This study develops conceptual models of how a land–water interface affects the strength and structure of squall lines. Two-dimensional numerical simulations using the Advanced Regional Prediction System model are employed. Five sets of simulations are performed, each testing eight wind shear profiles of varying strength and depth. The first set of simulations contains a squall line but no surface or radiation physics. The second and third sets do not contain a squall line but include surface and radiation physics with a land surface on the right and a water surface on the left of the domain. The land is either warmer or cooler than the sea surface. These three simulations provide a control for later simulations. Finally, the remaining two simulation sets examine squall-line interaction with a relatively cool or warm land surface. The simulations document the thermodynamic and shear characteristics of squall lines interacting with the coastline. Results show that the inclusion of a land surface did not sufficiently affect the thermodynamic properties ahead of the squall line to change its overall structure. Investigation of ambient shear ahead of the squall line revealed that the addition of either warm or cool land reduced the strength of the net circulation in the inflow layer as measured by ambient shear. The amount of reduction in shear was found to be directly proportional to the depth and strength of the original shear layer. For stronger and deeper shears, the reduction in shear is sufficiently great that the buoyancy gradient circulation at the leading edge of the cold pool is no longer in balance with the shear circulation leading to changes in squall-line updraft structure. The authors hypothesize two ways by which a squall line might respond to passing from water to land. The weaker and more shallow the ambient shear, the greater likelihood that the squall-line structure remains unaffected by this transition. Conversely, the stronger and deeper the shear, the greater likelihood that the squall line changes updraft structure from upright/downshear to upshear tilted.
A squall line is a line of active thunderstorms, either continuous or with breaks, including contiguous precipitation areas resulting from the existence of the thunderstorms (Glickman 2000). Many squall lines last for hours and are capable of producing a variety of damaging weather. Although only the strongest squall lines typically are associated with tornado activity, many produce high winds, hail, or other significant weather.
Many observational studies have noted the importance of ambient wind shear to squall-line strength and longevity (e.g., Barnes and Sieckman 1984; Bluestein and Jain 1985; Bluestein et al. 1987; Evans and Doswell 2001). Convective-scale modeling has confirmed the correlation between shear and squall-line characteristics. Thorpe et al. (1982) proposed that long-lived tropical squall lines are a consequence of confining the ambient shear to the lowest levels, similar to results of Dudhia et al. (1987).
A theory describing the structure and life cycle of squall lines was proposed by Rotunno et al. (1988, hereafter RKW), Weisman et al. (1988, hereafter WKR), and revisited by Weisman and Rotunno (2004). This theory involves the relative magnitudes of low-level horizontal vorticity associated with the ambient low-level wind shear and the cold pool circulation. A developing squall line initially has updrafts that tilt downshear due to the influence of horizontal vorticity associated with the ambient shear. Later in the life cycle, rain-filled downdrafts undergo evaporative cooling that form a cold pool at the surface. The buoyancy gradient at the leading edge of the cold pool generates a circulation that opposes the vorticity associated with the shear. A relative balance between these vorticity sources leads to more erect updrafts and deeper lifting of boundary layer air ahead of the squall line. Any further strengthening of the cold pool leads to the development of an upshear-tilted system, sometimes producing a rear-inflow jet (Weisman 1992; Lafore and Moncrieff 1989).
The literature reveals that squall lines are sensitive to shear and convective available potential energy (CAPE) as environmental parameters and cold pool strength as the primary internal parameter (e.g., RKW; WKR; Weisman and Rotunno 2004). Land–water interfaces could significantly impact these environmental parameters, and, perhaps indirectly influence resulting cold pool characteristics. Therefore, land–water interfaces might impact the strength and structure of squall lines. It has been theorized that the coastline just west of Tallahassee, Florida (Fig. 1), reduces the intensity of north–south-oriented, nonsupercell squall lines as they approach the city. Although this is a much discussed topic in Tallahassee, no research concerning the effects of coastline shape on squall lines has apparently been completed locally or elsewhere.
The primary objective of the current study is to develop two-dimensional conceptual models that describe whether and how coastlines affect squall lines. Two-dimensional numerical simulations are used to develop the conceptual models. It is unlikely that two-dimensional conceptual models can completely explain any apparent squall-line demise near Tallahassee. Nonetheless, this preliminary study investigating two-dimensional processes will provide valuable insight that can be explored in future studies incorporating three-dimensional flows.
2. Model setup and input
All simulations employed the Advanced Regional Prediction System (ARPS) model (Xue et al. 2000) in its two-dimensional configuration. Table 1 shows our model specifications. Since previous studies have indicated that the Coriolis force exerts a minimal effect on two-dimensional mesoscale simulations of short duration (e.g., Fovell 1991), we assumed it to be zero. Only Kessler (1969) warm rain microphysics was used for precipitation processes. Creating a configuration that minimized lateral boundary feedback was a major goal. Many studies cited in the introduction have examined this issue, and our goal was to configure the ARPS model in a similar way. Benchmark simulations that reproduced the results from these earlier studies indicated that boundary condition problems were undetectable in our runs. Our model domain was chosen to represent the two-dimensional scenario of a north–south-oriented squall line along the U.S. Gulf Coast, near Tallahassee, Florida, where the coastline orientation is approximately parallel to the squall line (Fig. 1). Simulations with a land surface contained the land on the rightmost one-third of the domain and a water surface on the leftmost two-thirds portion. This configuration represents the conditions that a north–south-oriented squall line would experience as it approached the coastline apex near Tallahassee (line A–B in Fig. 1).
Many mesoscale modeling studies have initialized the base-state atmosphere using conditions typical of squall lines in the Midwest United States (e.g., Klemp and Wilhelmson 1978; RKW; Weisman 1992; Fovell and Ogura 1988). We hypothesized that thermodynamic profiles associated with Gulf Coast squall lines would be different. To investigate, a squall-line climatology was performed for the Gulf Coast. Four years of data (1997–2000) were examined during October through April when squall lines occur most often. Sixty-two days were found to contain an intense line of convection (>45 dBZ) passing Tallahassee. Tallahassee sounding data were used to describe the pre-squall-line environments of the individual days. Sea surface temperatures (SST) and surface air temperatures just south of Tallahassee were from a site operated by the National Data Buoy Center (NDBC 2001; Fig. 1). Soil temperature–moisture and air temperatures over land were obtained from a monitoring station near Tallahassee (Fig. 1; SCAN 2001). Means of the above data provided the initial temperature–moisture profile along with soil temperature/moisture and SST for our model runs (Table 1). In addition, surface roughness values were obtained from suggested values in the ARPS user’s guide. These values are listed in Table 1. Land surface roughness values for evergreen forest were used since the area around Tallahassee is mostly of that type.
The climatological thermodynamic profile used for the base state is shown in Fig. 2. We specified the surface air temperature equal to the SST at the start of the simulations, thereby ensuring that the water temperature would not alter air temperatures over the water. Thus, any air temperature perturbations are caused by the squall line and/or land surface. The mean humidity profile ahead of Gulf Coast squall lines (Fig. 2) is moister than Midwest profiles, and the mean temperature profile also exhibits differences. Although the environments of nonsevere (severe) Midwest squall lines had an average CAPE of 1374 m2 s−1 (2260 m2 s−1) (Bluestein and Jain 1985; Bluestein et al. 1987), the Gulf Coast environments have an average CAPE of 1512 m2 s−1, consistent with the majority of our squall lines being nonsevere. The mean surface temperature for Midwest severe squall lines is 8°C warmer than along the Gulf Coast.
The mean wind shear profile for our Gulf Coast squall lines is ∼18.0 m s−1 over the lowest 2.5 km of the sounding (not shown). Many previous modeling studies have categorized 17.5 m s−1 (2.5 km)−1 as moderate shear (e.g., RKW; Fovell 1991). We chose a representative range of Gulf Coast shear profiles and depths for testing (Fig. 3). Since the simulated squall line should propagate through the domain at a realistic speed, a wind profile similar to Fovell and Ogura (1988) was used. That is, wind velocities near the surface had an easterly (negative, toward the left) component that gradually changed to a westerly (positive, toward the right) component with altitude. It should be noted that no adjustments for frictional effects were made to the wind profiles. Therefore, base-state wind profiles are not in frictional balance. Two shear depths were tested. Shallow-shear simulations contained shear over the lowest 2.5 km of the atmosphere, while deep-shear simulations exhibited shear over the lowest 5 km. The two shear depths were tested over a range of strengths (7.5, 12.5, 17.5, and 22.5 m s−1) based on the climatology.
Convection was initialized with a 2.5-K warm potential temperature ellipsoid having a radius of 10 km in the horizontal and 1400 m in the vertical. The location of the perturbation varied in each simulation based on wind shear. The initial bubble was placed so each squall line intersected the coastline at the same point in time for each simulation.
Five sets of simulations were performed, each testing all eight wind shear profiles (Fig. 3). The first set included a squall line but no surface or radiation physics. The second and third sets of simulations did not include a squall line but did contain either a relatively warm or cool land surface with the surface and radiation physics. These three sets of simulations served as controls since they investigated circulations induced solely by either the squall line or land surface. The remaining two simulation sets included a squall line and surface and radiation physics. Table 2 lists the five sets of simulations and their abbreviations.
One should note that both the surface and radiation physics are used in simulations with a land surface. The use of surface physics alone could have been used to prescribe the land and water surface temperatures and allowed the constant land–water surface temperatures to enforce temperature, moisture, and momentum fluxes. However, it was decided to allow the land surface to heat and cool in a simulated diurnal cycle similar to the way that sea–land breeze processes typically are modeled. This required that both surface and radiation physics be used for control simulations.
Additional simulations with neutral surface and radiation physics were also performed. In these simulations, the land surface and surface air temperatures were equal. However, since the warm and cool land simulations represent the extreme cases of surface processes acting on the environment, only the two cases will be discussed here.
3. Environmental properties
We first describe how the land–sea interface affects environmental CAPE and low-level wind shear during day and night conditions. Convective available potential energy was calculated two ways, that is, using the surface parcel method (CAPE) and the most unstable parcel in the lowest 300 hPa (MUCAPE). CAPE and MUCAPE were calculated at every grid point ahead of the squall line at 1-km intervals out to 40 km for CS, ESLC, and ESLW. In the control simulations without a squall line (CLC, CLW) we calculated CAPE and MUCAPE at 1-km intervals from the coastline inland to 40 km. In both cases, these individual values were averaged to provide a mean at every time step of the simulation. Mean values were computed because an inspection of early results showed that shear and instability at a single point ahead of the squall line were unrepresentative due to wind and temperature perturbations. The choice of 40 km was based on manual inspection of the simulations, which indicated that the greatest variability occurred within this range ahead of the squall line.
Results from the three sets of control simulations (Table 3, left) reveal how the squall line and land surfaces independently affect CAPE and MUCAPE. Conversely, results from the experiment simulations (Table 3, right) show the combined effects of both the land surface and squall line. Mean values of CAPE and MUCAPE are given at 5 h into the simulation. Thus, they were derived over land for those simulations with a land surface. Results prior to 5 h (not shown) indicate that all simulations with land deviate only slightly from the base state. Only when the squall line approaches land does the instability ahead of it change.
In all three control simulations (Table 3), CAPE exhibits varying degrees of change from the base-state value of 1512 m2 s−2 (Fig. 2). Both CS and CLC show reductions in CAPE, with the greatest reductions occurring with CLC. CAPE in these simulations is ∼1400 m2 s−2 smaller than the base state. Conversely, the CLW simulation exhibits CAPE that is between 339 and 719 m2 s−2 greater than the base state. Comparing the three sets of control simulations shows that heating and cooling of near-surface air parcels affect this surface-based stability parameter more than does the squall line itself.
MUCAPE is a useful tool for evaluating whether parcels within 300 hPa of the surface can be lifted to produce greater buoyancy than surface parcels. In all the control simulations MUCAPE varies much less than CAPE (Table 3, left). For example, CLC and CLW show MUCAPE between 199 and 719 m2 s−2 greater than the base state of 1512 m2 s−2. Interestingly, MUCAPE for the cool land simulations is greater than the base state, indicating that the cool land increases a parcel’s instability at some level above the surface. This is contrary to the effect on surface-based parcels where CAPE was reduced, indicating that the instability of parcels aloft is affected much less by surface cooling than are surface parcels. This increase of MUCAPE in the cool land simulations is investigated in more detail in section 4. Identical values of CAPE and MUCAPE in CLW indicate that the surface is the most unstable parcel in the lowest 300 hPa.
The experiment simulations (Table 3, right) show the combined effects of a squall line and land surface on instability. The results are similar to those of the control simulations with a land surface, that is, changes in CAPE and MUCAPE from the base state are similar. Thus, the land appears to play a greater role in changing the environmental instability than the squall line. However, it is important to note that the experiment simulations show that CAPE and MUCAPE are, on average, smaller than in the CL simulations. The addition of a squall line may explain this additional decrease. Processes related to the squall line itself help to reduce CAPE and MUCAPE. Examination of model soundings and various cross sections from the CS runs (not shown) show the largest contributor to this reduction is the warming in the middle and upper levels from outflow ahead of the squall-line updraft.
To summarize, the control and experiment simulations reveal that the increase or decrease in instability ahead of the squall line is approximately the sum of influences from the squall line and the relatively cool or warm land. However, the land surface exerts the greatest influence on the changing instability.
Low-level ambient shear is vitally important in controlling the strength and structure of squall lines. Specifically, RKW, WKR, and more recently Weisman and Rotunno (2004) show that the net circulation in the inflow layer of the squall line (as is associated with the ambient vertical shear) and its interaction with the circulation associated with the cold pool have an impact on squall-line structure. This net circulation of the inflow layer is measured most simply by calculating the bulk difference between the surface wind and the wind at the top of the inflow layer. We follow that approach to approximate the net impact of the vertical shear. Although tendencies in shear magnitude could result from changes in cold pool depth, we do not believe that depth changes are significant. For simulations without a squall line, shear was calculated between the surface and top of the specified shear layer (either 2.5 or 5.0 km). Winds at these two levels were subtracted at every grid point ahead of the squall line out to 40 km (or from the coastline inland to 40 km for simulations without a squall line). The individual shear values over the 40-km range then were averaged to provide a mean shear at every time step. An overview of shear values for the various simulations is shown in Fig. 4. It should be noted that the plots for weak shear in both the shallow and deep cases (Figs. 4a,b) are highly variable. This variability occurs because base-state wind speeds in the shear layer never exceed 4.0 m s−1 (Fig. 3). These weaker wind speeds are affected greatly by wind perturbations due to the squall line and thus contribute to greater variability in shear (Figs. 4a,b). Although the plots for the weak-shear cases exhibit this limitation, they are included for completeness.
Considering the moderate-shear cases first (Figs. 4c,d), mean shear values ahead of the squall line are nearly equal during the first 160 min among the CS, ESLC, and ESLW simulations for both shear depths. Once the squall line approaches the influence of the coastline (>200 min), a decrease in shear is noticeable for the CS run in both the shallow- and deep-shear simulations (Figs. 4c,d). This decrease is due to the squall line’s modification of its upstream environment. Such decreases in low-level ambient shear have been observed in previous two-dimensional simulations (e.g., Garner and Thorpe 1992; Fovell 2002; Weisman and Rotunno 2004).
The ESLC and ESLW simulations also exhibit decreased mean shear. Comparing shears after the initial development period, the mean shear of the ESLC and ESLW simulations generally is smaller than those of the CS. For example, the shallow-shear simulations for ESLC and ESLW exhibit values averaging 5.2 and 5.8 m s−1 less than the CS, respectively. The deep-shear land simulations for ESLC (ESLW) exhibit a mean shear averaging 4.4 (3.4) m s−1 less than the CS.
The strong-shear simulations for both the shallow and deep layers (Figs. 4e,f) have similarities to the moderate-shear cases (Figs. 4c,d). For example, shallow and deep CS runs exhibit a slight decrease in shear. However, for the strong-shear cases during the initial development period prior to ∼180 min, both ESLC and ESLW have smaller shear than the CS. Recall from the 22.5 m s−1 profile (Fig. 3) that both the shallow- and deep-shear cases had a −8.5 m s−1 surface wind that is stronger than the other shear profiles. This greater wind speed advects the land air over the water faster and farther than do the other wind profiles. Therefore, the squall lines encounter the effects of the land at the start of the ESLC and ESLW simulations. Specifically, the modification of the shear environment by offshore sea (onshore land) breeze circulations due to heating or cooling of the land surface reaches the squall line earlier in the simulation than for the moderate and weak-shear profiles. This is the reason that shear values for the ESLC and ESLW simulations are 5–15 m s−1 less than those of the CS. These effects are further illustrated and explained in sections 4a and 4b. An interesting observation in both the moderate- and strong-shear cases is that shear in the ESLC and ESLW simulations exhibits a gradual decrease from ∼180 min to the end of the run. Thus, the land decreases the base-state shear ahead of the squall line a great deal more than in moderate-shear cases. The greater the original ambient shear, the greater the reduction of that shear. The physical processes behind this characteristic are further investigated in section 4.
To better depict the relative contributions of the squall line and land surfaces to the reduction in shear, Fig. 5 contains time series of mean shear for the cool and warm land simulations of the three shallow-shear profiles, that is, the CS, CL, and ESL cases. Cool land simulations are plotted in the left-hand column and warm land in the right-hand column. Thus, Fig. 5 reveals how the squall line and the land independently affect the net circulation in the inflow layer. One should recall that shear is calculated over different parts of the model domain. For example, in experiments with a squall line, shear is calculated 40 km ahead of the line as it moves through the domain. Conversely, in simulations without a squall line, shear is calculated over a fixed range beginning at the coastline and extending 40-km inland. This makes shear in the CL simulations relatively constant over the entire run (black dashed, Fig. 5). Therefore, comparisons between differing control simulations and experiment simulations should be made where the squall line reaches the coastline (∼300 min).
Figure 5 shows that shear in the CLC and CLW simulations reacts differently depending on the temperature of the land. CLC simulations exhibit a reduction of shear strength from the base state of ∼1–5 m s−1. Furthermore, this reduction in shear remains relatively constant throughout the simulation. On the other hand, CLW simulations exhibit a reduction in shear from the base state that decreases throughout the simulation. This is due in part to increasing positive u perturbations caused by the developing onshore sea-breeze circulation. The net circulation reduction in the CLW simulations is ∼2–7 m s−1 from the base state by 300 min into the simulation. One also should note the relation of base-state shear strength to the amount of shear reduction. The strong-shear simulations of CLC and CLW exhibit the greatest reduction in shear from the base state, ∼5 and 7 m s−1, respectively.
One could hypothesize that the ESLC and ESLW simulations would exhibit the combined shear effects of the CS and CL simulations independently. However, this is not always the case. For example, in the strong-shear ESLC simulation (Fig. 5e, ∼300 min) summing the reduction in shear from the CS and CLC simulations does not completely account for the reduced shear in the experiment simulations. The ESLW strong-shear simulations also exhibit this characteristic (Fig. 5f). On the other hand, the reduction in shear for the weak- and moderate-shear simulations (Figs. 5a–d) is approximately equal to the combined effect of both the squall line and land surface. For example, Fig. 5d shows that the CLW and CS each reduce the shear by ∼3–4 m s−1 at 300 min, with ESLW showing a reduction of ∼7 m s−1. These varying results for strong-shear cases, noted in Fig. 5, are difficult to explain utilizing bulk shear values alone. Section 4 presents detailed analyses of selected cases to provide greater insight into these results.
To summarize, results reveal that the increase or decrease in instability ahead of the squall line is approximately the sum of influences from the squall line plus the relatively cool or warm land. The land surface exerts the greatest influence on the changing instability. Examining low-level ambient shear reveals that when a land surface is included in the simulation the reduction in shear ahead of the squall line appears to be a function of both the strength and depth of the original shear layer. The physical mechanisms that cause changes to instability and shear are examined further in section 4.
4. Detailed analyses of selected cases
Two simulations will be examined in detail to understand changes in environmental properties and squall-line structure and intensity as they pass onto a land surface. The moderate shallow shear [17.5 m s−1 (2.5 km)−1] and strong deep shear [22.5 m s−1 (5.0 km)−1] configurations best depict these changes.
a. Moderate shallow shear [17.5 m s−1 (2.5 km)−1]
Figure 6 contains cross sections of buoyancy, system-relative flow, and cloud water centered on the squall line’s updraft before passing the coastline (4 h, left column) and afterward (5 h 50 min, right column). Buoyancy is defined similar to RKW:
where the bar and prime denote the mean and perturbation, respectively, θ is potential temperature, and qυ, qc, and qr are mixing ratios of water vapor, cloud water, and rainwater, respectively. The parameters in Fig. 6 indicate little change in squall-line updraft structure as it passes onshore. In the cool land simulation one should note the shallow layer of negative buoyancy along the surface ahead of the squall line that is due to nocturnal cooling of the land (Fig. 6d).
Figure 7 shows corresponding cross sections of equivalent potential temperature (θe), with the cold pool outlined in red. At both times of the CS run there is a layer of warm θe air near the surface ahead of the squall line (Figs. 7a,b). The CS low-level thermodynamic environment ahead of the line exhibits virtually no change, consistent with the CAPE/MUCAPE values (Table 3).
The addition of the land surface affects the squall line’s θe structure. Compared to the CS, the ESLC simulation (Figs. 7c,d) exhibits changes after coastline passage. For example, before nearing the coast (from ∼350 km onward), the layer of cooler θe along the surface (bottom right of Fig. 7c) is due to nocturnal cooling. This layer extends 65 km offshore due to the easterly wind component near the surface. When the squall line passes the coastline (Fig. 7d), there is a noticeable difference between the low-level θe structure of the CS and ESLC simulations (Figs. 7b,d). For example, the ESLC has cooler θe within the surface inversion layer, while θe above the inversion is warmer. The CAPE for this case is 1046 m2 s−2 smaller than the control with the same shear (Table 3). The larger area of θe greater than 326 K compared to the CS also should be noted. This warmer θe air above the inversion likely is ingested into the squall line’s updraft, helping sustain its strength and explaining the slight increase in MUCAPE in the CS and ESLC simulations (Table 3).
The source of the increased θe above the nocturnal inversion is an interesting feature that warranted further investigation. The area of elevated θe was found to be present not only in all ESLC simulations but the CLC simulations as well. This indicates that the increase is likely related to the boundary layer processes associated with the development of the nocturnal inversion and not the squall line. The potential temperature θe can only increase over ambient values via diabatic processes, such as heating or cooling of the land surface or evaporation from the ocean, etc. All other processes internal to the model approximately conserve θe. It is clear from analyzing the cool land simulations that diabatic processes indeed are increasing both qυ and potential temperature (both components of θe) just above the inversion shortly after the formation of the nocturnal inversion (not shown). However, there is no clear evidence how and why this occurs. For example, values of qc (cloud water mixing ratio) above zero were observed in the layer of elevated θe. This feature is interesting and warrants a further study that is beyond the scope of this paper. Furthermore, it is clear that the formation of this warmer θe air does not alter the conclusions made about elevated instability in cool land simulations. That is, even without the apparent increase in θe, MUCAPE values are very similar to base-state values, allowing the squall line access to instability.
The ESLW simulations indicate a different alteration to the θe structure (Figs. 7e,f). Ahead of the squall line, θe values in the lowest 1 km increase from <326 K before passage to >326 K afterward. This heating creates a warmer and better mixed layer compared to the CS and ESLC simulations (Figs. 7b,d,f). As a result, warmer values of θe are ingested into the squall line’s updraft after it passes the coastline. CAPE and MUCAPE (Table 3) are much greater than in either the CS or ESLC simulations. Also evident is the warmer θe air extending into the squall line’s updraft. In summary, the cross sections of θe indicate that environmental changes ahead of the squall line differ depending on the temperature of the underlying land. Furthermore, the heating and cooling of the layer just along the surface confirm the changes in CAPE values seen in Table 3.
We next examine modification of the ambient shear within the inflow layer. In section 3 changes to the net circulation of the inflow layer were examined by calculating the bulk shear between the bottom and top of the inflow layer (Figs. 4 and 5). However, in this section we examine variations to the ambient shear within this layer. Figure 8 is a cross section of vertical shear (∂u/∂z) calculated from adjacent model levels. Since the base-state ambient shear at the beginning of the simulation is linear (see Fig. 3), the original value of ∂u/∂z is constant over the entire shear layer. For the moderate shallow-shear cases with 17.5 m s−1 shear, ∂u/∂z is 0.7 × 10−2 s−1. Thus, any departure from this value represents a change from the original ambient shear. The contour outlining the shaded areas in Fig. 8 represents ∂u/∂z of the original shear (0.7 × 10−2 s−1), with shaded (nonshaded) areas having stronger (weaker) shear.
Ambient low-level shear ahead of the squall line during the CS exhibits little change during the 1 h 50 min period (Figs. 8a,b). This is similar to results in Fig. 4c where the net vertical shear in the inflow layer was reduced slightly in the CS runs but remained nearly constant from 150 min through the end of the simulation. The major conclusion from Figs. 8a,b is that the squall line does not significantly affect the net vertical shear in the inflow layer during the period shown here. Thus, temporal changes to the shear layers of ESLC and ESLW simulations are due largely to wind perturbations induced by the land and not by the squall line itself.
During the ESLC simulations (Figs. 8c,d), the low-level ambient shear changes much more than during the control run. This is consistent with the net vertical shear results in Fig. 4c. Before the squall line passes the coastline, there is enhanced shear in the lowest 500 m ahead of the line centered near 360 km (Fig. 8c). Conversely, there is reduced shear 1 km above the surface centered ahead of the line at 370 km. Further investigation reveals the processes responsible for altering the shear. Figure 9 shows cross sections of buoyancy, wind vectors of the perturbation of the u component, and ∂u/∂z centered on the coastline for the ESLC simulation and the CLC simulation. The vector plotted in Figs. 9a,b differ from those in Figs. 6 and 11(later) in that perturbations of u-component winds are displayed rather than system-relative flow. One should recall that the CLC simulation in Fig. 9a has no squall line, and therefore no system from which to calculate system-relative flow. Thus, perturbations of the u component from the base-state winds are used to compare between Figs. 9a,b. Both cross sections are taken at 3 h 20 min into the simulation so the squall line–induced perturbations will not distort the pattern in Fig. 9b.
The CLC (Fig. 9a) exhibits a pattern similar to that in Fig. 8c, that is, increased shear along the surface with decreased shear above (centered just offshore near 370 km). Since this pattern of shear enhancement and reduction is present both with and without a squall line, it is clear that it is associated with cooling of the land surface and not the squall line itself (Figs. 9a,b). Vertical motion and divergence near 400 km (not shown) reveal a possible explanation. Downward motion along the buoyancy gradient near the coastline induces convergence near 0.6 km and divergence at the surface. The downward motion also creates an associated u-perturbation pattern, that is, the large black arrows in Figs. 9a,b. The relative lengths of the arrows approximate the magnitude of the u perturbation. The u perturbations oriented away from the buoyancy gradient at the surface and toward the buoyancy gradient at ∼0.6-km altitude support the presence of a negative horizontal vorticity circulation at the coastline (Fig. 9a). The squall line complicates the u-perturbation pattern by creating additional negative perturbations above the nocturnal inversion up to 2.7 km (Fig. 9b). These additional perturbations lessen the increased shear along the surface. Although this shear pattern appears similar to a coastal jet phenomenon described by Hsu (1979), it is not certain whether the processes are exactly similar.
Figure 10 shows maximum and minimum vertical velocities for the same simulation as Fig. 8. No large changes in the strength or frequency of the updrafts and downdrafts are observed during the squall line’s interaction with the increased shear region (around 4 h). Furthermore, other parameters near the same time exhibit little effect on the squall line (e.g., updraft orientation and CAPE/MUCAPE). Although the increased shear does not appear to significantly affect squall-line intensity, interactions between this feature and the squall lines merit further study.
As the squall line moves from the water onto the cool land, it encounters a different shear profile (Figs. 8c,d). Specifically, the squall line now encounters reduced shear along the surface that is ∼500 m thick and extends over the entire land portion. The ARPS model equations that govern the friction coefficients decrease near-surface wind speeds when a land surface is present. Thus, we hypothesize that the reduced shear is due to friction decreasing near-surface wind speeds and the nocturnal inversion limiting momentum transfer from winds above the surface. As a result, wind speed near the surface is reduced as is the shear.
Some results of the ESLW simulation (Figs. 8e,f) are similar to those of the cool land case. For example, after the squall line passes the coastline, there is a layer of reduced shear along the surface (Fig. 8f). Near-surface wind speeds are reduced due to frictional coefficients, just as in ESLC. However, unlike ESLC, this shear reduction is further aided by wind perturbations from the formation of an onshore sea breeze due to surface heating. This heating of the land induces a small positive u component ∼2 m s−1 (not shown) that is counter to the ambient shear, thereby further reducing the near-surface shear. One should note that the layer of reduced shear is deeper for the warm land simulations than the cool land runs. Enhanced low-level mixing and wind perturbations due to surface heating and the absence of an inversion are likely causes.
To summarize, the addition of a cool or warm land surface alters the shear environment within the original shear layer in similar ways, although this modification is due to different processes. The magnitude of vertical shear near the surface becomes smaller in both the ESLC and ESLW simulations. The original ambient shear strength now is confined to a layer that is elevated above the surface. This alteration of the near-surface shear is sufficient enough to have an affect on the net circulation in the inflow layer. This can be seen in the smaller bulk shear values for ESLW and ESLC than CS (Figs. 4c and 5c,d).
b. Strong deep shear [22.5 m s−1 (5.0 km)−1]
Results from the strong deep-shear simulation are presented similarly to those of the moderate shallow-shear case of the previous section. However, the times chosen to describe the squall line before and after coastline passage are 20 min later because the current squall line propagates slower due to the greater low-level easterly wind component (Fig. 3).
Figure 11 contains cross sections of buoyancy, system-relative flow, and cloud water centered on the squall line’s updraft before passing the coastline (4 h 20 min, left column) and afterward (6 h 10 min, right column). Although the previous moderate shallow-shear simulations indicated little change in squall-line updraft structure with the addition of a land surface (Fig. 6), the strong deep-shear cases exhibit significant differences (Fig. 11). The CS run exhibits an upright to downshear-tilted cloud field (updraft) and a shallow cold pool through the entire simulation (Figs. 11a,b). However, when a cold or warm land surface is introduced, the squall lines change from a vertical updraft to an upshear-tilted updraft (Figs. 11c–f). It should be noted that the extent of the cold pool also increases. Figures 12c–f confirms that the change in updraft orientation is associated with an increase in cold pool strength, as evidenced by the decrease in θe. This is consistent with RKW theory, which states that squall lines with stronger cold pools typically are characterized by more upshear-tilted updrafts than vertical or downshear-tilted updrafts. This change in updraft orientation likely is due to the significant decrease in the net circulation of the inflow layer (Fig. 4f), which is greatest with the strong shear cases. RKW theory suggests that stronger cold pools are associated with greater upshear tilt, as is observed in Figs. 12d,f.
For the cool land surface (Figs. 12c,d), some θe features are similar to those of the moderate shallow-shear cases discussed previously. For example, the ESLC also has smaller values of near-surface θe ahead of the squall line (Fig. 12c) compared to the CS (Fig. 12a). The warmer θe air above the nocturnal inversion also is similar to the moderate shallow-shear case. These changes to the pre–squall line environment are consistent with the CAPE and MUCAPE calculations (Table 3). There are also differences with the moderate-shear case. For example, the effects of the nocturnal inversion now reach the squall line while still over water (Fig. 12c) due to stronger surface wind speeds (Fig. 3), which advect the cooler/drier air farther offshore. This is the primary reason for the difference in shear between the CS and ESL simulations at the beginning of the runs in Fig. 4f.
The inclusion of a warm land surface to the strong deep-shear case produces a θe structure that is similar to that of moderate shallow shear (Figs. 7e,f and 12e,f). The increase in near-surface θe ahead of the squall line is due to surface heating (Figs. 12e,f) and is consistent with values of CAPE and MUCAPE (Table 3). Similar to the ESLC simulations in Fig. 12c, stronger wind speeds along the surface advect the relatively warm θe air farther offshore than in the other shear simulations (Fig. 12e). The presence of an upright to upshear-tilted updraft also is similar to ESLC. In both ESLC and ESLW, θe in the cold pool decreases from 314 to 310 K after the squall line passes the coastline (Figs. 12d,f). Again, this is consistent with the orientation of the updraft changing from an upright to an upshear configuration.
To summarize, many of the squall line’s θe characteristics are similar in both the moderate shallow- and strong deep-shear simulations; however, greater changes occur in the deep strong-shear cases. Since the thermodynamics ahead of the squall line are similar for the two shear orientations, the differences in θe likely are related to shear.
Figure 13 shows the vertical distribution for each shear of the simulations, where ∂u/∂z corresponding to the original shear (0.4 × 10−2 s−1) separates the shaded and unshaded areas. This threshold is smaller than for moderate shallow shear because the shear now extends over a greater depth. One should recall that the shear remained relatively unaltered in the 2.5-km shear layer throughout the moderate shallow CS (Figs. 8a,b). However, the CS run for the deep-shear simulations indicates modifications (Figs. 13a,b). The shear now is reduced in a 2-km-thick layer centered ∼3 km above the surface just ahead of the squall line. This reduction in midlevel shear results from a negative (easterly) u-component perturbation that is produced by both the disruption of the mean flow by the squall line and outflow from main updraft (not shown). A similar feature has been documented in previous studies (e.g., Weisman and Rotunno 2004; Fovell 2002). This midlevel perturbation also was noted in the shallow-shear simulations, but it did not affect the original shear layer as much because the perturbations occurred above 2.5 km. However, with shear now extending to 5 km, midlevel perturbations do modify the original shear layer, although they have little effect on the net circulation within the inflow layer. Specifically, Fig. 4f shows that values of bulk shear for the CS run are only slightly less than the original shear strength throughout the run.
The ESLC simulation (Figs. 13c,d) exhibits the same midlevel perturbation as the CS run; however, there also is reduced shear at the surface. As discussed earlier, this reduction is due to weaker winds below the nocturnal inversion. The depth of the reduced shear along the surface also is greater than the shallow-shear case. This reduced shear is much greater than for any other shear profile. Specifically, both midlevel and surface perturbations now act to reduce the original ambient shear down to a mere 1-km layer that is elevated above the surface (Fig. 13d).
The ESLW simulation (Figs. 13e,f) also exhibits a reduction in shear along the surface. This reduction in near-surface shear is deeper than the shallow-shear case (Figs. 8e,f). Wind perturbations combined with an unstable layer near the surface, associated with the heating of the land surface, create a deeper-shear reduction for this case. Coupled with the reduction in shear at midlevels, the depth of the original shear layer is reduced to <1 km, shallower than the ESLC simulation.
To summarize, it is important to note that the original strength of the shear layer in both the ESLC and ESLW simulations is confined to a thin layer just above the surface. The CS simulation shows that the effects of midlevel perturbations alone do not adversely affect the net circulation in the inflow layer. However, when combined with the effects from a warm or cool land surface, the net circulation in the inflow layer is reduced by a greater amount (Fig. 4d).
c. The cold pool
Table 4 summarizes squall-line updraft orientations for all shear configurations at 2.5 and 7.5 h into each run. Each paired entry gives the orientation of the squall-line updraft before and after passing the coastline at 5 h. One should note that updraft orientations do not change in any of the CS runs and that the inclusion of a land surface in all 7.5 m s−1 shear simulations does not affect updraft orientation. Conversely, the inclusion of a land surface in simulations with 22.5 m s−1 shear does change the updraft orientation. Results using 17.5 m s−1 shear are mixed. The shallow-shear runs exhibit no change in updraft orientation, while their deep-shear counterparts do change. These results indicate that changes in updraft orientation in ESLC and ESLW simulations are sensitive to the strength and depth of the net circulation in the inflow layer.
We next examine the strength of the cold pool by calculating the parameter C the integrated buoyancy from the surface to the top of the cold pool (RKW; WKR). Buoyancy is assumed to decrease linearly to zero at the top of the cold pool, simplifying the integration to
where Bmin is the minimum buoyancy [see (1)] for a 2-km layer along the surface rearward from the leading edge of the cold pool, and H represents the depth of the cold pool.
Figure 14 contains time series of C for the CS, ESLC, and ESLW simulations for each of the six shear configurations. Most simulations exhibit increased cold-pool strength during the first ∼150 min, indicating that the squall line is developing from a thermal bubble to a mature system. Later, cold pool strengths for both weak-shear layer simulations become relatively constant (Figs. 14a,b), with cold pools for the land cases ∼5 m s−1 weaker than the control. We hypothesize that the parameterization of the land surface produces greater mixing in the lower atmosphere near the surface, thereby causing the differences between cold pool strengths of the control and land simulations.
Elevated shear layers just ahead of the squall line can have important consequences on cold pool strength. Weisman and Rotunno (2004) found that elevated shear profiles produce weaker cold pools than surface-based shears of the same strength. They theorized that elevated shear in the midlevels may work against system-scale downdrafts, reducing the amount of midlevel air that reaches the surface, and thereby weakening the surface cold pool. However, since this study contains midlevel shear in all simulations, the link between weakening cold pools and elevated shear layers induced by the land surface is not conclusive. This characteristic of weakening cold pools is interesting and warrants further study.
The moderate-shear cases (Figs. 14c,d) exhibit stronger cold pools after the initial development period than the weaker-shear cases. After ∼180 min, the cold pools of both the deep- and shallow-shear simulations with a land surface exhibit slight weakening. However, it maintains a nearly constant strength for the duration of the simulation. One should note that the ESLW deep-shear simulation does not follow this pattern (Fig. 14d). Further investigation reveals that the squall line’s updraft remains vertically orientated for approximately half the period (∼300 min), with the weak cold pool resulting from the continued vertical updraft. Once the updraft orientation progresses to an upshear tilt, the cold pool strengthens. It is not known why this simulation provides an environment for the squall line’s updraft to remain vertical.
Cold pools of the strong-shear simulations with a land surface (Figs. 14e,f) behave similar to the moderate-shear cases. They exhibit an initial strengthening, with a gradual weakening over the remainder of the simulation. Conversely, the cold pool of the CS simulation maintains a relatively constant strength. One should note the greater strengthening of the cold pool during the land simulations compared to the weaker cold pool in the control. Table 4 and Fig. 11 showed that updrafts of squall lines in strong-shear simulations for ESLC and ESLW changed from vertical to upshear-tilted configurations, while no such transition occurred in the CS simulation. The strong cold pools are consistent with RKW theory.
Finally, we examine the relative strengths of ambient shear and the cold pool similar to RKW using the ratio of their strengths (C/Δu). This ratio (Fig. 15) was obtained from values in Figs. 4 and 14. The plots for weak shear are not shown due to the large variability in shear discussed earlier. Results reveal that although the moderate-shear cases exhibit a weakening cold pool and net decreased circulation in the inflow layer (Figs. 4 and 14), their relative balance remains similar to the CS simulations (Fig. 15). On the other hand, for the deep-shear simulations, the relative balance of the cold pool and shear is altered significantly with the addition of a land surface. Weakening of ambient shear causes the increase in C/Δu.
To summarize, the strengths of the cold pools observed here, coupled with the updraft orientations observed previously (Table 4), are consistent with RKW theory. Specifically, upshear-tilted updrafts are associated with strong cold pools, while vertical or downshear-tilted updrafts are associated with weak cold pools.
Two shear cases have revealed much about the thermodynamic and shear characteristics of squall lines as they interact with a coastline. Although a cool land surface induces an inversion and stable layer near the surface, unstable air continues to be available to the squall line (Figs. 6c,d and 11c,d). Specifically, the squall lines continue to propagate by ingesting warmer θe air above the inversion. The ESLW simulations show that instability increases in the lower atmosphere (Figs. 7e,f and 12e,f). These findings in section 4 are consistent with Table 3. Specifically, instability continues to be available to the squall line independent of the land surface. Therefore, in a two-dimensional framework the inclusion of land does not sufficiently affect the thermodynamic properties ahead of squall line to change the storm’s overall structure.
The investigation of ambient shear ahead of a squall line reveals interesting processes that alter shear within the original layer. Analyses of the moderate shallow-shear simulations indicate that both warm and cool land surfaces reduce the original near-surface shear ahead of a squall line. However, this reduced shear occurs for different reasons. Cool land simulations reduce shear through the development of a nocturnal inversion, while the warm land simulations reduce shear by inducing sea-breeze-like perturbations near the coastline.
The strong deep-shear simulations with a land surface reduce shear near the surface in the same way as the moderate shallow-shear cases. However, the deeper original shear layer is affected more by midlevel perturbations caused by the circulation associated with the squall line. The strength of the original shear profiles now is reduced from an original depth of 5 km to only a 0.5- to 1.5-km elevated layer that is centered ∼1 km above the surface. This is greater than the reduction seen in the moderate shallow-shear case.
The analysis of shear in both the moderate shallow-shear and strong deep-shear simulations indicate the physical processes that reduce the net circulation in the inflow layer. Within this context, the results of section 3 are better understood. Specifically, the inclusion of a land surface reduces the ambient shear in a layer adjacent to and near the land surface, producing a small but sometimes significant decrease in the net circulation of the inflow layer. Section 3 showed that the decrease in net circulation was greatest for the strong deep-shear simulation (Figs. 4 and 5). Consistent with RKW theory, this decrease in net circulation likely caused the transition from a vertical updraft to the upshear-tilted updraft that was observed in the strong deep-shear simulations (Figs. 11c–f). Six of the 12 simulations exhibited a major change in updraft structure (Table 4). Strong shallow and moderate to strong deep shear all produced these changes in storm structure.
5. Summary and conclusions
This study has sought to develop a conceptual model describing whether and how coastlines affect squall lines. We focused on the southeastern Gulf of Mexico Coast near Tallahassee, Florida. Two-dimensional numerical simulations using the ARPS model over a range of shear profiles were employed.
The simulations document the thermodynamic and shear characteristics of squall lines interacting with the coastline. Unstable air continued to be available to the squall line when either a cool or warm land surface was included. Therefore, in a two-dimensional framework the inclusion of a land surface did not sufficiently affect the thermodynamic properties ahead of the squall line to change its overall structure. Investigation of ambient shear ahead of a squall line revealed more interesting processes that affected its structure and strength. Specifically, the addition of either warm or cool land reduced the strength of the original shear in a layer near the land surface. However, the net circulation in the inflow layer of the squall lines was affected much less. The amount of net circulation reduction in the inflow layer was found to be directly proportional to the depth and strength of the original shear layer. For stronger and deeper shears, the reduced shear was sufficiently great that the buoyancy gradient at the leading edge of the cold pool was no longer in balance with vorticity associated with the shear. As a result, the orientation of the squall-line updraft progressed from upright/downshear to upshear.
From a two-dimensional conceptual model perspective, we can hypothesize two ways by which a squall line might respond to passing from water to land. Figure 16 illustrates this two-dimensional conceptual model by showing the updraft orientation, cold pool, shear profile, and circulations generated by the cold pool and ambient shear both before passing the coastline (left column) and afterward (right column). It should be noted that the wind vectors defining the shear profiles illustrated in Fig. 16 are generic and do not exactly represent winds observed in the simulations of this study. However, the ambient shear and changes to the shear are similar to those observed in the simulations. The weaker and more shallow the ambient shear, the greater likelihood that the squall line will mature into an upshear-tilted system and be relatively unaffected by a transition from water to land (Fig. 16a). Conversely, the stronger and deeper the shear, the greater likelihood that the squall line will mature into a vertical or downshear-tilted system and then progress to an upshear-tilted system after passing from water to land (Figs. 16b,c). This occurs because land surface processes sufficiently reduce the net circulation in the inflow layer to unbalance the opposing cold pool circulation, thereby affecting updraft orientation.
It should be noted that we have not performed a detailed comparison of observed squall lines from the climatology noted in section 2 with simulated squall lines. However, we have examined both datasets in a qualitative manner. This has yielded mixed results. Some observed squall lines indeed exhibit behaviors similar to those seen in this study. However, some do not. Adding to the complexity is the fact that observed squall lines occur in a three-dimensional environment where the coastline is not exactly perpendicular to the squall line. Two-dimensional modeling obviously cannot account for three-dimensional circulations that might affect the strength and longevity of squall lines as they come ashore. Future three-dimensional simulations with contrasting land surfaces may reveal additional processes that affect squall lines. Therefore, it would be premature to draw conclusions from the comparison of observed and simulated squall lines at this point.
This research was funded by Subaward S00-191127 from the Cooperative Program for Operational Meteorology, Education, and Training (COMET) under a cooperative agreement between the National Oceanic and Atmospheric Administration (NOAA) and the University Corporation for Atmospheric Research (UCAR). The views herein are those of the authors and do not necessarily reflect the views of NOAA, its subagencies, or UCAR.
The authors appreciate the help of Dr. Ming Xue and Dr. Dan Weber of the University of Oklahoma and Robert Gilliam of Coast Weather for help with ARPS configuration. Special thanks to Dr. Robert Fovell of UCLA for his help evaluating the model output.
We appreciate the helpful comments provided by two anonymous reviewers who helped clarify portions of the text.
* Current affiliation: National Weather Service Forecast Office, Caribou, Maine
Corresponding author address: Henry E. Fuelberg, Department of Meteorology, The Florida State University, Tallahassee, FL 32306-4520. Email: email@example.com