Multicellular behavior in a simplified squall-line model

"A simplified squall-line model revisited"

Robert G. Fovell and Pei-Hua Tan
Quarterly Journal of the Royal Meteorological Society
(in press)

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The discussion below is based upon, and further extends, the material covered in the Fovell and Tan (1998) paper, which should probably be reviewed first. This page presents a brief overview of the paper. Only a portion of the paper's content is covered below. Please direct comments, questions, and/or reprint requests to Robert Fovell.

Available here is a copy of the paper in Adobe Acrobat PDF format.

Links to sections on this page:

  • Motivation and Background
  • Model design
  • Results
  • Deficiencies of the parameterized moisture model
  • Conclusions
  • References
  • Motivation and Background

    Fovell and Tan (1998; hereafter FT) studied the generation, propagation,and dissipation of the mature multicellular storm's constituent convective cells. They showed that the typical new cell first appears within the the cold pool's forced updraft and quickly becomes a positively buoyant free updraft. The buoyancy induces a local circulation that, at first, serves to intensify the cold pool forced updraft, aiding the new cell's intensification. However, once the cell begins moving rearward within the FTR flow, the buoyancy-induced circulation starts actively suppressing the forced lifting, even as it forces the entrainment of potentially cold air (from the cold pool and/or the middle troposphere ahead of the storm) into the cell. This entrainment causes the lower portion of the growing cell to become convectively stable while destabilizing the forced updraft farther below. The growing cell thereby becomes ``cut off'' from the forced updraft, and continues propagating rearward within the FTR airflow. It was concluded that the cellular transience was a direct result of the convectively-generated, buoyancy-induced circulation.

    To further our understanding of the cut off and cell regeneration processes, we attempted to identify the simplest dynamical framework capable of capturing this behavior. First, the model was made two-dimensional, as it has been demonstrated that multicellular behavior can be dynamically similar in the two- and three-dimensional frameworks (e.g., Rotunno et al. 1988; FT). Next, condensate loading was deactivated and the complex subgrid turbulence parameterization was replaced by a simple eddy diffusion intended primarily to restrain computational instability. These were found to have little dynamical effect other than to permit the cells to become somewhat stronger and longer-lived. The explicit appearance of precipitation and its attendant timescales were obviated by the adoption of a maintained, lower tropospheric heat sink. Testing revealed that the sink's artificially generated cold pool permitted realistic, long-lived multicellular storms to form with relatively little sensitivity attached to the cooling rate employed.

    Finally, the chief role of water vapor is to release latent heat to the surrounding air upon condensing. As the dominant (but not sole) condensation production mechanism is lifting, very simplified models have parameterized moisture by making condensation warming proportional to ascent velocity. Our simplified model follows the implementation discussed in Garner and Thorpe (1992; hereafter GT).

    Our study was specifically motivated by GT's reported failure to find any multicell-type storm behavior in the experiment they conducted. Based on FT, we believed that the parameterized moisture (PM) model does contain the necessary physics to support sustained multicellular behavior. Below, we show that when an initial sounding with sufficient convective instability is employed, realistic multicellular temporal behavior is obtained with the PM model.

    Model design

    In the PM model, the equations concerning moisture are eliminated and the prognostic equation for potential temperature q is rewritten (neglecting mixing) as:

    equation (1)
    The first term on the right hand side (RHS) is the parameterization for condensation heating. The flag b is one if air is rising at a particular location, otherwise it is zero. That is, heating (via condensation) is presumed to only occur with ascent. The second term parameterizes evaporative cooling, and is responsible for creating and maintaining the subcloud cold pool. This will be done by prescribing a cooling zone and continually "sponging" the air therein to a prescribed temperature.

    Next, condensation warming is made proportional to ascent velocity, but only in a portion of the domain dubbed the unstable region . This is justified in the following manner. The heating term may be written as:

    equation (2)
    where "Lv" is the latent heat of vaporization, "cp" the specific heat at constant pressure, p is (nondimensional) pressure and "qvs" is the saturation mixing ratio.

    In a Lagrangian view, the first equivalence on the right-hand side (RHS) illustrates the condensational heating is generated owing to the change of qvs with time along a saturated parcel's path. The second equivalence is based on the fact that the motion affecting the qvs change is primarily in the vertical direction. The third expression shows that the path taken by the saturated parcel is along a moist adiabat. qp is the potential temperature of such a parcel, and its vertical gradient is the slope of a moist adiabat in temperature-height space. The last term reveals that heat release is proportional to ascent velocity (w).

    The figure below depicts the model design:

    Figure 1 from paper
    Figure 1 - Model setup

    The "unstable region" is where rising motion is presumed to generate latent heating. The "cooling zone" is where evaporation cooling is acting. (The paper explains what the other symbols mean.) In practice, it is necessary to keep the cooling zone in sync with the cold pool it produces lest the results become quite unphysical. Our cooling zone is "storm-adaptive", meaning its location is chosen to align with the subcloud cold pool, wherever it is and however it happens to move.

    Results

    GT's sounding contained about 400 J/kg of convective available potential energy, or CAPE. With this sounding, the model tends to settle into steady state solutions. The "successful" steady solution has a storm with a deep (but steady) updraft while the "unsuccessful" steady solution has no deep convection, only a forced updraft associated with the cold pool lifting. These two simulations differ with respect to the strength of the low-level vertical wind shear. The key point is that multicellular behavior was essentially absent.

    The figure below shows an unsuccessful (left) and successful (right) steady state, made using GT's sounding. These are vertical (x-z) cross-sections across the storm. (Only a portion of the simulation domain is shown, and the horizontal axis is labeled relative to the left side.) The contoured field is vertical motion, with solid (dashed) contours indicating ascent (descent). The shaded field is perturbation potential temperature.

    Next, we consider simulations made using a more favorable sounding, one with about 1800 J/kg. This value is more typical of springtime severe storm events according to Bluestein and Jain's (1985) climatology.

    Figure 3 from paper (modified)
    Figure 2 - PM simulation with low CAPE sounding

    When a more convectively favorable (but also more realistic) sounding is adopted, multicellular behavior is ubiquitous. Below shows the results of one case at four times during a single "repeat cycle". The sequence of pictures is quite similar to that seen in the more physically realistic cloud model and analyzed by FT. Further similarities, and some caveats, are discussed in the paper.

    Figure 5 from paper

    Figure 3 - PM simulation with moderate CAPE sounding

    Deficiencies of the parameterized moisture model

    The PM model accomplishes some substantial simplifications, and is quite economical to run. Unfortunately, our model solutions present some problems that point to inherent deficiencies in the model. Most importantly, the degree to which the storm modifies its own upstream environment as it organizes appears to be quite excessive. This is important because the upstream environment (into which the storm is propagating) directly feeds back upon the storm.

    Figure 7 from paper
    Figure 4 - Upstream vertical profiles of the horizontal wind

    The figure above shows vertical profiles of the horizontal wind taken at a location ahead of the storm during the mature phase. Shown are: the initial profile; the profile from the PM model simulation shown in Fig. 2; a modified PM model simulation (see below); and two simulations from "full physics" cloud models. The latter indicate little alteration from the initial profile occurs in the important lower layer. In contrast, the PM model simulation evinces substantial differences, especially at the low levels.

    The excessive upstream modification issues from a fundamental inconsistency in the PM model. In reality, as convective cells retreat towards the storm's rear, they "run out" of water vapor and thus condensation heating eventually ceases. In the PM model, however, rising motion creates warming, which serves to maintain the rising motion that creates the warming. Thus, as the cells age and retreat, parameterized condensation warming never ceases.

    As a result, excessive warming accumulates in the storm's trailing region (see x < 20 km in Fig. 2). This warming:

    Figure 8 from paper
    Figure 5 - Upstream vertical profiles of the horizontal wind

    As a test of our explanation, we attempted a crude "fix" by incorporating a "convective sponge" into the model. This sponge, located within the unstable zone, removed warming from the trailing region at a time scale long compared to the evolution and movement of the convective cells but short relative to the trailing region's accumulation of warming. Figure 5, above, shows x-z cross-sections from the original and sponged simulations. Comparing the simulations, it is seen that:

    Conclusions

    GT employed a PM model to elucidate the role of vertical wind shear in organizing squall-line storms. During maturity, a typical storm possesses a large-scale background circulation in which sequentially generated, short-lived convective cells are embedded. GT chose the simplified model because, in their view, it inherently "suppressed cell decay and redevelopment", permitting them to focus on the much steadier background circulation. Indeed, their model yielded "extraordinarily steady" solutions that were either successful (consisting of a single, persistent deep updraft) or unsuccessful (devoid of deep convection) during maturity. "Multicellular" storms were ostensibly absent.

    Based on FT's analysis, however, we suspected the PM model should support cell redevelopment. Our examination showed that GT's initial environment lacked sufficient convective instability to drive the episodic entrainment process critical to cellular transience. Given a commonly available amount of instability, even the PM model was found to support realistic-looking multicellular storms. Steady unsuccessful and successful storms still existed, but in between, the parameter space region occupied by multicell storms was substantially larger.

    Less realistic was the degree to which PM model storms influenced their upstream environments. Analysis suggested the exaggerated impact could be traced to a fundamental shortcoming of the simplified model: that convective cells, once formed, did not dissipate, even as they propagated far away from the storm's leading edge. This permitted an excess of parameterized condensation warming to build up in the storm's trailing region, with a substantial impact on the storm's overall circulation.

    GT's study helped demonstrate that both shear intensity and shear layer depth combine to influence the mature squall-line storm's background, quasi-steady circulation. Indeed, by examining an environment with small convective instability, they showed the transition between the successful and unsuccessful cases can be very narrow, thereby emphasizing the contrast between these two extreme states without the distraction posed by multicellular transience. Our contribution is to show that the PM model also supports reasonable multicellular behavior when more realistic environmental conditions are employed. However, our analysis also points to deficiencies in the PM framework that serve to limit its general applicability.

    Acknowledgement

    This work was supported by the National Science Foundation (NSF) under grant ATM94-21847.

    References

    Bluestein, H. B., and M. H. Jain, 1985: Formation of mesoscale lines of precipitation: severe squall lines in Oklahoma during the spring. Journal of the Atmospheric Sciences, 42,1711-1732.
    Fovell, R. G., and P.-H. Tan, 1998: The temporal behavior of numerically simulated multicell-type storms, Part II: The convective cell life cycle and cell regeneration. Monthly Weather Review, 126, 551-577.
    Garner, S. T., and A. J. Thorpe, 1992: The development of organized convection in a simplified squall-line model. Quarterly Journal of the Royal Meteorological Society, 118, 101-124.
    Rotunno, R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong, long lived squall lines. Journal of the Atmospheric Sciences, 45, 463-485.

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    Page created September, 1999, by Robert Fovell