative Model for Multiscale Atmospheric Simulation; Wicker and Wilhelmson, 1995) model is used to simulate horizontal shear frontogenesis at high resolution in two dimensions. COMMAS is a three-dimensional, nonhydrostatic cloud model incorporating horizontal grid nesting discussed by Skamarock et al. (1989). A coarse grid domain 4000 km wide and 18 km tall is employed, with horizontal grid resolution of 16 km and vertical resolution of 250 m.

An initial base-state zonal wind profile U(z) is chosen, characterized by nearly constant shear throughout the troposphere, diminishing aloft. The meridional (along-front) temperature gradient is determined from U(z). Slab symmetry is assumed with along-front velocity v(x,z) predicted, relative humidity treated as invariant along the front and a semi-slip layer is used at the surface. The along-front vertical shear and time of frontal collapse were found to be sensitive to the surface drag. More details may be found in Jewett (1996).

The most unstable mode was determined numerically. The simulation was then continued to frontal collapse, diagnosed from the areal coverage of the vorticity maximum found near the surface. Collapse was accompanied by development of a distinct lower-level updraft, increased doubling times and stabilization of the frontal width.

Two nested grids were employed, with inner grid resolution of 1.8 km. The solution was continued to and beyond collapse on the innermost grid, with the horizontal damping increased over the final 15 hours. Water vapor, initially diagnosed from a specified humidity profile, was allowed to fully evolve over the final three hours of the simulation. The final along-front sounding was retrieved and compared to desired vertical profiles of potential temperature and water vapor, yielding error profiles. The initial sounding was altered consistent with these errors and the simulation was repeated. In the case presented here the final along-front sounding was within 0.3 deg.C and 0.1 g kg^-1 of the desired profiles.

3. RESULTS

Once the along front temperature and water vapor profiles approximate the desired sounding, the initial state was considered complete. The front at this time was characterized by a relative vorticity maximum of 12f and maximum (local) temperature gradient of 27 deg.C (100 km)^-1. The latter is near the low end of the range (33-56 deg.C (100 km)^-1) for the intense front studied by Sanders (1955) but well below the large values found in high-resolution BAO tower data examined by Young and Johnson (1984).

The modeled low-level updraft "jet" position led (was east of) the pressure trough which led the vorticity maximum, with these maxima approaching one another over the duration of the simulation. The updraft (not shown) was located near the nose of the front with weak rising motion to the east. A stationary gravity wave at the leading edge of the front was indicated by the alternating regions of rising and sinking motion above the updraft jet, diminishing near the critical level (5.5 km) as in the simulation by Snyder et al. (1993). A low level southerly jet was found near the eastern (nested grid) boundary with northerly flow behind the front.

When the simulation was continued in two dimensions, a cloud formed less than 30 minutes later, approximately 5 km behind (west of) the low-level frontal updraft maximum. The subsequent convective tops exceeded 12 km. The initial convection triggered gravity waves which then moved away from the convection. These waves were manifested as surface pressure and wind perturbations and in distortions of the frontal surface. As noted elsewhere, determining what constitutes the leading edge of the front is complicated by the presence of convection.

The pre-convective innermost-grid fields from the two-dimensional (2D) model were expanded in the along-front (meridional) direction for use in single-grid three dimensional simulations. Periodic boundary conditions were employed at the north/south boundaries and along-front variations were neglected for these experiments. Thermal perturbations were introduced to induce three-dimensional behavior.

"Frontal" experiments were carried out with the full frontal fields present, while "isolated" simulations had the vertical profiles of thermodynamic and wind fields at the front expanded in the horizontal, removing the cross-front variability. The presence of frontal lifting aided in convective initiation, as expected: isolated experiments required thermal perturbations of 1deg.C or more for convection to begin. The isolated experiments exhibited significant sensitivity (in updraft evolution) to these perturbations, a sensitivity missing from the simulations with the front present.

Identical moisture fields were then used in each case to provide comparable convective inflow properties and isolate the impact of across-front shear and frontal lifting. After initial convective cell splitting, subsequent cell-cell interaction properties differed with the front present than without. The result was comparable updraft strength (up to 35 m s^-1 but typically 15-20 m s^-1) but a longer-lived squall line with the front present. The frontal squall line was characterized by new cell formation every 20-40 minutes with new cell formation occurring ahead of the primary rain-producing cells as their downdrafts spread northeastward. Trajectories for the two cases reflect the different environments east of the line (Fig. 1). In the frontal case, the presence of the low-level jet allows source air southeast of the line to approach the convection.

Two differences are notable between the along-line average fields of the frontal and isolated convection. The cross-front circulation (meridional vorticity) is generally stronger in the frontal squall line, particularly early in the simulation. At two hours, the maxima are comparable though the frontal average circulation appears deeper and tilts upward and to the west. In addition, the low-level convergence contributions to vertical vorticity is significantly larger for the frontal squall line than for the isolated one. This is true throughout the simulation, even when deep convection and low-level gust fronts have been established in both cases.

4. CONCLUSIONS AND FUTURE WORK

The 2D shear frontogenesis problem has been integrated beyond frontal collapse at high resolution and used to study the role of the mesoscale environment on the evolution of frontal convection. The front has been found to influence not only the initiation but also the mature structure of the squall line, including its vertical and meridional vorticity structure, cell-cell interaction and line longevity.

Fig. 1. Cloud water and trajectories for the squall line with frontal forcing (left) and without (right).

The initial simulations were carried out under weak (2 m s^-1 km^-1) ambient cross-frontal shear, and have resulted in only modest (under 40 cm s^-1) pre-convective vertical velocities at the front. Work is underway to study the impact of higher-shear environments and further efforts are planned to explore higher vertical resolution and possible mixing changes so that stronger, more realistic fronts may be attained. The results of these experiments and continued study of the impact of frontal forcing will be presented at the conference.

5. ACKNOWLEDGMENTS

The authors are grateful to Chris Snyder and William Skamarock of NCAR/MMM for several helpful discussions. Crystal Shaw and David Wojtowicz of NCSA provided invaluable visualization assistance. This work was supported by the National Science Foundation under grant ATM 92-14098. The simulations were carried out on the Pittsburgh Supercomputing Center C90. Additional computing and other support was provided by NCSA.

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