a. Ground-based mobile radar analysis

The multiple ground-based radar analysis is briefly summarized in the present section, with details described by Ziegler et al. (2007). The ground-based mobile radar data have been extensively edited using NCAR’s SOLO software program (Oye et al. 1995). After time-to-space adjustment of data locations at a velocity of 225° at 4.6 m s⁻¹ to correct for the movement of updraft and reflectivity cores and misocyclones, Barnes weighting (Barnes 1973; Koch et al. 1983) is used to interpolate radial velocity and reflectivity data to a 3D Cartesian analysis grid with NCAR’s REORDER software (Oye et al. 1995). The Barnes weighting function has the form w = exp(−r ²/κ), where r is the distance between a grid point and a datum. The low-pass-filter response of the Barnes analysis (Fig. 1) is controlled by prescribing its smoothing parameter κ (Table 1). The spatial dimensions of the Cartesian radar analysis domain are 50 km × 50 km horizontally and 2.5 km vertically, while the corresponding horizontal and vertical radar analysis grid spacings are 0.5 and 0.25 km, respectively.

Gridded single Doppler fields are combined to produce fields of composite reflectivity and synthesized 3D airflow employing upward integration of mass continuity from w = 0 at ground and the overdetermined two-radar analysis option of NCAR’s Custom Editing and Display of Reduced Information in Cartesian Space (CEDRIC) software (Mohr et al. 1986). The interpolated reflectivities from DOW radars are linearly scaled for optimal consistency with the calibrated SR1 reflectivities. A gridded reflectivity analysis is composited by assigning each gridpoint the first nonmissing objectively analyzed single radar value from either DOW2, DOW3, XPOL, or SR1 (i.e., in that order of precedence). Multi-Doppler radar analyses are obtained at 3-min intervals during the period of 1815–2015 UTC (Table 2). The wind synthesis employs an optimal combination of radars that minimizes sampling errors of the shallow cold front (Ziegler et al. 2007). Judging from the temporal continuity of individual moving cores of reflectivity, vertical velocity, and vertical vorticity in results to be presented, a 3-min analysis interval appears sufficient to resolve the evolution of the meso-γ scale (∼1–10 km wavelength) boundary layer circulations of interest for this study.

b. Lagrangian analysis of thermal variables

The essential aspects of the Lagrangian analysis scheme are summarized in this section, with details described by Ziegler et al. (2007). In brief, a Lagrangian principle is employed to propagate sparse in situ observations along up- and downstream air trajectories assuming conservation following the motion, providing an enhanced dataset for 3D objective analysis. The Lagrangian analysis proceeds via a multistep approach, including the preconditioning of wind and in situ data, the generation of air trajectories from in situ data and grid-column soundings (described below), and a 3D, two-pass Barnes objective analysis of all Lagrangian trajectory data. The Barnes weighting function takes the form w = exp[−(r ²/κ_s) − (t²_i/τ_i) − (t²_L/τ_L)], where t_i is the time difference between an observation time and the nominal map time and t_L is elapsed time along a trajectory. The spatial and temporal low-pass-filter responses (Fig. 1) are controlled by setting the Barnes smoothing parameters κ and τ (see Table 1).

In situ observations from mobile mesonets, mobile soundings, and aircraft are augmented in mesoscale boundary layer updrafts by pseudo-soundings derived by adjusting a reference sounding profile according to the local surface Lagrangian analysis value derived from the dense mobile mesonet surface analysis (Ziegler et al. 2007). In the prefrontal BL case (i.e., on either side of the dryline), the local grid-column sounding is obtained by averaging percentages of the moist and dry side reference soundings along a mixing line with a mass fraction based on the local mixing ratio value of the surface analysis. In the postfrontal BL case, the reference sounding adjustment increases linearly from zero at the BL top to the difference between the surface reference sounding and surface analysis values. Three unique, airmass-specific reference soundings are employed to globally represent observed soundings in the respective air masses (i.e., predryline, between front and dryline, and postfrontal). Lagrangian variables include water vapor mixing ratio, potential temperature, and virtual potential temperature.

After decimating (i.e., sampling at a subinterval of) the input in situ data to restrict the analysis to resolvable scales, the analysis propagates in situ and gridpoint data along forward and backward 4D trajectories employing a quadratic Runge–Kutta predictor–corrector time integration scheme with trilinear spatial and linear time interpolation between neighboring input multi-Doppler analyses. The Lagrangian data are decimated and interpolated to a subdomain of the radar analysis grid employing a two-pass Barnes spatial and temporal interpolation scheme (Barnes 1973; Ziegler et al. 2007). In the 24 May case, the subdomain dimensions are 25 km in each horizontal direction and 2.5 km vertically. Lateral boundary conditions are imposed from the airmass-specific reference soundings via forward trajectories from lateral boundary points. Gridpoints with height z > z_LCL have achieved water saturation, implying the presence of cumulus cloud. Areal cumulus coverage from the Lagrangian analysis is validated with photogrammetric cloud base analyses (e.g., Rasmussen et al. 2003) and gridded Geostationary Operational Environmental Satellite (GOES-8) visible images following methods described by Ziegler et al. (2007), while selected local Lagrangian analysis profiles are compared directly with observations reported by G06 and K06.

a. Doppler analysis and cloud field

The dryline and a convergence line are observed by the mobile radars and mobile mesonets at 1848 UTC (Fig. 3a), while the cumulus cloud field is concentrated northeast of the convergence line (Fig. 3b). A strong cold frontal shearing zone marked by high values of vertical vorticity and reflectivity moves rapidly southeastward through the IOR during the period of radar observations, passing DOW3 between 1924 and 1945 UTC (Figs. 3c,e) and passing the FC just prior to 2006 UTC (Fig. 3g). At 1959, the FC observers note a “. . . large dust column 1 km east . . . near [the] triple point,” while at 2000 UTC the “. . . cold front is passing FC” accompanied by strong gusty winds and the cold front passes the MIPS around 2006 UTC (Fig. 3g,h, 16; K06). The dryline moves slowly eastward between 1848 and 2006 UTC, marked by veering winds and slightly enhanced reflectivities greater than 20 dBZ. In contrast, the highest reflectivities of over 25 dBZ are observed along and just behind the cold front. The FC observers note airborne straw and small leaves in addition to blowing dust following frontal passage, suggesting that postfrontal reflectivities may be significantly enhanced by these large particulate scatterers. Combined with the rapid southward movement of the cold front, the classical triple point intersection of the dryline and cold front moves southward after 1924 UTC (Figs. 3c,e,g).

The cumulus field is concentrated to the east of the dryline and cold front after 1924 UTC (Figs. 3d,f,h), with a broad band of brighter cloud tops developing along the front northeast of the triple point. The western edge of the bright cloud band extends north of the cold front and triple point roughly along the axis of the dryline aloft (Figs. 3d,f,h), implying advection of the predryline air mass and the dryline gradient itself over the front as previously suggested by Weiss and Bluestein (2002). The hypothesis that the dryline gradient is preserved following postfrontal advection is also supported by the Lagrangian analysis results to be shown (e.g., Figs. 14 and 15). However, the northern and western extremity of the cloud field becomes progressively more ragged in appearance with increasing distance north of the front, implying the action of a dissipative process (e.g., shearing deformation and mixing, subsidence, and evaporation). The southeast edge of the postfrontal stratus cloud shield (Fig. 2a) develops bands coincident with roll-like reflectivity features probably associated with Kelvin–Helmholtz rolls (to be discussed in section 4a) or gravity waves (Fig. 3e–h; see also G06).

The radar analyses reveal finite-length bands of positive and negative vertical vorticity oriented at a large angle to the flow (transverse vorticity bands) ahead of the cold front, and numerous misocyclones are also analyzed in all three air masses (Figs. 3a,c,e,g). Several attachment points of transverse vorticity bands with the cold front are evident [e.g., (17, 35), Fig. 3c; (25, 31), Fig. 3e; (23, 16) and (31, 23), Fig. 3g]. Animations of the 3-min analyses over the 2-h analysis period indicate that individual updraft and reflectivity cores, misocyclones, and transverse vorticity bands ahead of the front all are rather coherent and move steadily with the local horizontal wind (e.g., approximately from the southwest at 5 m s⁻¹). Time sequences of various fields at fixed heights reveal the linear translation of reflectivity cores (Fig. 4a), misocyclones (Fig. 4b), and updraft cores (Figs. 4c,d) with the local low-level flow, demonstrating that these boundary layer features may persist for up to 30 min or more as they move downstream. Interestingly, several reflectivity cores are embedded and move northeastward within the southeastward-advancing frontal surface (Fig. 4a). The differential motions of the front and individual prefrontal vorticity cores are consistent with the previously mentioned attachment of vorticity bands to the cold front.

At 1848 UTC, individual mobile mesonet traverses are used to help locate the dryline and convergence line in zones of enhanced vertical motion, vertical shear, and reflectivity plumes (Fig. 5a). Strong updrafts, collocated reflectivity plumes, and enhanced vertical shear mark the dryline as it moves eastward between 1924 and 1945 UTC (Figs. 5b,c). Several BL circulations are evident on either side of the dryline (e.g., at x = 15.5 km, Fig. 5a; x = 5, 20 km, Fig. 5b; x = 20 km, Fig. 5c), indicating the presence of rolls oriented along the low-level southerly flow (i.e., longitudinal rolls). The sloping cold front is marked by strong updrafts, vertical vorticity up to 5 × 10⁻³ s⁻¹, and a deep reflectivity plume along and rearward of its leading edge at 1945 and 2006 UTC (Figs. 5c,d). GOES-8 images projected into the cross sections indicate that clouds are present above and downstream from updraft cores, though not all updrafts form clouds. Since individual misocyclones exhibit a degree of quasi-steadiness in a vortex-relative reference frame (e.g., Fig. 4b), the transient vorticity cores in the spatial cross sections are actually due to the aforementioned motion of misocyclones and vorticity bands into the plane. A pronounced roll circulation coincides with the reflectivity plume just behind the surface cold frontal position (Fig. 5d; see also W-band radar analysis in Fig. 10b of G06), accompanied by intense upper-level diffluence and a sloping front-relative rearward flow and a high-reflectivity layer that approximately conserves reflectivity following the motion (Figs. 5d and 3d,f,h).

The previously noted transverse vorticity bands are associated with transverse BL rolls (their possible physical forcing mechanisms to be discussed in section 4). A series of transverse rolls spaced about 4–5 km apart move steadily northeastward, distinguished by persistent vorticity and vertical velocity extrema and reflectivity plumes in updrafts (Fig. 6). For example, a well-defined roll (core 3, Fig. 6) maintains the amplitude of its collocated updraft and reflectivity plumes and the flanking opposite-sign vertical vorticity centers between 1912 and 1936 UTC. The association between upward and downward oscillations of airflow in the plane with undulations of a reference (positive) normal velocity contour and associated vertical vorticity cores suggests that the transverse rolls generate along-axis vertical vorticity by tilting and stretching the westerly boundary layer shear (i.e., the shear component parallel to the roll axis). The transverse vorticity bands are finite length (Figs. 3a,c,e,g), supporting the speculation that the longitudinal and transverse roll modes coexist but destructively interfere. Satellite imagery suggests that clouds are located above and downstream from updraft cores and move with the rolls (Fig. 6).

The longitudinal and transverse rolls are frequently distinguished by reflectivity plumes in their updrafts (Figs. 5 –6). However, reflectivity maxima are also noted in downdrafts contained in selected cross sections due to advection of scatterers downstream into the plane from an adjacent finite-length longitudinal roll updraft and its associated reflectivity plume. The existence of BL reflectivity plumes (i.e., caused by microinsects) is consistent with the ambient stratification of reflectivity and the notion that radar scatterers move approximately as passive tracers (i.e., as moisture) with terminal velocities substantially smaller than (though possibly in proportion to) peak updrafts (Geerts and Miao 2005).

The frontal and dryline characteristics from the present ground-based radar analyses are qualitatively compared with the airborne pseudodual Doppler analysis of W06 in the area where the respective analysis domains overlap (Fig. 2a). Although the frontal and dryline shears and reflectivity maxima are broadly comparable (e.g., Fig. 4 of W06 versus Figs. 3c –h), the peak vertical vorticity values of the present analysis are roughly 2–3 times the magnitude of the pseudodual Doppler analysis values due to the finer time and space resolution and smaller filtering of the ground-based radars. For example, a transverse vorticity band attached to the frontal shear zone in the present analysis at (17, 35) and 1924 UTC (Fig. 3c) is revealed as a southeastward-extended lobe of the main frontal vorticity maximum in the 1915–1927 UTC pseudodual Doppler analysis (Fig. 4a of W06). However, the longitudinal and transverse roll updrafts to the east of the front and dryline are discernable only in the present analysis.

b. Mobile mesonet analysis

Low-speed dryline traverses by mobile mesonets (i.e., probes) P1, P5, and P9 provide up to 20 m along-leg spatial resolution profiles from 1833 to 1955 UTC (Fig. 7). One or more dryline vapor mixing ratio gradients are observed on each leg, with widths of 0.5–1 km and magnitudes of up to 3 g kg⁻¹ km⁻¹. The observed dryline movement is variable, with multiple cycles of an eastward surge followed by a short period of near-stationarity observed by probes P5 (Fig. 7a) and P1 (Fig. 7b) and an east–west oscillation observed by P9 (Figs. 7c,d). Considering the southwesterly wind and the dryline orientation at the locations of traverses (Fig. 3), the observed dryline displacements are consistent with wavelike perturbations moving northward along the dryline. Here, P1 and P5 observe maxima of virtual potential temperature along or east of the dryline, with winds veering west of the dryline (Figs. 8a,b); P9 observes a double dryline (e.g., Ziegler and Hane 1993) with gradients of moisture, virtual temperature, and veering winds centered at x = 17 and x = 22 km (Fig. 8c).

Selected frontal traverses by the mobile mesonets reveal rather complex horizontal thermal gradients on both sides of the cold front around the triple-point intersection. Moisture minima just ahead of the cold front indicate that P1 and P5 traverse the front to the south of the triple point, while P9 traverses the cold front to the north of the triple point (Figs. 8d–f). The sharp temperature drop associated with the cold front is preceded by a narrow zone of sharply veering winds (Figs. 8d–f). While potential temperature decreases west of the moisture rise marking the front (not shown), the virtual potential temperature profile just behind the front may either decrease (Figs. 8d,f) or remain unchanged (Fig. 8e) depending on the relative magnitudes of the initial temperature decrease and moisture increase.

Dust devils are observed near the dryline ahead of P1 during its 1850–1902 and 1925–1936 UTC traverses (Fig. 3a,c). The dust devils are located within the dryline moisture gradient (Figs. 7b, 8b), the later dust devil occurring in a zone of sharply veering winds. Using a time-to-space adjustment of the dust devil locations relative to the closest radar analysis to confirm dust devil location in a zone of radar-derived wind shear (not shown), it is speculated that the dust devils or their parent misocyclones may form via a horizontal thermal-shearing instability (Kanak et al. 2000). Other mobile mesonets also report dust devils along or near the dryline, although their timing and location are not reported with sufficient accuracy to position them with respect to the analysis grid.

c. Ground-based mobile soundings

Ground-based mobile soundings are obtained behind the cold front (Fig. 9a) and at two locations on the dryline (Figs. 9b,c). A well-mixed BL that is absolutely unstable to dry convection (i.e., the convective BL or CBL) is present along the dryline, with conditions slightly warmer and drier at the northern location (Fig. 9b) than 15 km to the south (Fig. 9c). The southern dryline sounding is convectively unstable, with a convective available potential energy (CAPE) of 1152 J kg⁻¹, and moderately capped with a convective inhibition (CIN) of 59 J kg⁻¹. A second M-CLASS sounding at 2056 UTC east of the IOR (not shown), though similar to the 1920 UTC M-GLASS sounding (Fig. 9b), has slightly deeper BL moisture and zero CIN. The postfrontal 2006 UTC M-GLASS sounding (Fig. 9a) contains a shallow CBL topped by a strong frontal inversion. An elevated residual layer (ERL) in the soundings proceeds from the transport of the deep, dry CBL between the surface dryline and cold front by horizontal and vertical advection relative to the surface boundaries. Cumulus development on the northern portion of the dryline (Fig. 3d) is assisted by a shallow layer of weak instability just above cloud base in the 1920 UTC M-GLASS sounding (Fig. 9b inset), while the other soundings are stable at all levels in the cloud-bearing layer. Reference soundings for the three air masses (Fig. 9d) are derived from the mobile soundings and a King Air stepped traverse analysis (Ziegler et al. 2007).

d. Surface Lagrangian moisture analysis

The surface-level Lagrangian analysis sharply delineates the evolving dryline and cold front and defines the areal coverage of moisture necessary for cloud development (Fig. 10). An axis of weak along-dryline confluence provides frontogenetic forcing (not shown) to bring individual trajectories into close proximity, thus maintaining the dryline moisture gradient as observed by mobile mesonet traverses in the analyses. The predryline, dry sector, and postfrontal air masses are characterized by vapor mixing ratios of 9–10, 7–8, and 11–12 g kg⁻¹, respectively (see also Figs. 7 –8), while MIPS time series changes (K06) are consistent with the rapid southeastward frontal movement combined with analyzed cross-frontal gradients at the MIPS site (e.g., Fig. 10h). The triple point moves southward after 1933 UTC due to the rapid southeastward frontal movement combined with slow eastward dryline motion. The dryline develops undulations with spacings of 5–15 km, consistent with the previously mentioned dryline oscillations inferred from mobile mesonet traverses. Similar dryline undulations have been inferred by McCarthy and Koch (1982), prompting them to propose the term mesoscale dryline wave to describe this phenomenon. Intense convergence and shearing provide the frontogenetic forcing (not shown) to maintain a strong moisture gradient across the cold front.

A series of persistent longitudinal moisture bands spaced 1–5 km apart are located to the east of and roughly parallel to the dryline (Fig. 10). The longitudinal moisture bands are approximately stationary or may vacillate slightly in the cross-flow direction. Other longitudinal moisture bands are located west of the dryline and are aligned along confluence bands (e.g., moisture band southwest of P2; Figs. 10a–c). Pockets of drier air form west of the dryline between the moisture bands, locally increasing the horizontal moisture gradient across the dryline. The location of P1’s 1929 UTC dust devil observation is along the dryline and just northeast of the advancing dry pocket located to the west of P4 (Fig. 10c).

An important capability of the Lagrangian analysis is the derivation of the LCL height field. Surface parcels at 1942 UTC in the sharply contrasting predryline, dry sector, and postfrontal air masses have LCL values of about 1.8–2, 2.2–2.8, and 1.2–1.4 km, respectively (Fig. 10f), the dry air mass having the greatest heterogeneity. The postfrontal and predryline LCL height values are broadly consistent with layer-averaged LCL heights from the mobile soundings (Fig. 9).

a. Roll dynamics

The previously noted transverse rolls (Figs. 3 and 6) appear to be consistent with the inflection point instability (e.g., Stensrud and Shirer 1988), which is related to the Kelvin–Helmholtz instability. Generally BL rolls can be produced by three types of instability (Brown 1980): 1) thermal instability, the combination of Rayleigh–Benard convection with horizontal flow in which the most unstable orientation minimizes cross-roll shear (e.g., longitudinal rolls on either side of the dryline in Fig. 5); 2) parallel instability, in which roll circulations extract energy from the mean shear parallel to the roll axis via the Coriolis force (Lilly 1966); and 3) inflection point instability, in which rolls extract energy from the BL shear normal to the roll axis. The growth rate of the inflection point instability is proportional to the magnitude of the shear at the inflection point (Brown 1980). Depending on the BL shear profile, the inflection point instability may generate a variety of roll orientations which often differ from the roll orientations produced by either the thermal or parallel instabilities. Depending on the degree of shear and unstable stratification in the BL, a most-unstable mode of both the inflection point and thermal instabilities may coexist (Gossard and Moninger 1975).

An inflection point was identified in the high-resolution BL wind profile (i.e., ∼50-m altitude spacing at ∼5 m s⁻¹ rise rate for 10-s interval data) of the 1906 UTC M-CLASS sounding (Fig. 9c), establishing the necessary (but not sufficient) condition for inflection point instability. The low-order spectral model of Stensrud and Shirer (1988) verified the existence of inflection point instability in the input 1906 UTC M-CLASS sounding. With input of the observed roll spacing of 5 km and the assumption that roll depth equaled the BL depth of 1.25 km, the low-order spectral model was used to estimate the orientation of the most unstable mode as 275°. This computed orientation is in favorable agreement with the roll orientation suggested by Fig. 3. The cross section in Fig. 6 has been rotated to be orthogonal to the most unstable mode’s orientation to better reveal the roll structure. Consistent with the sounding, the mean Doppler-derived horizontal wind component profiles in each cross section in Fig. 6 were calculated and found to further support the existence of an inflection point in the BL. In contrast to the linear analysis of Gossard and Moninger (1975) that assumed a straight hodograph and obtained a 2D dynamical (inflection point) solution lacking perturbation vertical vorticity, the observed transverse rolls in the present study appear to produce vertical vorticity banding due to the observed turning wind with height and tilting of the associated along-roll shear component.

b. Comparison of GOES-8 and cloud camera analyses

Good internal consistency is found between GOES-8 cloudiness and cumulus cloud base areas derived from the photogrammetric analysis (Fig. 11). Individual cloud base centers move approximately with the subcloud winds, initially northeastward ahead of the cold front and then northward as subcloud winds back in response to the solenoidally induced secondary cold frontal vertical circulation (see also Figs. 3e,f and 5d). Cloud bases were analyzed at a 90-s interval (Ziegler et al. 2007), and animations reveal the regularity of the cloud-base motions. Roughly 50% of the cloud-base areas are forced or active clouds situated in updraft below the LFC (Stull 1985). The total cloud base area is 25%–50% of the total cloud-top area, consistent with the notion of the cumuli as detraining plumes that broaden with height.³ An evolution is suggested in which clouds initiate at the centers or on the downwind edges of updrafts (as also concluded from MIPS observations by K06), followed by advection of the cloud bases over areas with either weaker updrafts or downdrafts. Thus, clouds exhibit both active and inactive periods in their individual evolutions. In broad consistency with the previously noted persistent movement of updrafts near the LCL height (Fig. 4d), some cloud bases persist for periods of at least 12–21 min (e.g., cell 2 in Figs. 11a–c; cell 5 in Fig. 11a–d).

The photogrammetric and radar analyses further emphasize the role of vertical circulations associated with BL updraft cells and the cold front in forcing cumulus development (Fig. 12). For example, at 1942 UTC cloud 2 has approximately the same tilt as and is centered within the mesoscale updraft above the frontal location (Figs. 11b, 12a), while at 1957 UTC the bases of clouds 6 and 9 are also embedded in the frontal updraft (Figs. 11d, 12b). Several clouds are in the process of separating from the updraft that formed them (e.g., cloud 1, Figs. 11b and 12a; cloud 4, Figs. 11d and 12b). Cloud 3, having been in updraft at 1936 UTC (Fig. 11a), has separated from its parent updraft (Figs. 11b, 12a) prior to attaching to the frontal updraft at 1948 UTC (Fig. 11c). Cloud 5 follows a similar evolution to cloud 3, except that it is in the process of attaching to the prefrontal BL updraft at 1957 UTC (Figs. 11, 12b).

c. Lagrangian boundary layer analysis

The moist boundary layer contains undulations and plumes of vapor mixing ratio, and several plumes achieve water-saturated volumes within which cumulus or cumulus fractus clouds may be inferred (Fig. 13). These water-saturated volumes are thus complementary to and yet distinct from clouds observed by the ground-based camera or GOES-8. The leading edges of the dryline and cold frontal surfaces intersect along a northeastward-sloping triple point curve. The intense, deep updrafts along the cold front produce a nose of enhanced moisture punctuated by plumes in updraft cores above and slightly rearward of the surface frontal location. The frontal surface (Figs. 13b–f) displays the convergence-forced nose tilted slightly toward the warm air at several locations, the forward tilt possibly caused by surface friction and suggesting a similarity to density currents (Schultz 2005). The frontal surface also displays a lobe-and-cleft structure suggesting an additional similarity to density currents.

The previously noted plumes east of the dryline coincide with updrafts (including longitudinal rolls) that circulate cool, moist air from the top of the BL through the ERL (Fig. 14), developing water-saturated volumes with bases around 1.75 km. The relatively dry, warm, stable layer above the ERL slopes upward in the sheared mesoscale updrafts to the east of the dryline, thereby preventing the saturated volumes from deepening. Although updrafts between the cold front and dryline tend to be deeper and stronger than updrafts to the east of the dryline, drier air and larger LCL heights (e.g., Fig. 10f) inhibit development of water saturation west of the dryline. Nearly stationary longitudinal rolls west of the dryline produce persistent downward mesoscale entrainment of dry air from above the inversion, resulting in strong heterogeneity of the dry BL prior to cold frontal passage. These deep, longitudinal roll-induced dry intrusions to the west of the dryline are manifested by the previously noted dry bands at the surface (Fig. 10). A very shallow, cool, and moist CBL behind the cold front is preceded by an upward bulge of postfrontal air in the rotor circulation above the surface frontal location (Figs. 14i–n), thus providing conditions increasingly favoring shallow cumulus formation as the plume depth approaches the parcel LCL height of about 1.25 km (e.g., Fig. 10f).

The predryline and postfrontal BLs exhibit horizontal virtual temperature gradients that support the action of thermally direct secondary circulations. The surface dryline associates with a vertical circulation whose updraft is frequently displaced toward the warm, dry side of the dryline (Fig. 14). Cooler virtual temperatures in the predryline and postfrontal BLs (Figs. 14b,d,f,h,j,l,n) imply the sustained generation of horizontal vorticity and vertical shear by a persistent thermally direct solenoid (e.g., Ziegler et al. 1995). However, plumes of rising warm air and sinking cool air in the lowest 1 km modulate both the sign and magnitude of the horizontal temperature gradient in the predryline BL. The postfrontal plume of cold updraft air is similar to the cold frontal hydraulic head feature reported by Shapiro et al. (1985). The unstable stratification in the dry CBL between the cold front and dryline spans the lowest 0.5–1 km (Figs. 14b,d,f,h,j,l), in agreement with a King Air stepped traverse analysis (Ziegler et al. 2007), while the postfrontal BL is unstable in the lowest ∼250 m (Figs. 14j,l,n).

The secondary cold frontal circulation displaces the dry and moist BLs at the triple point intersection accompanying the dryline occlusion process (Fig. 15). The combination of ceilometer and shortwave insolation observations by MIPS (Figs. 16a and 19c of K06) indicate that clouds are either directly above or shadowing the site at 1933, 1951, and 2000 UTC in agreement with the positions of water-saturated volumes based at 1.75–2 km near the MIPS location in the Lagrangian analysis (Fig. 15). Water-saturated volumes with bases of about 1.25 km are noted in the postfrontal rotor circulation (Figs. 15b–d). Successive frontal updraft plumes persist for up to 20 min as they traverse the frontal nose from its leading to its rear edge, and some of these plumes force small postfrontal water-saturated volumes. The intense deformation of the BL above the frontal nose occludes the dryline and lifts the former (surface-based) BL between the front and dryline to form a shallow ERL penetrated by cumulus based within the frontal rotor (Figs. 15e,f). The KA samples the folded transition layer above the ERL about 3.5 km west of the surface front as a horizontal temperature and moisture gradient resembling, though distinct from, the actual upper-level dryline to the east (Figs. 15e,f versus Fig. 10 of G06). Consistent with development of water-saturated volumes behind the surface front (Figs. 15e,f), the KA penetrates cumulus cloud tops between 1 and 3 km west of the surface front on its next (reverse direction) leg at ∼2.2 km AGL and 2009 UTC (not shown). Deeper front-to-rear flow north of the triple point is manifested as a shear zone including a closed, 20 km wide transient mesoscale circulation at 1 km in the postfrontal ERL around the triple point location (Fig. 3d,f,h).

Moist BL air is lifted into the ERL and its capping stable layer by updrafts, producing bulges of virtually cooler and more moist air than the adjacent quiescent inversion and forcing water saturated volumes where the local parcel LCL has been exceeded (Figs. 14 –15). Conceptualizing the forcing of individual cumuli by observed longitudinal and transverse BL rolls (Fig. 16), a cloud is centered in a roll updraft above its level of nondivergence (e.g., as in Fig. 10 of Weckwerth et al. 1996). Although the roll updraft derives energy from buoyancy at heights below the updraft maximum, at higher (ERL) levels the (laterally entraining and mixed) updraft becomes negatively buoyant and penetrative. The special case of a homogeneous BL saturation point or LCL (Betts 1984), which results in a flat cloud base since all cloud-base parcels have the same LCL, may be produced locally by vertical advection in the mesoscale updraft when the roll is oriented with the flow (Ziegler et al. 1997). Broadly speaking, the Lagrangian analysis results reveal an increasing LCL with height due to vertical mixing, which in turn produces slightly convex cloud-base surfaces due to parcels nearer individual cloud cores arriving from lower BL levels (Figs. 14 –15).

Regarding surface layer variability due to roll effects in the BL (Weckwerth et al. 1996), it has been noted that the dry bands in the surface Lagrangian analysis west of the dryline are related to penetrative downdrafts of deep longitudinal rolls. Although the Lagrangian analysis assumes that the local grid-column sounding is correlated to surface measurements in BL updrafts, it makes no a priori assumption that observed longitudinal surface moisture bands are in phase with longitudinal rolls. For example, the surface moisture band just east of the dryline through the Fig. 14 cross section is connected to a prominently moist, cool longitudinal roll updraft at 1915 UTC (Fig. 10b versus Figs. 14c,d at x = 9 km). Other locations and times have less clearly defined connections between surface moisture bands and longitudinal rolls due to finite roll extent and advection of lifted air away from a downstream updraft edge (i.e., as microinsects and reflectivity in section 3a), periodic superposition of longitudinal and transverse roll modes locally creating more complex trajectories (e.g., Figs. 14c,d,k,l), and BL mixing of parcels from neighboring Lagrangian trajectories with differing source region properties (Ziegler et al. 2007). Although Weckwerth et al. (1996) suggested that the high-frequency surface layer variability (presumably forced by patch-scale surface layer sensible and latent heat fluxes) is unrelated to the overlying roll structure, it is speculated that roll-scale surface layer variability may be forced by downward roll-induced fluxes that overcompensate upward surface layer fluxes to provide a net flushing effect of the normally moist, unstable surface layer.

d. Comparison of water-saturated volumes in Lagrangian analysis and GOES-8 cumulus field

Although water-saturated volumes and observed clouds develop on either side of the surface cold front, the most extensive cloud and water-saturated areas are in the moist sector east of the dryline (Fig. 17). Series of updraft cores aligned in the direction of the subcloud airflow lift boundary layer moisture progressively higher following the parcel motion, forming cells and bands of high relative humidity (Figs. 17a,c,e,g). In agreement with the relation of observed clouds to airflow (see section 4b), high relative humidity is generated in updraft cores and subsequently advected downstream in the Lagrangian analyses. Hence, both observed clouds and high relative humidity bands experience active and inactive periods in their evolution following the local parcel motion. The presence of southwest–northeast-oriented dryline-crossing convergence bands with enhanced moisture that support cumulus formation east of the dryline is in agreement with observations (Hane et al. 1997) and cloud–mesoscale model simulations (Ziegler et al. 1997) of the severe 26 May 1991 Woodward, Oklahoma, dryline storm case.

The locations of clouds and water-saturated volumes are broadly consistent and are frequently located in or on the downwind edge of updraft cores (Figs. 17b,d,f,h). The coverage of clouds and water-saturated volumes becomes more extensive with time—particularly just ahead of and along the cold front—as the triple point moves southward. Some water-saturated volumes tend to form bands in the along-wind direction around the LCL height in locations where observed cloud tops may be nonbanded. As previously noted, the GOES-8 satellite would not resolve areas of cumulus fractus, and the latter would be characterized by very high mean relative humidity as cloud evaporates during mixing with drier overlying air. Furthermore, the absence of subgrid-scale mixing in the Lagrangian analysis may limit top–down entrainment drying of the very shallow downwind edges of water-saturated volumes to regions of elevated subsidence warming, possibly causing the total water-saturated volume to be overestimated. Retrieved postfrontal water-saturated volumes also appear to be somewhat overestimated relative to GOES-8 cloud tops at 2000 UTC (Figs. 18g,h and 12), again possibly due to lack of subgrid Lagrangian mixing in the analysis.

Weiss and Bluestein (2002) have suggested that the dryline and its associated secondary circulation are lifted at its triple-point intersection with an outflow boundary, possibly providing a focus for CI north of the triple point location. The outflow boundary in the Weiss and Bluestein (2002) case is normal to the dryline and their moist layer is much deeper than the outflow layer, implying that the solenoidal secondary outflow circulation is parallel to the dryline and thus would be able to advect the across-dryline thermal gradients to the north of the surface boundary. The deep frontal nose occludes the 24 May dryline from the surface to around 1.5 km (Figs. 13d,f, 14m,n, 15b–d, 17e–h), limiting front-to-rear horizontal advection of the dryline gradient in the present case to a relatively shallow layer within several hundred meters of cloud base.

e. Evaluating the cumulus formation hypothesis in the IOR

The parcel continuity principle for cumulus cloud formation requires that a rising air parcel must achieve its LCL while residing within the mesoscale updraft that provides the lifting to water-saturate the parcel (ZR98). Following from the parcel continuity principle, it is hypothesized that the time required for an air parcel to cross and eventually exit the updraft horizontally must equal or exceed the time required for the parcel to rise from its entrainment level H (i.e., the origin level of air entering the updraft) to its LCL. Obtaining time scales of horizontal and vertical advection from length divided by velocity scales, the latter time relation may be written as L/U ≥ (LCL − H)/W, where L is the horizontal updraft length scale, U is the horizontal velocity scale, and W is the vertical velocity scale. Forming a dimensionless ratio R from the above time relationship yields R_LCL = WL/[U(LCL − H)] ≥ 1. For a lifted parcel to achieve the LFC, it is hypothesized that R_LFC = WL/[U(LFC − H)] ≥ 1.

The above scale parameters have been determined from backward trajectories that originate from the bases of water-saturated volumes at 1.75 and 2 km to the east of the dryline in the 1924–2000 UTC Lagrangian analyses. The base of a water-saturated volume (i.e., equivalent to a cloud base) is indicated by the joint condition that Z* = z/Z_LCL ≥ 1 at the current grid point and Z* < 1 at the next lower grid point. The duration of each trajectory corresponds to the smallest multiple of the Lagrangian analysis time spacing that allows the trajectories to disperse throughout the BL (i.e., 18 min). The initial LCL value for a given trajectory is interpolated to the Lagrangian point from the earliest Lagrangian analysis time for that trajectory, while the length and velocity scales are time averages based on the displacement vector and time period between the initial and cloud-base locations.

About 87% of cloud-base trajectories originating in the moist BL below 1.25 satisfy the dimensionless ratio R_LCL > 1 (Fig. 18a; Table 3), verifying the cumulus formation hypothesis and identifying penetrative updraft plumes as the source of lifting of moist BL air to form clouds. The Lagrangian analysis mimics mixing on cumulus scales by objectively combining high-LCL trajectories based in the drier and warmer ERL with adjacent low-LCL, cloud-forming trajectories originating in the moist BL to maintain water saturation at cloud edges. Hence, about 35% of cloud-forming trajectories originating in the ERL above 1.25 km satisfy the dimensionless ratio R_LCL > 1 (Fig. 18b; Table 3), indicating the action of parcel moistening and cooling from mesoscale mixing prior to achieving cloud base. The initial LCL values tend to cluster around the corresponding cloud base LCL values for trajectories originating in the moist BL (Fig. 18c), with greater magnitude and frequency of decreased LCL for trajectories originating above 1.25 km (Fig. 18d), demonstrating that moist layer trajectories experience weaker mesoscale mixing than ERL trajectories. Other updraft trajectories which achieve high relative humidities without forming clouds either experience weaker vertical motion or entrain higher-LCL air than cloud-forming trajectories, then exit the updraft before water saturation is achieved (not shown).

f. Evaluating the convection initiation hypothesis

Given a value of LFC = 3.1 km (Figs. 9b,c), the condition R_LFC ∼ 1 would require a mean updraft strength substantially greater than 1 m s⁻¹ to achieve CI in the IOR. Since the average updraft scale value in the ERL is only ∼0.4 m s⁻¹ (Table 3) and would be expected to decrease with height in the overlying stable layer, deep convection is effectively suppressed near the triple point from a combination of stability, shear, and weak penetrative vertical motions or strong compensating downward motions (e.g., Figs. 14m,n, 15b–d).

What conditions support the initiation of deep convection in western Oklahoma, about 80 km east of the triple point? Subjective analysis based on parcel calculations of the west-to-east dropsonde array D1–D6 is used to infer the mesoscale environment on either side of the line of storms which developed between D2 and D3 (Fig. 2b). Dropsondes D1–D3 suggest that the moist BL east of the dryline is being undercut and lifted by a cooler, more moist, westward-moving internal BL⁴ (Fig. 19). The moist internal BL is inferred to contact the surface between D2 and D3. A surge of southeasterly BL flow and enhanced cumulus cover along the leading edge of the implied convergence line (Fig. 2a versus Fig. 2b), coupled with the inferred west-to-east slope of the moist internal BL, support the inference of focused deep convergence and mesoscale updrafts at the CI location. The internal BL and convergence line are probably maintained by a horizontal flux directed toward the deeper, drier BL (Fig. 19) rather than by land surface characteristics and surface layer flux variations as described by Segal and Arritt (1992). W06 also inferred a mesoscale updraft at the CI location, although they based their conceptual interpretation on the coincidence of a dropsonde-deduced upward moisture bulge and a lidar-detected aerosol plume.

Horizontally variable inhibiting layers of parcel virtual temperature deficit are present above both the moist BL and the ERL in the present analysis (Fig. 19). At the CI location, the BL lid achieves a local minimum while the ERL lid does not exist. A strong lapse rate, a recognized principle ingredient for deep convection (Doswell 1987) that would assist rapid intensification of cloudy updrafts exceeding the LFC, is present above the LFC around the CI location (not shown). Assuming scale parameter values based on the dropsonde observations at the CI location (Table 3), an updraft strength of 1 m s⁻¹ would be sufficient to attain a value of R_LFC ∼ 1. Thus, it is speculated that the collocation of a locally weak lid with enhanced moisture and deep mesoscale lifting along a sloping internal BL between D2 and D3 provide the ingredients for CI in the region east of the triple point and IOR on 24 May 2002. A very similar roll-induced CI event east of a dryline may have initiated the development of the tornadic Moore, Oklahoma supercell on 3 May 1999 (Edwards et al. 2000).