Moist Absolute Instability: The Sixth Static Stability State

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1207 Bulletin of the American Meteorological Society 1. Introduction Static stability considers the temperature of a dis- placed parcel relative to the environmental tempera- ture surrounding the parcel. Traditionally, five static stability states are recognized (Saucier 1955; Hess 1959): 1) absolutely stable γ < Γ s , 2) saturated neutral γ = Γ s , 3) conditionally unstable Γ s < γ < Γ d , 4) dry neutral γ = Γ d , 5) dry absolutely unstable γ > Γ d , where γ is the observed environmental lapse rate, and Γ s and Γ d are the moist- and dry-adiabatic lapse rates, respectively. Of particular interest here is state 5, dry absolutely unstable. Typically, this state exists in a shallow surface-based layer (usually < 100 mb deep) and results from an imbalance between the rate at which air adjacent to the ground is heated by conduc- tion and the rate at which dry convective eddies (re- stricted to dry-adiabatic overturning) can transport the heated air upward (Hodge 1956; Slonaker et al. 1996). It is most often observed on clear dry days when sur- face heating by incoming shortwave radiation is in- tense. Under these conditions, dry convective eddies Moist Absolute Instability: The Sixth Static Stability State George H. Bryan and J. Michael Fritsch Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania Corresponding author address: George H. Bryan, 503 Walker Building, University Park, PA 16802. E-mail: [email protected] In final form 22 October 1999. ©2000 American Meteorological Society ABSTRACT It is argued that a sixth static stability state, moist absolute instability, can be created and maintained over mesoscale areas of the atmosphere. Examination of over 130 000 soundings and a numerical simulation of an observed event are employed to support the arguments in favor of the existence of moist absolutely unstable layers (MAULs). Although MAULs were found in many different synoptic environments, of particular interest in the present study are the deep (100 mb) layers that occur in conjunction with mesoscale convective systems (MCSs). A conceptual model is proposed to explain how moist absolute instability is created and maintained as MCSs develop. The conceptual model states that strong, mesoscale, nonbuoyancy-driven ascent brings a conditionally unstable environmental layer to satura- tion faster than small-scale, buoyancy-driven convective elements are able to overturn and remove the unstable state. Moreover, since lifting of a moist absolutely unstable layer warms the environment, the temperature difference between the environment and vertically displaced parcels is reduced, thereby decreasing the buoyancy of convective parcels and helping to maintain the moist absolutely unstable layer. Output from a high-resolution numerical simulation of an event exhibiting this unstable structure supports the con- ceptual model. In particular, the model indicates that MAULs can exist for periods greater than 30 min over horizontal scales up to hundreds of kilometers along the axis of the convective region of MCSs, and tens of kilometers across the convective region. The existence of moist absolute instability suggests that some MCSs are best characterized as slabs of saturated, turbulent flow rather than a collection of discrete cumulonimbus clouds separated by subsaturated areas. The processes in MAULs also help to explain how an initially unsaturated, stably stratified, midlevel environment is transformed into the mesoscale area of saturated moist–neutral conditions commonly observed in the stratiform region of mesoscale con- vective systems.

Transcript of Moist Absolute Instability: The Sixth Static Stability State

Page 1: Moist Absolute Instability: The Sixth Static Stability State

1207Bulletin of the American Meteorological Society

1. Introduction

Static stability considers the temperature of a dis-placed parcel relative to the environmental tempera-ture surrounding the parcel. Traditionally, five staticstability states are recognized (Saucier 1955; Hess1959):

1) absolutely stable γ < Γs,

2) saturated neutral γ = Γs,

3) conditionally unstable Γs < γ < Γ

d,

4) dry neutral γ = Γd,

5) dry absolutely unstable γ > Γd,

where γ is the observed environmental lapse rate, andΓ

s and Γ

d are the moist- and dry-adiabatic lapse rates,

respectively. Of particular interest here is state 5, dryabsolutely unstable. Typically, this state exists in ashallow surface-based layer (usually < 100 mb deep)and results from an imbalance between the rate atwhich air adjacent to the ground is heated by conduc-tion and the rate at which dry convective eddies (re-stricted to dry-adiabatic overturning) can transport theheated air upward (Hodge 1956; Slonaker et al. 1996).It is most often observed on clear dry days when sur-face heating by incoming shortwave radiation is in-tense. Under these conditions, dry convective eddies

Moist Absolute Instability:The Sixth Static Stability State

George H. Bryan and J. Michael FritschDepartment of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

Corresponding author address: George H. Bryan, 503 WalkerBuilding, University Park, PA 16802.E-mail: [email protected] final form 22 October 1999.©2000 American Meteorological Society

ABSTRACT

It is argued that a sixth static stability state, moist absolute instability, can be created and maintained over mesoscaleareas of the atmosphere. Examination of over 130 000 soundings and a numerical simulation of an observed event areemployed to support the arguments in favor of the existence of moist absolutely unstable layers (MAULs).

Although MAULs were found in many different synoptic environments, of particular interest in the present studyare the deep (≥ 100 mb) layers that occur in conjunction with mesoscale convective systems (MCSs). A conceptual modelis proposed to explain how moist absolute instability is created and maintained as MCSs develop. The conceptual modelstates that strong, mesoscale, nonbuoyancy-driven ascent brings a conditionally unstable environmental layer to satura-tion faster than small-scale, buoyancy-driven convective elements are able to overturn and remove the unstable state.Moreover, since lifting of a moist absolutely unstable layer warms the environment, the temperature difference betweenthe environment and vertically displaced parcels is reduced, thereby decreasing the buoyancy of convective parcels andhelping to maintain the moist absolutely unstable layer.

Output from a high-resolution numerical simulation of an event exhibiting this unstable structure supports the con-ceptual model. In particular, the model indicates that MAULs can exist for periods greater than 30 min over horizontalscales up to hundreds of kilometers along the axis of the convective region of MCSs, and tens of kilometers across theconvective region.

The existence of moist absolute instability suggests that some MCSs are best characterized as slabs of saturated,turbulent flow rather than a collection of discrete cumulonimbus clouds separated by subsaturated areas. The processesin MAULs also help to explain how an initially unsaturated, stably stratified, midlevel environment is transformed intothe mesoscale area of saturated moist–neutral conditions commonly observed in the stratiform region of mesoscale con-vective systems.

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are unable to transport heat upward fast enough tomaintain the dry-adiabatic lapse rate. In other words,the absolutely unstable state is simply a manifestationof a rate imbalance wherein the large-scale radiativeprocesses acting to destabilize the atmosphere exceedthe small-scale convective processes acting to stabi-lize. In principle then, the absolutely unstable state canbe maintained as long as the rate imbalance continues,and can exist over areas much larger than the scale ofindividual convective eddies.

In view of the fact that nature is able to create andmaintain a dry absolutely unstable state, it is conceiv-able then that there may be a sixth stability state wherea saturated lapse rate (γ

s) that is steeper than the moist-

adiabatic lapse rate can be created and maintained, thatis,

6) moist absolutely unstable γs > Γ

s.

Although Saucier (1955) and Hess (1959) do not pre-clude the existence of a saturated lapse rate that isunstable, they do not specifically mention the criteriafor moist absolutely unstable conditions, nor has itbeen explained how this structure is created or re-moved. Furthermore, the temporal and spatial scalesof moist absolutely unstable conditions has never beenexplored.

The claim that moist absolute instability can becreated and maintained flies counter to the acceptedview that moist, fast-growing, nonhydrostatic modes(e.g., convective clouds/thunderstorms) will ensueimmediately following saturation (if the lapse rate issteeper than moist adiabatic) and that the unstable statewill be quickly eliminated or neutralized (e.g.,Bjerknes 1938; Lilly 1960). However, this conven-

tional view does not take into account the rate at whichprocesses may be creating the unstable state, or the rateat which processes remove the unstable state. In otherwords, as with the creation of the dry-superadiabaticlayer, it may be possible that a moist absolutely un-stable state can be created faster than (moist) convec-tive turbulence can eliminate it.

It is important to note here that moist absolute in-stability is not equivalent to conditional instability.1

In a typical conditionally unstable situation, the envi-ronment is unsaturated and an initially unsaturatedparcel is lifted to saturation [i.e., raised to its lifted con-densation level (LCL)]. Further lifting of the parcelalong a moist adiabat sometimes results in the saturatedparcel becoming warmer than its environment. If thisoccurs, nonhydrostatic buoyancy-driven vertical accel-erations support continued upward displacement of theparcel; that is, upward displacement of the parcel isunstable. However, this is not always the case. Forexample, the entire sounding shown in Fig. 1a is con-ditionally unstable. For parcels originating below900 mb, further lift above the LCL can eventually re-sult in positive accelerations. On the other hand, par-cels originating from above 850 mb never becomepositively buoyant.

Consider now the moist absolutely unstable con-dition that results if the entire lower troposphere, as

FIG. 1. Idealized sounding: (a) initial conditionally unstable sounding, (b) layer lifting is applied (thin black lines represent thepath of selected parcels within the lifted layer), and (c) resulting structure after lifting, which features a deep moist absolutely un-stable layer.

1The term “conditional instability” in this paper is defined bystatic stability state 3 (following Saucier 1955 and Hess 1959).Sometimes, conditional instability is used to describe a sound-ing that contains a parcel that can become positively buoyantafter being lifted to its lifted condensation level and then to itslevel of free convection. Emanuel (1997) has proposed the term“metastability” to describe this latter state.

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depicted in Fig. 1a, is lifted to saturation (Figs. 1b,c).All parcels in the saturated layer of Fig. 1c are unstableto any displacement in either direction, up or down.2

Thus, as its name implies, the layer in Fig. 1c is in-herently unstable. Intuitively, it would seem that thisstructure could not be maintained as a separate stabilitystate. However, evidence exists that moist absolutelyunstable layers over 100 mb deep do develop (Kainand Fritsch 1998). In fact, Kain and Fritsch argued thatthis unstable state can extend several hundred kilome-ters in the horizontal and can persist for time periodslonger than the lifetime of moist convective turbulence(i.e., cumulus clouds). These conditions can often oc-cur at the inflow region of mesoscale convective sys-tems, where a deep layer of strong mesoscale ascentextends for tens to hundreds of kilometers.

The goal of this paper is to establish that a sixthstability state, moist absolute instability, is sometimespresent in the low to midtroposphere. The conse-quences of this state on the structure of mesoscaleconvective systems are also explored. To this end, ob-servations from the standard radiosonde network arepresented in section 2. A conceptual model for the cre-ation and maintenance of moist absolutely unstablelayers is proposed in section 3. The results from a non-hydrostatic cloud-scale-resolution numerical simula-tion of an event with moist absolute instability areexamined in section 4. The implications of this stateon the structure and organization of mesoscale con-vective systems are discussed in section 5. A summaryand concluding remarks are provided in the final twosections.

2. Rawinsondeobservations

Data from the standard rawin-sonde network in the United Stateswas examined to see if moist abso-lutely unstable layers (MAULs) areobserved. Data from the 72 rawin-sonde sites in the continentalUnited States from 1 January 1997to 31 August 1999 were analyzed.

Soundings from nonstandard release times (e.g., notreleased at 0000 UTC or 1200 UTC) were includedin the study. Only the mandatory and significant leveldata were available.

A sounding was considered to have a MAUL if itcontained a saturated layer in which the equivalent po-tential temperature (θ

e) decreased with height. The defi-

nition of θe recommended by Bolton (1980) was used.

Saturation was defined as a dewpoint depression of≤ 1°C. This criterion for saturation was chosen becauseof the reported accuracy of radiosonde humidity sen-sors (0.2°–0.5°C; WMO 1996) and because of the typi-cal dry bias at high relative humidity (Schmidlin 1998).

Results of this investigation confirmed the exist-ence of MAULs. Table 1 lists some properties of theMAULs that were identified. A surprising 24.1% ofthe 134 196 soundings had layers that fit the criterialisted above. However, most of these layers were onlyslightly greater than moist adiabatic and were shallow(a few tens of millibars deep). Soundings with MAULsthat are deep (≥ 100 mb) and with relatively stronglapse rates [∂θ

e/(∂ z) ≤ −3 K km−1] composed 1.1% of

the dataset, which is an average of 1.5 deep, intenseMAULs every day in the continental United Statesrawinsonde network. Although MAULs were foundin every month of the study, there was a greater ten-dency for MAULs to be found in summer months.

It is important to recognize that not all of theMAULs reported by rawinsonde ascents are physicallyrealistic. There are several ways in which apparent (butunrealistic) MAULs can appear in rawinsode ascents,including

All MAULs 32 407/24.1% 40.3/29.4 −6.29/−3.22

MAULs withdepth ≥ 100 mb 3281/2.4% 140.4/128.0 −3.30/−2.60

MAULs with∂θ

e/∂z ≤ −3 K km−1 18 866/14.1% 35.9/25.0 −10.76/−6.56

MAULs withdepth ≥ 100 mb 1433/1.1% 138.8/127.0 −5.60/−4.82and ∂θ

e/∂z ≤ −3 K km−1

TABLE 1. Properties of the moist absolutely unstable layers (MAULs) in the rawin-sonde study.

Number/percent Depth (mb) ∂∂∂∂∂θθθθθe/∂∂∂∂∂z (Km−−−−−1)

of total soundings mean/median mean/median

2An unstable downward displacement doesrequire, however, access to water conden-sate in order to maintain saturation or near-saturation during its descent.

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• instrument error,• wet or ice-covered humidity sensors in a rawin-

sonde package that continue reporting saturatedconditions after leaving clouds, and

• rapid horizontal advection of a balloon-bornesounding through a saturated environment with astrong horizontal temperature gradient.

Furthermore, humidity chamber tests have shown thatradiosonde humidity sensors can lose accuracy aftersaturation is reached (Blackmore and Taubvurtzel1999). These problems suggest that many of theMAULs identified in the standard rawinsonde data arenot realistic. However, it is reasonable to assume thatsome of the 1433 deep, intense MAULs that were iden-tified are physically realistic.

Examination of soundings that contain MAULstogether with the environment they sampled wouldhelp answer the question of whether MAULs arephysically realistic. An informal investigation wasconducted in the April–August period of 1997–98 togain insight into the environments in which MAULswere observed. Soundings east of the Rockies wereexamined if they sampled the near environment ofmoist convection. All events with radar reflectivity≥ 40 dBZ (based upon the national network of WSR-88D radars) within 100 km of a sounding site andwithin 1 h of a sounding release time (i.e., between1000 and 1200 UTC and 2200 and 0000 UTC) wereexamined on a “time available basis”; that is, there wasno automated routine for obtaining data. MAULevents that were identified in this informal investiga-tion indicate that nearly all deep MAULs occurred inproximity to moist convection (i.e., thunderstorms,mesoscale convective systems, or stratocumulus lay-ers). The fact that MAULs were found in both deepprecipitating convection and shallow nonprecipitationconvection suggests that MAULs can be created andmaintained by different processes.

It is interesting to note that many of the MAULsoundings were observed in close proximity to thezone where the inflow to mesoscale convective sys-tems (MCSs) was being lifted by the MCS’s moist-downdraft outflow. In these cases, the MCS outflowboundary typically was within a few tens of kilome-ters of the sounding site, suggesting that MAULs areonly a few tens of kilometers wide. Thus, there appearsto be only a small window of opportunity to observeMAULs with rawinsondes. Our search for MAULs inthe United States rawinsonde network in 1997 and1998 revealed two additional factors that reduced the

likelihood of observing MAULs: 1) the odds that theoutflow boundary of a mature MCS was near a sound-ing site at sounding-release time are exceedinglysmall, and 2) when conditions are ripe to sample aMAUL, they are not ideal conditions for the releaseof a rawinsonde (it is quite likely that some rawinsondeoperators were unable or unwilling to release the bal-loon in instances where heavy rainfall and lightningwere approaching). Considering all of the above fac-tors, it is not at all surprising that MAULs would gounnoticed or that the existence of such a state wouldbe viewed with great skepticism.

3. Saturated absolute instability inmesoscale convective systems

The remainder of this paper promotes a conceptualmodel for saturated absolute instability that is ob-served in the inflow regions of mesoscale convectivesystems. Some conceptual models of moist convectiveoverturning in MCSs depict an ensemble of individualconvective towers (in various stages of developmentand decay) emanating from a well-mixed convectiveboundary layer (e.g., Arakawa and Schubert 1974).These models fit the theoretically supported view that,in the presence of a deep conditionally unstable state,moist convective overturning will be dominated byfast-growing nonhydrostatic modes, that is, thunder-storms. However, following the early work ofMoncrieff and Green (1972), Betts et al. (1976), Zipser(1977), Houze (1977), Ogura and Chen (1977), andLeMone et al. (1984), a wealth of evidence (Table 2)has been compiled showing that, under certain condi-tions, the atmosphere convectively overturns in a man-ner more resembling mesoscale slabs (or sheets) ofascending air overrunning slabs of descending air.These slabs are typically several hundred kilometerswide in the cross-flow direction and a few tens to sev-eral hundred kilometers long in the along-flow direc-tion (e.g., Roux et al. 1984; Chong et al. 1987; Smulland Augustine 1993; Trier and Parsons 1993). Typesof MCSs exhibiting slab overturning include certainsquall lines, elevated convection events, and narrowcold frontal rainbands.

Typically, ascending slabs develop along elongatedswaths of strong dynamic3 lifting, such as that found

3The term “dynamic lifting,” as used here and elsewhere in thepaper, refers to vertical motions not generated by buoyancy-drivenacceleration.

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along surface-based outflow layers, along frontal zones,or possibly by the release of moist symmetric insta-bility. Dual-Doppler radar analyses suggest that, insome instances, dynamically driven ascent of severalmeters per second develops in a low-level layer severalkilometers deep and that this rapidly ascending layermay extend horizontally for over 100 km. For example,Fig. 2a shows a vertical cross section perpendicular toa convective line observed during PRE-STORM(Smull and Augustine 1993). Low-level inflow of highθ

e air is directed from right to left and is being forced

upward by outflow from a surface-based cold pool.Note the low-level vertical motion maximum of 10 m s−1

centered near 3.5 km; this low-level maximum isclearly distinct from a stronger maximum, presumablydriven by buoyancy, centered near 10.5 km. Analysesof other MCSs also show two distinct maxima in as-cent located at similar elevations (e.g., Biggerstaff andHouze 1993; Hildebrand et al. 1996; Kingsmill andHouze 1999). Figure 2b shows a horizontal plot ofDoppler-derived vertical motion at 1.0 km aboveground for a MCS observed during COPT 81 (Chonget al. 1987). Low-level inflow for this system, whichis directed from left to right, is forced strongly upwardalong the outflow boundary; in this region, ascentreaches magnitudes of 3–6 m s−1. The dual-Doppleranalysis region of Fig. 2b shows a 30-km long swathof uninterrupted ascent, but the low-level reflectivityimage (not shown) suggests that this swath of ascentis over 80 km long. This example of a continuous low-level swath of strong ascending motion is in sharpcontrast to a collection of cumulonimbus updrafts

Newton (1950) Heymsfield and Schotz (1985) Houze et al. (1989)

Fujita (1955) Smull and Houze (1985) Moncrieff (1989)

Newton and Newton (1959) Leary and Rappaport (1987) Zhang et al. (1989)

Houze (1977) Chong et al. (1987) LeMone and Jorgensen (1991)

Ogura and Chen (1977) Dudhia et al. (1987) Frankhauser et al. (1992)

Zipser (1977) Smull and Houze (1987) Smull and Augustine (1993)

Leary and Houze (1979) Chalon et al. (1988) Trier and Parsons (1993)

Ogura and Liou (1980) Fovell and Ogura (1988) Lemone and Moncrieff (1994)

Moncrieff (1981) Lafore et al. (1988) Skamarock et al. (1994)

Thorpe et al. (1982) Rotunno et al. (1988) Yuter and Houze (1995)

Gamache and Houze (1982) Roux (1988) Pandya and Durran (1996)

Maddox (1983) Weisman et al. (1988) Jorsensen et al. (1997)

Roux et al. (1984) Cotton et al. (1989) Kain and Fritsch (1998)

TABLE 2. Papers supporting the occurrence of slab overturning.

where only a small percent of the environmental area iscomposed of updrafts. In other words, the entire low-level mesoscale environment is ascending as opposed toascent only in individual cumulonimbus updrafts (whichcan emerge from the slab at mid and upper levels).

Observed by radar, this slab convective overturn-ing often appears as a mesoscale zone of contiguousecho that may extend for hundreds of kilometers (e.g.,Figs. 3a,b). A swath of strong echo, called the “con-vective region” of mesoscale convective systems (e.g.,Houze et al. 1989; Loehrer and Johnson 1995), is of-ten found along the inflow side, parallelling a frontor outflow boundary. As documented by Houze et al.(1990) and McAnelly and Cotton (1986), there is con-siderable variation in small-scale structure within theconvective regions of mesoscale convective systems.For example, the convective region in Fig. 3a showsa virtually solid swath of reflectivity values > 40 dBZat the leading edge of the slab, while the convectiveregion in Fig. 3b shows a line of discrete convectivecells embedded within a nearly unbroken swath ofslightly weaker reflectivities. The individual cells ofFig. 3b resemble and are similar in scale to the tradi-tional models of distinct “hot towers” and would beconsidered individually as thunderstorms. In otherinstances, the number of these embedded cells is muchgreater, however their size is much smaller. In a verydetailed and careful analysis of an MCS, Yuter andHouze (1995a,b) found a broad-size distribution ofcellular elements in the convective region.

The long solid swaths of strong moist ascent, suchas shown in Fig. 3a, produce copious electrical activ-

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ity but hardly fit the traditional model of “a thunder-storm” (e.g., as shown in Fig. 3c). One might ask what,exactly, should be termed a thunderstorm? Should theentire 100-km long swath of high reflectivity be la-beled as one thunderstorm? Colman (1990a) pointedout that thunderstorms fitting the traditional conceptualmodel (i.e., isolated cells) often pass between observa-tion sites without being reported, whereas during manyelevated convection events several surrounding observ-ing sites will simultaneously report thunder. Colmanproposed that these large mesoscale areas of convec-tive precipitation are fundamentally different from thetraditional concept of cumulonimbus thunderstorms.Due to the different structure of moist convective

FIG. 3. WSR-88D base reflectivity images from the lowest el-evation scan (0.5°): (a) Mobile, AL, 1258 UTC 22 Jan 1998; (b)Nashville, TN, 1326 UTC 22 Apr 1996; and (c) Greenville, SC,2241 UTC 7 May 1998.

FIG. 2. Dual-Doppler radar observations of mesoscale convec-tive systems. (a) Cross section of vertical velocity (w, contour in-terval is 2 m s−1, negative contours are dashed, and zero contouris excluded). Adapted from Smull and Augustine (1993). (b) Hori-zontal view of w at 1.0 km above ground (shaded regions are up-drafts with contours corresponding to +3 and +6 m s−1, nonshadedcontours are downdrafts of −0.5 and −2 m s−1, and arrows indicatehorizontal system-relative flow). Adapted from Chong et al. (1987).

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events, and because the processes that dictate these struc-tures are fundamentally different, we propose the terms“cellular convection” for the traditional buoyancy-driven thunderstorm model and radar signature (e.g.,Fig. 3c) and “slab convection” for dynamically drivenevents with radar signatures like that in Fig. 3a. Note,however, that according to the definitions of Bluesteinand Jain (1985) and Hane (1986), the convective re-gions of both systems would qualify as squall lines.

Naturally, the organizational differences evident inFig. 3 raise many questions about the organization ofconvection. For example, whatfactors determine the small-scalestructure within the convectiveregion? Previous studies haveidentified the role of verticalwind shear, cold pool intensity,magnitude of thermodynamicinstability, and the release ofsymmetric instability. Most rel-evant to this paper is that the at-mosphere can create mesoscaleareas of saturation in a condi-tionally unstable environment.Furthermore, these conditions donot necessarily result in a fieldof individual convective towers.It is within these mesoscale satu-rated slabs that ascent may rivalthe vertical motions created bybuoyancy, thus creating the po-tential for sustained moist abso-lutely unstable conditions.

Figure 4 presents examplesof soundings, two of which ex-hibit MAULs, taken at points

preceding, within, and following the convective regionof MCSs. The locations of the soundings relative tothe structure and circulation of an idealized MCS areshown in Fig. 5. The idealized convective system wasconstructed on the basis of the studies listed in Table2. Ahead of the system, the atmosphere is condition-ally unstable with a deep, well-mixed boundary layer.Parcels rising from the well-mixed layer are unable toovercome the convective inhibition and reach theirlevel of free convection. As the outflow boundary ofthe convective system approaches, the environment is

FIG. 4. Skew T–logp soundings representative of the conditions at points a–d, respectively, in Fig. 5: (a) Midland, TX, 0000 UTC12 Jun 1997; (b) Birmingham, AL, 1200 UTC 9 Aug 1997; (c) Lake Charles, LA, 1200 UTC 18 Jun 1997; and (d) Detroit, MI, 1200 UTC21 Jun 1997.

FIG. 5. Idealized cross section through slab convective overturning. Flow vectors aresystem-relative, scalloped lines indicate cloud boundaries, solid lines are θ

e contours every

4 K (thin dashed line is an intermediate contour and heavy dashed line marks axis of high-est values), heavy solid line indicates outflow boundary or frontal zone, light shading high-lights midlevel layer of low θ

e air, and dark shading depicts the MAUL. Points a–d indicate

the locations of the soundings in Fig. 4.

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lifted strongly such that a layer of the lower tropo-sphere saturates, thereby creating a MAUL.

Conventional theory states that a MAUL will bequickly removed by nonhydrostatic buoyancy-drivenoverturning, that is, convective clouds will quicklydevelop and replace the MAUL with a moist neutral(or stable) profile. However, this conventional viewbased only on parcel theory does not account for thedeep layer of powerful mesoscale vertical motion thatcreated the MAUL in the first place. It is likely thatthe buoyancy-driven vertical motion that can removethe MAUL is actually less than the mesoscale verti-cal motion that created the MAUL. For example, con-sider first the vertical motions that parcel theory yields.Assuming that the environment shown in Fig. 4b isunchanging with time, parcel theory yields a verticalvelocity of approximately 6 m s−1 for undilute ascentfrom 900 to 800 mb. However, as noted by Lucas et al.(1994a,b) and others, this vertical velocity value islikely to be a considerable overestimate of the actualbuoyancy-induced vertical motion since it does not in-clude such factors as mixing/entrainment and water load-ing. In fact, applying the simple cloud model of Anthes(1977), which includes entrainment and water loading,to the sounding shown in Fig. 4b produces vertical ve-locities that are generally less than two-thirds of thevelocities that result from applying parcel theory.

Consider now the mesoscale vertical motions thatare likely to occur in a typical MAUL environmentwherein a low-level jet intersects a convectively gen-erated mesoscale outflow boundary. For a 10 m s−1

low-level jet and a 1-km deep cold pool advancing at10 m s−1, the ascent would be 2.0 m s−1 if the lifting isdistributed uniformly over a horizontal distance of10 km. Of course, in many instances cold pools aredeeper, low-level jets are stronger, and the lifting oc-curs over shorter distances so that the mesoscale as-cent can be much stronger, that is, on the order of5–10 m s−1. Observations (e.g., Fig. 2) show that suchlarge magnitudes of ascent can occur along mesoscaleoutflow boundaries—the zone where MAULs havebeen observed.

Thus, it appears possible that there may be low-level layers in which the magnitude of dynamicallydriven mesoscale ascent can become comparable toor even exceed the magnitude of nonyhydrostatic par-cel vertical motions forced by buoyancy, thereby fa-cilitating the formation and maintenance of a MAUL.Moreover, if the changes in the mesoscale environ-ment as a result of the strong mesoscale ascent areconsidered, the likelihood that the mesoscale ascent

will be larger than the buoyancy-forced vertical mo-tions is even greater. This is because lifting a moistabsolutely unstable layer warms the environment.Therefore, the temperature difference between a par-cel and its environment would tend to be less when aMAUL is present than when the atmosphere is rela-tively quiescent.

To illustrate the differences in parcel ascent in qui-escent and strongly ascending environments, considera mesoscale area with a sounding (Fig. 6a) that exhib-its a MAUL similar to that shown in Fig. 4b. If parceltheory is assumed, a parcel rising from the 1.0-kmlevel will arrive at the 3.5-km level in 431 s with avertical velocity of 15.3 m s−1. When the parcel arrivesat this level, it will be 2.5°C warmer than the environ-ment. Even after considering entrainment and waterloading (which would reduce the vertical velocity ofthe parcel by about 1/3), it is clear that the parcel wouldstill quickly accelerate upward and would be consid-erably warmer than the environment.

Consider now what happens if there is strong me-soscale dynamically driven ascent (w−). Assume thatw− is 5 m s−1 at the 1.0-km level and that it increaseswith height in the lower troposphere according to

∂∂w

z= − −1 1 1m s km .

Assume also that horizontal advection can be ignoredand that, due to some local effect, a parcel embeddedwithin the mesoscale environment arrives at the1.0-km level with a vertical motion of 5.5 m s−1

(0.5 m s−1 faster than the mesoscale environment).After about 400 s (Fig. 6b), the environment willchange (warm) to that shown in Fig. 6c. The parcelrising from the 1.0-km level will arrive at the 3.5-kmlevel with a vertical velocity of 7.7 m s−1 and will be0.5°C warmer than its environment (Fig. 6d). Notethat, even though the parcel in this ascending environ-ment started with a large vertical velocity (5.5 m s−1, asopposed to 0 m s−1 for the quiescent environment case),it arrives at the 3.5-km level with a vertical velocityconsiderably less than the quiescent case (7.7 m s−1 asopposed to 15.3 m s−1), and that it is only 0.5°C warmerthan the environment (as opposed to 2.5°C for the qui-escent case). Furthermore, since w− at 3.5 km is7.5 m s−1, the parcel in the ascending environment caseis rising only 0.2 m s−1 faster than its environment,while the parcel in the quiescent environment is ris-ing 15.3 m s−1 faster than its environment.

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This example shows how strong me-soscale ascent of a MAUL would tend toreduce the temperature difference be-tween a parcel and its environment tovalues smaller than that which would beexpected if the environment were quies-cent, thereby decreasing the buoyancy-driven acceleration of the parcel. This isbecause of the important, but often over-looked, aspect of moist absolutely un-stable layers—that ascent in theseconditions produces local warming (cf.the 2–4-km layer in Figs. 6a and 6c). Thiseffect favors the perpetuation of theMAUL until parcels reach the middle tro-posphere where temperature differencesbetween buoyancy-driven parcels and themesoscale environment may finally be-come large enough for individual buoy-ant updrafts to emerge.

This proposed conceptual model forthe formation and maintenance of moistabsolutely unstable layers is, in somerespects, analogous to the manner inwhich dry absolutely unstable layers arecreated and sustained in that it evolves asa result of a rate imbalance. In the drycase, the imbalance arises because theheating of air in the surface layer exceedsthe rate at which dry convective eddiescan carry the heat upward. In this situa-tion, the vertical temperature gradient in-creases, even to the point where itexceeds the dry-adiabatic lapse rate. Inthe moist case, the agent for creating theabsolutely unstable layer is not radiativeheating at the surface—rather, it is thedynamically driven environmental vertical motion, w−.Specifically, if

w− ≥ w′,

where w′ represents the buoyancy-driven verticalmotion of a parcel, then the rate at which mesoscaleascent creates the moist absolutely unstable conditionwill be greater than the rate at which cloud-scale tur-bulent eddies can overturn and eliminate the absolutelyunstable layer. For example, if an entire low-level layerof the environment were ascending at 10 m s−1 but thestrongest vertical motions that buoyancy forces couldcreate in that layer were only 5 m s−1, then there could

be no buoyancy-driven descending air. The atmo-sphere would continue to ascend everywhere in thelayer and therefore the moist absolutely unstable con-dition would persist.

Note that w′ is proportional to the vertical integralof the temperature difference between the parcel andthe environment, that is, it is proportional to convec-tive available potential energy (CAPE). Thus, the ver-tical distribution of CAPE in the low levels, not justthe total value of CAPE for the entire sounding, maybe important in determining the organizational modein the convective region of MCSs, that is, whether theconvective region appears solid or cellular. A largevalue of low-level CAPE (implying a large value of

FIG. 6. A comparison of the buoyancy of a parcel ascending in a static moistabsolutely unstable environment vs a parcel ascending in a rapidly rising moistabsolutely unstable environment. (a) Parcel path ascending within a steady-stateenvironment. Thick solid lines depict the steady-state environmental sounding;thin solid line represents a path of undilute moist-adiabatic ascent for a parcel start-ing at 1 km above ground. The dot is the location of the parcel after 431 s.(b) Illustration of the change in environmental profile as a result of strong lowertropospheric mesoscale ascent. Arrows indicate the path of the ascending layer.(c) The new environmental sounding after 400 s of lifting (thick solid black lines).Gray dashed lines are the initial environmental sounding shown in (a). (d)Temperature differences (∆T) between a parcel (black dot) and the ascending en-vironment (solid black line) and ∆T between the parcel and a steady-state envi-ronment (dashed gray line). Note that the dot in (d) is at the same temperature andelevation as in (a). In all panels, solid gray lines are isotherms and thin dashedgray lines are moist adiabats.

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w′ at low levels) increases thelikelihood that isolated parcelswill develop vertical motionslarger than the environmentalascent, and therefore cellularupdrafts will dominate ratherthan the slab ascent.

4. Numerical simulation

To address the issues raisedby the observations and our con-ceptual model of moist absoluteinstability, a mesoscale convec-tive system was simulated witha very high-resolution numeri-cal model. An event that fea-tured a developing MAUL in thestandard sounding network wasselected.

a. Description of the eventThe convective system initi-

ated along a cold front over thesouthern Great Plains on theevening of 5 October 1998.During the overnight hours, theconvective system advancedseveral hundred kilometersahead of the cold front and by1200 UTC displayed a nearlycontinuous convective line andtrailing stratiform region fromsouthern Texas to northeasternArkansas (Figs. 7 and 8). Thesurface inflow was nearly per-pendicular to the convective lineindicating that strong lower-tropospheric ascent was occurringalong the mesoscale outflowboundary. Upper-air analyses(e.g., Fig. 9) reveal that the in-flow to the convective systemextended through a deep layerand was very moist (dewpointdepressions along the convec-tive line were generally ≤ 5°C).

Of particular interest to thisstudy is the sounding fromCorpus Christi, Texas (CRP)

FIG. 7. Subjective surface mesoanalysis at 1200 UTC 6 Oct 1998. Contour interval is 2mb. Analysis convention follows Young and Fritsch (1989).

FIG. 8. Regional radar composite at 1200 UTC 6 Oct 1998. Four levels of shading corre-spond to, from lightest to darkest, 15–30, 30–40, 40–50, and > 50 dBZ.

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(Fig. 10a). This sounding contains three MAULs sepa-rated by pockets of moist but unsaturated air. The firstMAUL above the surface is 100 mb deep, and has alapse rate significantly greater than the moist-adiabaticlapse rate. NEXRAD data (Fig. 11), taken at the sametime that the sounding was released, reveal an ap-proaching outflow boundary only 25 km away fromthe rawinsonde facility (which is collocated with theNEXRAD facility). Assuming the CRP sounding wasreleased on time (rawinsondes are supposed to be re-leased at 1100 UTC), then it sampled the environmentimmediately ahead of the convective line where strongmesoscale lifting was likely to be occurring. TheNEXRAD data display a nearly solid swath of reflec-tivity greater than 40 dBZ, which is further evidenceof strong low-level mesoscale ascent and indicative ofslab convective overturning.

The data from the CRP sounding compares favor-ably with the nearby sounding at Brownsville, Texas(BRO), which was released well ahead of the convec-tive line (Fig. 10b). Specifically, if about 50 mb of low-level lifting is applied to the BRO sounding, the resultresembles the CRP sounding. Furthermore, when theCRP sounding is considered within the context of con-stant pressure plots (Fig. 9), it matches the synopticanalyses of temperature, height, and wind. This sug-gests that the CRP sounding ac-tually represents the inflowenvironment to the convectivesystem, and that it was not “con-taminated” by one of the pro-cesses listed in section 2 thatcould create incorrect MAUL-like structures in rawinsondeascents.

b. Model description andexperimental designA multiple-nested version of

the Pennsylvania State Univer-sity–National Center for Atmo-spheric Research MesoscaleModel (MM5; Dudhia 1993) wasused for the numerical simula-tion. The experiment was de-signed such that the innermostdomains could explicitly resolveconvective processes using themodel’s nonhydrostatic equa-tions. Recent studies have dem-onstrated the ability of MM5 to

explicitly reproduce convective processes and mesoscaleconvective systems [e.g., Liu et al. (1997), a simulationof Hurricane Andrew; and Skamarock (1994), simu-lations of supercell thunderstorms].

The experimental design is summarized in Table 3,and the model domains are illustrated in Fig. 12. Thetwo coarse-resolution domains (domain 1, ∆x =36 km; and domain 2, ∆x = 12 km) were initializedwith gridded fields from the National Centers for En-vironmental Prediction (NCEP). The NCEP fieldswere also used as boundary conditions for domain 1.Domains 1 and 2 were two-way interactive such thatthe boundary conditions for domain 2 were suppliedby domain 1 at every time step. The explicit moisturescheme of Reisner et al. (1998) was used in conjunc-tion with the Kain and Fritsch (1990) convectiveparameterization. The Reisner scheme contains pre-dictive equations for cloud water, rain, snow, ice, andgraupel.

Domain 3 used a grid spacing of 4 km. Output fromdomain 2 (including cloud and precipitation fields)served as initial conditions and boundary conditionsfor domain 3. Following the work of Weisman et al.(1997), no convective parameterization was applied.Thus, the nonhydrostatic model equations produce allconvective overturning. The subgrid-scale turbulence

FIG. 9. Subjective analysis of 850-mb geopotential height (contour interval 40 m) at1200 UTC 6 Oct 1998. The locations of Corpus Christi, TX (CRP), and Brownsville, TX(BRO), are indicated.

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parameterization is based on K theory and accountsfor fluxes of momentum, potential temperature, mix-ing ratio, and microphysical quantities. The eddy co-efficients (K values) are based on the local Richardsonnumber, which has a different formulation for satu-rated and unsaturated conditions, and on the local mo-mentum deformation.

The output from domain 3 provided the initial andboundary conditions for a very high-resolution run(domain 4, ∆x = 1.33 km). No convective parameter-ization was used on this domain, and the subgrid-scaleturbulence scheme is the same as that used on domain3. The following section presents analyses from do-mains 3 and 4 to examine the properties of MAULs.

c. Analysis of the spatial and temporal scale ofmoist absolute instabilityIn general, the simulation of the surface features

(not shown) compares favorably with the surface me-

soanalysis and with the radar reflectivity pattern (cf.Figs. 8 and 13). Most importantly, both experimentswith nonhydrostatic explicit convection (i.e., domains3 and 4) generate MAULs. Sample soundings fromthe southwestern portion of domain 4 are included asan example (Fig. 14). These soundings reveal the tran-sition from an initially unsaturated environment aheadof the convective system (Fig. 14a) to a state that re-sembles the CRP sounding just ahead of the outflowboundary (cf. Figs. 10a and 14b). Above the outflowboundary, there is a 300-mb deep MAUL (Fig. 14c).Farther back into the system, that is, in the stratiformregion, the profile is approximately moist neutral inthe middle and upper troposphere with a weak “on-ion” (Zipser 1977) structure at low levels (Fig. 14d).

Figure 15 displays the horizontal distribution of thesaturated4 unstable layer. A MAUL at least 100 mbdeep stretches continuously along and rearward of azone of strong (> 1 m s−1) low-level mesoscale ascent(Fig. 16) where the outflow boundary of moist-downdraft-generated cold air forces warm moist airupward. The magnitude of the upward motion is con-sistent with the earlier estimates of vertical motionsforced by low-level inflow overriding advancing coldpools (section 2b) and with Doppler-radar-observedvalues (cf. Figs. 2 and 16). Figure 15 confirms one rea-son why MAULs are difficult to capture with rawin-sonde ascents, that is, the MAUL layer is only a fewkilometers to a few tens of kilometers wide. Thus, aballoon must be released only a few minutes beforethe outflow boundary passes in order to sample theMAUL.

Examination of the conditions during passage ofthe convective system reveals that the moist absolutelyunstable state typically lasted about 30 min at most in-dividual grid points (e.g., Fig. 17a) but persisted forup to 45 min at some points. Thus, the model simula-tion supports the contention that MAULs can last fortime periods longer than the lifetime of individualmoist convective elements. Also, note that the MAULis created where powerful low-level upward motionlifts the conditionally unstable environment to saturation(Fig. 17b). After the strongest ascent ceases (after1100 UTC in Fig. 17), the MAUL begins to weakenin intensity and depth, presumably due to turbulentmixing. It is not until after all positive vertical motionceases that the MAUL disappears.

4A grid point in the model is considered saturated if the cloud watermixing ratio exceeds 0.01 g kg−1.

FIG. 10. Observed soundings at 1200 UTC 6 Oct 1998: (a) CRP,(b) BRO.

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Parcel trajectories were computed from 1-min-resolution model output. Analysis of conditions alongthe trajectories shows that moist absolutely unstableconditions are experienced by parcels for 15 minor more. Note that this result from aLagrangian reference frame agrees withthe result from the Eulerian reference inthe previous paragraph, since the meanmovement of the MCS is southeast at12 m s−1 and the mean wind speed in theMAUL is 15 m s−1. Using these values,and assuming a mean MAUL width of20 km, moist absolutely unstable condi-tions would be expected to last for 28min in an Eulerian reference frame andfor 12 min in a Langrangian referenceframe.

It is interesting that deep convectiveoverturning never occurs at the gridpoint in Fig. 17, despite the existenceof a deep, long-lived, absolutely unstablelayer. Conventional parcel theory statesthat buoyancy-driven cumulonimbusconvection would ensue under these con-ditions. Deep penetrative thunderstormcells do, however, develop in other por-tions of the MAUL. These cells are evi-dent on constant-σ-level analyses (e.g.,Fig. 18c) and on vertical cross sections(Fig. 19a) as towers of locally warm θ

e

anomalies that emerge at middle andupper levels. The towers of high θ

e air are

surrounded on all sides by much lower(by several K) θ

e values and fit the tra-

ditional view of thunderstorm “cells”(Byers and Braham 1948) and “hot tow-ers” (Riehl and Malkus 1958). In con-trast to the localized “bubbles” at upperlevels, the distribution of θ

e in the

MAUL has a considerably differentstructure. The highest θ

e air in the

MAUL extends in a contiguous swathacross the domain (Fig. 18b). Note, also,that the highest θ

e air from the boundary

layer “disappears” as it is mixed in theMAUL (Figs. 17c and 19a). Only a smallpercent of the broad swath of high θ

e

boundary layer (Fig. 18a) actuallyreaches higher levels with little mixing(Fig. 18c).

d. Analysis of buoyancyThe existence of cellular θ

e towers emanating from

some locations within a MAUL raises the question ofhow buoyancy works in MCSs. The magnitude of

FIG. 11. WSR-88D base reflectivity image (0.5° elevation) from CRP at1056 UTC 6 Oct 1998. Shading is the same as in Fig. 8.

FIG. 12. Configuration of model domains.

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buoyancy is typically defined as being proportional tothe difference between the local virtual temperature5

(T′v) and the environmental virtual temperature (−T

v).

From parcel theory, the vertical acceleration of a par-cel due to buoyancy is

∂∂w

tg

T T

Tv v

v

= ′−. (1)

Although parcel theory concepts are routinely applied,a consistent definition for −T

v does not exist. The cel-

lular towers in Figs. 18c and 19a are surrounded onall sides by colder environmental air. Thus, one mightdefine −T

v as the temperature some small distance away

from (but not inside) one of these towers. This defi-nition is consistent with observational studies of cu-mulus clouds, where buoyancy is typically defined asthe temperature measured inside the cloud minus thetemperature just outside of the cloud. In contrast, it ismore difficult to define the buoyancy of a parcel

within the saturated high θe swath of Fig. 18b.

Temperatures in the direction perpendicular to the axisof the high θ

e swath are cooler, whereas neighboring

parcels within the swath have nearly identical tem-perature. Therefore, it is unclear how to define −T

v for

a parcel in the high θe swath. Perhaps −T

v should be de-

fined as the average temperature around a circle cen-tered on a parcel, rather than the temperature in onerandomly chosen direction.

The different environments of parcels in a slabversus parcels in cellular towers are further illustratedin Figs. 20 and 21. A θ

e cross section taken perpen-

dicular to the outflow boundary is presented inFig. 20. Three θ

e cross sections taken parallel to the

outflow boundary are presented in Fig. 21: one is inthe conditionally unstable environment ahead of theMCS (Fig. 21a), one is just behind the surface outflowboundary (Fig. 21b), and one is through a convectivetower trailing behind the outflow boundary (Fig. 21c).Notice in these cross sections how the horizontal gra-dient of θ

e varies as the layer of high θ

e air ascends in

the slab. The value of buoyancy at points A, B, and Cin these cross sections would produce large differ-ences depending on how −T

v is defined. Specifically,

Table 4 lists the virtual temperature difference (∆Tv =

T ′v − −T

v) between each grid point and the virtual tem-

Horizontal grid 36 12 4 1.33spacing, dx (km)

Grid points (north– 109 × 109 163 × 130 196 × 154 196 × 154south) × (east–west)

Vertical layers 39 39 39 39

Explicit Reisner et al. Reisner et al. Reisner et al. Reisner et al.precipitation (1998) (1998) (1998) (1998)

Convective Kain and Fritsch Kain and Fritsch None Noneparameterization (1990) (1990)

Initial conditions NCEP NCEP Domain 2 Domain 3

Boundary conditions NCEP Domain 1 Domain 2 Domain 3

Initialization time 0000 UTC 6 Oct 0000 UTC 6 Oct 0600 UTC 6 Oct 0900 UTC 6 Oct

Forecast length 24 h 24 h 9 h 3 h

TABLE 3. Design of numerical simulation

Domain ID: 1 2 3 4

5Virtual potential temperature is also widely used in definitionsof buoyancy.

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perature 3 km6 away from the grid pointin various directions. As noted above, thereare points within the unstable slab (e.g.,point B) where, for all practical purposes,the temperature is the same as neighboringpoints within the slab (as noted by ∆T

e

and ∆Tw in Table 4). Only the temperature

difference in the north and south direc-tion would produce large positive buoy-ancy. In contrast, point C is surroundedon all sides by colder air and should beexperiencing the strongest buoyancy-induced vertical acceleration by Eq. (1).

Thus, it seems that buoyancy actingon parcels in the low-level swath of highθ

e air (i.e., in the MAUL) would tend to

be smaller than buoyancy acting on par-cels within towers emerging from theMAUL. Moreover, as discussed in sec-tion 3b, because the low-level environ-ment is rising moist adiabatically nearlyas fast as the parcels, the temperature dif-ference between parcels and the environ-ment remains much smaller than thatexpected from traditional applications ofparcel theory. In summary, buoyancy-in-duced accelerations in the MAUL arelikely to be much smaller than that sug-gested by parcel theory, which furthersupports the notion that small-scalemoist convection will not remove a satu-rated absolutely unstable state as quicklyas conventional wisdom expects.

e. Analysis of the mean stateAnother intriguing characteristic revealed by cross

sections through the convective line is the developmentof the moist stable mean state well behind the outflowboundary, that is, in the stratiform region. Individualcross sections through the system (e.g., Fig. 19) alwayscontain complicated and potentially confusing struc-tures. Yet overall, it is clear that the conditionally un-stable state in the prestorm environment (the far rightside of Fig. 19a) is eventually transformed to a stable(relative to moist vertical mixing) environment (theleft side of Fig. 19a).

FIG. 13. Simulated reflectivity (dBZ) from domain 3 at 1115 UTC 6 Oct 1998.

To obtain an appreciation for the mean state of theconvective system rather than individual snapshotsthrough convective elements, horizontal and tempo-ral averaging was performed to obtain a cross-section

6There is no physical significance to choosing 3 km here. Thequalitative results of this experiment will not change if a smalleror larger (by 1–5 km) distance is chosen.

TABLE 4. Difference in virtual temperature (°C) between thegrid points in Figs. 20–21 and points 3 km to the east (∆T

e), west

(∆Tw), north (∆T

n), and south (∆T

s).

A −0.04 0.04 −0.02 0.02 0.00

B −0.02 −0.01 +2.67 +1.18 +0.96

C +2.68 +2.10 +2.00 +1.93 +2.18

∆∆∆∆∆Te ∆∆∆∆∆T

w ∆∆∆∆∆Tn ∆∆∆∆∆T

sAverage

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averaged state. The temporal averaging was performedusing model output at 1-min increments over a 30-minperiod. The resulting mean fields reveal that theMAUL weakens rearward of the leading edge, therebycreating the stable (relative to moist mixing) profile(Fig. 22a). In the absolutely unstable slab, high θ

e air

from the base of the MAUL is mixed with low θe air

from the top of the MAUL. Since parcels in a MAULare unstable if displaced up or down (as long as theyremain saturated), this mixing process is very efficient.High-resolution three-dimensional time animationsshow that this vertical mixing is accomplished prima-rily by saturated eddies that bring “blobs” of midlevellow θ

e air downward while simultaneously carrying

high θe boundary layer air upward. Moreover,

Droegemeier and Wilhelmson (1987) showed that thestrongly sheared interface region between the ascend-ing slab and the colder air below is highly turbulent.Therefore, the top and bottom of the MAUL layerwould be expected to exhibit strong moist mixing. Thesmall-scale overturning would entrain mass into thetop and bottom of the slab. This conceptual modelsuggests that some mesoscale convective systems

could be characterized as vertically expanding slabsof saturated buoyantly turbulent flow composed of acontinuous spectrum of moist buoyant elements. Themean cross section also reveals that, despite the exist-ence of locally downward-moving air, the mean ver-tical velocity in the MAUL is upward everywhere(Fig. 22b). Doppler radar studies of the mean verticalvelocity in both convective and stratiform regions ofMCSs have produced the same conclusion (e.g.,Gamache and Houze 1982; Srivastava et al. 1986).

5. Implications to the conceptual modelof mesoscale convective systems

The observations and model output of moist abso-lutely unstable conditions supports a conceptual model

FIG. 14. Soundings from domain 4 at 1100 UTC 6 Oct 1998.

FIG. 15. Graphical depiction of regions where a moist ab-solutely unstable layer exists (shading), simulated reflectivity≥ 30 dBZ (bold contour) at σ = 0.780 (about 800 mb), and sur-face wind barbs from domain 4 at 1100 UTC 6 Oct 1998. Levelsof shading represent the depth (mb) of the moist absolutely un-stable layer.

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of MCSs as vertically expanding slabs of moist, tur-bulent mixing. This conceptual model agrees with theinterpretation of other investigators (e.g., Yuter andHouze 1995) who demonstrated that a full spectrumof convective overturning accomplishes the verticalmass transport in MCSs; that is, the transport is notdominated by a few large convective towers with in-tervening subsaturated areas.

The results also suggest that the differentiationbetween “convective” and “stratiform” regions ofsome MCSs is not always distinct. Rather, continuousmoist turbulent mixing can extend from the condition-ally unstable inflow environment at the front of thesystem to the moist neutral state at the rear of the sys-tem. This interpretation agrees with other studies [e.g.,Zipser et al. (1983) and Leary and Rappaport (1987),both based on radar analyses], who noted that the re-gion between the convective and stratiform regionswas not an abrupt transition from convective towersto stratiform precipitation; rather, the transition wasaccomplished gradually, though not uniformly, with

a decreasing number of convective towers farther backinto the convective system.

If the formation of a MAUL does coincide withstrong but predominantly small-scale moist mixing,it would help to explain two features often observedwith mesoscale convective systems:

• the highest values of equivalent potential tempera-ture (θ

e) evident in the inflow to the mesoscale slab

of ascent disappear as the flow passes upwardthrough the MAUL (e.g., Zipser et al. 1981;Rotunno et al. 1988); and

• the culmination of this mixing process is the trans-formation of the MAUL into a deep, saturated, nearlyuniform value of θ

e (i.e., moist neutral state) over a

mesoscale region in the upper half of the troposphere.

FIG. 16. Vertical velocity (m s−1) at σ = 0.900 (about 1 km aboveground) from domain 4 at 1100 UTC 6 Oct 1998.

FIG. 17. Time series of conditions at a grid point from domain4. (top) Depiction of times when a MAUL existed at the grid point(shading). Contours represent the lapse rate of temperature withinthe MAUL (in K km−1). (middle) Vertical velocity (m s−1, con-tour interval 0.5 m s−1, values > 0 are shaded). (bottom) θ

e (K,

contour interval 5 K, values > 345 K are shaded). Time resolu-tion is 1 min. The grid point in this analysis is the same as thatpresented in Fig. 14b.

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The second feature, a nearly uniform value of θe, is

most readily evident in the upper portion of “onion”soundings taken through the trailing stratiform regionsof MCSs (e.g., Fig. 4d; Zipser 1977; Leary 1980). Notethat this view simplifies the problem of how deep con-vection transforms its initially subsaturated, stablystratified, midlevel environment into the mesoscaleregion of saturated near-neutral condition observed inthe trailing stratiform region. It seems difficult, if notimpossible, to create this latter condition with a collec-tion of cumulonimbus towers. Also note that meso-scale regions of saturation obtained through slaboverturning facilitates arguments for production of dy-namically balanced mesoscale structures by moist con-vection, since it eliminates the problem of having toexplain away gravity wave energy losses and the lackof midlevel detrainment from deep convective towers.

The existence of slab convective overturning high-lights two fundamental problems with convective pa-rameterization in mesoscale models: 1) that buoyantparcels sometimes follow slantwise paths and traversemore than a single grid element in a convective cloudlife cycle, and; 2) that even if saturation occurs in aconditionally unstable environment, there is no guar-antee that deep moist convective towers will develop.Therefore, the simple cloud models used in convectiveparameterization cannot accurately represent the con-vective processes that occur in MCSs. Nevertheless,Kain and Fritsch (1998) were able to show that, to agood approximation, the combination of parameter-

FIG. 18. Equivalent potential temperature (θe) from domain 4 at 1100 UTC 6 Oct 1998: (left) σ = 0.995 (lowest model level), (cen-

ter) σ = 0.860 (about 850 mb), and (right) σ = 0.480 (about 500 mb). Shading interval is 5 K.

FIG. 19. Cross sections from domain 4 at 1100 UTC 6 Oct 1998:(a) equivalent potential temperature (shaded, K) and cloud water(contour, representing 1 g kg−1), (b) vertical velocity, where dashedcontours correspond to −6, −3, and −1 m s−1, and solid contourscorrespond to +1, +3, and +6 m s−1.

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ized convection and resolvable-scale processes permitsthe formation of moist absolutely unstable layers andslantwise mesoscale ascent. When they forced the con-vective parameterization to eliminate the moist abso-lutely unstable layers as quickly as they formed, thesolution became unphysical suggesting that the moistabsolutely unstable layers play an important role in theoverall convective process.

The occurrence of moist absolutely unstable lay-ers may help explain why parcel vertical motions aresometimes much smaller than what would be expectedfrom parcel theory (e.g., see LeMone and Zipser 1980;Zipser and LeMone 1980; Lucas et al. 1994a,b). Asounding through a moist absolutely unstable layercould show large CAPE, indicating that strong verticallyupright upward motions should occur. However, as isevident in the Rotunno et al. (1988) simulation, thehighest θ

e air can rise in a slantwise manner while tur-

bulent mixing simultaneously reduces the cloud-scalebuoyancy. If this process is happening uniformly allalong the slab, then the temperature of the environmenton either side of an ascending parcel is essentially thesame as the parcel’s temperature. Since the environ-ment of a parcel is colder only in two directions, onewould expect the acceleration due to buoyancy to be lessthan that stated by parcel theory (where a lifted parcelis assumed to be surrounded by air of uniform prop-erties). The exact consequences of this arrangementare, of course, unknown. Nevertheless, this conceptualmodel suggests that vertical accelerations should bemuch less than that based upon parcel theory.

It has been argued that moist symmetric instabil-ity can give rise to a slantwise-shaped updraft in me-soscale convective systems (e.g., Seman 1994). Whilethis may be true for some mesoscale convective sys-tems, the results here support slantwise updrafts with-out invoking (though not precluding) the existence ofsymmetric instability. For example, consider a station-ary situation wherein a low-level jet overrides a surface-based outflow boundary and creates a saturated layerin a conditionally unstable environment. If the buoy-ancy-induced vertical motion is much smaller than thehorizontal flow, the saturated parcels will be advectedhorizontally much faster than they will ascend, that is,slantwise flow results. Of course, in some instances,continued acceleration by buoyancy forcing eventu-ally causes the vertical velocity to greatly exceed thehorizontal velocity, thereby resulting in essentiallyupright flow and the emergence of convective towers.LeMone et al. (1984) presented a similar argument toexplain the low tilt (about 30° above horizontal) of the

leading edge of convective systems observed duringthe GATE experiment.

FIG. 20. North–south cross section of θe (contour interval 2 K)

at 1100 UTC, 6 Oct 1998. The bold bars depict distances of 3 kmto the north and south of points A, B, and C. Temperature differ-ences across these bars are listed in Table 4.

FIG. 21. Same as Fig. 20 except the cross sections are east–west and taken through points A, B, and C shown in Fig. 20.

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6. Conclusions

Observations and numerical experiments indicatethat a sixth static stability state, moist absolute insta-bility, can occur in the low–midtroposphere. This sta-bility state exists when the atmosphere creates andmaintains a saturated environment with a lapse ratesteeper than the moist-adiabatic lapse rate. This stateis not simply a subset of one of the five other well-known states (Saucier 1955; Hess 1959), since it ex-plicitly describes a saturated state, that is, it is notconditional upon saturation being achieved some-how—saturation is present. Observations and a nu-merical simulation show that a moist absolutelyunstable state can exist in layers over 100 mb deep,can contiguously span distances of several hundredkilometers, and can persist for 30 min or more. Thelatter two of these properties are analogous to the dryabsolutely unstable state.

Although the presence of moist absolutely unstablelayers has been shown in other papers (e.g., Table 5),it usually is not acknowledged. In the few works thatdo recognize the existence of this static stability state,it seems to be construed as a fleeting condition re-moved nearly instantaneously by powerful buoyancy-forced overturning. However, it is argued here that, asa general principle, a moist absolutely unstable layercan be maintained if the rate at which the unstablestate is being created by mesoscale processes isgreater than the rate at which it is being removed bycloud-scale turbulent overturning. Such a rate imbal-ance is likely to exist in the inflow region of certainmesoscale convective systems where dynamicallydriven mesoscale ascent can rival or even exceed thevertical velocities produced by buoyancy.

It is important to recognize that ascent in the pres-ence of moist absolute instability produces warming,not cooling. Therefore, the temperature difference be-tween parcels and their environment is reduced, andparcel theory (which assumes a stationary environ-ment) cannot be applied. Since actual buoyancy forcesare reduced relative to that described by parcel theory,the spatial and temporal scales of moist absolute in-stability can be much larger than has been previouslythought. The conventional view of deep cumulonim-bus growth ensuing immediately after the creation ofa MAUL does not adequately describe the processes.

Implications of the existence of MAULs on theconceptual model of MCSs were also presented. ViewingMCSs as vertically expanding slabs of moist, turbu-lent mixing helps explain several features of MCSs.In particular, the generation of mesoscale regions ofsaturation can be accomplished much more readilythrough this conceptual model than through an en-semble of discrete cumulonimbus towers. The exist-ence of mesoscale regions of saturation has been usedto help explain the generation of midlevel mesovor-tices, rear inflow jets, wake lows, etc., in MCSs (e.g.,Johnson and Hamilton 1988; Chen and Frank 1993;Yu et al. 1999). Also, others have shown how thestratiform region is a large contributor to the surface-based cold pool/mesohigh (e.g., Zhang et al. 1994).Thus, we believe that MAULs play an integral part indetermining MCS properties and behavior.

7. Concluding remarks

We recognize that what actually happens in slabswith moist absolutely unstable layers may depart from

FIG. 22. Same as Fig. 19, except the fields are obtained by spa-tially and temporally averaging the model output (see text fordetails of averaging); in (a), the thin contour represents the0.1 g kg−1 cloud water contour, and the thick contour outlines theMAUL, and; in (b), the dashed contours at −0.3 m s−1 and the solidcontours at +0.3, +0.8, +1.3 and +2.5 m s−1.

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the ideas presented here. Nevertheless, it is argued herethat moist absolute instability is a basic state that formsin the developing stage of many MCSs and lasts through-out their mature stage. We hypothesize that moist ab-solute instability may be important in determining theinternal structure of the convective system. It is conceiv-able that, just as the depth of the surface-based mixedlayer strongly affects the size and number of dry eddiesin the dry planetary boundary layer, the strength anddepth of the moist absolutely unstable layer may af-fect the size and number of moist eddies. In other words,the properties (e.g., depth and intensity) of the moistabsolutely unstable layer may help explain the varia-tions in the cellular structure of the convective regionof MCSs. A similar analogy between the dry planetaryboundary layer and the moist layer of convective sys-tems was proposed by Zipser and LeMone (1980).

Numerical simulations have given us the opportu-nity to inexpensively explore the structure of MAULs.However, high-resolution (both spatially and tempo-rally) observations are needed to evaluate the perfor-mance of these numerical simulations. Given the rarityof past observations of MAULs, a specially designedfield project appears to be necessary. Assuming themodel-predicted MAUL structure is correct, specialobservational methods would be necessary to observe

its properties. For example, serial ascents of balloonsfrom fixed locations ahead of an approaching MCS ordropsondes into the convective region might be aneffective way to observe the three-dimensional struc-ture of a MAUL. The use of airborne remote sensorsor rocket-borne sensors could help solve the problemassociated with horizontal drift of balloon-borne sen-sors. Or, successive aircraft penetrations of a MCS atmultiple elevations would be insightful. Of course, thetypical problems associated with measuring tempera-ture and relative humidity in saturated conditionswould have to be addressed.

We have performed additional numerical simula-tions to investigate the sensitivity of simulated MAULstructure to horizontal and vertical resolution, the rep-resentation of subgrid-scale turbulence, and differentformulations of precipitation microphysics. In all ourexperiments, MAULs exist regardless of thesechanges. Since model grid spacings less than 4 km arepartially resolving turbulent mixing, while at the sametime the subgridscale turbulence parameterization isaccounting for the same processes, it is possible thatthe simulations presented here are overcounting theeffects of turbulent mixing. If this is true, then it fur-ther supports the existence and perpetuation of moistabsolutely unstable layers, since turbulent mixing

Davies-Jones and Henderson (1974) Multiple figures in appendix A Rawinsondes

Zipser et al. (1981) Fig. 13 Rawinsonde

Rotunno et al. (1988) Figs. 11, 12, and 14 Idealized numerical simulation

Crook and Moncrief (1988) Fig. 9 Idealized numerical simulation

Colman (1990b) Fig. 9 Rawinsonde

Ryan et al. (1992) Fig. 14 Rawinsonde

Weisman (1992) Fig. 6 Idealized numerical simulation

Yang and Houze (1995) 3a Modified rawinsonde

Ziegler et al. (1997) Fig. 18 Observed numerical simulation

Kain and Fritsch (1998) Figs. 1, 3, and 10 Rawinsondes and simulation

Ziegler and Rasmussen (1998) Fig. 18 Modified rawinsonde

TABLE 5. List of papers that contain figures with moist absolutely unstable layers.

Study Figure Method of observation

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should remove the unstable structure. The fact thatturbulent mixing may be overdone in the simulationssupports the assertion that forced mesoscale ascent canoverwhelm turbulent mixing, thus maintaining themoist absolutely unstable layer.

Finally, as noted in section 2, it is likely that moistabsolutely unstable layers are not restricted to justmesoscale convective systems. Stratocumulus layers(radiative cooling > turbulent mixing) seem to be ableto support a moist absolutely unstable layer, albeit amuch weaker structure than that produced by power-ful mesoscale ascent in a conditionally unstable envi-ronment. It is also conceivable that the powerfulmesoscale ascent observed in the eyewall region oftropical cyclones may produce moist absolutely un-stable conditions in the lowest few hundred millibars.If this condition is eliminated in a manner similar tohow it is eliminated in mesoscale convective systems,then it may be instrumental in the formation of thesaturated, moist-adiabatic environment characteristicof this region. The main point remains, however, thata moist absolutely unstable layer will be supportedwherever a mechanism for forced cooling and satura-tion is greater than the compensating rate of stabiliza-tion by buoyancy-driven accelerations and/or turbulentmixing.

Acknowledgments. The authors appreciate many helpful dis-cussions with several people who shared their ideas and opin-ions on this topic. Their input has greatly strengthened the ideaspresented here. We wish to acknowledge the valuable input fromJack Kain, Rob Rogers, Peter Bannon, George Young, JohnClark, Bill Frank, Dave Stauffer, Nelson Seaman, JohnWyngaard, and Bob Maddox. We also wish to acknowledge theconstructive comments and suggestions from the reviewers: BradSmull, Peggy LeMone, Doug Lilly, and an anonymous reviewer.Special thanks go to Bob Hart for endless help with program-ming and graphical presentation of model output, and to PhillipSpencer for reviewing the first draft of this paper. This work wassupported by NSF Grant ATM 9806309 and NASA Grant NAG5-2927.

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