Microphysical and Thermodynamic Structure and Evolution of the Trailing Stratiform Regions of Mesoscale Convective Systems during BAMEX. Part II: Column Model Simulations

Joseph A. Grim Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois

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Greg M. McFarquhar Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois

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Robert M. Rauber Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois

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Andrea M. Smith Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois

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Brian F. Jewett Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois

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Abstract

This study employed a nondynamic microphysical column model to evaluate the degree to which the microphysical processes of sublimation, melting, and evaporation alone can explain the evolution of the relative humidity (RH) and latent cooling profiles within the trailing stratiform region of mesoscale convective systems observed during the Bow Echo and Mesoscale Convective Vortex Experiment (BAMEX). Simulations revealed that observations of a sharp change in the profile of RH, from saturated air with respect to ice above the melting layer to subsaturated air with respect to water below, developed in response to the rapid increase in hydrometeor fall speeds from 1–2 m s−1 for ice to 2–11 m s−1 for rain. However, at certain times and locations, such as the first spiral descent on 29 June 2003 within the notch of lower reflectivity, the air may remain subsaturated for temperatures (T) < 0°C. Sufficiently strong downdrafts above the melting level, such as the 1–3 m s−1 downdrafts observed in the notch of lower reflectivity on 29 June, could enable this state of sustained subsaturation. Sensitivity tests, where the hydrometeor size distributions and upstream RH profiles were varied within the range of BAMEX observations, revealed that the sharp contrast in the RH field across the melting layer always developed. The simulations also revealed that latent cooling from sublimation and melting resulted in the strongest cooling at altitudes within and above the melting layer for locations where hydrometeors did not reach the ground, such as within the rear anvil region, and where sustained subsaturated air is present for T < 0°C, such as is observed within downdrafts. Within the enhanced stratiform rain region, the air is typically at or near saturation for T < 0°C, whereas it is typically subsaturated for T > 0°C; thus, evaporation and melting result in the primary cooling in this region. The implications of these results for the descent of the rear inflow jet across the trailing stratiform region are discussed.

* Current affiliation: National Center for Atmospheric Research, Boulder, Colorado.

Corresponding author address: Joseph A. Grim, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: grim@ucar.edu

Abstract

This study employed a nondynamic microphysical column model to evaluate the degree to which the microphysical processes of sublimation, melting, and evaporation alone can explain the evolution of the relative humidity (RH) and latent cooling profiles within the trailing stratiform region of mesoscale convective systems observed during the Bow Echo and Mesoscale Convective Vortex Experiment (BAMEX). Simulations revealed that observations of a sharp change in the profile of RH, from saturated air with respect to ice above the melting layer to subsaturated air with respect to water below, developed in response to the rapid increase in hydrometeor fall speeds from 1–2 m s−1 for ice to 2–11 m s−1 for rain. However, at certain times and locations, such as the first spiral descent on 29 June 2003 within the notch of lower reflectivity, the air may remain subsaturated for temperatures (T) < 0°C. Sufficiently strong downdrafts above the melting level, such as the 1–3 m s−1 downdrafts observed in the notch of lower reflectivity on 29 June, could enable this state of sustained subsaturation. Sensitivity tests, where the hydrometeor size distributions and upstream RH profiles were varied within the range of BAMEX observations, revealed that the sharp contrast in the RH field across the melting layer always developed. The simulations also revealed that latent cooling from sublimation and melting resulted in the strongest cooling at altitudes within and above the melting layer for locations where hydrometeors did not reach the ground, such as within the rear anvil region, and where sustained subsaturated air is present for T < 0°C, such as is observed within downdrafts. Within the enhanced stratiform rain region, the air is typically at or near saturation for T < 0°C, whereas it is typically subsaturated for T > 0°C; thus, evaporation and melting result in the primary cooling in this region. The implications of these results for the descent of the rear inflow jet across the trailing stratiform region are discussed.

* Current affiliation: National Center for Atmospheric Research, Boulder, Colorado.

Corresponding author address: Joseph A. Grim, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: grim@ucar.edu

1. Introduction

Mesoscale convective systems (MCSs) are common during the late spring and summer across the central United States (Johns 1993) and are frequently associated with strong straight-line winds. Common structural features of mature squall-line MCSs include the leading convective line, the trailing stratiform region (TSR), front-to-rear flow aloft, and a rear inflow jet (RIJ; see review by Houze 2004). Biggerstaff and Houze (1991, 1993) and Braun and Houze (1994) showed that hydrometeors within the TSR originate within the convective line and are advected rearward within the front-to-rear flow aloft and later fall out into the rear-to-front flow within the RIJ. The RIJ plays a crucial role in bringing dry midlevel air from the rear of the system; it is this dry air into which the hydrometeors fall (e.g., Smull and Houze 1987). Microphysical processes, specifically sublimation and melting of ice and evaporation of rain, act to cool and moisten the thermodynamic profile within the TSR (e.g., Zhang and Gao 1989; Yang and Houze 1995). Dynamical processes, such as mesoscale updrafts and downdrafts, also play an important role in producing the temperature (T), relative humidity (RH), and precipitation structures within the TSR (Smull and Houze 1987; Rutledge et al. 1988; Biggerstaff and Houze 1993). In the past, it has been difficult to isolate the relative importance and magnitude of these processes within the TSR.

The Bow Echo and Mesoscale Convective Vortex Experiment (BAMEX; Davis et al. 2004) was conducted, in part, to address the question of the relative importance of microphysical and dynamical processes within the TSR. BAMEX provided a unique dataset of 17 spiral aircraft descents performed by the National Oceanic and Atmospheric Administration (NOAA) P-3 aircraft within the TSRs of 12 separate MCSs (McFarquhar et al. 2007, hereafter MF07; note that a corrigendum for this article appears in this issue). This paper is the third in a series examining these measurements. MF07 presented analyses on how the vertical profiles of hydrometeor shapes, sizes, phases, and concentrations above, within, and below the melting layer of the TSRs of BAMEX MCSs varied with the thermodynamic structure of the environment. Smith et al. (2009, hereafter Part I) expanded the work of MF07 by using airborne Doppler radar observations and level II Weather Surveillance Radar-1988 Doppler analyses to examine the meteorological context of the observed microphysical and thermodynamic structures. A fourth paper, Grim et al. (2009), presents high-resolution multi-Doppler observations of the entire life cycle of a squall line within the 29 June 2003 MCS and investigated the forcing mechanisms for the development and intensification of the RIJ associated with this squall line.

In total, 12 of the 17 BAMEX spiral descents were performed during some stage in the evolution of a typical MCS (Houze et al. 1989) with a TSR (Part I). For the purpose of analyzing the structure of BAMEX MCSs, Part I used these data to investigate the structure of the TSR at different stages of typical MCS development: the formative (their Fig. 3), mature (their Fig. 4), and the weakening stages. In the formative stage, the TSR is primarily composed of two regions, a region where stratiform precipitation reaches the ground and a rear anvil region where the precipitation sublimates and/or evaporates completely before reaching the ground. Only the first spiral on 29 June 2003 (Grim et al. 2009) was performed within the TSR during the formative stage of a BAMEX squall-line MCS. This spiral was performed within a notch of lower reflectivity. The “notch” was originally defined as the concavity in the back edge of the TSR precipitation echo (Smull and Houze 1985), although it has also come to refer to the associated weak echo channel that extends from the concavity at the rear of the system through the TSR toward the convective line (e.g., Przybylinski 1995; Alfonso and Naranjo 1996; Weisman 2001). In this paper, the notch refers to the continual low reflectivity feature that encompasses the concavity at the rear of the TSR and any weak echo channel extension that continues through the TSR toward the convective line. An example of the notch from the 29 June MCS is indicated with a dashed line in Fig. 1a.

For the mature and weakening stages of a typical squall-line MCS, Part I divided the TSR into three zones. The transition zone referred to the region of diminished reflectivity immediately behind the convective line (Smull and Houze 1987; Biggerstaff and Houze 1991). The enhanced stratiform rain region was the generally uniform region of increased radar reflectivity to the rear of the transition zone where precipitation reached the ground. Reflectivity within this zone typically exceeded 25 dBZ and brightband effects were often apparent on low-level radar reflectivity scans. Last, the rear anvil region was the region behind the enhanced stratiform rain region in which precipitation fell from the storm anvil, but did not reach the ground. Of the 11 BAMEX spirals fitting this conceptual model, Part I showed that two were within the rear anvil region, nine were within the enhanced stratiform rain region, and none were within the transition zone.

MF07 showed that, with the exception of the 29 June spiral, the RH with respect to ice (RHi) for T < 0°C never fell below 90% and averaged near 100% (Fig. 2).1 However, the RH with respect to water (RHw) decreased steadily with increasing T for T > 0°C to an average RHw of 71% at 9°C. Willis and Heymsfield (1989) observed this same sharp contrast of saturated air above the 0°C isotherm and unsaturated air below in the RH field within the 10–11 June 1985 MCS. They hypothesized that this phenomenon is the result of a dynamical transition near the melting layer, with mesoscale ascent above and mesoscale descent below.

A primary objective of this study is to evaluate the degree to which microphysical processes alone can explain the observed evolution of the RH profile within the TSRs of MCSs observed during BAMEX. To accomplish this goal, a high vertical resolution nondynamic microphysical column model was developed that simulates the phase changes (i.e., sublimation, melting, and evaporation) that occur as hydrometeors fall into dry air within the TSR and determines their effect on the evolution of the moisture and hydrometeor mass profiles. The hydrometeors that were input into the top of the model were from the hydrometeor size distributions observed at 5 km above ground level during the aircraft spiral descents. Since the model simulates the evolution of hydrometeor populations as they fall through the RIJ, the axis in the column model should not be considered to be vertical above a single point on the ground, but rather a quasi-Lagrangian axis that follows the trajectory of the hydrometeors. Vertical air motion was not included in the simulations to isolate the effects of the microphysical processes.

The simulations were used to assess whether microphysical processes alone can explain the observed sharp contrast in RH between saturation above and subsaturation below the melting layer (Willis and Heymsfield 1989; MF07; Part I), as well as the timing for the development of this structure. The role of different phase change processes (i.e., sublimation, melting, and evaporation) on cooling rates and the evolution of the thermodynamic profiles was also quantified in order to determine the timing and magnitude of these processes relative to one another. Sensitivity tests, in which the original thermodynamic profile and input hydrometeor size distributions were varied under the range of conditions sampled during BAMEX, were used to determine the degree to which variations in these input parameters affected the evolution of the MCS profiles of RH, and if the sharp contrast in RH would develop across the melting layer in this range of conditions.

Simulations were performed using input hydrometeor size distributions and upstream soundings from each of the 12 BAMEX cases with typical MCS evolution (Part I). This article presents three of these cases, representative of the different zones, stages, humidity profiles, and hydrometeor size distributions observed within the TSR during BAMEX: the 29 June 2003 spiral 1, the 4–5 July 2003 spiral 1, and the 25–26 June 2003 spiral 1. The 29 June spiral was located within the notch behind the convective line during a period of rapid intensification of a bow echo, while the 25–26 June and 4–5 July spirals were located within the enhanced stratiform rain region (Part I). The cases represent three different stages in the evolution of a squall-line MCS (Fig. 1): the formative (29 June), mature (4–5 July), and weakening (25–26 June) stages. They were also representative of the range of rear inflow humidity profiles (Fig. 3) and hydrometeor size distributions (Fig. 4).

2. Column model description

In each simulation, the model was initially devoid of hydrometeors and initialized with a sounding obtained within the dry rear inflow air to the rear of the MCS. The model input size distributions N(m) were binned as a function of hydrometeor mass m and were derived from the 2D cloud and precipitation optical array probe (2D-OAP) data obtained by the NOAA P-3 aircraft at 5.0 km. These size distributions were continually input at the model top. The size distributions used in the three sensitivity tests encompassed the range of those observed, as seen from the profiles of mass median diameter for BAMEX cases exhibiting typical MCS evolution (Fig. 4). The mass median diameter is the diameter for which half of the total mass is from larger-sized hydrometeors and half from smaller-sized hydrometeors. The hydrometeors input into the top of the model represent particles that originated within the convective line and fell from the front-to-rear flow aloft into the dry air brought in from the rear of the TSR (Fig. 5). As the hydrometeors fell, they sublimated, melted, and evaporated, altering the thermodynamic profile from the associated moistening and latent cooling. Following Zawadzki et al. (2005), the model does not directly consider hydrometeor interactions such as aggregation, collision, and coalescence. However, it indirectly accounts for the effect of aggregation on fall speed, and subsequently on rates of phase change, by adjusting hydrometeor fall speeds based on a mass-weighted fall speed estimated from observed vertical profiles of size distributions. Vapor diffusion is not included since the thermodynamic profile of this nondynamic model approaches, but does not exceed saturation, except within the few hundred meter deep melting layer late in the simulation.

The model domain extended from the surface to 5.0 km so that it encompassed both the nonfreezing and subfreezing portions of the atmosphere through which the RIJ flowed, as the 0°C level was initially located between 3.6 and 4.4 km above ground level, depending on the initial sounding. The 5.0-km altitude of the model top was chosen because most BAMEX spirals started between 5.0 and 6.0 km. Since melting and other phase change processes sharply affect the vertical profiles of N(m), RH, and T, the column model was set to 10-m vertical resolution. No outside forcing, such as advection or turbulent mixing, was applied.

The 2D-OAPs observed the size distributions in terms of the maximum hydrometeor dimension, hereafter D. However, the size distributions were converted to a dependence on m because equations describing the evolution of the size distributions and the release of latent heat depend on hydrometeor mass. Since ice crystals, their aggregates, and graupel have irregular shapes, m is typically represented as a function of D. Following Locatelli and Hobbs (1974), Brown and Francis (1995), Mitchell (1996), and others, MF07 used a relationship of the form m = aDb to characterize the BAMEX spirals. MF07 derived the a and b parameters by minimizing the χ2 difference between the radar reflectivity derived from the measured size distributions and that estimated at the aircraft position from the NOAA P-3 radar. The appropriate a and b parameters were determined separately for each BAMEX spiral and are listed in Table B1 of MF07. Techniques used to process and quality control these data, and the uncertainties associated with these techniques, are described by MF07. The hydrometeors were distributed into bins based on their mass.

Following Rogers and Yau [1989, their Eq. (7.17)], the equation for the rate of evaporation of all raindrops in size bin j, dMr,j/dt|evap, can be written as
i1520-0493-137-4-1186-e1
where mr,j is the average mass of rain hydrometeors in bin j and N(mr,j) is the number distribution function of all rain hydrometeors in bin j, which has width Δmr,j. For descriptions of other variables, as well as the values of constants, see Table 1. Equation (1) neglects kinetic and ventilation effects as well as solution and curvature effects and assumes that the vapor density and the saturation vapor density are uniform across the surface of the raindrop (Rogers and Yau 1989).
Following Rogers and Yau [1989, their Eq. (9.4)], the equation for the rate of sublimation for all ice hydrometeors in size bin j, dMs,j/dt|subl, is given by
i1520-0493-137-4-1186-e2
where ms,j is the average mass of ice hydrometeors in bin j and N(ms,j) is the number distribution function of all ice hydrometeors in bin j, which has width Δms,j. Similar to Eq. (1), Eq. (2) neglects kinetic and ventilation effects and assumes that the vapor density and the saturation vapor density are uniform across the surface of the hydrometeors.
Following Szyrmer and Zawadzki [1999, their Eq. (12)], the equation describing the melting rate of all ice hydrometeors in size bin j, dMs,j/dt|melt, can be written as
i1520-0493-137-4-1186-e3
where δQ is the heat transfer per distance per unit time from melting, given by
i1520-0493-137-4-1186-e4
where Tp is the temperature at the surface of the hydrometeor, ρυ is the vapor density of the ambient air, and ρυp is the vapor density of the air at the surface of the hydrometeor. The first term on the right-hand side of Eq. (4) is the conduction of heat from surrounding air, while the second term is the latent heat released from water vapor condensation. In Eq. (4), Szyrmer and Zawadzki (1999) neglected the following lesser heat transfer terms: 1) the transfer of heat by conduction through the possible water layer on the hydrometeor surface, 2) the storage of sensible heat within the hydrometeor, and 3) the transfer of heat by radiation. The Tp is typically near freezing during melting, so it is approximated as 273.16 K, while ρυp is approximated as the saturation vapor density at 273.16 K.
The following equations are for the time rate change of T, dT/dt, and the water vapor mixing ratio, dw/dt, from sublimation, melting, and evaporation from Rogers and Yau (1989) and Szyrmer and Zawadzki (1999), summed from the contributions of each bin:
i1520-0493-137-4-1186-e5
and
i1520-0493-137-4-1186-e6
Following Langleben (1954), the fall speeds of liquid and solid hydrometeors are given by
i1520-0493-137-4-1186-e7
i1520-0493-137-4-1186-e8
where Vr(mr,j) is the velocity of a liquid hydrometeor of mass (mr,j) in bin j and the αr and βr parameters are coefficients chosen to best match observed rain fall speeds from Zawadzki et al. (2005). Likewise, Vs(ms,j) is the velocity of an ice hydrometeor of mass (ms,j) in bin j and the αs and βs parameters are coefficients chosen to best match observed ice fall speeds for graupel-like snow of lump type (Locatelli and Hobbs 1974), as this ice type was frequently observed in the BAMEX hydrometeor images (e.g., Figs. 4–7 of MF07) and corresponds to the habit that has similar a and b parameters to those derived using the BAMEX data.
MF07 showed that aggregation modified N(m) as hydrometeors fell through BAMEX TSRs. Aggregation results in faster fall speeds and therefore decreases the mass of hydrometeors per volume of air. Although aggregation was not explicitly accounted for in the model, the fall speeds described by Eq. (8) were adjusted to account for the aggregation-induced increase in fall speed with increasing T using the BAMEX observations. To do this, the mass-weighted fall speed, Vw, was first calculated from the spirals using each 1-min-averaged size distribution for −10°C < T < 0°C, according to the equation used by McFarquhar and Black (2004):
i1520-0493-137-4-1186-e9
A linear least squares fit provided a slope, ΔVwT, that described the rate at which Vw increased with T. This rate was 0.016, 0.013, and 0.060 m s−1 K−1 for the 29 June, 4–5 July, and 25–26 June spirals, respectively. This slope was used to adjust the fall speeds for each hydrometeor as a function of T using the relation
i1520-0493-137-4-1186-e10
where Vs(ms,j, T) is the adjusted fall speed of ice of mass (ms,j) in bin j for a given T.
In the layer between 0°C and the level where the hydrometeors become totally melted, the fall velocity, Vm(ms,j), of the melting hydrometeors of mass (ms,j) in bin j was weighted between the fall velocity of an ice hydrometeor, Vs(ms,j,T), and the rain fall velocity, Vr(mr,j). This weighting was done according to a function, F( f ), of the melted fraction, f, following the fall speed relation observed in Mitra et al.’s (1990) wind tunnel experiments, using the following equation:
i1520-0493-137-4-1186-e11
where F( f ) is approximated as
i1520-0493-137-4-1186-e12
The variable f was calculated as the fraction of the total hydrometeor mass that was melted. This relationship was applied for all melting hydrometeors. Mitra et al. (1990) observed that during the initial stages of melting, the fall velocity of a hydrometeor increased very little with increased melting, whereas after a majority of the mass of the original hydrometeor had melted, its fall speed began to increase very rapidly.

The positive definite advection scheme of Smolarkiewicz and Szmelter (2005) that limits numerical diffusion was used for hydrometeor sedimentation. Vertical air motions were not included in the model, as the goal of this study was to evaluate whether microphysical processes alone could explain the observed evolution of the BAMEX RH profiles. In the absence of vertical air motion, there was little condensation or deposition, as the RH approached, but usually did not exceed, 100%. The one exception was in conjunction with melting within an already saturated portion of the column; the depth of the layer in which this occurred did not exceed 600 m for any of the simulations. The condensate was immediately assumed to be liquid cloud water.

The 70 bins used to characterize the hydrometeor distributions ranged in mass from 7.69 × 10−6 to 2.50 × 10−2 g and in D from 0.128 to 20 mm; each mass bin limit was larger than the previous limit by a factor of 21/6, following McFarquhar and List (1991). The positive definite advection scheme of Smolarkiewicz and Szmelter (2005) was also separately used to redistribute hydrometeors into smaller bins as they lost mass through sublimation and evaporation. The model was run for 5000 s, a representative time for the development time of the TSRs observed in BAMEX. This time was well beyond the time that precipitation reached the ground and was sufficiently long for the model to approach saturation for T < 0°C.

The model thermodynamic profile was initialized using upstream soundings obtained from dropsondes released from a Learjet for the 4–5 July and 25–26 June cases and an operational National Weather Service rawinsonde for the 29 June case. Two of these soundings were obtained in the rear inflow upstream environment away from any precipitation. For the 25–26 June case, the only available sounding was near the rear edge of the TSR. The release times and locations for these soundings are given in Table 2. These profiles were representative of the range of RH levels in the air brought into the back of the systems by the RIJ in all the BAMEX cases (Fig. 3). The 29 June and 4–5 July soundings were unsaturated below 5.0 km, while the 25–26 June sounding was saturated for T < 1°C. Because the RH and hydrometeor mass profiles measured by the aircraft during the spirals represented states to which the upstream profile should evolve, they were compared with the evolution of the model RH and hydrometeor mass profiles to assess whether the simulated microphysical processes caused temporal evolution similar to that observed in nature.

3. Column model results

a. Discussion of individual simulations

Figure 6a shows a time–height contour plot of the model hydrometeor mass per volume of air, q, for the 29 June simulation, where q is defined as the sum of the masses (mj) of hydrometeors in all size bins within a volume of air, . The simulation was initialized using N(m) observed from the first spiral and an upstream sounding on 29 June. A sharp contrast in q of more than 50% developed across the ∼600-m-deep melting layer, after the hydrometeors reached this layer at ∼1000 s. A sharp contrast in RH also appeared across the melting layer, with RHw differences >20% (Fig. 6b). The RHi was at or near saturation (RHi > 90%) at altitudes above the 0°C isotherm after 2500 s into the simulation, while at altitudes below the melting layer, RHw remained below 85%. Willis and Heymsfield (1989) observed a similar structure in the RH field across the melting layer within the 10–11 June 1985 MCS and hypothesized that it was the result of a dynamical transition near the melting layer, with mesoscale ascent above the layer and mesoscale descent below. However, since this model does not consider dynamical processes, it is clear that the sharp contrast in the RH field can develop in the absence of vertical air motion. Equations (1), (2), and (6) reveal that the rate of increase in water vapor mixing ratio is directly proportional to q. Therefore, the sharp contrast in RH, and thus in the water vapor mixing ratio, across the melting layer in Fig. 6b, must have been related to the sharp contrast in q in Fig. 6a, which in turn was the result of a rapid increase in hydrometeor fall speed from 1–2 m s−1 for ice to 2–11 m s−1 for rain, as hydrometeors changed phase across the melting layer.

The sharp difference in RH and in the rate of increase in water vapor mixing ratio across the melting layer was also reflected in the total cooling rate (Qt) from sublimation (Qs), melting (Qm), and evaporation (Qe; Figs. 6c and 7a–c), as both the rate of increase in water vapor mixing ratio and Qt are proportional to the mass phase change rate. The maximum Qs of 8.2 K h−1 occurred at 350 s and 4.6-km altitude (Fig. 7a), while the maximum Qe of only 3.1 K h−1 was much weaker and occurred much later at a height of 2.6 km at 3100 s (Fig. 7c). The Qm was the strongest of all the mechanisms, reaching a maximum of 18.4 K h−1 at 5000 s, but was confined to the ∼600-m-deep melting layer (Fig. 7b). Both Qs and Qm resulted in a lowering of the 0°C isotherm with time from its initial level at 3.65 km above ground level to 2.75 km at 5000 s (Figs. 6c and 7a,b). After 3700 s, the heating rate from condensation of water vapor onto cloud droplets (Qc) resulted in warming of less than 5 K h−1 within a shallow ∼300-m-deep layer; Qc counteracted Qm and was the result of Qm depressing the 0°C isotherm within saturated air (Fig. 7d).

The difference in Qt from each process was more evident when considering the mean cooling rate from sublimation for T < 0°C (Qs), evaporation for T > 0°C (Qe), and melting within the melting layer (Qm) (Fig. 8). The maximum in Qs was at 800 s with a value of 3.9 K h−1, while Qe was barely half as strong at only 2.1 K h−1, maximizing at 4600 s. The maximum in Qm of 4.8 K h−1 also occurred at 4600 s. The magnitude of Qs was greater than Qe for the first 1800 s of the simulation as hydrometeors populated the column above the 0°C level and brought the column closer to ice saturation, while Qe was stronger thereafter and maintained a quasi-steady value throughout the rest of the simulation. The maximum Qe was 46% lower than the maximum Qs, predominantly because rain mixing ratios were ∼60% lower than those of ice because of the faster fall velocities of raindrops relative to ice.

The 4–5 July simulation, with input hydrometeor size distributions from the enhanced stratiform rain regions during the mature stage of squall-line evolution, was similar to the 29 June simulation, except that the input N(ms,i) had a q of 2.50 g m−3, as compared with 1.40 g m−3 for the 29 June case (cf. Figs. 9a and 6a). For this reason, different contour intervals were used to show the evolution of q, Qt, Qs, Qm, and Qe in Figs. 9 and 10 for the 4–5 July case than in Figs. 6 and 7 for the 29 June case. The higher q for the 4–5 July case resulted in an ∼60% faster increase in water vapor mixing ratio, and thus a faster increase in RHi, for T < 0°C relative to the 29 June simulation (cf. Figs. 9b and 6b), as well as a maximum Qs and Qe ∼2 times greater than 29 June (cf. Figs. 10a,c and 7a,c). The maximum Qm and Qc within the ∼300-m-deep melting layer (cf. Figs. 10b,d and 7b,d) were up to 4 times greater than 29 June. The melting layer was shallower in this simulation primarily due to the sharper lapse rate across the melting layer in the initial sounding. A simulation was also performed for the 25–26 June case where the input N(ms,i) had a q of 1.08 g m−3. Similar qualitative results were seen, but rates of cooling and RH change were smaller than for 29 June or 4–5 July (figures not shown). Despite the differences between simulations in the timing of the evolution and minor differences in structure, the sharp contrast in RH above and below the melting layer developed and persisted for every simulation, including simulations of the nine other BAMEX cases not shown here.

b. Comparisons between simulations and observations

For each of the three simulations, the mean RH difference was calculated between the observed and simulated profiles for all model output times. The time when the mean RH difference was minimized was noted and used to verify that the model sufficiently reproduced the evolution of RH and q within a reasonable time. For the 4–5 July spiral conducted within the enhanced stratiform rain region during the mature stage of an MCS, the observed RHi was ≥94% for T < 0°C (Fig. 11b). Precipitation had been falling at this location between 1–2 h, while in the simulation the same level of saturation occurred after 55 min (Fig. 11b). Likewise, for the 25–26 June spiral conducted within the enhanced stratiform region during the weakening stage of an MCS, the observed RHi was ≥100% for T < 0°C (Fig. 11c). Precipitation had been falling at this location for 2 h. The corresponding simulation was initialized using an observed sounding where a sharp contrast in RH was already present across the melting layer (Fig. 11c). After 37 min in the simulation, the same degree of saturation occurred as was observed within the observed spiral profile (Fig. 11c). Therefore, although it was not possible to directly compare the timing between the observations and simulations, the simulations still produced a sharp contrast in RH across the melting layer. Likewise, for the 4–5 July spiral from the mature stage, the simulation produced a structure of q at the time of closest RH comparison (Fig. 11b) similar to that observed during the spiral (Fig. 12b), as the median difference in q was only 0.06 g m−3. For the 25–26 June spiral during the weakening stage of squall-line evolution the median q difference between the simulation at 37 min and the spiral observations was only 0.10 g m−3 (Fig. 12c).

Reliable vertical air motion estimates from dual-Doppler analyses were not possible due to the tight turns of the spirals. However, vertical air motions estimated from the aircraft navigation instruments showed 60-s-averaged downward motions for T < 0°C ranging from 0.0 to 1.4 m s−1 (Figs. 13b,c) for the 4–5 July and 25–26 June spirals. The uncertainty of these estimates is likely ∼1 m s−1 due to the effect of centrifugal force on the inertial navigation equipment during the spirals (D. Jorgensen 2007, personal communication). Despite the uncertainty in the vertical air motion estimates, it can be stated that downward air motions were at most weak for these two cases. Thus, it appears that the simulated microphysical processes brought the air to saturation quickly for T < 0°C, and that microphysical processes alone were sufficient to produce the profile of q and the sharp contrast in the RH profile across the melting layer described here and in Part I and MF07.

For the 29 June spiral located within the notch of a developing squall-line MCS, the observed RHi at T < 0°C averaged 85% (Fig. 11a), even though precipitation had been falling at this location for just over an hour (Grim et al. 2009). After only 10 min the model reached the same level of saturation as was observed during the spiral descent (Fig. 11a), while after a simulated hour, the average RHi for T < 0°C was 99% (not shown). Similarly, for this case there was a much larger median q difference of 0.24 g m−3 between the observations and the simulation at the time of closest RH comparison (Fig. 12a). This indicates that for this case, microphysical processes alone cannot explain the observations of subsaturated air for T < 0°C in the notch and profile of q. The observed degree of subsaturation in the observations was likely attributable to downward motions, such as the 1–3 m s−1 downdrafts observed in this area from quad-Doppler radar analyses (Grim et al. 2009), corroborated by observations of ice at T ≤ +7°C (MF07) and lowered reflectivity within the notch. Downward motions were also confirmed in 60-s-averaged air motion estimates from the aircraft navigation instruments, which ranged from 0.0 to 3.2 m s−1 (Fig. 13a). Apart from the first spiral on 29 June, the strongest 60-s downdraft estimate for the 11 other spiral descents performed during some stage in the evolution of a typical MCS with a TSR (Part I) was 1.6 m s−1 (not shown). It cannot be ruled out that differing air trajectories within the rear inflow may have also contributed to the presence of subsaturated air for T < 0°C. Nevertheless, it appears that the downdrafts, in addition to the microphysical processes, are needed to explain the q profile and RHi profile for T < 0°C for the 29 June spiral described here and in Part I and MF07. The comparisons between the observations and simulations for the three BAMEX cases reveal that in the absence of vertical motions >∼1 m s−1, microphysical processes alone can produce the sharp contrast in RH that develops across the melting level.

c. Implications for the descent of the RIJ

The evolution of the simulated RH and cooling rate profiles has implications for the descent rate of the RIJ as it flows forward from the rear of the system. When the air in the TSR is at or near saturation for T < 0°C but unsaturated below, such as within the enhanced stratiform rain region on 4–5 July, 25–26 June, and other BAMEX cases, the downward forcing of the RIJ at altitudes where T ≥ 0°C will mainly be from Qe and Qm. On the other hand, within the rear anvil region where the air has not reached saturation for T < 0°C, the downward forcing of the RIJ would be throughout the depth of the precipitation, but particularly focused at altitudes within and above the melting layer from Qs and Qm.

For the case of traditional MCS evolution (Part I), implications from this modeling study are that sublimation would be the strongest cooling mechanism within the rear anvil region, while melting and evaporation would be the strongest cooling mechanisms within the enhanced stratiform rain region. In the notch and within the transition zone, sustained depression of RHi for T < 0°C by sufficiently strong downward motions could result in a prolonged period of sublimational cooling so that the cooling would occur throughout the depth of precipitation. In this conceptual model of traditional MCS evolution (Part I), the flow of air through the different zones would result in a descent of the RIJ for T < 0°C within the rear anvil of the system to levels where T > 0°C within the enhanced stratiform rain region. If and where downdrafts result in sustained depression of RHi, such as within the notch on 29 June, this forcing for the descent of the RIJ would extend throughout a greater horizontal and vertical region of the atmosphere and therefore allow a stronger forcing for the descent rate of the RIJ, as was observed in Grim et al. (2009).

d. Column model sensitivity tests

To determine the relative influence of the initial model soundings, N(ms,i) and fall velocity parameters on the evolution of RH and q, nine additional simulations were performed, as summarized in Table 3. The first set of three simulations involved varying the shape of the hydrometeor size distribution input at the model top, based on those observed at 5.0 km from the same three spirals used in the studies described in section 3a. However, because Qt and the rate of increase of RH is highly dependent on the total mass of hydrometeors, and because the total mass of hydrometeors were 1.40, 2.50, and 1.08 g m−3 for the 29 June, 4–5 July, and 25–26 June cases, respectively, N(ms,i) was normalized so that the same total mass of 1.40 g m−3 was input for all three simulations by employing a scaling factor η so that Nn(ms,i) = ηN(ms,i). All three simulations used the initial T profile from the 29 June case, while the initial RH profile was arbitrarily assigned as 50% throughout the depth of the column. This value was chosen to enhance the Qt differences for T < 0°C for a more direct comparison between the simulations, as the actual 29 June upstream profile RHi averaged 76% for T < 0°C.

Figure 14 shows Nn(ms,i) as a function of D for each of the three sensitivity simulations. Nn(ms,i) for 4–5 July was dominated by small hydrometeors, as it had a greater number of hydrometeors for D < 2.2 mm than the 29 June Nn(ms,i). The shape of Nn(ms,i) for 25–26 June was qualitatively closer to that of 29 June, although the 25–26 June Nn(ms,i) had a greater number of hydrometeors for D < 6.1 mm than the 29 June Nn(ms,i).

Variations in the shape of the model input Nn(ms,i) resulted in q differences that were easiest to interpret by comparing data at the same time and height for two cases at a time. Figure 15a shows the q field from the 29 June sensitivity simulation (SS). To better visualize the minor differences between the 29 June SS and those of the other cases, time–height q difference fields are displayed in Figs. 15b,c. At most altitudes and times, differences between the SSs were minimal, as evidenced by differences in q < 0.1 g m−3 throughout > 95% of the area in the time–height contour plots (Figs. 15b,c). The only exceptions were the larger q for the 29 June SS within the first ∼1000 s of the simulation and near the melting level, reaching a difference of 0.30 g m−3 when compared with the 4–5 July SS (Fig. 15b) and 0.15 g m−3 for the 25–26 June SS (Fig. 15c). The 29 June SS had a greater number of large hydrometeors (D > 6.1 mm) that fell faster than in the other cases. Thus, a greater portion of the mass fell more quickly to lower levels.

Variations in the input Nn(ms,i) resulted in only small variations in the rate of RH increase between the simulations, as maximum differences in RH were only 10% between the 29 June SS and the other SSs (Figs. 15e,f). By 5000 s, RHi was ≥ 98% for T < 0°C for all three simulations. For example at T = 0°C, the altitude below which melting commenced, RHw reached 98% at 4900, 4000, and 4700 s for the 29 June, 4–5 July, and 25–26 June SSs, respectively. On the other hand, RHw at 5°C and 5000 s was only 73%, 79%, and 73%, respectively, for the 29 June, 4–5 July, and 25–26 June SSs. Therefore, the most notable finding from these simulations is that although there were small differences in the timing and rate of RH increase, by 5000 s all three simulations were within 2% of saturation for T < 0°C, yet had RHw values <80% at 5°C. These simulations show that regardless of the shape of the input Nn(ms,i), the sharp contrast in the RH field always developed across the melting layer.

In the second set of simulations, the initial profiles of RH and T were varied according to the soundings obtained upstream of the rear inflow for the three cases (Fig. 3). In the third set of simulations, three simulations were performed where the ice fall speed parameters were varied between graupel-like snow of lump type, unrimed aggregates of dendrites, and lump graupel (Table 3; Locatelli and Hobbs 1974) to determine how the uncertainty in ice crystal shapes, which impacts ice hydrometeor fall speeds, affects the simulations. In the interest of brevity, the details of these simulations are not discussed; however, each simulation revealed that although variations in the thermodynamic profile and hydrometeor structure affected the timing for the evolution of the RH and q profiles, the sharp contrast in RH with saturation for T < 0°C and subsaturation for T > 0°C always developed.

4. Conclusions

This study employed a microphysical column model to evaluate the degree to which the microphysical processes of sublimation, melting and evaporation alone can explain the evolution of the relative humidity profile within the trailing stratiform region of mesoscale convective systems observed during the Bow Echo and Mesoscale Convective Vortex Experiment. To accomplish this goal, the model was developed to simulate the phase changes that occur as hydrometeors fall into dry air within the TSR and determine their effect on the evolution of RH. The hydrometeors that were input into the top of the model were from the hydrometeor size distributions observed during BAMEX aircraft spiral descents. Vertical air motion was not included in the simulations to isolate the effects of the microphysical processes. Three cases, representative of those observed during BAMEX, were used for the simulations described in this article. These cases represented the formative, mature, and weakening stages of the evolution of a typical squall-line MCS with a TSR.

The main conclusions from this study are as follows:

  1. The simulations showed that the sharp change in the observed RH profile across the melting layer with saturation with respect to ice above and subsaturation with respect to water below can develop in the absence of vertical air motion, contrary to Willis and Heymsfield (1989)’s hypothesis that the change was the result of a dynamical transition near the melting layer, with mesoscale ascent above and mesoscale descent below the layer. The sharp contrast in RH can develop in any region and is predominantly the result of an increase in hydrometeor fall speed as the particles change phase across the melting layer from 1–2 m s−1 for ice to 2–11 m s−1 for rain. Since the hydrometeor mass per volume of air, q, was greater above the melting layer than below, sublimation led to a more rapid increase in RH with respect to ice (RHi) for T < 0°C compared to the effect of evaporation for T > 0°C.

  2. For the 4–5 July and 25–26 June spirals located within the enhanced stratiform rain region, the observed RHi was ≥94% for T < 0°C while 60-s-averaged vertical air motions were around 1 m s−1 or less. Precipitation had been falling at these locations for over 1 h, while in the simulation the same level of saturation occurred after 55 and 37 min, respectively. Therefore, although it was not possible to directly compare timing, the simulations were able to reproduce the RH structure for cases with negligible vertical air motions; this shows that microphysical processes alone could explain the existence of the sharp contrast in RH across the melting layer for these and other BAMEX cases. It was also demonstrated that microphysical processes alone could explain the vertical structure of total hydrometeor mass q for these cases.

  3. For the 29 June spiral located within the notch of lower reflectivity of a developing squall-line MCS, the observed RHi at T < 0°C averaged 85% even though precipitation had been falling in this region for just over an hour. However, after hydrometeors had fallen through this level for an hour in the simulation, the RHi at T < 0°C averaged 99%, indicating that microphysical processes alone could not explain the observations of sustained subsaturated air for T < 0°C in this case. The observed degree of subsaturation on 29 June would have only been possible due to dynamic processes, specifically the 1–3 m s−1 downdrafts in this area derived from quad-Doppler radar analyses (Grim et al. 2009) and corroborated by in situ observations of downdrafts of similar magnitude and of ice at T ≤ +7°C (MF07) within the notch. It was also demonstrated that microphysical processes alone could not explain the vertical structure of q for this case. The comparisons between the observations and simulations for the three BAMEX cases reveal that in the absence of vertical motions >∼1 m s−1, microphysical processes alone can produce the sharp contrast in RH that develops across the melting level.

  4. For the primary simulation in this study (29 June), the mean sublimational cooling rate for T < 0°C was strongest at 800 s at 3.9 K h−1, while the mean evaporational cooling rate for T > 0°C was strongest at 4600 s at only 2.1 K h−1. Likewise, the mean sublimational cooling rate was greater than the mean evaporational cooling rate for the first 1800 s, while the mean evaporational cooling was strongest thereafter. Melting was the strongest of all the cooling mechanisms after 1000 s, reaching a maximum cooling rate of 18.4 K h−1 at 5000 s, but was confined to the ∼600-m-deep melting layer. The results of this simulation were qualitatively similar to all other simulations performed for this study. Sublimation was most important where precipitation had been falling for a short time, such as in the rear anvil region, or in other areas with sustained subsaturation, such as in the presence of sufficiently strong downdrafts. On the other hand, evaporation has a greater effect on the cooling rate within the enhanced stratiform rain region where precipitation has been falling longer, while melting has the strongest effect of all mechanisms, but is confined to the shallow melting layer.

  5. Sensitivity studies were performed by varying the following model inputs across the range of BAMEX observations: the shape of the input hydrometeor size distribution, the upstream sounding used for model initialization, and ice fall speed parameters. Results of these sensitivity tests revealed that although there were differences in the timing and rate of RH increase, each and every simulation produced a sharp contrast in the RH profile across the melting level. This reveals that regardless of the initial microphysical and thermodynamic conditions within a typically evolving squall-line MCS, a sharp contrast in the RH field should develop across the melting layer of MCSs in the absence of any dynamic motions, the result of the increase in hydrometeor fall speed as the hydrometeors change phase across the melting layer.

The 4–5 July and 25–26 June spirals were representative of conditions observed within the enhanced stratiform rain region at the mature and weakening stages of MCS development, respectively, as there was an observed sharp contrast in the RH field between saturation for T < 0°C and subsaturation for T > 0°C for all nine BAMEX spirals in this region. However, the downward motion that was present in the 29 June case (Grim et al. 2009) suggests that when descending air is present for T < 0°C, the air above the melting layer may remain in a subsaturated state, especially at the formative stage of MCS evolution within the notch of lower reflectivity and possibly later in the transition zone in well-developed TSRs.

The evolution of the RH and cooling rate profiles has implications for the descent rate of the rear inflow jet (RIJ) as it flows forward and descends from the rear of the system. Where the air is at or near saturation for T < 0°C but unsaturated below, such as within the enhanced stratiform rain region on 4–5 July, 25–26 June, and other BAMEX cases (Part I), the downward forcing of the RIJ will only occur at T ≥ 0°C and will be from evaporational and melting-induced cooling. On the other hand, within the rear anvil region, as well as locations where downward motions result in a state of subsaturation for T < 0°C, such as within the 29 June notch of lower reflectivity, the downward forcing of the RIJ by sublimational, evaporational, and melting-induced cooling will be stronger and extend over the entire depth of the precipitation. In the case of traditional MCS evolution (Part I), this would result in descent of the RIJ from subfreezing temperatures within the rear anvil of the system, to above freezing temperatures within the enhanced stratiform rain region. To confirm this idea for the descent of the RIJ, further studies are necessary that could employ a two- or three-dimensional microphysical and dynamical model initialized with observed hydrometeor size distributions, thermodynamic profiles, and wind fields.

Acknowledgments

This material is based upon work supported by the National Science Foundation under Award NSF-ATM-0413824. We thank everyone who participated in the field during BAMEX, making this research possible. We acknowledge helpful discussions with, and the assistance of, M. Timlin, B. Guarente, and D. Jorgensen. We also thank Piotr Smolarkiewicz for his assistance in incorporating his MPDATA advection scheme into our model.

REFERENCES

  • Alfonso, A. P., and L. R. Naranjo, 1996: The 13 March 1993 severe squall line over western Cuba. Wea. Forecasting, 11 , 89102.

  • Biggerstaff, M. I., and R. A. Houze Jr., 1991: Kinematic and precipitation structure of the 10–11 June 1985 squall line. Mon. Wea. Rev., 119 , 30343065.

    • Search Google Scholar
    • Export Citation
  • Biggerstaff, M. I., and R. A. Houze Jr., 1993: Kinematics and microphysics of the transition zone of the 10–11 June 1985 squall line. J. Atmos. Sci., 50 , 30913110.

    • Search Google Scholar
    • Export Citation
  • Braun, S. A., and R. A. Houze Jr., 1994: The transition zone and secondary maximum of radar reflectivity behind a midlatitude squall line: Results retrieved from Doppler radar data. J. Atmos. Sci., 51 , 27332755.

    • Search Google Scholar
    • Export Citation
  • Brown, P. R. A., and P. N. Francis, 1995: Improved measurements of the ice water content in cirrus using a total-water probe. J. Atmos. Oceanic Technol., 12 , 410414.

    • Search Google Scholar
    • Export Citation
  • Davis, C., and Coauthors, 2004: The Bow Echo and MCV Experiment: Observations and opportunities. Bull. Amer. Meteor. Soc., 85 , 10751093.

    • Search Google Scholar
    • Export Citation
  • Eastin, M. D., P. G. Black, and W. M. Gray, 2002: Flight-level thermodynamic instrument wetting errors in hurricanes. Part I: Observations. Mon. Wea. Rev., 130 , 825841.

    • Search Google Scholar
    • Export Citation
  • Grim, J. A., R. M. Rauber, G. M. McFarquhar, B. F. Jewett, and D. P. Jorgensen, 2009: Development and forcing of the rear inflow jet in a rapidly developing and decaying squall line during BAMEX. Mon. Wea. Rev., 137 , 12061229.

    • Search Google Scholar
    • Export Citation
  • Houze, R. A., 2004: Mesoscale convective systems. Rev. Geophys., 42 , RG4003. doi:10.1029/2004RG000150.

  • Houze, R. A., S. A. Rutledge, M. I. Biggerstaff, and B. F. Smull, 1989: Interpretation of Doppler weather radar displays of midlatitude mesoscale convective systems. Bull. Amer. Meteor. Soc., 70 , 608619.

    • Search Google Scholar
    • Export Citation
  • Johns, R. H., 1993: Meteorological conditions associated with bow echo development in convective storms. Wea. Forecasting, 8 , 294300.

    • Search Google Scholar
    • Export Citation
  • Langleben, M. P., 1954: The terminal velocity of snowflakes. Quart. J. Roy. Meteor. Soc., 80 , 174181.

  • Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79 , 21852197.

  • McFarquhar, G. M., and R. List, 1991: The evolution of three-peak size raindrop distributions in one-dimensional shaft models. Part II: Multiple pulse rain. J. Atmos. Sci., 48 , 15871595.

    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., and R. A. Black, 2004: Observations of particle size and phase in tropical cyclones: Implications for mesoscale modeling of microphysical processes. J. Atmos. Sci., 61 , 422439.

    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., M. S. Timlin, R. M. Rauber, B. F. Jewett, J. A. Grim, and D. P. Jorgensen, 2007: Vertical variability of cloud hydrometeors in the stratiform region of mesoscale convective systems and bow echoes. Mon. Wea. Rev., 135 , 34053428. ; Corrigendum. 137, 1493.

    • Search Google Scholar
    • Export Citation
  • Mitchell, D. L., 1996: Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities. J. Atmos. Sci., 53 , 17101723.

    • Search Google Scholar
    • Export Citation
  • Mitra, S. K., O. Vohl, M. Ahr, and H. R. Pruppacher, 1990: A wind tunnel and theoretical study of the melting behavior of atmospheric ice particles. IV: Experiment and theory for snowflakes. J. Atmos. Sci., 47 , 584591.

    • Search Google Scholar
    • Export Citation
  • Przybylinski, R. W., 1995: The bow echo: Observations, numerical simulations, and severe weather detection methods. Wea. Forecasting, 10 , 203218.

    • Search Google Scholar
    • Export Citation
  • Rogers, R. R., and M. K. Yau, 1989: A Short Course in Cloud Physics. 3rd ed. Pergamon, 290 pp.

  • Rutledge, S. A., R. A. Houze, M. I. Biggerstaff, and T. Matejka, 1988: The Oklahoma-Kansas mesoscale convective system of 10–11 June 1985: Precipitation structure and single-Doppler radar analysis. Mon. Wea. Rev., 116 , 14091430.

    • Search Google Scholar
    • Export Citation
  • Smith, A. M., G. M. McFarquhar, R. M. Rauber, J. A. Grim, M. S. Timlin, and B. F. Jewett, 2009: Microphysical and thermodynamic structure and evolution of the trailing stratiform regions of mesoscale convective systems during BAMEX. Part I: Observations. Mon. Wea. Rev., 137 , 11651185.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., and J. Szmelter, 2005: Multidimensional positive definite advection transport algorithm (MPDATA): An edge-based unstructured-data formulation. Int. J. Numer. Methods Fluids, 47 , 12931299.

    • Search Google Scholar
    • Export Citation
  • Smull, B. F., and R. A. Houze, 1985: A midlatitude squall line with a trailing region of stratiform rain: Radar and satellite observations. Mon. Wea. Rev., 113 , 117133.

    • Search Google Scholar
    • Export Citation
  • Smull, B. F., and R. A. Houze, 1987: Rear inflow in squall lines with trailing stratiform precipitation. Mon. Wea. Rev., 115 , 28692889.

    • Search Google Scholar
    • Export Citation
  • Szyrmer, W., and I. Zawadzki, 1999: Modeling of the melting layer. Part I: Dynamics and microphysics. J. Atmos. Sci., 56 , 35733592.

  • Weisman, M. L., 2001: Bow echoes: A tribute to T. T. Fujita. Bull. Amer. Meteor. Soc., 82 , 97116.

  • Willis, P. T., and A. J. Heymsfield, 1989: Structure of the melting layer in mesoscale convective system stratiform precipitation. J. Atmos. Sci., 46 , 20082025.

    • Search Google Scholar
    • Export Citation
  • Yang, M-H., and R. A. Houze, 1995: Sensitivity of squall-line rear inflow to ice microphysics and environmental humidity. Mon. Wea. Rev., 123 , 31753193.

    • Search Google Scholar
    • Export Citation
  • Zawadzki, I., W. Szyrmer, C. Bell, and F. Fabry, 2005: Modeling of the melting layer. Part III: The density effect. J. Atmos. Sci., 62 , 37053723.

    • Search Google Scholar
    • Export Citation
  • Zhang, D-L., and K. Gao, 1989: Numerical simulation of an intense squall line during 10–11 June 1985 PRE-STORM. Part II: Rear inflow, surface pressure perturbations, and stratiform precipitation. Mon. Wea. Rev., 117 , 20672094.

    • Search Google Scholar
    • Export Citation
  • Zipser, E. J., R. J. Meitin, and M. A. LeMone, 1981: Mesoscale motion fields associated with a slowly moving GATE convective band. J. Atmos. Sci., 38 , 17251750.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Composite WSR-88D reflectivity images at 2.0 km above mean sea level during the time of each spiral, with the spiral flight pattern overlaid on each at (a) 0533 UTC 29 Jun 2003, (b) 0008 UTC 5 Jul 2003, and (c) 0213 UTC 26 Jun 2003. The horizontal scale is indicated on the sides of (a)–(c), while the latitudinal and longitudinal positions of the lower-left-hand corner of each plot are indicated in the lower-left-hand corner. The notch region is indicated with a dashed line in (a).

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 2.
Fig. 2.

RH as a function of T for spirals executed within typically evolving TSRs during BAMEX. For T < 0°C, RH with respect to ice is plotted; for T > 0°C, RH with respect to water is plotted. The dark dashed line shows relative humidity with respect to ice at water saturation for T < 0°C. Specific spirals discussed in the text are indicated in the legend.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 3.
Fig. 3.

RH profiles of upstream soundings for the BAMEX cases with typical trailing stratiform structure and evolution. The three profiles used for the simulations discussed in this study are indicated in the legend, while their 0°C level is also indicated.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 4.
Fig. 4.

Mass median diameter (Dmm) calculated from size distributions as a function of T for all BAMEX cases with typical MCS evolution. The key indicates the three cases used for the sensitivity simulations discussed in the paper. The source region for these cases in the notch, enhanced stratiform rain region, and rear anvil are also noted.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 5.
Fig. 5.

Schematic of the 1D model configuration.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 6.
Fig. 6.

Model output time series contour plots for the 29 Jun 2003 simulation of (a) hydrometeor mass concentration q (g m−3), (b) relative humidity with respect to ice for T < 0°C and with respect to water for T ≥ 0°C, and (c) total model output cooling rate (shaded, K h−1) from sublimation, melting, evaporation and condensation. The y axis is the height above ground level, while the x axis is the time from the beginning of the simulation. The thick black and white dashed line indicates the 0°C isotherm. The thin dashed white line in (b) is the 99% RH contour.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 7.
Fig. 7.

Contour plot for the 29 Jun 2003 simulation of total model output cooling rate from (a) sublimation, (b) melting, (c) evaporation, and (d) condensation onto cloud droplets. The thin black dashed lines in (c) indicate the 1 and 3 K h−1 contours. The 0°C isotherm is indicated by a thick black and white dashed line.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 8.
Fig. 8.

The 29 Jun 2003 simulated mean cooling from sublimation for T < 0°C, evaporation for T > 0°C, and melting within the melting layer. Means are calculated over the entire depth of the respective layer.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 9.
Fig. 9.

As in Fig. 6, but for the 4–5 Jul 2003 simulation. Note the contour intervals in (a) and (c) are larger than those in Figs. 6a and 6c.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 10.
Fig. 10.

As in Fig. 7, but for the 4–5 Jul 2003 simulation.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 11.
Fig. 11.

RH profiles for model input (thick black lines), model output at the time of closest RH comparison (thin black lines), and spiral observations (thick gray lines) for the (a) 29 Jun, (b) 4–5 Jul, and (c) 25–26 Jun cases.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 12.
Fig. 12.

Hydrometeor mass per volume of air (q) profiles from the model output at the time of closest RH comparison (+) and spiral observations (o) for the (a) 29 Jun, (b) 4–5 Jul, and (c) 25–26 Jun cases.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 13.
Fig. 13.

Vertical air motion estimates from aircraft inertial navigation instruments during the three microphysical spirals: (a) 29 Jun spiral 1, (b) 5 Jul spiral 1, and (c) 26 Jun spiral 1. The 1-s data are shown by the black lines, while 60-s-averaged data are shown by the gray lines.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 14.
Fig. 14.

The model input hydrometeor number concentration as a function of maximum dimension for the three cases indicated in the legend. A scaling factor was applied to the number distribution for the 4–5 Jul and 25–26 Jun cases so that the total mass for each simulation was normalized to 1.40 g m−3.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Fig. 15.
Fig. 15.

Results of model sensitivity tests on variations in the shape of the hydrometeor number distributions. (a) The 29 Jun simulated hydrometeor mass concentration, q. (b) The difference in q between 29 Jun and 4–5 Jul. (c) The difference in q between 29 Jun and 25–26 Jun. (d)–(f) As in (a)–(c), but for RH.

Citation: Monthly Weather Review 137, 4; 10.1175/2008MWR2505.1

Table 1.

Variables used in the paper, their descriptions, and the values of constants.

Table 1.
Table 2.

The release locations and times of the upstream soundings used in the column model.

Table 2.
Table 3.

A list of the 12 model simulations described in this paper with their respective input thermodynamic profile and input hydrometeor size distribution. Here U1 = observed upstream sounding from 29 Jun—formative; U2 = observed upstream sounding from 4–5 Jul—mature; U3 = observed upstream sounding from 25–26 Jun—weakening; F = 50% RH profile using 29 Jun temperature data; S1 = observed hydrometeor size distribution for 29 Jun; S2 = observed hydrometeor size distribution for 4–5 Jul; and S3 = observed hydrometeor size distribution for 25–26 Jun.

Table 3.

1

Herein, as well as in MF07 and Part I, the Zipser et al. (1981) correction was applied to the temperature measurements to correct for the effects of sensor wetting, following the approach of Eastin et al. (2002). Also, all future references to RH without subscripts will refer to the entire RH field (both RHi and RHw) with respect to its appropriate phase.

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  • Alfonso, A. P., and L. R. Naranjo, 1996: The 13 March 1993 severe squall line over western Cuba. Wea. Forecasting, 11 , 89102.

  • Biggerstaff, M. I., and R. A. Houze Jr., 1991: Kinematic and precipitation structure of the 10–11 June 1985 squall line. Mon. Wea. Rev., 119 , 30343065.

    • Search Google Scholar
    • Export Citation
  • Biggerstaff, M. I., and R. A. Houze Jr., 1993: Kinematics and microphysics of the transition zone of the 10–11 June 1985 squall line. J. Atmos. Sci., 50 , 30913110.

    • Search Google Scholar
    • Export Citation
  • Braun, S. A., and R. A. Houze Jr., 1994: The transition zone and secondary maximum of radar reflectivity behind a midlatitude squall line: Results retrieved from Doppler radar data. J. Atmos. Sci., 51 , 27332755.

    • Search Google Scholar
    • Export Citation
  • Brown, P. R. A., and P. N. Francis, 1995: Improved measurements of the ice water content in cirrus using a total-water probe. J. Atmos. Oceanic Technol., 12 , 410414.

    • Search Google Scholar
    • Export Citation
  • Davis, C., and Coauthors, 2004: The Bow Echo and MCV Experiment: Observations and opportunities. Bull. Amer. Meteor. Soc., 85 , 10751093.

    • Search Google Scholar
    • Export Citation
  • Eastin, M. D., P. G. Black, and W. M. Gray, 2002: Flight-level thermodynamic instrument wetting errors in hurricanes. Part I: Observations. Mon. Wea. Rev., 130 , 825841.

    • Search Google Scholar
    • Export Citation
  • Grim, J. A., R. M. Rauber, G. M. McFarquhar, B. F. Jewett, and D. P. Jorgensen, 2009: Development and forcing of the rear inflow jet in a rapidly developing and decaying squall line during BAMEX. Mon. Wea. Rev., 137 , 12061229.

    • Search Google Scholar
    • Export Citation
  • Houze, R. A., 2004: Mesoscale convective systems. Rev. Geophys., 42 , RG4003. doi:10.1029/2004RG000150.

  • Houze, R. A., S. A. Rutledge, M. I. Biggerstaff, and B. F. Smull, 1989: Interpretation of Doppler weather radar displays of midlatitude mesoscale convective systems. Bull. Amer. Meteor. Soc., 70 , 608619.

    • Search Google Scholar
    • Export Citation
  • Johns, R. H., 1993: Meteorological conditions associated with bow echo development in convective storms. Wea. Forecasting, 8 , 294300.

    • Search Google Scholar
    • Export Citation
  • Langleben, M. P., 1954: The terminal velocity of snowflakes. Quart. J. Roy. Meteor. Soc., 80 , 174181.

  • Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79 , 21852197.

  • McFarquhar, G. M., and R. List, 1991: The evolution of three-peak size raindrop distributions in one-dimensional shaft models. Part II: Multiple pulse rain. J. Atmos. Sci., 48 , 15871595.

    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., and R. A. Black, 2004: Observations of particle size and phase in tropical cyclones: Implications for mesoscale modeling of microphysical processes. J. Atmos. Sci., 61 , 422439.

    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., M. S. Timlin, R. M. Rauber, B. F. Jewett, J. A. Grim, and D. P. Jorgensen, 2007: Vertical variability of cloud hydrometeors in the stratiform region of mesoscale convective systems and bow echoes. Mon. Wea. Rev., 135 , 34053428. ; Corrigendum. 137, 1493.

    • Search Google Scholar
    • Export Citation
  • Mitchell, D. L., 1996: Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities. J. Atmos. Sci., 53 , 17101723.

    • Search Google Scholar
    • Export Citation
  • Mitra, S. K., O. Vohl, M. Ahr, and H. R. Pruppacher, 1990: A wind tunnel and theoretical study of the melting behavior of atmospheric ice particles. IV: Experiment and theory for snowflakes. J. Atmos. Sci., 47 , 584591.

    • Search Google Scholar
    • Export Citation
  • Przybylinski, R. W., 1995: The bow echo: Observations, numerical simulations, and severe weather detection methods. Wea. Forecasting, 10 , 203218.

    • Search Google Scholar
    • Export Citation
  • Rogers, R. R., and M. K. Yau, 1989: A Short Course in Cloud Physics. 3rd ed. Pergamon, 290 pp.

  • Rutledge, S. A., R. A. Houze, M. I. Biggerstaff, and T. Matejka, 1988: The Oklahoma-Kansas mesoscale convective system of 10–11 June 1985: Precipitation structure and single-Doppler radar analysis. Mon. Wea. Rev., 116 , 14091430.

    • Search Google Scholar
    • Export Citation
  • Smith, A. M., G. M. McFarquhar, R. M. Rauber, J. A. Grim, M. S. Timlin, and B. F. Jewett, 2009: Microphysical and thermodynamic structure and evolution of the trailing stratiform regions of mesoscale convective systems during BAMEX. Part I: Observations. Mon. Wea. Rev., 137 , 11651185.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., and J. Szmelter, 2005: Multidimensional positive definite advection transport algorithm (MPDATA): An edge-based unstructured-data formulation. Int. J. Numer. Methods Fluids, 47 , 12931299.

    • Search Google Scholar
    • Export Citation
  • Smull, B. F., and R. A. Houze, 1985: A midlatitude squall line with a trailing region of stratiform rain: Radar and satellite observations. Mon. Wea. Rev., 113 , 117133.

    • Search Google Scholar
    • Export Citation
  • Smull, B. F., and R. A. Houze, 1987: Rear inflow in squall lines with trailing stratiform precipitation. Mon. Wea. Rev., 115 , 28692889.

    • Search Google Scholar
    • Export Citation
  • Szyrmer, W., and I. Zawadzki, 1999: Modeling of the melting layer. Part I: Dynamics and microphysics. J. Atmos. Sci., 56 , 35733592.

  • Weisman, M. L., 2001: Bow echoes: A tribute to T. T. Fujita. Bull. Amer. Meteor. Soc., 82 , 97116.

  • Willis, P. T., and A. J. Heymsfield, 1989: Structure of the melting layer in mesoscale convective system stratiform precipitation. J. Atmos. Sci., 46 , 20082025.

    • Search Google Scholar
    • Export Citation
  • Yang, M-H., and R. A. Houze, 1995: Sensitivity of squall-line rear inflow to ice microphysics and environmental humidity. Mon. Wea. Rev., 123 , 31753193.

    • Search Google Scholar
    • Export Citation
  • Zawadzki, I., W. Szyrmer, C. Bell, and F. Fabry, 2005: Modeling of the melting layer. Part III: The density effect. J. Atmos. Sci., 62 , 37053723.

    • Search Google Scholar
    • Export Citation
  • Zhang, D-L., and K. Gao, 1989: Numerical simulation of an intense squall line during 10–11 June 1985 PRE-STORM. Part II: Rear inflow, surface pressure perturbations, and stratiform precipitation. Mon. Wea. Rev., 117 , 20672094.

    • Search Google Scholar
    • Export Citation
  • Zipser, E. J., R. J. Meitin, and M. A. LeMone, 1981: Mesoscale motion fields associated with a slowly moving GATE convective band. J. Atmos. Sci., 38 , 17251750.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Composite WSR-88D reflectivity images at 2.0 km above mean sea level during the time of each spiral, with the spiral flight pattern overlaid on each at (a) 0533 UTC 29 Jun 2003, (b) 0008 UTC 5 Jul 2003, and (c) 0213 UTC 26 Jun 2003. The horizontal scale is indicated on the sides of (a)–(c), while the latitudinal and longitudinal positions of the lower-left-hand corner of each plot are indicated in the lower-left-hand corner. The notch region is indicated with a dashed line in (a).

  • Fig. 2.

    RH as a function of T for spirals executed within typically evolving TSRs during BAMEX. For T < 0°C, RH with respect to ice is plotted; for T > 0°C, RH with respect to water is plotted. The dark dashed line shows relative humidity with respect to ice at water saturation for T < 0°C. Specific spirals discussed in the text are indicated in the legend.

  • Fig. 3.

    RH profiles of upstream soundings for the BAMEX cases with typical trailing stratiform structure and evolution. The three profiles used for the simulations discussed in this study are indicated in the legend, while their 0°C level is also indicated.

  • Fig. 4.

    Mass median diameter (Dmm) calculated from size distributions as a function of T for all BAMEX cases with typical MCS evolution. The key indicates the three cases used for the sensitivity simulations discussed in the paper. The source region for these cases in the notch, enhanced stratiform rain region, and rear anvil are also noted.

  • Fig. 5.

    Schematic of the 1D model configuration.

  • Fig. 6.

    Model output time series contour plots for the 29 Jun 2003 simulation of (a) hydrometeor mass concentration q (g m−3), (b) relative humidity with respect to ice for T < 0°C and with respect to water for T ≥ 0°C, and (c) total model output cooling rate (shaded, K h−1) from sublimation, melting, evaporation and condensation. The y axis is the height above ground level, while the x axis is the time from the beginning of the simulation. The thick black and white dashed line indicates the 0°C isotherm. The thin dashed white line in (b) is the 99% RH contour.

  • Fig. 7.

    Contour plot for the 29 Jun 2003 simulation of total model output cooling rate from (a) sublimation, (b) melting, (c) evaporation, and (d) condensation onto cloud droplets. The thin black dashed lines in (c) indicate the 1 and 3 K h−1 contours. The 0°C isotherm is indicated by a thick black and white dashed line.

  • Fig. 8.

    The 29 Jun 2003 simulated mean cooling from sublimation for T < 0°C, evaporation for T > 0°C, and melting within the melting layer. Means are calculated over the entire depth of the respective layer.

  • Fig. 9.

    As in Fig. 6, but for the 4–5 Jul 2003 simulation. Note the contour intervals in (a) and (c) are larger than those in Figs. 6a and 6c.

  • Fig. 10.

    As in Fig. 7, but for the 4–5 Jul 2003 simulation.

  • Fig. 11.

    RH profiles for model input (thick black lines), model output at the time of closest RH comparison (thin black lines), and spiral observations (thick gray lines) for the (a) 29 Jun, (b) 4–5 Jul, and (c) 25–26 Jun cases.

  • Fig. 12.

    Hydrometeor mass per volume of air (q) profiles from the model output at the time of closest RH comparison (+) and spiral observations (o) for the (a) 29 Jun, (b) 4–5 Jul, and (c) 25–26 Jun cases.

  • Fig. 13.

    Vertical air motion estimates from aircraft inertial navigation instruments during the three microphysical spirals: (a) 29 Jun spiral 1, (b) 5 Jul spiral 1, and (c) 26 Jun spiral 1. The 1-s data are shown by the black lines, while 60-s-averaged data are shown by the gray lines.

  • Fig. 14.

    The model input hydrometeor number concentration as a function of maximum dimension for the three cases indicated in the legend. A scaling factor was applied to the number distribution for the 4–5 Jul and 25–26 Jun cases so that the total mass for each simulation was normalized to 1.40 g m−3.

  • Fig. 15.

    Results of model sensitivity tests on variations in the shape of the hydrometeor number distributions. (a) The 29 Jun simulated hydrometeor mass concentration, q. (b) The difference in q between 29 Jun and 4–5 Jul. (c) The difference in q between 29 Jun and 25–26 Jun. (d)–(f) As in (a)–(c), but for RH.

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