Finescale Vertical Structure and Dynamics of Some Dryline Boundaries Observed in IHOP

a. Data sources and processing

This study primarily uses data collected aboard the University of Wyoming’s King Air (WKA) aircraft. We examine data from 30–40-km-long transects across fine lines at elevations ranging between 150 and 1600 m above ground level (AGL), in particular the gust-probe winds along the flight track (roughly normal to the fine line) as well as water vapor mixing ratio (r) and potential temperature (θ). Water vapor is measured by a rapid-response Lyman-alpha probe, which was calibrated by a slow-response chilled-mirror dewpoint sensor.

The WKA carried the 95-GHz (W band) Wyoming Cloud Radar (WCR). The WCR simultaneously operated two fixed antennas, primarily in profiling (up/down) or vertical-plane dual-Doppler (VPDD) modes (Fig. 2 in Geerts et al. 2006). In the profiling mode, radar data portray the vertical structure of the CBL over its entire depth except for an ∼220-m-deep blind zone centered at flight level. The VPDD mode allows an estimation of the along-track two-dimensional (2D) air circulation below the aircraft at a resolution of ∼30 m. The extraction of the echo motion from the Doppler velocity measured from a moving platform, and the dual-Doppler synthesis, are discussed in Damiani and Haimov (2006).

Several other IHOP data sources were used. Low-elevation-angle reflectivity from various scanning ground-based radars were used to place the WCR transects in the context of radar fine lines. Data from both aircraft dropsondes and ground-based balloon sondes, collected in close proximity to the fine lines, were used to determine the CBL depth and airmass contrast.

b. Density-gradient-driven circulations

Radar fine lines are a manifestation of sustained linear convergence within the CBL (Wilson et al. 1994; Geerts and Miao 2005). The central hypothesis of this paper is that this convergence primarily results from a horizontal difference in buoyancy and thus in virtual potential temperature (θ_υ). The horizontal scale of this convergence and θ_υ difference (Δθ_υ) needs to be determined. Positive θ_υ anomalies are buoyant; that is, they tend to rise spontaneously, at least if they are rather small scale (e.g., Houze 1993, p. 225; Doswell and Markowski 2004). Buoyant ascent implies a horizontal vorticity dipole (viewed in a vertical cross section) and roughly circular features (viewed on a map) with a diameter of O(1 km), depending on the CBL depth (e.g., Stull 1988, p. 461). These features should be present irrespective of the spatial organization of thermals, that is, whether or not the thermals are aligned by horizontal convective rolls (HCRs).

A horizontal θ_υ gradient also drives a convergent solenoidal circulation that may lead to a density current, whereby the less dense air is forced over the denser air. In this case the buoyancy-induced horizontal vorticity is a single extreme, although under suitable ambient shear, a vorticity dipole may be present across the boundary (e.g., Rotunno et al. 1988). As will be illustrated below, such a singular extreme or dipole has a horizontal scale larger than that of thermals. Also, features tend to be elongated on a map since, to first order, the secondary circulation is 2D. The circulation produces a radar fine line, which separates the air masses of different density.

The slope of this fine-line echo, and of the associated updraft in a vertical plane, is evidence of wind shear (∂u/∂z), which can be large scale or local. If it is large scale, all echo/updraft plumes should be tilted. A tilted echo/updraft plume at the boundary only, surrounded by upright thermals, is evidence of local baroclinicity at that boundary. The Lagrangian change (D/Dt) of horizontal vorticity (η) due to baroclinicity can be estimated as

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where x is the boundary-normal direction [in the cases examined here, pointing (south)east], η = (∂u/∂z) − (∂w/∂x), w is vertical velocity, and g is gravitational acceleration. In the cases examined below, the length scale is greater than the height scale (the depth of the CBL h) by a factor of 2 or more; thus, wind shear dominates η. In what follows we assume along-boundary uniformity (∂/∂y = 0). To start, we treat (1) as an initial value problem and examine the development of shear (u_h − u₀)/h within an initially motionless CBL as a result of a steady gradient Δθ_υ/Δx, during a period Δt. Initially, advection by the baroclinically generated flow can be ignored. Thus (1) can be integrated vertically and in time to obtain

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where θ_υ is the average θ_υ over 0 < z < h. The Δθ_υ driving this circulation is largest near the ground (where it is referred to as Δθ_υ,0) and decreases with height, as illustrated in Fig. 1 for two dryline cases described in the literature, and as confirmed in section 3a below.

The CBL depth h is defined as the level where potential temperature starts to increase with height. Experimentation has yielded the following objective criteria for sounding data: h is at the base of the layer where (dθ/dz) > [0.5 K (200 m)⁻¹] and (dθ/dz) > [1.0 K (1000 m)⁻¹], and nowhere within the 1000-m layer does θ decrease by over 0.2 K. The CBL depth on the denser side of the dryline (h_de) often is considerably less than the depth on the lighter side (h_li) (e.g., Fig. 17 in Atkins et al. 1998). In the two dryline cases shown in Fig. 1, h_li (on the dry side) was 2–3 times larger than h_de. Flight levels higher than that shown in Fig. 1 were not flown, but linear extrapolation of Δθ_υ data shown in Fig. 1 suggests that Δθ_υ nearly vanishes at h_de. The ratio of Δθ_υ at h_de to Δθ_υ,0 is defined as R_θ, that is,

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For the cases shown in Fig. 1 and in section 3a, R_θ averages 0.37, ranging between 0.20 and 0.51. The above integral can be solved over 0 < z < h_de using (2), and the shear can then be estimated as

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This approximation is useful only in the initial stages (Δt small), before frictional dissipation and advection become important. Later, an equilibrium develops, in which the steady-state secondary circulation (a form of kinetic energy) tries to destroy the horizontal Δθ_υ (a form of potential energy) that is maintained by advection and/or surface heat fluxes. The convergence associated with this circulation can be estimated as follows, starting with (1):

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That is, the tendency term is ignored in the total derivative. The above relationship can be integrated over h_de:

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We now apply the chain rule twice, and assume 2D incompressible continuity [(∂u/∂x) + (∂w/∂z) = 0] and w = 0 at z = 0 and z= h_de, to modify the right-hand side of the above equation as follows:

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The first and third terms cancel. Thus,

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Observations indicate that the boundary-normal confluence is strongest near the surface and, by extrapolation, vanishes near h_de. The average ratio of Δu at h_de to Δu₀, defined as R_u, is only 0.17 for the cases illustrated in Fig. 1 and section 3a. Thus, Δu vanishes at a slightly lower level than Δθ_υ. For simplicity we use the same linear expression (2) for the profiles of Δu and Δu², but with a slope R_u. Then a finite-difference expression of (4) becomes

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or

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In the absence of “ambient” flow, u₀ merely is the horizontal component of the solenoidal circulation. Using (2), (5) can be approximated as follows:

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where the subscript “0” refers to measurements near the surface, in practice below 0.5h_de. The magnitude of the confluence Δu₀ in (6) is affected by the rates of decline of Δθ_υ and Δu with height in the CBL affect, and by u₀. In general, R_u should be close to zero, since diffluent return flow should occur in the upper CBL; however, the density contrast can be found over a greater depth. In practice, u₀ is calculated as the average low-level flow on the “dense” side of the boundary, minus the “ambient” flow (defined as the average low-level boundary-normal flow in nearby soundings on opposite sides of the boundary), and is positive toward the boundary. Note that u₀ is in the denominator of (6); when u₀ is small, as with some weak boundaries, its uncertainty can make confluence estimates based on (6) unreliable.

Expression (6) fundamentally is an application of the Bjerknes circulation theorem (Bjerknes 1898) and relates the steady-state low-level cross-boundary confluence (−Δu₀) to Δθ_υ,0 at corresponding horizontal scale. The term −Δu₀ is similar to convergence, but it does not imply a scale (Δu₀ is not divided by Δx), and the along-boundary component (∂υ/∂y) is ignored. A similar expression has been obtained by Grossman et al. (2005), but they start from a circulation integral, and ignore the variation of Δθ_υ with height.

Another relationship between confluence and density contrast can be obtained from density current theory. The boundaries examined herein may not have a sufficient Δθ_υ to drive a classic atmospheric density current, as documented for instance for thunderstorm-generated gust fronts (e.g., Mueller and Carbone 1987) or cold fronts (e.g., Wakimoto and Bosart 2000); nevertheless, the theory may apply. Laboratory experiments suggest that the speed of a density current (U_dc) can be estimated as follows (Simpson and Britter 1980):

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This equation is based on the horizontal momentum conservation equation (e.g., Houze 1993); U_dc bears similarity to the shallow water wave speed. Some form of (7) is commonly encountered in the literature, including in atmospheric applications. In (7) K corresponds with the Froude number; experimental values for K range from 0.7 to 1.0 or higher for atmospheric density currents (e.g., Wakimoto 1982; Mueller and Carbone 1987; Kingsmill and Crook 2003); U_env is the ambient low-level flow normal to and ahead of the density current. Laboratory work by Simpson and Britter (1980) indicates that b = 0.70. Numerical work by Liu and Moncrieff (1996) suggests that b = 0.74, ranging between 0.71 and 0.78. The density current depth (D_dc) is assumed to be equal to h_de, although this is uncertain (see section 4d below). The θ_υ difference normally is measured on the ground; therefore Δθ_υ,0 is used in (7).

The movement of a boundary provides poor evidence for the density-current nature of the boundary (e.g., Smith and Reeder 1988). First, the estimation of the observed motion of the boundary is complicated by along-line variability. Second, the estimation of the theoretical boundary motion using (7) has several uncertainties, including the determination of the “ambient” low-level flow U_env. This determination is complicated by the ambient wind shear and variable CBL depth.

We can however measure the flow confluence (−Δu) with some accuracy, and it can be compared with the following estimate from density current theory. First, observations have shown that the feeder flow (U_max) exceeds the density current speed by about 40% (Simpson et al. 1977),

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Thus the confluence normal to a density current, −ΔU_dc, can be inferred from (7) and (8), assuming K = 0.85 and b = 0.74:

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The neglect of the term 0.04U_env implies an uncertainty <1 m s⁻¹, which is less than other sources of error in this estimation. Both (6) and (9) relate the steady-state near-surface cross-boundary confluence to Δθ_υ,0 over the same horizontal scale. The main difference is that in the case of a solenoidal vortex (6), |Δu| ∝ h_deΔθ_υ,0, while in the case of a density current (9), |Δu| ∝ h_deΔθ_υ,0.

Even though the term Δx does not appear in either (6) or (9), the horizontal scale over which these differences are computed clearly matters. The question of scale was raised by Atkins et al. (1998) and is further explored here. WKA wind and thermodynamic data are averaged over either Δx = 3 km or Δx = 10 km on either side of the leading edge of the boundary along all available low-level flight legs (below 0.5h_de). The averaging is necessary in order to reveal small differences (the signal) embedded in much larger perturbations of convective origin (the noise). The choice of these scales is based on the following. A distance of 3 km should exceed the diameter of most coherent eddies (thermals) in the fair-weather CBL: aircraft data (e.g., Kaimal et al. 1976) and WCR vertical profile data (Miao et al. 2006) indicate that in the mid-CBL the diameter of most eddies is 1.5h or less. However HCRs generally have wavelengths longer than 3 km, and 10 km is about the maximum flight track distance generally (but not always) available on either side of the boundary in IHOP. The distance between the centers of the averaging domains on either side of the dryline equals the averaging distance Δx, because we do not assume a buffer zone around the boundary. The third and largest scale is the boundary-normal distance between soundings. In the cases examined here, this distance (Δx) ranges from 15 to 62 km. Sounding data differences are computed based on averages between the ground and 0.5h_de.

The theory is tested first for a vigorous but shallow cold front observed on 24 May 2002 in west Texas (Xue and Martin 2006; Karan and Knupp 2006). This cold front had all the characteristics of a density current (Geerts et al. 2006): large Δθ_υ,0 values (3–6 K over scales of 3–19 km) and strong convergence (−Δu) at the head (8–11 m s⁻¹ over the same scales) (Table 1). Both the solenoidal vortex Eq. (6) and the experimental density current Eq. (9) overestimate the low-level confluence at all scales, compared to observed values (Table 1).

a. 22 May dryline

On 22 May 2002 the IHOP armada studied a dryline fine line near the S-band dual-polarization Doppler radar (S-Pol) in the Oklahoma Panhandle. Two fine lines developed: a more defined one to the east (the “primary dryline”) and a less apparent line to the west (Fig. 2; Fig. 3 in Weiss et al. 2006). These lines merged north of the IHOP operations. The humidity and temperature contrasts between the moist and dry air masses were considerable (Fig. 3; as well as Fig. 4 in Demoz et al. 2006); the air mass between the two drylines had intermediate properties. The soundings shown in Fig. 3 indicate that the moist-air θ_υ was 4.5 K lower than that on the dry side (Table 1). Even larger θ_υ differences across the dryline complex existed at the surface (Fig. 2). The dry-side CBL was remarkably deep, and about twice as deep as the moist-side CBL depth (h_de), which is too deep for the CBL depth to be inferable from WCR profiles (Miao et al. 2006); the temperature of the upper ∼1 km of this CBL was below the threshold of most insects. But east of the eastern dryline, WCR-inferred CBL heights corresponded well with the thermodynamic CBL height (Fig. 4).

Clear-air reflectivity imagery, for instance from S-Pol, indicates that the convergence zone of the primary dryline had a sharply defined western edge and a more fuzzy eastern edge (Fig. 2; top panels of Fig. 2 in Demoz et al. 2006; Fig. 4a in Weiss et al. 2006). This contrast is most apparent at greater radar range, where S-Pol sampled the upper CBL. That suggests that lofted insects were carried eastward over moist-air wedge. In other words, westerly shear across the dryline (Fig. 3) tilted the dryline updraft eastward and caused an eastward trailing echo anvil.

This eastward tilt of both fine lines is apparent in transects of WCR reflectivity, for instance at 2220 and 2243 UTC (Fig. 4). The echo anvil is most obvious east of the eastern dryline at 2243 UTC (Fig. 4h). The air was moister and cooler on the east side of both lines, but the eastern line, with higher reflectivity values, had a larger temperature and humidity contrast, as well as more convergent flow. The latter is evident from the gust probe wind normal to the dryline (Figs. 4b,f), and from the WCR vertical velocity field (Figs. 4c,g). The flight-level along-track confluence resulted from slight changes in the direction of a strong wind, mainly across the eastern dryline (see wind barbs in Figs. 4b,f): the wind in the CBL generally blew at ∼20 m s⁻¹ from the south-southwest, along the dryline, but east of the dryline it was more southerly and stronger. The eastern line was especially marked by strong updrafts, up to ∼5 m s⁻¹. The dryline echoes penetrated well above h_de (Figs. 4d,h; Fig. 9 in Weiss et al. 2008), notwithstanding the low temperature near the echo tops (12°C at 2700 m AGL).

The θ_υ gradient across the primary dryline is about 1.0 K over 3 km, and 1.3 K over 10 km (Table 1). No measurable local θ_υ gradient exists across the secondary western dryline. (Only 3-km averages are available for this boundary.) The 10-km Δθ_υ across the primary dryline is only 30% of the Δθ_υ across 62 km (Table 1), implying a broader (meso-β) θ_υ gradient.

The updraft tilt is consistent with the θ_υ gradient across the primary dryline; that is, it appears to be due to baroclinically generated horizontal vorticity. The weak θ_υ gradient across the western dryline may explain why this line gradually disappeared, mostly between 2220 and 2320 UTC (e.g., Fig. 2 in Demoz et al. 2006).

A cross-dryline circulation was well established at 2326 UTC (Fig. 5). A 6.7 m s⁻¹ strong rear-to-front current (highlighted in the red box in Fig. 5b) advected low-θ_υ air toward the leading edge, which was tilted about 45° from vertical. Because the primary dryline was quasi stationary at this time, the flow shown in Fig. 5b can be thought of as relative to the boundary, which resembled a density current head. At flight level (∼1540 m AGL) this head was intercepted between 7300 < x < 8200 m (Fig. 5b); air in this region had r and θ values between those characterizing the dry and the moist air masses at lower levels (Fig. 4e). This confirms observations by Ziegler and Hane (1993) that the head is a mixing zone. One mixing mechanism must be the recirculation of flow into the head: to the rear of the head, a strong downdraft mixes air into the rear-to-front current (Fig. 5b). At the time of the WKA crossing, the air in the head was generally rising but negatively buoyant (Fig. 5a). This negative buoyancy and the strong downdraft behind the head are additional indications of density current dynamics.

Farther east of the primary dryline the moist air was sampled intermittently at flight level (not shown), which roughly corresponds with h_de (Figs. 4d,h; Fig. 1). Thus the CBL top had undulations, possible trapped lee waves behind the density current head (e.g., Weckwerth and Wakimoto 1992; Jin et al. 1996). The WCR reflectivity profiles reveal no evidence of breaking Kelvin–Helmholtz (KH) waves. Such waves were observed in the case of the 24 May cold-frontal density current, marked by a thrice-stronger θ_υ gradient over 10 km (Table 1). In that case the minimum value of the Richardson number (Ri) at the interface between denser and lighter air was ∼0.1 (Geerts et al. 2006). The moist-side temperature and wind profiles on 22 May (from the sounding shown in Fig. 1), filtered to a vertical resolution of 100 m (as done in Geerts et al. 2006), yield a minimum Ri of 0.4 just above h_de. KH instability occurs when Ri < 0.25 (e.g., Miles and Howard 1964; Mueller and Carbone 1987). Thus the θ_υ deficit of the 22 May dryline density current appears insufficient, or rather the resulting shear at the interface is too weak, to generate breaking KH waves.

The horizontal vorticity within the ∼1-km-diameter solenoid highlighted by black streamlines in Fig. 5b is about 2 × 10⁻² s⁻¹. An earlier VPDD transect, at 2201 UTC (1.4 h earlier), showed no coherent circulation across the dryline; at that time the dryline plume was essentially upright. Flight-level data from the primary-dryline crossings below 0.5h_de show a steady increase of Δθ_υ over 3 km from 0.69 to 1.31 K between 2222 and 2356 UTC. The mean θ_υ gradient [1.03 K (3 km)⁻¹; Table 1] can produce the observed horizontal vorticity in 0.75 h, according to (3). Thus the circulation at 2326 UTC (Fig. 5b) could have been generated in the time available and may have become rather steady. Even during the short time period between 2220 and 2243 UTC an increase in echo tilt of the primary dryline is apparent (Figs. 4d,h) and, correspondingly, an increase in θ_υ gradient and in confluence. (It is possible that this difference between the two transects in Fig. 4 is not a uniform temporal change but is rather due to along-line variability advecting into the geographically fixed track from the south.) Between 2300 and 0000 UTC, the primary dryline began to retrograde (move westward), at a speed of 2–3 m s⁻¹ by 0000 UTC.

Vertical variations of the airmass difference across the 22 May primary dryline are shown in Fig. 6. In all transects the moist air mass is sufficiently cooler, such that it is also denser. Both Δr and Δθ_υ decrease with height, as do the VORTEX drylines (Fig. 1), but the level where the extrapolated Δr and Δθ_υ values reach zero is lower, only slightly above h_de. The flow is convergent in all transects except one¹ (Fig. 6c), and Δu also tends to be strongest at low levels. The dry air rises relative to the moist air in most transects, especially at low and middle levels (Fig. 6c). The slopes of Δθ_υ and Δu are used in the estimation of R_θ and R_u [Eq. (6); Table 1].

The dryline convergence zone (DCZ) can be several kilometers wide yet the term humidity “discontinuity” is appropriate at the scale of the coherent eddies captured by the WCR. The rapid change in r is evident in Figs. 4a,e, and the horizontal gradient Δr/Δx averaged over 300 m (Fig. 6d) across the dryline is almost 10 times as large as that averaged over 3 km (Fig. 6a), and nearly the entire humidity change is concentrated in 300 m. Yet the θ_υ change is less discontinuous: Δθ_υ/Δx over 300 m (Fig. 6d) is only 3 times larger than that over 3 km (Fig. 6b). The presence of a humidity jump sharper than the θ_υ change generally applies to the other IHOP cases studied here; data for the two VORTEX cases shown in Fig. 1 do not allow this finescale comparison.

The observed cross-dryline confluence (−Δu₀) is compared to the one expected assuming a steady-state solenoidal circulation (6) and a density current (9) (section 2b) in Table 1. Both theoretical estimates are high (as for the 24 May cold front), and far higher than observed at a length scale of 62 km, indicating that (6) and (9) do not apply at a larger scale in the presence of a large-scale θ_υ gradient. This agrees with the dryline study of Atkins et al. (1998): they find that density current theory can be applied at 5 km, but not at 50 km.

In summary, the moist air mass just east of the 22 May primary dryline developed a θ_υ deficit of sufficient magnitude to drive solenoidal circulation with sloping updraft and an echo plume trailing toward the moist air. WCR transects and flight-level data support the notion of a density current, with a well-defined leading head and low-level rear-to-front flow. Density current characteristics are evident in all WKA/WCR transects except the earliest one, notwithstanding significant along-line variability and an along-line flow far stronger than the solenoidal circulation.

b. 19 June dryline

On 19 June 2002 the IHOP armada examined a synoptic-scale frontal shear zone in northwest Kansas (Murphey et al. 2006; SG07). Weak southwesterly flow converged at a prefrontal dryline with a southerly low-level jet confined in the moist air mass (Fig. 7). Deep convection erupted along the dryline near 2130 UTC, in particular in the vicinity of misocyclones that modulated the moisture and vertical velocity field (Murphey et al. 2006; Marquis et al. 2007). These misocyclones resulted from strong horizontal wind shear across the dryline, far stronger than on 22 May. This is evident by comparing the flight-level wind barbs in Fig. 4 to those in Fig. 8. SG07 have shown that the dryline updraft and echo plume tilted toward the west in an early phase, when the dryline progressed eastward, and later their slope reversed, toward the moist side, while the dryline became quasi stationary. The change in slope of the updraft was accompanied by a circulation reversal. Soundings were collected on both sides of the dryline, in relative proximity to the dryline, both in the early and later phases (Fig. 7). Initially θ_υ was slightly lower on the dry side, which is unlike any dryline reported on in this study, but has been recorded before (Fig. 4 in Crawford and Bluestein 1997). In the course of ∼1.5 h, between 1330 and 1500 local solar time, the CBL warmed and deepened on the dry side, resulting in a lower mixing ratio, due to the entrainment of dry free-tropospheric air into the deeper CBL. Yet on the moist side the stable layer above the CBL subsided, and the CBL temperature and humidity changed little. As a result, the humidity and mainly temperature contrasts across the dryline increased, and the net effect was that air on the moist side became denser.

In both phases the updraft and echo slopes are dynamically consistent with the observed buoyancy gradient across the dryline: in the early phase air on the dry side is denser (Fig. 8a), but as the dry side warms faster than the moist side, the θ_υ gradient has a reversed sign in the late phase (Fig. 8d). The transition from a westward-tilted boundary, with denser air on the dry side, to an eastward-tilted dryline with denser air on the moist side is examined further in Fig. 9, using WKA data within the CBL. Some drying occurs during the early afternoon, but the humidity difference persists. Thus the reversal of the θ_υ gradient is entirely due to differential warming: the dry-side CBL warms more than the moist-side CBL, due to advection and/or surface sensible heat flux. The Δθ_υ is small both in the early and the late phases, less than 0.5 K at the 3-km scale (Table 1), and less than 1.0 K at the 10-km scale and according to the sounding pairs. So the resulting solenoidal circulation should be weak.

Indeed, weak solenoidal circulations, weaker than the one observed on 22 May (Fig. 5b) have been documented in both phases (SG07), although an updraft/downdraft dipole is not always apparent (e.g., Fig. 8e). Indirect evidence for the secondary circulation and its reversal arises from the WCR reflectivity profile across the dryline. The higher reflectivity on the moist (denser) side of the 22 May primary dryline (Figs. 2, 4h) was interpreted as the result of a solenoidal circulation. In the early traverses the WCR reflectivity peaks near the humidity jump that marks the dryline and continues to be high to the west (Fig. 9d), suggesting a solenoidal circulation with upper-CBL transport to the west; during the last two traverses the lowest reflectivity values are found to the west, and higher values are found near and to the east of the dryline. The WCR vertical velocity pattern is consistent with this (Fig. 9e): in the early (late) phase rising motion tends to occur just east (west) of the dryline; however, this signal difficult to discern in a vigorously convective BL.

Low-level WKA dryline traverses indicate that the confluence is 6–7 m s⁻¹ over 3 km for both phases (Table 1). This is stronger than what can be expected from baroclinicity at this scale (6–7 m s⁻¹). This applies at other scales as well (except for the 10-km scale in the early phase; Table 1). It is remarkable that it applies even to the largest scale: the Δu between the two late-phase soundings, 38 km apart, is above the two theoretical Δu estimates. As mentioned before (section 3a), the density current confluence at such scale tends to be an overestimate in the presence of a background θ_υ gradient.

Thus some other mechanism may have contributed to finescale convergence leading to the 19 June dryline fine line. Additional evidence for this arises from the fact that at some time between the two phases illustrated in Fig. 8, Δθ_υ must have been zero for the reversal to occur. Yet throughout the period, Doppler-on-Wheels (DOW)-3 reflectivity and velocity data indicate that the dryline remained well defined and that the cross-dryline flow was convergent. Horizontal-plane WCR velocity data for an along-dryline flight leg at 2040–2047 UTC indicate strong convergence at <1-km scale (Fig. 11 in SG07).

It is not clear what mechanism explains the rather strong finescale convergence during all phases of the 19 June dryline. One possibility is that it was driven by buoyancy relative to both adjacent air masses. Such buoyancy, with a θ′_υ magnitude of ∼1 K, was evident from a dropsonde transect (Fig. 13b in SG07) and, on a smaller scale, from a stepped WKA traverse (Fig. 12a in SG07), both just prior to CI. It is evident also on a scale of a few kilometers, although the magnitude is only ∼0.5 K at 2135 UTC (Fig. 8d). This buoyancy may explain why mainly ascending motion occurs at this time, rather than a solenoidal circulation (Fig. 8e). The flight-level wind field (shown below Fig. 8d) suggests strong vertical vorticity near the dryline between 1.2 < x < 2.0 km, roughly collocated with the main updraft in the WCR transect. At this time the WKA intersected an intensifying misocyclone, labeled “J” in Fig. 6 of Marquis et al. (2007).

A second possibility is downward transfer of momentum toward the dryline, on either side of the dryline, although evidence presented in section 4b argues against that process. Third, larger-scale dynamics contributed throughout the period, in particular the synoptic-scale wind shear associated with the decaying cold front and the west-bound ageostrophic acceleration toward the high plains where daytime surface heating caused surface pressure falls (Murphey et al. 2006). The acceleration of the moist-side southerly flow is quite apparent from the WKA data between 2004 to 2135 UTC (Fig. 8) and from several soundings (e.g., Fig. 7). Still, it is not clear how this leads to finescale convergence.

The largest Δθ_υ value occurred in the last WKA flight leg and probably continued to increase afterward. An animation of the 0.5° elevation scan of the Goodland, Kansas, Weather Surveillance Radar-1988 Doppler (WSR-88D) radar shows that after 2135 UTC, the dryline accelerated toward the northwest. Thunderstorms erupted just east of the dryline and convective outflow may have enhanced the buoyancy deficit on the moist side and the westward propagation of the dryline, although thunderstorm outflows do not fully explain this retrogression, since the dryline also retrogressed in the gap region between thunderstorms.

a. θ_υ gradients across drylines, and finescale convergence

Several observational studies have documented a Δθ_υ across the dryline, with values of about ∼1.0 K (ranging between 0.5 and 1.9 K) over a distance of ∼10 km (Table 2). The May 22 dryline Δθ_υ is similar, but all others in this study have Δθ_υ < 1.0 K over 10 km (Table 1). The other drylines in this study also generally are weaker in terms of humidity contrast and confluence than the 22 May IHOP, the 6 May 1995 VORTEX, and the 7 June 1994 VORTEX drylines (Table 1) and, unlike these three cases, occurred under clear synoptic forcing and/or outside the main geographic area of drylines. In all cases listed in Table 2b, the moist air mass is the denser one. The 19 June case, with a reversal in the sign of Δθ_υ and slope of the dryline updraft (SG07), is by no means a classic dryline.

Even in a boundary layer with vigorous convective motions, relatively small horizontal θ_υ differences drive a solenoidal circulation in which the less-dense air (usually the dry air) rises over the denser air. The sharp humidity contrast found along the dryline (e.g., NSSP Staff 1963; Figs. 4, 8) is believed to be the direct result of the low-level confluence associated with the solenoidal circulation. This convergent circulation can be sustained as long as some meso-β θ_υ gradient is present.

The null hypothesis of this study, that the presence and strength of convergence lines is independent of their air density contrast, can be rejected by the ensemble of boundaries analyzed herein. A clear correlation exists between Δu and Δθ_υ (Table 1), although exceptions exist, in particular on 18 and 19 June. Baroclinic theory predicts confluence values similar to those observed, although this depends on the scale selected (Fig. 10). At larger scales the theory tends to yield an overestimate, but at all scales the linear regression slopes of predicted versus observed confluence, at matching scales, is close to 1:1, at least for the solenoidal confluence Eq. (6), where |Δu| ∝ Δθ_υ,0 (Fig. 10). The predicted:observed Δu slope is smaller for the density current Eq. (9) at all scales (Fig. 10); that is, the confluence at weak (strong) θ_υ boundaries is over- (under-) estimated. This suggests that the power in the proportionality, 0.5 [|Δu| ∝ Δθ_υ,0 in Eq. (9)], is too small.

The solenoidal forcing is believed to be the leading mechanism of linear, irregular (non-wave-like), finescale convergence over flat terrain. It should apply generally, not just in the geographic domain of drylines. Fine lines of often unclear origin are frequently found in the CBL during the warm season (e.g., Wilson and Schreiber 1986; Koch and Ray 1997). Finescale convergence lines (drylines or other radar fine lines) are expected to form whenever the meso-β θ_υ gradient (over Δx = 25 km or longer) exceeds some threshold. Our study suggests that this threshold is relatively small, <1.0 K (25 km)⁻¹ in some cases.

It is conceivable that on days with a large east–west gradient in daytime surface buoyancy flux over the southern/central Great Plains, this threshold is exceeded in several locations; thus several roughly parallel dryline boundaries may form in the afternoon, as observed in this study (on 22 May and 18 June) and elsewhere (e.g., Hane et al. 1997, 2002). Multiple fine lines are common in west Texas (C. Weiss 2006, personal communication). Closely spaced ancillary lines may coalesce into a single line, possibly by differential propagation related to differences in Δθ_υ, and the absorption of weaker boundaries by stronger ones (Kingsmill and Crook 2003).

b. Differential CBL depth, westerly momentum transfer, and dryline formation

The higher surface sensible heat flux west of the typical dryline formation zone results in a deeper CBL on the dry side, and this, in addition to the elevated topography to the west, allows westerly shear to produce convergence when westerly momentum is mixed vertically in the CBL (e.g., Hane et al. 1993). This process applies to the meso-β scale. It may also produce finescale convergence, especially in the presence of a CBL depth discontinuity (Hane et al. 1997).

The necessary conditions for this process are a deeper CBL on the west side (h_li > h_de) and “westerly” shear (or, more precisely, dryline-normal shear) in the h_li growth layer. The first condition is generally satisfied for the cases examined here, the second one is not, at least not for the cases for which suitable soundings are available. On 22 May 2002 strong westerly shear and momentum are present above the CBL top, but they did not increase between the two soundings; in fact, they weakened somewhat near h_li (Fig. 11a) during 2235 and 2329 UTC, a period during which Δθ_υ across the primary dryline increased (section 3a, and section 4e below). Earlier, the dry-side CBL may have ingested westerly momentum from aloft as it deepened.

A more conclusive validation necessitates a time period of diurnal h_li increase: then at time 1 westerly shear is needed in the layer of CBL growth, and at time 2 increased westerly momentum is expected throughout the CBL. On 19 June 2002 (Fig. 11b) there is westerly shear above h_li in the early phase, but in the h_li growth layer, there is no westerly momentum on the dry side, and by the late phase, westerly momentum has not increased in the CBL. The strongest evidence that vertical momentum transfer in the deepening CBL does not drive momentum changes on the dry side of the developing dryline comes from the 6 May 1995 VORTEX case (Fig. 11c). Between 2013 and 2300 UTC, westerly momentum decreases, even though there is some westerly shear in the growth layer.

Even if differential vertical momentum transfer does occur, it may be a consequence of the development of a meso-γ Δθ_υ. The evidence presented here indicates that it is the latter that drives the circulation, the fine line, and the discontinuity in CBL depth.

c. Solenoidal circulation and mixing in the dryline convergence zone

Horizontal mixing does occur within the DCZ (e.g., Ziegler and Hane 1993; Atkins et al. 1998; Karan and Knupp 2006; Weiss et al. 2008), especially when the 10-km Δθ_υ becomes large enough for a density current to develop with leading head and trailing turbulent wake. A first estimate of the DCZ width is given by the circulation around the density current head, about 2 km wide on 22 May (Fig. 5).

A clear circulation did not occur in the other, lower-Δθ_υ cases in this study. Even on those days a circulation may have been present, but obscured by far stronger convective eddies. To extract evidence of a circulation, we examine the vertical profiles of the 3-km difference of WCR vertical velocity (Δw) and reflectivity (ΔZ) across the dryline (Fig. 12). The 3-km average is chosen to capture the solenoidal flow and reduce the convective “noise.” Figure 12 only includes the “classical” drylines cases, with a denser moist side. Rising motion of the less dense air relative to the denser air implies negative Δw values (Fig. 12b). A tilt in the updraft plume toward the denser air would imply an increase in mean Δw with height. These features generally are observed on 22 May and on the three other days (Fig. 12b), although there is much scatter, and the difference from one flight leg to the next is large.

Inspired by the echo anvil spreading over the denser, moist air on 22 May (Figs. 2, 4) and over the cold postfrontal air on 24 May (Geerts et al. 2006), we examine the difference in reflectivity. Reflectivity may have more temporal continuity than vertical velocity, since it depends on some time integral of vertical motion (Geerts and Miao 2005). The solenoidal circulation implies near-zero ΔZ values near the surface and positive ΔZ in the middle and upper CBL, due to the spreading of the insect plume over the wedge of denser air. This is observed for 22 May, but in the other three cases the ΔZ profiles are widely scattered (Fig. 12a). This suggests that a clear secondary circulation is present only on 22 May, and that in general mixing in the DCZ is less a result of a steady secondary circulation and more due to transient eddies (thermals) or horizontal variations (misocyclones).

The humidity trace generally shows a sharper discontinuity at the dryline than the θ_υ trace, and θ_υ is more likely than r to continue to decrease into the dense-air wedge, in the cases examined here (e.g., Fig. 4). These two characteristics have been documented in other dryline studies (NSSP Staff 1963; Parsons et al. 1991; Ziegler and Rasmussen 1998; Atkins et al. 1998; Karan and Knupp 2006). We believe that this is because the meso-β θ_υ gradient is essential for the circulation to occur, while the meso-β humidity gradient, a common characteristic of dryline environments (e.g., Fig. 11 in Ziegler and Hane 1993), is more circumstantial. For all drylines listed in Table 1 (except the anomalous early phase on 19 June), and all scales, the potential temperature term (which makes the moist side more dense) is 2.8 times larger than the water vapor term (which makes the moist side less dense) in the expression for Δθ_υ. Thus to a first order water vapor can be regarded as a passive tracer.

d. A dryline as a density current

The typical Δθ_υ is small across a dryline, compared to that across cold fronts and gust fronts (Table 2), yet often large enough for the dryline boundary to assume density current characteristics (e.g., Ziegler and Hane 1993; Atkins et al. 1998). The critical 10-km Δθ_υ for density current characteristics to appear in a CBL may be close to 1.0 K, a value exceeded only on 22 May and the two VORTEX cases in Table 1. This value may depend on ambient shear. Florida sea breezes occur with an average Δθ_υ of only 1.1 K and a shallow marine CBL (Atkins and Wakimoto 1997). A sea breeze was maybe the first atmospheric phenomenon to be compared to a laboratory density current (e.g., Clarke 1955). In many cases the dryline may well behave as an “inland sea breeze” (Sun and Ogura 1979; Sun 1987; Bluestein and Crawford 1997) at the meso-γ scale.

In principle a solenoidal circulation occurs over the depth of the θ_υ difference, which varies between h_de and h_li (Figs. 1, 6). If Δθ_υ is sufficient and sufficiently long lived for a density current to develop, its depth D_dc is not h, but rather a function of ambient shear normal to the dryline and h (Xue et al. 1997). For instance, the 24 May cold-frontal density current (Table 1) occupied only ∼37% of the warm-side h. Published D_dc values vary widely (Table 2). Some studies report D_dc values less than h (Atkins and Wakimoto 1997) or even less than h_de (Atkins et al. 1998). The uncertainty in flow depth implies an uncertainty in the theoretical low-level confluence (Table 1). The fact that density current theory generally overestimates confluence (Fig. 10) may be due to an overestimate of D_dc. Another factor is that the feeder flow strength (8) probably is the maximum value in the rear-inflow current (Simpson et al. 1977), while WKA and sounding data represent averages.

Retrogression occurred in later stages in all cases studied here, except on 24 May, when a cold front moved in. In some cases, as on 19 June, changes in Δθ_υ may explain or contribute to dryline retrogression. Dryline propagation is affected by the ambient low-level flow, which is variable and may be diurnally modulated. In most papers where the dryline has been characterized as a density current, retrogression is observed (Table 2), although Crawford and Bluestein (1997) report on retrogressing drylines without density current characteristics. Larger-scale factors contribute to this retrogression (e.g., Bluestein and Crawford 1997; Shaw et al. 1997), but on the scale of the density current, the hydrostatically higher surface pressure in the moist, cooler air drives ageostrophic flow westward, even if that direction locally is upslope (Mahrt 1982).

e. Diurnal dryline trend

It is remarkable that notwithstanding the clear synoptic “forcing” in all but one case in this study, and the range in geographic locales (from northwest Texas to northwest Kansas), a diurnal trend is apparent in the cross-dryline differences (Fig. 13). The humidity contrast does not change much, but −Δθ tends to increase with time toward 0000 UTC. The net result is that −Δθ_υ tends to increase (Fig. 13b); this is consistent with an increase in low-level confluence, although such a trend is not clearly present (Fig. 13d). At a scale of 3 km, the gust probe data do not reveal a trend toward dry air rising over the moist air (Fig. 13c).

A similar trend emerges from previous dryline studies (Table 2b), although detailed data are often missing. The 7 June 1994 (Ziegler and Rasmussen 1998) and 6 May 1995 (Atkins et al. 1998; Ziegler and Rasmussen 1998) dryline case studies appear to be among the best available. In these studies flight-level water vapor was measured by a chilled-mirror dewpoint sensor on the National Oceanic and Atmospheric Administration (NOAA) P-3 aircraft. This is a slow-response sensor; thus it displayed a hysteresis when the aircraft encountered a sharp moisture gradient (Ziegler and Hane 1993). Overshooting (undershooting) occurs when the probe experiences a sudden humidity increase (decrease). Overshoots (undershoots) often appear as sharp spikes (exponential decays) in the time series of r. The width of the spikes varies from 10 to 20 s, and the exponential adjustment can take 30 s (∼3.3 km along-track). For this reason, no reliable 3-km averages can be taken. One cannot accurately correct bad data, so we removed them. For overshoots, we determined the first and last stable values at each side of the spikes. For undershoots, we eliminated 30 s of data from the last trustable point at the moist side. Averages of any variable were then computed from the 1-Hz NOAA P-3 data over 10 km from either side of the best-guess dryline location, excluding the flagged times.

The resulting differences for the two VORTEX cases (Fig. 14) are generally larger than the 3-km differences for the IHOP drylines (Fig. 13). The 10-km Δr, Δθ_υ, and Δu values (∼5.2 g kg⁻¹, ∼1.9 K, and ∼8.3 m s⁻¹ respectively) are significantly larger than on 22 May 2002 (Table 1). But the diurnal trends of Δr, Δθ, and Δθ_υ are similar. Dryline-normal confluence Δu tends to increase as well, consistent with the Δθ_υ trend (Fig. 14d). Notwithstanding the larger Δθ_υ, there is still no evidence for ascent of dry air over moist air at a scale of 10 km (Fig. 14c).

The diurnal trend of Δθ_υ in both IHOP and VORTEX drylines suggests that Δθ_υ is largely driven by regional differences in surface heat fluxes, which are strongly diurnally modulated. The difference in surface buoyancy fluxes probably peaks before 0000 UTC (∼5 h 20 min after local solar noon), but the sign of the difference may be maintained until at least 0000 UTC. The regional θ_υ gradient then increases at finer scales by baroclinic circulations. Thus dryline characteristics probably are strongly affected by regional differences in surface heat fluxes. We hope to examine this further in a future campaign that includes regional flux estimates.