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Observed upper air soundings occurring within two hours and 167 km of derechos are collected and analyzed to document atmospheric stability and wind shear conditions associated with long-lived convective windstorms. Sixty-seven derechos, accompanied by 113 proximity soundings, are identified during the years 1983 to 1993. Owing to the large variability of the synoptic scale environments associated with derechos, each derecho is further divided into categories based on the strength of synoptic-scale forcing associated with each event.
Derechos are shown to develop and persist in a wide range of shear and instability. This is especially true when all events are considered, regardless of the synoptic-scale environment. Although this range of shear and instability narrows when derechos are grouped by synoptic-scale forcing strength, considerable variation of values remains, primarily with the shear. These results suggest that ambient shear and instability values alone are not sufficient to distinguish derecho environments from those associated with non-severe MCS environments. When system-relative winds are examined, it is found that midlevel system-relative winds are consistently weak, while low-level inflow is strong. This is especially valid for events associated with weak synoptic-scale forcing. Given favorable thermodynamic environments, weak system-relative midlevel winds appear to promote development of strong cold pools at the ground and outflow-dominated storms.
These results indicate that there is a larger range of shear and instability environments associated with derechos than has been examined in numerical cloud simulation experiments. The results also show that there is little correlation between events with strong cold pools and those with correspondingly strong low-level ambient shear, suggesting that a shear-cold pool balance is not observed in most of the events. Owing to the larger variance in CAPE/shear found in this observational study, forecasters should be aware of the potential for derecho formation within environments of lower CAPE and shear than those of "typical" warm season derechos. This is especially true within environments of strong synoptic-scale forcing.
Convective windstorms long have been discussed in the literature, and are responsible for considerable damage, and numerous casualties across the United States each year. Though the convection responsible for damaging surface winds can vary in size from a single thunderstorm to a large convective complex, long-lived rapidly moving squall lines account for the most severe and widespread convectively-induced wind damage. Fujita (1978) introduced the term "bow echo" in the late 1970s to describe bow-shaped radar reflectivity signatures associated with the majority of these windstorms. Observations have revealed that these radar echo structures can vary in size from a few km to more than 200 km in length, and can last for 18 h or more in extreme cases.
Nontornadic damaging winds associated with deep convection are almost always generated by outflow from the base of a downdraft (Johns and Doswell 1992). Negative buoyancy, attributable to the effects of evaporative cooling when precipitation falls through a layer of unsaturated air, is a very important contributor in the development and maintenance of strong downdrafts (e.g. Browning and Ludlam 1962; Hookings 1965). Once this convectively-cooled air reaches the surface, it forms a "pool" of cold air that can build into a "mesohigh" as the convection becomes more organized and intense. It is an intense mesohigh that Hamilton (1970) attributes to the "bulging echo" of a line echo wave pattern [LEWP; as identified by Nolen (1959)], and which Fujita (1978) attributes to bow echoes. Fujita (1978) and many other recent studies (e.g. Przybylinski and Gery 1983; Przybylinski 1995) emphasize the association of bow echoes with long swaths of damaging straight line winds.
Johns and Hirt (1987; hereafter JH87) conducted an extensive study of convective windstorms occurring during the warm season, calling the long-lived, widespread cases "derechos", after Hinrichs (1888). Examination of radar-echo configurations associated with these events strongly suggests that derechos are associated with "bow echoes" or bowing segments of varying scales within a larger squall line (JH87; Przybylinski and DeCaire 1985). JH87 found that the low levels are very moist and support extreme values of conditional instability (average Lifted Index of -9), though the instability is less when systems are accompanied by strong 500 mb shortwave troughs. These findings were supported by Johns et al (1990), who examined 14 very intense derechos that occurred during the months of June and July. They found that CAPE values generally were greater than 2400 J kg-1 near the genesis region of the strong derecho cases, though CAPE increased to an average maximum of 4500 J kg-1 as the convective system moved eastward. Average surface to 700 mb (corresponding roughly to 0-3 km) shear vector magnitudes were found to be near 15 m s-1, with surface to 500 mb (corresponding roughly to 0-6 km) shear vector magnitudes around 20 m s-1.
By examining synoptic-scale meteorological aspects of a large number of derechos, JH87 and Johns et al (1990) found that long-lived derechos are associated with rather well-defined parameter patterns. However, both studies sampled events only during the warm season. This bias was addressed by Johns (1993), who stated that combinations of wind speeds in the low-to-midtroposphere and instability appear to vary widely when considering all bow echo situations when damaging winds occur. This is especially true when derechos are associated with strong extratropical cyclones; derechos in such cases can occur any time of the year.
A number of numerical cloud modeling studies (Rotunno et al. 1988 [hereafter referred to as RKW]; Weisman et al 1988; Weisman 1992; Weisman 1993) have sought to simulate long-lived severe squall line development. These studies explore the storm-scale evolution in the development and maintenance of long-lived bow echoes, with an emphasis on the effects of environmental shear. Results from Weisman's (1992, 1993) simulations indicate "optimum" conditions for sustained bow echo development occur when vertical wind shear of 20 m s-1 or greater exists within the lowest 2.5 km AGL (in conditions with no shear above the 2.5 km level). The shear is hypothesized as a necessity to balance the horizontal circulation generated along the leading edge of the cold pool (RKW; Weisman 1992, 1993). In addition to the shear constraints, simulations by Weisman (1992; 1993) further restrict the range of environments favorable for bow echoes to those with CAPE in excess of 2200 J kg-1. Given the discrepancies between operational observations and results of numerical simulations, and the inherent bias towards warm season events, Johns (1993) highlighted the need to examine in more detail the low-to-midtropospheric wind structure and instability associated with a large number of derechos occurring year-round. Our study is an attempt to carry out this suggestion and improve forecast techniques concerning long-lived bow echos by examining proximity soundings associated with numerous derechos. Although it is recognized that proximity soundings have some potential shortcomings (discussed in Brooks et al.1994b), we have identified proximity soundings associated with a large number of derechos to refine our knowledge of the range of environments conducive to long-lived bow echoes. We then compare these environments with the results of the numerical simulation experiments.
Storm Data publications were examined for the years 1988 to 1993 to identify derechos occurring within the contiguous United States. Derechos were inferred from convective wind damage patterns in a way similar to that done in JH87. To be included as a derecho, each event must:
Cases identified for the years 1988 to 1993 were supplemented by those cases used by Johns et al (1990) that encompassed the summer months from 1983 through 1987. From this set of candidate events, each case then was examined for proximity soundings. To qualify as a proximity sounding, the observed sounding must have been taken within both two h and 167 km (100 miles) of the wind damage path, or the bow echo location as shown by the radar charts. Further, the soundings must have been uncontaminated by the convection, and located directly within or near the ensuing damage path. In this way, the proximity soundings were assumed to be representative of the environment immediately ahead of the derecho.
For the qualifying proximity soundings, the 0-2 km, 0-3 km, and 0-6 km (all AGL) shear values were computed for each sounding using the vector difference between wind vectors at the surface and the top of the layer. These levels were chosen in an effort to investigate both the lower and deeper layer shear associated with this events. Hourly radar charts then were used to estimate the speed and direction of the convective systems, so that estimates of the lower (0-2 km), middle (4-6 km), and upper (6-10 km) level system-relative winds (hereafter, SRW) could be tabulated. Bulk Richardson number shear (referred to as BRN shear in this paper; Droegemeier et al. 1993; Stensrud et al. 1997) also was calculated for each sounding. BRN shear here is defined as the magnitude of the difference between the 0-6 km density-weighted mean wind and the density-weighted mean wind of the lowest 0.5 km.
Hourly surface observations were obtained and analyzed within two h before and after the corresponding sounding time. A few of the soundings located near the damage path were judged to have surface and/or boundary layer conditions unrepresentative of the inflow environment, owing to the presence of shallow storm outflow or a front. For these cases, the surface temperature and dew point of each sounding were modified as needed to represent the surface conditions immediately ahead of the derecho. From these modified proximity soundings, Convective Available Potential Energy (hereafter, CAPE) and Downdraft Convective Available Potential Energy (hereafter, DCAPE) were computed. Surface equivalent potential temperature also was computed and plotted to determine cold pool intensities with each event.
Since derechos can occur under a variety of synoptic regimes, the cases were classified into those associated with 1) weak synoptic-scale forcing and 2) strong synoptic-scale forcing. The "weak" and "strong" forcing categories correspond roughly to Johns' (1993) "warm season" and "dynamic" synoptic patterns associated with bow echo development. This was accomplished by obtaining the 1200 UTC 500 mb and surface charts prior to development, and assessing subjectively the strength of the forcing. Events that occurred ahead of an advancing high amplitude midlevel trough and an accompanying strong surface cyclone were considered "Strong Forcing" (hereafter, SF). Those that occurred under relatively quiescent conditions were labeled as "Weak Forcing" (hereafter, WF) events. Events that did not fit clearly as either SF or WF were categorized as "Hybrid" events.
a. Cases found
Using the preceding criteria, 67 derechos with at least one proximity sounding are identified. Derechos with proximity soundings are identified in nearly every month of the year over the 11-year extent of the study, with 27 SF and 30 WF events (Fig. 1). Hybrid cases comprise 10 events. In all, 113 soundings (47 SF, 51 WF, and 15 Hybrid) fit our proximity criteria, an average of 1.7 soundings per derecho. The maximum number of proximity soundings from a single derecho is three. The addition of the 13 derechos in Johns et al (1990) accompanied by proxy soundings tends to bias our results slightly in favor of warm season cases, since they only included events from May to August. However, five of these 13 derechos are classified as SF or Hybrid, which should limit any bias in this data set based on our decision to classify each event by forcing strength. Each sounding is also classified according to its location to the derecho life-cycle. Those taken within the first three h of the derecho are categorized as "initiation" soundings; while those within three h of a derecho's demise are categorized as "end" soundings. Those in between are labeled "along path" soundings. The three h threshold is chosen to be consistent with results of the numerical simulations (Weisman et al 1988; Weisman 1992; 1993), who found that simulated bow echoes entered their mature stage at around 220 minutes from initiation.
Figure 1 indicates that SF events occur in all seasons, with a relative maximum in the late spring. Weak forcing events, on the other hand, are confined to the warm season (May through August), consistent with the observations of Johns (1993). The high frequency axis found by JH87 across the northern states is evident in Fig. 2. Also, an axis extending southeastward across the southern plains, and another into the southern and middle Atlantic states is also apparent, which supports similar axes found by Bentley and Mote (1998).
Weisman and Klemp (1986) state that vertical shear influences the ability of a gust front to initiate new convective cells, and relates to the ability of an updraft to produce an enhanced, quasi-steady storm structure. Since shear has been emphasized as an important parameter for bow echo longevity, we examined the shear profiles for each proximity sounding. Observed shear values associated with the soundings have a wide range of values (Fig. 3). The 0-2 km shear vector magnitudes range from near 3 m s-1 to 30 m s-1, with the middle 50 percent of shear vector magnitudes between 8 m s-1 and 16 m s-1. The standard deviation is 5.8 m s-1. Figure 3 also shows that 0-3 km shear vector magnitudes are very similar to the 0-2 km values. The deep layer shear, defined as 0-6 km here, has a larger range of values, with shear vector magnitudes ranging from 1 m s-1 to 36 m s-1, and a standard deviation of 13.3 m s-1. These observed values of vector shear are generally lower than shear values over the lowest 2.5-5 km used in numerical simulation experiments with idealized bow echoes (Weisman, 1992; 1993), and those suggested by Johns et al (1990).
Comparing WF events to SF events (Fig. 4), it is evident that SF events develop and persist in stronger shear environments than WF events, in general. Johns (1993) has noted that "Dynamic" pattern (comparable to SF events in this study) can be accompanied by tornado outbreaks, which is consistent with the known preference for tornadoes to occur in strongly-sheared environments. In fact, there were 314 tornadoes associated with SF events, compared to 126 tornadoes with WF cases. This yields an average near 11.5 tornadoes per SF event, but only 4 tornadoes for each WF event.
Owing to the apparent dominance of convective outflows associated with long-lived bow echo behavior, system-relative wind values are also investigated in this study to examine the applicability of this concept to derecho formation. In recent years, some studies have focused on ways to distinguish between tornadic and non-tornadic supercells (Brooks et al 1994a,b; Stensrud et al. 1997; Thompson 1998). Brooks et al (1994a) have suggested that many supercells fail to produce sustained low-level mesocyclones and tornadoes because they become outflow-dominated; that is, the cold pool undercuts the updraft, cutting off the moist inflow. Brooks et al hypothesize this behavior to be caused by weak storm-relative wind speeds at midlevels of the storm that allow too much precipitation to fall near the updraft, enhancing the strength of the downdraft and associated "cold pool" at the surface near the updraft. Figure 5 shows that midlevel (4-6 km) and upper-level (6-10 km) system-relative winds (SRW) are fairly weak with the derechos, especially with WF events. Average values of midlevel SRW range from 7.5 m s-1 with WF events, to 11.5 m s-1 for SF cases. The average values of upper-level SRW are 7.7 m s-1 and 12.5 m s-1 respectively. A more detailed discussion on the relevance of the midlevel SRWs can be found in section 4b.
Despite the weaker shear in WF events, SRW values indicate that low-level inflow tends to be stronger in these cases than with the SF events (Fig. 5). This is consistent with "progressive" derecho environments found by JH87. The 0-2 km system-relative inflow exceeds 11 m s-1 for all but the lowest quartile of the cases in both WF and SF events, with a median value of 16 m s-1 and 14.5 m s-1 respectively. The rapid forward motion of bow echoes is responsible for much of the low-level system-relative inflow. However, the weak flow and shear in the WF events suggest a larger proportion of their forward motion and resultant increased low-level inflow might be attributed to new cell development along the leading edge of the rapidly moving cold pool, and not the movement of the meso-a scale (Orlanski 1975) environment supportive of convection. In other words, propagation plays an enhanced role in the motion of WF events, as has been postulated by JH87 and Corfidi (1998). In contrast, SF events likely owe a large proportion of their ground-relative motions to the stronger mean flow environments within which they exist.
Given the similarities between outflow-dominated supercells and enhanced cold pool development mentioned above, BRN shear is also considered for our derecho soundings. Stensrud et al (1997) investigated BRN shear as a diagnostic tool to discriminate between tornadic and non-tornadic thunderstorms without regard to storm motion, using a mesoscale model on nine severe weather events. They found that outflow-dominated convection, unsupportive of sustained low-level mesocyclones, is likely when BRN shear values are less than 40 m2 s-2, whereas low-level mesocyclones are favored with BRN shear values values from 40 m2 s-2 to 100 m2 s-2. Thompson (1998) found a wide range of BRN shear values associated with 131 observed tornadic and non-tornadic supercells, however. Thompson indicated the majority of outflow-dominated (and therefore more likely to be non-tornadic) supercells were associated with BRN shears from 20 m2 s-2 to 50 m2 s-2, with 39% exceeding the 40 m2 s-2 range suggested by Stensrud et al (1997). Figure 6 reveals that three-fourths of our proximity soundings associated with derechos had BRN shear values less than 55 m2 s-2, with 50% of the soundings between 16 m2 s-2 and 55 m2 s-2. This is very similar to Thompson's findings regarding BRN shear values associated with non-tornadic supercells, although it overlaps the 40 m2 s-2 threshold found by Stensrud et al. to distinguish between tornadic and non-tornadic supercells. When considering only WF events, the 75th percentile value drops to 40.5 m2 s-2, which is close to the threshold found by Stensrud et al. However, for the SF events, the value of BRN shear appears to become less valuable as a tool to discriminate bow echo development from environments conducive to supercell tornadoes, given the large number of SF cases exceeding the upper thresholds set for non-tornadic supercells found by both Stensrud et al and Thompson.
Convective available potential energy (CAPE) has been computed using both a mean-mixed layer parcel over the lowest 100 mb (MXCAPE), and the most unstable parcel in the lowest 300 mb (MUCAPE). MUCAPE values generally are larger than the MXCAPE calculation, reaching some extreme values in some cases. Generally, MUCAPE values are not aswidely acepted as MXCAPE values. The virtual temperature correction is used in these calculations (Doswell and Rasmussen 1994). Both the MUCAPE and MXCAPE values (Fig. 7a, Fig. 7b, respectively) are greater on average for the WF events than the SF events; WF events are primarily warm season occurrences (Fig. 1) when instability tends to be larger, as suggested in JH87 and Johns et al (1990). Lapse rates associated with the derechos in this study exhibit larger average mid-tropospheric (700 mb to 500 mb) values (7.3 C km-1) in the WF cases than in the SF cases (6.7 C km-1).
Most of the WF events display CAPE values within the range that Weisman (1993), JH87, and Johns et al (1990) found to be associated with long-lived bow echo development. Only 7 of the 51 soundings associated with WF events have MUCAPE values below Weisman's (1993) threshold of 2000 J kg-1. Whereas surface-based conditional instability is present in most of the cases, as observed by the generally high values of MXCAPE, a few derechos develop and persist within regions of only conditionally stable surface air. In these cases, the conditional instability is elevated above the surface layer (see, e.g., JH87; Schmidt and Cotton 1989). Figure 7 reveals that most WF derechos occur with relatively high MXCAPE or MUCAPE values, but SF events often are associated with MUCAPE values less than 2000 J kg-1; some SF cases have very small values of MUCAPE (approaching 0 J kg-1).
The surface equivalent potential temperature (qe) difference across the derecho's outflow boundary is used to estimate the strength of the cold pool produced by convective downdrafts. The maximum difference of qe values (Dqe) across the gust front for each event is calculated within 167 km (100 miles) and two h of each sounding. Twelve of the 47 SF cases (25%) had no noticeable surface qe minimum within the cold pool, as these events were aligned along a strong cold front with progressively lower surface qe values behind the front. For these cases, the surface qe value immediately behind the cold front was used. Figure 8 shows that WF events typically produced greater surface Dqe than SF events, which suggests stronger cold pools with WF cases, although considerable overlap between SF and WF events can be seen. The median values of surface Dqe were 22o C in WF events and only 14o C for SF cases.
A second method to estimate cold pool strength uses downdraft convective available potential energy [DCAPE; Emanuel (1994)], as formulated by Gilmore and Wicker (1998; hereafter, GW98). It generally is understood that entrainment of dry air into downdrafts strengthens them through increased evaporative cooling (Fawbush and Miller 1954; Foster 1958; Browning and Ludlam 1962; Hookings 1965). Therefore, DCAPE can be considered as an estimate of the potential outflow strength for a given thermodynamic profile; DCAPE provides an estimate of downdraft and associated cold pool intensity before development. GW98 describe a number of caveats concerning the use of DCAPE as a proxy for cold pool strength; we will not repeat those here. We concur with those concerns, but we are only using this index in a qualitative sense, to estimate when one cold pool may be stronger than another. When comparing DCAPE values by forcing type (Fig. 9), the pattern is similar to that of the surface Dqe (Fig. 8). DCAPE is noticeably higher with the WF cases, which resembles the MUCAPE relationship shown in Fig. 7. Using DCAPE as a proxy for cold pool strength seems justified by Fig. 10, which exhibits a roughly linear relationship between DCAPE and the surface Dqe in these cases; the linear correlation coefficient is 0.5 for this relationship.
d. Kinematic and Thermodynamic Relationship
Previous studies regarding supercell environments [Rasmussen and Wilhelmson (1983); Turcotte and Vigneux (1987) and Johns et al (1993), among others] have found that supercells occur in both very weak and very strong conditional instability environments. In very general terms, they found an inverse relationship between shear and instability; that is, strong shear tends to be associated with the weak instability cases, and vice versa. Our study shows a similar relationship between shear and instability within derecho environments. The proximity soundings are divided into three categories of MUCAPE depending on percentile rank. The 25th percentile of MUCAPE is used to designate the upper value of "weak" instability cases, whereas the 75th percentile of MUCAPE forms the bottom value of "strong" instability events. Those events between the 25th and 75th percentile values are labeled as "moderate" instability. The range of shear associated with each of these instability categories (Fig. 11) shows when the instability is "weak," the shear is stronger, on average. This relationship is most clear for the low-level shear values, although there is a suggestion of a similar relationship for the deep layer shear.
Through idealized numerical simulation experiments using a non-hydrostatic cloud model, Weisman (1992, 1993) has indicated that long-lived bow echoes favor a "... restricted range of environmental conditions with CAPE of at least 2000 m2 s-2 and vertical wind shears of at least 20 m s-1 in the lowest 2.5-5 km AGL ...". Weisman further suggests that long-lived bow echoes especially favor environments where the majority of the shear is confined to the lowest 2.5 km. The RKW conceptual schematic is reproduced here (Fig.12) as a convenience to the reader. Presumably, if this theory is to be of operational relevance, the magnitude of the low level shear should be useful in forecasting the longevity of severe squall lines.
RKW uses buoyancy distribution as an estimate of the cold pool strength, which corresponds to the magnitude of the cold pool circulation at its leading edge. We feel the surface Dqe should be closely related to the buoyancy distribution used by RKW, and is a reasonable operational proxy for their estimate of cold pool strength and the corresponding magnitude of the horizontal circulation generated. RKW theory also employs the shear over a layer corresponding to the depth of the cold pool, which makes a direct comparison using operationally available data difficult. As a simple estimate, we have used the 0-2 km and 0-3 km low-level vector shears as proxy variables for the shear over the depth of the cold pool.
Figure 13 suggests the existence of an inverse relationship between DCAPE and mean wind when considering all derechos. Careful examination of this figure shows that this is the result of the separation into SF, WF, and hybrid categories; the SF cases are found in the upper left part of the figure, the WF cases are found in the lower right part, and the hybrid cases are in between, with some hint that they are more like the WF cases than the SF cases. If this relationship is viewed in terms of the 0-6 km shear instead of the 0-6 km mean wind (Fig 14), a similar separation among the categories is found. This finding lends some credence to several earlier sensitivity experiments (Wilhelmson and Klemp 1978; Weisman and Klemp 1982; Pophin 1989; and Brooks et al. 1994a) indicating that, in strongly sheared environments, the downdraft tends to become diluted owing to greater entrainment. However, the relationship between DCAPE and 0-6 km shear is not as clear-cut as that between DCAPE and the 0-6 km mean wind. Therefore, it is of some interest to examine how shear varies with the mean wind for our cases; it can be argued that shear and mean wind ought to be related. As can be seen in Fig. 15, the observations do suggest that the shear increases as the mean wind increases. However, if the separate categories of SF, WF, and hybrid events are considered, in each category it appears that the shear is not dependent on the mean wind. Instead, the dominant characteristic is that the WF and SF events are distinguished primarily by their 0-6 km mean wind values, such that within each category, the 0-6 km shear can vary widely. The hybrid cases again seem to fall more or less in between the SF and WF distributions and, like the WF and SF events, do not validate a shear-mean wind relationship.
If a shear-outflow balance is indeed necessary for long-lived squall lines, the low-level ambient shear and the corresponding cold pool strength should be closely correlated for the derechos investigated here. This is especially true for the 51 WF soundings, since most of these cases are likely supported by strong cold pools, whereas many of the SF events exhibit relatively weak cold pools. Figure16a and Fig. 16b reveal that our data show a significantly different picture of this relationship; virtually no correlation is apparent between the shear and the cold pool strength. Linear correlation coefficients are -0.21 for DCAPE and -0.28 for surface Dqe, with linear correlation coefficients of -0.11 and -0.27, respectively, for just the WF events. Similar correlations were found when using the 0-3 km shear (not shown).
RKW theory suggests an outflow-shear balance is necessary mainly during the mature stage of the long-lived bow echo. Since we stratified our soundings into categories based on the time within the life cycle of a derecho, we could test this suggestion. The results (Fig. 17a, Fig. 17b) show that the proximity sounding location relative to the life cycle of the derecho is not responsible for the absence of a systematic relationship between low-level shear and cold pool strength.
To gain a better understanding of environmental factors contributing to bow echoes, thirteen MCSs that did not meet the criteria to be defined as long-lived derechos have been investigated. In fact, these cases produced little or no severe weather [i.e., hail > .75 in (2 cm), wind > 50 kt (25 m s-1), or tornadoes]. All the non-derecho events affected the Great Plains during the warm season (June through August), and occurred under weak synoptic-scale forcing. Therefore, the environments associated with these non-derecho MCSs are compared herein only to the WF derecho events. When the same proximity criteria are applied to these events, 31 soundings are obtained near non-derecho MCS's.
An analysis of the MUCAPE and DCAPE from the 31 proximity soundings for the non-derecho MCSs reveals that most of these events develop within similar thermodynamic environments to those associated with WF derechos (Fig 18). However, Fig. 19 indicates that the deep layer mean wind and the system speed of the non-derecho MCSs tend to be less than for the derecho events. Despite the weaker mean flow, 0-2 km shear values were fairly similar between the non-derecho and derecho soundings (Fig. 20), though the deep layer shear (0-6 km) values were noticeably stronger with the derecho soundings.
Figure 21 indicates that the 0-2 km system-relative inflow is stronger with the derecho events (likely due to the fast system speeds of the derechos) than the non-derecho MCSs, although the 4-6 km SRWs are not markedly dissimilar between the two data sets. The comparable thermodynamic and similar midlevel SRW environments, indicate both WF derechos and non-derecho MCSs occur within surroundings considered to be favorable for outflow-dominated convection. These results suggest the potential for strong cold pools does not appear to be sufficient by itself to distinguish between long-lived severe bow echoes and non-derecho MCSs when large-scale forcing is weak. Other factors likely aid in maintaining severe wind gusts at the surface in addition to the cold pool potential. The most obvious factor within this data set appears to be the strength of the mean flow, which appears to affect the 0-2 km SRW, as well as the forward movement speed of the cold pool and of the storms themselves.
6. Discussion and conclusions
Long-lived convective windstorms can occur throughout the year within a wide range of environments, covering large portions of the CAPE/shear parameter space. Synoptic-scale forcing plays an important role in supporting some types of convective wind storms. Mean deep layer flow is usually stronger and conditional instability is much weaker when strong synoptic-scale forcing is present, when compared to cases occurring within benign synoptic-scale environments. In fact, MUCAPE values less than 1000 J kg-1 are observed with more than 25 percent of strong forcing (SF) cases. This suggests that when a high-amplitude, midlevel trough and an accompanying strong surface cyclone are present, long-lived convective wind storms can occur within weak CAPE and DCAPE environments. In these situations, other factors besides CAPE and DCAPE are apparently important in producing damaging surface winds. In contrast, when synoptic-scale forcing is more innocuous, much higher values of CAPE and DCAPE appear necessary to maintain a sustained convective wind threat. Three-fourths of the WF events occurred within MUCAPE values more than 2600 J kg-1.
Shear values from 0-2 km, 0-3 km, and 0-6 km exhibit a wide range of values for the 67 derechos examined by this study. Three-fourths of all the derechos occurred with 0-2 km shear vector magnitudes less than 16 m s-1, and values ranged from near 3 m s-1 to 30 m s-1. Most of these events also developed and persisted within 0-6 km shear vector magnitudes less than 20 m s-1. These shear values are even observed with WF events, where strong cold pools and high values of CAPE are common. This finding raises questions about the operational value of recent cloud model numerical simulations. Figure 22 reveals the range of CAPE and shear Weisman (1993) found to be associated with near-surface wind from a mature bow echo within his numerical cloud model. Our proximity soundings near mature derechos (Fig. 23a, Fig. 23b) indicate a considerable range of CAPE/shear environments for mature derechos that is much greater than those suggested by the numerical bow echo simulations, particularly with regard to the shear. In addition, when estimates of cold pool strength are compared to the corresponding ambient shear, no statistical correlation is found. Our results raise questions about the validity of any hypothesized shear-outflow balance, at least insofar as it can be estimated in an operational setting. Our observations are more consistent with the findings of Garner and Thorpe (1992) who found that neither the low- level vorticity nor the depth of the shear layer is by itself a good predictor of squall-line development in their simulations.
On the other hand, we have examined the system-relative winds and found they show a more consistent association with long-lived bow echoes than the low-level shear. Recall that Brooks et al (1994a) and Thompson (1998) have suggested that storms with weak midlevel storm-relative winds should produce an outflow-dominated storm. In unstable environments that are not excessively capped, new cells then can develop along the outflow boundary. Large convective systems such as bow echoes obviously are quite different from supercells; however, the results of our study suggest system-relative wind arguments may have a similar application in explaining long-lived bow echo behavior.
In most derecho environments, we have shown that the 4-6 km SRWs are consistently weak (Fig 5). Although strong low-level inflow is observed to be common, with average 0-2 km SRWs in excess of 15 m s-1, midlevel (4-6 km) SRWs are, on average ,much weaker (9 m s-1). This is most pronounced in the WF cases, though the majority of SF and Hybrid events also reveal the same weakness in the midlevel SRW. Thompson (1998) found that only 19% of his tornadic supercell cases occurred within 500 hPa SRW less than 10 m s-1. In the present study, 75% of the WF events occurred when 4-6 km SRW is less than 10.5 m s-1. There remains considerable overlap between SRW values of SF events and for those of tornadic supercells (Thompson 1998). However, since 11.5 tornadoes accompany each SF derecho on average, this may actually support the finding that SF derechos can exist in environments not supportive of enhanced cold pools.
A comparison between WF derecho and non-derecho MCSs implies that the strength of the mean flow, and its possible effects on speed of movement, also may be important in the development of sustained severe wind gusts at the surface. This argument is further supported by an inverse relationship between 0-6 km mean flow and DCAPE with long-lived convective windstorms. This relationship seems to provide a clear separation between the SF and WF environments in terms of the mean wind, and little connection is found between the deep layer mean wind and the deep layer shear.
Although results from cloud model numerical simulations produce long-lived bow echoes within idealized environments that resemble some of our observed WF cases, our findings indicate that derechos also occur under a wide variety of CAPE/shear conditions that are different from the environments used in the simulation experiments. Forecasters should be alert to the potential for derecho formation within environments characterized by weaker CAPE and low-level shear than suggested by cloud model experiments, especially when rapidly moving baroclinic disturbances are present.
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Figure 1. Monthly distribution of derecho events with at least one proximity sounding for the years 1983- 1993. Events are separated by forcing type.
Figure 2. Graphical plot of each derecho centroid, along with the number and location of proximity soundings used in this study.
Figure 3. Plot of the range of 0-2 km, 0-3 km, and 0-6 km (all AGL) shear associated with derechos. Box and whisker plot of shear vector magnitude with each sounding. Boxes denote the 50 percent of values between the 25th and 75th percentiles, with thin vertical line extending to the maximum and minimum values.
Figure 4. As in Fig. 3 except for 0-2 km and 0-6 km shear vector magnitudes with SF and WF events.
Figure 5. As in Fig. 3 except for 0-2 km and 4-6 km system-relative winds with SF and WF events.
Figure 6. As in Fig. 3 except for bulk-richardson number shear for All, WF, SF, and Hybrid events.
Figure 7. As in Fig. 3 except for: Fig. 7a) CAPE generated by lifting the most-unstable parcel (MUCAPE). Fig. 7b) CAPE generated by lifting a mean-mixed parcel through the lowest 100 m (MXCAPE). Both plots use the virtual temperature correction.
Figure 8. As in Fig. 3 except for difference in surface equivalent potential temperature (qe) of ambient environment immediately ahead of outflow boundary and minimum within cold pool for All, WF, SF, and Hybrid events.
Figure 9. As in Fig. 3 except for downdraft convective available potential energy (DCAPE) for All, WF, SF, and Hybrid events.
Figure 10. Scatter plot of DCAPE values versus associated maximum surface qe difference across each cold pool (Dqe). Each plot is annotated with its corresponding large-scale forcing type.
Figure 11. As in Fig. 3 except for 0-2 km and 0-6 km shear vector magnitudes distributed in varying MUCAPE environments. "Weak", "Moderate" and "Strong" categories represent MUCAPE classified by percentile rank in Fig. 6A (see text).
Figure 12. The four stages of evolution with an "idealized" simulated bow echo (After Fig. 18 from RKW). (a) through (d) show the gradual development of a vertical updraft along the leading edge of the outflow boundary, eventually supported by an elevated rear inflow jet [dashed arrow in (d)]. This is based on a hypothesized relationship between the inherent circulation along the leading edge of the cold pool (shaded area) and the low level ambient shear.
Figure 13. Scatter plot of DCAPE versus 0-6 km mean wind. Each plot is classified by forcing type.
Figure 14. As in Fig. 13, except for DCAPE versus 0-6 km shear.
Figure 15. As in Fig. 13, except for 0-6 km mean wind vs 0-6 km shear.
Figure 16. As in Fig. 12 except (Fig. 16a) DCAPE versus 0-2 km shear vector magnitude and (Fig. 16b) maximum difference in surface qe across the cold pool versus 0-2 km shear.
Figure 17. [Fig. 17a, Fig. 17b] As in Fig. 16 except classified by life-cycle stage of bow echo associated with each sounding.
Figure 18. As in Fig. 3 except for DCAPE and MUCAPE associated with 13 non-derecho producing MCSs.
Figure 19. As in Fig. 3 except for 0-6 km mean wind and speed of forward movement to the overall MCS for both non-derecho and derecho producing WF events.
Figure 20. As in Fig. 3 except for (a) 0-2 km and 0-6 km shear vectors for both non-derecho and derecho producing WF events.
Figure 21. As in Fig. 3 except for 0-2 km and 4-6 km system-relative flow (SRW) associated with WF derecho and non-derecho events.
Figure 22. Maximum near-surface (350 m) wind (m s-1) for the (a) 2.5 km shear and (b) 5 km shear from Weisman's numerical simulation [after Fig. 25 in Weisman (1993)], plotted against corresponding CAPE used. Us represents the maximum magnitude of the wind for each wind profile.
Figure 23. Plot of the observed range of (Fig. 23a) 0-2 km shear vector and (Fig. 23b) 0-6 km shear vector from "along path" proximity soundings associated with mature derechos, plotted against corresponding MUCAPE. Each plot is categorized by the strength of the associated synoptic-scale forcing.