Environmental stability control of the intensity of squall lines under low-level shear conditions

Authors


Abstract

[1] The environment for the development and evolution of linearly organized convective systems, i.e., squall lines is diverse for their existence in various climate regions. Understanding the behavior of squall lines under various environmental conditions is required for diagnosing and forecasting the development and intensity of the convective systems. The present study investigates the effects of environmental static stability on the squall-line intensity by conducting a systematic series of idealized cloud-resolving simulations of squall lines that develop in line-perpendicular, low-level westerly shear. Changing the temperature lapse rate with convective available potential energy (CAPE) being unchanged, we showed that the environmental stability in a convectively unstable layer well describes the intensity of the simulated squall lines. A less stable stability is favorable for generating stronger convective systems. The amount of CAPE does not account for the difference in the squall-line intensity in different temperature environments. An environment with a less static stability leads to the development of stronger cold pool, which will strongly controls the scale and strength of convective updrafts, the intensity of tropospheric overturning, and thus the organization and intensity of squall lines. The CAPE value can only be a good measure for diagnosing the development and intensity of the convective systems so long as the environmental static stability is identical. The static stability is a controlling parameter in determining the intensity of squall lines.

1. Introduction

[2] Linearly organized mesoscale convective systems, i.e., squall lines, develop in various climate regions of the world and induce severe wind and rain storms that harm human lives and social infrastructures. Diagnosing and forecasting the development and intensity of squall lines under various environmental conditions are a challenging but an essential task in mesoscale meteorology.

[3] The environment for squall lines is characterized mainly by the vertical profiles of temperature, moisture, and horizontal wind. Previous studies have stressed that the dynamical interaction between the low-level ambient wind shear and evaporatively induced surface cold-air pool controls the structure and intensity of squall lines [e.g., Rotunno et al., 1988, hereafter RKW; Weisman et al., 1988, hereafter WKR; Fovell and Ogura, 1989; Robe and Emanuel, 2001; Weisman and Rotunno, 2004, hereafter WR04].

[4] It has also been stressed that moisture content not only in the planetary boundary layer but also in the free troposphere has an impact on the squall-line structure and intensity [e.g., Barnes and Sieckman, 1984; Nicholls et al., 1988; Crook, 1996; Ferrier et al., 1996; LeMone et al., 1998; Lucas et al., 2000; Mechem et al., 2002; James et al., 2005]. The cold-pool–shear interaction comes to play a more dominant role in determining squall-line characteristics in drier environments [Takemi, 2006]: under drier boundary layer conditions, organized squall lines develop only with low-level shear that is dynamically balanced by cold pool (i.e., an optimal shear in the RKW theory); and even under moist conditions, the strength of low-level shear still determines the structure and intensity of squall lines.

[5] In comparing the characteristics of squall lines in various regions of the world such as the Tropics and the midlatitudes, the most controlling factor may be the environmental temperature, that is, static stability. Tao et al. [1995] examined numerically the effect of ice-phase melting processes, which depends on the environmental temperature, on the growth and maintenance of squall lines both in midlatitude continental and tropical oceanic regions and found that the impact of melting is more significant in the midlatitude case than in the tropical counterpart in determining the squall-line structure. Chin et al. [1995] pointed out that the tropical squall line is more efficient in pumping low-level moisture upward than the midlatitude system in spite of a weaker convective instability in the tropical environment.

[6] A significant difference between tropical and midlatitude convection is found for vertical velocities. There are a number of studies on the velocity field within cumulus clouds in various temperature environments. Zipser and LeMone [1980] showed that the size and intensity of updrafts and downdrafts are significantly weaker in the tropical system than in the midlatitude one by comparing their observational results with the data obtained during the Thunderstorm Project in Florida and Ohio [Byers and Braham, 1949]. Lucas et al. [1994a] suggested that the weaker vertical velocities in the Tropics are due to smaller buoyancy that is attributed to more effective water loading and entrainment. These vertical velocity characteristics were further investigated numerically by Xu and Randall [2001] who showed that the largest differences between the tropical and midlatitude cases are found in the strongest vertical velocities which largely depend on thermal buoyancy and water loading.

[7] There are other studies that investigate the impact of environmental temperature profile on convective storms and squall lines in midlatitudes. McCaul et al. [2005] showed that stronger updrafts in cooler temperature environments are resulted from the larger positive buoyancy due to fusion processes that start at lower altitudes than in warmer environments. By keeping convective available potential energy (CAPE) unchanged but varying boundary layer moisture content and tropospheric temperatures, James et al. [2006] indicated that moister environments (i.e., warmer tropospheric temperature), by reducing the rate of evaporation, produce weaker cold pools and stressed that the strength of cold pools determines the three-dimensional structure of convective lines. These studies did not explicitly deal with tropical convective systems; but their analyses of the sensitivity to environmental temperature seem to be consistent with the studies on tropical cumulus convection mentioned earlier.

[8] In our previous works on the sensitivity of squall lines to environmental shear, moisture, and temperature profiles, Takemi [2006] examined the effects of tropospheric moisture profile under a single temperature environment. Takemi [2007], extending the study of Takemi [2006], compared the intensity of squall lines simulated in two contrasting temperature environments characteristic of the Tropics and the midlatitudes under a comparable CAPE condition and found that the midlatitude system is significantly stronger than the tropical one. Takemi [2007] concluded that the static stability can be regarded as a key parameter that describes the squall-line intensity. These previous studies motivated us to explore more systematically the impacts of environmental temperature on the strength of mesoscale convective systems through cloud-resolving simulations. It is, however, extremely difficult to examine every possible combination of environmental conditions such as temperature, moisture, and shear. Thus the numerical simulations are performed with some simplifications and thereby the essential dynamics of convective systems are focused on.

[9] In the present study, we investigate the effects of static stability on the intensity of squall lines that develop under environments with low-level shear perpendicular to the convective lines. For this purpose, we conduct a series of cloud-resolving simulations with idealized settings and show the relationship between squall-line characteristics and static stability from the large set of simulations. We discuss the dependence of squall-line intensity on the environmental static stability and the mechanisms of the stability control of squall lines.

2. Model Setup and Experimental Design

2.1. Model Configuration and Setup

[10] In the present study, we use a compressible, nonhydrostatic cloud model, the Advanced Research Version 2.1.2 of the Weather Research and Forecasting (WRF) Model [Skamarock et al., 2005]. The model is configured in a three-dimensional domain having a horizontally homogeneous base state under low-level westerly shear conditions. Low-level westerly shears are focused here since this shear condition is most favorable for long-lived, strong squall lines according to the RKW theory. By assuming such a shear profile, we intend to discuss the dynamics of convective lines that develop perpendicular to the shear. This type of squall lines are widely investigated observationally, theoretically, and numerically [e.g., Houze, 1993].

[11] In order to concentrate on the dynamics of convection, we follow the philosophy of RKW and WKR on the model setup and hence configure the model with a minimum but essential set of physics processes. Included parameterized physics are the warm-rain and ice-phase microphysics scheme of Hong and Lim [2006], which is a modified version of Lin et al. [1983], and the turbulence mixing scheme of Deardorff [1980] that uses a prognostic value of turbulent kinetic energy, with a modification of Takemi and Rotunno [2003, 2005]. The Coriolis effect, surface friction, land-surface processes, and atmospheric radiation processes are neglected.

[12] The model domain has a dimension of 300 km (the east-west, x, direction) × 60 km (the north-south, y) × 17.5 km (the vertical, z), with an open condition at the east and west lateral boundaries, the periodic condition at the north and south lateral boundaries, free surface at a constant pressure at the top boundary, and free slip at the bottom boundary. The upper 6-km layer is set to be wave-absorbing for minimizing the effects of reflection at the model top. The domain is discretized on the Arakawa C-grid with a spacing of 500 m in the horizontal and 70 levels in the vertical. The horizontal grid spacing of 500 m is employed in the recent cloud-resolving simulations [James et al., 2005, 2006]. The vertical grid spacing corresponds to about 250 m; this may be a little coarse for squall lines in the tropical environment because of their shallow cold pools [Zipser, 1977]. However, Takemi [2007] checked the sensitivity of the squall-line features (such as precipitation intensity and cold pool strength) to vertical grid spacing under tropical and midlatitude temperature conditions and found that there were no significant differences in the responses to environmental profiles. Thus the vertical grid spacing of 250 m is sufficient for discussing the convection dynamics.

2.2. Experimental Design

[13] In order to determine the environmental temperature and moisture, we use the analytic form of temperature and moisture profiles of Weisman and Klemp [1982, hereafter WK82], which originally was intended to represent a typical condition for strong convective storms in midlatitudes. The WK82 analytic functions for environmental potential temperature θenv and relative humidity RH are given as follows:

equation image

and

equation image

where ztr = 12000 m is the tropopause level, θtr and Ttr represent potential and actual temperatures at the tropopause (in WK82 θtr = 343 K and Ttr = 213 K), θ0 = 300 K the surface potential temperature, g the gravity acceleration, and Cp denotes specific heat at constant pressure.

[14] Various temperature profiles representing different environmental static stability can be defined here by changing the value of θtr. In Takemi [2007], the midlatitude environment was defined as θtr = 343 K and the tropical environment as θtr = 358 K: these values were chosen from the comparison with the United States Standard Atmosphere [Holton, 1992] and the observations in the tropical western Pacific [Takemi et al., 2004]. Here we change this parameter more systematically as θtr = 343, 348, 353 and 358. A smaller (larger) θtr value, that is, a smaller (larger) θenv, means a colder temperature environment, and is regarded as a midlatitude (tropical) environment. Static stability, defined here as temperature lapse rate, is also used to describe the temperature environment (i.e., higher static stability indicates a warmer environment). Note that the tropopause height is fixed at a constant level irrespective of θtr in order to exclude the effects of high tropopause in warmer environments (such as on a CAPE value). The tropospheric moisture profiles above the 1.5-km height are defined by (2). On the other hand, the water vapor mixing ratios in the lowest 1.5-km levels are determined with a constant value of qv0; however, if RH becomes greater than 95%, the mixing ratios are reduced in order for RH to be this upper limit to prevent a saturated condition. The choice of the qv0 value is described shortly.

[15] A series of numerical experiments are performed by systematically changing the combination of θtr and qv0. Since our focus here is not on the effects of unstable available energy (i.e., CAPE) but on the effects of environmental temperature profile itself, the combination is chosen to be consistent with our concept. If only θtr is varied with a fixed value of qv0, the value of CAPE would be at the same time changed. In this case, the convection response to θenv profile can not be separated from the response to CAPE. Rather, we change the value qv0 for different θtr cases so as to keep CAPE unchanged.

[16] There are one reference experiment and three series of numerical experiments, each series consisted of the cases with θtr = 343, 348, 353, and 358. The reference case is defined as θtr = 343 K and qv0 = 16 g kg−1, a little moister than the original WK82 sounding (their choice was qv0 = 14). With this condition CAPE is 3709 J kg−1. Increasing θtr with qv0 maintained makes the CAPE values decrease as 1772, 2668, and 1081. We can then create series of experiments by adjusting qv0 with CAPE maintained: the θenv profile having a constant CAPE is set by decreasing (increasing) qv0 with smaller (larger) θtr. In this way, three series of sensitivity experiments are defined as the environments with CAPE = 1.7 × 103 (referred to as the C17 cases), 1.0 × 103 (referred to as the C10 cases), and 2.6 × 103 (referred to as the C26 cases). All the experimental cases are listed in Table 1. Each case is named with C followed by the first two digits of CAPE plus T followed by the last two digits of θtr (e.g., C17T43 means CAPE = 1.7 × 103 and θtr = 343). The CAPE values examined here are within the range of the environments typically seen in the midlatitudes [Bluestein and Jain, 1985] and in the Tropics [Lucas et al., 1994a; LeMone et al., 1998].

Table 1. Thermodynamic Parameters for the Numerical Experimentsa
SeriesCaseθtrqv0RHsfcCAPECINLCLLFCLNBPWC
  • a

    θtr (K), qv0 (g kg−1), surface relative humidity (RHsfc) (%), convective available potential energy (CAPE) (J kg−1), convective inhibition (CIN) (J kg−1), lifting condensation level (LCL) (m), level of free convection (LFC) (m), level of neutral buoyancy (LNB) (m), and precipitable water content (PWC) (kg m−2), are listed.

 C37T4334316.07337092172310671255547.6
C17C17T4334313.160173462111617911139044.4
 C17T4834814.56617674791815461125447.9
 C17T5335316.07317723172312581107551.3
 C17T5835817.7811772155218891093854.7
C10C10T4334312.155108688126822151030342.8
 C10T4834813.260106174110119311008546.2
 C10T5335314.5661064579181704992149.8
 C10T5835816.0731081387231392979053.4
C26C26T4334314.46626343993114471217446.0
 C26T4834816.07326682572311511212949.4
 C26T5335317.7812648135218201204752.5
 C26T5835819.087263363775381197055.2

[17] The thermodynamic diagrams as defined here are shown in Figure 1 for the C17 cases. Note that if θtr is the same the θenv profiles for the other CAPE cases are exactly the same as shown in Figure 1, while the moisture profiles have different low-level mixing ratios (see Table 1). It is also noted that among the same CAPE cases CIN decreases and qv0 increases as increasing θtr. Figure 2 depicts the potential temperature anomaly from θenv for the air parcel originating at the lowest grid level (i.e., 125-m height) through pseudoadiabatic ascent in the C17 cases. The shape of the vertical profiles of temperature anomalies appears to be similar among the cases shown. These profiles, however, are shifted toward a lower part of the troposphere with higher θtr, which means that the contribution of the buoyancy in the lower levels to the CAPE amount is more significant with higher θtr. This further indicates that a higher θtr case that at the same time has larger qv0 and smaller CIN is expected to produce a stronger convective system. The present study examines how the response to θtr emerges under the present settings.

Figure 1.

Skew T-logp diagrams for the C17 cases with θtr = 343 K, θtr = 348 K, θtr = 353 K, and θtr = 358 K. Bold solid lines indicate temperatures, and bold dashed lines dew-point temperatures. Note that a higher temperature profile corresponds to a higher-θtr case.

Figure 2.

Potential temperature anomaly from the environment obtained by pseudoadiabatically raising the air parcel at the lowest scalar level in the C17 cases.

[18] For each specific θtr and qv0 value, the wind profiles examined are westerly shears of 5 and 15 m s−1 over the lowest 2.5-km depth, which represents respectively a weak and a strong shear environment. The total number of numerical experiments therefore amounts to 26 (13 temperature and moisture cases multiplied by 2 shear cases).

[19] The present study focuses on squall lines that develop perpendicular to shears. As was used in many idealized studies such as in RKW and WKR, the model is therefore initialized with a linearly y-oriented, elliptical thermal of x radius of 10 km and vertical radius of 1 km having a 1.5-K potential temperature excess (random perturbation added) at the thermal center and decreasing to zero at the edge. Random perturbations are intended to accelerate the development of along-line variabilities. The line thermal is centered at the middle of the x range and at the height of 1 km. The simulations are conducted for 4 h. For all the cases, the initial perturbations lead to the development of convective cloud lines for the first 1 h; then the regeneration of convective cells occurs and squall lines develop. In most cases the simulated squall lines strengthen to be a mature system, and in several cases the squall lines significantly weaken by the end of the simulation period. The analyses are conducted for the model outputs at 5 min interval.

3. Results

3.1. Characteristics of System Structure

[20] Here we describe the structures of the simulated squall lines by comparing the results obtained under different θtr conditions. The responses seen in the cases under various moisture conditions with a single value of θtr = 343 K, on the other hand, were examined in detail by Takemi [2006]. He found that the squall-line strength becomes greater as CAPE increases: thus, CAPE can be regarded as a parameter that accounts for the squall-line strength and organization, as long as the temperature environment is the same. In the followings, characteristic features seen in the responses to θtr under the same CAPE conditions are described. The results of the C17 cases are presented.

[21] The C17 results with the weak low-level shear are demonstrated at first. Figure 3 shows the horizontal cross sections of the vertical velocity at the 5-km height around the leading edge of the evaporatively induced cold pool that advances eastward at the end of the simulation time (4 h) at which the convective systems are well organized. The height of 5 km is chosen to examine the intensity of convection. The cold-pool boundary is defined as a surface location where potential temperature perturbation is −1 K. The updrafts in the cases except C17T58 have a cellular structure that is elongated in the x direction; these updraft cells are extending well rearward of the surface gust front, which is a similar feature to the one shown in WR04 (their Figure 13). The cells seem to be regularly distributed in the y direction. On the other hand, the locations of the updraft cells in C17T58 seem to be sparse and are limited within the region about 10 km behind the cold pool edge. The size of the cells seems to be much smaller than that in the other cases. It can also be seen that the width of the band of updrafts shrinks as θtr increases. It is noted that at a lower level (e.g., 1 km) a continuous region of updrafts extends linearly at the leading edge of the cold pool for all the cases except C17T58.

Figure 3.

Horizontal cross section of vertical velocity at the 5-km height (contoured) and the cold-pool boundary at the surface (bold dashed line) at 4h for the weak-shear cases of (a) C17T43, (b) C17T48, (c) C17T53, and (d) C17T58. Vertical velocity is contoured at a 3 m s−1 interval. A 60 km by 60 km portion of the domain is shown.

[22] For all the C17 cases, the along-line variability such as a bow-echo structure is not significant. Therefore an along-line averaging is useful for examining the vertical structure of the system. Figure 4 indicates the vertical cross section of the simulated squall lines averaged in the y direction at 4 h. It is seen that as θtr increases, the across-line width of the system decreases, the volume of surface cold pool decreases, and the degree of the rearward tilt of the system decreases. The precipitation area also diminishes as θtr increases.

Figure 4.

Vertical cross section of system-relative wind vectors, cold-pool boundary (bold dashed line), and rain fields (shading) averaged in the y direction for the weak-shear cases of (a) C17T43, (b) C17T48, (c) C17T53, and (d) C17T58. The unit vector (in m s−1) is indicated in the lower right of each panel. Dashed lines indicate potential temperature perturbation of −1 K, and solid lines total water mixing ratio of 0.1 g kg−1. The fields of rainwater mixing ratio between 0.1 and 1 g kg−1 are lightly shaded, and those greater than 1 g kg−1 are darkly shaded. A 100 km by 12 km region is indicated.

[23] This response of the system structure is basically controlled by the strength of the cold pool. As an measure of the strength of cold pool, a theoretical speed C of the cold pool as a gravity current, defined by RKW, is employed as follows:

equation image

where H is the height of the cold pool, and B is buoyancy that includes water condensate loading. The cold-pool perturbations are defined as negative anomalies of more than −1 K from the environmental potential temperature, and the parameter C is calculated in the cold-pool region between its leading edge and 20-km behind. The time series of the cold-pool strength shown in Figure 5 confirms that the cold pool becomes more intensified with the decrease of θtr. RKW introduced a ratio of cold-pool strength C to low-level environmental shear Δ U and diagnosed the system structure in terms of this ratio CU. Here, CU becomes much larger than 1 as θtr decreases, which suggests that the system tends to tilt rearward in the lower-θtr cases according to the RKW theory. The structures seen in Figure 4 are consistent with the theory.

Figure 5.

Time series of cold-pool intensity (see text for the definition) for the C17 cases.

[24] The response seen in the system structure to θtr appears more pronounced in the strong-shear cases than in the weak-shear cases. The horizontal cross section at the 5-km height in the strong shear (Figure 6) indicates that updrafts are continuously and linearly organized along the leading edge of the cold pool with the lower values of θtr while such a linear organization is not able to be identified with the higher values of θtr.

Figure 6.

The same as Figure 3 except for the strong-shear cases.

[25] In Figures 3 and 6, the horizontal scale of each updraft cell seems to be larger as θtr decreases. This feature is clearly demonstrated by calculating power spectral density for the along-line (the y direction) spatial variation of vertical velocity at a certain level. The along-line spatial spectral densities were computed in the range of 10-km ahead and 40-km behind the cold pool position and were averaged in this x range; then the averaged along-line spectra were further averaged in time during 1–4 h. The computational procedure of the spectra is the same as Takemi and Rotunno [2003]. Figure 7 depicts the power spectral densities in the along-line direction at the 1-km and 5-km height for the C17 weak-shear cases. The spectral distribution at the 1-km height clearly indicates that the scale of peak power and the overall power itself increases as θtr decreases. Although such a feature seems not to be so significant for the spectra at the 5-km height, there is definitely a tendency toward a larger scale with the decrease of θtr. This is consistent with what is shown in Figure 3. James et al. [2006] showed that the scale of the coherent features within a squall line is closely related to the cold pool strength and stronger cold pools favor larger scales, which is also true for the present results. The relationship between updraft cells and cold pools is further discussed in Section 4.

Figure 7.

Power spectral density of vertical velocity at (a) the 1-km level and (b) the 5-km level for the along-line (y) direction. A k−2/3 line is also plotted for reference.

3.2. Statistics of System Intensity

[26] In order to compare the intensity of the simulated squall lines under the various environmental conditions, the peak values for updraft velocity and precipitation intensity are useful parameters [WKR; WR04; McCaul et al., 2005]. At every model output time (i.e., 5-min interval), the maximum values of updraft velocity and precipitation intensity are calculated within an analysis domain defined as follows: the domain has a 50 km by 60 km area whose east boundary is at 10 km ahead of the eastward-moving cold-pool front and west boundary is at 40 km behind the cold-pool front. The location of the cold pool front translates with time and thus the analysis domain moves accordingly. This domain is used for the analyses described hereinafter. From the time series of these maxima during 1 to 4 h, means and standard deviations are then calculated. It is noted that the precipitation intensity is defined as the accumulated precipitation for 5 min.

[27] Figure 8 shows the means and standard deviations of the maximum updraft for all the experimental cases. As θtr increases, the peak updraft unanimously decreases for all the experimental series. It should be emphasized that the environment with an identical amount of CAPE does not lead to a comparable strength of updrafts; this is not consistent with the parcel theory that gives theoretical maximum updraft as (2 CAPE)1/2 by assuming adiabatic ascent of air parcel. The major difference among the identical CAPE cases with various θtr is static stability and low-level moisture content. On the other hand, with the same θtr value, updraft strength (and hence system intensity) depends closely on the amount of CAPE, as found in our previous study [Takemi, 2006]. Therefore CAPE can be a proper parameter in diagnosing the strength of updrafts so long as the environmental temperature is identical. The comparison between the results with the weak and the strong shears indicates that the sensitivity to the θtr value is more significant in the stronger shear cases.

Figure 8.

The mean (symbols) and standard deviation (error bars) of the maximum updraft velocity in the analysis domain during 1–4 h for all the cases with the low-level weak and strong shears.

[28] The statistics for the precipitation intensity maxima are shown in Figure 9. In contrast to the features identified in Figure 8, the peak precipitation generally increases as θtr increases. This feature is more pronounced in the stronger shear cases, although some cases with higher θtr values fail to follow the trend because of the absence of an organized squall-line structure. In terms of peak precipitation intensity, the results seem to indicate that the environment with higher θtr is more favorable. In other words, a warmer temperature environment produces more intense precipitation as long as the environmental CAPE is the same. With the same temperature environment, however, the peak precipitation intensity increases as CAPE becomes larger.

Figure 9.

The same as Figure 8, except for the maximum precipitation intensity at the surface.

[29] In addition to the peak values, the statistics for precipitation intensity averaged over the analysis area are examined. The mean precipitation intensity is equivalent to the total precipitation produced by the convective system in the area. Therefore this property is a useful parameter for diagnosing an overall system intensity. Figure 10 shows the means and standard deviations obtained from the time series of the area-averaged precipitation intensity. It is seen that the mean precipitation decreases as θtr increases under the same CAPE conditions, a trend similar to that seen for the peak updraft. In addition, similar to the peak updraft statistics, the amount of CAPE has a good correlation with the mean precipitation intensity if θtr is the same.

Figure 10.

The same as Figure 8, except for the mean precipitation intensity averaged over the analysis area.

[30] In order to explain the difference in the intensity of tropical and midlatitude squall lines in terms of an environmental stability index, Takemi [2007] introduced a parameter that represents the stability for convective overturning: temperature lapse rate Γ in a convectively unstable layer that is between the heights of low-level maximum and middle-level minimum equivalent potential temperatures. Temperature lapse rate is referred to as static stability by Takemi [2007] and also in the present study. Figure 11 exhibits the statistics of the area-averaged precipitation intensity for the cases having the three different CAPE values. The mean precipitation intensities under the same CAPE conditions are clearly delineated in terms of Γ for the both shear cases: the condition with lower static stability leads to more precipitation. With Γ being comparable, on the other hand, a larger CAPE condition is favorable for producing a larger amount of precipitation. The dependence on Γ looks sharper in the cases with the stronger shear. It is also seen that even with sufficiently large CAPE but higher stability the mean precipitation intensity can be notably smaller than with less CAPE but lower stability (e.g., compare the C26 case with Γ ∼ 6.2 and the C17 case with Γ ∼ 6.9). Therefore it is suggested that the environmental static stability should be a critical parameter in diagnosing the system intensity. This point will be further discussed in a later section.

Figure 11.

The same as Figure 8, except for the mean precipitation intensity depicted against temperature lapse rate for the C17, C10, and C26 cases with (a) weak shear and (b) strong shear.

3.3. Updraft and Downdraft Statistics

[31] The characteristics of convective updrafts and downdrafts within precipitating cells will determine the structure and intensity of cells and hence squall-line systems. In this subsection, we examine the features of updrafts and downdrafts based on the statistics in the analysis domain of 50 km by 60 km. In order to focus on convective motion, we chose grid points at which the magnitudes of the vertical drafts were greater than or equal to 1 m s−1 (which was used by LeMone and Zipser [1980] and Wei et al. [1998]) within the analysis domain. Updrafts and downdrafts are hereafter referred to as those having a speed ≥1 m s−1. Mean, maximum, and minimum values are calculated in the analysis area at each height. These statistical values are further averaged over time during 1–4 h.

[32] Figure 12 shows the vertical distributions of the mean and the maximum updrafts and the fractional area of updrafts in the analysis area for the C17 cases with the weak shear. The differences due to θtr seem to be more pronounced in the maximum updrafts than in the means especially at middle and upper levels. The shape of the peak updraft profiles is quite similar to the observations both in the Tropics and in the midlatitude [LeMone and Zipser, 1980; Zipser and LeMone, 1980], and is relevant to heating due to microphysical processes [Xu and Randall, 2001]. The difference in the peak updraft speed is also significant in the lowest 1-km layer, which is obviously due to the difference in the forcing of cold pools (see Figures 4 and 5). In contrast to the velocity profiles, the difference in the fractional area of convective updrafts is quite large at every height. Updraft area extends more widely as θtr decreases; this feature can also be found in the spectral distribution shown in Figure 7. The shape of the updraft area profiles has double peaks at the 2-km and the 8-km heights. The first peak is obviously due to cold pool forcing. The secondary peak aloft, on the other hand, is due to entrainment/detrainment processes, since the updraft area increases as the mean updraft decreases. This is also indicated in Figure 4 in the sense that the updraft area extends more rearward.

Figure 12.

The temporal averaged vertical profiles of (a) the mean (solid lines) and maximum (dashed) updraft velocity and (b) fractional area of updrafts (≥1 m s−1) in the analysis area for the C17 cases.

[33] The above characteristics of the updrafts are closely tied with buoyancy and condensation processes. In order to diagnose these processes, we examine in Figure 13 the vertical profiles of potential temperature anomaly θ′ from the environmental values and cloud-water mixing ratio qc averaged at the updraft grids at each height during 1–4 h. It is indicated that the profiles of both mean and maximum θ′ largely differ depending on the environmental temperature, especially above the 3-km height. Although the difference in the mean qc profile is not so significant as in the θ′ case, the maximum qc value above the 3-km height becomes larger as θtr decreases, which is a feature similar to the θ′ profile. In addition, it was shown that both means and maxima of ice-phase properties, snow and graupel mixing ratios, differed in the same way as in those of θ′: snow and graupel contents increased as θtr decreased (not shown). Overall, the total condensate content increases as the environmental temperature becomes colder.

Figure 13.

The same as Figure 12, except for (a) the mean (solid lines) and maximum (dashed) potential temperature perturbation and (b) the mean (solid) and maximum (dashed) cloud-water mixing ratio associated with the updrafts in the analysis area.

[34] It was shown in Figure 2 that the theoretical buoyancy of a surface air parcel through pseudoadiabatic ascent was almost the same with each other among the different θtr cases; however, the actual θ′ maxima vary significantly in response to the θtr value and exceed the theoretical buoyancy by 1–3 K when θtr ≤ 348. The results showing that ice-phase properties increased with the decrease of θtr suggest that the actual θ′ values (which are larger than the theoretical values) in the lower θtr cases are mostly resulted from additional heating due to the conversion from water to ice. In addition, considering that updrafts become stronger and extend wider as height increases from 5 km to 8 km and that the total ice-phase amount is larger than the cloud-water content, it is suggested that the effects of convergence also contribute to making actual θ′ significantly larger than the theoretical buoyancy. The characteristics of the profiles of buoyancy and water substances shown here are consistent with each other in the sense that more condensation positively feeds back on the positive buoyancy and more buoyancy leads to stronger updrafts and hence more efficient condensation.

[35] Figure 14 compares the vertical profiles of the mean and the maximum downdrafts and the fractional area of downdrafts for the weak-shear cases of the C17 series. Characteristics similar to those seen for updrafts can be identified: more unstable environment (smaller θtr) leads to stronger downdraft peaks and also a larger area of downdrafts. The difference due to the θtr value is again more significant in the peaks than in the means.

Figure 14.

The same as Figure 12, except for downdrafts.

[36] Examining the vertical profiles of mean/minimum potential temperature perturbation at the downdraft grids in the analysis domain (Figure 15a), it is seen that in the lowest 2-km layer negative perturbations become larger as θtr decreases; in other words, stronger downdrafts are associated with colder temperature perturbations. On the other hand, the vertical profiles of mean/minimum relative humidity (Figure 15b) indicate that the middle and upper layer of 2–10 km heights becomes drier as θtr decreases. Therefore considering that the environmental relative humidity in the 2–10-km layer is exactly the same among the cases shown, the drier condition in a lower θtr case is expected to lead to greater cooling due to precipitation evaporation. This is consistent with the fact that rain-water mixing ratio decreased as θtr decreased (not shown).

Figure 15.

The same as Figure 12, except for (a) the mean (solid lines) and minimum (dashed) potential temperature perturbation and (b) the mean (solid) and minimum (dashed) relative humidity associated with the downdrafts in the analysis area.

[37] The characteristics of the convective updrafts and downdrafts shown above can be identified in the other experimental series with different CAPE values. Figures 16 and 17 show the vertical profiles of the mean and the maximum updrafts and the fractional area of updrafts in the analysis area for the weak shear cases of the C10 and C26 series, respectively. Similar to the features found in the C17 cases, it is seen that the difference in the peaks is more pronounced than that in the means and that the peak speed and the updraft area become larger as θtr decreases. It is indicated from the comparison of Figures 12, 16, and 17 that the strength of updrafts varies more sensitively to the environmental temperature profile as the environmental CAPE decreases. In other words, the environmental static stability plays a more significant role in controlling the updraft intensity in a lower CAPE environment. The comparison among the different CAPE series further shows that the magnitude of maximum updrafts generally increases as the environmental CAPE increases; this suggests that the amount of CAPE still controls the updraft intensity as long as the environmental temperature profile is identical.

Figure 16.

The same as Figure 12, except for the C10 cases.

Figure 17.

The same as Figure 12, except for the C26 cases.

4. Summary and Discussion

[38] The present sensitivity analyses indicated that the intensity of the simulated squall lines that develop in low-level shears perpendicular to the convective lines is strongly dependent on the environmental temperature profile. This dependence was clearly shown by the experimental series with surface-based CAPE being maintained. The results indicating that wider and stronger updrafts were produced in colder environments are consistent with the previous observational studies [LeMone and Zipser, 1980; Lucas et al., 1994a; Xu and Randall, 2001] in spite of the idealized modeling setup. According to the parcel theory, the strength of updrafts and hence the organization and intensity of squall lines are expected to be more or less controlled by the amount of CAPE. However, stronger squall lines were simulated with smaller θtr but with CAPE being unchanged. Moreover, some results showed that a stronger system is generated even with smaller CAPE and lower stability than with larger CAPE and higher stability, irrespective of the magnitude of the low-level shear. In addition to updraft strength and precipitation intensity, stronger cold pools are generated in a less stable environment (which will be discussed shortly). It was shown that stronger cold pools induce wider and stronger updraft cells that lead to the formation of intense convective systems and heavier precipitation. This result is consistent with the sensitivity study of James et al. [2006] who showed that the scale of coherent structures within the squall-line system is closely related to the cold pool strength and stronger cold pools favor larger scales.

[39] One might argue that the different responses of squall-line intensity to environmental profile are caused not only by temperature difference but also by moisture difference. Takemi [2006] showed that a drier condition in the low levels has a more detrimental impact on the squall-line intensity under the same temperature condition. On the other hand, under the present temperature setting a drier low-level condition (i.e., a smaller θtr case) positively affects the squall-line intensity. Because the influences of moisture profile vary depending on temperature profile, the sensitivity results with CAPE unchanged are considered to be mainly due to the difference in temperature profile.

[40] Comparing the results with the two shear profiles, it is indicated that the simulated squall lines are stronger in the strong shears than in the weak shears if the lapse rate is large, while the squall lines become stronger in the weak shears than in the strong shears if the lapse rate is small. This mechanism can be understood by the RKW theory by comparing cold pool strength and shear magnitude. In other words, the intensity of the shear-perpendicular squall lines examined here is strongly controlled by the strength of cold pools.

[41] A stronger cold pool induces slab-like convective lifting at their leading edge, while a weaker cold pool produces relatively weak lifting that leads to a discrete cellular feature of updrafts [James et al., 2005]. The slab-like ascent above cold pool is considered to be due to moist absolutely unstable layers (MAUL) that are characterized by a saturated layer in which equivalent potential temperature decreases with height [Bryan and Fritsch, 2000; Mechem et al., 2002]. The present analysis showing a wider area of convective updrafts in the presence of stronger cold pool is consistent with these previous studies that deal with the slab-like lifting and the MAUL environment. A wider area of updrafts, in other words, suggests that the size of updraft cells becomes larger in the colder environments. According to Lucas et al. [1994a, 1996] who observationally showed that the diameters of updraft cores over the midlatitude continents are larger than those over the tropical oceans for convective clouds, the larger updraft cells are considered to reduce the detrimental effects of entrainment of environmental air and to be favorable for maintaining the cells more buoyant. Tao et al. [1995] also pointed out that stronger updrafts can experience less detrainment in the middle troposphere. The present analysis of potential temperature excesses above the levels of free convection clearly indicated that the maximum excesses in the warmest environment are substantially smaller than those obtained from adiabatically lifted parcels (compare Figures 2 and 13 for C17T58). This seems to be the evidence for active entrainment of environmental air in warmer environments.

[42] Less diluted updrafts in the colder environments, by maintaining their strength, are effective in driving and enhancing deep convective overturning. Stronger convective overturning would activate the interaction between the convective system and the environment. Therefore drier middle layers seen in the colder environments (Figure 15) are considered to be the manifestation of this active interaction. The drier environmental conditions in the low-levels, in contrast, do not seem to affect the relative humidity of downdrafts in the low-levels. Therefore it is the drier middle layer that is favorable for the precipitation evaporation that will generate stronger cold pool [Zipser, 1977]. In this way, larger and stronger updraft cells lead to stronger cold pool.

[43] The analysis of peak precipitation intensity was a seemingly unexpected result that shows that the peak intensity increased as θtr increased under identical CAPE conditions, which is an opposite sense found in the means of precipitation intensity and updraft. This relationship between peak precipitation intensity and environmental temperature may be due to moister conditions for downdrafts in the warmer environment and hence less evaporation of precipitation. The moist condition is therefore considered to be preferable for producing heavier precipitation in the very short term.

[44] McCaul et al. [2005] examined the sensitivity of supercellular convective storms to environmental temperature and found that the peak updraft velocities were larger in a colder environment while the peak precipitation intensity exhibited a wide range of variability and even a trend opposite to the peak velocity. However, by defining precipitation efficiency as the ratio of peak rainfall at the ground to precipitable water, they showed that the precipitation efficiency has the same trend against environmental temperature as the peak updraft velocity. On the other hand, the peak precipitation intensity in our study did not show such a trend despite using the same precipitation efficiency. This may be due to a difference in the governing dynamics of convection between squall lines and supercells.

[45] We have shown that the intensity of squall lines is dependent more on the environmental temperature lapse rate in a convectively unstable layer than on CAPE. This leads to a doubt on using parcel theory in diagnosing the activity of deep convection within squall-line systems or the overall intensity of the system. Our previous study [Takemi, 2007] showed that among the standard stability indices for diagnosing thunderstorm potential and intensity a parameter that takes into account environmental temperature lapse rate is more suitable than a parameter calculated based on adiabatically lifted parcel. We consider that the reason why the environmental stability in a convective unstable layer well describes the system intensity is due to the fact that updrafts in the layer that is moist absolutely unstable [Bryan and Fritsch, 2000] exhibit a slab mode of layer overturning [Mechem et al., 2002; James et al, 2005]. Thus a simple parcel thinking seems not to be appropriate for the convective overturning within organized convective systems. The present analysis strongly suggests that the magnitude of the static stability controls the intensity of overturning and therefore squall lines as a system.

[46] The dominant scale of convective updrafts becomes smaller at the middle levels than at the lower levels (Figure 7). In addition, updrafts in the middle (and also in the upper layer) had a discrete cellular feature (Figures 3 and 6). Considering that the static stability is relevant to the characteristics of convective updrafts, the discrete cellular feature seen above the convectively unstable layer for all the simulated squall lines can be explained by the fact that the layer is absolutely stable (see Figure 1). Updrafts need to penetrate into this absolutely stable layer in order for convective systems to be maintained and further enhanced; the penetration into the stable layer will lead to a discrete cellular feature of the updrafts.

[47] In the present modeling setup, we assume that the tropopause heights are the same among the different θtr cases. This assumption imposed some limitation on the shape of buoyancy: theoretical parcel buoyancies among the cases were nearly identical (Figure 2). Comparing the buoyancy profiles, Lucas et al. [1994a] described that the tropical oceanic environment is “skinny” while the buoyancy shape over the continental United States is “fat”. The difference in the shape of buoyancy profile will affect the updraft strength and thus the intensity of convective systems. Lucas et al. [1996] suggested that the shape of CAPE should be relevant to the difference in the updraft strength over the continent and the ocean. The present modeling setup is not appropriate for investigating these effects.

[48] Further, the shape of buoyancy profile affects the parcel acceleration, the level of maximum ascent, and hence the strength of convection: among the cases examined here, the highest θtr case in which CAPE is weighted toward the lower troposphere will potentially produce strongest convective cells. This is expected to be true in considering the effects of buoyancy shape in similar temperature environments. In this study, on the other hand, the lower tropospheric stability is shown to have profound effects on the squall-line strength: an effect that we consider is more significant than the buoyancy shape. A further work is required in order to explore and clarify the relative importance between the stability and the buoyancy shape under comprehensive environmental conditions.

5. Conclusions

[49] We have extended the studies of Takemi [2006, 2007] who examined the sensitivity of squall lines to environmental shear, moisture, and temperature profiles to systematically investigate the effects of environmental static stability on the structure and intensity of squall lines. The motivation of our study is to comprehend the difference of the squall-line intensity under various temperature conditions that represent tropical, sub-tropical, and midlatitude regions, which has partly been discussed in previous studies [e.g., Zipser and LeMone, 1980; Lucas et al., 1994a; Xu and Randall, 2001]. Because of the diversity of shear conditions for squall lines [Bluestein and Jain, 1985; LeMone et al., 1998], we restrict to shears that are line-perpendicular, low-level westerlies.

[50] The results of the sensitivity simulations reveal that the environmental static stability in a convectively unstable layer of the lower half of the troposphere well delineates the intensity of squall lines in both weak and strong shears. An environment with a less stable stability is favorable for generating stronger updrafts and also stronger cold pools. The intensity of cold pools significantly affects the scale and strength of convective updrafts, which will lead to the enhancement of tropospheric overturning and hence the development of stronger convective systems.

[51] It has long been argued that CAPE can be a parameter that diagnoses the development and strength of convective storms and systems. Fankhauser [1988] showed that there is no clear impact of CAPE on thunderstorms in terms of their precipitation efficiency. Lucas et al. [1994b] insisted that the difference in updraft strength between continental and oceanic convective storms cannot be attributed to the difference in CAPE. The present analysis clearly indicates that the amount of CAPE can only be a good measure for diagnosing the intensity of convective systems so long as the environmental lapse rate is identical.

[52] The present study strongly suggests that the first thing we should do in order to diagnose the organization and strength of squall lines is to examine the environmental temperature lapse rate, that is, the static stability, in a convectively unstable layer. Then other parameters such as CAPE, precipitable water, moisture content in the low levels and in the middle levels as well, and other standard stability indices are to be consulted. Since the temperature lapse rate in a specific region generally depends on the climatological and geographical features of the region, the intensity of the convective systems that develop in a region of interest is critically influenced by its climate. In comparing the features of convective systems in various climate regions, one should take into account the climatological features of the temperature environment.

[53] The present study specifically focuses on the squall lines that develop in line-perpendicular, low-level westerly shears. However, an optimal shear profile for generating the strongest system may differ depending on the temperature environment. In the tropical environment, easterly shears and line-parallel shears are also important for squall lines [LeMone et al., 1998]. This type of environments should be investigated in a future study.

Acknowledgments

[54] The comments by three anonymous reviewers were greatly appreciated for improving the original manuscript. This work was supported partly by Grant-in-Aid for Scientific Research 19740287 from Japan Society for the Promotion of Science. The GFD Dennou Library (http://www.gfd-dennou.org/index.html.en) was used for drawing some of the figures and computing power spectral density.

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