1. Introduction
The initiation of deep moist convection, commonly referred to as convection initiation, requires that parcels of air reach their level of free convection (LFC) and then achieve and maintain positive buoyancy over a significant upward vertical excursion. The location and timing of convection initiation is of acute interest to forecasters owing to the obvious association between convective storms and precipitation and severe weather, in addition to less obvious impacts, such as the effects of convection on energy demand, future numerical weather predictions, and occasionally subsequent convective storm development.
The presence of an LFC and convective available potential energy (CAPE) requires a relatively large lower- to middle-tropospheric lapse rate (larger than the moist adiabatic lapse rate, on average) and low-level moisture. The difficulty in making detailed predictions of convection initiation ultimately arises from the fact that the presence of CAPE is not a sufficient condition for convection initiation. Air typically requires some forced ascent in order to reach its LFC, owing to the presence of at least some convective inhibition (CIN) on most environmental soundings. Deep moist convection commonly is initiated along convergent mesoscale boundaries (Wilson and Schreiber 1986), such as fronts (e.g., Hobbs and Persson 1982; Koch 1984; Parsons et al. 1987; Koch et al. 1997; Koch and Clark 1999), drylines (e.g., Rhea 1966; Ogura and Chen 1977; Schaefer 1986; Hane et al. 1997; Ziegler et al. 1997), outflow boundaries (e.g., Purdom 1976; Matthews 1981; Droegemeier and Wilhelmson 1985; Kingsmill 1995), or sea and land breezes (e.g., Lhermitte and Gilet 1975; Purdom 1976; Wakimoto and Atkins 1994; Atkins et al. 1995; Fankhauser et al. 1995; Kingsmill 1995). Convective storms also have been observed to be initiated by circulations driven by differential heating [e.g., cloudy–clear air boundaries (e.g., Segal et al. 1986), heating of sloped terrain (e.g., Braham and Draginis 1960; Orville 1964; Raymond and Wilkening 1980), horizontal sensible heat flux variations (e.g., Segal and Arritt 1992)] and forced lifting by gravity waves or bores (e.g., Ferretti et al. 1988; Carbone et al. 1990; Karyampudi et al. 1995).
Synoptic-scale dynamics often prime the mesoscale environment for convection initiation by way of large-scale, mean ascent, which tends to reduce CIN and deepen the low-level moist layer. On the other hand, synoptic-scale dynamics also can discourage convection initiation by way of mean subsidence, which has the opposite effects. Large-scale vertical motions can be anticipated reasonably well from model guidance and from the diagnosis of quasigeostrophic forcings. Thus, in forecasting convection initiation—a distinctly mesoscale process—it often is important to identify synoptic-scale disturbances (Doswell 1987).
Unfortunately, producing skillful convection initiation forecasts is not as simple as the above discussion may suggest. For example, although mesoscale boundaries like those cited above are relatively easy to identify using operational observing systems, rarely does convection develop along the entire length of such boundaries. Instead, convective storms typically are initiated along only limited segments of mesoscale boundaries. Another example of the difficulty in convection initiation forecasting is with regard to the CIN measured on “environmental” soundings (e.g., Weckwerth et al. 1996). In some cases, CIN is observed to be entirely absent, yet deep cumulus convection still fails to develop (e.g., Ziegler and Rasmussen 1998). In other cases, nearby soundings indicate that significant CIN remains, yet deep cumulus clouds or thunderstorms are observed. Perhaps there are issues pertaining to sounding representativeness—mesoscale heterogeneities in the temperature and moisture fields generally are not resolved in real time nor in ex post facto studies. Or perhaps it is the assumptions made in using soundings to assess the likelihood of convection that are problematic. For example, mixing occurs along trajectories of air rising to the saturation level and LFC. Thus, as noted by Ziegler and Rasmussen (1998), convection initiation is not as simple as reaching the so-called convective temperature or eliminating CIN, although reducing CIN is certainly one aspect of creating an environment favorable for convection initiation. The kinematic fields in convective storm environments also are quite heterogeneous. Convective storms have been observed to develop where horizontal convective rolls intersect mesoscale boundaries (e.g., Atkins et al. 1995), and vertical vortices also have been identified in close proximity to growing cumulonimbi (e.g., Kingsmill 1995).
Increases in convection initiation forecasting skill arguably have advanced at a slower rate than our ability to anticipate convective storm type, organization, and associated severe weather threats. The convection initiation component of the International H2O Project (IHOP; Weckwerth et al. 2004) was designed to obtain dense observations of temperature, moisture, and wind within the atmospheric boundary layer in order to improve our understanding of the processes responsible for the aforementioned difficulties in anticipating convection initiation. In this paper, we investigate a convection initiation “failure” case from IHOP on 12 June 2002. Herein “failure” is defined as the failure of cumulus convection to develop into sustained cumulonimbus clouds.
The analysis presented in this paper is based on observations largely collected by ground-based instrumentation. Four truck-borne Doppler radars were arranged in a diamond-shaped configuration (∼18 km on a side), with mobile soundings, a mobile wind profiler, a mobile radiometer, mobile mesonets, and two aircraft obtaining kinematic and thermodynamic measurements within this intensive observation region (IOR) defined by the four radars. The 12 June 2002 case is of interest because cumulus congestus clouds developed within the IOR, but these clouds failed to develop further into cumulonimbi. Approximately 40 km east of the IOR, severe, precipitating convection was initiated, but the processes responsible for convection initiation there are not the subject of this paper. Airborne Doppler radar observations of convection initiation east of the IOR will be presented in a future paper (T. Weckwerth 2004, personal communication).
The observations obtained in this case permit an investigation of the details of convection initiation failure—details that have contributed to the difficulties in making skillful, precise predictions of the location and timing of the onset of deep moist convection. High-resolution wind syntheses derived from the multiple-Doppler radars allow for accurate trajectory calculations and permit credible retrievals of thermodynamic information. Stereophotogrammetric cloud observations combined with the retrieved wind fields permit a quantitative analysis of the relationships between boundary layer kinematic structures and cloud development. With the aid of these datasets, the following questions will be addressed:
What are the relationships between boundary layer kinematic structures (e.g., rolls, vertical vortices, updrafts) and thermodynamic fields, including the cloud field?
How do mesoscale boundaries interact with the convective boundary layer?
What processes lead to the largest vertical excursions of air parcel trajectories?
2. Data and analysis techniques
a. Remote and in situ observing systems
The observations utilized in this study were obtained by a wide variety of observing platforms (Fig. 1). Four mobile radars collected data continuously from 1936 to 2130 UTC. Three of the mobile radars [two Doppler On Wheels (DOW2 and DOW3) radars and an X-band dual-polarimetric radar (XPOL)] were similar to those described by Wurman et al. (1997). The wavelength, stationary half-power beamwidth, and Nyquist velocity were 3 cm, 0.93°, and 16.0 m s−1, respectively. Volumes were completed every 90 s, during which time 16 elevation angles were scanned from 0.5° to 14.5°. The azimuth interval between each ray was 0.7°. Within the analysis region, the data spacing (note the oversampling implied by the sampling intervals in azimuth and elevation angle) was approximately 70–250 m in the horizontal and 50–300 m in the vertical. The fourth mobile radar [Shared Mobile Atmospheric Research and Teaching (SMART) Radar (SR1)] has been described by Biggerstaff and Guynes (2000). The wavelength, stationary half-power beamwidth, and Nyquist velocity were 5 cm, 1.5°, and 14.6 m s−1, respectively. Volumes were completed every 180 s, during which time 15 elevation angles were scanned from 0.5° to 25.2°. The azimuth interval between each ray was 1.0°. Within the analysis region, the data spacing was approximately 70–350 m in the horizontal and 50–400 m in the vertical.
Nine automobile-borne surface observing systems (“mobile mesonets”; Straka et al. 1996) obtained temperature, relative humidity, pressure, and wind velocity measurements with a frequency of 1 Hz. Additional in situ measurements were provided by three mobile sounding units [one Mobile Cross-Chain Loran Atmospheric Sounding System (M-CLASS; Frederickson 1993) and two Mobile GPS/Loran Atmospheric Sounding Systems (M-GLASS; Bluestein 1993)] and dropsondes (Hock and Franklin 1999) released from the Flight International Learjet, which was flying at approximately 700 mb. Two aircraft, the Naval Research Laboratory (NRL) P-3 and the University of Wyoming King Air (UWKA), also provided direct thermodynamic observations above the surface (1-Hz frequency). The flight tracks are displayed in Fig. 1.
Two video cameras (CAM1 and CAM2) obtained cloud imagery for the duration of the deployment. One camera was positioned near the XPOL radar, looking northward, and the other camera was positioned near SR1, looking westward (Fig. 1). Clouds were mapped using the stereo photogrammetric cloud mapping techniques described by Rasmussen et al. (2003). Integrated liquid water content data from the Desert Research Institute (DRI) mobile radiometer (Huggins 1995), where available, were used to confirm the photogrammetrically determined cloud positions.
b. Radar data objective analysis and wind synthesis
Radial velocity data were edited to remove errors caused by low signal-to-noise ratio, second-trip echoes, sidelobes, ground clutter, and velocity aliasing. The correct azimuth orientations of the radars were obtained by comparisons of the ground clutter patterns to the known positions of landmarks visible in the clutter patterns. The orientations of two of the radars (DOW2 and XPOL) were confirmed by solar alignment scans (Arnott et al. 2003). The propagation of azimuth errors into the wind synthesis is explored in appendix A.
Radial velocity data were interpolated to two different Cartesian grids. One was a coarse 50 × 50 × 2 km3 grid having a horizontal and vertical grid spacing of 200 m (Fig. 1). This grid encompassed nearly all of the region sampled by two radars, within which dual-Doppler analysis was possible, and defines the “IOR” described in section 1. A finer grid was nested within the larger grid, where the spatial resolution of the radars was greatest. It spanned 24 × 24 × 2 km3, had a horizontal and vertical grid spacing of 100 m, and encompassed the region sampled by all four mobile radars (i.e., the region containing the most accurate wind syntheses). The lowest level of both grids was 100 m above the mean elevation of the radars.
The interpolation was accomplished by way of a Barnes objective analysis (Barnes 1964; Koch et al. 1983), using an isotropic, spherical weight function and smoothing parameter, κ, of 0.36 km2. This choice of smoothing parameter yields a 40% theoretical response for features having a wavelength of 2.0 km, which is approximately 4 times the data spacing at a range of 30 km from the radars (approximately the coarsest data spacing in the dual-Doppler analysis region). This relatively conservative choice for κ follows the recommendations of Trapp and Doswell (2000). For computational reasons, data beyond a “cutoff” radius, Rc, of 1.25 km from each grid point were not considered in the calculation of the weights, even though the theoretical contribution to the weight function remains nonzero and positive, albeit very small, for distances between a datum and grid point greater than Rc. Objective analyses were produced using other smoothing parameters and cutoff radii. The sensitivity of the objective analysis to the choice of κ and Rc is investigated in appendix A.
Advection was removed from the objectively analyzed radial velocity grids, whereby an “optimal” advection velocity was determined by minimizing the local time tendencies of the velocity components (Matejka 2002). The sensitivity of the wind syntheses to the specification of the advection velocity also is explored in appendix A.
Three-dimensional wind syntheses were produced using the overdetermined dual-Doppler approach and the anelastic mass continuity equation (integrated upward), rather than a direct triple- or quadruple-Doppler solution. The former approach has several advantages over the latter approaches, as demonstrated by Kessinger et al. (1987). The wind syntheses above approximately 1.7 km were not considered to be very reliable due to the fact that the signal-to-noise ratio from two of the radars (DOW3 and XPOL) was unacceptably small at these elevations. The time resolution of the analyses is 90 s, over which time synchronized scans were completed by three of the four radars (DOW2, DOW3, and XPOL). Every other analysis (180-s intervals) is obtained using a four-radar overdetermined dual-Doppler solution. Comparisons between the synthesized wind fields and in situ wind measurements made by the UWKA and NRL P-3 (smoothed so that the scales represented in the velocity time series were comparable to those resolved in the radar-derived wind syntheses) indicated good agreement between the radar-derived wind fields and those measured by the other two platforms.
c. Pressure and buoyancy retrieval
Within the 24 × 24 × 2 km3 domain, where wind syntheses were the most trustworthy, dynamic retrievals of pressure and buoyancy perturbations were performed. The technique used was identical to that described by Gal-Chen (1978) and later used by Hane and Ray (1985), among others. Indirect and direct methods were undertaken to check the validity of the retrieved pressure and buoyancy fields. The results of momentum checking (Gal-Chen 1978), autocorrelation analysis, and comparisons to in situ observations are discussed in appendix B.
It is crucial that the time derivatives of the velocity components be accurately known, especially in a convective boundary layer characterized by rapid evolution. For this reason, three-radar wind synthesis solutions were used at all analysis times, rather than four-radar solutions at every other analysis time. DOW2, DOW3, and XPOL completed volume scans every 90 s, whereas SR1 completed a volume scan every 180 s. Wind syntheses obtained by solving the three-radar overdetermined dual-Doppler equations unavoidably differ slightly from those obtained by solving the four-radar overdetermined dual-Doppler equations (at least this is the case if the fourth radar contributes any useful information). The differences between the three-radar and four-radar solutions were subtle indeed—the linear correlation coefficients (rms differences) between the three- and four-radar solutions for the u, υ, and w wind components averaged 0.99, 0.99, and 0.91 (0.08, 0.03, and 0.16 m s−1), respectively. In spite of the only minor differences in the three- and four-radar wind field solutions, the impact on the time derivatives owing to alternating between three- and four-radar wind syntheses was much more obvious. Thus, only three-radar solutions to the wind field were used in the dynamic retrievals, in order to maximize the fidelity of the time derivative calculations, which were centered in time (Crook 1994).
The finite differencing necessary to compute the forcings (e.g., velocity advection, local accelerations, turbulence parameterization) for the pressure field can produce 2Δ noise (where Δ is the grid length) even if the velocity field itself is free of such noise. For this reason, some additional smoothing by way of a Leise filter was imposed on the input fields appearing in the Poisson pressure equation that must be solved iteratively (Gal-Chen and Kropfli 1984).
The retrieved perturbation pressure and buoyancy fields obtained using Gal-Chen's (1978) technique only can be known to within a constant that varies with height; thus, the three-dimensional perturbation pressure field and buoyancy field (which is really a perturbation buoyancy field; see Hane et al. 1988) cannot be known unless direct measurements augment the retrieval (although issues of point measurements versus volume averages arise) or an additional constraint is imposed, such as the thermodynamic equation (e.g., Roux 1985).
3. Overview of the 12 June 2002 IHOP case
Figure 2 presents upper-air analyses for the 850-, 500-, and 250-mb levels at 0000 UTC 13 June 2002 [all subsequent times will be in UTC; UTC = central daylight time (CDT) + 5 h]. A relatively zonal regime was present in the middle and upper troposphere in the central United States. The polar jet stream was located on the northern fringe of the IHOP domain, where winds approached 35 m s−1 at 250 mb. A col was present in the 850-mb geopotential height field in northwestern Oklahoma and southwestern Kansas, with warm, moist southerly flow present to the southeast of this feature.
Surface analyses are superposed on visible satellite imagery at 2000 and 2200 UTC within the IHOP domain in Fig. 3, and enlarged views of a subset of this region appear at approximately 30-min intervals between 1934 and 2203 UTC in Fig. 4. An outflow boundary near the Oklahoma–Kansas border separated warm, moist, generally southerly flow in western and central Oklahoma from slightly cooler but comparably moist easterly flow in southern Kansas. The character of the clouds north of the outflow boundary, which displayed waves, suggested that this air mass was more stable than the air mass to the south (Fig. 3). A weak cold front extended south-southwestward from the outflow boundary in the eastern Oklahoma panhandle to the central Texas panhandle. North of the outflow boundary, a surface trough extended north-northeastward along roughly the same line as the cold front. It is possible that the surface trough was the same larger-scale boundary as the cold front, only that its density gradient had become ill-defined owing to the superpositioning of convective outflow from nocturnal thunderstorms occurring the previous evening. A dryline also was present, extending from the outflow boundary southwestward into the eastern Texas panhandle, where it intersected the cold front. The warmest surface temperatures (a maximum of 39.5°C was observed at 2134 UTC) and driest surface dewpoints (a minimum of 11.0°C was observed at 2103 UTC) were observed in the narrow region bounded by the dryline to the east, cold front to the west, and outflow boundary to the north (Fig. 4). The warm, moist air mass to the east of the dryline and south of the outflow boundary, as well as the slightly cooler air mass to the north of the outflow boundary, contained CAPE exceeding 2000 J kg−1 and virtually no CIN near 2100 UTC (Fig. 5).1 CAPE also was present at locations in the relatively hot, dry low-level air mass west of the dryline and south of the outflow boundary, but a small amount (2–23 J kg−1) of CIN was present.
A low intensified along the outflow boundary during the afternoon hours. Animations of reflectivity from the National Center for Atmospheric Research (NCAR) S-band dual-polarization Doppler radar (S-POL; not shown), which also was situated in the eastern Oklahoma panhandle, depicted a spectacular cyclonic circulation about this low pressure cell. Objectively analyzed equivalent reflectivity factor from the S-POL radar (Fig. 6) revealed that the mesoscale boundaries analyzed in Figs. 3 and 4 (i.e., the dryline and outflow boundary) also were associated with reflectivity fine lines.
The IHOP mobile observing facilities were deployed during the early afternoon to northwestern Oklahoma where the dryline and outflow boundary intersected. This area was deemed to be the most likely location for convection initiation. Between 1934 and 2103 UTC (Fig. 4), the dryline mixed eastward, out of the IOR. In the next 30 min, the cumulus clouds along the dryline explosively developed into several thunderstorms (Figs. 3, 4 and 6), approximately 40 km east of the center of the IOR, just beyond the easternmost dual-Doppler lobes formed by the mobile radars. Damaging winds and large hail were reported in conjunction with some of the storms. Although convection initiation was not captured within the IOR, towering cumulus clouds—apparently indicative that plumes of air had surpassed the LFC—developed along the outflow boundary within the region of dense observations between 2100 and 2130 UTC (Figs. 4, 7 and 8). Curiously, this deep vertical growth occurred during the time when the outflow boundary was accelerating southeastward through the IOR, apparently in response to the passage of the low to the northeast (Fig. 4). It is the formation of these deep cumulus clouds that is the subject of greatest interest in this paper.
4. Boundary layer kinematic fields
a. Mesoscale boundaries
The horizontal convergence (−∇ · v) and vertical vorticity (ζ) fields at 100 m above ground level (AGL; hereafter all heights are AGL) and vertical velocity (w) at 1.5 km are displayed at 30-min intervals from 1945 to 2115 UTC within the large wind synthesis domain in Figs. 9 and 10. The placement of surface boundaries is based on the synthesized wind fields, mobile mesonet observations (refer to Fig. 4), and radar reflectivity (e.g., Fig. 6). What is perhaps the most obvious aspect of Figs. 9 and 10 is the humbling complexity of the kinematic fields, which might tempt one to conclude that the radial velocity data were insufficiently smoothed prior to the production of three-dimensional wind syntheses. Yet the fields have vertical and temporal continuity, which would not be anticipated in the presence of nonmeteorological noise. For example, the temporal autocorrelation of the vertical velocity field is ≥0.9 during the entire deployment (see appendix A). Although there is some artificial coupling in the vertical introduced by the objective analysis, there is no artificial coupling of fields in time. Each analysis is independent of prior and ensuing analyses. Thus, there is considerable confidence in the robustness of the derived kinematic fields in Figs. 9 and 10.
Figures 9 and 10 reveal that the mesoscale boundaries are not simply regions of quasi-two-dimensional “slabular” ascent.2 Instead, the low-level convergence and associated vertical motion fields along the dryline and outflow boundary are highly three-dimensional, apparently the result of the superpositioning of motions associated with gravity waves, boundary layer convective overturning, which dominates, and much weaker mesoscale ascent along the dryline and outflow boundary. Similar along-boundary variability has been noted in past convection initiation studies (e.g., Kingsmill 1995; Atkins et al. 1995), although the boundaries typically have coincided with unbroken corridors of at least positive convergence. It is perhaps clear from visual inspection of Figs. 9 and 10 that no popular spatial averaging technique would be capable of rendering kinematic fields resembling those presented in many conceptual models, whereby corridors of unbroken convergence and ascent, and enhanced relative vorticity, are assumed to be collocated with wind shift lines. Indeed, attempts to remove the motions associated with thermals in order to obtain mean mesoscale motions that resemble such conceptual models, using broader spatial filters and time averaging (not shown), proved unsuccessful for this case. Conceptual models are purposely idealized and thus greatly simplified. One worry, however, is that the details excluded from previous conceptual models for probably well-intentioned reasons may very well turn out to be crucial in addressing outstanding questions pertaining to convection initiation. This matter will be discussed in greater detail in section 7. Since observations having the spatial and temporal resolution of those presented herein are rare, some unavoidable uncertainty exists as to the generality of our observations.
Boundary layer convection dominates the kinematic fields on both sides of the dryline and outflow boundary. There is a mild suggestion of organization into rolls and cells, especially on the warm side of the outflow boundary, although not to the degree documented by Weckwerth et al. (1997). Maximum vertical velocity magnitudes at 1.5 km are approximately 4 m s−1 on the warm side of the outflow boundary and approximately 3 m s−1 on the cool side of the outflow boundary. Updrafts tend to be associated with relative maxima in radar reflectivity factor (linear correlation coefficients were ∼0.4 during the deployment),3 probably as a result of insect lofting (Wilson et al. 1994). Along what have been referred to as mesoscale boundaries (i.e., the dryline and outflow boundary), there is no outstanding enhancement of upward vertical velocities, although this does not necessarily imply that the characteristics of air parcel trajectories are similar along and away from the boundaries, as will be discussed later.
b. Gravity waves
Gravity waves are readily apparent north of the outflow boundary in the radar reflectivity data [e.g., Fig. 6 (particularly the 1930–2030 UTC panels)] and in the retrieved perturbation pressure fields near the surface (Fig. 11). The oscillation of the horizontal wind vector field throughout the boundary layer due to the passage of the wave fronts is very evident in animations (not shown). The waves are not easily discernible in the radar reflectivity data nor the low-level pressure field after approximately 2100 UTC. This case nicely demonstrates that the influence of gravity waves can extend into a neutrally stratified, convective boundary layer.
The wavelength of the waves averages approximately 10 km and the motion was toward the west at approximately 4 m s−1. Soundings indicate a neutrally stratified boundary layer on the cool side of the outflow boundary, capped by a stable layer between approximately 700 and 800 mb (Fig. 5). The zonal wind speed in the stable layer has a westerly component; thus, the waves have a westward propagation. In the underlying neutrally stable boundary layer of the outflow air mass, however, the zonal wind speed is easterly, averaging 5–6 m s−1. Thus, the boundary layer updrafts associated with the waves are located roughly a quarter-wavelength west (downstream) of the pressure troughs (Fig. 11). The vertical velocity field, however, is perhaps less orderly (i.e., far from being quasi-two-dimensional) than one might expect in the presence of gravity waves. This probably is a result of the interaction of the gravity wave motions with convective cells.
c. Vertical vorticity extrema
The vertical vorticity field is equally as complex as the convergence and vertical velocity fields, with relative minima and maxima associated with the divergence and convergence associated with the boundary layer convection cells. The most significant vorticity maxima develop along the outflow boundary after 2045 UTC (Figs. 10 and 13), particularly where significant updrafts on the warm side of the outflow boundary intersect the outflow boundary. These maxima have magnitudes on the order of 10−2 s−1. The magnitudes of the vorticity extrema generally decrease with height from their largest values near the surface, although all of the significant vorticity extrema span the depth of the boundary layer. Several intense dust devils were observed near the outflow boundary from the position of SR1 (Fig. 1), but the relationship between the dust devils and any of vorticity anomalies resolved in the radar-derived wind syntheses is not known.
It is also clear from Figs. 12 and 13 that the relationship between the vertical velocity and vertical vorticity fields is quite complex. For example, the intimate linkages between vortices and convergence maxima and clouds are not observed to the same degree in this case as in some other recent studies. For example, Kingsmill (1995) and Marquis et al. (2004) have observed vorticity maxima along mesoscale boundaries separated by a well-defined wavelength, with local enhancements of horizontal convergence located roughly a quarter-wavelength downstream of the vorticity maxima, apparently due to the interaction of the vortices with the wind shift lines. It may be that the processes governing the development of the vortices observed in this case differ from those operating in the past studies cited. A detailed analysis of the evolution and dynamics of the boundary layer vortices is beyond the scope of the present study; however, such an investigation is provided by Markowski and Hannon (2006).
5. Relationship between kinematic and thermodynamic fields
The near-ground buoyancy gradient along the outflow boundary is notably weak throughout the data collection period, largely as a result of larger moisture concentrations on the cool side of the boundary (Fig. 4). The virtual potential temperature gradient measured at the surface by the mobile mesonets is approximately 1 K (10 km)−1 at the surface within the IOR (Fig. 4). The retrieved virtual potential temperature gradient at 0.1 km is even weaker (e.g., Fig. 14), with slightly more buoyant air north of the outflow boundary at times (e.g., Fig. 14). These retrieval results, although surprising, are supported by sounding observations (e.g., compare the nearly simultaneous 1933 and 1934 UTC soundings obtained on opposite sides of the outflow boundary in Fig. 5, whereby the surface temperatures are similar but the specific humidity is ∼4 g kg−1 larger on the sounding north of the boundary). There also is some suggestion from the soundings (Fig. 5) that the lapse rates north of the outflow boundary had a greater tendency to be superadiabatic within the surface layer. This effect also would reduce the near-ground buoyancy gradient across the outflow boundary.
A larger buoyancy gradient is present across the outflow boundary in the middle to upper portions of the boundary layer (Fig. 14), although even here the gradient is relatively modest by mesoscale standards [generally less than 1 K (5 km)−1]. In section 7 we discuss the possibility that the absence of a horizontally contiguous, unbroken slab of mesoscale ascent along the outflow boundary may be related to the weak baroclinity along the boundary.
South of the outflow boundary, in situ data from aircraft flying between 0.4 and 0.7 km, not surprisingly, reveal that updrafts tend to be collocated with virtual potential temperature excesses (Fig. 15, top). Furthermore, boundary layer updrafts also tend to be situated above regions of virtual potential temperature excess at the surface, as evidenced by mobile mesonet observations (Fig. 16). In contrast, the correlation between updrafts (Fig. 12 and 13) and retrieved positive buoyancy anomalies (Fig. 14) is relatively small in the middle to upper boundary layer. Perhaps this observation is partly a result of the buoyancy fields necessarily having been smoothed to a greater degree than the vertical velocity fields, or perhaps the updrafts simply are not positively buoyant more than approximately a kilometer above the ground. North of the outflow boundary, the relationship between buoyancy and vertical velocity is ill defined at all levels (Fig. 15, bottom), perhaps owing to the influence of gravity wave dynamics.
The in situ aircraft data also reveal that boundary layer updrafts (downdrafts) are closely associated with moist (dry) anomalies. This is most obvious south of the outflow boundary, in the relatively dry air mass (Fig. 15, top). In the relatively moist air mass north of the outflow boundary, specific humidities were nearly constant at flight level (Fig. 15, bottom). Although we cannot be certain of how much mesoscale upwelling of moisture was occurring along the outflow boundary like that documented along other mesoscale convergence zones (e.g., Wilson et al. 1992), circumstantial evidence suggests that little moisture upwelling was occurring along the outflow boundary. This suggestion is based on the lack of a prominent specific humidity maximum in the aircraft data time series during the times of passage through the outflow boundary (e.g., Fig. 15), and the lack of a persistent, spatially continuous corridor of strong convergence along the outflow boundary.
6. Relationships between cumulus cloud development and boundary layer kinematic and thermodynamic fields
Shallow cumulus clouds were observed in the IOR throughout the deployment from 1930 to 2130 UTC (Figs. 7 and 8). Between 2100 and 2130 UTC, some of the clouds grew to more significant depths (Figs. 4 and 8). Photogrammetric cloud analyses indicated that the tops of the tallest clouds in the IOR exceeded 7 km during this period. Below we provide a discussion of the relationships between kinematic and thermodynamic boundary layer structures and cloud formation. Emphasis is placed on the development of the deepest clouds in the IOR after 2100 UTC.
a. Shallow cumulus cloud development prior to 2100 UTC
As one would probably anticipate, the area occupied by cumulus clouds was much smaller than the area occupied by updrafts (Fig. 12). Not all updrafts were associated with cumulus clouds, and where they were, the clouds spanned smaller horizontal scales than their parent updrafts. These observations are likely indicative of entrainment and moisture heterogeneity. Clouds generally were situated above updrafts, although some clouds were observed in regions of nearly zero or slightly negative vertical velocity (e.g., the clouds near “A” and south of “D” at 2045 UTC; Fig. 12). The latter, however, were situated in regions where updrafts had been present 5–10 min earlier; that is, cumulus clouds not located within updrafts were at least observed to be located within regions having histories of ascent.
Cumulus cloud development was not enhanced along the outflow boundary. The clouds grew in number gradually during the deployment throughout the entire IOR (Figs. 7 and 12). Cloud bases were determined from photogrammetry to range from 1.6 to 2.5 km, with lower (higher) cloud bases observed north (south) of the outflow boundary where the relative humidity was larger (smaller). Thus, the cloud bases were roughly 0.1–1.0 km above the level at which vertical velocity fields are displayed in Figs. 12, 13 and 14.
b. Deep cumulus cloud development between 2100 and 2130 UTC
Cumulus clouds continued to increase in number after 2100 UTC, and several of these grew to heights well above the LFC (e.g., cloud “F” in Fig. 8 reached an altitude of 7.2 km at 2125 UTC). Although shallow cumulus cloud development was not confined to the outflow boundary, deep cumulus cloud development was observed almost exclusively along the outflow boundary (Figs. 8 and 13). Interestingly, vertical velocities within the boundary layer were no larger beneath the deepest cumulus clouds than they were beneath the shallow cumulus clouds. For example, between 2107 and 2125 UTC, updrafts exceeding 3 m s−1 were observed at an elevation of 1.5 km on both sides of the outflow boundary (Fig. 13), and as documented in section 4, the outflow boundary was not a region of spatially continuous, enhanced vertical velocity (Figs. 9 and 10). The deepest cloud at 2115 (labeled as “E” in Fig. 8) and 2125 UTC (labeled as “F” in Fig. 8) is situated above 1–2 m s−1 updrafts at 1.5 km, whereas updrafts as strong as 3–4 m s−1 frequently were associated with clear skies or only shallow cumulus development, especially in the warm sector south of the outflow boundary.
Trajectories into shallow and deep cumulus clouds were compared in an attempt to understand why the development of deep cumulus clouds was confined to the outflow boundary despite the fact that there was no apparent enhancement of vertical velocities along the outflow boundary. Trajectories were computed using trilinear spatial interpolation and a fourth-order Runge–Kutta time integration algorithm using a time step of 10 s. The three-dimensional wind fields were assumed to vary linearly in time between the two Doppler analyses closest to the current time of a point along a trajectory. An error analysis of the trajectories is presented in appendix B.
Backward trajectories originating from clouds B, F, G, and H at 2125 UTC are displayed in Fig. 17. The cloud bases range from 1.7 to 2.1 km; thus, the bases generally are located slightly above the level where trajectories originate (1.7 km, the highest level deemed to have reliable wind velocity fields). The top of cloud F was 7.2 km at 2125 UTC, and cloud G grew to a similar height shortly after 2125 UTC (Fig. 8). Clouds F and G were located along the outflow boundary (Fig. 13). Clouds B and H were shallow cumulus clouds that developed several kilometers north and south of the outflow boundary, respectively (Fig. 13). Trajectories entering the strong updraft (>4 m s−1 at 1.5 km) ∼5 km southeast of cloud G (labeled “U” in Fig. 13) also were examined. It is not known whether this updraft was associated with shallow cumulus development or no cumulus development because the updraft was not within the field of view of either CAM1 or CAM2. It is only known that this updraft was not associated with deep cumulus cloud formation.
The most obvious difference in the trajectories entering the deep clouds along the outflow boundary versus those entering the shallow clouds that formed away from the boundary is the slope of the trajectories (Fig. 17). The trajectories entering the deep clouds along the outflow boundary were much more vertical than those entering the shallow clouds away from the boundary. The more upright trajectories along the boundary were a result of the relative minimum in both horizontal wind speed (Fig. 10) and vertical wind shear along the boundary (Fig. 18). Indeed, updrafts along the boundary were more erect than those away from the boundary.
The differences in the updraft and trajectory slopes may imply differences in the dilution of buoyancy and reduction of potential buoyancy (a function of equivalent potential temperature, θe) for vertical excursions occurring along and away from the outflow boundary. The highly elongated, gently sloped excursions occurring away from the boundary are perhaps more susceptible to the detrimental effects of entrainment. Several soundings south of the outflow boundary (most notably the 2046 and 2059 UTC soundings; Fig. 5) indicated that the moisture concentration was not constant with height, but rather there was a decrease of 1–2 g kg−1 between the surface and the top of the boundary layer; thus, entrainment en route to the cloud base would have resulted in a reduction of potential buoyancy. Furthermore, in the 2115 and 2125 UTC analyses, the bases of the clouds developing along the outflow boundary tended to be wider than those that developed away from the outflow boundary (Fig. 13); this observation might be indirect evidence of less entrainment along the trajectories entering the clouds that developed along the outflow boundary. Additional discussion follows in the next section.
7. Comments on convection initiation
a. Role of the outflow boundary in enabling deep cumulus cloud development
Although this case has been regarded as an example of convection initiation “failure,” some aspects probably are similar to those present in “success” cases. For example, although no precipitating convection developed within the IOR, some plumes of air did in fact attain their LFC. We are unable to address what processes occurring above the boundary layer might have been detrimental to convection initiation owing to the paucity of scatterers above the boundary layer and corresponding lack of Doppler radar observations there. However, the boundary layer history of ascending plumes of air likely is important even at elevations significantly above the boundary layer.
The deepest clouds formed along the outflow boundary that was present within the IOR throughout the data collection period. This by itself is not a surprising result. After all, convection initiation is well known to occur along mesoscale boundaries, as summarized in the introduction. But one obvious question arising from this case study is this: what was the role of the outflow boundary in promoting the deepest clouds?
Conventional wisdom perhaps would have suggested that the role of the outflow boundary was simply to provide convergence and ascent, forcibly lifting air to its LFC. But this scenario clearly is problematic in the present case, owing to the dominance of boundary layer thermals on the vertical velocity field. As discussed in section 4, even after much spatial and temporal smoothing, mesoscale vertical motions induced by the outflow boundary were unable to be retained from the convection-dominated kinematic fields. The magnitude of the vertical motions along the outflow boundary was no larger than those observed within thermals away from the outflow boundary, particularly in the warm sector to the south, where the largest vertical velocities were obtained (e.g., Figs. 9 and 10). Furthermore, the outflow boundary was not associated with a continuous corridor of convergence and ascent along its leading edge, probably owing to the superpositioning of the vigorous convective motions with the mesoscale confluence along the outflow boundary.
Another reasonable a priori hypothesis for the role of the outflow boundary in promoting the deepest cumulus clouds might have been mesoscale moisture upwelling along the boundary. Such upwelling (e.g., Wilson et al. 1992) could have promoted convection initiation by deepening the moist layer, thereby reducing the amount of θe dilution resulting from entrainment within rising plumes of air. The data that could reveal such a moisture enhancement in the 12 June 2002 case are limited; for example, only two aircraft passages through or along the outflow boundary occurred during the 2100–2130 UTC time period. But for the limited amount of data that do exist, no evidence could be found suggesting a local deepening of the moist layer in the vicinity of the outflow boundary. As discussed in section 5, in situ data from the aircraft failed to reveal a prominent specific humidity maximum along the outflow boundary (Fig. 15). The inability to observe a moisture enhancement along the outflow boundary might be consistent with the lack of a persistent, spatially continuous corridor of strong convergence.
In the previous section, profound differences were noted between the trajectories entering the deep cumulus clouds along the outflow boundary and those entering the shallow cumulus clouds away from the outflow boundary (Fig. 17), with the former trajectories (and their associated updrafts) being more vertical than the latter. The differences in updraft slope imply differences in the magnitude of entrainment along the trajectories (e.g., Weisman 1992). In addition to the obvious differences in cloud depth along the outflow boundary versus away from it, the cloud width was enhanced along the outflow boundary (e.g., the 2115 and 2125 UTC panels of Fig. 13), which might be circumstantial evidence of reduced θe dilution within the rising plumes along the outflow boundary.
The above observations lead us to hypothesize that the role of outflow boundary in promoting the deepest cumulus clouds in this case was not related to enhanced vertical velocities or mesoscale moisture upwelling. Instead, we hypothesize that the role of outflow boundary might only have been to promote updrafts that were less susceptible to θe dilution (Fig. 19). This scenario differs somewhat from that illustrated by Crook (1996) and Crook and Klemp (2000), who showed that vertical excursions could be dynamically enhanced when the flow and shear above a convergence line is decreased, rather than “thermodynamically enhanced” via reducing entrainment, which is what is being proposed here. Our findings also might suggest some applicability to convection initiation of the theory presented by Rotunno et al. (1988), which relates the slope of the updraft along the leading edge of a density current to the magnitudes of the density excess and ambient wind shear.
If entrainment more adversely affected rising plumes of air away from the outflow boundary than along the outflow boundary, one might reasonably ask why vertical velocities along the outflow boundary would not be larger than those away from the outflow boundary. The vertical velocity fields synthesized in this study all are located below the lifting condensation level (LCL), where soundings revealed that potential temperature was constant with height within the IOR (at least above the surface layer); however, many soundings also revealed that specific humidity decreased by 1–2 g kg−1 from the surface to the top of the boundary layer (Fig. 5). Given these thermodynamic profiles below the LCL, entrainment would reduce the specific humidity but not the potential temperature, and because buoyancy is much more strongly a function of potential temperature, vertical velocities below the LCL would not be affected significantly by the entrainment of slightly drier air. However, the reduction of θe below the LCL corresponds to a reduction of the potential buoyancy and vertical velocity that can be realized above the LCL and LFC, since the magnitude of the buoyancy in a deep cumulus cloud depends in large part on the magnitude of the latent heat release. Thus, vertical velocities above the LCL (and cloud depths) might be anticipated to be more adversely affected than vertical velocities below the LCL by θe dilution occurring below the LCL. In reference to the opening paragraph of this section, it is in this way that the boundary layer history of ascending plumes can be important even at elevations significantly above the boundary layer.
The above thermodynamic arguments regarding entrainment do not consider the entrainment of momentum, which would weaken updrafts regardless of the impact of entrainment on buoyancy. South (on the warm side) of the outflow boundary, where vertical velocities were as strong or even occasionally stronger than along the outflow boundary, it is possible that the thermals originating at the surface were subjected to a larger initial buoyancy force, thereby offsetting the more significant momentum entrainment.
b. The failure of convection initiation
A major challenge we face in this study is that it is not possible to know how the atmosphere would have evolved had the processes observed in this case not been operating. This is the inherent difficulty in analyzing null cases, which is probably one reason why relatively few are documented in the literature (Doswell et al. 2002)—at least a disproportionate number of cases when one considers the fact that convection fails to develop over far more regions than it does develop over. The best we can do is document recurring processes and environmental characteristics present in null cases that are absent in “success” cases, in order to determine the conditions that promote convection initiation.
One aspect of this case that might have been unfavorable for convection initiation along the outflow boundary is the aforementioned absence of a continuous, persistent corridor of convergence. This finding is similar to that made by Arnott et al. (2004) in another IHOP case (10 June 2002) along a segment of a cold front where deep convection failed to be initiated. In past studies documenting convection initiation “successes,” although significant along-line variability occasionally was observed, the mesoscale boundaries to which convection initiation was attributed coincided with unbroken or nearly unbroken corridors of convergence and updraft (e.g., Kingsmill 1995; Atkins et al. 1995; Richardson et al. 2004).
In section 5 the possibility was raised as to whether the lack of a horizontally contiguous, unbroken slab of mesoscale ascent along the outflow boundary was related to the weak baroclinity along the boundary. Indeed, Arnott et al. (2004) and Stonitsch and Markowski (2004) have found a strong relationship between baroclinity and the organization of the vertical motion field (i.e., its horizontal continuity) along mesoscale boundaries in other IHOP cases. These studies suggest that the organization of the vertical motion field along mesoscale boundaries depends on the relative significance of density current or frontal dynamics compared to motions associated with thermals, with the vertical motion field along boundaries becoming increasingly “slabular” as density current or frontal dynamics become more dominant.
One also might wonder why a radar reflectivity fine line would be observed in conjunction with a mesoscale boundary along which a spatially continuous corridor of convergence is absent (Fig. 6), but the fine line was relatively diffuse. A well-defined convergence zone also was absent along the dryline during the period when the dryline was sampled by the ground-based radars, but we cannot comment on the kinematic structure of the dryline at the time when thunderstorms were initiated east of the IOR. It may be noteworthy that the fine line associated with the dryline became much more prominent east of the IOR near the time of convection initiation (see 2100 UTC panel of Fig. 6).
The soundings obtained in the IOR in the vicinity of the outflow boundary near the time when deep cumulus clouds developed (e.g., the 2046 and 2059 UTC soundings; Fig. 5) do not suggest the same magnitude of mesoscale ascent and moist layer deepening as the sounding near the location of convection initiation farther east (e.g., the 2056 UTC sounding; Fig. 5). The latter sounding has virtually no CIN, whereas the former soundings have a modest amount of CIN (∼20 J kg−1), unless CIN is computed assuming undiluted ascent or by lifting a parcel originating in the superadiabatic contact layer. It is possible that the previously cited promotion of “θe dilution-resistant” updrafts along the outflow boundary was sufficient for the development of deep cumulus clouds, but that θe dilution was not entirely absent owing to the lack of moisture upwelling so that there simply was not enough potential buoyancy remaining once the LFC was achieved in order to support precipitating cumulonimbus clouds. Unfortunately, no soundings were obtained in close proximity to the deep cumulus clouds along the outflow boundary during the 2100–2130 UTC period.
c. Conceptual models of convection initiation
One critical issue seems to be related to the superpositioning of motions induced by mesoscale dynamics (e.g., density current dynamics, which has been invoked in theoretical studies of outflows and drylines) and motions associated with the ubiquitous buoyant convection in the boundary layer. How are their relative contributions to the vertical motion field affected by the baroclinity present along the mesoscale boundaries? Do the relative contributions mostly impact the magnitude of the vertical motions or the spatial patterns of the vertical motions, and what are the consequences for parcel trajectories in the vicinity of mesoscale boundaries?
As already noted numerous times throughout, boundary layer thermals dominated the horizontal convergence and vertical motion fields in this case, and it is likely that they would be equally as dominant or at least assume first-order importance in most warm-season convection initiation cases. Many past conceptual models of convection initiation have been based on mesoscale dynamics, and many of these models are two-dimensional. From the perspective of mesoscale dynamics and convection initiation, thermals often are regarded as noise and are excluded from such models. This approach is certainly understandable—after all, much convection initiation forecasting success can be realized simply by identifying mesoscale or synoptic-scale wind shifts or radar fine lines. But the present case strongly suggests that advances made in our conceptual models of convection initiation should include a prominent role for boundary layer convection in addition to mesoscale boundaries. This fundamentally requires three-dimensionality. Even when a quasi-two-dimensional mesoscale boundary is present, significant along-boundary heterogeneity is guaranteed in the presence of boundary layer convection. This point also has been raised by some previous studies; for example, Atkins et al. (1995) presented a conceptual model in which the deepest cumulus clouds were initiated at the intersections of convective rolls with a sea-breeze front. The possible importance of vortices along boundaries in convection initiation also has been raised by many investigators (e.g., Kingsmill 1995; Kanak et al. 2000; Lee and Finley 2000; Marquis et al. 2004, among others), and the development and evolution of such vortices may be closely connected to boundary layer convection (e.g., Shapiro and Kanak 2002), and perhaps the interaction of convective cells or rolls with mesoscale boundaries (e.g., Atkins et al. 1995). We speculate that the complex superpositioning of boundary layer thermals and mesoscale motions are probably why determining precisely where convection initiation will occur has been so difficult, even along well-defined mesoscale boundaries.
8. Summary and conclusions
This paper has examined the kinematic and thermodynamic structure of the boundary layer in the vicinity of an outflow boundary and dryline on 12 June 2002, processes associated with the development of both shallow and deep cumulus clouds, and processes that may have contributed to the failure of the initiation of sustained, precipitating cumulonimbus clouds. The observations presented herein permit the following conclusions pertaining to this study:
The convergence and vertical motion fields were dominated by motions associated with boundary layer thermals rather than dynamics associated with the mesoscale boundaries.
The influence of internal gravity waves propagating through a statically stable layer capping the boundary layer can extend throughout the underlying neutrally stratified boundary layer.
The deepest cumulus clouds occurring within the region of intensive observations developed along an outflow boundary, where trajectories into the clouds were nearly vertical; shallow cumulus clouds developed away from this outflow boundary, where vertical velocities were equally as large but trajectories were much more inclined from the vertical.
The role of the outflow boundary in enabling deep cumulus cloud development was to promote updrafts in proximity to the boundary that were less susceptible to θe dilution, rather than to provide enhanced vertical velocities or a region of persistent mesoscale convergence within which moisture upwelling occurred.
The lack of a persistent, spatially continuous corridor of mesoscale ascent along the outflow boundary and associated moisture upwelling contributed to convection initiation failure along the outflow boundary.
We also would encourage additional study of the relationship between radar reflectivity fine lines and the vertical velocity field. Reflectivity fine lines may be the best way of inferring the presence of vertical motion or its history in real time. But it is precisely because radar reflectivity may be a better indicator of updraft history rather than instantaneous vertical velocity that makes this topic worthy of additional attention. We also believe that it would be extremely worthwhile to further explore how gravity waves and mesoscale boundaries interact with convective boundary layers. Finally, the relationships between the vertical velocity and vertical vorticity fields received only superficial treatment. A much more thorough investigation of the nature of vortices, their evolution, forcings, and intricate feedbacks to vertical motion, and possible convection initiation ramifications are presented in a companion paper (Markowski and Hannon 2006).
Acknowledgments
We wish to thank Drs. Yvette Richardson, John Clark, Josh Wurman, Erik Rasmussen, Conrad Ziegler, Bart Geerts, and Tammy Weckwerth for many fruitful discussions over the course of this work, and Dr. Manos Anagnostou, Dr. Kevin Knupp, and Justin Walters for providing XPOL radar data and (University of Alabama in Huntsville) Mobile Integrated Profiling System (MIPS) data. We also received invaluable assistance from Dr. Jerry Guynes, Curtis Alexander, Mike Buban, Steve Williams, Marisa Ferger, and particularly Nettie Arnott, who graciously allowed us to use her advection correction program and other DOW postprocessing programs. IHOP could not have occurred without the leadership and devotion of Drs. David Parsons and Tammy Weckwerth, the dedication of the Joint Office of Science Support, and all of the student participants who spent countless hours collecting data in the field. Software developed by NCAR was heavily used in this work. Radar editing was performed using SOLO, objective analyses of radar data were produced by REORDER, and wind syntheses were produced by CEDRIC. This research was supported by National Science Foundation Grant ATM-0130307 made to Pennsylvania State University.
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APPENDIX A
Wind Synthesis Sensitivity Analysis
A number of sensitivity tests were undertaken to examine the robustness of the three-dimensional wind syntheses. In this appendix, the effects of radar azimuth errors, objective analysis parameters, and advection velocity on the wind syntheses are assessed. Trajectory uncertainties also are investigated.
Azimuth errors
Prior to the interpolation of radar data to a Cartesian grid, it is imperative that the orientation of the radar is accurately known. This orientation can be determined by identifying landmarks in the ground clutter pattern whose positions are known, or by scanning the sun (its position is well established from astronomical tables), as already discussed. All orientation uncertainty typically cannot be eliminated, especially when identifying ground clutter targets, owing to a finite beamwidth and possible uncertainties in the reported positions of the landmarks. The impact of azimuth errors on the interpolation and subsequent wind synthesis ultimately depend on the azimuthal radial velocity gradients, which are range and weather dependent.
To quantify the propagation of azimuth angle errors into the wind syntheses, radial velocity data from each of the four mobile radars were rotated by 1° (roughly a full half-power beamwidth) at five randomly selected analysis times. The rotations were made in both the counterclockwise and clockwise direction in order to determine the largest effect on the wind syntheses. It is believed that this approach represents a “worst case” scenario—it is very unlikely that all four radars would have been incorrectly oriented by a full degree of azimuth. The largest rms error (smallest linear correlation coefficient) in the vertical velocity field for five randomly chosen analysis times was 0.18 m s−1 (0.92). For smaller azimuth errors of 0.5°, or for errors that affected less than four radars (in the case of a four-radar overdetermined dual-Doppler synthesis), the vertical velocity errors were correspondingly smaller. For example, when two of four radars have 1° azimuth errors, the vertical velocity rms error falls to ∼0.10 m s−1 and the linear correlation coefficient increases to ∼0.97, depending on which radars contain azimuth errors. The vertical velocity error statistics also were computed at 1 km AGL rather than within the entire analysis volume, so that the error statistics would not be biased toward smaller values owing to the fact that vertical velocity approaches zero near the ground regardless of any divergence errors introduced. At 1 km, the vertical velocity rms error (linear correlation coefficient) was 0.22 m s−1 (0.90) when all four radars were subjected to a 1° azimuth error. Errors in the divergence and vertical vorticity field also were assessed. When two (four) radars were perturbed by 1° of azimuth, the rms errors for both divergence and vertical vorticity averaged ∼0.2 × 10−3 s−1 (∼0.5 × 10−3 s−1).
Specification of advection velocity
Objective analyses and wind syntheses also were completed after perturbing the advection velocity, which had been obtained using the strategy proposed by Matejka (2002). Advection velocity perturbations of 2 m s−1 were applied to the components in the x and y directions. On this day, these perturbations represent approximately 100% relative errors from the “optimal” advection velocity determined using Matejka's approach. These advection velocity perturbations had virtually no effect on the wind syntheses (wind velocity component rms differences and linear correlations with respect to the unperturbed syntheses computed at five randomly chosen analysis times were <1 cm s−1 and >0.99). The insensitivity is largely due to the fact that volume scans were completed in approximately 90 s, in which time coherent boundary layer structures translate less than two grid lengths.
Objective analysis parameters
Compared to azimuth errors and advection velocity errors, assuming that they are reasonably accounted for, the effect of the Barnes smoothing parameter, κ, on the objective analyses of radial velocity data and subsequent wind syntheses is considerably greater. Objective analyses were produced using a range of smoothing parameters: 0.18, 0.36, 0.54, and 0.72 km2. The theoretical response functions are plotted in Fig. A1. Modifications in the degree of smoothing do not result in changes in the overall patterns of the interpolated radial velocities and wind syntheses, at least away from the domain boundaries, which is not necessarily the case when azimuth or advection velocity errors propagate into wind syntheses. However, the details retained in the syntheses and amplitudes of the divergence extrema (among others) may be significantly affected by the specification of κ (e.g., Fig. A2). For example, rms differences in the vertical velocity fields obtained using κ = 0.18 km2 versus κ = 0.72 km2 are ∼0.30 m s−1 at 1 km AGL. These results suggest that at least as much effort should be put into judiciously choosing an appropriate value of κ as is placed on removing so-called navigation errors and advection.
The sensitivity of the objectively analyzed radial velocities to the choice of the cutoff radius, Rc, also was investigated. Cutoff radii ranging from 0.25 to 2.0 km were used in a suite of objective analyses, and the analysis using Rc = 2.0 km was regarded as the “truth.” The interpolated radial velocity fields using Rc < 2.0 km then were compared to the interpolated radial velocity field obtained using Rc = 2.0 km. Figure A3 indicates that, for the ranges of κ used herein, the choice of Rc = 1.25 km (see section 3) does not result in significant distortion of the interpolated radial velocity field. The objective analyses have nearly converged toward the “truth” for Rc values approaching 1 km.
Trajectory calculations
Errors in the synthesized wind components accumulate in time in the calculations of trajectories. The sensitivity of trajectory integrations to wind synthesis errors was quantified by computing 100 trajectories, initiated at z = 200 m, from each of four different regions of the synthesis domain. Along each trajectory at each time step, the u, υ, and w wind components were perturbed randomly such that the variances of the random perturbations matched the theoretical u, υ, and w variances (Ray and Sangren 1983), which depend on the number of radars, radar geometry, and the radial velocity variance (assumed to be 1 m2 s−1; Doviak and Zrnic 1993, p. 292). For the set of trajectories having the largest uncertainties, the x, y, and z uncertainties (σx, σy, and σz, respectively) after 300 s were 46, 52, and 57 m, respectively, which is less than a grid length (Fig. A4). After 600 s, the x, y, and z uncertainties were 73, 76, and 114 m, respectively.
APPENDIX B
Comparison of Retrieved Buoyancy to In Situ Observations
Confidence can be gained that the retrieved buoyancy fields have credibility by way of indirect and direct means. Indirect evidence in the form of internal consistency checks (“momentum checking”; Gal-Chen 1978; Fig. B1) and scan-to-scan temporal continuity (Fig. B2) suggests, at least circumstantially, that the retrieved buoyancy fields are useful.
The relative error, Er (Gal-Chen 1978), consistently averages less than 0.30 after 2045 UTC, and during no time period is the average Er within the boundary layer >0.40 (Fig. B1). The scan-to-scan time correlation of vertical velocity is >0.85 for the entire deployment, but the pressure and buoyancy correlations are considerably more variable (Fig. B2). The volatility of the pressure and buoyancy retrieval is evidenced by the fact that small drops in vertical velocity time correlations (e.g., the 2045–2100 UTC period, during which the w time correlation falls from ∼0.92 to ∼0.83 on average) lead to much larger drops in pressure and buoyancy time correlations, probably indicative of less certain ∂w/∂t estimations.
Direct verifications of the quality of the dynamic retrievals are obviously more desirable than indirect verifications, but making comparisons between retrieved thermodynamic variables and direct observations can be problematic owing to the fact that the latter are point measurements whereas the former represent volume averages (on the order of 106 m3) that have not even been derived from data collected simultaneously. In comparing the retrieved thermodynamic variables to in situ point measurements (e.g., mobile mesonet and aircraft, both with 1-Hz sampling frequency), some averaging of the in situ measurements must be applied. The goal of such smoothing is to remove signals in the in situ observations that are present on spatial and temporal scales not resolved by the wind syntheses. In other words, temporal scales less than ∼100 s and spatial scales less than ∼200 m should be filtered from the time series of in situ observations. Unfortunately, both objectives cannot be met simultaneously, because the in situ observing platforms in this case are constantly moving; that is, the in situ observations cannot be filtered in any sense to yield the sort of volume-and-time-averaged buoyancy values that are retrieved from the multiple-Doppler wind syntheses. Therefore, one must resort to what are essentially empirical smoothing choices. For the mobile mesonet (aircraft) data, a 60-s (10 s) running mean filter was applied to the data used for comparison. These choices seem to retain spatial scales roughly comparable to those present in the wind syntheses, although the issue of temporal resolution differences remains (e.g., an aircraft traveling at 100 m s−1 obtains data over the length of a grid box in 1 s, whereas the radar data that have affected the wind synthesis in that grid box have been collected over a time span of 90 s).
In Figs. B3 and B4, smoothed time series of mobile mesonet and NRL P-3 virtual potential temperatures are plotted against retrieved virtual potential temperatures (see section 3) that have been interpolated in space and time to the mobile mesonet and NRL P-3 positions (the University of Wyoming King Air did not perform transects within the region where dynamic retrievals were performed). During most time periods, the intercomparisons are what many might regard as favorable, despite the concerns discussed above. In fact, it is perhaps surprising that the mobile mesonet observations compared so well with the retrieved buoyancy (Fig. B4), given that information from the wind syntheses essentially has been extrapolated to the surface and the surface layer has a much different (unstable) stratification compared to the rest of the boundary layer. At some times and locations (e.g., the P6 time series in Fig. B4), however, it is seems as though the volume-averaging limitations of the retrievals may have significantly contributed to the poor comparisons. Nevertheless, the authors believe that, during most time periods, the retrievals provide thermodynamic information that is sufficiently trustworthy for at least qualitative analysis.
Observations obtained during the 1930–2130 UTC mobile radar deployment on 12 Jun 2002. The locations of camera, mobile mesonet, dropsonde, rawinsonde, aircraft (NRL P-3 and UWKA), mobile radar (DOW2, DOW3, XPOL, SR1), and mobile radiometer (DRI) observations are indicated using the symbology defined in the legend. The square encloses the 50 × 50 km2 mobile radar analysis region (the same region indicated in Figs. 3, 4 and 6). The positions of mesoscale boundaries at 2100 UTC also are overlaid
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Upper-air analyses for the 250-, 500-, and 850-mb levels at 0000 UTC 13 Jun 2002. Black lines represent isohypses in decameters. Dashed lines on the 500- and 850-mb analyses represent isotherms (°C). Dashed lines on the 250-mb analysis represent isotachs (m s−1), with values greater than 40 m s−1 hatched. Temperature, dewpoint temperature, wind speed, and direction are also plotted (half barb—2.5 m s−1; full barb—5 m s−1; flag—25 m s−1)
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Surface analyses and visible satellite imagery at 2000 and 2200 UTC 12 Jun 2002. Thin black lines are isobars (2-mb intervals, leading “10” omitted from the contour labels), and thin dashed lines are virtual isentropes (2-K intervals). Temperature (°C), dewpoint temperature (°C), wind speed (half barb—2.5 m s−1; full barb—5 m s−1), and wind direction are plotted in the station models. The bold dashed line indicates a surface low pressure trough, the bold dash–dot line indicates an outflow boundary, the bold line with filled barbs indicates a cold front, and the bold line with unfilled scallops indicates a dryline. The dashed box indicates the mobile radar analysis region, and the four filled squares within this region indicate the positions of the mobile radars
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Enlarged view of visible satellite imagery, with surface analyses overlaid, at 1934, 2003, 2034, 2103, 2134, and 2203 UTC 12 Jun 2002. Thin black lines are isobars (2-mb intervals, leading “10” omitted from the contour labels), and thin dashed lines are virtual isentropes (2-K intervals). Temperature (°C), dewpoint temperature (°C), wind speed (half barb—2.5 m s−1; full barb—5 m s−1), and wind direction are plotted in the station models. Station models having a filled square at the base of the wind barb are observations obtained from mobile mesonets. The bold dash–dot line indicates an outflow boundary, the bold line with filled barbs indicates a cold front, and the bold line with unfilled scallops indicates a dryline. The dashed box indicates the mobile radar analysis region, and the four radar truck icons within this region indicate the positions of the mobile radars (as in Fig. 3)
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Skew T–logp diagrams of the soundings obtained during the 1930–2130 UTC mobile radar deployment. Isobars (solid) are drawn at 100-mb intervals; isotherms (solid) are drawn at 10°C intervals; isentropes (solid) are drawn at 20-K intervals; pseudoadiabats (dashed) are drawn at 8°C intervals; lines of constant water vapor mixing ratio line (dashed) also are included (2, 3, 5, 8, 12, and 20 g kg−1). The locations of the rawinsondes and dropsondes are indicated in the schematic at the top right of each thermodynamic diagram
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Equivalent radar reflectivity factor recorded by the NCAR S-Pol radar at 1930, 2000, 2030, 2100, 2130, and 2200 UTC 12 Jun 2002. The dashed box indicates the mobile radar analysis region, and the four radar truck icons within this region indicate the positions of the mobile radars
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Video frames of cloud field from CAM1 (looking north) and CAM2 (looking west) at 2015 and 2045 UTC. The locations of CAM1 and CAM2 are shown in Fig. 1. The labels reference clouds appearing in the Doppler wind syntheses displayed in Fig. 12. Clouds visible in both CAM1 and CAM2 imagery have been given the same label
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Video frames of cloud field from CAM1 (looking north) and CAM2 (looking west) at 2107, 2115, and 2125 UTC. The locations of CAM1 and CAM2 are shown in Fig. 1. The labels reference clouds appearing in the Doppler wind syntheses displayed in Fig. 13. Clouds visible in both CAM1 and CAM2 imagery have been given the same label. The heights of some of the deep cloud tops also have been indicated
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Horizontal cross sections of horizontal convergence (−∇ · v) at 0.1 km, vertical vorticity (ζ) at 0.1 km, and vertical velocity (w) at 1.5 km at 1945 and 2015 UTC on the coarse (50 × 50 km2) grid. Horizontal wind vectors also appear on each panel (the tail of each vector is located at every 20th grid point). The positions of the dryline, outflow boundary, and gravity wave fronts also have been overlaid. (top left) The position of the nested wind synthesis grid (24 × 24 km2) is indicated with the dashed square
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
As in Fig. 9, but for 2045 and 2115 UTC
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Perturbation pressure fields at 0.1 km at (left) 2015 and (right) 2045 UTC within the 24 × 24 km2 wind synthesis domain (see Fig. 9). Contours have been drawn at 0.04-mb intervals. Negative contours are dashed. The perturbations are with respect to the domain-averaged pressure perturbation at 0.1 km. Vertical velocities greater than 0.5 m s−1 at 1.5 km have been shaded gray. The outflow boundary is depicted using the same symbology as in Fig. 3, and phase fronts have been drawn through pressure troughs using dashed lines
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Horizontal cross sections of the (left) vertical velocity (w) field at 1.5 km and (right) vertical vorticity (ζ) field at 0.1 km within the 24 × 24 km2 wind synthesis domain (see Fig. 9) at 2015 and 2045 UTC. Horizontal wind vectors at 1.5 and 0.1 km also are displayed in the vertical velocity and vertical vorticity panels, respectively (see scale in upper-left panel). The outflow boundary is depicted using the same symbology as in Fig. 3. Gravity wave phase fronts have been drawn through pressure troughs as in Fig. 11. Cloud positions determined from photogrammetry are shaded gray, and some of the clouds appearing in Fig. 7 have been labeled with the letters A–H. The locations and fields of view of the two cameras used for the photogrammetric cloud analysis are indicated in the left panels. The contours depicting the w field at 1.5 km are drawn at 1 m s−1 intervals, with positive (negative) contours drawn as solid (dashed) lines and the 0 m s−1 contour suppressed. The contours depicting the ζ field at 0.1 km are drawn at 2 × 10−3 s−1 intervals, with positive (negative) contours drawn as solid (dashed) lines and the 0 s−1 contour suppressed
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
As in Fig. 12, but for 2107, 2115, and 2125 UTC. Some of the clouds appearing in Fig. 8 have been labeled with the letters A–H. The “U” label indicates the updraft referred to in Fig. 17. The flight track of the NRL P-3 aircraft also is indicated (tick marks are at 1-min intervals)
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Horizontal cross sections of the virtual potential temperature perturbation (θ′υ) field at (left) 1.5 and (right) 0.1 km within the 24 × 24 km2 wind synthesis domain (see Fig. 9) at 2015 and 2125 UTC. The virtual potential temperature perturbations at 1.5 and 0.1 km are with respect to the domain-averaged virtual potential temperature perturbation at 1.5 and 0.1 km, respectively. Horizontal wind vectors also are displayed (see scale in upper-left panel). The outflow boundary is depicted using the same symbology as in Fig. 3. Gravity wave phase fronts have been drawn through pressure troughs as in Fig. 11. Cloud positions determined from photogrammetry are shaded gray. The locations and fields of view of the two cameras used for the photogrammetric cloud analysis are indicated in the left panels. Contours of the θ′υ field are drawn at 0.5-K intervals, with positive (negative) contours drawn as solid (dashed) lines. The flight track of the NRL P-3 aircraft between 2122 and 2126 UTC also is indicated (tick marks are at 1-min intervals)
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Time series of virtual potential temperature (θυ; solid, black) and specific humidity (q; solid, gray) from the NRL P-3 aircraft from (top) 2106:25–2109:55 and (bottom) 2122:10–2125:40 UTC. The synthesized vertical velocity (w; dashed; black) interpolated to the aircraft position also is overlaid. Aircraft data were smoothed with a 10-s running mean filter. The flight level was at approximately 0.6 km AGL for both time periods. The abscissa is labeled with both x-grid coordinate and UTC time. The flight tracks also are overlaid in Figs. 14 and 13
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Time series of mobile mesonet (“probe 6”) virtual potential temperature (θυ; solid) at 3 m AGL vs synthesized vertical velocity (w; dashed) at 1.5 km AGL from 2100 to 2130 UTC. The mobile mesonet data were smoothed with a 12-s running mean filter
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Trajectories traced backward from 2125 UTC from two deep cumulus clouds along the outflow boundary (black trajectories; clouds labeled as “F” and “G” in the lower-left panels of Figs. 8 and 13), two shallow cumulus clouds away from the outflow boundary (gray trajectories; clouds labeled as “B” and “H” in the lower-left panels of Figs. 8 and 13), and an updraft south of the outflow boundary lying outside of the region where cloud mapping was possible (gray trajectories; labeled “U” in the lower-left panel of Fig. 13). The three-dimensional perspective is from the west-northwest and includes horizontal wind vectors at 0.1 km, the position of the outflow boundary using the same symbology as in Fig. 3, and photogrammetrically determined cloud positions (gray). Two additional views from the south and west also are provided. In these views, a few of the trajectories have reference markings along them at 90-s intervals to provide a sense of the time scales involved
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Vertical wind shear vectors between 1.5 and 0.1 km (v1.5 km − v0.1 km) within the 24 × 24 km2 wind synthesis domain (see Fig. 9). Photogrammetrically determined cloud positions are shaded gray
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Idealization of the trajectories into the shallow and deep cumulus clouds observed away from and along the outflow boundary, respectively. Away from the outflow boundary, the trajectories into the shallow cumulus clouds significantly depart from the vertical. Along the outflow boundary, the trajectories into the deep cumulus clouds are much more vertical owing to the relative minimum in horizontal wind speed and vertical wind shear present along the boundary. The differences in the trajectory slopes, which also were a manifestation of differences in the slopes of the updrafts in this case, may imply differences in the dilution of buoyancy and potential buoyancy (a function of equivalent potential temperature) for vertical excursions occurring along and away from the mesoscale boundary
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Fig. A1. Theoretical response functions as a function of wavelength, λ, for the range of Barnes smoothing parameters tested. The four curves shown represent the theoretical responses when κ = 0.18 km2, κ = 0.36 km2, κ = 0.54 km2, and κ = 0.72 km2
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Fig. A2. Vertical velocity and horizontal wind vectors at 1 km AGL at 2100 UTC within the 24 × 24 km2 domain, based on wind syntheses in which radial velocities obtained from the mobile radars were objectively analyzed using a Barnes smoothing parameter of (top left) κ = 0.18 km2, (top right) κ = 0.36 km2, (bottom left) κ = 0.54 km2, and (bottom right) κ = 0.72 km2. Positive vertical velocities are shaded and negative vertical velocities are indicated using dashed contours at 1 m s−1 intervals, starting at −1 m s−1
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Fig. A3. Sensitivity of objectively analyzed radial velocities, VR, to the cutoff radius, Rc, for Barnes smoothing parameters of κ = 0.18 km2, κ = 0.36 km2, κ = 0.54 km2, and κ = 0.72 km2 (the SR1 data at 2000 UTC were used for this analysis, without loss of generality). In the calculation of the rms errors, the radial velocity field analyzed using Rc = 2.00 km has been regarded as the truth
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Fig. A4. Uncertainties in the x, y, and z positions of trajectories (σx, σy, and σz, respectively) as a function of time. The uncertainties were estimated by randomly perturbing u, υ, and w along sets of 100 trajectories, initiated from four different regions of the synthesis domain at z = 200 m, such that the u, υ, and w uncertainties (σu, συ, and σw, respectively) matched the theoretical uncertainties governed by the number of radars and their geometry. A radial velocity uncertainty (σVR) of 1 m s−1 was assumed. The plot above displays the position uncertainties for the set of trajectories having the largest position errors
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Fig. B1. Relative errors, Er, in the pressure retrievals, averaged over the lowest 1.5 km. The error bars indicate the range of Er about the mean in the lowest 1.5 km at each analysis time
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Fig. B2. Lag-1 autocorrelations for the vertical velocity, pressure, and buoyancy averaged over the lowest 1.5 km
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Fig. B3. Comparisons of retrieved virtual potential temperatures against direct measurements made by the NRL P-3 aircraft. The time series from 2013 to 2015, 2048 to 2050, and 2122 to 2124 UTC represent transects from west to east at z = 500 m and 3 < y < 6 km. The time series from 2107 to 2109 UTC represents a transect from east to west at approximately y = −1.5 km and z = 500 m. The linear correlation coefficients, r, also are displayed
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Fig. B4. Comparisons of retrieved virtual potential temperatures against direct measurements made by mobile mesonet units (P2, P4, P6, and P9). The linear correlation coefficients, r, also are displayed
Citation: Monthly Weather Review 134, 1; 10.1175/MWR3059.1
Here and hereafter, CAPE and CIN were computed using the mean potential temperature and specific humidity within the boundary layer, as well as virtual temperature deviations from the environment (Doswell and Rasmussen 1994).
This term has been borrowed from James and Fritsch (2003) and James et al. (2005), who used it to describe different modes of ascent within the leading updrafts of squall lines.
B. Geerts (2004, personal communication) has reported a similar correlation in University of Wyoming Cloud Radar observations obtained in another IHOP case (24 May 2002).
