1. Introduction
In most respects, the development (i.e., the formation, intensification, and subsequent decay) of extratropical cyclones (ETC) is a well-understood process. That understanding has progressed from the thermal theory of cyclogenesis that was prominent in the nineteenth century (Kutzbach 1979), through the polar front theory of cyclones that was developed during the early twentieth century by Bjerknes and others (e.g., Bjerknes 1919; Bjerknes and Solberg 1922), continuing with the work of Sutcliffe (1939, 1947) and Petterssen (1955), and into contemporary interest in explosive cyclogenesis (e.g., Sanders and Gyakum 1980; Roebber 1984; Sanders 1986; Lupo et al. 1992). Summaries of the progress that has been made in understanding the development of ETCs can be found in the volumes deriving from the Palmén Memorial Symposium on Extratropical Cyclones and the International Symposium on the Life Cycles of Extratropical Cyclones (e.g., Newton 1990; Hoskins 1990, 1999; Reed 1990; Uccellini 1990; Bosart 1999; Volkert 1999).
Today, cyclone development is seen to be related to a variety of mechanisms. These mechanisms can be grouped into those related to dynamic effects, that is, cyclonic vorticity advection aloft (Sanders 1986; MacDonald and Reiter 1988), vorticity preconditioning (Gyakum et al. 1992), and favorable jet streak positioning (Uccellini et al. 1984; Uccellini and Kocin 1987); and thermal effects, that is, upper-tropospheric/ lower-stratospheric warm-air advection (Hirschberg and Fritsch 1991a,b; Lupo et al. 1992), latent heat release (Pauley and Smith 1988; Reed et al. 1988), surface energy fluxes (Kuo et al. 1991), and reduced static stability (Smith and Tsou 1988). Alternately, cyclogenesis can be viewed as a response to changing potential vorticity (e.g., Davis and Emanuel 1991; Hakim et al. 1996).
These studies are examples of the remarkable progress that has been made over the past century and a half in scientific understanding of the synoptic-scale forcing processes that are important in ETC development. Yet, an important question regarding ETC development remains to be answered, namely, “What, if any, is the role of subsynoptic processes in ETC development?” While the synoptic-scale impact of synoptic-scale ensembles of subsynoptic heating are well known, little is known about the impact of individual subsynoptic heating elements nor about the role of subsynoptic transport processes. This is not to say that the potential importance of such processes has gone unrecognized by the scientific community. Holopainen and Nurmi (1979) warned that “… forcing due to unresolved horizontal scales may need more attention than is often believed.” Using the dense network of rawinsonde stations in Europe to investigate the impact of subgrid-scale processes on upper-air winds, they observed that the total flow field was stronger than the smoothed flow field and described this effect as the smoothed flow being “… accelerated by the horizontal sub-grid scale processes.” The specific forcing mechanism was flux convergence of momentum. They further advocated the use of output from high-resolution numerical models to extend the study of scale interactions past the use of real data from a synoptic-scale upper- air network.
Maddox (1980) presented a method of separating meteorological data into macroscale and mesoscale components. In that study, he observed that a mesoscale perturbation, that is, a mesoscale convective system, could interact with the macroscale pattern to sufficiently modify the upper-air pattern so as to be detectable in the synoptic-scale upper-air observations. In studying scale interactions with respect to the kinetic energy budget, Carney and Vincent (1986) used an enhanced network of upper-air observations from one synoptic case during the Second European Stratospheric Arctic and Mid-latitude Experiment (SESAME) field program to examine the influence of organized deep convection on the synoptic-scale flow. They found both significant generation of kinetic energy at the synoptic scale and dissipation of kinetic energy to the subsynoptic scale. In addition, they found evidence of momentum transport processes that were the result of scale interactions between the synoptic-scale motion field and the subsynoptic-scale mass field.
More recently, Newton and Holopainen (1990) observed, “A question not explicitly considered at length in this monograph concerns the feedback of subsynoptic-scale features on the larger flow.” They then predicted, “It is probably a safe forecast that scale interaction questions of this type will come up at many meetings in the future.” Also in that volume, Shapiro and Keyser (1990) noted the debate over downscale versus upscale impacts between mesoscale and synoptic-scale processes. They further observed that research into scale interaction processes would and should continue in order to advance the understanding of atmospheric development processes.
To address this question, Rausch and Smith (1996) analyzed the Experiment on Rapidly Intensifying Cyclones over the Atlantic (ERICA) intensive observation period (IOP)-4 cyclone. They presented a diagnosis that included, in addition to synoptic-scale forcing, the role that subsynoptic-scale processes played in extratropical cyclone development. Their analysis looked at forcing terms that included the exchange of “information” between the synoptic scale and subsynoptic scale as represented by vorticity and temperature exchange processes. The objective of the work described herein is to further explore the importance of such synoptic/subsynoptic exchanges using a more successful simulation of the ERICA IOP4 storm.
2. Diagnostic technique
a. Diagnostic equation
b. Explanation of terms
Equation (1) can be thought of as a combination of dynamic and thermodynamic forcing mechanisms. Term (b) and terms (f) through (i) are the dynamic forcing mechanisms, which describe the adjustment of the mass field to a new momentum field that is altered by vorticity changing processes. Terms (c) through (e) are the thermodynamic forcing mechanisms, which describe the adjustment of the momentum field to a new mass field that is altered by temperature-changing processes. Term (j) arises from the expression of geostrophic relative vorticity and represents the departure of the geostrophic relative vorticity from the vorticity of the geostrophic wind. Term (k) is an adjustment term that represents the departure of the geostrophic relative vorticity tendency from the relative vorticity tendency of the actual wind field.
The dynamical forcing mechanisms occur in response to nonuniform changes in the wind field, during which unbalanced motions and corresponding horizontal divergence (convergence) occur as the atmosphere attempts to reestablish a balanced state. Divergence (convergence) aloft in turn forces surface pressure decreases (increases) and surface geostrophic vorticity increases (decreases).
The thermodynamic forcing mechanisms alter the structure of the upper-level height fields which again force unbalanced motions, horizontal divergence (convergence), and corresponding surface pressure decreases (increases). Further, these terms possess two features that distinguish them from the dynamical mechanisms. First is the Laplacian operator, which emphasizes the importance of the horizontal distribution of heating (Smith 2000). Second is the combined influence of inverse pressure weighting and double integration of the thermodynamic terms, which when combined reveal that these mechanisms are more heavily weighted when placed lower in the atmosphere (Rausch and Smith 1996), confirming the results of Tracton (1973), Anthes and Keyser (1979), and Gyakum (1983) regarding the release of latent heat. These studies demonstrate that the three-dimensional distribution of heating can be as important as the total amount of heating in determining ETC development.
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 (except on small spatial scales), ascent (descent) results in adiabatic cooling (warming), which in turn forces surface pressure and geostrophic vorticity changes that generally are of opposite sign to those induced by the other mechanisms. Thus, the adiabatic term opposes the development (decay) forced by the other terms, an effect that is less for reduced static stability.
3. Filtering
a. Methodology
b. Filter selection
When searching for an appropriate filter, one must consider both the characteristic response curve of the filter and the practicality of actually applying the filter to a given dataset. Ideally, a given filter would have a rectangular response function, as shown in Rorabaugh (1993, p. 54). In this study a second-order Shapiro filter (Shapiro 1970) was selected because of previous experience with this filter (e.g., Lupo and Smith 1995; Rausch and Smith 1996; Rolfson and Smith 1996). This previous work had produced tested programming routines that were adaptable to the MM5 model output. The second-order Shapiro filter [see Rausch and Smith (1996) for the mathematical form] yields the response curve shown in Fig. 1.
c. Cutoff wavelength determination
Examination of Fig. 1 reveals that for the second- order filter applied 1000 times to data with a grid spacing of 60 km, less than 10% of the information for wavelengths shorter than 1000 km is retained in the filtered data fields. In contrast, greater than 85% is retained at wavelengths longer than 2000 km. This filtering scheme ensures that most of the synoptic-scale information, that is, wavelengths longer than 2000 km, will be retained and that nearly all of the subsynoptic- scale information, that is, wavelengths shorter than 1000 km, will be removed. Based on this analysis, it seems appropriate to apply the filter as described. Coincidentally, 2000 km corresponds to Orlanski's (1975) boundary between macro-β scale (baroclinic waves) and meso-α scale (fronts).
4. Data and computational methodology
a. Data
To perform an investigation of this nature, a high- resolution dataset generated by a reliable computer model is required, since conventional data usually do not resolve subsynoptic fields. Furthermore, to improve the initialization of the model and assess its capability to simulate a particular synoptic system, it is desirable to obtain a dataset for a cyclone that was intensely observed both in space and time. The ERICA (Hadlock and Kreitzberg 1988) IOP4 storm that occurred in January 1989 is an ideal candidate for such a study. The IOP4 cyclone had a significant amount of nonroutine data available to verify the actual development of the storm (Neiman and Shapiro 1993). These data were also intended to improve the performance of numerical models, especially mesoscale models, simulating the storm. In addition, Purdue's Synoptic Research Group had previously studied the storm and felt that this knowledge would benefit this study (Rausch and Smith 1996).
The National Center for Atmospheric Research (NCAR) provided the dataset used in this study, which is output from the fifth-generation Pennsylvania State University–NCAR Mesoscale Model, version 1 (MM5V1; Grell et al. 1994). MM5 had previously been successfully used to simulate the ERICA IOP4 storm (e.g., Reed et al. 1994).
The MM5 simulation of ERICA IOP4 used a fixed staggered Arakawa B-grid (79 × 139 grid points) at 60- km resolution with 23 layers in the vertical. The model was run in full-physics mode for a 36-h period after initialization at 0000 UTC 4 January 1989. In that mode, the model included explicit predictions of cloud water, rainwater, and ice for the resolvable-scale precipitation, a cumulus parameterization scheme developed by Grell (1993), the boundary layer model of Blackadar (1979), surface sensible and latent heat fluxes, and surface friction. Even though the full-physics run of MM5 contained surface sensible and latent heat fluxes and surface friction, no data regarding those processes were explicitly saved as part of the model output history variables. The variables available at 1-h intervals in the output were u and υ wind components, temperature, mixing ratio, cloud water, rainwater, pstar (where pstar = psfc − ptop, psfc = surface pressure, and ptop = a constant 100 mb; i.e., the top of the model domain), ground temperature, accumulated convective precipitation, and accumulated stable precipitation.
Although Reed et al. (1994) focused on an adiabatic simulation of IOP4, they also described a full-physics run that was performed to demonstrate the ability of MM5 to adequately simulate the IOP4 storm. It is the results of the full-physics run that were used in this study. The MM5 performed significantly better on this 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 UTC 5 January 1989), MM5 produced a cyclone with minimum central pressure of 945 mb compared to that of the LAMPS model's 977 mb. The actual storm center was at 936 mb at that point (Neiman and Shapiro 1993). The MM5 also appeared to be superior to the LAMPS in its location of the storm center, although the MM5 storm movement was somewhat slower than observed (Fig. 2).
b. Computational methodology
The original sigma-coordinate model fields were converted to standard pressure levels at 50-mb increments from 1000 up to 150 mb. In this conversion, a linear log p interpolation scheme was used, and sea level pressure and pressure level heights were calculated. This conversion was necessary to ensure compatibility with the coordinate system (isobaric) used in (3).
Once the model output was in the proper format, Z–O equation calculations were initiated. The first step was to calculate vertical motion, omega (ω = dp/dt), using the kinematic method, which involves vertically integrating the continuity equation. A problem of cumulative bias error is commonly encountered when using the kinematic method to calculate vertical motions based on radiosonde data (Chien and Smith 1973). However, this problem was not evident in this study when profiles of vertical motion were examined, presumably because continuity is satisfied in the model fields, data errors are absent in the model horizontal wind field, and truncation errors are reduced by the use of high-resolution data and fourth-order finite differencing.
The three-dimensional wind field, u, υ, and ω, and temperature field were filtered to obtain the bar and prime fields [See Eq. (2)]. These fields were then used to calculate the vorticity advection, temperature advection, adiabatic temperature change, vertical vorticity advection, tilting, and divergence terms in (3), (4), and (5). The total diabatic heating, friction, and the ageostrophic tendency fields were also filtered to obtain their respective bar and prime components.
5. Synoptic discussion
Due to its extremely low sea level pressure and explosive deepening rate, the ERICA IOP4 storm has been one of the most intensely studied storms of all time. Neiman and Shapiro (1993) and Reed et al. (1994) present 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 tropical cyclones.
MM5 was initialized at 0000 UTC on 4 January 1989 and produced a surface cyclone of 997 mb. By 0600 UTC 5 January 1989, 30 h into the simulation, the sea level pressure had decreased to 941 mb. In comparison, the synoptic-scale (filtered) cyclone had a central pressure of 998 mb at initialization and deepened to 955 mb at 30 h. Figure 3 shows the central sea level pressure for the observed IOP4 cyclone, as well as for both the total and synoptic-scale model-derived IOP4 storm. Because the emphasis in this study is the impact on the synoptic-scale development, the discussion that follows will focus on the filtered MM5 output.
Figures 4 and 5 show analyses of the filtered (synoptic-scale) MM5 output for 1200 UTC 4 and 5 January 1989, which highlight the surface and upper-air features of the IOP4 storm during the time of maximum central pressure decrease and after development has ceased, respectively. Surface cyclone positions and central pressures are summarized in Figs. 2 and 3. By 1200 UTC 4 January 1989 (Fig. 4), the surface cyclone had moved from coastal North Carolina to the warm waters of the Gulf Stream near 36.5°N, 66.4°W and had experienced a 12-h deepening of 24 mb to 974 mb. A closed low was also present at 850 mb and, with its position just northwest of the surface low, appeared to produce low- level warm-air advection (WAA) into the cyclone system. Also of note is the 850-mb cold-air advection (CAA) that is evident to the west of the system. A deepening 500-mb short wave had moved offshore to become oriented north to south just west of 70°W. The 500-mb vorticity maximum had intensified over the previous 12 h from 20 to 22 × 10−5 s−1 and moved to a position just southwest of the surface cyclone, suggesting strong cyclonic vorticity advection (CVA) over the surface cyclone. The 200-mb trough had also deepened and moved eastward to become oriented meridionally along 75°W, inferring more pronounced stratospheric WAA.
Over the ensuing 18 h the IOP4 storm experienced a further central pressure decrease of 19 mb to 955 mb as it continued to move northeastward. The total pressure decrease of 43 mb over the 30-h period represents a deepening rate of 2.0 Bergerons (see Sanders and Gyakum 1980 for definition) at 38°N. By 1200 UTC 5 January 1989, the IOP4 storm had passed the period of rapid deepening and was now entering the dissipation stage. The surface low was at 956 mb and had moved north-northeast to a position just south of Newfoundland (Fig. 5). Although the 850-mb low had deepened by an additional 34 m over the previous 12 h, the flow and isotherm patterns suggested CAA into the storm environment. At this time, the system was vertically stacked through 500 mb, and the position of the 500-mb vorticity maximum coincided with the position of the surface cyclone. Although the 200-mb trough continued to deepen, the warm pool was nearly over the surface cyclone, suggesting that the stratospheric WAA was now ahead of the surface cyclone.
6. Results
a. Basic Z–O results
As a check for computational accuracy, “analyzed” geostrophic vorticity tendencies were determined at 3-;h intervals using the MM5 fields, which were available every hour. The geostrophic vorticity was calculated by taking the Laplacian of the height field and then filtering to obtain the synoptic-scale analyzed geostrophic vorticity. Tendencies were then calculated using a 1-h backward finite difference.
The Z–O calculated geostrophic vorticity tendencies were calculated at 3-h intervals and then compared to the analyzed tendencies. A sample of the results for 1200 UTC 4 January and 1200 UTC 5 January 1989 are shown in Figs. 6 and 7, with the center of the synoptic-scale cyclone provided for reference. These results are representative of the results obtained at all map times. Visual inspection reveals strong correlation in both pattern and magnitude between the total Z–O tendencies and the analyzed tendencies. This strong correlation also applies to a comparison of synoptic-scale Z–O tendencies (sum of all synoptic-scale terms) with the analyzed tendencies. Notice that the surface cyclone is clearly within the analyzed positive-tendency region at 1200 UTC 4 January 1989 (Fig. 6a), when it was experiencing explosive deepening. The cyclone is also in the positive region of the Z–O total and synoptic- scale tendencies (Figs. 6b,c). By 1200 UTC 5 January 1989 (Figs. 7a–c), the cyclone has entered the dissipation stage and is situated within the negative-tendency region for the analyzed, Z–O total, and Z–O synoptic- scale tendencies.
With regard to the subsynoptic-scale contribution to the Z–O geostrophic vorticity tendency, notice that the cyclone is within the negative region at both map times (Figs. 6d and 7d). Only at the 3-h point in the model simulation (0300 UTC 4 January 1989; not shown) was the cyclone within an area of significantly positive subsynoptic-scale geostrophic vorticity tendencies. This influence changed by the 6-h simulation point. By 1200 UTC 4 January 1989 (Fig. 6d), the cyclone was embedded in a region of strong negative subsynoptic-scale tendencies. The subsynoptic-scale processes are important in the earliest stage of development in contributing to explosive development. Thereafter, they quickly act to limit development and prohibit an even stronger explosive 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 values (MAV) for these quantities for the entire domain, as well as correlation coefficients (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 analyzed, but that the total MAV is consistently closer in value to the analyzed than is the synoptic scale. In addition 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 shifted to the immediate cyclone environment, consisting of a computational domain of 16 × 16 grid spaces centered on the cyclone center. This was done for three reasons. The first was to examine in greater detail the region where the forcing mechanisms were most important in directly affecting the development of the IOP4 cyclone. The couplet of high and low geostrophic vorticity tendencies near the cyclone center seen in Figs. 6 and 7 was considered to be indicative of this region, and the display area was adjusted to capture this couplet through the 36-h simulation. This region included nearly all of the area where there were cyclonically curved isobars around the IOP4 cyclone, especially in the early stages of development, when the cyclone was still relatively compact. The second reason, and directly related to the first, was to examine the area where the “signal” was the strongest. Even at the earliest stages of development, Z–O geostrophic vorticity tendencies were larger in the vicinity of the IOP4 cyclone than elsewhere in the domain. The third reason was to use the limited display area to assist in choosing a region over which to calculate statistical parameters. This was done to reduce the influence that the propagation of spurious “information,” as commonly occurs when employing a multiple filter application methodology, might have on the interpretation of results, either subjectively through visual inspection of displayed results or objectively through calculations of statistical parameters.
Similar to Table 1, Table 2 shows statistical comparisons for the limited computational domain. The values presented lead to similar conclusions regarding the magnitude similarity of MAVs, and the high CCs. For this subdomain, the delta values are larger but so also are the CCs when compared to values in Table 1. Also, at 7 of the 12 map times, the CCs between the Z–O total and the analyzed is higher than between the Z–O synoptic scale and analyzed.
b. Determination of important terms
Due to the number of terms involved and the number of map times for which calculations were made, it became obvious that some method of summarizing all of the results and then focusing on a fewer number of important terms was required. Table 3 presents the MAV of the geostrophic vorticity tendency for all 30 terms calculated using the Z–O equation (3). The table includes values for all 12 map times within the subdomain specified above for Table 2. In addition, the MAV for the Z–O total, Z–O synoptic-scale, Z–O subsynoptic- scale, and analyzed geostrophic vorticity tendencies are included. Terms that have been deemed important contributors to development, that is, to the Z–O total, are in bold font. Importance is defined as having a magnitude of 0.75 or greater for six or more map times. Therefore, the important terms are those that are consistently of order 1 × 10−9 s−2. Using the terminology introduced in section 3a, the important terms at the synoptic scale are vorticity advection bb, temperature advection bb, diabatic heating b, adiabatic term bb, and ageostrophic vorticity tendency b. Important subsynoptic-scale terms are temperature advection bp, diabatic heating p, and the adiabatic term bp.
c. Forcing processes
Table 4 presents the geostrophic vorticity tendencies of the important terms and the Z–O synoptic scale, subsynoptic scale, and total at the cyclone center. In addition, maps of the important terms are presented to show the distribution and progression of the contributing processes over the limited display domain for the same two map times previously displayed.
Table 4 reveals that synoptic-scale vorticity advection by the synoptic-scale wind makes a positive contribution (integrated CVA) to development at all map times. After a strong contribution early in the simulation, it steadily weakens after the 21-h point (2100 UTC 4 January, 9 h before minimum pressure) and becomes negligible at the 33-h point (0900 UTC 5 January) as the cyclone enters the dissipation stage. Figure 8, which displays the distribution of this term at the two map times, shows a vorticity advection maximum that is located ahead of, propagates downstream faster than, and rotates cyclonically around the cyclone, the latter in response to the upper-airflow becoming closed, as the cyclone matures. These results are similar to those presented by Lupo et al. (1992) and can be related to the approach and eventual superposition of the midtropospheric vorticity maximum over the surface cyclone as it matures.
In contrast to the vorticity advection, the synoptic- scale temperature advection by the synoptic-scale wind is positive (integrated WAA) through only the first 15 h of the simulation and then becomes negative, as cold air becomes entrained in the cyclone (Table 4). However, note that the negative contribution is not significant until the 24-h point (0000 UTC 5 January), 6 h before minimum pressure. Figures 9a and 9c show a maximum and minimum tendency couplet forced by synoptic-scale temperature advection that moves somewhat downstream from and rotates cyclonically around the surface cyclone, in response to the rotation of the warm and cold air around the cyclone. With both the vorticity and temperature advection, the maxima increase in magnitude from the 12-h point (1200 UTC 4 January) to the 24-h point (0000 UTC 5 January; not shown) and then decrease to the 36-h point (1200 UTC 5 January). The temperature advection bp contribution (Table 4 and Figs. 9b,d) shows that after 9 h of simulation synoptic-scale winds couple with the subsynoptic temperature field to produce an important, although generally smaller in magnitude than the synoptic term, reduction (downscale exchange) in the cyclone's synoptic-scale geostrophic vorticity. This reflects the ensemble influence of the synoptic-scale wind advecting subsynoptic colder air into the cyclone environment.
With the exception of the synoptic-scale term at the 3-h point, diabatic heating contributed positively and strongly throughout the entire simulation. The synoptic- scale term is especially strong from the 9-h (0900 4 January) through 27-h (0300 5 January) points in the simulation, while upscale exchange from subsynoptic diabatic heating is seen throughout the period. The depiction of the two terms in Fig. 10 reflects the direct impact of the synoptic-scale heating field (Figs. 10a,c) and the ensemble influence on the synoptic scale of the subsynoptic heating components (Figs. 10b,d). Since the heating was determined from the First Law of Thermodynamics, detailed examination of individual terms is not possible. However, the patterns in Fig. 10 do suggest certain heating features. Figures 10a,c show synoptic-scale positive surface geostrophic vorticity tendency areas due to heating that initially maximize near the cyclone center and then eventually move somewhat downstream. Both positive areas suggest the influence of latent heat release associated with the cyclone and associated cold front. The negative-tendency areas in the warm sector may reflect downward sensible heat transfer to the cooler ocean, a conclusion similar to that of Danard and Ellenton (1980). Interestingly, despite the low-level advection of cold air from the continent west of the cyclone and the expected upward sensible heat transfer, the geostrophic vorticity tendencies are negative. This may reflect the indirect influence of the adjacent latent heating region. This can occur because the integrated divergence forced by the heating can yield integrated convergence and surface geostrophic vorticity decreases in areas adjacent to the heating area that is sufficiently strong to overwhelm the effect of any in situ heating. This reflects the influence of the Laplacian operator on the heating quantity, as noted by Danard and Ellenton (1980) and discussed by Smith (2000). The role of sensible heating of the advecting cold air appears to be more strongly felt in the subsynoptic term, with a large positive tendency east of the Carolinas on 4 January (Fig. 10b) and south of Maine on 5 January (Fig. 10d). In addition to latent heating influences, the positive area centered over the cyclone on 5 January may also reflect the influence of upward sensible heat transfer, as noted by Giordani and Caniaux (2001) for the interior of an occluded marine cyclone.
The two important adiabatic terms reflect the impact of both synoptic-scale and subsynoptic-scale vertical motions on the synoptic-scale static stability field. The adiabatic temperature change implied in both of these terms opposes the cyclone's development throughout the entire simulation (Table 4). The similarity between the adiabatic term patterns in Fig. 11 and the corresponding diabatic heating (Fig. 10) and temperature advection (Fig. 9) terms suggests the dominance of these thermal processes in forcing the vertical motion field.
The synoptic-scale ageostrophic vorticity tendency term varied markedly during the simulation, from providing a significant positive contribution, to a significant negative contribution, to a negligible contribution (Table 4). This general decrease in magnitude as the cyclone matured and presumably achieved a more balanced state is illustrated by the reduced magnitudes seen in Fig. 12. In addition, it should be noted that, although not consistently important, other terms do make notable contributions at various map times. These include the advection of subsynoptic vorticity by the synoptic-scale wind, advection of synoptic-scale temperature by the subsynoptic wind, the synoptic-scale friction, the subsynoptic ageostrophic vorticity tendency, and even occasionally some of the subsynoptic/subsynoptic terms.
Table 4 shows a pattern for the combined Z–O synoptic-scale contributions (Z–O b) that is similar to the synoptic-scale vorticity and temperature advection 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 contribution 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 contribution to development at 0300 UTC 4 January made by all of the forcing processes. The total term briefly becomes negative at 1500 UTC 4 January (3 h), as the subsynoptic terms briefly become dominant, and then resurges to a secondary maximum at 2100 UTC 4 January (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 simulation 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 partitioning the individual variables in the equation into synoptic and subsynoptic-scale components. The expanded Z–O equation was then used to diagnose the contribution to development made by the 30 terms in the equation.
The data used in the study consisted of model output from a full-physics run of the MM5 model in which the ERICA IOP4 cyclone was simulated. Each variable in the model output was first partitioned into synoptic and subsynoptic-scale components through the use of a second-order Shapiro filter. The variables were then used to calculate the terms in the Z–O equation. These vertically integrated results were filtered again to eliminate any subsynoptic-scale contribution that may have been introduced through aliasing.
Based on the results presented in section 6, several conclusions become evident. The synoptic-scale vorticity advection, temperature advection, diabatic heating, and adiabatic term were always important. This confirms that previous work using the Z–O equation, most of which examined only synoptic-scale influences at coarser resolution, identified the consistently important processes (King et al. 1995; Lupo et al. 1995; Rolfson and Smith 1996; Vasilj and Smith 1997; Walthorn and Smith 1998; Strahl and Smith 2001).
However, the results also show that a higher-resolution diagnosis based on a filtering procedure such as the one used in this study can reveal additional processes that can make important contributions to ETC development. Four additional terms were consistently important for this case: advection of subsynoptic temperature by synoptic-scale winds, subsynoptic-scale diabatic heating, interaction of synoptic-scale static stability with subsynoptic-scale vertical motion, and synoptic-scale ageostrophic vorticity tendency. Thus, at this resolution only three subsynoptic terms are consistently important. However, though not consistently important, other synoptic/subsynoptic-scale, subsynoptic/ subsynoptic, and strictly subsynoptic terms occasionally exhibited a notable impact on synoptic-scale ETC development.
Acknowledgments
The authors wish to thank the Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research for providing the model output used in this study. Constructive and helpful reviews from two anonymous reviewers are greatly appreciated. Partial support for this research was provided by a grant from the Purdue Research Foundation.
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Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;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)
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
Sea level pressure for the IOP4 observed cyclone (lower curve), for the MM5-total cyclone (middle curve), and for the MM5 synoptic-scale cyclone (top curve), where “total” indicates the total model-derived pressure and “synoptic scale” indicates the filtered or synoptic-scale contribution to the total model-derived pressure
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
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-mb geopotential height (solid, m) and absolute vorticity (dashed, 10−5 s−1), and (d) 200-mb geopotential height (solid, m) and temperature (dashed, K). Black dot shows position of cyclone center.
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
As in Fig. 4 except for 1200 UTC 5 Jan 1989.
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
Geostrophic vorticity tendency (10−9 s−2) 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 position of cyclone center.
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
As in Fig. 6 except 1200 UTC 5 Jan 1989.
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
Geostrophic vorticity tendencies (10−9 s−2) due to advection by synoptic-scale wind of synoptic-scale vorticity. Map times are Jan 1989. Black dot shows position of cyclone center
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
As in Fig. 8 except advection by synoptic-scale wind of (a), (c) synoptic-scale temperature and (b), (d) subsynoptic-scale temperature
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
As in Fig. 8 except (a), (c) synoptic-scale diabatic heating and (b), (d) subsynoptic-scale diabatic heating
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
As in Fig. 8 except influence of (a), (c) synoptic-scale vertical motion and (b), (d) subsynoptic-scale vertical motion on synoptic-scale static stability
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
As in Fig. 8 except synoptic-scale ageostrophic vorticity tendency
Citation: Monthly Weather Review 132, 4; 10.1175/1520-0493(2004)132<0956:AIOECD>2.0.CO;2
Mean absolute values (MAV; 10−9 s−2 ) of geostrophic vorticity tendencies and correlation coefficients (CC) for the entire domain for all computational times
Mean absolute values (MAV; 10−9 s−2 ) of geostrophic vorticity tendencies and correlation coefficients (CC) for the limited domain for all computational times
Table 3a. Mean absolute values (MAV; 10−9 s−2 ) 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
Table 3b. Mean absolute values (MAV; 10−9 s−2 ) 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
Geostrophic vorticity tendencies (10−9 s−2 ) at the cyclone center for the “important” terms and for the Z–O synoptic-scale, subsynoptic-scale, and total