1. Introduction
The evolution of an extratropical transition (ET) event is difficult to forecast with numerical weather prediction models. On the one hand, ET is very sensitive to the phasing between the tropical cyclone (TC) and an approaching midlatitude trough (Klein et al. 2002; Ritchie and Elsberry 2007); on the other hand, the structure of the downstream flow can influence reintensification during ET (McTaggart-Cowan et al. 2003, 2004). Thus, small uncertainties in either the location of the TC or the structure of the midlatitude trough can lead to large errors in both the track and the intensity forecast during ET. Furthermore, the increased translation speed and the possible rapid intensification when the TC enters the midlatitudes pose serious problems for forecasters (Jones et al. 2003).
A deterministic forecast alone yields no quantitative information about the uncertainty of either the forecast or the predictability of the atmospheric situation. Because there are often large errors in deterministic forecasts of ET (Jones et al. 2003), it is essential to obtain information about the probability of a particular forecast. Ensemble forecasts not only give information about the predictability of synoptic events, but they also represent a large set of dynamically consistent possible evolutions of the events. Furthermore, they can give information about scenarios that are less likely but still possible.
An ensemble forecast of a poleward-moving TC is often characterized by a large variability among the individual members, indicating low predictability (Harr et al. 2008). Through investigation of the representation of ET events in an ensemble prediction system we can gain insight into both the predictability associated with an ET event and the dominant dynamical mechanisms for ET.
Harr et al. (2008) presented a statistical methodology to examine the behavior of the individual ensemble members in the regions of high variability associated with ET. The method consists of a combination of empirical orthogonal function (EOF) analysis and clustering of the first two principal components. Thereby we can group ensemble members together that contribute in a similar way to the main variability. The method was applied to the case of Typhoon Nabi (2005) and EOF patterns were found associated with the east–west location and the amplitude of a so called trough–ridge–trough pattern.
In this paper the analysis is applied to five TCs that underwent ET. They were chosen such that they included both strong and weak ET events that occurred over the North Atlantic and the western North Pacific Ocean basins. One of the main goals of this investigation is to consider how ensemble forecasts could be made more accessible to operational forecasters. Thus, the grouping of ensemble members will be examined here with respect to its use in dividing the large number of ensemble members into a few scenarios that can be used for operational forecasts more easily.
In section 2 a synoptic overview of the five ET cases is given. In section 3 the uncertainty associated with ET in the ensemble prediction is shown in terms of the variability between the ensemble members. In section 4 the recurring variability patterns and selected clusters that illustrate the different scenarios are presented. Conclusions are provided in section 5.
2. Overview of cases
For this investigation of the impact of ET on ensemble prediction we used forecasts from the ensemble prediction system (EPS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). The EPS includes a set of 50 integrations calculated with perturbations added to the analysis, and one control forecast calculated with unperturbed initial conditions. The initial perturbations are described by rotated singular vectors (Molteni et al. 1996; Leutbecher and Palmer 2008). The different initial states are a priori assumed to be equally likely. The horizontal resolution of the ensemble members for our cases is ∼80 km (TL255) with 40 levels in the vertical (Buizza et al. 2003). These forecasts, along with the ECMWF high-resolution deterministic forecast that had a horizontal resolution of ∼40 km (TL511) and 60 vertical levels at the time of this investigation, are compared with the ECMWF analysis. The ensemble and deterministic forecasts are initialized twice daily. The ensemble forecasts are available on a 1° latitude × 1° longitude grid and the deterministic forecasts and analyses are on a 0.5° latitude × 0.5° longitude grid.
We have investigated the representation in the EPS of the North Atlantic Hurricanes Fabian (2003) and Philippe (2005) and the western North Pacific Typhoons Maemi (2003), Tokage (2004), and Saola (2005). These cases are divided into strong (Fabian, Maemi, and Tokage) and weak (Philippe and Saola) events. The strong events are characterized by a reintensification after ET and a marked influence on the midlatitude flow. The weak events either decay before ET or do not reintensify after ET and do not appear to influence the midlatitude flow. The weak events are chosen because of large forecast errors associated with their representation of ET. An overview of the cases with their time of recurvature and of ET can be found in Table 1. (The terms investigation time, FCST1, and FCST2 are discussed later.)
As in Harr et al. (2008), the key variable for our investigation is the potential temperature on the dynamic tropopause [defined as the 2-potential vorticity unit (PVU; 1 PVU ≡ 10−6 K m2 kg−1 s−1) surface]. The choice of this variable has the advantage that the dynamics of one conserved variable can be viewed along the surface of another conserved variable in adiabatic, frictionless conditions (Hoskins et al. 1985).
a. The strong events
Each of the TCs Fabian (2003), Maemi (2003), and Tokage (2004) interacted with a midlatitude trough, seen as a region of low potential temperature on the dynamic tropopause. In the case of Fabian, the trough was already deep before the interaction and approached from upstream as the decaying TC moved toward the midlatitudes (Fig. 1a). The decaying Fabian merged with the midlatitude low pressure system associated with the trough, but ex-Fabian was clearly the dominant system. A trough also could be seen upstream of Maemi (Fig. 1c). However, the trough was weaker than in the case of Fabian and appeared to intensify as the outflow from Maemi impinged on the midlatitude jet. It is difficult to identify an upstream trough as Tokage approached the midlatitude jet (Fig. 1e). In this case, the ridge downstream of Tokage, seen as anomalously high potential temperature on the dynamic tropopause, amplified dramatically as the outflow of Tokage interacted with the midlatitude jet. This amplification led to the formation of an upstream trough, as described by Bosart and Lackmann (1995) for Hurricane David (1979). In all three cases a distinct pattern formed, which consisted of the trough that interacted with the TC, a ridge directly downstream, and a second trough downstream of the ridge. Recent studies of ET describe how the TC outflow can contribute to the ridge building (Henderson et al. 1999) and to the subsequent amplification of the downstream trough (Riemer et al. 2008).
The synoptic development after the ET is quite different in each of the cases. Fabian interacted with the upstream trough that rolled up cyclonically during ET. A strong blocking ridge associated with weak zonal flow emerged downstream of the ET system and inhibited the system from moving eastward. The ex-TC turned back to the northwest and the whole system reintensified strongly (Fig. 1b).
In the case of Maemi, the extratropical cyclone that resulted from the ET and a low pressure center associated with the downstream trough of the trough–ridge–trough pattern developed equally strongly. As in the case of Fabian, Maemi was prevented from traveling eastward directly after its ET by a strong blocking ridge. The trough associated with the ET rolled up cyclonically and both ex-Maemi and the downstream low intensified moderately (Fig. 1d). The ridge did not weaken until 60 h after ET so that ex-Maemi could then travel eastward (not shown). The downstream low then intensified to a strong low pressure system over the west coast of North America.
The ridge that developed as Tokage’s outflow interacted with the midlatitude jet had a northeast–southwest orientation with quite strong southwesterly flow. Therefore, in contrast to the cases of Fabian and Maemi, it moved to the east quite quickly. A strong potential temperature gradient can be seen directly to the northwest of Tokage near to the crest of the ridge 12 h after the TC had interacted with the midlatitudes (Fig. 1f). The associated high vertical wind shear and the positive stretching deformation acted to flatten the ridge and to reduce the perturbation kinetic energy at upper levels (Webster and Chang 1997). After the significant weakening of Tokage because of its landfall in Japan, the ET system reintensified moderately as a small-scale trough to the west of the ridge rolled up cyclonically. Through the continuing tilt of the ridge to the northeast, the anticyclonic upper-level flow acts to thin the downstream trough that consequently formed a cutoff low at about 175°E (Fig. 1f).
b. The weak events
The weak events of Philippe and Saola were chosen for this investigation because their deterministic forecasts were highly inaccurate. Saola underwent ET and its remnants were absorbed by a large-scale midlatitude low pressure system that subsequently intensified. However, the deterministic forecast failed to predict the ET. Philippe decayed to a remnant low on 1800 UTC 23 September, but a strong ET was predicted incorrectly by the deterministic forecasts initialized up to 4 days before its decay.
Saola recurved ahead of a very weak midlatitude trough (Fig. 2a). A second upstream trough steered the ex-TC eastward (Fig. 2b). At that time a large-scale quasi-stationary extratropical low pressure system was situated northeast of ex-Saola and affected the track of the TC. The pattern has a strong resemblance to the northeast pattern described in Harr and Elsberry (2000). The influence of the upstream trough decreased, and 48 h later Saola’s remnants were absorbed by the downstream low.
The position of Saola in the 84-h deterministic forecast that is verified at 0000 UTC 27 September 2005 (Fig. 2c) indicates that Saola did not recurve, even though the initialization time of this forecast was only 24 h before the recurvature time. In the deterministic forecast Saola decayed south of Japan. Only the forecast from 0000 UTC 24 September, which was initialized following the turn of Saola toward the northwest, predicted the recurvature.
Philippe was a very small-scale system that could not be resolved in the ECMWF analysis after 1200 UTC 21 September. However, the surface reflection of an upper-level cold low could be seen at about 30°N, 65°W (Fig. 3a). When Philippe was reported as decayed on 1800 UTC 23 September, its remnant vorticity center could still be seen [National Hurricance Center (NHC) 2006 official report; available online at http://www.nhc.noaa.gov]. Thus, we suggest that the remnants of Philippe reinforced the cold low. On 26 September (not shown) a strong ridge that seemed to be sustained by the outflow of Hurricane Rita (2005) had developed upstream of the remnants of Philippe. The ridge inhibited an upstream midlatitude trough from approaching and interacting with the cold low at this time. The surface low pressure system ahead of that upstream trough, situated at about 45°N, 60°W (Fig. 3b), had already absorbed the remnant low of ex-TC Rita (NHC 2006 official report; available online at http://www.nhc.noaa.gov) and subsequently absorbed the cold low containing the remnants of Philippe. The resulting system intensified strongly ahead of a strong upper-level potential temperature gradient on 0000 UTC 29 September (not shown). Thus, Philippe contributed indirectly to the reintensification of the midlatitude system.
The deterministic forecast for 1200 UTC 23 September, initialized at 1200 UTC 19 September (i.e., 4-day forecast; see Fig. 3c), predicted a larger-scale TC Philippe than that observed. Philippe’s position and the upper-level development were forecast quite well for that time. However, 12 h later in the same forecast (not shown) Philippe interacted with an upstream trough that extended far south and the ex-TC reintensified strongly. On 1200 UTC 27 September (i.e., 8-day forecast; see Fig. 3d) the strong ET system merged with a midlatitude low that was connected to a second upstream trough.
3. Uncertainty associated with ET
In this section the variability in the EPS associated with the ET events is described using the TC tracks from the analysis, the deterministic forecast, and the ensemble forecasts for each case. The tracks are calculated by locating the minimum mean sea level pressure in a region defined by two boxes. One of them extends 3°S–7°N, 5°E–5°W beyond the previous TC position. The other extends 5° in the east–west and 7° in the north–south directions, with its southwest corner 5°E of the TC position. This accounts for the high translation speed of the system after ET. A maximum pressure change of 30 hPa in 12 h is allowed to exclude the detection of other TCs close by. In addition, Hovmoeller plots of the standard deviation of the 500-hPa geopotential from the 51 ensemble members are averaged over the latitude band of 40°–50°N. This particular measure of the ensemble spread in this latitude band illustrates both the variability in the midlatitude pattern of troughs and ridges, and the variability in the representation of the tropical cyclone in question as it moves into the midlatitudes.
The Hovmoeller plots described above were examined for forecasts initialized daily at 1200 UTC from a date well before recurvature until shortly after recurvature. Based on these Hovmoellers, two forecast times were chosen for each case (Table 1): the first is well before recurvature, when the variability between the ensemble members was highest (FCST1), and the second is close to or at the time of recurvature (FCST2). Through this choice we are able to observe the decrease in the uncertainty associated with the recurvature from the first to the second forecast time and to isolate the uncertainty associated with the ET itself from that associated with the recurvature.
a. The strong events
A comparison of the enhanced variability in the vicinity of the ET events shows certain similarities between the three strong events. Local maxima in standard deviation can be seen upstream, around, or downstream of the ET event. The relative strengths of these maxima differ from case to case, as described below.
1) Fabian
The track of Fabian in the deterministic forecast for FCST1 was quite similar to its analysis up to recurvature, but the deterministic forecast did not capture the acceleration afterward. Six hours after ET time there is a difference of over 800 km (Fig. 4a) between the TC position in the analysis and the deterministic forecast. Both the analysis and deterministic forecast are situated within the tracks of the ensemble members. The ensemble tracks indicate uncertainty in the forecast of the recurvature, that is, after 48–60 h. In some ensemble members the TC accelerates after recurvature, whereas in others, especially those situated at the eastern edge of the plume (at about 35°N, 60°W), it remains slow moving or even decays. Thus, a separation of over 1000 km between the individual positions is seen after 72 h. The ensemble members for the forecast from FCST2 (Fig. 4b), when the TC motion had already changed from northwestward to northward, no longer show the substantial increase in spread after the recurvature. However, close to the ET time (after about 60 h in Fig. 4b) the TC positions in the members vary noticeably, indicating uncertainty in the ET event. The track in the deterministic forecast lies in the middle of the ensemble tracks while the analysis track differs markedly from the deterministic forecast and lies on the flank and sometimes even outside of the ensemble tracks.
The uncertainty in the recurvature for FCST1 can be seen as increased standard deviation from 0000 UTC 7 September (60-h forecast) at about 50°W (Fig. 4c). High values extend from the ET time and position (black dot) and even higher values can be found upstream at about 60°W from 12 h after the ET in Fig. 4c. This can be explained through high variability in the ensemble associated with the mature midlatitude system that developed from the ET of Fabian. The system cannot move to the east because of the blocking ridge mentioned in section 2a. Thus, it loops backward to interact with another upstream trough. This second interaction can be seen in Fig. 4c as the local maximum associated with the ET event and that associated with the upstream trough in the mature midlatitude system merge on 0000 UTC 12 September. Another plume with high values of standard deviation can be found well downstream of the ET event. These are linked to a downstream trough that deepened in association with the amplification of the blocking ridge directly downstream of the ET of Fabian. In the ensemble forecast from FCST2 the plumes with high standard deviation associated with the ET of Fabian and with the downstream trough have decreased strongly in amplitude. However, they can still be distinguished clearly from 30 h after the ET (Fig. 4d). The highest variability in the forecast from 5 September is connected to the interaction of the ET system with the second trough mentioned above that approached from upstream of the ET event.
2) Maemi
In the case of Maemi, again there is significant variability associated with the recurvature after about 48 h in the tracks for FCST1 (Fig. 5a). The track spread increases during ET, so that the locations of the TC in the ensemble members differ by over 2000 km after 4 days. During recurvature, the analysis and deterministic forecast are on the eastern edge of the set of ensemble tracks. The spread in the ensemble members for FCST2 (Fig. 5b), initialized when the motion of Maemi had an eastward component in the analysis, is much smaller and increases more slowly than for the earlier forecast time. Nevertheless, shortly after ET (from 48 h) the spread increases. Both the analysis and deterministic forecast tracks are close together until ET time for FCST1 and FCST2, but they differ by over 700 km for 18 h after ET in FCST2.
The Hovmoeller plots from FCST1 and FCST2 (Figs. 5c,d) show enhanced values of standard deviation in the vicinity of the ET but much higher values exist downstream of the ET event. This illustrates that the variability in the downstream trough (section 2a) is higher than that of the ET itself. The standard deviation is largest from 14 to 17 September at about 180°. The region of higher values from 1200 UTC 17 September at about 135°W is still connected to the variability in the downstream trough, but the wave has flattened at that time and the predictability has increased. In FCST2 the enhanced values at about 180° from 14 to 16 September (Fig. 5d) have decreased strongly, as in the case of Fabian for the later forecast time. Nevertheless, the variability in the downstream trough is still larger than in any other region at this time.
3) Tokage
Before ET time the deterministic track forecasts for FCST1 and FCST2 of Tokage are quite close to the analyzed track (Figs. 6a,b) and both fall within the ensemble track forecasts. There is uncertainty associated with the time of recurvature for FCST1 (Fig. 6a). Furthermore, a noticeable increase in spread can be seen at the time of ET, and here the analysis track lies at the edge of the ensemble tracks while the deterministic forecast is situated in the center. All but two ensemble members show the tracks to be farther north than in the analysis. In Fig. 6b it can be seen that there are several tracks south of the analysis and around it in the ensemble members from FCST2. Tokage can no longer be identified in the group of southern forecasts after a forecast time of 84 h. The northern group of ensemble members continues to track Tokage.
The weakening of Tokage during ET associated with its landfall in Japan is not captured in either the ensemble or deterministic forecasts. In FCST1 (Fig. 6c) at 108 h the central mean sea level pressure varies between 945 and 985 hPa in the ensemble forecasts compared with the analyzed value of 993 hPa. Only three members show a weakening of the central mean sea level pressure to the same value as the analysis, and this only after 132 h. In FCST2 (Fig. 6d), a subset of ensemble members shows no or only a weak reintensification after ET and similar central pressure values to the analysis after 72 h. Some members do not track the ex-TC after 84 h of forecast time. The remaining members and the deterministic forecast weaken during the transformation stage, but they reintensify after ET.
The plume of high standard deviation originating at ET time in the FCST1 Hovmoeller plot (Fig. 6e) is clearly associated with the ET system itself. Compared to the other two strong events the high values decrease quite quickly. However, a large maximum downstream at about 150°W on 23 October indicates a downstream propagation of the uncertainty associated with the ET. A similar downstream propagation can be seen in the Hovmoeller plot for FCST2 (Fig. 6f). One day after ET there are two localized maxima that decrease in amplitude quite quickly. One is directly associated with the ET of Tokage and one with the ridge downstream of the ET at about 180°. Two days after ET the uncertainty is associated with the downstream trough at about 135°W.
The three strong events illustrate that the variability associated with an ET event can be found either upstream, around the ET system, or in the downstream development. It has been shown that the recurvature and the ET event are the main sources of uncertainty. In general, the closer the forecast time is to the ET the more predictable the flow.
b. The weak events
The variability within the ensemble forecasts for TCs Saola and Philippe exhibits similar behavior as that for the strong events in that there are plumes of high uncertainty associated with and downstream of the ET events. In the weak events the main source of variability is the interaction of the ex-TC with a large-scale midlatitude low pressure system. Different realizations of this interaction could be characterized either by the ex-TC or the midlatitude low intensifying after the merger, or two systems of similar strength merging. Furthermore, a distinct number of ensemble members forecast a decay of the TC and a reintensification of the midlatitude low without an interaction between the two.
1) Saola
In the ensemble track forecast of Saola from FCST1 (Fig. 7a) only a few ensemble members recurve and only six of them do not decay in the early stage of ET. The deterministic forecast agrees with the majority of the ensemble members and does not predict the recurvature, while the members that contain the recurvature, especially the six nondecayers, are grouped around the analysis. Thus, a low probability is assigned to the recurvature by the ensemble. In FCST2, however, there is better agreement among the ensemble members, with all having about the same direction of motion. Nevertheless, a closer inspection shows that Saola cannot be identified after 36–48 h in many members that lie on the southern edge of the plume of tracks. In the deterministic forecast Saola moves in the same direction as in the analysis, but whereas the final analyzed position of Saola is 40°N, 150°E at 0000 UTC 27 September, Saola reaches that position 24 h later in the deterministic forecast.
The Hovmoeller plot from FCST1 for Saola (Fig. 7c) shows a distinct maximum in standard deviation values downstream of the ET event around 48 h after ET at about 160°W. We attribute this maximum to uncertainty in the ensemble associated with the prediction of a midlatitude trough with which Saola will interact (black triangle). In the ensemble forecast, however, the uncertainty at 160°W cannot be attributed to Saola, because the TC enters the latitude band between 40° and 50°N in only 6 of the 51 ensemble members. Thus, the Hovmoeller plot does not show much uncertainty associated with the ET of Saola itself (black dot). In FCST2 (Fig. 7d), however, a weak plume with a higher standard deviation can be seen at 1200 UTC 26 September at about 175°W emanating from the ET of Saola. The highest variability develops following the interaction of ex-Saola (black triangle) with the midlatitude trough.
2) Philippe
A large spread can be seen in the ensemble track forecasts for Philippe (Fig. 8a,b). In FCST1 (Fig. 8a), Philippe decays south of 30°N without recurving in the western ensemble members, but recurves north of 30°N in the eastern ones. The deterministic forecast track lies on the eastern edge of the ensemble tracks and shows a recurvature. Only one ensemble member lies to the east of the deterministic forecast from 0000 UTC 23 September. Two of the recurving ensemble members follow the deterministic forecast quite well. In the analyzed track Philippe is located at the edge of the ensemble envelope but close to the deterministic forecast. However, Philippe decays at 1200 UTC 23 September, whereas it can be identified for an additional 2 days in the deterministic forecast. In FCST2 (Fig. 8b), more members recurve and do so farther south. About 60% of the members decay after 144-h forecast time. One member is very similar to the deterministic forecast that shows Philippe far to the east after 168 h. For both of these forecast times Philippe can be identified in the deterministic forecast for a much longer time than in the analysis.
The variability in the environment of Philippe at the time of its decay cannot be shown in the Hovmoeller plots (Figs. 8c,d) because the TC is situated south of the latitude band of 40°–50°N. A white circle denotes Philippe’s longitudinal location at 1200 UTC 23 September. The higher standard deviation plume that can be seen for FCST1 (Fig. 8c) from 22 September at about 65°W and for FCST2 (Fig. 8d) from 23 September at about 55°W is due to variability associated with a midlatitude trough. This midlatitude trough formed a weak cutoff low (at about 30°N, 70°W in Fig. 3a) that steered the remnants of Philippe to the north. On 1200 UTC 27 September, the time when the cold low that had been reinforced by Philippe merged with the large-scale midlatitude low pressure system, a prominent maximum of standard deviation can be seen in both Hovmoeller plots. Thus, large uncertainty in the ensemble is associated with the different realizations of the merger and the development thereafter. The values in the maximum for FCST2 are lower than in FCST1 and the highest variability area is narrower.
In general, an operational forecaster might give more weight to the high-resolution deterministic forecast because it is more likely to capture small-scale systems like TCs that undergo ET. For example, in the case of Philippe, a forecaster might suggest that the ensemble cannot resolve Philippe. These weak events suggest that ensemble forecasts both assign probabilities to the deterministic forecast and indicate scenarios that are possible even if they are not very probable. This study shows that for the case of Philippe the forecaster should regard any single deterministic forecast with caution. In Saola’s case the recurvature was already indicated in the ensemble forecast 3 days prior to its occurrence, while the deterministic forecast did not predict it until its onset.
4. Clustering the ensemble members
In section 3 we found an increase of standard deviation among the ensemble members (i.e., low predictability) associated with the five ET events. The ensemble forecast becomes less uncertain when the forecast time is close to or at the point of recurvature. To investigate the source of these uncertainties the high standard deviation is examined in all five cases with the aid of the analysis method described in Harr et al. (2008). The goal was to obtain physically relevant scenarios related to the high uncertainty. Furthermore, we want to gain insight into the relation between the EOFs and these scenarios.
The EOFs are calculated for each case for the time at which a noticeable increase in the ensemble standard deviation could be seen in the plume originating from the ET location on the Hovmoeller plot. As in Harr et al. (2008), this time is referred to as the investigation time. We did not use the time of maximum standard deviation in the plumes because this occurred typically several days after ET. For this later time we probably would not be able to depict the different ET scenarios that are responsible for the variability in the ensemble members. The investigation times for the five cases can be found in Table 1. Because the ECMWF ensemble has 51 members we can perform the analysis for one ensemble forecast, rather than combining four forecasts, as in Harr et al. (2008).
During Philippe’s life cycle the ensemble forecasts exhibited high variability in the midlatitude flow that was unrelated to Philippe. Because we are interested in the contribution of the ensemble members to the variability associated with Philippe, we confined the region for which we calculated the EOFs to 10°–40°N, 50°–80°W. In this region EOF 1 and 2 represent over 30% of the total variability both in FCST1 and FCST2.
In all five cases the main variability, as depicted by the first two EOFs, is caused by different representations of the trough–ridge–trough pattern described in section 2a. Two predominant patterns can be identified (Fig. 9): The shift pattern describes the east–west displacement of the trough–ridge–trough pattern and the horizontal tilt of the troughs and the ridge. The amplitude pattern describes the amplification or flattening of the ridge (Fig. 9). A positive contribution to the shift pattern represents an eastward shift and a negative contribution to the shift pattern represents a westward shift. A positive contribution to the amplitude pattern represents an amplification and a negative contribution represents a flattening of the ridge. Note that the signs at the centers of action are arbitrary.
The identification of the shift (Fig. 9a) and amplitude (Fig. 9b) patterns in the EOFs is illustrated for Maemi and Fabian (FCST1) and for Saola (FCST2). For Maemi, the location of the centers of action relative to the trough–ridge–trough pattern for EOF 1 (Fig. 10a) and EOF 2 (Fig. 10b) is almost exactly the same as that in the schematic. Thus, for Maemi, the shift (EOF 1) and amplitude (EOF 2) patterns are separated optimally in the EOFs. In the case of Fabian, EOF 1 (Fig. 10c) is more a mixture between the shift and amplitude pattern and EOF 2 (Fig. 10d) mainly describes the amplitude of the pattern. For Saola, EOF 1 (Fig. 10e) describes the amplitude and EOF 2 (Fig. 10f) the shift pattern. The variability patterns of Tokage (not shown) are almost identical to those of Maemi. For Philippe (not shown), EOF 1 depicts variability in the amplitude of the ridge and EOF 2 shows variability in the amplitude of the upstream trough as well as the shift of the ridge.
The temporal evolution leading to and resulting from the variability among EPS members is examined using the fuzzy cluster analysis of the principal components associated with EOF 1 and EOF 2 to describe the contribution of the individual ensemble members to the main variability. The combination of the principal component analysis with the clustering analysis has the advantage that the development of the grouped members before and after the time of investigation can be observed (Harr et al. 2008).
The number of clusters was always less for FCST2 (Table 3) than for FCST1 (Table 2). It was shown in section 3 that the variability was smaller for FCST2 in all the cases. This agrees with the hypothesis of Harr et al. (2008) that the number of scenarios decreases as the forecast time approaches the ET time. In all cases the first two EOFs contribute about 25%–40% to the total variability for FCST1 (Table 2) and 20%–30% for FCST2 (Table 3). Hence, clustering EOF 1 and EOF 2 takes into account a large part of the total variability in the shift and amplitude of the key synoptic-scale features associated with the ET and downstream circulations. For Philippe the percentage is highest, because the region over which the EOFs are calculated is smaller than for the other four cases as mentioned above. For the other four cases, decreasing the domain size does not alter the structure of the EOFs.
Only the magnitudes and relative signs of the centers of action are important. To examine the links between the representation of the ET in the individual clusters and the contribution of each cluster to the EOFs, the pattern of Maemi has been taken as a reference and the signs of the other cases have been changed accordingly. The nature of the contribution to the EOF in question is given for each cluster in Tables 2 and 3.
For the five cases some remarkable similarities can be found between clusters with the same sign for their contribution to the EOFs. These are described below in terms of the shift and amplitude pattern based on FCST1 for all cases except Soala. Because there is no interaction of Saola with the midlatitude flow in most of the ensemble members of FCST1 (section 3b), applying the analysis method to the ensemble forecast for this investigation time does not yield meaningful results with respect to different representations of ET. Thus, FCST2 for Saola is discussed. In the case of Philippe the discussion below refers to the trough at about 30°–35°N, 70°–80°W and the ridge at about 30°–35°N, 50°–70°W (Fig. 3a).
a. Positive shift pattern
The clusters that contribute positively to the shift pattern (Figs. 11c, 12c, 13a,b, 15a and 16a,b) are either in a mature state or have decayed already. In all but one positive shift case, the downstream ridge on the dynamic tropopause either is tilted southwest–northeast (Figs. 11c, 12c, 13b, 16a,b) or is significantly eroded (Fig. 13a). A positive contribution to the shift pattern favors the formation of a cutoff low from the downstream trough. This can be seen clearly for Tokage (Figs. 13a,b). For Saola, the ridge is shifted downstream rather than tilted (Fig. 15a). This leads to the ET system being close to the midlatitude potential temperature gradient in a favorable region for reintensification. These positive contributors to the shift pattern develop and decay quickly (not shown). The systems reintensify deeply in the Fabian cluster and in both Tokage clusters, moderately in the Maemi cluster, and weakly in the Saola and in one of the Philippe clusters (see Fig. 16a and Table 2). In the second Philippe cluster (Fig. 16b) the trough passes north of Philippe and the TC decays.
b. Negative shift pattern
The negative contributors to the shift pattern (Figs. 11a,b, 12d, 13c, 15b and 16c,d) represent a delayed development of the ET system because the westward shift of the trough delays its interaction with the tropical system. The second Fabian cluster (Fig. 11b) will be discussed in section 4e. In the other cases the troughs have begun to wrap up cyclonically as in the cyclonic paradigm and the ridges are oriented meridionally. The surface pressure shows the systems either in their early stage of ET (up to 24 h before peak intensity) or just reaching their peak intensity. Subsequently, they reintensify strongly and develop into persistent almost stationary systems after interaction with the midlatitudes, as illustrated for Tokage (Fig. 14). Moreover, the north–south orientation of the ridges and the nearly stationary ET systems allow the downstream troughs to persist and the associated downstream surface pressure systems (e.g., at about 140°–160°W in Fig. 14b) to intensify. In the case of Saola the ex-TC is well east of the upstream trough, a region that is not favorable for reintensification (Fig. 15b). The TC weakens further and is absorbed subsequently by the midlatitude system downstream. For Philippe this combination of a negative contribution to the shift pattern and a strong positive contribution to the amplitude pattern (as described below) gives a particularly favorable configuration for a strong ET in this smallest cluster (Fig. 16d).
c. Positive amplitude pattern
A positive contribution to the amplitude pattern indicates a high-amplitude trough–ridge–trough pattern (Figs. 11a, 12b, 13b, 15a and 16a,d). In the clusters of the strong events the TCs moved toward the baroclinic zone and appeared to steepen the potential temperature gradient through their outflow. All of the strong events that contribute positively to the amplitude pattern reintensify strongly. The weak events do not seem to be active in the ridge building, but their position close to the midlatitude potential temperature gradient leads to a strong reintensification for one of the Philippe clusters (Fig. 16d) 36 h after the time shown. The other Philippe cluster reintensifies weakly at a later time (Fig. 16a). The Saola cluster has already reintensified weakly (Fig. 15a). In the Saola cluster the ex-TC moves to the west and merges with the large-scale midlatitude system 24 h later. The position of the approaching upper-level troughs for the strong events was favorable for a further steepening leading to cyclogenesis upstream (Hirschberg and Fritsch 1991).
d. Negative amplitude pattern
A negative contribution to the amplitude pattern indicates more zonal upper-level flow than in the ensemble mean (Figs. 11b, 12a, 13a,c, 15b and 16b,c). This is particularly marked for Fabian, Maemi, and Philippe. For Fabian (Fig. 11b) and Maemi (Fig. 12a) the ridge is large scale and shallow and there is no wrap up in the upstream trough. Fabian decayed after completion of its recurvature (3 days before the time shown in Fig. 11b) without undergoing ET because the upstream trough was too far west and thus was not favorable for an interaction. Ex-Maemi’s track was influenced by the upstream midlatitude trough that steered it to the east, but it did not reintensify because it was to the east of the potential temperature gradient. These two clusters (Figs. 11b and 12a) show no ET or ET without reintensification. No upstream trough can be seen in the Philippe cluster (Fig. 16c) and the ex-TC has decayed already. The strength of Saola in the midlatitudes is noticeably weaker in Fig. 15b than in Fig. 15a because of its weaker upstream trough and weaker potential temperature gradient between the upstream trough and the ridge. Therefore, Saola merges with the large-scale midlatitude system downstream 24 h later than in the cluster with positive contribution to the amplitude pattern.
For Tokage (Figs. 13a,c) the flow patterns differ from a typical negative contributor to the amplitude pattern. The ridges are slightly shallower than in Fig. 13b but the ET systems undergo deep reintensification. This is primarily due to the high-amplitude trough–ridge pattern of the ensemble mean. Also, in the case of Tokage, the shift pattern explains a much larger part of the total variability (22.0%) than the amplitude pattern (10.8%; see Table 2). Therefore, the influence of the amplitude pattern on the development of the individual clusters is much weaker.
e. Outliers
Another noticeable parallel can be found in the clusters for Fabian, Tokage, and Philippe. All three of them have one comparatively small cluster (Table 2), with a cluster mean (Figs. 11b, 13a and 16d) that exhibits a markedly different development of the atmospheric flow pattern than the ensemble mean and the other cluster means. For Maemi a cluster representing a markedly different scenario also exists (Fig. 12a), but it is not smaller than the other Maemi clusters. The different development in the case of Tokage (Fig. 13a) also can be seen in the strong positive contribution to the shift and in the case of Philippe (Fig. 16d) in the strong positive contribution to the amplitude pattern. In the cases of Fabian (Fig. 11b) and Maemi (Fig. 12a) the outliers show quite a zonal flow. In the case of Tokage the outlier is the one that shows the fastest development and decay of the ET system. Here the dynamical tropopause is already flattening while in the other Tokage clusters the ridge is in the process of steepening or reaching its peak. For Philippe the outlier is the only one that shows a strong reintensification. Note that the outliers show the highest differences to the analysis.
f. Comparison with analysis and deterministic forecast
In all of the cases except Saola the clusters found in the ensemble forecasts from FCST1 yield quite different possible scenarios, which all have comparable probabilities. Although the analysis is most often within the ensemble spread (section 3a), none of the clusters resemble the analysis for Maemi (cf. Figs. 1d and 12) and Tokage (cf. Figs. 1f and 13). This does not necessarily mean that no member is similar to the analysis, but that a low probability is assigned to the development that can be seen in the analysis. The ensemble forecast for Fabian yields one cluster (cf. Figs. 1b and 11c) that is in reasonable agreement with its analysis. The smaller standard deviation of the ensemble forecast of Fabian compared to the other strong events (section 3a) suggests that the predictability for Fabian in FCST1 is higher than that for Maemi and Tokage. For Philippe the cluster that shows an ET with strong reintensification (Fig. 16d) is most similar to the deterministic forecast (not shown). From the number of members in the Philippe clusters (Table 2) we conclude that the ensemble assigns a very low probability to the deterministic forecast and a distinctly higher probability to the clusters that do not show reintensification and are therefore more similar to the analysis.
It is remarkable that for FCST2 the outliers do not appear in any of the cases (Table 3). Thus, they are considered to play a major role in the high standard deviation for FCST1 (section 3a), which decreases abruptly at the later forecast time. The number of clusters for FCST2 is equal for Tokage and otherwise is smaller (Table 3), with a noticeable decrease from five to two clusters, for Maemi and Philippe. Furthermore, for all cases the largest or one of the dominant (Tokage) clusters is closest to the analysis in terms of the position of the ET system and of the development of the flow pattern. This indicates that forecasts initiated at times close to or after recurvature are characterized by a higher predictability. The initial conditions excluded the outlying developments that could be seen in the small clusters. Nevertheless, maxima in these standard deviations could still be seen for FCST2 (section 3a). Similar relations between the development in the clusters and their contributions to the shift and amplitude patterns can be drawn for FCST2 as for FCST1. There is still a distinct variability associated with the ET systems that is not due to uncertainties in the forecast of recurvature.
Through the investigation of the two weak events it could be seen that the ensemble forecast yields valuable additional information to the deterministic forecast in assigning probabilities to it. The analysis method works even for the very weak case of Philippe and for the forecast from FCST2 for Saola. However, applying the method successfully to analyze an event implies that a high percentage of the total variability in a domain is associated with that event. This was not the case for FCST1 for Saola. To capture the small number of members that do recurve, it might be helpful to use a clustering method that takes into account a time period instead of only a single time.
5. Conclusions
The variability in the ECMWF EPS during five ET events has been investigated for strong and weak ET events in both the North Atlantic and the western North Pacific. All five cases exhibited a characteristic trough–ridge–trough pattern in the midlatitudes on the dynamic tropopause, consisting of the trough that interacts with the respective TC, a ridge directly downstream, and a second trough downstream of the ridge. The ET events were associated with high uncertainty in the EPS.
The regions of the highest uncertainty in the strong events could be found from 18 to 60 h after ET in the trough upstream of the ET, directly associated with the ET and in the downstream trough. In the weak events the highest uncertainties could be found at the location where their remnants merged with the respective midlatitude system rather than at their position following ET.
Uncertainties in the forecast could be associated both with the recurvature and with the ET itself. A small error in the forecast of recurvature can result in the decaying tropical cyclone not moving into the region relative to the upstream trough that is favorable for reintensification. Initializing the forecast at times when the relative location of the respective upstream trough to the recurving TC was better defined yielded lower uncertainty for the same forecast lead time. In general, the uncertainty decreased with decreasing forecast time.
The EOFs of potential temperature on the dynamic tropopause showed robust structures associated with the ETs in all five cases. The variability in the EPS revealed thereby is related to physical scenarios. The uncertainty was based mainly on the following two variability patterns: one pattern describes an east–west shift of the trough–ridge–trough pattern, and the other describes a modulation of the amplitude of the trough–ridge–trough pattern.
Through clustering the principal components it could be seen that similar signs of contribution of the individual clusters to the variability patterns in all five cases led to similar developments of the ETs. A higher-amplitude trough–ridge–trough pattern was associated with a stronger reintensification of the ET system and a lower amplitude with a weaker reintensification. An eastward shift of the trough–ridge–trough pattern corresponded to a faster motion and development of the ET system and a westward shift to a slower motion and development. The application of this method in operations has the potential to give the forecaster an indication of the future development of the system.
With the aid of the analysis method we were able to extract a range of very different possible scenarios in the regions of high variability. Through the clustering, probabilities could be assigned to each of these developments based on the number of members contained in each cluster. Furthermore, indications of atmospheric evolutions associated with the ETs that are not probable but are possible are given. Hence, the large number of ensemble members exhibiting very different developments during ET is reduced to a manageable number of ET scenarios that are provided with a probability of the ET event occurring.
For most of the forecasts from FCST2 fewer clusters were found. These were typically larger than in FCST1 and the largest clusters were most similar to the analysis, indicating a higher predictability. Outliers that showed very different developments from the analysis were no longer found. This result supports the hypothesis of Harr et al. (2008) that a decrease in the number of clusters is an indication of lower uncertainty.
The importance of ensemble prediction was confirmed using cases in which the deterministic forecasts were inaccurate. In one of the cases a low probability was assigned to the erroneous deterministic forecast, and in another an early indication was given of the development that could be found in the analysis but was not shown in the deterministic forecast.
Acknowledgments
This study was sponsored by the Office of Naval Research, Marine Meteorology Program. Acknowledgement is made for the use of ECMWF’s computing and archive facilities through the special project “The impact of tropical cyclones on extratropical predictability.” We are grateful to Ron McTaggart-Cowan and an anonymous reviewer for their thorough and insightful reviews, which helped us improve this manuscript.
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Analyses of Fabian on (a) 0000 UTC 7 Sep and (b) 0000 UTC 10 Sep 2003; Maemi on (c) 0000 UTC 12 Sep and (d) 0000 UTC 15 Sep 2003; and Tokage on (e) 1200 UTC 19 Oct and (f) 1200 UTC 21 Oct 2004. Fabian, Maemi, and Tokage are marked by a gray TC symbol before ET and by a white TC symbol after ET. Potential temperature on the dynamic tropopause (shaded, K) and surface pressure (contours, hPa) are shown.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Analysis on (a) 0000 UTC 24 Sep and (b) 0000 UTC 27 Sep; and (c) 84-h deterministic forecast from 1200 UTC 23 Sep. Saola’s remnants are marked by a gray TC symbol. Potential temperature on the dynamic tropopause (shaded, K) and surface pressure (contours, hPa) are shown.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Analyses (a) 6 h prior to and (b) 96 h after Philippe’s decay; and (c) 4- and (d) 8-day deterministic forecasts from 1200 UTC 19 Sep. Philippe and the position of its remnants respectively are marked by a gray TC symbol. Potential temperature on the dynamic tropopause (shaded, K) and surface pressure (contours, hPa) are shown.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Tracks for Fabian based on 12-hourly location of minimum sea level pressure from (a) FCST1 and (b) FCST2. ECMWF analysis (black line with circles) until 0000 UTC 9 Sep, deterministic forecast (black line with triangles) until 1200 UTC 9 Sep, and ensemble forecast (colors) for up to 7 days are shown. Analysis and deterministic forecast (dashed) after analyzed ET. Right-lower corners of (a) and (b) show positions of the ensemble members at the analyzed ET time (x, color corresponding to forecast time); the analysis and deterministic forecast are only shown until the analyzed ET time. Hovmoeller plot for (c) FCST1 and (d) FCST2 is also shown; the standard deviation of 500-hPa height (m) in the 10-day ensemble forecast for Fabian is averaged between 40° and 50°N. ET position is marked by a black dot.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
As Fig. 4 but for Maemi, and analysis until 1200 UTC 15 Sep; the deterministic forecast is until 1200 UTC 16 Sep (FCST1) and 0000 UTC 18 Sep (FCST2).
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
(top) As in Figs. 4a,b but for Tokage; analysis is until 0000 UTC 22 Oct, and the deterministic forecast is until 1200 UTC 22 Oct. (middle) Analysis (black line with circles), deterministic forecast (black line with triangles), and ensemble forecast (colors) of the central surface pressure of Tokage from (c) FCST1 and (d) FCST2 is shown for 5 days. (bottom) As in Figs. 4c,d but for Tokage.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
As Fig. 4 but for Saola; analysis is until 1200 UTC 26 Sep, and the deterministic forecast is until 1200 UTC 26 Sep (FCST1) and 0000 UTC 28 Sep (FCST2). ET position is marked by a black dot, analyzed position of absorption of remnants of Saola is marked by a black triangle.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
As Fig. 4 but for Philippe; analysis is until 1200 UTC 23 Sep, and the deterministic forecast is until 1200 UTC 25 Sep (FCST1) and 1200 UTC 26 Sep (FCST2). Position of decay of Philippe is marked by a white circle; position of absorption of remnants is marked by a black triangle.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
(top) Schematic of the first two EOFs (thin solid and dashed lines) denoting (a) the shift and (b) the amplitude pattern. The thick black line represents the strong potential temperature gradient on the dynamic tropopause in the midlatitudes with low potential temperature to the north and high potential temperature to the south. (bottom) Synoptic patterns that result from the contribution to the variability patterns.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Ensemble mean of potential temperature on the dynamic tropopause (shaded, K) for (top) Maemi, (middle) Fabian, and (bottom) Saola. Maemi and Fabian FCST1 and Saola FCST2 is shown (see Table 1). (a), (c), (e) EOF 1 and (b), (d), (f) EOF 2 are shown in contours at an interval of 2.0 K. The percentage of their contribution to the total variability is marked in white in the top left corner.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Three clusters for Fabian for the ensemble forecast from FCST1 valid on 0000 UTC 10 Sep, that is, the investigation time.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Four of the five clusters for Maemi for the ensemble forecast from FCST1 valid on 0000 UTC 15 Sep, that is, 12 h after the investigation time. The fifth cluster (not shown) resembles the ensemble mean.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Three clusters for Tokage for the ensemble forecast from FCST1 valid on 1200 UTC 21 Oct, that is, 12 h after investigation time.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Same cluster as Fig. 13c, but for (a) 1200 UTC 22 Oct and (b) 1200 UTC 23 Oct.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Two clusters for Saola for the ensemble forecast from FCST2 valid on 0000 UTC 27 Sep, that is, the investigation time.
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Four of the five clusters for Philippe for the ensemble forecast from FCST1 valid on 1200 UTC 23 Sep, that is, the investigation time. The fifth cluster (not shown) resembles that shown in (b).
Citation: Monthly Weather Review 136, 9; 10.1175/2008MWR2249.1
Key data of the investigation times of the three typhoons (Japan Meteorological Agency; information available online at http://www.jma.go.jp/jma/indexe.html) and two hurricanes (NHC 2006; information available online at http://www.nhc.noaa.gov).
Number of clusters for FCST1, number of members in each of the clusters and percentage contribution of the shift and amplitude pattern to the total variability, and contribution of the individual clusters (+: positive, −: negative, ++: strong positive contribution) to the respective variability pattern are shown. Strength of ET: 0, no ET; 1, little or no reintensification, central mean sea level pressure (MSLP) ≥ 1000 hPa; 2, moderate reintensification, central MSLP 985–999 hPa; and 3, deep reintensification, central MSLP < 985 hPa [similar to Klein et al. (2000)].
