1. Introduction
Meteorological research on diabatic Rossby waves (DRWs) has been intensifying in recent years after a DRW was detected for the first time in numerical weather prediction (NWP) model output for a high-impact weather event. According to a mesoscale model hindcast simulation, a DRW served as an important precursor to the “Lothar” storm after Christmas 1999, which was one of the most harmful winter storms over Europe in the last few decades (Wernli et al. 2002). The explosive intensification of this storm was poorly predicted by deterministic NWP forecasts and therefore fairly unexpected. The shallow sea level pressure (SLP) minimum associated with the DRW traveling rapidly across the North Atlantic Ocean was not a clear indication for the forecasters of the severe weather event that was about to develop.
Originally, DRWs were discovered in highly idealized model setups (Raymond and Jiang 1990; Snyder and Lindzen 1991; Parker and Thorpe 1995). Common characteristics of these models were cloud-diabatic heating in a baroclinic background atmosphere producing a positive potential vorticity (PV) anomaly at low-tropospheric levels. The following basic conditions for DRW existence and propagation emerged from these simulations. The vortex of the positive low-level PV anomaly (that is accompanied by a weak SLP minimum) induces a poleward low-level jet of warm moist air at its downstream side. This stream ascends along the poleward-sloping isentropes until condensation occurs. Below the level of maximum latent heating a positive diabatic PV tendency occurs, which leads to the reformation of the DRW downstream of its original position. Once generated, a DRW can be regarded as a self-preserving system that propagates rapidly by continuous diabatic PV regeneration under the conditions of at least moderate baroclinicity and sufficient moisture supply. With this characterization of DRWs we emphasize the aspect of wavelike regeneration and propagation (as opposed to material advection). The studies by Moore and Montgomery (2004, 2005) introduced the term diabatic Rossby vortex (DRV), which emphasizes the feature’s coherent vortexlike structure. Note, however, that both terms, DRW and DRV, are referring to the identical feature, which can be regarded as a wave–vortex hybrid (R. Moore 2012, personal communication). Further aspects of the DRV/DRW terminology issue are briefly discussed in appendix A. Apart from the particular propagation mechanism of DRWs, another most useful dynamical distinction between DRWs and typical extratropical cyclones is found in the energetics (e.g., Moore and Montgomery 2004, 2005).
Since the SLP signature associated with DRWs is typically weak and no upper-level wave signature is required for the propagation mechanism, a DRW often does not appear as a striking phenomenon on standard weather charts and in satellite imagery. Nevertheless, the low-level vortex associated with a DRW can be a key precursor for an explosive cyclone intensification in cases where (i) an approaching synoptic-scale upper-level trough starts interacting with the low-level PV vortex or (ii) the low-level PV vortex starts interacting with a straight upper-level jet and induces the formation of a small-scale upper-level trough. A prominent example for the second scenario was found for the development of Lothar (Wernli et al. 2002; Rivière et al. 2010). It is not known which of the two intensification scenarios occurs more frequently. Note that the interaction of low-level vortices and upper-level structures has been discussed as a likely process for explosive cyclone intensification (Gyakum et al. 1992), also in situations where the low-level vortex does not correspond to a DRW.
So far, four DRW events over the North Atlantic, all explosively intensifying, were investigated in detail: the Lothar storm in 1999, two cases in 2005 (Moore et al. 2008; Boettcher and Wernli 2011), and a DRW that developed within the frequently investigated “Perfect Storms” in 1991 (Cordeira and Bosart 2011). Investigation of different operational forecasts for one of these DRWs revealed that the low-level baroclinicity downstream and the moisture to the south of the system were found to be the most important factors leading to the DRW propagation (Boettcher and Wernli 2011). Sensitivity experiments where the moist diabatic processes were turned off, led to much weaker systems and no subsequent explosive intensification (Wernli et al. 2002; Moore et al. 2008). For three of the cases, different development scenarios that arose either from experiments applying PV inversion (Moore et al. 2008; Rivière et al. 2010) or by considering operational forecasts with various lead times (Boettcher and Wernli 2011) revealed that for the explosive intensification, the phasing of the low-level PV vortex with a preexisting upper-level disturbance is crucially important. The amplitude and the position of the low-level system with respect to the upper-level PV structure (Rivière et al. 2010) as well as the intensity and shape of the upper-level trough (Boettcher and Wernli 2011) are key for the explosive DRW intensification. The process of the interaction of the low-level PV anomaly with a synoptic-scale upper-level trough is thus comparable with the extratropical transition of tropical cyclones, which potentially leads to a reintensification of the cyclone as an extratropical system (e.g., Klein et al. 2002; Ritchie and Elsberry 2003, 2007). An important difference between the two processes is the shallower low-level PV anomaly of a DRW compared to the typically deep positive PV anomaly of a recurving tropical cyclone, which renders the interaction with the synoptic-scale upper-level trough even more sensitive for the DRWs.
Whereas the dynamics of DRWs and their intensification was investigated in detail for this selection of events, a more climatological picture is still missing. It is not clear, for instance, where and how frequent DRWs occur and how often they intensify explosively. This study is a first approach to address these questions and to quantify the occurrence, the geographical distribution, and the intensification of DRWs in the Northern Hemisphere (i.e., over the North Atlantic and the North Pacific Oceans). A sophisticated tracking algorithm that is described in section 2 is applied to 10 yr of operational European Centre for Medium-Range Weather Forecasts (ECMWF) analyses. Section 3 addresses the frequency of occurrence and intensification of DRWs. The geographical distribution and scenarios of DRW generation are investigated in section 4. Eventually section 5 focuses in particular on the explosively intensifying systems. Finally, the results are summarized and discussed in section 6.
2. Data and DRW tracking
The data used in this climatological study are operational analyses from the ECMWF for the years 2001–10, interpolated on a 0.6° horizontal grid and available every 6 h. In the vertical the data were interpolated on five pressure levels (950, 850, 750, 500, and 250 hPa) used for the DRW tracking tool.
Additional variables calculated from the analyses are potential temperature (TH), potential vorticity (PV), and the upper-level induced quasigeostrophic (QG) vertical motion. To calculate this field, the QG omega equation diagnostic from Clough et al. (1996) has been applied. The tool enables one to calculate the height-attributable solution of the QG omega equation. The vertical motion field has been calculated that is induced by the dynamics in the upper troposphere (between 500 and 100 hPa). The amplitude of this field at 700 hPa is used to quantitatively evaluate the influence of the upper-level dynamics on the low-tropospheric vertical motion.
A specific algorithm has been designed to identify positive low-level PV anomalies that behave according to the DRW mechanism described above. Note that this is not a straightforward task since diabatically produced low-level PV anomalies are ubiquitous over the midlatitude oceans, in particular in the central areas and along the fronts of “normal” extratropical cyclones (e.g., Hoskins and Berrisford 1988; Neiman et al. 1993; Malardel et al. 1993; Rossa et al. 2000). It is, therefore, necessary to specify a set of conditions to isolate DRW-related PV anomalies from the more standard low-tropospheric high-PV features. The first step is to identify low-level cyclones characterized by 1) a local minimum in SLP and 2) a collocated high value of low-tropospheric PV.
For the first condition, all SLP minima are considered that have been identified with the cyclone identification algorithm of Wernli and Schwierz (2006). This algorithm, as applied in this study, identifies SLP minima that are enclosed by a closed SLP contour whose SLP value is at least 0.5 hPa larger than the SLP minimum. In this way the algorithm also identifies fairly weak local minima [in the study by Wernli and Schwierz (2006) the minimum SLP difference between the minimum and the closed contour was 2 hPa].
For the second condition, we impose that the 850-hPa PV value, averaged over the grid point with the local SLP minimum and its eight neighbors, is larger than 0.8 potential vorticity units (PVU; 1 PVU = 10−6 K m2 kg−1 s−1). This threshold is somehow arbitrary (as will be other thresholds used in this algorithm) but appears to be reasonable to identify DRWs.
For all grid points that fulfill the above criteria, the track is extended if at the next time step (i.e., 6 h later) another SLP minimum collocated with a high value of 850-hPa PV can be found within a box that extends 12° to the east, 2° to the south, and 4° to the north from the previous position. If there are several DRW candidates within this region, the one with the highest PV value is taken. This tracking approach is continued and tracks are only considered further if they persist for at least 24 h.
The selected cyclone tracks are characterized by a lifetime of at least 1 day and high low-level PV in their center. These characteristics are, for instance, also valid for many tropical cyclones and for other low-level high-PV features, which do not propagate because of the DRW mechanism. Therefore, further criteria are required to specifically identify DRWs. To this end, the following additional DRW-specific criteria must be fulfilled during at least three consecutive time steps (i.e., 12 h) along the cyclone track:
Substantial low-level baroclinicity: The potential temperature difference at 950 hPa in a region downstream of the cyclone center must exceed a threshold value. This measure is taken in a region moving with the cyclone [see the small gray box in Fig. 1, which extends from the SLP minimum to the east from grid point (GP) 2 to GP 8, 3 GP to the south, and 8 GP to the north]. Baroclinicity Δθ is measured by the difference of the averages of the 10% lowest and 10% highest values of the 950-hPa potential temperature values in the box, and the threshold is taken as Δθ ≥ 5 K.
Fast propagation: The cyclone propagation speed must be larger than 250 km within 6 h (which corresponds to 11.6 m s−1) in order to exclude slow-moving features (such as tropical cyclones) that do not propagate according to the DRW mechanism.
Sufficient moisture: The moisture is measured by the average of the 10% highest relative humidity values at 850 hPa in the box around the DRW (see the large gray box in Fig. 1, which again moves with the cyclone and extends from 8 GP west to 8 GP east and from 6 GP south to 5 GP north of the SLP minimum). This relative humidity value must exceed 90% to indicate saturation and condensational latent heating.
Very weak upper-level forcing: The averaged upper-level-induced QG ascent at 700 hPa in the area of the cyclone (large gray box in Fig. 1) must be smaller than 0.5 × 10−2 m s−1 and the averaged PV at 250 hPa in the same box must be less than 1 PVU to exclude significant upper-level induced, synoptic-scale lifting. Such a strong upper-level forcing would be typical for so-called “type B” cyclones (Pettersen and Smebye 1971).
An example DRW (at 1200 UTC 19 Dec 2005 over the North Atlantic) in order to illustrate key parameters of the DRW identification and tracking scheme. Shown is PV at 850 hPa (shading, PVU) and PV at 250 hPa (thick black lines for 1.5 and 2 PVU). Thin black lines depict PV at 850 hPa 6 h earlier for the evaluation of the propagation speed. The small gray box is used for quantifying the baroclinicity at 950 hPa, and the larger gray box is for calculating the averaged PV at 250 hPa and the upper-level-induced QG ascent at 700 hPa. See text for details.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
Applying these additional criteria (i.e., 3–6) reduces the number of tracks significantly and eventually delivers the final “DRW tracks.” Note that these tracks, which extend over at least five time steps, fulfill conditions 1) and 2) at all time steps (from genesis to lysis), whereas criteria 3–6 are fulfilled only at least 3 times and these times are not necessarily at the beginning of the tracks. The phase during which criteria 3–6 are fulfilled is called the “DRW propagation period,” since these criteria correspond to the theoretical concept of the DRW propagation and regeneration mechanism. As a consequence DRW tracks can have an initial phase prior to the DRW propagation period, then by construction all have a propagation period, and finally some have a postpropagation phase. During this final phase, the DRW might evolve into a standard extratropical cyclone (through coupling with or self-inducing an upper-level PV anomaly) or it might rapidly decay. This three-phase behavior is schematically shown in Fig. 2. The automatically identified DRW tracks have been manually validated with the aid of 6-hourly charts of low-level PV, SLP, and upper-level tropopause contours produced from the ECMWF analyses in order to iteratively optimize the thresholds used in this DRW identification algorithm.
Schematic of a DRW track illustrating the DRW tracking algorithm and the three phases of the DRW life cycle: genesis, propagation, and (intensification and) decay phase.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
3. Statistics of DRWs and their intensification
The DRW identification has been confined to the areas of the North Atlantic (20°–80°N, 110°W–40°E) and North Pacific (20°–80°N, 100°E–110°W), respectively. The areas mainly cover the ocean basins where the critical conditions for DRW propagation of sufficient moisture, a well-defined low-level horizontal temperature gradient, and small surface friction are more likely to occur than over the continents. During the 10-yr study period, 431 DRW tracks are found over the North Atlantic and 809 over the North Pacific, corresponding on average to about 43 and 81 yr−1, respectively. DRWs preferentially occur in the summer months (Fig. 3). Over the Atlantic1 a distinct maximum of DRW occurrence is found in August and over the Pacific in June. In both areas, the summer maxima of DRW frequency are probably related to the increased moisture availability in the ocean boundary layer during the warm season. In addition, the two Pacific peaks in June and October can be related to specific regional weather phenomena (see section 4b).
Monthly number of DRWs during the years 2001–10 in the (a) North Atlantic and (b) North Pacific.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
The darker segments of the histogram in Fig. 3 mark the DRWs that intensify explosively as meteorological “bombs” with a SLP deepening of at least one Bergeron2 after the criterion of Sanders and Gyakum (1980). In both regions hardly any bombs occurred between June and August. The frequency of these explosively intensifying systems increases in autumn and winter, associated with increased baroclinicity along the DRW tracks during the cold season (on average Δθ= 12.5 K) compared to the warm season (Δθ = 9.5 K). During the considered 10 years, 54 bombs were found over the Atlantic (i.e., 12.5% of all DRWs) and 119 over the Pacific (14.7%), corresponding to on average 5 and 12 events per year, respectively. Some details of these particularly relevant DRW events are listed in a separate document (coordinates and minimum SLP value for DRW genesis, start of intensification, and maximum intensity; available online at http://www.iac.ethz.ch/people/maxibo/drwbombs.pdf). This information might be useful for performing detailed case studies for some of these events.
Figure 4 shows a histogram of the DRW deepening rates. Obviously most of the DRWs are characterized by a fairly moderate intensification, in agreement with Fig. 3. In the warm season from May to October (shown by the black line in Fig. 4) most systems have no or weak intensification. A life cycle of a typical weakly intensifying DRW is described in appendix B. The gray columns in Fig. 4 show that the distribution of the intensification rates during the cold season (November–April) is fairly evenly distributed from weak to strong intensification. The peak DRW intensification is found in winter with a value of 3.2 Bergeron (corresponding to a pressure decrease of 53 hPa in 24 h). This event led to a major North Pacific storm in early December 2007. This storm became known under the name “great coastal gale of 2007” (Crout et al. 2008; Hofmann 2010) and severely affected the North American west coast. The DRW aspects of this case will be briefly described in appendix B.
Histogram of DRW intensification (measured in Bergeron, see text for details) for the warm season May–October (black line) and the cold season November–April (gray columns) in the (a) North Atlantic and (b) North Pacific.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
To put the number of DRW-related bombs into perspective, we identified all explosively intensifying extratropical cyclones in the considered 10-yr time period with the cyclone tracking algorithm of Wernli and Schwierz (2006). On average, the frequency of extratropical cyclone bombs amounts to 38 yr−1 in the Atlantic and 55 yr−1 in the Pacific, respectively. The fraction of DRW-induced bombs for every month is considerable (see Fig. 5) and amounts, on average to about 15% in the Atlantic and more than 20% in the Pacific. Even in the summer months that are characterized by a small amount of bombs, and in particular in the fall months in the Pacific region, the DRW contribution to the total number of bombs is remarkable. This indicates that DRWs, in a statistical sense, play a significant role as a precursor disturbance for the development of bombs over both the North Atlantic and North Pacific.
Monthly number of “cyclone bombs” (gray bars) during the years 2001–10 in the (a) North Atlantic and (b) North Pacific. Bombs with a DRW precursor are indicated by dark gray shading.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
4. DRW tracks and DRW genesis
This section describes the geographical distribution of DRW tracks and their seasonality, and compares the DRW track pattern qualitatively to an overall cyclone track climatology. Then the conditions during the genesis of the low-level positive PV anomalies associated with the DRWs will be investigated.
a. DRW tracks
The tracks of the centers of DRWs primarily extend along the midlatitude baroclinic zone of the ocean basins (Fig. 6). They follow a fairly straight, predominantly zonally aligned path (except for the systems that propagate into the eastern part of the ocean basins where they typically move poleward). The maxima of DRW occurrence are located at about 40°N in the Atlantic and 35°N in the Pacific, respectively. In both oceans the DRW track density field overlaps with the overall midlatitude storm track (e.g., Wernli and Schwierz 2006). However, the propagation of DRWs is typically more zonal, whereas most extratropical cyclone tracks are bent to the north. This is shown by, for example, Dacre and Gray (2009) for North Atlantic cyclones (their Fig. 2a), leading to an overall frequency maximum of North Atlantic cyclones between Greenland and Iceland and of North Pacific cyclones near the Aleutian Islands, respectively. Note that hardly any DRWs move into these regions. Some DRWs reach the downstream continent; 22 Atlantic DRWs reach western Europe and 34 Pacific DRWs reach the North American west coast. This indicates that systems like Lothar (which moved into central Europe) and the great coastal gale of 2007 (reaching close to Washington State) are not uncommon. Clearly a longer time period must be investigated to obtain a more robust estimate of the typical frequency of land-falling DRWs. Note also that very few DRWs approach the downstream continent during their propagation phase (cf. section 2). This indicates that either the conditions for DRW propagation are not favorable in the eastern part of the ocean basins (due to reduced baroclinicity and/or boundary layer humidity) or that DRWs are overtaken by an upper-level disturbance before reaching the eastern oceans.
Track density of DRW centers in the years 2001–10 from genesis till decay (number of events within 3° × 3° boxes) in the (a) North Atlantic and (b) North Pacific. The black lines denote values of 1 and 30. Black dots show the DRW genesis positions in the warm season May–October and open circles in the cold season November–April, respectively.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
Most starting points of DRW tracks (see black dots and white circles in Fig. 6) are registered over the eastern part of the continents and in the western to central ocean basins. In the cold season (November–April, white circles), starting positions are on average slightly farther south, mainly due to the southward shift of the midlatitude baroclinic zone. The warm season genesis points south of 30°N most likely correspond to remnants of tropical cyclones [see section 4b(2)]. The hotspots of DRW genesis to the east of Cape Hatteras and Japan, respectively, are known as regions of frequent cyclogenesis (Wernli and Schwierz 2006, their Fig. 6). This indicates that it is not the location of genesis that qualifies DRWs as a special category of extratropical cyclones (but rather their propagation mechanism and their specific energetics).
b. Processes of DRW genesis
1) Precipitation at DRW genesis
In this section we investigate aspects of the generation of the positive low-level PV anomalies at the first time step of the DRW tracks. Note that at this initial time the cyclone fulfills the criteria of an associated SLP minimum and of 850-hPa PV larger than 0.8 PVU, but not necessarily the DRW propagation phase criteria 3–6 described in section 2. In principle there are several physical processes that can lead to the diabatic low-level PV production prior to DRW genesis: cloud condensational latent heating, radiation, and nonconservative forces like surface friction and turbulence. Since the first of these processes is essential for the DRW propagation it is insightful to estimate its relevance also for DRW genesis. In the absence of observation-based latent heating fields in the region of DRW genesis, we consider satellite-based precipitation observations as a first-order proxy for the latent heating in the vicinity of DRWs.
For each DRW genesis event, 6-hourly accumulated precipitation estimates are derived from the Tropical Rainfall Measuring Mission (TRMM) multisatellite precipitation analysis (downloaded from webpage http://mirador.gsfc.nasa.gov/ on 19 April 2012; Huffmann et al. 2007). The accumulation period covers the 3 h before and after the time of DRW genesis. Spatially, an average is computed within a radius of 500 km around the initial track position in order to capture the mesoscale environment of the center of the evolving DRW and to account for the potential propagation of the PV feature during the considered time period. The frequency distribution of precipitation in the vicinity of DRW genesis (Fig. 7) indicates that many of the DRW tracks start with a significant amount of rain in their vicinity. The median of the domain-averaged values is about 0.8 mm (6 h)−1 for Atlantic and 1.1 mm (6 h)−1 for Pacific DRWs, which hints at the key relevance of moist-diabatic processes for the initial low-level PV generation.
Histogram of 6-hourly accumulated precipitation from TRMM satellite measurements averaged within a radius of 500 km around the DRW genesis position. The time period corresponds to ±3 h from the time of genesis. Note that six cases in the Atlantic and eight cases in the Pacific are not shown due to missing satellite data.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
A number of cases are categorized into the first column of the histogram in Fig. 7 with less than 0.2 mm (6 h)−1; 50% of these events in the Atlantic and 20% in the Pacific are starting over land, pointing to frictional processes as the likely initiator of the incipient PV anomaly. Detailed inspection of the remaining events starting in a weak-rain environment has shown that these PV anomalies either emerged from a very small-scale precipitation event or could be tracked a few time steps back into regions where more precipitation was reported. The latter can occur if the PV anomaly is initially not associated with a local SLP minimum or its amplitude is weaker than 0.8 PVU and only later fulfills these criteria (recall that according to our algorithm DRW genesis is characterized by a low-level PV threshold and a local SLP minimum).
2) Synoptic-scale environment of DRW genesis
It is also insightful to investigate the synoptic-scale flow associated with the DRW genesis. An empirical classification of the most frequent flow patterns has been performed based upon charts of low-level temperature, SLP, and upper-level PV. Schematics of these patterns are shown in Fig. 8. A property all DRW genesis events have in common is their development on the equatorward side of a region with a strong meridional temperature gradient. Also common to all categories is a localized moist low-level flow toward the colder air that leads either to cloud formation via large-scale isentropic ascent or to the triggering of a convective system. However, the reasons for this flow vary substantially between the different categories. Note that the schematics represent idealized representations of the often complex real flows. Also there are smooth transitions between the categories and for these reasons we refrain from statistically quantifying our manual analysis and present the results in a qualitative fashion.
Schematics of typically observed synoptic-scale configurations for DRW genesis. White ellipses denote DRW track starting positions and gray ellipses indicate the start of the DRW propagation phase (a gray ellipse is shown if the two coincide). The scenarios are (a) flow around a subtropical high against the baroclinic zone; (b) flow around a cyclone against the baroclinic zone; (c) surface cyclone formation induced by forcing from upper-level trough; and (d),(e) PV remnants from a mesoscale convective system or tropical cyclone, respectively, moving into the baroclinic zone.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
The most frequent situation (scenario a) is the generation of the initial PV anomaly by the flow against the midlatitude baroclinic zone at the western flank of a (typically persistent) low-tropospheric subtropical high pressure system (Fig. 8a). This pattern provides favorable conditions for DRW propagation since warm and moist air is continuously advected against the baroclinic zone. A similar flow situation (scenario b) occurs if a preexisting cyclone approaches the baroclinic zone from the south (Fig. 8b). The poleward flow at its eastern flank can ascend along the northward-sloping isentropes causing condensation and PV generation. The cyclone equatorward of the baroclinic zone can either be a surface cyclone beneath an upper-level cutoff or, observed more frequently in the Pacific, a recurving tropical cyclone or its remnants.
A third possibility (scenario c) for generating the initial disturbance is large-scale lifting induced at the downstream side of an upper-level trough (Fig. 8c). This situation might look similar to the classical “type B” cyclogenesis situation. However, in contrast to this type of extratropical cyclone development, the DRWs developing according to this scenario do not couple with the upper-level disturbances, which typically weaken in these cases after DRW genesis. Consequently the low-level cyclones do not intensify into mature extratropical cyclones, but instead propagate rapidly downstream into the region of the upper-level ridge. As a variant of this scenario, in some cases the upper-level trough is associated with a surface cyclone and the DRW develops as a disturbance along the intense warm front of this preexisting cyclone, which typically decays as the DRW moves downstream.
Another fundamentally different scenario is the transformation of a preexisting cyclonic vortex into a propagating DRW as it moves into a baroclinic zone (scenario d). This can occur for instance with PV anomalies generated within mesoscale convective systems, such as along the mei-yu front (e.g., Chen et al. 2008) (Fig. 8d). These mei-yu-related mesoscale convective vortices are a special category in our DRW climatology. The mei-yu front, which is active in late spring and early summer in eastern Asia, is usually characterized by weak to moderate baroclinicity, strong horizontal wind shear, and a strong humidity gradient (Lai et al. 2011). Along the front, mesoscale convective systems and vortices develop frequently (e.g., Chen et al. 2008; Jiayi et al. 2002). If such a low-level vortex propagates into a stronger baroclinic environment it is properly captured by our algorithm as a DRW. A comparable situation occurs when DRWs form from PV remnants of former tropical cyclones undergoing extratropical transition (e.g., Jones et al. 2003), which move into strongly baroclinic regions (Fig. 8e). Both variants of this scenario mainly occur in the Pacific where they contribute to the summer to autumn peak in the annual cycle of the DRW frequency (Fig. 3). In May and June noticeably many DRW genesis points are found to the southeast of Japan in the region of the mei-yu front. Extratropical transition of tropical cyclones occurs most often in late summer and autumn. Another particularity in the Pacific area is the orography of Japan and Taiwan close to the climatological location of the intense baroclinic zone, which is beneficial for diabatic PV generation by orographically induced precipitation formation.
How can the DRW events previously discussed in the literature be classified according to these genesis scenarios? The DRW that resulted in the Lothar storm (Wernli et al. 2002; Rivière et al. 2010) was generated at 1800 UTC 23 December 1999 to the northeast of Florida and can be classified as a hybrid of scenarios a and c. The subtropical high caused a southerly flow toward the midlatitude baroclinic zone off the East Coast and a weak upper-level trough was present upstream over the United States. A large precipitation area in the region of the initial SLP signal indicates low-level PV generation by moist-diabatic processes. The role of the synoptic-scale upper-level trough was studied by Descamps et al. (2007) based upon sensitivity experiments with modified upper-level flow conditions. The generation of the North Atlantic DRWs in 2005 investigated by Moore et al. (2008)3 and Boettcher and Wernli (2011) can both be assigned to scenario c. In both cases, the low-level PV anomaly that developed into a DRW was generated in a convective precipitation system induced by a tropopause-level trough. The DRW within the Perfect Storms in 1991 shows a complex evolution and can eventually be identified as a disturbance on the warm front of the Perfect Storm [see Fig. 3d of Cordeira and Bosart (2011)]. It can thus be related to a variant of scenario c.
5. Explosive DRW intensification
Of particular societal relevance is the fraction of DRWs that undergo explosive intensification (cf. section 3). A bit less than 15% of all DRWs intensify explosively during the considered 10 years. From previous case studies of explosive DRW intensification (Wernli et al. 2002; Rivière et al. 2010; Boettcher and Wernli 2011) there is evidence that this process involves the coupling of the low-level DRW vortex with a synoptic-scale upper-level positive PV anomaly. This upper-level trough can either develop independently and far upstream of the DRW (Boettcher and Wernli 2011; Moore et al. 2008; Cordeira and Bosart 2011) or it can be induced in a bottom-up process by the DRW itself (Wernli et al. 2002).
A careful manual analysis of many DRW bomb cases indicates that the bottom-up scenario is relatively rare. In our 10-yr climatology we found 10 clear bottom-up events with no preexisting upper-level trough approaching from upstream.4 For the majority of DRW bomb events, the explosive intensification involves the interaction of the DRW with an upper-level trough approaching from upstream. As an aside we note that this type of cyclone intensification bears resemblance to the type-C development proposed by Deveson et al. (2002). Some of the findings of Plant et al. (2003) and Ahmadi-Givi et al. (2004) about cyclones of type C agree with this category of DRW intensification, where both a strong upper-level forcing and remarkably strong low-level latent heat release advance the explosive intensification. However, the DRW cases also feature strong low-level baroclinicity, which is not regarded as a typical ingredient of type-C development. Note that our categorization of DRW intensification is based upon a manual inspection of 6-hourly charts of upper-level and low-level PV. As a further step, it would be a useful extension to develop a fully objective algorithm to identify bottom-up developing DRW bombs.
Finally, we consider the results of a composite analysis of the Atlantic and Pacific DRW bomb cases, separately for the scenario with an approaching upper-level trough (163 cases; Fig. 9) and for the 10 manually identified bottom-up cases (Fig. 10). The composites are centered at the position of the low-level DRW [i.e., fields were shifted such that the center of the DRW is located at coordinates (0, 0) on a rotated stereographic grid] and show PV on 850 and 250 hPa (on the left) and almost zonally oriented vertical cross section of PV (on the right) at the beginning of the 24-h period of the strongest intensification, and 12 and 24 h later. For the majority of the events, Fig. 9 shows that the low-tropospheric DRWs are overtaken by a positive upper-level PV anomaly during their intensification phase. At the beginning of the 24-h period of maximum SLP deepening (Figs. 9a,b) the low-level DRW is still ahead of the approaching upper-level trough and the low and upper-level regions with PV > 0.8 PVU have not yet merged. Twelve hours later (Figs. 9c,d) the upper-level trough has a more pronounced meridional extension and the low-level PV anomaly starts merging with the upper-level trough. At the end of the explosive development (i.e., again 12 h later; Figs. 9e,f), the upper-level trough in the composite has evolved into a shape that resembles the LC2 cyclonic wave-breaking configuration (Davies et al. 1991; Thorncroft et al. 1993). The low-level vortex is vertically aligned with the upper-level PV anomaly leading to the formation of a vertically coherent “PV tower” (e.g., Rossa et al. 2000; Čampa and Wernli 2012). Note that above the cyclone center, the tropopause has descended to 400 hPa compared to about 250 hPa one day earlier. This composite analysis therefore corroborates the findings from previous studies and highlights the interaction of the DRW with an upper-level trough as a key for its intensification into a bomb for the majority of cases.
Composites of explosively intensifying DRWs at (a),(b) the beginning of the 24-h period of the strongest pressure deepening; (c),(d) 12 h later; and (e),(f) at the end of the strongest pressure deepening phase (i.e., at about the time of minimum SLP). (left) PV at 250 hPa (shading, PVU) and PV at 850 hPa (black contours for 1, 1.5, and 2 PVU). (right) PV (shading, in PVU) in vertical cross sections along the black lines shown in (left).
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
Composites (as in Fig. 9) of 10 explosively intensifying DRWs identified as bottom-up cases.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
Figure 10 shows the analogous composites for the 10 bottom-up cases. Because of the much lower number of events, the composite fields are less smooth. The differences to the majority of DRW bombs with an approaching upper-level trough are however striking. At the beginning of the intensification (Figs. 10a,b) the upper-level PV structure reveals a straight zonally oriented jet and no indication of an approaching synoptic-scale trough. Twelve hours later (Figs. 10c,d) the DRW is beneath the still rather straight upper-level jet and no merging takes place of the low-level vortex with an upper-level PV anomaly. However, again 12 h later (Figs. 10e,f) the composite structure looks very similar to the one for the majority of the bomb cases (cf. with Figs. 9e,f) with an upper-level synoptic-scale wave and a vertically coherent PV tower. This scenario is qualitatively similar to the bottom-up development reported for the Lothar storm by Wernli et al. (2002).
6. Summary and discussion
The frequency and geographical occurrence of DRWs has been analyzed using 10 years of operational ECMWF analyses in the North Atlantic and North Pacific. A specific tracking algorithm was developed to identify DRW tracks in numerical model data. The algorithm is designed to select DRW tracks from the general set of cyclone tracks, using criteria that represent the key characteristics of the DRW propagation mechanism, like increased low-level PV, substantial baroclinicity, rapid propagation speed, and the absence of upper-level forcing in a sufficiently moist environment. Every DRW track consists of a DRW propagation phase (during which all criteria are fulfilled) and potentially a pre- and postpropagation phase. During the latter, most DRWs decay whereas in about 14% of the cases explosive cyclone intensification occurs. These DRW-induced cyclone “bombs” account for 15% of all explosive cyclone developments in the Atlantic and for more than 20% in the Pacific. A composite analysis shows that in the majority of the bomb events a positive upper-level PV anomaly approaching from upstream is involved in the explosive development of DRWs. However, a minority of DRWs intensify without a preexisting synoptic-scale upper-level trough. The cyclonic circulation of these “bottom-up” developing DRWs induces the formation of an upper-level trough when they approach the jet axis.
About twice as many DRWs are found over the North Pacific (on average 81 yr−1) than the North Atlantic area (on average 43 yr−1). DRWs occur most frequently in summer whereas explosive intensification of DRWs is found preferentially in autumn and winter. In the North Pacific, the main reason for the summer frequency maximum is DRW genesis associated with mesoscale convective vortices formed along the mei-yu front in June–July, and the contribution from decaying tropical storms inducing DRWs as they approach the region of strong baroclinicity. The track density of DRWs indicates a preferred zonal propagation along the midlatitude baroclinic zone. Genesis regions extend from the eastern parts of the continents to the central ocean basins. Only few tracks reach the western side of the downstream continent, with a slightly higher probability in the Pacific region.
The generation of the initial low-level positive PV anomaly occurs predominantly by moist-diabatic processes. Five scenarios of the synoptic-scale flow pattern conducive to DRW formation have been identified (Fig. 8). They all include a pronounced low-level temperature gradient. According to scenarios a and b DRWs can be generated when the flow induced by a surface anticyclone or an upper-level (or low-level) cyclone impinges upon the baroclinic zone causing large-scale ascent or triggering moist convection. DRW genesis also occurs due to forcing of ascent at the downstream side of an upper-level trough. For scenario c it is important that the triggering upper-level trough and the diabatically produced low-level vortex do not phase lock, which leads to the rapid downstream propagation of the low-level PV anomaly as a DRW (and typically the decay of the upper-level trough). Finally, scenarios d and e differ in the sense that initially low-level PV is diabatically produced in a region with only weak or medium baroclinicity (e.g., mesoscale convective vortices in the mei-yu front or tropical cyclones after extratropical transition). This PV feature then moves into an intense baroclinic zone where it starts propagating as a DRW.
This 10-yr climatology for the first time yields statistical information about the frequency of DRWs, their genesis regions and mechanisms, and their typical intensification rate. The results are based upon a carefully designed DRW tracking algorithm, which is characterized by several subjectively chosen threshold values. As a consequence, it has been very important to manually test the output of the DRW identification and iteratively optimize the choice of the threshold parameters. It is far from trivial to automatically identify all subjectively identified DRWs and, at the same time, not to include too many spurious low-level PV features. Careful manual validation has shown that the algorithm as presented in this study provides very reasonable results and is not overly sensitive to moderate changes of the thresholds. In some cases, DRWs in the very early phase are not associated with a local SLP minimum. This part of the DRW tracks is missed by our approach and might lead to a weak bias in the lifetime of the DRWs and of moving the DRW genesis points too far downstream. A promising extension of our feature-based DRW identification algorithm would be, in principle, to consider the energetics of the cyclonic systems (e.g., Parker and Thorpe 1995; Moore and Montgomery 2004, 2005). However, such an analysis appears to be hardly possible for a long-term climatological investigation.
The study provides a climatological picture of DRWs in the Northern Hemisphere, and of their potential to support explosively deepening cyclones. In the future, an extended climatology with a longer dataset would be desirable to generalize our findings, to extend them to the entire globe, and to reveal a potential trend in the frequency and intensity of DRWs. It would also be very interesting to investigate DRWs in future climate simulations (i.e., in an environment with warmer temperatures, increased moisture supply, but potentially reduced baroclinicity). Note, however, that output from fairly high-resolution numerical models is required to identify DRWs. Because of their fairly small-scale and the intense diabatic processes involved, we hypothesize that they cannot be adequately represented by numerical models with resolutions of T106 or below. In terms of numerical weather prediction the correct forecasting of the cases of very rapid DRW intensification constitutes an important challenge as shown by Boettcher and Wernli (2011). The 10-yr database of (explosively deepening) DRWs provides several interesting cases for further in-depth investigations of the involved processes, and in particular of their predictability.
Acknowledgments
We gratefully acknowledge funding from the German Research Foundation (research group PANDOWAE, FOR896) and the Swiss National Science Foundation (Project 200021-130079). The detailed and constructive reviews from Gwendal Rivière and Rich Moore were very helpful for improving the clarity of the paper and highly appreciated. We are also very thankful for the detailed and insightful terminology discussion with Rich Moore and Ron McTaggart-Cowan. The code for the QG vertical motion diagnostic was derived from routines in NDDIAG, a diagnostics package developed and supported by NCAS-CMS (UK National Centre for Atmospheric Science Computational Modelling Services). We thank Sue Gray (University of Reading) for making this package available to us. We are also grateful to Patricia Heckendorn for developing an initial version of the DRW tracking algorithm and to Michael Sprenger for the composite tool. NASA is acknowledged for providing TRMM precipitation estimates.
APPENDIX A
The Wave–Vortex Terminology Issues
The flow feature examined in the present study can be viewed as a hybrid with both wave- and vortexlike characteristics. Therefore each of the two terms that have been introduced in the relevant literature—diabatic Rossby wave (DRW) and diabatic Rossby vortex (DRV)—can be justified using physical arguments. However, neither is able to fully reveal the complex and particular nature of these features. The main intentions of this brief appendix are to (i) emphasize that both terms refer to the same atmospheric flow feature that arises from the same underlying physical processes, and (ii) summarize a few historical aspects of this terminological dichotomy.
The feature we are looking at is a rapidly propagating, low-level, diabatically regenerated positive PV anomaly. Snyder (1991) was the first to look at the PV dynamics of this feature, which he referred to as a “diabatic wave.” He wrote “The heating therefore acts to propagate the distribution of PV … to the east. The propagation of a dry Rossby wave is similar, except the perturbation PV changes through advection of the basic state PV rather than through diabatic generation,” thereby relating the dynamics of this feature to the dynamics of classical (dry) Rossby waves. Parker and Thorpe (1995) subsequently built upon this work and created the notion of a DRW. In section 6 of their paper they noted the isomorphism of the equations describing DRWs and normal Rossby waves. Interestingly they also noted in the abstract that the “system is described as solitary or isolated,” which points to the localized vortexlike appearance of the feature. It is this isolated character of the PV anomaly that motivated Moore and Montgomery (2004) to suggest the alternative term DRV.
Both terms have their pros and cons because of the hybrid character of the feature. Problematic aspects of the wave terminology are that (i) the mathematical isomorphism derived by Parker and Thorpe (1995) is highly idealized and does not provide a clear picture of the “restoring force” involved in the DRW mechanism, and (ii) the appearance of the feature is not wavelike, it rather corresponds to an isolated vortex. In contrast, the main difficulty associated with the vortex terminology is that this notion might be too general and distract from the key aspect of the continuous diabatic regeneration and propagation mechanism, which is fundamentally different from classical (materially conserved) vortices and not the same as diabatically generated low-level PV anomalies (e.g., in tropical cyclones). In addition, the term “Rossby vortex” is used to describe planetary-scale solitary anticyclones akin to Jupiter’s Great Red Spot (Williams and Wilson 1988), in contrast to a mesoscale cyclonic DRV. We conclude that neither of the two terms, DRW and DRV, is clearly superior which is why probably both terms will continue existing. In this study, we use the term DRW throughout for consistency with previous studies from this research group to describe this fascinating, essentially diabatic phenomenon.
APPENDIX B
Two Examples of DRW Life Cycles
a. North Atlantic DRW 138
The Atlantic DRW 138B1 is a typical example of the frequent type of DRWs that remain moderately intense cyclones and do not experience an explosive deepening as a cyclone bomb. The initial PV anomaly of this DRW develops in a large precipitation area off the North American east coast at 38°N, 74°W on the late 7 April 2003. Precipitation and the associated formation of the initial low-level PV disturbance are induced by the lifting downstream of an upper-level trough. The DRW generation can therefore be assigned to scenario c (see section 4b). The fairly large low-level PV anomaly propagates as a DRW along the midlatitude baroclinic zone toward the east during the next 60 h (Fig. B1a). During this long propagation phase the low-level PV anomaly is located below a large-scale upper-level ridge. At the end of the propagation phase the DRW approaches the jet at the eastern flank of the ridge (Fig. B1b; at 40°N, 29°W). To the west of the DRW a new cyclone develops, which is visible in Fig. B1b at about 48°W. During the next 12 h the cyclone upstream intensifies, leading to the rapid formation of a pronounced downstream ridge (Fig. B1c). As a consequence, the DRW is again located beneath an upper-level ridge (Fig. B1c; at 40°N, 18°W). It propagates farther to the east and slowly decays. The track of this DRW is almost perfectly zonal and the surface pressure decrease remains fairly moderate (Fig. B1d).
Life cycle of the North Atlantic DRW 138: PV at 850 hPa (shading, PVU), SLP (thin lines, interval 5 hPa) and PV at 250 hPa (thick lines for 1.5 and 2 PVU) at (a) 0000 UTC 9 Apr 2003, (b) 0000 UTC 11 Apr 2003, and (c) 1200 UTC 11 Apr 2003. (d) Temporal evolution of the cyclone’s minimum SLP (hPa).
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
b. North Pacific DRW 551
The Pacific DRW 551 reveals a spectacular life cycle, starting with a rather exceptional genesis process (Hofmann 2010). The primary low-level PV anomaly is generated by the southwesterly flow of Typhoon Mitag against the midlatitude baroclinic zone on 27 November 2007 (not shown). This process corresponds to scenario b, as shown in Fig. 8 (see section 4b). Afterward, the PV anomaly propagates at the southern edge of the baroclinic zone to the northeast. Two days after the genesis of the low-level PV anomaly, two tropical depressions merge with and amplify the system, which instigates the propagation phase of the DRW (Fig. B2a; at 29°N, 139°E). During the following two days the DRW propagates more than 3000 km to the east below a pronounced upper-level ridge. The propagation phase is characterized by a nearly constant central SLP (Fig. B2d). At the end of the propagation phase, on 1 December 2007, the DRW approaches the axis of the upper-level jet with a slightly weakened low-level PV anomaly. On the following day an upper-level wave develops along the jet, which starts to interact with the low-level system (Fig. B2b; at 36°N, 159°W). On 2 December the central SLP of the cyclone deepens by 32 hPa in 12 h (Fig. B2c; at 38°N, 153°W) and reaches a minimum SLP of 944 hPa in the eastern North Pacific. Despite a distance of more than 2000 km between the cyclone center and the West Coast the strong pressure gradient and the huge spatial dimension of the cyclone led to dramatic surface winds over the western United States. These winds, together with intense precipitation and flooding, caused devastating damages in the U.S. states Oregon and Washington [see again Hofmann (2010) and Crout et al. (2008)]. This example again highlights the potential of DRWs to intensify explosively into high-impact weather systems.
Life cycle of the North Pacific DRW 551: as in Fig. B1, at (a) 0000 UTC 29 Nov 2007, (b) 0000 UTC 2 Dec 2007, and (c) 1800 UTC 2 Dec 2007.
Citation: Monthly Weather Review 141, 3; 10.1175/MWR-D-12-00012.1
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For brevity, from here on the term “Atlantic” denotes the North Atlantic region specified above, and “Pacific,” the North Pacific region.
ΔSLP (Bergeron) = ΔSLP (hPa) × [sin(60°)/sin(φ)]/24h, where φ denotes the averaged latitude of the cyclone center during this 24-h interval. The deepening rate is then determined as the maximum value of ΔSLP for all 24-h intervals along the DRW track.
This system is not registered by our tracking algorithm because the track disconnected at one time step due to too weak low-level PV when the system crossed the Appalachians.
These DRWs occurred at 0600 UTC 17 October 2002, 1200 UTC 6 March 2003, 1800 UTC 18 March 2004, 1200 UTC 16 December 2004, and 1200 UTC 22 January 2007 in the North Atlantic, and at 1200 UTC 7 October 2003, 1800 UTC 12 December 2005, 0600 UTC 4 November 2007, 1200 UTC 1 December 2007, and 0600 UTC 7 March 2010 in the North Pacific (dates refer to the start time of the 24-h intensification period).
The complete list of identified DRWs is available from the authors.
