VOLUME 127 MONTHLY WEATHER REVIEW JANUARY 1999

Evolution of Slantwise Vertical Motions in NCEP's Mesoscale Eta Model

MUKUT B. MATHUR AND KEITH F. B RILL National Centers for Environmental Prediction, Washington, D.C.

CHARLES J. SEMAN Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey

(Manuscript received 18 July 1997, in ®nal form 30 December 1997)

ABSTRACT Numerical forecasts from the National Centers for Environmental Prediction's mesoscale version of the ␩ coordinate±based model, hereafter referred to as MESO, have been analyzed to study the roles of conditional symmetric instability (CSI) and frontogenesis in copious precipitation events. A grid spacing of 29 km and 50 layers are used in the MESO model. Parameterized convective and resolvable-scale condensation, radiation physics, and many other physical processes are included. Results focus on a 24-h forecast from 1500 UTC 1 February 1996 in the region of a low-level front and associated deep baroclinic zone over the southeastern United States. Predicted precipitation amounts were close to the observed, and the rainfall in the model was mainly associated with the resolvable-scale condensation. During the forecast deep upward motion ampli®es in a band oriented west-southwest to east-northeast, nearly parallel to the mean tropospheric thermal wind. This band develops from a sloping updraft in the low-level nearly saturated frontal zone, which is absolutely stable to upright convection, but susceptible to CSI. The updraft is then nearly vertical in the middle troposphere where there is very weak conditional instability. We regard this occurrence as an example of model-produced deep slantwise convection (SWC). Negative values of moist potential vorticity (MPV) occur over the entire low-level SWC area initially. The vertical extent of SWC increases with the lifting upward of the negative MPV area. Characteristic features of CSI and SWC simulated in some high-resolution nonhydrostatic cloud models also develop within the MESO. As in the nonhydrostatic SWC, the vertical momentum transport in the MESO updraft generates a subgeostrophic momentum anomaly aloft, with negative absolute vorticity on the baroclinically cool side of the momentum anomaly where out¯ow winds are accelerated to the north. Contribution of various processes to frontogenesis in the SWC area is investigated. The development of indirect circulation leads to low-level frontogenesis through the tilting term. The axis of frontogenesis nearly coincides with the axis of maximum vertical motion when the SWC is fully developed. Results suggest that strong vertical motions in the case investigated develop due to release of symmetric instability in a moist atmosphere (CSI), and resultant circulations lead to weak frontogenesis in the SWC area.

Emanuel 1983b; Seltzer et al. 1985). Ascending motion in such bands occurs nearly along the sloping moist isentropes (Bennetts and Hoskins 1979; Emanuel 1. Introduction 1983a). Frontogenetical forcing has also been investi- Various mechanisms have been considered to explain gated as a mechanism for enhancing slantwise vertical the mesoscale organization of precipitation in the form motions in symmetrically unstable regions (Emanuel of rainbands in midlatitudes (e.g., see Parsons and 1985; Sanders and Bosart 1985). Our main purpose here Hobbs 1983). In some instances the rainbands are is to investigate the role of CSI and frontogenesis in the aligned along the thermal wind, and conditional sym- development of slantwise vertical motions in a predic- metric instability (CSI) theory (Bennetts and Hoskins tion from the operational mesoscale model (MESO) of 1979; Emanuel 1983a) has been applied to explain the the National Centers for Environmental Prediction formation of such bands (Bennetts and Sharp 1982; (NCEP). A complete diagnosis of moist symmetric instability entails evaluation of moist potential vorticity (MPV, see section 2 for a de®nition). Vertical and horizontal gra- Corresponding author address: Dr. Mukut B. Mathur, NCEP/En- vironmental Modeling Center, W/NP22, Rm 205, WWBG, NOAA, dients of wind and equivalent potential temperature are 5200 Auth Rd, Camp Springs, MD 20746-4304. needed for evaluating the MPV distribution, and these E-mail: [email protected] gradients vary substantially in both space and time in

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Unauthenticated | Downloaded 09/25/21 01:44 AM UTC 6 MONTHLY WEATHER REVIEW VOLUME 127 mesoscale convective areas. In particular, the equivalent developing precipitation bands should not propagate potential temperature gradients vary considerably in the relative to the mean ¯ow in the cross-band direction vertical, and these gradients may change signi®cantly, (Xu 1986), or have very slow cross-band propagation for instance, during the slantwise convective adjust- toward the warm air (Seman 1994). Rapid propa- ment. Thus, data with high spatial resolution at short gation of precipitation bands would warrant inves- time intervals are needed. Both high vertical and hor- tigation of gravity wave mechanisms (see, e.g., Sto- izontal resolution are used in MESO and the predicted bie et al. 1983; Einaudi et al. 1987; Koch et al. 1988; ®elds can be saved at desired time intervals (see section Schneider 1990). 2). Therefore, data from MESO are well suited for 6) Frontogenesis and upper-level jet streak forcings studying symmetric instability. We have found that the should be weak, as these processes can also generate distribution of MPV using a vertical spacing of 25 mb precipitation bands (Ley and Peltier 1978; Bosart and (spacing used in our study, see section 2) is often dif- Sanders 1986; Uccellini and Koch 1987). ferent from that evaluated using a lower resolution (e.g., In the case presented in this paper, a single slanted 200 mb). Note that in many previous observational and mesoscale updraft develops at low levels in a stably numerical studies of symmetric instability, data with strati®ed region with negative MPV, on the baroclini- lower spatial and time resolutions were utilized. As an cally cool side of a weak surface cold front. The pre- example, Bennetts and Sharp (1982) used a 10-level cipitation pattern develops a quasi-linear two-dimen- numerical model with a horizontal resolution of 100 km. sional structure approximately parallel to the mean tro- Seltzer et al. (1985) utilized geostrophic absolute vor- pospheric thermal wind, with centers of strong upward ticity from a low (vertical and horizontal) resolution motion in the associated vertical motion ®eld (section analysis and observed soundings to evaluate symmetric 3). Development of distinct mesoscale updrafts in CSI instability. Later studies such as Knight and Hobbs precipitation bands has been previously documented (1988), Persson and Warner (1991), and Lindstrom and (Seltzer et al. 1985; Lindstrom and Nordeng 1992) and Nordeng (1992) showed that high model resolution is is consistent with the theory of Xu (1986). It will be important for simulating CSI or slantwise convection shown in section 4 that the vertical transport of hori- (SWC). zontal momentum creates adjacent regions of inertial The organization of the paper is as follows. An over- instability and stability in the upper troposphere similar view of the MESO and diagnostic procedures employed to those simulated in the idealized two-dimensional in- is given in section 2. Time evolution of the horizontal tegrations (Seman 1994; Blanchard et al. 1998), and this structure in the SWC area in a MESO forecast is pre- development causes a signi®cant modi®cation of diver- sented in section 3. Development of SWC employing gence and creates mesoscale perturbations in the jet vertical cross sections of various ®elds including MPV streak. In section 5, the distribution of diabatic and other and condensational heating is discussed in section 4. frontogenetical forcing terms is discussed. Additional The case discussed here was selected because the ob- results are given in section 6, and our conclusions appear served signi®cant precipitation amounts over a large in section 7. area were predicted well, and the following criteria for CSI, which include those discussed in Seltzer et al. (1985), were satis®ed (see sections 3±4). 2. Methodology 1) The atmospheric conditions in the vicinity of the Numerical predictions mainly from the ®ne (MESO) precipitation bands should be approximately two- and coarse (Eta) mesh versions of the ␩ coordinate± dimensional, with larger variations in thermodynam- based model of NCEP are currently utilized as guidance ic and kinematic properties in the cross-band and to produce short-range weather forecasts (up to 48 h) vertical directions. over the United States and adjoining areas. The ␩ co- 2) There should be a region of negative MPV in the ordinate is de®ned in Mesinger (1984). Both models use vicinity of the developing bands (Bennetts and Hos- a primitive set of equations. A grid spacing of 29 (48) kins 1979; Emanuel 1983a,b). km and 50 (38) layers are presently utilized in the op- 3) The bands should be oriented approximately parallel erational MESO (Eta) model.1 The domains of both to the thermal wind and strongest in the region of models extend over and beyond the U.S. mainland, and instability (Stone 1966, 1970; Busse and Chen 1981; the MESO domain is a subset of the Eta domain. The Antar and Fowlis 1983; Miller and Antar 1986). lateral boundary conditions are updated in both models 4) The mesoscale updrafts should be relatively narrow using the forecasts from the AVIATION (global) model (Xu 1986) and slanted from the vertical (Emanuel of NCEP. The initial conditions for Eta and MESO are 1983a; Seman 1994), and if the atmosphere is sat- urated should be oriented approximately along sur- faces of equivalent potential temperature ␪e (Ben- 1 NCEP has replaced Eta and MESO with a 45-layer version of netts and Hoskins 1979; Emanuel 1983a). MESO with 32-km horizontal grid spacing that is integrated four 5) CSI and slantwise convection theory implies that the times daily, beginning on 3 June 1998.

Unauthenticated | Downloaded 09/25/21 01:44 AM UTC JANUARY 1999 MATHUR ET AL. 7 obtained with the use of a Regional Data Assimilation of increasing the horizontal resolution, and perhaps the System (RDAS). The analysis from NCEP's Global Data vertical resolution, is signi®cant in the SWC areas in Assimilation System (GDAS) is used as a ®rst guess for NCEP's ␩ coordinate±based models. The enhancement the analysis at the initial time of both Eta and MESO of vertical motion with an increase in the resolution is RDAS. An overview of the global forecast model and usual in hydrostatic models. GDAS is provided in Kanamitsu (1989), and RDAS is The postprocessed data on constant pressure (p-) sur- described in Rogers et al. (1996). The RDAS data as- faces (25-mb interval) from MESO are routinely avail- similation procedure consists of producing a 3-h forecast able at a lower resolution of 40 km on a Lambert con- from an analysis, and utilizing this forecast as a ®rst formal grid. The procedure employed is described in guess for the next analysis. The Eta RDAS is carried Treadon (1993). The processed data were used in this over a 12-h period. As an example, the 0000 UTC study and the General Meteorological Package (des- GDAS analysis is used in Eta RDAS to produce the Jardins et al. 1996, 1997) for plotting meteorological initial conditions for the Eta model forecast beginning data was utilized for analyzing the data. The forecasts at 1200 UTC of the same day. The MESO RDAS is from MESO in a few copious precipitation events during performed over a 3-h interval. As an example, the 1996 were examined. Although, we have recorded the GDAS 1200 UTC analysis is used in MESO RDAS to development of slantwise vertical motions in many cas- produce initial conditions for the MESO forecast be- es, we present results from only one case here for the ginning at 1500 UTC of the same day. The data cutoff purpose of illustrating the SWC development in MESO. time for MESO is later than for Eta. Except for the As noted above in this section, another example of SWC above differences in the resolution, domain, and initial development in the ␩ coordinate±based models was dis- conditions, the prediction programs of the two models cussed in an earlier study (Mathur and Baldwin 1995). are the same. Changes in model atmospheric structure during the Many physical processes, including the convective evolution of SWC in the 24-h MESO forecast from 1500 parameterization based on a modi®ed Betts±Miller UTC 1 February 1996 are discussed in the following (1986) scheme (Janjic 1994), resolvable-scale conden- sections. Widespread snow or rain occurred over the sation, explicit cloud water/ice prediction, and short- southeastern United States during the above forecast and longwave radiation, are incorporated in both mod- period, with observed equivalent liquid amounts of 2± els. The resolvable-scale condensation is invoked for 5 cm along a weak frontal zone extending from central relative humidity (RH) greater than saturation relative Louisiana to eastern North Carolina. Intense SWC de- humidity (SATRH), where SATRH is prescribed to be veloped along this front during the 9±18-h period in the 0.75 for land points and 0.90 for the over the water MESO forecast. In the operational MESO run, the fore- points. For RH values greater than SATRH, a fraction casts are routinely output at 3-h intervals except that of (RH Ϫ SATRH) q is condensed and the remaining s the condensational heating rates are not saved. To study part is used to increase the RH. Here qs is the saturation mixing ratio. Note that RH in the model can become the vertical distribution of condensation heating rates in 100% with this scheme. The above formulation of re- SWC columns, we integrated the current version (im- solvable-scale condensation is documented in Zhao and plemented operationally in February 1997) of the model Carr (1997). for this study and stored condensational heating rates The convective release of latent heat in upright col- during the forecast. Also, the forecast data were saved umns is evaluated in the two models using the modi®ed at 1-h intervals during the above-cited SWC period in Betts±Miller scheme cited above. A parameterization this integration. The current 1997 operational version procedure for slantwise convection is not employed. of MESO uses more advanced physical parameterization Strong upward motion and condensational heating in procedures than the 1996 operational version. The struc- deep slanted columns often occur in both MESO and ture of SWC in both versions was, however, similar. Eta forecasts. Horizontal and vertical structures in a few The distribution of vertical velocity in pressure co- cases investigated are found to be similar to those ex- ordinates (␻) at 500 mb in the SWC area is discussed pected in SWC (see sections 3±4). Resolvable-scale in section 3; it is shown that the maximum upward condensation is found to be much greater than the pa- motion in a propagating updraft over the southeastern rameterized convective condensation in the SWC areas. United States increases between 9 and 13 h (times given The intensity of vertical motions and precipitation is refer to the number of hours into the forecast), and generally greater in MESO than in Eta in the SWC areas. thereafter it decreases. In section 4 we present cross In a previous study the development of SWC in 38- sections of various ®elds along a line that passes through layer versions of MESO and Eta in a 1993 blizzard case the middle tropospheric maximum upward motion point over the eastern United States was presented (Mathur and is perpendicular to the mean tropospheric thermal and Baldwin 1995). A grid spacing of 40 (80) km was wind between 850 and 300 mb (westerly over the max- employed in MESO (Eta) in the above case; the inten- imum in ␻ discussed here). The cross sections at 10, sities of vertical motion and precipitation in the SWC 12, 13, and 15 h are shown to capture the time evolution area were greater in MESO than in Eta. Thus, the impact of SWC, cross sections of geostrophic pseudoangular

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FIG. 1. Forecast surface ®elds at 13 h: (a) mean sea level pressure (2-mb intervals), (b) winds (half-barb ϭ 2.5 m sϪ1) at 10-m level above the ground, and temperature (1 K intervals) at 2-m level above the ground.

momentum Mg and the equivalent potential temperature at 13 h indicates an inverted trough extending from the ␪e are discussed ®rst. Here Mg is de®ned as northwestern Gulf of Mexico to Virginia (Fig. 1a). This trough was nearly stationary during the 9±18-h SWC M ϭ fs Ϫ u , g gn forecast period cited in section 2, and was most pro- where the normal component of the geostrophic wind nounced at 13 h. The winds at 10 m, and the temperature ugn is taken as positive if it blows out of the plane of at 2 m, above the model ground level at 13 h (Fig. 1b) the cross section, s is the horizontal distance from the indicate the locations of the frontal zones. Frontogenesis origin of the cross section, and f is the Coriolis param- occurred in the area extending from southern Louisiana eter. to western Virginia, and a broad zone of enhanced tem- The vertical structure of moist potential vorticity is perature gradient developed by 13 h (the cold front ``C'' examined to further ascertain whether the conditions cited above). In this regard notice that northerlies prevail favorable for CSI developed during the integration. to the north of the front C, whereas winds are mostly MPV is de®ned as from the east to the east of the front C (Fig. 1). The SWC area formed on the cool side of the front C, in -u northern Louisiana. Despite the weak winds, the potenץ␪ eץ ␷ץ ␪ץ␪eeץ MPV ϭϪg ␨ Ϫϩ , p tial temperature gradients increased a little in the frontץ yץ pץ xץ pץ ΂΃a C area during the SWC period, and these were of the where is the absolute vorticity, (u, ) the horizontal ␨a ␷ order of 6±8 K (100 km)Ϫ1 at low levels in some parts components of the wind, and g is the acceleration due of the front C, with weaker gradients in the surrounding to gravity. areas. A zone of high temperature gradient extended from the western Gulf of Mexico eastward to the Florida 3. Horizontal structure in the frontal area panhandle (the stationary front ``S'' cited above). Front S was initially a cold front that moved over the northern During the forecast period discussed in this paper Gulf of Mexico. Southerlies strengthened to the south widespread snow or rain was reported along a cold front of this front during 10±13 h, and this front remained (hereafter referred to as front C) that extended from nearly stationary during the next several hours. southern Louisiana to western Virginia. Signi®cant rain- fall amounts were also observed along the Gulf Coast in association with a stationary front (hereafter referred b. Vertical motion to as front S) described below. The forecast frontal struc- ture and a comparison of observed and forecast precip- The distribution of ␻ between 10 and 15 h at 500 mb itation are now presented. is shown in Fig. 2. A maximum in upward motion de- velops by 10 h over Louisiana with maximum upward velocity (Ϫ25 ϫ 10Ϫ3 mb sϪ1) between 700 and 500 a. Surface features mb. This maximum upward motion area is displaced It was noted in section 2 that the maximum vertical toward the east with time, and the maximum upward motion at 500 mb developed over the southeastern Unit- velocity occurs at 13 h at 500 mb. The minimum in ␻ ed States at 13 h. The forecast mean sea level pressure at this hour is Ϫ24 ϫ 10Ϫ3 mb sϪ1 at 700 mb, Ϫ46 ϫ

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FIG. 2. Forecast vertical motion (dashed, 10 ϫ 10Ϫ3 mb sϪ1 intervals; zero line solid) at 500 mb: (a) 10 h, (b) 12 h, (c) 13 h, and (d) 15 h. North±south solid line segments show cross section locations. Local minima of ␻ (maxima of upward velocity) indicated by N.

10Ϫ3 mb sϪ1 at 500 mb, and Ϫ33 ϫ 10Ϫ3 mb sϪ1 at 350 development of multiple mesoscale updrafts under CSI mb. After 13 h, the maximum upward velocity decreases conditions has been documented in the observational as it is displaced farther to the east (Fig. 2d). We will case study of Seltzer et al. (1985, their Fig. 1 shows refer to this translating maximum of upward motion as variation in radar echo intensity along the updraft), and cell A in the following. in numerical studies (e.g., Lindstrom and Nordeng 1992, The circulation in the above-cited updraft region sat- their Fig. 7a). Development of relatively narrow up- is®es the criteria for CSI listed in section 1. Notice that drafts is consistent with the theory of Xu (1986) (criteria as cell A intensi®es, the upward vertical motion area 4). Mean thermal winds between 850 and 300 mb around elongates toward the west-southwest and additional this elongated upward motion area are mostly from the maxima develop. [In this elongated upward motion area west to west-southwest with relatively little variation in two maxima develop at 500 mb (Fig. 2), and 3 (5) the direction of the thermal wind; the axis of the elon- centers develop by 15 (17) h at 700 mb (not shown).] gated upward motion area is nearly aligned with the We will refer to this elongated area of upward motion mean thermal wind (this satis®es criteria 1 and 3). In as the ␻ band, or simply band, in the following. The section 4a it will be shown that an area of negative MPV

Unauthenticated | Downloaded 09/25/21 01:44 AM UTC 10 MONTHLY WEATHER REVIEW VOLUME 127 exists in the vicinity of the band (criteria 2). Note also imum divergence area during the period 10±12 h (Fig. that the band translates with the mean ¯ow, which sat- 4), above the region of midtropospheric upward motion. is®es criteria 5 for CSI. It should be noted that the Notice also that the upward motion, weaker than at 500 development of such precipitation bands has been at- mb (Fig. 2), occurs in the band area at 350 mb (Fig. 5). tributed in previous studies to either symmetric insta- The size of the wind minimum area increases consid- bility (Bennetts and Hoskins 1979; Emanuel 1979) or erably by 15 h (Fig. 4d) and it grows further during 15± frontogenesis (Bjerknes 1919; Sawyer 1956; Eliassen 18 h (not shown). Notice also that a minimum wind 1959; Hoskins and Bretherton 1972; Ley and Peltier speed (Ͻ30 m sϪ1) area develops near the Louisiana 1978). The contribution of these two dynamical pro- coast during 10±15 h. The development of the wind cesses in the development of strong upward motion will minima in the upper levels of the ␻ bands is due to be discussed in sections 4±5. It will be evident that the vertical momentum transport, and its evolution is dis- band develops due to release of CSI and the resultant cussed further in section 4. circulation induces weak frontogenesis (criteria 6). An area with negative absolute vorticity (AV) appears just to the north (on the baroclinically cool side) of the c. Precipitation band area at 12 h (Fig. 5b); the negative AV area be- comes elongated and the maximum negative AV values Observed and predicted precipitation amounts accu- move farther to the north of the band area during 12± mulated over the 24-h period ending at 1500 UTC 2 15 h. The development of upper-level negative AV February 1996 are shown in Fig. 3. The river forecast anomalies on the baroclinically cool side of updrafts has center network of observations and radar data were used also been simulated in numerical studies of dry sym- for producing the analysis shown in Fig. 3a. These data metric instability (Thorpe and Rotunno 1989) and SWC have been routinely employed for some time at NCEP (Lindstrom and Nordeng 1992; Seman 1994). Notice to obtain the observed rainfall analysis (M. Baldwin that the 350-mb winds (Fig. 4) in an area to the north 1997, personal communication). of the negative AV area (Fig. 5) have increased by about Observed (liquid equivalent) amounts of 2±5 cm oc- 5msϪ1 during the 10±13-h period. Previous studies curred along front C, and 2±3-cm maximum amounts have shown that negative AV at the out¯ow level causes occurred near the coastal Gulf of Mexico area (Fig. 3a). an increase in the mesoscale out¯ow winds in the neg- The forecast total precipitation amounts in the front C ative AV region (Seman 1994; Blanchard et al. 1998) area are somewhat larger than the observed, and the (see also section 4b). model overpredicts the rainfall amounts over the Gulf Scattered areas with negative MPV occur at 350 mb Coast area (Fig. 3b). Notice that the precipitation over during the entire integration period. A large negative the Gulf Coast is associated with both parameterized MPV area extends southwestward from just south of the convective and resolvable-scale condensation, whereas ␻ band at 10 h (Fig. 4a). An area with negative MPV the precipitation in the front C area is mainly due to develops over the maximum vertical motion area of the the resolvable-scale condensation (Figs. 3c±d). band by 12 h (Fig. 4b), and it covers most of the band area by 15 h (Fig. 4d). Horizontal and vertical advec- d. Upper-tropospheric ¯ow tions of MPV between 10 and 15 h at 350 mb were computed; the increase in the maximum negative MPV The maximum divergence at 350 mb during the pe- value during 10±15 h was somewhat larger than that riod 10±15 h (Fig. 4) is located close to the 500-mb implied by these two terms. Processes that might have maximum upward motion area (Fig. 2). The maximum generated negative MPV were not investigated. divergence at 350 mb increases considerably between 10h(8ϫ 10Ϫ5 sϪ1) and 13 h (24 ϫ 10Ϫ5 sϪ1). Recall that the 500-mb upward motion also increased during 4. Slantwise vertical motions the above period (section 3b). The level of maximum divergence rises as the upward motion increases; the Cross sections are presented to show the time evo- maximum divergence occurs at 450 mb at 10 h and near lution of various ®elds during the development of slant- 300 mb after 12 h. The lifting of the level of maximum ed vertical motion structure. As noted in section 2, the divergence is caused by the warming in the band area, cross sections are drawn along a line that passes close especially in the middle troposphere, that arises due to to the 500-mb maximum upward motion point and is the upward transport of sensible and latent heat in the perpendicular to the thermal winds. Recall that the max- band (see section 6a). Notice that from 13 to 15 h both imum vertical motion area is displaced eastward in time the 350-mb maximum divergence (Figs. 4c±d) and 500- (Fig. 2), and therefore the location of the cross sections mb maximum upward motion (Figs. 2c±d) values have presented below shifts to the east with time. Note that decreased. for the south to north cross sections presented, Mg ϭ

Southwesterly winds prevail over the maximum di- fy Ϫ ug, where y is the horizontal distance from the vergence area at 350 mb during the 10±15-h period (Fig. origin of the cross sections and ug is the westward com- 4). A wind minimum (Ͻ40msϪ1) develops in the max- ponent of the geostrophic wind.

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FIG. 3. Accumulated 24-h precipitation amounts (1-cm intervals) at 1500 UTC 2 February 1996: (a) observed, (b) forecast total, (c) forecast (resolvable scale), and (d) forecast (convective scale). Areas with amounts greater than 0.1 cm are shaded. Local maxima indicated by X.

a. Conditional symmetric instability humidity along ␪e and ␪ei pro®les through a saturated A necessary condition for CSI to occur in a saturated point (base of the pro®les) would be the same below baroclinic atmosphere is that the slope of ␪ surfaces be the freezing level. Above the freezing level the tem- e perature (speci®c humidity) would be higher (lower) for greater than that of the Mg surfaces (Bennetts and Hos- kins 1979; Emanuel 1983a). This is equivalent to re- the ␪ei than for the ␪e pro®le. Because the formation of quiring negative moist potential vorticity for CSI to oc- ice during resolvable-scale condensation is included in cur (Bennetts and Hoskins 1979). The above theory MESO but is not included in the diagnostic evaluation assumes that the basic-state ¯ow is two-dimensional, of ␪e, the difference in the ␪ei and ␪e pro®les should be frictionless, and in thermal wind balance, and diabatic taken into account when interpreting MESO forecasts. effects other than that due to condensation are neglected Consider a case where ␪e is the same between two levels (Bennetts and Hoskins 1979; Emanuel 1983a). L1 and L2 above the freezing point, and L1 is the lower level. (As an example, see the 320 K contour in Fig. The equivalent potential temperature ␪e in this study ␪e is computed using Eq. (38) in Bolton (1980); the for- 6b between 600 and 500 mb; the freezing level was mation of ice at subfreezing temperatures is not included located near 700 mb.) Note that ␪ei will be greater at in this diagnostic calculation. If the ice phase was in- L1 than at L2. Therefore, a neutral pro®le (␪e constant cluded, then the diagnosed equivalent potential tem- in vertical) above the freezing level may be condition- perature ␪ei would be greater than ␪e at all points with ally unstable because of formation of ice during a MESO nonzero speci®c humidity. The temperature and speci®c forecast. Thus, the areal extent of the conditionally un-

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FIG. 4. Forecast winds (half-barb ϭ 5msϪ1) and isotachs (thick dotted, 10 m sϪ1 intervals), areas with negative moist potential vorticity (shaded), divergence and convergence (solid and dashed, respectively; Ϫ4, 4, 8, 16 ϫ 10Ϫ5 sϪ1 contours) at 350 mb: (a) 10 h, (b) 12 h, (c) 13 h, and (d) 15 h.

stable region above the freezing level discussed later in duce an equivalent potential temperature that is lower this section may be larger than that implied by area with than that would be obtained using 100% saturation cri- p Ͼ 0. teria for resolvable-scale condensation. Recall that onlyץ/␪eץ The distribution of equivalent potential temperature a fraction of excess moisture[Ͼ(SATRH) qs] is con- in MESO might be also controlled by the saturation densed in MESO, so that the RH, at a later time, can criteria (less than 100%, SATRH Ͻ 1, see section 2) approach 100% (section 2). Therefore, the impact of used for invoking resolvable scale condensation. Ther- using SATRH Ͻ 1 in MESO will not be as large as modynamic considerations show that when the resolv- would be expected if all excess moisture is condensed able-scale condensation is evaluated at RH less than [condition postulated in Mathur (1983)].

100%, then the lapse rate in the conditionally unstable South to north cross sections of ␪e and Mg at 10 h regions is adjusted toward a rate steeper than the pseu- show the development of the slanted vertical motions doadiabatic (Mathur 1983). This effect will tend to pro- in the lower troposphere near 32ЊN (Fig. 6a). Close

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FIG. 5. Forecast vertical motion (0 solid, negative dashed, 10 ϫ 10Ϫ3 mb sϪ1 intervals, local minima indicated by N) and negative absolute vorticity areas (shaded) at 350 mb: (a) 10 h, (b) 12 h, (c) 13 h, and (d) 15 h.

inspection of the relative orientation of the ␪e and Mg circulation vectors (¯ow in the plane of the cross sec- surfaces in Fig. 6a reveals that the ␪e surfaces are tion) below 400 mb become nearly aligned with the ␪e slightly more vertical than the Mg surfaces in the lowest ϭ 320 K contour that lies nearly along the axis of 100±200 mb of the atmosphere; a potential for CSI slantwise vertical motions. Notice also that at 10 h,

(p Ͻ 0) conditions (to upright convectionץ/ ␪eץ) therefore exists in this region (criteria 2 of section 1). stable The CSI is realized because the RH is greater than 90% prevail on the cool side of the axis of cell A below and signi®cant resolvable-scale condensation (latent 600 mb (Fig. 6a). heat release) takes place in the area (Fig. 7a). As shown In the region of maximum upward motion in the mid-

/␪eץ) by Bennetts and Hoskins (1979) and Emanuel (1983a), dle troposphere, conditionally unstable conditions -p Ͼ 0) exist (Fig. 6a), and nearly upright vertical moץ a CSI updraft will be oriented along the surfaces of neutral buoyancy. In our case of widespread saturation, tions have developed. Resolvable-scale condensation Ϫ1 these surfaces will coincide with ␪e surfaces. Note that with maximum heating rate of 3 K h occurs in the a slantwise updraft develops approximately along the upright vertical motion region (Fig. 7a). This may be

␪e surfaces between 10 and 13 h (Figs. 6a±c) in the considered an example of development of grid-scale region where CSI conditions exist, and by 13 h the convection. Previous studies (e.g., Molinari and Dudek

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FIG. 6. Cross sections through the maximum vertical motion areas. Ordinate is pressure (mb); abcissa is lat±long. Geostrophic pseudoangular Ϫ1 momentum Mg, (solid, Ϫ48, Ϫ36, Ϫ24, Ϫ18, Ϫ12, Ϫ6, 0, 6, 12, 18, 24, 36, 48, 72 m s contours), equivalent potential temperature (dashed, 5 K intervals, except 320 K, which is thick solid), and vertical motion (dotted, Ϫ32, Ϫ16, Ϫ8, Ϫ4, Ϫ2, 0, 2 ϫ 10Ϫ3 mb sϪ1 contours): (a)

.p) Ͼ 0 are shaded. Circulation vectors (thinned) are also shownץ/␪eץ) h, (b) 12 h, (c) 13 h, and (d) 15 h. Areas with 10

1992) have suggested that grid-scale forcing may sat- ist in the above-cited negative MPV region between 400 urate vertical columns in a ®ne mesh model, and grid- and 300 mb at 12 h; note that the vertical motion con- scale convection may become dominant and determine tours slant southward toward the above-cited upper-tro- the vertical distribution of condensational heating in pospheric negative MPV area (Fig. 6b). such columns. With the lifting of the level of maximum vertical Note that the negative values of MPV exist over near- motion, the depth of slantwise vertical motions has in- ly the entire upward motion region of cell A below 450 creased in the lower part of the troposphere (cf. Figs. mb at 10 h (Fig. 8a). A comparison of Figs. 6a±b and 6a±b), and the level of maximum heating has also shift- 8a±b shows that between 10±12 h the level of maximum ed upward (cf. Figs. 7a±b). Also, the heating rates of upward motion has shifted upward, and the condition- 1±3KhϪ1 occur over a wider area at 12 h than at 10 ally unstable region with negative MPV in the midtro- h. Note also that ␪e in the middle troposphere in the pospheric region of cell A has also moved upward. The southern part of the updraft has also increased during upper portion of this negative MPV area becomes con- the above period and a nearly moist adiabatic lapse rate nected with the negative MPV area that is located be- has developed in the updraft area between 700 and 350 tween 30Њ and 32ЊN. [The negative MPV areas to the mb (see the ␪e ϭ 320 K contour in Fig. 6b). Note that south of the updraft and over the updraft are not con- at 13 h the ␪e ϭ 320 K contour below 700 mb lies nected at 350 mb (Fig. 4b), but as can be seen from nearly along an Mg surface that nearly coincides with Fig. 8b these two negative areas are connected at the the axis of slanted upward motions (Fig. 6c). The evo- p Ͻ 0) ex- lution of ␪e and Mg surfaces between 10 and 15 h isץ/␪eץ) 325±300-mb levels.] Stable conditions

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FIG. 7. Cross sections through the maximum vertical motion areas. Total and resolvable-scale condensational heating rates (dashed and solid, respectively, 1 K hϪ1 intervals) and vertical motion (dotted, 10 ϫ 10Ϫ3 mb sϪ1 intervals): (a) 10 h, (b) 12 h, (c) 13 h, and (d) 15 h. Areas with RH exceeding 80% (lightly shaded) and 90% (heavily shaded) are also shown. similar to that expected during the release of CSI or A area in our study. This difference in structure between slantwise convective adjustment [Seltzer et al. 1985; M and Mg is related to the development of strong ageo- Wolfsberg et al. 1986; Persson and Warner 1991 (Fig. strophic winds; it will be shown in section 4b that the 7d)]. ageostrophic AV and geostrophic AV have opposite Previous studies using idealized initial data (Thorpe signs over most of the updraft area. and Rotunno 1989) and synoptic initial state (Lindstrom and Nordeng 1992) have shown that the buckling of b. Absolute vorticity absolute momentum (M) surfaces occurs in the release of the symmetric instability. In the above studies actual Development of negative AV at 350 mb was discussed winds were used for evaluating M (geostrophic winds in section 3d (Fig. 5). Heavy lines in Fig. 8 enclose the are used in evaluating Mg). Lindstrom and Nordeng in- areas with negative AV. It is evident that negative AV tegrated a primitive equation model with and without develops in a deep layer in the upper troposphere on the inclusion of a parameterization procedure for SWC. the baroclinically cool side of cell A. This AV structure Signi®cant buckling of M surfaces developed only in is what one would expect from vortex-line tilting by a the integration in which SWC parameterization proce- relatively narrow and intense updraft in a baroclinic dure was included. Recall that an SWC parameterization atmosphere (for another example, see Seman 1994). scheme is not used in MESO (section 2). Strong buck- A comparison of Figs. 6 and 8 shows that the 0 (Ϫ8) ling in Mg (Figs. 6b±d), but only a weak buckling in M AV contour at 12 (13) h lies just north of the cusplike surfaces (not shown), develops above 500 mb in the cell feature in the ␪e ϭ 320 K contour, and also just north

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FIG. 8. Cross sections through the maximum vertical motion areas. Vertical motion (dotted, 10 ϫ 10Ϫ3 mb sϪ1 intervals), areas with negative moist potential vorticity (shaded), and negative absolute vorticity (thick solid, 4 ϫ 10Ϫ5 sϪ1 intervals): (a) 10 h, (b) 12 h, (c) 13 h, and (d) 15 h.

of the local minimum in the Mg ®eld. For two-dimen- to promote further lifting in the area of the latent heat- -y implies that ␨ga will be neg- ing, reinforcing the convection and assisting in the deץ/Mgץsional ¯ows, ␨ga ϭ ative to the south side of this local minimum in Mg and velopment of new convection (Seman 1994; Blanchard positive to its north (Fig. 9a). Here ␨ga is the geostrophic et al. 1998). In this regard note the upper-level diver- AV and y is the distance from south to north. Ageo- gence is centered close to the southernmost edge of the strophic winds have a large rotational component; large AV Ͻ 0 region (Figs. 8 and 10), and develops a slanted negative values of ageostrophic AV develop to the north pattern. The slanted axis of divergence (convergence) side of this local minimum in Mg ®eld (Fig. 9b). The lies above (below) the slanted axis of vertical motion geostrophic AV and ageostrophic AV have opposite (Fig. 10). The levels of maximum vertical motion, con- signs over large areas, and the net AV has a dipolelike vergence, and divergence are displaced upward during structure in the middle and upper troposphere with the the period of intensi®cation (10±13 h). positive values on the warm side and negative values on the cool side of the updraft (Fig. 9c). The upper- c. Winds level net AV distribution simulated here has also been simulated in other numerical models of SWC (Seman Gradients in diabatic heating rates (Fig. 7c) and up- 1991; Lindstrom and Nordeng 1992; Seman 1994). ward motion (Fig. 6c) at 13 h in the middle troposphere As noted in section 3d, the mesoscale out¯ow winds are stronger to the north than to the south of the max- increased by about5msϪ1 through the negative AV imum upward motion axis. Mainly because of differ- area. Release of inertial instability in the negative AV ential heating, potential temperature gradients increase accelerates the out¯ow (Seman 1994; Blanchard et al. in a deep column (500±300 mb) between 10 and 13 h 1998). This enhanced out¯ow, in turn, has been shown to the north side of cell A (not shown). Consequently

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FIG. 9. Cross sections at 13 h through the area of maximum vertical motion. Vertical motion (dotted, 10 ϫ 10Ϫ3 mb sϪ1 intervals) and (a) geostrophic absolute vorticity, (b) ageostrophic absolute vorticity, and (c) absolute vorticity of the total wind (dashed, Ϫ64, Ϫ32, Ϫ16, Ϫ8 ϫ 10Ϫ5 sϪ1 contours; solid, 0, 8, 16, 32, 64 ϫ 10Ϫ5 sϪ1 contours).

large pressure gradients develop in the middle and upper ward ¯ux of low momentum air from the low levels troposphere to the north side of the updraft. Strong geo- (Newton 1950; Seman 1994), whereas the development strophic winds in the middle and upper troposphere are of the geostrophic wind structure is associated with the therefore predicted to the north side of the updraft (Fig. diabatic heating mechanism cited above. 11b). In contrast, the potential temperature gradients For an inviscid atmosphere, d␷/dt is proportional to decrease somewhat on the south side of the updraft in Ϫuag, and also to the difference M Ϫ Mg. Here uag is most of the 500±300-mb column between 10 and 13 h; the westerly component of the ageostrophic wind. No- consequently, weaker geostrophic winds develop on the tice that the ageostrophic easterly component (uag Ͻ 0) south side of the vertical motion axis (Fig. 11b). Note is large to the north side of the updraft between 300 that the geostrophic winds have a mostly westerly com- and 500 mb (Fig. 11c). Therefore in this region the wind ponent, and the above-cited distribution of wind speeds is being accelerated strongly to the north, and M and implies that the geostrophic vorticity will be negative Mg surfaces are not expected to lie close to each other. at upper levels in cell A and it will be positive to the As noted in section 4a, the pronounced buckling that north of cell A. This distribution of relative vorticity develops in Mg surfaces in this region does not appear gives rise to the geostrophic AV distribution shown in in M surfaces. Fig. 9a. Winds above 800 mb are from the west in the band 5. Frontogenesis area, and westerlies increase with height (Fig. 11a). Strong upward transport of low-level momentum occurs The intensity of a front is often speci®ed by the mag- in cell A and the band region (Fig. 12). The development nitude of the maximum horizontal potential temperature of subgeostrophic winds over a large depth of the up- gradient, and its change in intensity by the frontoge-

١p␪ is the potential ,١p␪|. Here|(draft above 500 mb is probably mainly due to this up- netical function (d/dt

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FIG. 10. Cross sections through the maximum vertical motion areas. Vertical motion (dotted, 10 ϫ 10Ϫ3 mb sϪ1 intervals), divergence and convergence (solid, dashed and shaded, respectively; 4 ϫ 10Ϫ5 sϪ1 intervals): (a) 10 h, (b) 12 h, (c) 13 h, and (d) 15 h.

temperature gradient on a constant pressure surface, and The ®rst two terms are shear S and con¯uence C terms, d/dt is the Lagrangian time derivative. A more general respectively. The third is the tilting T term, and the expression for the frontogenetical function (time rate fourth is the diabatic D term. Carlson points out that change of three-dimensional potential temperature gra- the maximum potential temperature gradient at every dient with height as the vertical coordinate) is derived point along the front may not be in the direction per- in Miller (1948) and Bluestein (1986). pendicular to the front. The time rate change of gradient of potential tem- Reed and Sanders (1953), and Haltiner and Martin perature in any direction (say y) on a pressure surface (1957) proposed that, for convenience, the y axis be y). It can be easily taken toward the lower potential temperature at eachץ/␪ץmay be obtained from (d/dt)(Ϫ shown that grid point so that the ®rst term S vanishes. We have adopted this last de®nition of the y axis to investigate ␪ the role of frontogenesis in the development of slantwiseץ ␻ץ ␪ץ ␷ץ ␪ץ uץ ␪ץ d Ϫϭ ϩ ϩ p motions discussed in section 4. The left-hand side ofץ yץ yץ yץ xץ yץy ΃ ΂΃΂΃΂΃΂΃΂΃΂΃ץdt΂ the above equation will be referred to as the frontoge- .␪ netical function in the followingץץ Ϫ . -t The south to north cross sections for the frontogeץ yץ ΂΃ netical function and its components C, T, and D at 10 Carlson (1991) takes the y direction to be perpendic- and 13 h are shown in Figs. 13±14. In the formative ular to the front, and provides physical interpretation of stage of cell A (10 h), the slanted upward motions extend each term on the right-hand side of the above equation. to about 700 mb. Frontogenetical forcing in this updraft

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FIG. 11. Cross sections at 13 h through the area of maximum vertical motion. Vertical motion (dotted, 10 ϫ 10Ϫ3 mb sϪ1 intervals) and (a) wind, (b) geostrophic wind, and (c) ageostrophic wind. Solid lines are isotachs (5, 10, 20, 30, 40, 50, 60, 65, 70 m sϪ1). Shaded areas indicate the areas where the wind speed is subgeostrophic.

p) is balanced by the resolvable-scale heatingץ/ ␪cץarea is mainly due to the T term (Fig. 13), indicating (Ϫ␻ that greater upward motion must be occurring on the that is associated with the supersaturation due to the p) Mathurץ/ qcץcooler rather than on the warmer side (effectively an vertical advection of moisture (Ϫ␻ indirect circulation). In this regard, note that the as- 1983). Here, ␪c and qc are, respectively, potential tem- cending motion is stronger on the cold side (north) than perature and saturated mixing ratio along a pseudoad- on the warm side in the updraft area. In a shallow layer iabat. Therefore we may write, near 600 mb in the updraft, the D and C terms are ␪ץץ frontogenetical and the T term is frontolytical. In the D ϭϪ ␻ c pץy΂΃ץ northern part of the midtropospheric updraft area both the T and D terms are strong but possess opposite signs and and nearly cancel each other. Strong frontogenesis is ␪ץץ also indicated near 400 mb in the region where the ␻ contours slant toward the south; the T term is strongly T ϭϪD Ϫ ␻ c . pץy΂΃ץ frontogenetic and greater in magnitude than the D term which is frontolytical. The structure of D (Fig. 13b) and T (Fig. 13c) is If the horizontal gradients of equivalent potential tem- similar to that expected in a pseudoadiabatic atmo- perature are small, then D and T would be zero near sphere with westerly thermal wind and a vertical mo- the maximum in ␻ on a pressure surface and D and T tion ®eld that is linear in the west±east direction. In would have opposite signs elsewhere. Notice that T is this case the y axis of cross sections shown would have zero along the axis of maximum vertical motion except south to north orientation. In a pseudoadiabatic at- near 600 mb, and D and T have opposite signs in many mosphere the cooling due to the vertical advection term parts of the upward motion area (Figs. 13b±c).

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FIG. 12. Cross section of the wind tendency (5 m sϪ2 3hϪ1 intervals) due to the vertical advection term through the area of maximum vertical motion (dotted, Ϫ40, Ϫ32, Ϫ24, Ϫ16, Ϫ8, Ϫ4, Ϫ2, 0, 2 ϫ 10Ϫ3 mb sϪ1 contours) at 13 h.

Figure 14 shows that a strong frontogenetical (fron- be partly because our grid spacing is much smaller than tolytical) lobelike structure has developed in the D(T) that in the Sanders and Bosart (1985) study, and also term on both the southern and northern sides of the because we are evaluating the mesoscale frontogenesis maximum vertical motion area in the middle tropo- resulting from SWC in which the tilting and diabatic sphere. It was noted in section 4b that the maximum terms become very important. In many studies using upward motion in cell A develops in the middle tro- observations, the tilting and diabatic terms are not eval- posphere at 13 h, and that slanted upward motions ex- uated because of a lack of suf®cient information. All tend to higher levels at 13 h than at 10 h. All three three terms at 13 h (Fig. 14) have similar magnitudes terms C, T, and D have greater magnitudes at 13 h (Fig. and do not cancel each other everywhere; this suggests 14) than at 10 h (Fig. 13). Frontogenesis in the lower that the diagnosis of frontogenesis in high-resolution part of the slanted column at 13 h is mainly due to the models should include all terms. T term, and in the upper portion to the D and C terms. Strong frontogenetical forcing develops at 13 h near Just to the north of the axis of maximum vertical motion 200 mb above the updraft area (Fig. 14a). The contri- around 300 mb, the C term has become strongly fron- bution to frontogenesis in this area is largely from the togenetical, and over parts of this area both D and T T term and to a smaller extent from the C term. The terms are also frontogenetic. Note also that the axis of tilting term is strong despite weak (mainly downward) total frontogenesis is displaced slightly to the baroclin- vertical motions because the vertical potential temper- ically warm side of the updraft from the axis of max- ature gradients are large. If the subsidence is greater on imum upward vertical motion (Fig. 14a). Emanuel the warmer side than on the cooler side then the T term (1983a) predicted a frontogenetical forcing by the SWC will be frontogenetic. A similar example of frontogen- circulations on the baroclinically warm side of the SWC esis in the middle troposphere in the region of subsi- updraft. dence was discussed by Reed and Sanders (1953). The Sanders and Bosart (1985) investigated the role of potential temperature gradient at 200 mb over the up- large-scale frontogenesis in a heavy snow storm case draft area increased from about 1 K (100 km)Ϫ1 at 10 over the northeastern United States, using mainly ra- h to 6 K (100 km)Ϫ1 at 14 h. Between 10 and 13 h, winsonde data that were located about 250 km apart. upward motion at 200 mb over the cell A area changes They evaluated the geostrophic frontogenesis, and found to downward motion (Fig. 6). Whether the above trans- it to be a maximum [about 1 K (100 km)Ϫ1 (3 h)Ϫ1] near formation and the development of high-level fronto- the surface. Frontogenetical forcing terms are much genesis occurred due to the intensi®cation of lower-level greater in our case (by an order of magnitude); this may vertical motions, or the high-level frontogenesis played

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FIG. 13. Cross sections at 10 h through the area of maximum vertical motion. Vertical motion (dotted, 10 ϫ 10Ϫ3 mb sϪ1 intervals) and frontogenetical forcings (positive solid, negative dashed and shaded, 1 K (100 km)Ϫ1 (3h)Ϫ1 intervals): (a) total, (b) condensational heating term D, (c) tilting term T, and (d) con¯uence term C.

any role in augmenting the intensi®cation of the SWC, experiment as MESOC and the original integration as were not investigated. simply MESO in the following. It was anticipated that the above change in convective parametrization might generate upright parameterized convection from higher 6. Additional results levels in MESOC, and might even induce upright ver- The modi®ed Betts-Miller convective parameteriza- tical motions in the region where slanted vertical mo- tion procedure is invoked in MESO if a parcel located tions developed in the MESO integration. Slanted ver- in the 130-mb thick layer near the ground is condition- tical motions also developed in MESOC. Thus, the de- ally unstable. The parcel with largest equivalent poten- velopment of the SWC in MESO is not affected by tial temperature in the 130-mb layer is used for eval- raising the level (from 130 to 300 mb) from which a uating convective condensation. It was noted in section parcel may originate in the convective parameterization 3a that the condensation in the SWC area is mostly due scheme. to resolvable scales. The base of convective clouds in The data in the additional experiments described in midlatitudes in the real atmosphere is sometimes located this section were saved, as is normally the case, at 3 h at a high level close to 700 mb. It was therefore con- intervals (see section 2). The impact of increasing the sidered judicious to reintegrate MESO increasing the depth of the lowest layer from which parameterized con- layer thickness from which a convective parcel may vective clouds can originate was quite signi®cant, es- originate from 130 mb to 300 mb (nearly the thickness pecially in the nature of rainfall near front S. Rainfall of SWC layer at 10 h in our case). We will refer to this amounts accumulated over 24 h from the initial time

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FIG. 14. Cross sections at 13 h through the area of maximum vertical motion. Vertical motion (dotted, 10 ϫ 10Ϫ3 mb sϪ1 intervals) and frontogenetical forcings (positive solid, negative dashed and shaded, 1 K (100 km)Ϫ1 (3h)Ϫ1 intervals): (a) total, (b) condensational heating term D, (c) tilting term T, and (d) con¯uence term C. were compared. The parameterized convective precip- and front S regions was nearly the same in both ex- itation over the SWC region was negligible in MESOC, periments. and absent in MESO. The area with resolvable-scale The resolvable-scale condensation over land in condensation exceeding 3 cm in the SWC region was MESO is invoked at a RH greater than 0.75 (section 1). larger in MESO than in MESOC. Maximum precipi- This criteria might be contributing to the development tation amounts along front S extending from southern of SWC in MESO, since it allows condensation to occur Louisiana to southern Alabama were somewhat larger at levels (especially higher levels) where the RH is much in MESO than in MESOC. In this region, the precipi- lower than 100% (see Fig. 7). The model was integrated tation was mostly due to the parameterized convection setting the criteria for resolvable condensation to occur in MESOC, whereas as can be seen from Figs. 1c±d if RH exceeds 100% (experiment MESOR). The layer both resolvable and parameterized convective rainfall thickness from which a convective parcel can originate occurred in MESO. Maximum vertical motion in the in MESOR was kept, as in MESOC, at 300 mb. The SWC area at 500 mb was weaker at 12 h in MESOC structure of slanted vertical motions was similar in ME- (Ϫ17 ϫ 10Ϫ3 mb sϪ1) than in MESO (Ϫ44 ϫ 10Ϫ3 mb SOC and MESOR. Thus, the development of SWC does sϪ1); and it was similar at 15 h in MESOC (Ϫ32 ϫ 10Ϫ3 not depend on the value of RH (between 75% and 100%) mb sϪ1), and MESO (Ϫ35 ϫ 10Ϫ3 mb sϪ1). The max- above which resolvable-scale condensation is invoked. imum upward motion at 500 mb in the front S region As in MESOC, the parameterized convective precip- was nearly the same in the two experiments, at both 12 itation over the SWC region was negligible in MESOR. and 15 h. The area with upward motion in the SWC Rainfall amounts (24-h accumulated) were somewhat

Unauthenticated | Downloaded 09/25/21 01:44 AM UTC JANUARY 1999 MATHUR ET AL. 23 greater in MESOR than in MESOC over the SWC and (section 4). Initially a weak slanted updraft formed in front S areas. Parameterized convective precipitation a stably strati®ed shallow layer below 700 mb where amounts over the front S area were smaller in MESOR conditional symmetrically unstable conditions prevailed than in MESOC. The areal coverage and intensity of (Figs. 6a and 8a). At the uppermost level of this CSI upward motion at 500 mb were similar in MESOR and updraft conditionally unstable conditions existed and MESOC over the SWC and front S areas, at both 12 nearly upright upward motions developed. Resolvable- and 15 h. scale condensation occurred in both systems and the vertical motions intensi®ed (Fig. 7). Initially the entire CSI updraft, as well as a portion of the upright updraft, 7. Concluding remarks contained negative moist potential vorticity (Fig. 8a). Data from NCEP's MESO model were utilized to The negative MPV area was lifted upward, especially investigate the evolution of slantwise convection in a in areas where upward motion was stronger. As a result, weak frontal zone. Compared to some previous numer- the slanted motions extended upward to above 700 mb ical (Bennetts and Sharp 1982; Lindstrom and Nordeng between 10 and 12 h. Maximum development occurred

1992; Zhang and Cho 1992) and observational (Sanders by 13 h when ␪e and Mg surfaces nearly coincided (Fig. and Bosart 1985; Seltzer et al. 1985) studies on the 6c, section 4a). This adjustment to near-neutral condi- development of slanted vertical motions, the data uti- tions for slantwise convection takes place with the lift- lized in our study has a high uniform vertical (25 mb), ing and northward displacement of the negative MPV and temporal (1 h), resolution. Although MESO utilizes region away from the SWC area (Fig. 8c). Thus, both a horizontal grid spacing of 29 km, the postprocessed vertical and horizontal advection of MPV affect CSI data were available on a 40-km grid spacing; this hor- updraft intensity. izontal resolution is comparable to those used in other The axis of maximum condensational heating be- numerical studies cited above. Use of high resolution, comes slanted in a fashion similar to the axis of vertical particularly in the vertical, allowed us to better delineate motion ®eld in the SWC area (Fig. 7). Parameterized the zones with conditional and symmetric instabilities (vertical) convective condensation is nearly absent and [see Persson and Warner (1991) for a discussion on condensation is mainly due to the resolvable scales in consistent horizontal and vertical resolution for simu- the SWC area. Another signature of slanted motions lating CSI]. High temporal resolution allowed us to appears in the divergence ®eld. The slanted axis of con- study in detail the time variation of various ®elds (sec- vergence (divergence) lies below (above) the axis of tions 4±5), which provided insight into the frontoge- vertical motion (Fig. 10). The levels of maximum ver- netical and symmetrically unstable conditions that tical motion, divergence, and convergence are displaced evolved in the region of slanted vertical motions. upward during the intensi®cation phase of the slanted Examination of the MESO forecast in the case pre- motions. sented in this paper and other cases suggests that the Strong pressure gradients and geostrophic winds hydrostatic MESO model, without a CSI parameteri- (Fig. 11b) develop above 500 mb to the north (cool) zation procedure included, simulates many features side of the axis of maximum vertical motion mainly found in other observational and numerical studies of because of robust condensational heating gradients. CSI. The slanted updrafts, a characteristic of CSI, are Winds are subgeostrophic (Fig. 11a) in this region, simulated explicitly. Slantwise vertical motions develop however, due to the upward transport of low momen- in the regions with negative moist potential vorticity tum from low levels (Fig. 12). Consequently, negative and stable strati®cation. The condensational heating is absolute vorticity values develop on the north side of associated with resolvable-scale motions and not with the SWC in a deep layer (section 4b). The northward parameterized upright convection. The mesoscale ver- acceleration of winds in the inertially unstable region tical motion ®eld develops into a single band with mul- leads to the northward displacement of negative MPV, tiple embedded updrafts, aligned along the mean ther- and northward extension of the CSI updraft and con- mal wind direction. The buckling in the M surfaces is densation (sections 4a, b). weaker than in the higher resolution nonhydrostatic The development of an elongated band aligned along models. The current horizontal resolution (29 km) is the thermal wind direction (section 3b, Figs. 2c±d) is probably de®cient in simulating the convective mo- therefore likely an expression of conditional symmetric mentum transports; the buckling of M surfaces in some instability (see section 4). The slantwise motions pro- ®ne-mesh nonhydrostatic models arose mainly due to mote frontogenesis along the warm side of the axis of such transports (e.g., see Seman 1994). It is likely that maximum vertical motion at low levels, mainly due to this forecast of CSI would be improved if MESO's hor- an indirect circulation (section 5). The diabatic term is izontal resolution is increased. not included in some studies on frontogenesis because Development of strong slantwise vertical motions be- of nonavailability of condensational heating rates. Cau- tween 10 and 15 h discussed in the case investigated in tion is warranted in interpreting results in such studies, this paper is attributed to a vertical coupling of a low- because frontogenetical forcing due to the diabatic term level CSI updraft with an upper-level convective updraft can be very large in strong updraft regions (Fig. 14b).

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Acknowledgments. We are very grateful to anony- models: Mathematical formulation and solution. J. Atmos. Sci., mous reviewers for their useful comments, one of whom 29, 11±37. Janjic, Z. I., 1994: The step-mountain eta coordinate model: Further provided us a better interpretation of many of our re- development of the convection, viscous sublayer, and turbulence sults, which has led to a considerable improvement in closure schemes. Mon. Wea. Rev., 122, 927±945. the presentation. The authors wish to thank Tom Black, Kanamitsu, M., 1989: Description of the NMC global data assimi- Eric Rogers, and Mike Baldwin for help in integrating lation and forecast system. Wea. Forecasting, 4, 335±342. the MESO model. Knight, D. J., and P. V. Hobbs, 1988: The mesoscale and microscale structure and organization of clouds and precipitation in mid- latitude cyclones. Part XV: A numerical modeling study of front- ogenesis and cold-frontal rainbands. J. Atmos. Sci., 45, 915±930. REFERENCES Koch, S. E., R. E. Golus, and P. J. Dorian, 1988: A mesoscale gravity wave event observed during CCOPE. Part II: Interactions be- Antar, B. N., and W. W. Fowlis, 1983: Three-dimensional baroclinic tween mesoscale convective systems and the antecedent waves. instability of a Hadley cell. J. Fluid Mech., 137, 425±447. Mon. Wea. Rev., 116, 2545±2569. Bennetts, D. A., and B. J. Hoskins, 1979: Conditional symmetric Ley, B. E., and W. R. Peltier, 1978: Wave generation and frontal instabilityÐA possible explanation of frontal rainbands. Quart. collapse. J. Atmos. Sci., 35, 3±17. J. Roy. Meteor. Soc., 105, 945±962. Lindstrom, S. S., and T. E. Nordeng, 1992: Parameterized slantwise , and J. C. Sharp, 1982: The relevance of conditional symmetric convection in a numerical model. Mon. Wea. Rev., 120, 742± instability to the prediction of mesoscale frontal rainbands. 756. Quart. J. Roy. Meteor. Soc., 108, 595±602. Mathur, M. B., 1983: On the use of lower saturation criteria for release Betts, A. K., and M. J. Miller, 1986: A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX of latent heat in NWP models. Mon. Wea. Rev., 111, 1882±1885. and arctic air-mass data sets. Quart. J. Roy. Meteor. Soc., 112, , and M. Baldwin, 1995: Development of vertical and slantwise 693±709. convection in ETA model's forecast for blizzard of 1993. Proc. Bjerknes, J., 1919: On the structure of moving cyclones. Geofys. 10th Conf. on Numerical Weather Prediction, Portland, OR, Publ., 1, 1±8. 108±109. Blanchard, D. O., W. R. Cotton, and J. M. Brown, 1998: Mesoscale Mesinger, F., 1984: A blocking technique for representation of moun- circulation growth under conditions of weak inertial instability. tains in atmospheric models. Riv. Meteor. Aeronaut., 44, 195± Mon. Wea. Rev., 126, 118±140. 202. Bluestein, H. B., 1986: Fronts and jet streaks: A theoretical per- Miller, J. E., 1948: On the concept of frontogenesis. J. Meteor., 5, spective. Mesoscale Meteorology and Forecasting, P. S. Ray, 169±171. Ed., Amer. Meteor. Soc., 173±215. Miller, T. L., and B. N. Antar, 1986: Viscous nongeostrophic baro- Bolton, D., 1980: The computation of equivalent potential temper- clinic stability. J. Atmos. Sci., 43, 329±338. ature. Mon. Wea. Rev., 108, 1048±1053. Molinari, J., and M. Dudek, 1992: Parameterization of convective Bosart, L. F., and F. Sanders, 1986: Mesoscale structure in the Meg- precipitation in mesoscale numerical models: A critical review. alopolitan snowstorm of 11±12 February 1983. Part III: A large- Mon. Wea. Rev., 120, 326±344. amplitude gravity wave. J. Atmos. Sci., 43, 924±939. Newton, C. W., 1950: Structure and mechanism of the prefrontal Busse, F. H., and W. L. Chen, 1981: On the (nearly) symmetric in- squall line. J. Meteor., 7, 210±222. stability. J. Atmos. Sci., 38, 877±880. Parsons, D. B., and P. V. Hobbs, 1983: The mesoscale and microscale Carlson, T. N., 1991: Mid-latitude Weather Systems. HarperCollins structure and organization of clouds and precipitation in mid- Academic, 507 pp. latitude cyclones. Part XI: Comparisons between observational desJardins, M. L., K. F. Brill, S. Jacobs, S. S. Schotz, P. Bruehl, R. and theoretical aspects of rainbands. J. Atmos. Sci., 40, 2377± Schneider, B. Colman, and D. W. Plummer, 1996: N-AWIPS 2399. user's guide, version 5.4. National Centers for Environmental Persson, P. O. G., and T. T. Warner, 1991: Model generation of spu- Prediction, Camp Springs, MD, 308 pp. [Available from NCEP/ rious gravity waves due to inconsistency of the vertical and NCO, W/NP14, Room 301, WWBG, NOAA, 5200 Auth Rd., horizontal resolution. Mon. Wea. Rev., 119, 917±935. Camp Springs, MD 20746-4304.] Reed, R. J., and F.Sanders, 1953: An investigation of the development , S. Jacobs, D. Plummer, and S. Schotz, 1997: N-AWIPS: AWIPS of a mid-tropospheric frontal zone and its associated vorticity at the National Centers for Environmental Prediction. Preprints, ®eld. J. Meteor., 10, 338±349. 13th Int. Conf. on Interactive Information and Processing Sys- Rogers, E., T. L. Black, D. G. Deaven, and G. F. Dimego, 1996: tems for Meteorology, Oceanography, and Hydrology, Long Changes to the operational ``Early'' Eta analysis/forecast system Beach, CA, Amer. Meteor. Soc., 296±298. at the National Centers for Environmental Prediction. Wea. Fore- Einaudi, F., W. L. Clark, D. Fua, J. L. Green, and T. E. VanZandt, casting, 11, 391±413. 1987: Gravity waves and convection in Colorado during July Sanders, F., and L. F. Bosart, 1985: Mesoscale structure in the Meg- 1983. J. Atmos. Sci., 44, 1534±1553. alopolitan snowstorm of 11±12 February 1983. Part I: Fronto- Eliassen, A., 1959: The formation of fronts in the atmosphere. The Atmosphere and the Sea in Motion, B. Bolin, Ed., The Rocke- genetical forcing and symmetric instability. J. Atmos. Sci., 42, feller Institute Press, 277±287. 1050±1061. Emanuel, K. A., 1979: Inertial instability and mesoscale convective Sawyer, J. S., 1956: The vertical circulation at meteorological fronts systems. Part I. Linear theory of inertial instability. J. Atmos. and its relation to frontogenesis. Proc. Roy. Soc. London, 234A, Sci., 36, 2425±2449. 246±262. , 1983a: The Lagrangian parcel dynamics of moist symmetric Schneider, R. S., 1990: Large-amplitude mesoscale wave disturbances instability. J. Atmos. Sci., 40, 2368±2376. within the intense midwest extratropical cyclone of 15 December , 1983b: On assessing local conditional symmetric instability 1987. Wea. Forecasting, 5, 533±558. from atmospheric soundings. Mon. Wea. Rev., 111, 2016±2033. Seltzer, M. A., R. E. Passarelli, and K. A. Emanuel, 1985: The pos- , 1985: Frontal circulations in the presence of small moist sym- sible role of symmetric instability in the formation of precipi- metric stability. J. Atmos. Sci., 42, 1062±1071. tation bands. J. Atmos. Sci., 42, 2207±2219. Haltiner, G. J., and F. L. Martin, 1957: Dynamic and Physical Me- Seman, C. J., 1991: Numerical study of nonlinear convective-sym- teorology. McGraw-Hill, 470 pp. metric instability in a rotating baroclinic atmosphere. Ph.D. the- Hoskins, B. J., and F. P. Bretherton, 1972: Atmospheric frontogenesis sis, University of WisconsinÐMadison, 185 pp. [Available from

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Dept. of Atmospheric and Oceanic Sciences, University of Wis- tional Centers for Environmental Prediction, W/NP, Room 101, consinÐMadison, Madison, WI 53706.] WWBG, NOAA, 5200 Auth Rd., Camp Springs, MD 20746- , 1994: A numerical study of nonlinear nonhydrostatic condi- 4304.] tional symmetric instability in a convectively unstable atmo- Uccellini, L. W., and S. E. Koch, 1987: The synoptic setting and sphere. J. Atmos. Sci., 51, 1352±1371. possible energy sources for mesoscale wave disturbances. Mon. Stobie, J. G., F. Einaudi, and L. W. Uccellini, 1983: A case study of Wea. Rev., 115, 721±729. gravity waves±convective storms interaction: 9 May 1979. J. Wolfsberg, D. G., K. A. Emanuel, and R. E. Passarelli, 1986: Band Atmos. Sci., 40, 2804±2830. formation in a New England winter storm. Mon. Wea. Rev., 114, Stone, P. H., 1966: On non-geostrophic baroclinic stability. J. Atmos. 1552±1569. Sci., 23, 390±400. Xu, Q., 1986: Conditional symmetric instability and mesoscale rain- , 1970: On non-geostrophic baroclinic stability: Part II. J. Atmos. bands. Quart. J. Roy. Meteor. Soc., 112, 315±334. Sci., 27, 721±726. Zhang, D.-L., and H. R. Cho, 1992: The development of negative Thorpe, A. J., and R. Rotunno, 1989: Nonlinear aspects of symmetric moist potential vorticity in the stratiform region of a simulated instability. J. Atmos. Sci., 46, 1285±1299. squall line. Mon. Wea. Rev., 120, 1322±1341. Treadon, R. E., 1993: The NMC Eta Model post processor. A doc- Zhao, Q., and F. H. Carr, 1997: A prognostic cloud scheme for op- umentation. NMC Of®ce Note 394, 44 pp. [Available from Na- erational NWP models. Mon. Wea. Rev., 125, 1931±1953.

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