956 MONTHLY REVIEW VOLUME 132

An Investigation of Extratropical Development Using a Scale-Separation Technique

KENNETH E. PARSONS Department of , Embry±Riddle Aeronautical University, Prescott, Arizona

PHILLIP J. SMITH Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana

(Manuscript received 24 February 2003, in ®nal form 23 October 2003)

ABSTRACT The explosive development phase of an extratropical cyclone (ETC) is examined using output generated by the ®fth-generation PSU±NCAR Mesoscale Model (MM5). A full-physics run of MM5 with 60-km grid spacing was used to simulate the intensive observation period (IOP)-4 of 4±5 January 1989 from the Experiment on Rapidly Intensifying over the Atlantic (ERICA). A diagnosis of the simulated ETC is performed using the Zwack±Okossi (Z±O) equation to examine the forcing mechanisms in¯uencing development. A second- order Shapiro ®lter is used to partition the terms in the Z±O equation into synoptic-scale and subsynoptic-scale contributions to the near-surface synoptic-scale geostrophic vorticity tendency. Results con®rm that previous work using the Z±O equation at coarser resolutions correctly identi®ed synoptic- scale processes as the most important cyclone development mechanisms. However, the results also show that both adiabatic and diabatic subsynoptic thermal processes can make important contributions to synoptic-scale ETC development.

1. Introduction Hoskins 1990, 1999; Reed 1990; Uccellini 1990; Bosart 1999; Volkert 1999). In most respects, the development (i.e., the formation, Today, cyclone development is seen to be related to intensi®cation, and subsequent decay) of extratropical a variety of mechanisms. These mechanisms can be cyclones (ETC) is a well-understood process. That un- grouped into those related to dynamic effects, that is, derstanding has progressed from the thermal theory of cyclonic vorticity advection aloft (Sanders 1986; Mac- that was prominent in the nineteenth cen- Donald and Reiter 1988), vorticity preconditioning tury (Kutzbach 1979), through the theory of (Gyakum et al. 1992), and favorable jet streak posi- cyclones that was developed during the early twentieth tioning (Uccellini et al. 1984; Uccellini and Kocin century by Bjerknes and others (e.g., Bjerknes 1919; 1987); and thermal effects, that is, upper-tropospheric/ Bjerknes and Solberg 1922), continuing with the work lower-stratospheric warm-air advection (Hirschberg and of Sutcliffe (1939, 1947) and Petterssen (1955), and into Fritsch 1991a,b; Lupo et al. 1992), latent heat release contemporary interest in (e.g., (Pauley and Smith 1988; Reed et al. 1988), surface en- Sanders and Gyakum 1980; Roebber 1984; Sanders ergy ¯uxes (Kuo et al. 1991), and reduced static stability 1986; Lupo et al. 1992). Summaries of the progress that (Smith and Tsou 1988). Alternately, cyclogenesis can has been made in understanding the development of be viewed as a response to changing potential vorticity ETCs can be found in the volumes deriving from the (e.g., Davis and Emanuel 1991; Hakim et al. 1996). PalmeÂn Memorial Symposium on Extratropical Cy- These studies are examples of the remarkable pro- clones and the International Symposium on the Life gress that has been made over the past century and a Cycles of Extratropical Cyclones (e.g., Newton 1990; half in scienti®c understanding of the synoptic-scale forcing processes that are important in ETC develop- ment. Yet, an important question regarding ETC de- Corresponding author address: Dr. Kenneth E. Parsons, Embry± Riddle Aeronautical University, 3700 Willow Creek Road, Prescott, velopment remains to be answered, namely, ``What, if AZ 86301. any, is the role of subsynoptic processes in ETC de- E-mail: [email protected] velopment?'' While the synoptic-scale impact of syn-

᭧ 2004 American Meteorological Society

Unauthenticated | Downloaded 09/24/21 12:22 PM UTC APRIL 2004 PARSONS AND SMITH 957 optic-scale ensembles of subsynoptic heating are well More recently, Newton and Holopainen (1990) ob- known, little is known about the impact of individual served, ``A question not explicitly considered at length subsynoptic heating elements nor about the role of sub- in this monograph concerns the feedback of subsynop- synoptic transport processes. This is not to say that the tic-scale features on the larger ¯ow.'' They then pre- potential importance of such processes has gone unrec- dicted, ``It is probably a safe forecast that scale inter- ognized by the scienti®c community. Holopainen and action questions of this type will come up at many meet- Nurmi (1979) warned that ``. . . forcing due to unre- ings in the future.'' Also in that volume, Shapiro and solved horizontal scales may need more attention than Keyser (1990) noted the debate over downscale versus is often believed.'' Using the dense network of rawin- upscale impacts between mesoscale and synoptic-scale sonde stations in Europe to investigate the impact of processes. They further observed that research into scale subgrid-scale processes on upper-air , they ob- interaction processes would and should continue in or- served that the total ¯ow ®eld was stronger than the der to advance the understanding of atmospheric de- smoothed ¯ow ®eld and described this effect as the velopment processes. smoothed ¯ow being ``. . . accelerated by the horizontal To address this question, Rausch and Smith (1996) sub-grid scale processes.'' The speci®c forcing mech- analyzed the Experiment on Rapidly Intensifying Cy- anism was ¯ux convergence of momentum. They further clones over the Atlantic (ERICA) intensive observation advocated the use of output from high-resolution nu- period (IOP)-4 cyclone. They presented a diagnosis that merical models to extend the study of scale interactions included, in addition to synoptic-scale forcing, the role past the use of real data from a synoptic-scale upper- that subsynoptic-scale processes played in extratropical air network. cyclone development. Their analysis looked at forcing Maddox (1980) presented a method of separating me- terms that included the exchange of ``information'' be- teorological data into macroscale and mesoscale com- tween the synoptic scale and subsynoptic scale as rep- ponents. In that study, he observed that a mesoscale resented by vorticity and temperature exchange pro- perturbation, that is, a mesoscale convective system, cesses. The objective of the work described herein is to could interact with the macroscale pattern to suf®ciently further explore the importance of such synoptic/sub- modify the upper-air pattern so as to be detectable in synoptic exchanges using a more successful simulation the synoptic-scale upper-air observations. In studying of the ERICA IOP4 storm. scale interactions with respect to the kinetic energy bud- get, Carney and Vincent (1986) used an enhanced net- work of upper-air observations from one synoptic case 2. Diagnostic technique during the Second European Stratospheric Arctic and a. Diagnostic equation Mid- Experiment (SESAME) ®eld program to examine the in¯uence of organized deep on To conduct the study, the Zwack±Okossi (Z±O) equa- the synoptic-scale ¯ow. They found both signi®cant tion, ®rst introduced in quasigeostrophic form by Zwack generation of kinetic energy at the synoptic scale and and Okossi (1986), is used as the tool to diagnose the dissipation of kinetic energy to the subsynoptic scale. development of an explosively deepening extratropical In addition, they found evidence of momentum transport cyclone. Derived from the equation of state, the vorticity processes that were the result of scale interactions be- equation, and the First Law of Thermodynamics, the tween the synoptic-scale motion ®eld and the subsy- generalized Z±O equation is (see Lupo et al. 1992 for noptic-scale mass ®eld. development)

uץ ␻ץ ␷ץ ␻ץ ␻ץ ␨ 1 ppssRQdpÇץ gds 2 T ϩϩS␻ ϩ ␨ aϪϪ ١ ´ ١pa␨ ) ϪٌϪppV ´ ϭ (ϪV pץ yץ pץ xץ pץ tpstϪ pf͵ ͵ cppץ pp΂΃΂΃ r [ (a) (b) (c) (d) (e) (f) (g)

␨agץ zץץ ␨a gץ ,١p ϫ F ϩ ␤ Ϫ dp ´ Ϫ ␻ ϩ k (t ] (1ץ tץy΂΃ץpfץ (h) (i) (j) (k)

-t is the near-surface geostrophic relative vor- eter; ␨a the absolute vorticity (␨ ϩ f ); ␨ag the ageostrophץ/␨gsץ where 2 ١p andٌp the horizontal del and Laplacian ;ticity tendency; V the horizontal vector; T the ic vorticity temperature; ␻ the vertical motion (dp/dt); p the pres- operators on an isobaric surface; Rd the dry-air gas con- Ϫ1 Ϫ1 sure; ps ϭ 950 mb; pt ϭ 100 mb; f the Coriolis param- stant (287 J kg K ); cp the speci®c heat for air at

Unauthenticated | Downloaded 09/24/21 12:22 PM UTC 958 MONTHLY WEATHER REVIEW VOLUME 132 constant pressure (1004 J kgϪ1 KϪ1); F the frictional verse pressure weighting and double integration of the force; QÇ the diabatic heating rate; S the static stability thermodynamic terms, which when combined reveal p); g the acceleration of grav- that these mechanisms are more heavily weighted whenץ/Tץparameter (RdT/cpp Ϫ y. The terms in (1) are placed lower in the (Rausch and Smithץ/fץity (9.8 m sϪ1); and ␤ ϭ identi®ed as: (a) geostrophic vorticity tendency at p ϭ 1996), con®rming the results of Tracton (1973), Anthes ps; (b) horizontal absolute vorticity advection term; (c) and Keyser (1979), and Gyakum (1983) regarding the horizontal temperature advection term; (d) diabatic heat- release of latent heat. These studies demonstrate that the ing term; (e) adiabatic term; (f) divergence term; (g) three-dimensional distribution of heating can be as im- tilting term; (h) vertical absolute vorticity advection portant as the total amount of heating in determining term; (i) frictional term; (j) beta term; and (k) ageo- ETC development. strophic vorticity tendency term. The adiabatic term represents the cooling (warming) that results from ascent (descent) of air in a column. Because the static stability is nearly always positive b. Explanation of terms (except on small spatial scales), ascent (descent) results Equation (1) can be thought of as a combination of in adiabatic cooling (warming), which in turn forces dynamic and thermodynamic forcing mechanisms. Term surface pressure and geostrophic vorticity changes that (b) and terms (f) through (i) are the dynamic forcing generally are of opposite sign to those induced by the mechanisms, which describe the adjustment of the mass other mechanisms. Thus, the adiabatic term opposes the ®eld to a new momentum ®eld that is altered by vorticity development (decay) forced by the other terms, an effect changing processes. Terms (c) through (e) are the ther- that is less for reduced static stability. modynamic forcing mechanisms, which describe the ad- justment of the momentum ®eld to a new mass ®eld that is altered by temperature-changing processes. Term 3. Filtering (j) arises from the expression of geostrophic relative a. Methodology vorticity and represents the departure of the geostrophic relative vorticity from the vorticity of the geostrophic Holopainen and Nurmi (1979, 1980) encouraged the wind. Term (k) is an adjustment term that represents the investigation of forcing due to unresolved, that is, sub- departure of the geostrophic relative vorticity tendency grid-scale, processes and maintained that the proper from the relative vorticity tendency of the actual wind technique for scale interaction (henceforth referred to ®eld. as synoptic/subsynoptic exchange) studies was to apply The dynamical forcing mechanisms occur in response a horizontal ®ltering procedure on the ``data'' produced to nonuniform changes in the wind ®eld, during which by a high-resolution numerical model. Following Hol- unbalanced motions and corresponding horizontal di- opainen and Nurmi's example, the following scale sep- vergence (convergence) occur as the atmosphere at- aration procedure is used in this paper: tempts to reestablish a balanced state. Divergence (con- (X) ϭ (X) ϩ (XЈ), (2) vergence) aloft in turn forces surface pressure decreases (increases) and surface geostrophic vorticity increases where X is any variable,X the synoptic-scale compo- (decreases). nent, and XЈ the subsynoptic-scale component. This par- The thermodynamic forcing mechanisms alter the titioning was accomplished through the use of a ®lter structure of the upper-level height ®elds which again which when applied to an un®ltered ®eld (X) produced force unbalanced motions, horizontal divergence (con- a ®ltered ®eld (X ). The ®ltered ®eld was then subtracted vergence), and corresponding surface pressure decreases from the un®ltered ®eld to obtain the difference ®eld, (increases). Further, these terms possess two features which represents the subsynoptic-scale component (XЈ). that distinguish them from the dynamical mechanisms. Applying (2), the synoptic-scale Z±O equation, with First is the Laplacian operator, which emphasizes the subsynoptic/synoptic exchange terms contributed by the importance of the horizontal distribution of heating vorticity equation (VSUB) and by the First Law of Ther- (Smith 2000). Second is the combined in¯uence of in- modynamics (TSUB), becomes

Vץ ␨ץ ␨ psץ ١␻ ϫϩVSUB ´ V ϩ ␻ ϩ k ´ ١ ١␨ ϩ ␨ ´ gs ϭ Pd Ϫ V pץ pץ t ͵ aaץ p ΂΃ t Ά []

␨ץ RQdpps Ç (١T ϩ S ␻ ϩϩTSUB ϩ FRIC Ϫ ag dp, (3 ´ ϪٌϪd 2 V tץ fcp͵ p p ΂΃·

Unauthenticated | Downloaded 09/24/21 12:22 PM UTC APRIL 2004 PARSONS AND SMITH 959 where ␨Јץ VЈϩ␻Ј ´ ١␨Јϩ␨Ј١ ´ VSUB ϭ VЈ pץ aa ␨Јץ VЈץ ١␨Ј ´ ١␻Ј ٙ Ϫϩag V ´ ϩ k t aץ pץ΂΃ VЈץ␨Јץ ١␻ ٙ ´ VЈϩ␻ ϩ k ´ ١ ϩ ␨ pץp ΂΃ץ a ␨ץ V ϩ ␻Ј FIG. 1. Response function for a second-order Shapiro ®lter applied ´ ١␨ aaϩ ␨Ј١ ´ ϩ VЈ .p 1000 times to data with a grid spacing of 60 kmץ Vץ (١␻Ј ٙ and (4 ´ ϩ k p b. Filter selectionץ΂΃ ١TЈϩS␻Ј When searching for an appropriate ®lter, one must ´ ١TЈϩSЈ␻ЈϪV ´ TSUB ϭϪVЈ consider both the characteristic response curve of the QÇ Ј ١T ϩ SЈ␻ ϩ . (5) ®lter and the practicality of actually applying the ®lter ´ Ϫ VЈ cp to a given dataset. Ideally, a given ®lter would have a TheFRIC term includes both the synoptic and subsy- rectangular response function, as shown in Rorabaugh noptic-scale frictional effects. A scale analysis of term (1993, p. 54). In this study a second-order Shapiro ®lter (j) in (1) revealed that it was at least one and sometimes (Shapiro 1970) was selected because of previous ex- two orders of magnitude smaller than the geostrophic perience with this ®lter (e.g., Lupo and Smith 1995; relative vorticity. Consequently, it was excluded from Rausch and Smith 1996; Rolfson and Smith 1996). This (3). previous work had produced tested programming rou- The application of (2) to any product term results, tines that were adaptable to the MM5 model output. The when expanded, in four terms. For example, the ex- second-order Shapiro ®lter [see Rausch and Smith panded temperature advection becomes (1996) for the mathematical form] yields the response curve shown in Fig. 1. (١T. (6 ´ ١TЈϩVЈ ´ ١TЈϩV ´ ١T ϩ VЈ ´ V (a) (b) (c) (d) c. Cutoff wavelength determination In (6), term (a) represents synoptic-scale forcing by syn- A further consideration in developing the ®ltering optic-scale processes, term (b) synoptic-scale forcing by methodology was to determine the desired cutoff wave- subsynoptic-scale processes, and terms (c) and (d) syn- length. The Rossby radius of deformation (LR) was used optic-scale forcing by synoptic/subsynoptic exchange. in that determination. According to Bluestein (1992, p. The terms in (6), as well as similar terms in (3), (4), 363), ``The Rossby radius of deformation is the effective and (5), can also be identi®ed with reference to the distance from the location of a disturbance to the region (synoptic-scale variable) and prime (subsynoptic-scale in which the effects of the disturbance are no longer variable) notation. In this manner, term (a) in (6) would felt very much.'' Mathematically, be the bar±bar (bb) term, term (b) the prime±prime (pp) NH term, term (c) the bar±prime (bp) term, and term (d) the L ϭ , (7) R f prime±bar (pb) term. Similarly, terms without a product /␪ץof ®ltered variables, for example, diabatic heating, can where N is the Brunt±VaÈisaÈlaÈ frequency [N ϭ (g z)1/2]; ␪ the potential temperature; z the height; Hץbe identi®ed simply as bar (b) for the synoptic-scale ␪ component and prime (p) for the subsynoptic-scale com- the characteristic vertical scale (i.e., the height of the ponent. The ®nal ®ltering operation, applied to all terms, 150-mb level minus the height of the 1000-mb level); ensures that for each of the forcing terms only the con- and f the Coriolis parameter. The value LR was cal- tribution to synoptic-scale geostrophic vorticity tenden- culated for the model domain for all 36 map times. cy is retained. The exchange terms (VSUB and TSUB) The values ranged from a maximum of 3698 km to a represent the ensemble in¯uence of subsynoptic trans- minimum of 1601 km, with values larger than 2000 port and heating processes on the synoptic-scale geo- km in the vicinity of the ERICA IOP4 storm (discussed strophic vorticity tendency, with enhancement (reduc- in section 5) at all map times. tion) of the vorticity tendency signifying upscale (down- Examination of Fig. 1 reveals that for the second- scale) exchange between the synoptic and subsynoptic order ®lter applied 1000 times to data with a grid spac- scales. ing of 60 km, less than 10% of the information for

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wavelengths shorter than 1000 km is retained in the ratio, water, rainwater, pstar (where pstar ϭ psfc ®ltered data ®elds. In contrast, greater than 85% is re- Ϫ ptop, psfc ϭ surface pressure, and ptop ϭ a constant tained at wavelengths longer than 2000 km. This ®l- 100 mb; i.e., the top of the model domain), ground tering scheme ensures that most of the synoptic-scale temperature, accumulated convective , and information, that is, wavelengths longer than 2000 km, accumulated stable precipitation. will be retained and that nearly all of the subsynoptic- Although Reed et al. (1994) focused on an adiabatic scale information, that is, wavelengths shorter than 1000 simulation of IOP4, they also described a full-physics km, will be removed. Based on this analysis, it seems run that was performed to demonstrate the ability of appropriate to apply the ®lter as described. Coinciden- MM5 to adequately simulate the IOP4 storm. It is the tally, 2000 km corresponds to Orlanski's (1975) bound- results of the full-physics run that were used in this ary between macro-␤ scale (baroclinic waves) and study. The MM5 performed signi®cantly better on this meso-␣ scale (fronts). storm than did the Limited Area Mesoscale Prediction System (LAMPS) model previously used by Rausch and Smith (1996). At the 24-h point in the simulation (0000 4. Data and computational methodology UTC 5 January 1989), MM5 produced a cyclone with a. Data minimum central pressure of 945 mb compared to that of the LAMPS model's 977 mb. The actual storm center To perform an investigation of this nature, a high- was at 936 mb at that point (Neiman and Shapiro 1993). resolution dataset generated by a reliable computer mod- The MM5 also appeared to be superior to the LAMPS el is required, since conventional data usually do not in its location of the storm center, although the MM5 resolve subsynoptic ®elds. Furthermore, to improve the storm movement was somewhat slower than observed initialization of the model and assess its capability to (Fig. 2). simulate a particular synoptic system, it is desirable to obtain a dataset for a cyclone that was intensely ob- b. Computational methodology served both in space and time. The ERICA (Hadlock and Kreitzberg 1988) IOP4 storm that occurred in Jan- The original sigma-coordinate model ®elds were con- uary 1989 is an ideal candidate for such a study. The verted to standard pressure levels at 50-mb increments IOP4 cyclone had a signi®cant amount of nonroutine from 1000 up to 150 mb. In this conversion, a linear data available to verify the actual development of the log p interpolation scheme was used, and sea level pres- storm (Neiman and Shapiro 1993). These data were also sure and pressure level heights were calculated. This intended to improve the performance of numerical mod- conversion was necessary to ensure compatibility with els, especially mesoscale models, simulating the storm. the coordinate system (isobaric) used in (3). In addition, Purdue's Synoptic Research Group had pre- Once the model output was in the proper format, viously studied the storm and felt that this knowledge Z±O equation calculations were initiated. The ®rst step would bene®t this study (Rausch and Smith 1996). was to calculate vertical motion, omega (␻ ϭ dp/dt), The National Center for Atmospheric Research using the kinematic method, which involves vertically (NCAR) provided the dataset used in this study, which integrating the continuity equation. A problem of cu- is output from the ®fth-generation Pennsylvania State mulative bias error is commonly encountered when us- University±NCAR Mesoscale Model, version 1 ing the kinematic method to calculate vertical motions (MM5V1; Grell et al. 1994). MM5 had previously been based on radiosonde data (Chien and Smith 1973). How- successfully used to simulate the ERICA IOP4 storm ever, this problem was not evident in this study when (e.g., Reed et al. 1994). pro®les of vertical motion were examined, presumably The MM5 simulation of ERICA IOP4 used a ®xed because continuity is satis®ed in the model ®elds, data staggered Arakawa B-grid (79 ϫ 139 grid points) at 60- errors are absent in the model horizontal wind ®eld, and km resolution with 23 layers in the vertical. The model truncation errors are reduced by the use of high-reso- was run in full-physics mode for a 36-h period after lution data and fourth-order ®nite differencing. initialization at 0000 UTC 4 January 1989. In that mode, Diabatic heating was calculated using the following the model included explicit predictions of cloud water, form of the First Law of Thermodynamics (Holton 1992, rainwater, and ice for the resolvable-scale precipitation, p. 60): Tץ a cumulus parameterization scheme developed by Grell QÇ (T Ϫ S␻, (8 ١ ´ the boundary layer model of Blackadar (1979), ϭϩV ,(1993) c t p ץ surface sensible and latent heat ¯uxes, and surface fric- p -t is the Eulerian temperature tendency, calץ/Tץ tion. Even though the full-physics run of MM5 con- where tained surface sensible and latent heat ¯uxes and surface culated using a 1-h backward ®nite-difference approx- friction, no data regarding those processes were explic- imation. Boundary layer friction was calculated by the itly saved as part of the model output history variables. method of Krishnamurti (1968), using the drag coef®- The variables available at 1-h intervals in the output cient based on an algorithm from the Goddard Labo- were u and ␷ wind components, temperature, mixing ratory for General Circulation Model (see

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FIG. 2. The 6-h positions and central pressures (mb; hundreds digit omitted) of observed IOP4 cyclone (open circles) and cyclone in the full-physics simulation (heavy squares). Solid and dashed lines depict the paths of the observed storm and the full-physics simulation, respectively. Corresponding times of the positions of the observed and the full-physics cyclone are indicated (after Reed et al. 1994).

Kalnay et al. 1983). A linear decrease of drag coef®cient ®nite differencing, and vertical integrals were estimated with height was assumed, with a value of zero at 850 by the trapezoidal rule. mb and above. The ageostrophic vorticity tendency was The three-dimensional wind ®eld, u, ␷, and ␻, and also calculated using a 1-h backward ®nite difference. temperature ®eld were ®ltered to obtain the bar and Horizontal derivatives were calculated by fourth-order prime ®elds [See Eq. (2)]. These ®elds were then used to calculate the vorticity advection, temperature advec- tion, adiabatic temperature change, vertical vorticity ad- vection, tilting, and divergence terms in (3), (4), and (5). The total diabatic heating, friction, and the ageo- strophic tendency ®elds were also ®ltered to obtain their respective bar and prime components.

5. Synoptic discussion Due to its extremely low sea level pressure and ex- plosive deepening rate, the ERICA IOP4 storm has been one of the most intensely studied of all time. Neiman and Shapiro (1993) and Reed et al. (1994) pre- sent a detailed discussion of the development of the storm. These studies analyze the large array of data provided by standard observing systems and also by special in situ and remote observing systems. Unique features of the IOP4 storm are the low pressure of 936 mb, the 24-h deepening rate of 60 mb, and a warm core that was structurally analogous to that observed in trop- ical cyclones. MM5 was initialized at 0000 UTC on 4 January 1989 and produced a surface cyclone of 997 mb. By 0600 FIG. 3. Sea level pressure for the IOP4 observed cyclone (lower UTC 5 January 1989, 30 h into the simulation, the sea curve), for the MM5-total cyclone (middle curve), and for the MM5 synoptic-scale cyclone (top curve), where ``total'' indicates the total level pressure had decreased to 941 mb. In comparison, model-derived pressure and ``synoptic scale'' indicates the ®ltered or the synoptic-scale (®ltered) cyclone had a central pres- synoptic-scale contribution to the total model-derived pressure. sure of 998 mb at initialization and deepened to 955

Unauthenticated | Downloaded 09/24/21 12:22 PM UTC 962 MONTHLY WEATHER REVIEW VOLUME 132 mb geopotential height (solid, ), and (d) 200-mb geopotential height (solid, m) and temperature (dashed, K). Black dot shows position of cyclone center. 1 Ϫ s 5 Ϫ m) and absolute vorticity (dashed, 10 . 4. The 1200 UTC 4 Jan 1989 synoptic-scale (a) sea level pressure (mb), (b) 850-mb geopotential height (solid, m) and temperature (dashed, K), (c) 500- IG F

Unauthenticated | Downloaded 09/24/21 12:22 PM UTC APRIL 2004 PARSONS AND SMITH 963 . 5. As in Fig. 4 except for 1200 UTC 5 Jan 1989. IG F

Unauthenticated | Downloaded 09/24/21 12:22 PM UTC 964 MONTHLY WEATHER REVIEW VOLUME 132 position of cyclone center. ) for 1200 UTC 4 Jan 1989 where (a) analyzed, (b) Z±O total, (c) Z±O synoptic scale, and (d) Z±O subsynoptic scale. Black dot shows 2 Ϫ s 9 Ϫ . 6. Geostrophic vorticity tendency (10 IG F

Unauthenticated | Downloaded 09/24/21 12:22 PM UTC APRIL 2004 PARSONS AND SMITH 965 . 7. As in Fig. 6 except 1200 UTC 5 Jan 1989. IG F

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TABLE 1. Mean absolute values (MAV; 10Ϫ9 sϪ2) of geostrophic vorticity tendencies and correlation coef®cients (CC) for the entire domain for all computational times. MAV Z±O synoptic CC total to CC synoptic scale H MAV analyzed MAV Z±O total Delta scale Delta analyzed to analyzed 3 2.06 2.06 0.00 1.67 0.39 0.98 0.95 6 1.74 1.71 0.03 1.28 0.46 0.97 0.93 9 1.48 1.54 0.06 1.23 0.25 0.95 0.93 12 1.37 1.52 0.15 1.22 0.15 0.94 0.91 15 1.53 1.66 0.13 1.39 0.14 0.93 0.92 18 1.20 1.14 0.06 1.05 0.15 0.93 0.89 21 1.15 1.19 0.04 1.09 0.06 0.92 0.89 24 0.90 0.96 0.06 0.96 0.06 0.91 0.85 27 1.55 1.51 0.04 1.30 0.25 0.96 0.90 30 1.08 1.12 0.04 1.02 0.06 0.94 0.89 33 0.97 1.06 0.09 0.98 0.01 0.92 0.86 36 0.83 0.94 0.11 0.90 0.07 0.89 0.77

Note: Delta represents the absolute value of the difference between Z±O calculated MAVs and analyzed MAVs. mb at 30 h. Figure 3 shows the central sea level pressure become oriented north to south just west of 70ЊW. The for the observed IOP4 cyclone, as well as for both the 500-mb vorticity maximum had intensi®ed over the pre- total and synoptic-scale model-derived IOP4 storm. Be- vious 12 h from 20 to 22 ϫ 10Ϫ5 sϪ1 and moved to a cause the emphasis in this study is the impact on the position just southwest of the surface cyclone, sug- synoptic-scale development, the discussion that follows gesting strong cyclonic vorticity advection (CVA) over will focus on the ®ltered MM5 output. the surface cyclone. The 200-mb had also deep- Figures 4 and 5 show analyses of the ®ltered (syn- ened and moved eastward to become oriented meridi- optic-scale) MM5 output for 1200 UTC 4 and 5 January onally along 75ЊW, inferring more pronounced strato- 1989, which highlight the surface and upper-air features spheric WAA. of the IOP4 storm during the time of maximum central Over the ensuing 18 h the IOP4 storm experienced a pressure decrease and after development has ceased, re- further central pressure decrease of 19 mb to 955 mb spectively. Surface cyclone positions and central pres- as it continued to move northeastward. The total pres- sures are summarized in Figs. 2 and 3. By 1200 UTC sure decrease of 43 mb over the 30-h period represents 4 January 1989 (Fig. 4), the surface cyclone had moved a deepening rate of 2.0 Bergerons (see Sanders and from coastal to the warm waters of the Gyakum 1980 for de®nition) at 38ЊN. By 1200 UTC 5 near 36.5ЊN, 66.4ЊW and had experienced January 1989, the IOP4 storm had passed the period of a 12-h deepening of 24 mb to 974 mb. A closed low rapid deepening and was now entering the dissipation was also present at 850 mb and, with its position just stage. The surface low was at 956 mb and had moved northwest of the surface low, appeared to produce low- north-northeast to a position just south of Newfoundland level warm-air advection (WAA) into the cyclone sys- (Fig. 5). Although the 850-mb low had deepened by an tem. Also of note is the 850-mb cold-air advection additional 34 m over the previous 12 h, the ¯ow and (CAA) that is evident to the west of the system. A isotherm patterns suggested CAA into the storm envi- deepening 500-mb short wave had moved offshore to ronment. At this time, the system was vertically stacked

TABLE 2. Mean absolute values (MAV; 10Ϫ9 sϪ2) of geostrophic vorticity tendencies and correlation coef®cients (CC) for the limited domain for all computational times. MAV Z±O synoptic CC total to CC synoptic scale H MAV analyzed MAV Z±O total Delta scale Delta analyzed to analyzed 3 3.62 4.76 1.14 3.34 0.28 0.99 0.95 6 3.62 3.25 0.37 3.15 0.47 0.97 0.91 9 4.18 3.32 0.86 3.02 1.15 0.98 0.99 12 4.58 3.97 0.61 3.51 1.07 0.94 0.95 15 5.09 4.35 0.74 3.66 1.43 0.95 0.98 18 5.58 4.44 1.13 4.10 1.48 0.96 0.97 21 5.82 5.09 0.73 4.00 1.82 0.96 0.97 24 5.45 4.68 0.77 3.94 1.51 0.97 0.95 27 7.48 6.96 0.52 5.06 2.42 0.99 0.98 30 6.22 6.07 0.14 4.20 2.01 0.99 0.97 33 5.23 5.45 0.23 3.79 1.43 0.99 0.96 36 4.12 4.78 0.66 3.21 0.91 0.99 0.95

Note: Delta represents the absolute value of the difference between Z±O calculated MAVs and analyzed MAVs.

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TABLE 3a. Mean absolute values (MAV; 10Ϫ9 sϪ2) of geostrophic vorticity tendencies for the limited domain for all computational times. Included terms are vorticity advection (vortadv), temperature advection (tempadv), diabatic heating (Qdot), adiabatic term (adiabatic), and divergence. Important contributing terms (see text for explanation) are in bold font. Vortadv Tempadv Qdot Adiabatic Divergence H bb bp pb pp bb bp pb pp bp bb bp pb pp bb bp pb pp 3 1.62 0.34 0.04 0.06 1.30 0.27 0.23 0.10 0.60 1.42 0.93 0.47 0.07 0.09 0.33 0.03 0.18 0.04 6 1.43 0.29 0.08 0.34 1.64 0.48 0.19 0.15 1.42 1.27 2.33 1.10 0.09 0.08 0.33 0.06 0.23 0.28 9 1.47 0.37 0.08 0.23 2.34 0.61 0.31 0.25 2.08 1.21 2.96 1.30 0.12 0.14 0.31 0.04 0.21 0.18 12 1.53 0.46 0.12 0.61 2.58 0.78 0.43 0.29 2.78 1.57 3.83 1.55 0.14 0.13 0.32 0.08 0.17 0.44 15 1.61 0.63 0.13 0.53 2.94 0.84 0.56 0.25 3.39 1.83 4.04 2.04 0.17 0.10 0.26 0.08 0.14 0.38 18 1.72 0.73 0.15 0.53 2.88 0.66 0.53 0.34 3.38 2.00 3.91 2.25 0.19 0.14 0.23 0.08 0.15 0.38 21 1.94 0.85 0.16 0.41 3.37 0.79 0.66 0.35 2.75 1.61 3.63 1.92 0.24 0.18 0.23 0.07 0.18 0.29 24 1.93 0.68 0.12 0.39 3.83 0.88 0.74 0.31 2.39 1.58 3.36 2.06 0.24 0.29 0.20 0.06 0.17 0.23 27 1.94 0.68 0.09 0.25 3.77 0.89 0.69 0.34 2.00 1.48 3.21 1.87 0.22 0.29 0.17 0.06 0.14 0.17 30 1.80 0.73 0.08 0.15 3.55 0.84 0.63 0.19 1.65 1.13 2.68 1.50 0.17 0.16 0.15 0.05 0.16 0.09 33 1.64 0.68 0.09 0.20 3.12 0.88 0.55 0.29 1.45 1.29 2.81 1.63 0.14 0.09 0.18 0.06 0.19 0.12 36 1.47 0.54 0.07 0.19 2.56 0.75 0.46 0.17 1.20 0.80 2.30 1.18 0.10 0.11 0.22 0.07 0.19 0.12

Note: The ``b'' denotes bar or synoptic-scale contribution, and ``p'' denotes prime or subsynoptic-scale contribution as in Eqs. (3), (4), and (5). through 500 mb, and the position of the 500-mb vorticity The Z±O calculated geostrophic vorticity tendencies maximum coincided with the position of the surface were calculated at 3-h intervals and then compared to cyclone. Although the 200-mb trough continued to the analyzed tendencies. A sample of the results for deepen, the warm pool was nearly over the surface cy- 1200 UTC 4 January and 1200 UTC 5 January 1989 clone, suggesting that the stratospheric WAA was now are shown in Figs. 6 and 7, with the center of the syn- ahead of the surface cyclone. optic-scale cyclone provided for reference. These results are representative of the results obtained at all map 6. Results times. Visual inspection reveals strong correlation in both pattern and magnitude between the total Z±O ten- a. Basic Z±O results dencies and the analyzed tendencies. This strong cor- As a check for computational accuracy, ``analyzed'' relation also applies to a comparison of synoptic-scale geostrophic vorticity tendencies were determined at 3-h Z±O tendencies (sum of all synoptic-scale terms) with intervals using the MM5 ®elds, which were available the analyzed tendencies. Notice that the surface cyclone every hour. The geostrophic vorticity was calculated by is clearly within the analyzed positive-tendency region taking the Laplacian of the height ®eld and then ®ltering at 1200 UTC 4 January 1989 (Fig. 6a), when it was to obtain the synoptic-scale analyzed geostrophic vor- experiencing explosive deepening. The cyclone is also ticity. Tendencies were then calculated using a 1-h back- in the positive region of the Z±O total and synoptic- ward ®nite difference. scale tendencies (Figs. 6b,c). By 1200 UTC 5 January

TABLE 3b. Mean absolute values (MAV; 10Ϫ9 sϪ2) of geostrophic vorticity tendencies for the limited domain for all computational times. Included terms are tilting term (tilting), vertical vorticity advection (vert vortadv), friction (fric), ageostrophic tendency (ageo), Z±O terms, and analyzed (anal). Important contributing terms are in bold font. Tilting Vert vortadv Fric Ageo Z±O H bb bp pb pp bb bp pb pp bp bp b p tot Anal 3 0.11 0.01 0.04 0.07 0.07 0.03 0.02 0.07 0.11 0.02 1.45 0.62 3.34 1.65 4.76 3.62 6 0.29 0.04 0.18 0.38 0.08 0.06 0.08 0.39 0.19 0.03 1.47 0.44 3.15 1.18 3.25 3.62 9 0.38 0.04 0.15 0.31 0.16 0.08 0.07 0.31 0.24 0.04 1.67 0.28 3.02 0.78 3.32 4.18 12 0.43 0.06 0.18 0.56 0.27 0.12 0.10 0.64 0.34 0.06 0.85 0.33 3.51 1.49 3.97 4.58 15 0.43 0.10 0.21 0.63 0.38 0.17 0.13 0.70 0.43 0.07 1.18 0.46 3.66 1.87 4.35 5.09 18 0.43 0.09 0.26 0.24 0.43 0.18 0.12 0.42 0.49 0.06 1.38 0.42 4.10 1.71 4.44 5.58 21 0.39 0.07 0.21 0.16 0.44 0.15 0.09 0.23 0.53 0.07 0.51 0.59 3.99 1.73 5.09 5.82 24 0.26 0.06 0.16 0.26 0.34 0.12 0.06 0.39 0.57 0.08 0.40 0.51 3.94 1.67 4.68 5.45 27 0.22 0.05 0.12 0.19 0.31 0.10 0.05 0.27 0.59 0.09 1.76 0.98 5.06 2.34 6.96 7.48 30 0.17 0.05 0.10 0.06 0.25 0.10 0.04 0.14 0.61 0.09 0.86 0.67 4.20 2.20 6.07 6.22 33 0.15 0.06 0.08 0.26 0.24 0.11 0.07 0.31 0.61 0.08 0.76 0.56 3.79 2.04 5.45 5.23 36 0.14 0.05 0.07 0.26 0.21 0.09 0.06 0.29 0.61 0.09 0.63 0.51 3.21 2.06 4.78 4.12

Note: The ``b'' denotes bar or synoptic-scale contribution, and ``p'' denotes prime or subsynoptic-scale contribution as in Eqs. (3), (4), and (5).

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TABLE 4. Geostrophic vorticity tendencies (10Ϫ9 sϪ2) at the cyclone center for the ``important'' terms and for the Z±O synoptic-scale, subsynoptic-scale, and total. Yort adv Temp adv Qdot Adiabatic Ageo Z±O H bb bb bp bp bb bp b b p tot 3 2.67 2.05 0.13 Ϫ0.73 1.49 Ϫ1.02 Ϫ0.27 1.48 4.86 1.58 6.44 6 2.43 2.65 0.23 2.90 1.20 Ϫ5.29 Ϫ2.43 1.32 4.12 Ϫ1.60 2.52 9 2.55 2.57 Ϫ0.34 4.92 3.07 Ϫ5.97 Ϫ3.49 Ϫ2.07 2.30 Ϫ0.15 2.15 12 2.45 1.23 Ϫ0.99 6.31 3.19 Ϫ7.57 Ϫ3.27 1.11 3.53 Ϫ1.89 1.65 15 2.57 0.74 Ϫ1.38 7.70 3.84 Ϫ7.94 Ϫ3.60 Ϫ1.14 1.73 Ϫ2.44 Ϫ0.71 18 2.17 Ϫ0.58 Ϫ1.52 6.58 1.91 Ϫ6.62 Ϫ2.51 2.38 3.39 Ϫ1.59 1.79 21 2.20 Ϫ0.33 Ϫ1.20 5.54 3.25 Ϫ5.29 Ϫ2.34 0.74 2.37 1.45 3.82 24 1.13 Ϫ2.07 Ϫ1.08 3.79 1.28 Ϫ2.04 Ϫ1.37 0.35 0.59 Ϫ0.58 0.01 27 1.01 Ϫ1.41 Ϫ0.13 3.03 0.91 Ϫ2.55 Ϫ1.87 0.09 Ϫ0.46 Ϫ0.71 Ϫ1.17 30 0.36 Ϫ1.59 0.31 2.91 1.42 Ϫ1.88 Ϫ1.55 0.14 Ϫ0.56 Ϫ0.38 Ϫ0.94 33 0.04 Ϫ1.24 Ϫ0.71 2.00 2.61 Ϫ1.16 Ϫ2.14 Ϫ0.45 Ϫ1.34 Ϫ2.42 Ϫ3.77 36 0.02 Ϫ0.26 Ϫ0.37 1.22 1.88 Ϫ1.36 Ϫ2.34 Ϫ0.54 Ϫ1.56 Ϫ1.96 Ϫ3.52

Note: The ``b'' denotes bar or synoptic-scale contribution, and ``p'' denotes prime or subsynoptic-scale contribution as in Eqs. (3), (4), and (5).

1989 (Figs. 7a±c), the cyclone has entered the dissi- (Figs. 6d and 7d). Only at the 3-h point in the model pation stage and is situated within the negative-tendency simulation (0300 UTC 4 January 1989; not shown) was region for the analyzed, Z±O total, and Z±O synoptic- the cyclone within an area of signi®cantly positive sub- scale tendencies. synoptic-scale geostrophic vorticity tendencies. This in- With regard to the subsynoptic-scale contribution to ¯uence changed by the 6-h simulation point. By 1200 the Z±O geostrophic vorticity tendency, notice that the UTC 4 January 1989 (Fig. 6d), the cyclone was em- cyclone is within the negative region at both map times bedded in a region of strong negative subsynoptic-scale tendencies. The subsynoptic-scale processes are impor- tant in the earliest stage of development in contributing to explosive development. Thereafter, they quickly act to limit development and prohibit an even stronger ex- plosive deepening than that observed with the IOP4 cyclone. A more quantitative comparison of analyzed, total, and synoptic-scale geostrophic vorticity tendencies is presented in Table 1. Shown are the mean absolute val- ues (MAV) for these quantities for the entire domain, as well as correlation coef®cients (CC) between the Z±O total and synoptic-scale geostrophic vorticity tendencies and the analyzed. Note that the Z±O total and synoptic- scale MAVs are both similar in magnitude to the ana- lyzed, but that the total MAV is consistently closer in value to the analyzed than is the synoptic scale. In ad- dition to all of the CCs being exceptionally high, that is, generally 0.9 or greater, the CCs for the Z±O total to the analyzed geostrophic vorticity tendency are higher than those for the Z±O synoptic scale to the analyzed. Thus, the inclusion of subsynoptic forcing processes improves the comparison between the Z±O and analyzed geostrophic vorticity tendencies. The statistics in Table 1, calculated using the entire domain, demonstrate the ability to obtain reliable results using the computational methodologies employed in this study. With that demonstrated, the focus was then shift- ed to the immediate cyclone environment, consisting of a computational domain of 16 ϫ 16 grid spaces centered on the cyclone center. This was done for three reasons. FIG. 8. Geostrophic vorticity tendencies (10Ϫ9 s Ϫ2) due to advection by synoptic-scale wind of synoptic-scale vorticity. Map times are Jan The ®rst was to examine in greater detail the region 1989. Black dot shows position of cyclone center. where the forcing mechanisms were most important in

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FIG. 9. As in Fig. 8 except advection by synoptic-scale wind of (a), (c) synoptic-scale temperature and (b), (d) subsynoptic-scale temperature. directly affecting the development of the IOP4 cyclone. nitude similarity of MAVs, and the high CCs. For this The couplet of high and low geostrophic vorticity ten- subdomain, the delta values are larger but so also are dencies near the cyclone center seen in Figs. 6 and 7 the CCs when compared to values in Table 1. Also, at was considered to be indicative of this region, and the 7 of the 12 map times, the CCs between the Z±O total display area was adjusted to capture this couplet through and the analyzed is higher than between the Z±O syn- the 36-h simulation. This region included nearly all of optic scale and analyzed. the area where there were cyclonically curved isobars around the IOP4 cyclone, especially in the early stages b. Determination of important terms of development, when the cyclone was still relatively compact. The second reason, and directly related to the Due to the number of terms involved and the number ®rst, was to examine the area where the ``signal'' was of map times for which calculations were made, it be- the strongest. Even at the earliest stages of development, came obvious that some method of summarizing all of Z±O geostrophic vorticity tendencies were larger in the the results and then focusing on a fewer number of vicinity of the IOP4 cyclone than elsewhere in the do- important terms was required. Table 3 presents the MAV main. The third reason was to use the limited display of the geostrophic vorticity tendency for all 30 terms area to assist in choosing a region over which to cal- calculated using the Z±O equation (3). The table in- culate statistical parameters. This was done to reduce cludes values for all 12 map times within the subdomain the in¯uence that the propagation of spurious ``infor- speci®ed above for Table 2. In addition, the MAV for mation,'' as commonly occurs when employing a mul- the Z±O total, Z±O synoptic-scale, Z±O subsynoptic- tiple ®lter application methodology, might have on the scale, and analyzed geostrophic vorticity tendencies are interpretation of results, either subjectively through vi- included. Terms that have been deemed important con- sual inspection of displayed results or objectively tributors to development, that is, to the Z±O total, are through calculations of statistical parameters. in bold font. Importance is de®ned as having a mag- Similar to Table 1, Table 2 shows statistical compar- nitude of 0.75 or greater for six or more map times. isons for the limited computational domain. The values Therefore, the important terms are those that are con- presented lead to similar conclusions regarding the mag- sistently of order 1 ϫ 10Ϫ9 sϪ2. Using the terminology

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FIG. 10. As in Fig. 8 except (a), (c) synoptic-scale diabatic heating and (b), (d) subsynoptic-scale diabatic heating. introduced in section 3a, the important terms at the syn- ically around the cyclone, the latter in response to the optic scale are vorticity advection bb, temperature ad- upper-air¯ow becoming closed, as the cyclone matures. vection bb, diabatic heating b, adiabatic term bb, and These results are similar to those presented by Lupo et ageostrophic vorticity tendency b. Important subsynop- al. (1992) and can be related to the approach and even- tic-scale terms are temperature advection bp, diabatic tual superposition of the midtropospheric vorticity max- heating p, and the adiabatic term bp. imum over the surface cyclone as it matures. In contrast to the vorticity advection, the synoptic- scale temperature advection by the synoptic-scale wind c. Forcing processes is positive (integrated WAA) through only the ®rst 15 Table 4 presents the geostrophic vorticity tendencies h of the simulation and then becomes negative, as cold of the important terms and the Z±O synoptic scale, sub- air becomes entrained in the cyclone (Table 4). However, synoptic scale, and total at the cyclone center. In ad- note that the negative contribution is not signi®cant until dition, maps of the important terms are presented to the 24-h point (0000 UTC 5 January), 6 h before min- show the distribution and progression of the contrib- imum pressure. Figures 9a and 9c show a maximum and uting processes over the limited display domain for the minimum tendency couplet forced by synoptic-scale same two map times previously displayed. temperature advection that moves somewhat down- Table 4 reveals that synoptic-scale vorticity advection stream from and rotates cyclonically around the surface by the synoptic-scale wind makes a positive contribution cyclone, in response to the rotation of the warm and (integrated CVA) to development at all map times. After cold air around the cyclone. With both the vorticity and a strong contribution early in the simulation, it steadily temperature advection, the maxima increase in magni- weakens after the 21-h point (2100 UTC 4 January, 9 tude from the 12-h point (1200 UTC 4 January) to the h before minimum pressure) and becomes negligible at 24-h point (0000 UTC 5 January; not shown) and then the 33-h point (0900 UTC 5 January) as the cyclone decrease to the 36-h point (1200 UTC 5 January). The enters the dissipation stage. Figure 8, which displays temperature advection bp contribution (Table 4 and Figs. the distribution of this term at the two map times, shows 9b,d) shows that after 9 h of simulation synoptic-scale a vorticity advection maximum that is located ahead of, winds couple with the subsynoptic temperature ®eld to propagates downstream faster than, and rotates cyclon- produce an important, although generally smaller in

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FIG. 11. As in Fig. 8 except in¯uence of (a), (c) synoptic-scale vertical motion and (b), (d) subsynoptic-scale vertical motion on synoptic-scale static stability. magnitude than the synoptic term, reduction (downscale in the warm sector may re¯ect downward sensible heat exchange) in the cyclone's synoptic-scale geostrophic transfer to the cooler , a conclusion similar to that vorticity. This re¯ects the ensemble in¯uence of the of Danard and Ellenton (1980). Interestingly, despite synoptic-scale wind advecting subsynoptic colder air the low-level advection of cold air from the continent into the cyclone environment. west of the cyclone and the expected upward sensible With the exception of the synoptic-scale term at the heat transfer, the geostrophic vorticity tendencies are 3-h point, diabatic heating contributed positively and negative. This may re¯ect the indirect in¯uence of the strongly throughout the entire simulation. The synoptic- adjacent latent heating region. This can occur because scale term is especially strong from the 9-h (0900 4 the integrated divergence forced by the heating can yield January) through 27-h (0300 5 January) points in the integrated convergence and surface geostrophic vortic- simulation, while upscale exchange from subsynoptic ity decreases in areas adjacent to the heating area that diabatic heating is seen throughout the period. The de- is suf®ciently strong to overwhelm the effect of any in piction of the two terms in Fig. 10 re¯ects the direct situ heating. This re¯ects the in¯uence of the Laplacian impact of the synoptic-scale heating ®eld (Figs. 10a,c) operator on the heating quantity, as noted by Danard and the ensemble in¯uence on the synoptic scale of the and Ellenton (1980) and discussed by Smith (2000). The subsynoptic heating components (Figs. 10b,d). Since the role of sensible heating of the advecting cold air appears heating was determined from the First Law of Ther- to be more strongly felt in the subsynoptic term, with modynamics, detailed examination of individual terms a large positive tendency east of the Carolinas on 4 is not possible. However, the patterns in Fig. 10 do January (Fig. 10b) and south of Maine on 5 January suggest certain heating features. Figures 10a,c show (Fig. 10d). In addition to latent heating in¯uences, the synoptic-scale positive surface geostrophic vorticity positive area centered over the cyclone on 5 January tendency areas due to heating that initially maximize may also re¯ect the in¯uence of upward sensible heat near the cyclone center and then eventually move some- transfer, as noted by Giordani and Caniaux (2001) for what downstream. Both positive areas suggest the in- the interior of an occluded marine cyclone. ¯uence of latent heat release associated with the cyclone The two important adiabatic terms re¯ect the impact and associated . The negative-tendency areas of both synoptic-scale and subsynoptic-scale vertical

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terms, that is, strongly positive early in the development period, then weakening or becoming negative midway through the period. The combined Z±O subsynoptic- scale contributions (Z±O p) show a negative contribu- tion to development at all but two of the map times (0300 UTC 4 January and 2100 UTC 4 January). The sum of these two, Z±O tot, also shows the strong con- tribution to development at 0300 UTC 4 January made by all of the forcing processes. The total term brie¯y becomes negative at 1500 UTC 4 January (3 h), as the subsynoptic terms brie¯y become dominant, and then resurges to a secondary maximum at 2100 UTC 4 Jan- uary (21 h), in phase with the change in sign of the subsynoptic terms. The Z±O total term then weakens, becomes negative by 0300 UTC 5 January (27 h), and remains negative through the remainder of the simu- lation in concert with synoptic-scale and subsynoptic- scale terms.

7. Discussion and conclusions A detailed analysis of a model-simulated rapidly deepening extratropical cyclone (ETC) was conducted using an expanded form of the Zwack-Okossi (Z±O) equation. The Z±O equation was expanded by parti- tioning the individual variables in the equation into syn- optic and subsynoptic-scale components. The expanded Z±O equation was then used to diagnose the contribu-

FIG. 12. As in Fig. 8 except synoptic-scale ageostrophic vorticity tion to development made by the 30 terms in the equa- tendency. tion. The data used in the study consisted of model output from a full-physics run of the MM5 model in which the motions on the synoptic-scale static stability ®eld. The ERICA IOP4 cyclone was simulated. Each variable in adiabatic temperature change implied in both of these the model output was ®rst partitioned into synoptic and terms opposes the cyclone's development throughout the subsynoptic-scale components through the use of a sec- entire simulation (Table 4). The similarity between the ond-order Shapiro ®lter. The variables were then used adiabatic term patterns in Fig. 11 and the corresponding to calculate the terms in the Z±O equation. These ver- diabatic heating (Fig. 10) and temperature advection tically integrated results were ®ltered again to eliminate (Fig. 9) terms suggests the dominance of these thermal any subsynoptic-scale contribution that may have been processes in forcing the vertical motion ®eld. introduced through aliasing. The synoptic-scale ageostrophic vorticity tendency Based on the results presented in section 6, several term varied markedly during the simulation, from pro- conclusions become evident. The synoptic-scale vortic- viding a signi®cant positive contribution, to a signi®cant ity advection, temperature advection, diabatic heating, negative contribution, to a negligible contribution (Table and adiabatic term were always important. This con®rms 4). This general decrease in magnitude as the cyclone that previous work using the Z±O equation, most of matured and presumably achieved a more balanced state which examined only synoptic-scale in¯uences at coars- is illustrated by the reduced magnitudes seen in Fig. 12. er resolution, identi®ed the consistently important pro- In addition, it should be noted that, although not con- cesses (King et al. 1995; Lupo et al. 1995; Rolfson and sistently important, other terms do make notable con- Smith 1996; Vasilj and Smith 1997; Walthorn and Smith tributions at various map times. These include the ad- 1998; Strahl and Smith 2001). vection of subsynoptic vorticity by the synoptic-scale However, the results also show that a higher-resolu- wind, advection of synoptic-scale temperature by the tion diagnosis based on a ®ltering procedure such as the subsynoptic wind, the synoptic-scale friction, the sub- one used in this study can reveal additional processes synoptic ageostrophic vorticity tendency, and even oc- that can make important contributions to ETC devel- casionally some of the subsynoptic/subsynoptic terms. opment. Four additional terms were consistently im- Table 4 shows a pattern for the combined Z±O syn- portant for this case: advection of subsynoptic temper- optic-scale contributions (Z±O b) that is similar to the ature by synoptic-scale winds, subsynoptic-scale dia- synoptic-scale vorticity and temperature advection batic heating, interaction of synoptic-scale static stabil-

Unauthenticated | Downloaded 09/24/21 12:22 PM UTC APRIL 2004 PARSONS AND SMITH 973 ity with subsynoptic-scale vertical motion, and II: Diagnosis using quasigeostrophic potential vorticity inver- synoptic-scale ageostrophic vorticity tendency. Thus, at sion. Mon. Wea. Rev., 124, 2176±2205. Hirschberg, P. A., and J. M. Fritsch, 1991a: Tropopause undulations this resolution only three subsynoptic terms are consis- and the development of extratropical cyclones. Part I: Overview tently important. However, though not consistently im- and observations from a cyclone event. Mon. Wea. Rev., 119, portant, other synoptic/subsynoptic-scale, subsynoptic/ 496±517. subsynoptic, and strictly subsynoptic terms occasionally ÐÐ, and ÐÐ, 1991b: Tropopause undulations and the development exhibited a notable impact on synoptic-scale ETC de- of extratropical cyclones. Part II: Diagnostic analysis and con- ceptual model. Mon. Wea. Rev., 119, 518±550. velopment. Holopanien, E., and P. Nurmi, 1979: Acceleration of a dif¯uent by horizontal sub-grid scale processesÐAn example of Acknowledgments. The authors wish to thank the Me- a scale interaction study employing a horizontal ®ltering tech- nique. Tellus, 31, 246±253. soscale and Microscale Meteorology Division, National ÐÐ, and ÐÐ, 1980: A diagnostic scale-interaction study employing Center for Atmospheric Research for providing the a horizontal ®ltering technique. Tellus, 32, 124±130. model output used in this study. Constructive and help- Holton, J. R., 1992: An Introduction to Dynamic Meteorology. 3d ed. ful reviews from two anonymous reviewers are greatly Academic Press, 511 pp. appreciated. Partial support for this research was pro- Hoskins, B. J., 1990: Theory of extratropical cyclones. Extratropical Cyclones: The Erik Palmen Memorial Volume, C. W. Newton vided by a grant from the Purdue Research Foundation. and E. O. Holopainen, Eds., Amer. Meteor. Soc., 64±80. ÐÐ, 1999: Sutcliffe and his development theory. 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