Understanding the dynamical structure and evolutional characteristics of convective storms has long been an active area of research in the meteorological community.   Investigations, both observational and numerical, have centered on the most nocuous of convective storms such as the paradigmatic supercell and the larger mesoscale genitors, convective squall line systems and complexes.  Supercell storm structure has received the greatest amount of attention due to the disproportional amount of damage and the loss of life procured by these storms (Klemp 1987; Johns and Doswell 1992; Przybylinski 1993; Moller et al. 1994).  A secondary investigative outgrowth in convective meteorology has focused on mesoscale convective systems (hereafter MCSs) and their severe progeny, the derecho (Johns and Hirt 1987).  Widespread damaging winds engendered from derecho-producing mesoscale convective systems (hereafter DMCSs) can cause F1 to F2 damage and thus requires intense examination.
     Understanding the quasi-steady nature of MCSs has been the focus of multiple observational investigations (Duke and Rogash 1992; Johns 1993; Johns et al. 1990; Przybylinski 1995; Bentley et al., forthcoming) and numerical modeling experiments (Schmidt et al.1990; Weisman 1990, 1992, 1993; Rotunno et al.1988; Skamarock et al. 1994). This paper is an examination of the current theory of strong, long-lived MCSs.  First, an explication of the environmental conditions necessary to create linear convection will be had. Secondly, this study will procure an understanding of the important dynamical relationship that forms between the convectively induced cold pool and low-level environmental shear, and to what purpose is this relationship important in the initiation, maintenance, and propagation of MCSs. This aspect of the study will require a physical interpretation of numerical model results.  Additionally, MCS commonalties, the rear-inflow jet and bookend vortices, will be introduced and related to MCS phase structure. Further, relating model observations to those surveyed in atmospheric observations will synthesize these data.

MCS Environment
     Any investigation into MCS dynamics must commence with an understanding of the environment that begets linear convection.  Bluestein and Jain (1985) categorized severe convective lines by analyzing 11 years of WSR-57 reflectivity data from Norman, Oklahoma.  In developing the four primary classes of convective line formation (broken line, back building, broken areal, embedded areal), Bluestein and Jain investigated and compared sounding and hodograph structures of the near-MCS environment in each of these cases.  Analysis found large latent instability (moderate to high CAPE) within the pre squall-line environments along with an average line-normal shear of 45? clockwise with respect to the squall line (Bluestein and Jain 1985; Rotunno et al. 1988).  This shear vector is distinctively different than the near 90? average line-normal shear vector needed to sustain MCS structure in modeling investigations (Weisman 1992; Przybylinski 1995).  Rotunno et al. (1988) conclude that the large skew in line-normal shear is caused by the large proportion supercells comprising squall lines that are characteristic of Oklahoma.
     Bentley et al. (forthcoming, hereafter BMB) define the synoptic-scale conditions associated with DMCSs in the northern Plains by analyzing surface, upperair, and reanalysis datasets of the DMCS near environment.  This climatological study confirms previous MCS investigations (Johns and Hirt 1987; Johns 1993) that demonstrate that the low to mid-level environment is significant in discerning MCS development, sustainment, and movement (BMB).
      Diagnosing a DMCS environment must begin with a determination of the convective instability and shear regimes.  BMB found that a high degree of convective instability is necessary for the development of DMCSs.  An averaged CAPE of 2609 J/kg and lifted index of - 4 degrees C was found from the 19 DMCS events examined in their study.   Notwithstanding, a wide variation in CAPE and lifted index values may be detected, especially if forecasting a cool season event.  A large theta-e ridge (maximum values of 336K - 342K) with a distinct gradient is also frequently found extending into a DMCS genesis region (BMB).  Both CAPE and the relative humidity of the low to midlevels are significant in determining cold pool strength (Rotunno et al. 1988; BMB).  Further, the strength of the convectively induced cold pool is dependent on the source region of the downdraft.  A stronger cold pool can be expected if the downdraft air originates at the level of minimum theta-e (Weisman and Przybylinski 1998).
     Subsequent to convective instability, diagnosing the low to midlevel environmental shear is significant in determining whether convection may initiate and become linear.  Using the Klemp Wilhelmson (1978) numerical model, Weisman (1992, 1993) found that moderate to strong low to midlevel vertical shear is a necessary characteristic of MCS environments.  Significant low to midlevel line-normal shear (shear that is perpendicular to the convective MCS line) is critical in controlling MCS structure and evolution (Weisman 1993, BMB).
      Because significant numbers of MCSs are nocturnal, the evening sounding should be studied with great precision to determine whether the correct shear environment is transpiring.  For determination of MCS environment in the daytime, morning sounding data must be augmented with profiler data to determine if the environmental shear conditions are favorable for long-lived MCSs.  Hodograph shape in MCS environments is often similar to conditions that are conducive to supercells (Bluestein and Jain 1985; Weisman and Przybylinski, 1998).  This constitutes a significant problem in determining whether supercells, a squall line composed of supercells, or a convectively linear MCS will develop.  However, BMG did discern line-normal, unidirectional flow occurring in the mid and upper-levels of the DMCS environment in most cases.  Analysis of hodograph and sounding data is out of the scope of this paper; the reader should review Bluestein and Jain (1985), Evans (1998), Weisman and Przybylinski (1998) for further discussion on these forecasting techniques.
     Johns and Hirt (1987) and BMG further describe the synoptic conditions favorable for producing MCS and DMCSs.  BMG found that nearly 50% of warm season DMCSs in the Northern Plains originate in northwest upper-flow patterns under a ridge of high pressure.  Other synoptic conditions favorable for the development of DMCSs include a midlevel short-wave trough migrating into the genesis region and a weak surface quasi-stationary thermal boundary that is often oriented east-to-west.  Both BMG and Johns and Hirt (1987) detected significant warm air advection (WAA) in the 850 and 700 mb levels that occurs poleward of the quasi-stationary thermal boundary.  WAA provides upward vertical motion that allows for the release of potential energy in the DMCS genesis region (Johns and Hirt 1987; Johns and Doswell 1992; BMG).  The before mentioned conditions are not always found in the DMCS environment (Przybylinski 1995).  Other dynamically induced DMCSs constitute a significant portion of cold-season DMCSs (Johns 1993).

Conceptual Model: MCS Kinematics, Thermodynamics, and Features
     Before an inquiry into the dynamical relationship of the cold pool and low level ambient shear within MCSs, it is necessary to discuss the kinematic structure of the archetypal mature MCS; that of a leading convective line with a trailing stratiform precipitation region.   MCS research within the last decade has focused on the presentation of two-dimensional and three-dimensional models of MCSs in order to aid operational meteorologist in understanding the evolutional and physical structure of MCSs (Przybylinski 1995).  The most referenced model is that of Houze et al. (1989), who provided a detailed two-dimensional schematic of MCS structure via investigation of Doppler radar imagery of MCSs that occurred in the PRE-STORM (Preliminary Regional Experiment for Stormscale Operational and Research Meteorology) experiment conducted in May and June of 1985.  The Houze et al. (1989) model yields a good general overview of air flows, circulations, and features found in a mature MCSs, albeit major discrepancies of individual flow genesis and bearing do arise in comparison with some models.  A brief discussion of these internal dynamics and features that constitute a leading line/trailing stratiform mature MCS will follow.
      The kinematic structure of a mature MCSs is characterized by two dominating flows.  First, an upward-sloping, high theta-e front-to-rear flow is initiated at the gust front upon where it enters the convective updraft and accelerates rapidly towards the tropopause (Houze et al. 1989; Weisman 1993). Thereafter, this flow exits rearward of the convective cloud structure into the large nimbostratus anvil cloud formed from the convective exhaust.  An important characteristic of this flow is the transport of ice crystals rearward into the anvil portion of the system, providing nuclei for the formation of stratiform precipitation rearward of the leading convective line (Houze et al. 1989).
     The second distinguishing storm-relative current is the downward-sloping rear-to-front flow (also referred to as the rear-inflow jet).  This distinctive low theta-e flow enters the rear of the storm in the midlevels where it remains elevated as it advances forward.  When the rear-to-front current approaches the convective line, the flow quickly descends eventually combining with precipitation downdrafts to aid in convergence at the gust front (Houze et al. 1989).  Fovell (1990) determined that the most significant contribution to the mass of the cold pool, and thus the affiliated convective regeneration, was by the rear-to-front flow.  The intensity of the rear-to-front flow varies greatly from one individual MCS to another because of flow modification by the ambient conditions and flow dependence on what evolutional stage the storm is in at the time (Smull and Houze 1987).
     Lemone et al. (1984) found that the horizontal flow acceleration in the middle layers of the stratiform region is due to a hydrostatically induced pressure perturbation.  A pressure minimum develops directly rearward of the convective updrafts producing a net flow inward toward the front of the convective line. Brown (1979) postulates that a secondary, elongated geopotential depression formulates in the middle layers due to latent heat release (from the freezing of supercooled water droplets) of the rearward exiting convective plume and the saturated ascent of rain cooled air from the stratiform region.   Numerical simulations by Weisman (1990, 1992, 1993) confirm formation of rear inflow in the vicinity of the melting layer.  The midlevel mesolows act to draw air inward due to the pressure gradient force.  Formation of both the front-to-rear and rear-to-front flows does not occur until the horizontal vorticity associated with the cold pool is intensified and overwhelms the circulation of the ambient shear (Weisman 1992).   This system-relative current of air is crucial in supplying potentially cold and dry midlevel air to aid in the genesis of convective and system-scale downdrafts (Weisman 1992; Smull and Houze 1987)

Cold Pool/Shear Interaction
     Significant to the sustainment of MCSs is the generation of a deep cold pool (Weisman 1992).  As previously described, CAPE and the relative humidity of the low and midlevels are significant determinants of cold pool strength and depth (Rotunno et al. 1988; BMB).  Studies using 2D and 3D nonhydrostatic convection-resolving models by Rotunno et al. (1988), Weisman (1988, 1992, 1993), and Skamarock et al. (1994) have focused on identifying the structure and evolution of the leading convective line.  By varying CAPE and wind shear vectors, these modeling efforts have provided detailed descriptions of the dynamics within MCSs.  The ensuing discussion will explain the dynamic situation between the cold pool and ambient vertical shear that is described in these modeling efforts.

The Cold Pool
     It is well documented that a cold pool engenders below the cumulonimbi due to evaporative cooling and precipitation loading in the convective-scale downdraft  (Weisman and Przybylinski 1998; BMG; Weisman 1993; Houze et al. 1989). Entrainment of midlevel low theta-e aids in enhancing evaporational cooling, further strengthening the downdraft and the cold pool (Rotunno et al. 1988).  It may be determined, using the hydrostatic equation, that since buoyancy is negative within the cold pool, the cold pool is characterized by higher pressure (relative to its surroundings).  Further, utilizing the horizontal momentum equation, it may be concluded that the cold pool will spread outward in response to induced horizontal pressure gradients (Weisman and Przybylinski 1998).  Generation of the horizontal pressure gradient produces vorticity at the edge of the cold pool.  This vorticity is characterized by diverging flow at the surface, upward motion at the leading edge of the cold pool, along with a return flow aloft toward the center of the cold pool.  If a warm pool (positively buoyant cumulonimbi) were placed over the cold pool, a mesolow is generated between the two pools (as previously described).  This dynamic situation produces vertically stacked vorticity couplets of opposite signs, creating strong midlevel convergence (Weisman and Przybylinski 1998).
      A cold pool spreading in a windless environment is likely to produce convergence and lifting along its leading edge which can trigger new cells (Weisman 1993).  However, if vertical wind shear is occurring in the environment, and if the low level wind shear vector is perpendicular to the spreading cold pool, cell regeneration may be expected to occur on a distinct flank of the spreading cold pool (Weisman 1993).  The ambient, low-level vertical wind shear generates a horizontal vorticity that is opposite the vorticity associated with the cold pool (Weisman and Przybylinski 1998).  The optimal conditions for cell regeneration along a spreading cold pool occur when the horizontal vorticity generated by the buoyancy gradient at the edge of the cold pool is balanced by the opposing horizontal vorticity inherent in the low-level vertical wind shear (Weisman 1993; Rotunno et al. 1988).  Weisman (1993) hypothesizes that this mechanism, alone, may explain the strength and longevity of MCSs.

Evolution of the MCS
      In the early stage of MCS evolution, convective cells form along some pre-existing linear forcing feature.  Ambient vertical wind shear provides additional horizontal vorticity to the already established horizontal vorticity produced by the positively buoyant, convective cell (Weisman and Przybylinski 1998).  The summation of the two circulations causes the convective cells to lean downshear (Rotunno et al. 1988; Weisman 1992).

    As precipitation continues to fall below the cumulonimbi, a cold pool is created.  The cold pool systematically expands and strengthens as the sequence of cells continually feeds the pool with negatively buoyant air (Weisman and Przbyklinski 1998). As previously described, this low-level cold pool is developed by several mechanisms: (1) precipitation fallout which induces downward momentum or drag, (2) evaporation of precipitation as it travels through mid-level dry air causing negative buoyancy (Houze, 1993).  The downdraft and the cold pool interact to form the mesohigh at the surface and to drive surface outflow, low-level convergence, and initiation of a gust front (Houze et al, 1989; Weisman, 1992; Bentley, 1995).
      As the cold pool is engendered below the convection, increased negative horizontal vorticity at the front of the cold pool corresponds with the positive horizontal vorticity inherent in the ambient shear.  When the cold pool circulation becomes strong enough to balance the horizontal vorticity associated with the ambient shear, a balance is achieved which gives rise to an equilibrium in the system, producing an erect updraft (Weisman 1992; Weisman and Przybylinski 1998).  This creates a region of substantial deep uplift at the edge of the cold pool, which allows for the development of strong convective cells.  Intense cells will continue to regenerate along the cold pool edge as long as these two horizontal vortices are coupled and a mesohigh is in place (Houze et al, 1989; Weisman, 1990; Rotunno et al., 1988).
     The early stages of MCS evolution involve the formation of a squall line composed of individual strong cells without the presence of a rearward stratiform rain region (Weisman et al., 1988).  The persistence of precipitation within the convective line systematically acts to strengthen the cold pool, increasing the depth of the pool.  Thus, the horizontal vorticity associated with the cold pool is intensified which overwhelms the circulation that is allied with the ambient shear (Weisman 1992; Weisman and Przybylinski 1998).  This causes the system to tilt upshear.  At this point in MCS evolution, the squall line is characterized by a sequence of cells that initiate at leading edge of the cold pool, then mature and eventually decay as they advect rearward over the cold pool (Weisman and Przybylinski 1998).  In addition, the cells that compose the squall line become less intense in this stage because the lifting at the leading edge is not as strong as it was when the updraft was being generated by a balanced vorticity couplet.  Further rearward advection of decaying cells produces the lighter, more stratiform region of precipitation behind the leading convective line that is characteristic of mature MCSs (Houze et al, 1989; Weisman, 1992).   The conceptual model put forth by Houze et al. (1989) is representative of this stage of MCS evolution.  Thus, two mesoscale storm-relative airflows and multiple mesolows and mesohighs dominate the system at this stage.
     The evolutional timeframe for an MCS to become upshear-tilted is dependent on a pair of factors.  First, the overall strength and depth of the cold pool determines the amount of lift available at the gust front at any point in the storm evolution (Weisman and Przybylinski 1998).  A deeper cold pool slows the upshear evolution. The environmental variables that determine the strength of the cold pool have previously been discussed.  Further, the magnitude and orientation of the shear determines if the vorticity associated with the cold pool may be balanced or unbalanced (Weisman 1992).  In general, the deeper and stronger the shear layer, the more intense the circulation associated with the ambient shear and, thus, the longer the upshear evolution will take (Weisman 1992, 1993; Weisman and Przybylinski 1998).  However, if the shear is too strong, the updrafts may be torn apart before they can grow into mature cells (Weisman and Przybylinski 1998).  As is clearly apparent, successful forecasting of MCS structure and strength is dependent on the examination of hodographs.

Rear-Inflow Jet
     As the system evolves, two separate flows become recognizable and converge to form an individual downdraft within the convective, squall line region (Bentley 1995).  The initiation of the first inflow occurs ahead of the system where uplift along the gust front is generated.  This flow separates at the cloud base; one branch continuing upward aiding in convection, the second current proceeds to the surface due to negative buoyancy created by precipitation.  This second branch acts to sustain outflow at the surface needed for the constant propagation of the gust front (Schmidt et al. 1991).
     The second major system-relative current is the rear-inflow jet (RIJ) that originates in the mid-levels within the elevated mixed layer of a maturing MCS (See dashed line in Figure 3c and 3d).   The rear inflow does not develop until the system becomes tilted upshear.  An upshear-tilted MCS is dominated by the spreading of convective cells spread rearward, which transports warm air aloft (Weisman 1992).   As previously discussed, the dynamic situation of a cold pool at the surface with warm air aloft produces a negative pressure perturbation in the midlevels.   This generation of an elongated mesolow in the midlevels produces a net inflow into the center of the system (Weisman and Przybylinski 1998).  Furthermore, the generation of the rear-inflow jet may be explained from a horizontal vorticity perspective (Weisman, 1992).  Negative horizontal vorticity forms in the midlevels due to positive buoyancy in the warm plume trailing the squall line.  Subsidence induced warming overwhelms evaporative cooling producing the positive buoyancy (Bentley, 1995).  Positive horizontal vorticity is formed at the rear of the cold pool due to negative buoyancy caused by outflow of air from the cold pool at the surface.  This vertically stacked horizontal vorticity couplet is responsible for the generation of the low ?e rear-inflow jet (Weisman and Przybylinski 1998).
     The intensity of the RIJ is controlled by the strength of the buoyancy gradients generated by the warm plume (front-to-rear flow) and the cold pool (Weisman and Przybylinski 1998).  Because the buoyancy gradients are directly related to the temperatures of the warm plume and the cold pool, the relative strength of the RIJ may be determined by the thermodynamic instability in the environment (Weisman 1992).  Increasing the maximum potential temperature excess for a rising parcel produces an increase in the potential warming of the warm plume (Weisman and Przybylinski 1998).  Further, increasing lapse rates and increasing dryness in the midlevels increases the potential cooling of the cold pool (Weisman and Prybylinski 1998; Weisman 1992).  Hence, a large amount of CAPE is conducive to the development of a strong rear-inflow jet (Weisman 1993).
     Additionally, Weisman (1993) determined that strong low-level vertical shear maximizes a parcel's potential temperature excess through the reduction of mixing along the parcel's path.  Stronger low-level vertical shear intensifies lifting at the edge of the cold pool.  This enhanced uplift produces a stronger front-to-rear flow that functionally transports warm air rearward.  Increasing the temperature of the warm plume enhances the horizontal vorticity rearward, which ultimately strengthens the RIJ (Weisman and Przybylinski 1998).  Finally, synoptic-scale influences (e.g. strong polar jet, intense mid-level-relative winds) may aid in the development of a rear-inflow jet (Johns 1993; Weisman and Przybylinski 1998).

The Role of the Rear-Inflow Jet
     Rotunno et al. (1988) describe that the cold pool dominated, upshear-tilted phase is generally the beginning of the decaying stage in MCS evolution (Weisman 1993).   However, if buoyancy gradients aloft are strong relative to the cold pool, a strong, elevated rear-inflow jet may halt the decay of the MCS (Weisman 1992; Weisman and Przybylinski 1998).  Along with an increase in system longevity, the overall intensity of the convective line may increase.  This addition in storm strength and duration may be explained via the addition of rear-inflow induced speed shear (Weisman 1993).  The speed shear associated with the rear inflow jet, below the level of maximum shear, produces horizontal vorticity that is the same sign as the ambient shear.  Above the level of maximum shear, negative horizontal vorticity is generated.  This speed shear induced horizontal vorticity is the same sign as the vorticity generated by the cold pool (Weisman 1992).  The juxtaposition of these horizontal vortices diminishes the net impact of the strong cold pool circulation that is overwhelming the ambient shear rotation (Weisman and Przybylinski 1998). Hence, the convective updrafts become vertically erect once more, intensifying the leading squall.  An intense (20 - 30 m/s relative to storm motion) RIJ is a characteristic of developing bow echoes (Weisman 1992).

     Weisman (1992), via modulation of simulations, established that an elevated RIJ is associated with large convective instability (CAPE) and strong vertical wind shear.  If the environment contains weak vertical shear and minimal CAPE, a descending RIJ may be established. A RIJ that surges to the surface well behind the convective line is attributed to weak buoyancy gradients affiliated with the warm air aloft.  In this case, the negative horizontal vorticity generated by the cold pool is of the same sign of the vorticity associated with the RIJ (Weisman and Przybylinski 1998).  This vorticity summation produces a cold pool circulation that overwhelms the ambient vertical shear creating a upshear-tilted, weakening MCS.

Bookend Vortices
     Common to mature MCS 3D structure are line-end vortices.  These "bookend" vortices are located at the extremities of the convective squall line forming a poleward mesocyclone and equatorward mesoanticyclone (Weisman and Przybylinski 1998). Three dimensional numerical simulations by Weisman (1993) and Skamarock et al. (1995) found that these vortex pairs are especially important in the generation of severe bow echoes that are affiliated with an increase in straight line winds at the surface.
     A tilting and stretching of the horizontal vortex intrinsic in the ambient vertical wind induces the vortices (Skamarock et al.1995).  Acceleration of the flow around the vortices causes a decrease in pressure fields. A region of higher pressures separates the low pressure analogous with each vortex, which produces an increase in flow (RIJ) between the two "bookend" vortices (Weisman 1990). An intensification of the RIJ of 10 - 15 m/s may occur if the bookend vortices are not widely spaced (<  60 km) along the squall line (Weisman and Przybylinski 1998).  Eventually, the Coriolis force allows the poleward vortex to eventually grow to dominance leading to an asymmetric MCS and skewing of the shear field (Houze et al. 1989).

Concluding Remarks
    This survey demonstrates that the low-level environment is critical in determining MCS strength and evolution.  The convectively generated cold pool and ambient low-level shear modulate convective updraft strength in the leading squall line.  When the horizontal vorticity associated with the cold pool balances the circulation induced by the low-level environmental shear, intense, erect updrafts are generated.  The system begins to tilt upshear as the cold pool induced horizontal vorticity strengthens.  RIJ initiation and strengthening may abate the detrimental affects the amplifying cold pool circulation has on the system.  The elevated RIJ generates horizontal vorticity opposite the cold pool circulation that reconstitutes system balance, allowing the system to reach a quasi-steady state.  Additionally, the generation of "bookend" vortices may intensify the RIJ, which could induce bowing in leading convective line echo structure, indicative of strong straight-line winds.
     Both numerical simulations and MCS observations verify that large amounts of convective instability and strong low-level ambient vertical shear are essential in the generation of a quasi-steady MCS.  MCS genesis regions are typically located under ridges of high pressure where convective instability is ordinarily high (BMB).   Increasing CAPE enhances buoyancy gradients within the MCS, which increases cell severity, strengthens the RIJ, creates stronger line-end vortices, and ultimately attenuates system lifetime (Weisman and Przybylinski 1998).  Additionally, MCS synoptic environments are typified by a quasi-stationary front upon where a surface low pressure center may form.  This surface low may engender line normal low-level winds that aid in strengthening system-relative convergence and augmenting system longevity (BMB).
     Future examinations and numerical simulations will likely focus on MCSs that form in strong-dynamic low instability environments (i.e. cold season events).  Additionally, regional Doppler radar data must be incorporated into future studies to further describe internal MCS kinematics.   Operationally, to successfully predict the intensity and evolution of MCSs, meteorologists must be able to assimilate the wealth of technological information (e.g. real-time mesoscale models and weather processing systems) available as well as understand MCS dynamics and structure.