PATRICK A. HARR. Department of Meteorology, Naval Postgraduate School, Monterey, California

Transcription

1 VOLUME 136 M O N T H L Y W E A T H E R R E V I E W SEPTEMBER 2008 Predictability Associated with the Downstream Impacts of the Extratropical Transition of Tropical Cyclones: Methodology and a Case Study of Typhoon Nabi (2005) PATRICK A. HARR Department of Meteorology, Naval Postgraduate School, Monterey, California DORIS ANWENDER AND SARAH C. JONES Institute for Meteorology and Climate Research, Universitat Karlsruhe/Forschungszentrum Karlsruhe, Karlsruhe, Germany (Manuscript received 1 May 2007, in final form 12 January 2008) ABSTRACT Measures of the variability among ensemble members from the National Centers for Environmental Prediction ensemble prediction system are examined with respect to forecasts of the extratropical transition (ET) of Typhoon Nabi over the western North Pacific during September In this study, variability among ensemble members is used as a proxy for predictability. The time longitude distribution of standard deviations among 500-hPa height fields from the ensemble members is found to increase across the North Pacific following the completion of the extratropical transition. Furthermore, the increase in ensemble standard deviation is organized such that an increase is associated with the extratropical transition and another increase extends downstream from the ET event. The organization and amplitude of the standard deviations increase from 144 h until approximately h prior to the completion of the extratropical transition, and then decrease as the forecast interval decreases. An empirical orthogonal function analysis of potential temperature on the dynamic tropopause is applied to ensemble members to identify the spatial and temporal organization of centers of variability related to the extratropical transition. The principal components are then used in a fuzzy cluster analysis to examine the grouping of forecast sequences in the collection of ensemble members. The number of forecast groups decreases as the forecast interval to the completion of the ET decreases. However, there is a systematic progression of centers of variability downstream of the ET event. Once the variability associated with the ET begins to decrease, the variability downstream of the ET event also begins to decrease. 1. Introduction The poleward movement of a decaying tropical cyclone (TC) often results in an extratropical transition (ET) to a rapidly moving, explosively deepening midlatitude cyclone (Jones et al. 2003). Extratropical transition is generally described as a two-stage process (Klein et al. 2000; Jones et al. 2003) that begins with the transformation stage in which the TC begins to respond to changes in its environment. During this stage, the ET process is extremely sensitive to the complex physical and dynamical interactions between the decaying TC and the midlatitude circulation into which it is moving (Harr and Elsberry 2000; Harr et al. 2000; Thorncroft Corresponding author address: Patrick A. Harr, Department of Meteorology, Naval Postgraduate School, Monterey, CA paharr@nps.edu and Jones 2000; Agusti-Panareda et al. 2004; Hart et al. 2006). In the extratropical stage, a reintensification of the remnant TC as an extratropical cyclone depends on the phasing between the decaying TC and a midlatitude environment that is favorable for midlatitude cyclogenesis (Klein et al. 2002; McTaggart-Cowan et al. 2001; Ritchie and Elsberry 2007). Because of the typical rapid translation speed of the decaying TC during ET (Jones et al. 2003), accurate extended-range prediction of the phasing between the remnant tropical circulation and the midlatitude environment into which it is moving is critical. However, the structural changes associated with the ET of the decaying TC often contribute to large errors in numerical forecasts from operational global forecast models at short (i.e., h) forecast intervals (Evans et al. 2006) and at forecast intervals longer than 72 h (Jones et al. 2003). The advection of vorticity by the divergent wind in the TC outflow is a known Rossby wave source DOI: /2008MWR American Meteorological Society 3205

2 3206 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 (Sardeshmukh and Hoskins 1988). Furthermore, the advection of potential vorticity (PV) by the balanced wind in the outflow and the modification of PV by diabatic processes may also act as Rossby wave sources (Bosart and Lackmann 1995; Henderson et al. 1999). Through excitation of Rossby waves, a decaying TC that undergoes ET may impact the midlatitude circulation far downstream. Errors in the analysis and ensuing forecasts of the structural characteristics during ET may also propagate rapidly downstream of the ET location. Therefore, ET may be associated with periods of decreased predictability that extend downstream of the location of the actual ET event. In this study, the relative predictability in global numerical weather forecasts with respect to the downstream impacts of an ET event over the western North Pacific is based on the operational ensemble prediction system (EPS) at the National Centers for Environmental Prediction (NCEP). The standard deviation among ensemble members as a measure of variability may be related to forecast skill (Buizza 1997; Scherrer et al. 2004) such that increased variability among ensemble members downstream of an ET event is associated with decreased predictability and reduced accuracy. Generally, variability among the ensemble members increases with forecast interval. However, it is found that the variability among ensemble members downstream of the ET event increases at a specific synoptic time that is independent of the forecast duration. Therefore, the downstream variability is due to the impact of the decaying TC on the downstream flow rather than the forecast duration. This relationship also appears to be independent of season and its associated changes in background variability. In this study and in Anwender et al. (2008), the time at which the downstream variability increases is labeled the investigation time. Variability among EPS members is characterized by a combination of an empirical orthogonal function (EOF) analysis that is applied to potential temperature on the dynamic tropopause and a fuzzy cluster analysis that identifies groupings of similar forecast scenarios contained in the collection of ensemble members. The field of potential temperature on the dynamic tropopause was chosen because important dynamical components that relate to midlatitude cyclone development are readily identifiable (Morgan and Nielsen-Gammon 1998). In the case of ET, potential temperature on the dynamic tropopause provides a clear visualization of the interaction between TC outflow and the midlatitude circulation into which the decaying TC is moving. Principal components computed from the EOF analysis are defined based on the projection of individual ensemble members on the EOFs. The principal components provide a framework for the fuzzy cluster analysis. The purpose of the cluster analysis is to characterize the variability among the ensemble members as a set of similar synoptic-scale patterns. Therefore, a large number of clusters defines a collection of ensemble members that contains a variety of possible forecast scenarios. To identify the temporal change in the variability associated with the forecasts of the ET event and its impacts on the downstream flow patterns, the EOF and cluster analyses are applied successively between 120 and 24 h prior to the investigation time. It is hypothesized that the number of forecast scenarios, which are identified as individual clusters of EPS members, decreases as the uncertainty associated with the downstream impact of the ET is reduced. The EOF/cluster methodology is defined in section 2. In section 3, the variability among NCEP ensemble members is examined relative to the ET of Typhoon (TY) Nabi (14W) in September The time evolution of the EOF patterns and clusters are defined in section 4 relative to the forecasts that are verified at the investigation time. Discussion and conclusions in section 5 examine the relation between the variability among ensemble members, cluster numbers, and predictability. In Anwender et al. (2008), the combined EOF and fuzzy cluster analysis is applied to forecasts of the ET of additional TCs over the western North Pacific and North Atlantic with the EPS at the European Centre for Medium-Range Weather Forecasts (ECMWF). 2. Method a. Data The analysis and forecast fields used for this study were from the NCEP EPS that was operational during September The EPS model was a reducedresolution version of the primary global deterministic model, and its output is available on a 1 latitude 1 longitude grid. The perturbations in the NCEP EPS were generated via the method of breeding the growing modes (Toth and Kalnay 1997). Five breeding cycles were run to obtain five pairs of positive and negative perturbations. Therefore, at each 6-h period, 10 ensemble members were generated, along with the one control forecast. Based on the official data from the World Meteorological Organization (WMO) Regional Specialized Meteorological Center (RSMC) at the Japan Meteorological Agency (JMA), TY Nabi was declared extratropical at 0600 UTC 8 September After this time, no official TC forecasts were issued for TY Nabi. Examination of the ensemble standard deviation to be pre-

3 SEPTEMBER 2008 H A R R E T A L sented in section 3 indicates that the variability among the ensemble members downstream of the ET of TY Nabi increases dramatically after 0000 UTC 9 September. Therefore, this time will be defined as the investigation period. b. Empirical orthogonal function analysis Empirical orthogonal function analysis has become a near-standard technique for determining the underlying structure that best mathematically explains the variability in a multivariate dataset (Richman 1986). The EOFs of potential temperature on the dynamic tropopause, which is defined as the 2-PV unit (PVU; 1 PVU 10 6 Km 2 kg 1 s 1 ) surface, are computed for a collection of ensemble members. A multivariate analysis based on a collection of the 10 ensemble members from a single EPS cycle would not provide enough degrees of freedom to produce a stable statistical representation. To increase the degrees of freedom in the analysis, a 40-member combined ensemble is constructed from the four EPS cycles run during each 24-h period. A common verification time was established for the four ensemble runs during each 24-h period that began at 0000 UTC and ended at 1800 UTC. The first ensemble members used in the EOF analysis were initialized during the 24-h period that began at 0000 UTC 5 September. The verification time was at 0000 UTC 9 September. Therefore, this collection consisted of the ten 120-h forecast ensemble members initiated at 0000 UTC 5 September, the ten 114-h forecast ensemble members initiated at 0600 UTC 5 September, the ten 108-h forecast ensemble members initiated at 1200 UTC 5 September, and the ten 102-h forecast ensemble members initiated at 1800 UTC 5 September. Subsequent collections of ensemble members are constructed for the 24-h periods that begin at 0000 UTC 6 7 September 2005, with all forecasts verified at 0000 UTC 9 September. Furthermore, a second set of EOF analyses are performed for the same period but use the forecasts that are verified at 0000 UTC 10 September Since the final EOF patterns result from a projection onto the potential temperature data, the EOF patterns are in units of kelvins. c. Fuzzy cluster analysis Once the EOF analysis was complete, the first and second principal components (PCs) for the collection of all 40 ensemble members were used as input to a fuzzy clustering routine (Scott and Symons 1971; Harr and Elsberry 1995). To start the iterative cluster procedure, a predefined number of cluster centers was randomly placed in the PC 1 PC 2 phase space. Each ensemble FIG. 1. Track of TY Nabi in 12-h increments between 0000 UTC 29 Aug and 1200 UTC 9 Sep. Storm positions at 0000 UTC are labeled with day (dd)/month (mm). member, which is now represented by the pair of PC values, is then assigned to the closest group center. New centers are computed by minimizing the distance from each point to each new cluster center. Each point is reexamined relative to the new cluster centers. If no points can be reassigned because they lie closer to another center, the iterations stop. Each member is assigned a weight that identifies their relative strength of membership to their cluster. For a point k, the weight associated with cluster i is defined as w i,k C j 1 1 d i,k d j,k 2 q 1, such that d i,k is the distance between point k and the centroid of cluster i, and d j,k is the distance between point k and the other cluster centers j. There are C total clusters, and q is a fuzziness coefficient that was set to 1.5 for this application. There were no perceptible differences in outputs for values of q between 1.1 and 2. For the 40 points that represent the entire ensemble, a mean strength w and the standard deviation w were determined. Any ensemble member whose weight value w was less than w w was not assigned to a

4 3208 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 FIG. 2. Sea level pressure (hpa, shaded below 1000 hpa) and 500-hPa heights (m) for 1200 UTC 5 10 Sep The location of TY Nabi through the ET process is marked by the tropical cyclone symbol. respective group because it lies in a boundary region between clusters. To define the total number of clusters valid for each collection of 40 ensemble members, the fuzzy cluster routine was repeated by incrementing the allowable cluster number by one. At each application, the final cluster members were evaluated to ensure that no group was dominated by a majority of members from a single ensemble run (i.e., so that one group did not contain all 10 members of the 0600 UTC ensemble run). If this had been the case, this result would indicate that the grouping was a function of the ensemble integration and not solely of the evolution of the synoptic-scale environment. Furthermore, inspection of the cluster assignments associated with individual ensemble members indicates that cluster membership is not related to breeding cycle. Progressive cluster analyses then attempted to logically break the previous clusters into a larger number of groups. When one group was subdivided into two separate groups, the meteorological charts (i.e., mean sea level pressure and potential temperature on the dynamic tropopause) of the initial group and the two new groups were examined to see if two distinct weather patterns truly existed. If not, the previous cluster number was considered the proper number of distinct scenarios contained in the collection of ensemble members. Examples of this procedure will be given in section 4b. 3. Variability among ensemble members during the ET of TY Nabi As TY Nabi followed a general north-northwest track across the Philippine Sea (Fig. 1), an approaching shortwave trough began to weaken the subtropical ridge and allow for a northward track with eventual recurvature early on 6 September (Figs. 1 and 2a,b). Prior to the recurvature of Nabi, a low pressure center

5 SEPTEMBER 2008 H A R R E T A L FIG. 3. Time longitude plots of 500-hPa height standard deviations (m) for the GFS ensemble prediction system members initialized at (a) 1200 UTC 3 Sep, (b) 1200 UTC 4 Sep, (c) 1200 UTC 5 Sep, (d) 1200 UTC 6 Sep, (e) 1200 UTC 7 Sep, and (f) 1200 UTC 8 Sep. The standard deviation is averaged between 40 and 60 N. Beginning at 0000 UTC 6 Sep, which was the recurvature time, the tropical cyclone symbols define the longitude of TY Nabi. The thick black line at 0000 UTC 9 Sep marks the investigation time, which is the verification time for forecasts used in the EOF and fuzzy cluster analyses. was located east of the Kamchatka Peninsula and the 500-hPa height pattern across most of the North Pacific toward 150 W had a strong zonal orientation (Figs. 2a,b). Following the recurvature of TY Nabi, there was increased interaction between the outflow from the typhoon and the midlatitude flow. A ridge formed immediately downstream of TY Nabi (Figs. 2c,d) and a trough began to form over the central North Pacific. As Nabi completed ET (Figs. 2e,f), the central Pacific trough moved eastward and a second ridge was built over the eastern North Pacific. Therefore, the movement of the decaying TY Nabi into the midlatitudes prompted a change from a rather zonally oriented flow pattern at 500 hpa to a pattern with high-amplitude trough and ridge features over the North Pacific. The variability among EPS members is defined by the time longitude distribution of the 500-hPa height standard deviations between 40 and 60 N computed from the ensemble members from each 1200 UTC initiation of the EPS from 3 to 8 September (Fig. 3). The

6 3210 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 FIG. 4. Spatial EOF patterns (contoured at an interval of 1.0 K, negative contours are dashed) for potential temperature on the 2-PVU surface for the time defined in each panel. The percent variability explained by each EOF is provided in the parentheses. The average potential temperature (K) for the 40 ensemble members (see text for the description of how the 40 members are defined) valid at the labeled time is shaded according to the color bar at the bottom. The forecast intervals used in the construction of each EOF pattern are listed at the bottom of each panel UTC cycle is chosen because it is about the middle point of the four EPS runs collected for the EOF analysis as described in section 2b. At 1200 UTC 3 September (Fig. 3a), when TY Nabi begins to move northnorthwestward (Fig. 1), plumes of increasing standard deviations with forecast intervals appear with a rather uniform distribution in longitude. In the forecasts from 1200 UTC 4 September (Fig. 3b), the magnitudes of the standard deviations in the three plumes that exist over the North Pacific downstream of the location of TY Nabi begin to increase. The increase in standard deviations is especially evident following 0000 UTC 9 September, which is labeled as the investigation time at which the EOF and cluster analysis will be centered. The organization of increased standard deviations in individual plumes across the North Pacific continues with successive initiation times of the EPS (Figs. 3c,d). Following recurvature of TY Nabi and during the transformation stage of the ET (Figs. 3e,f), the magnitudes of the individual plumes of standard deviations down-

7 SEPTEMBER 2008 H A R R E T A L FIG. 5. As in Fig. 4, but for forecasts verified at 0000 UTC 10 Sep stream of TY Nabi begin to decrease. However, even at these short forecast intervals the standard deviations downstream of Nabi continue to be much larger relative to other longitudes. 4. Predictability associated with the ET of TY Nabi As defined in section 2, an EOF analysis of potential temperature on the dynamic tropopause is used to identify the principal structures associated with the variability among ensemble members. A fuzzy cluster analysis is then used to group ensemble members based on similar evolutions of the synoptic-scale patterns associated with the ET of TY Nabi and the downstream environment across the North Pacific. a. Principal structures associated with variability among ensemble members The EOFs of potential temperature on the dynamic tropopause were defined for successive 24-h periods between 4 and 7 September (Fig. 4). As defined in section 2, the EOFs were computed for the collection of the 40 ensemble member forecasts from the four EPS runs during every 24 h that are verified at 0000 UTC 9 September. In this study, only the two leading EOFs, which typically contain 20% 30% of the variance, are examined because the organization of the spatial patterns and the amount of variability explained the rapid decrease after EOF 2. Also, the incorporation of PCs 3 5 did not result in different cluster patterns, which were defined by the potential temperature on the 2-PVU surface, 500-hPa heights, and sea level pressure patterns associated with the cluster mean. The leading EOF pattern for the ensemble members collected from the 120- to 102-h forecasts initialized on 4 September (Fig. 4a) primarily represents variability in the ensemble forecasts associated with the building of an upper-level ridge immediately downstream of the poleward-moving and decaying TC. In addition, a center of smaller amplitude is associated with the trough over the central North Pacific. The orientation and signs of the primary two centers in EOF 1 represent a zonal shift in the ridge that is defined by variability associated with the interaction with the TC outflow and the midlatitude circulation. In a positive sense, the EOF 1 pattern based on forecasts initialized on 4 September indicates that the ridge over the western North Pacific and the trough over the central North Pacific would be shifted westward. The EOF 2 pattern (Fig. 4b) also represents variability in the ensemble forecasts associated with the upper-level ridge over the western North Pacific and contains greater representation of the variability associated with the trough over the central North Pacific. This pattern represents variability in the amplitude of the ridge over the western North Pacific. In a positive sense, the EOF 2 pattern is associated with a more northward extension of the ridge over the western North Pacific and a thinning of the northern portion of the trough over the central North Pacific, while the southern portion extends toward the southwest. In a negative sense, the EOF 2 pattern defines a flattened ridge associated with less northward movement of high-theta air to the east of the decaying TC

8 3212 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 and a broadening of the northern portion of the trough over the central North Pacific while the base is shifted eastward. Also, EOF 2 contains an additional center of variability over western North America associated with the eastern extension of the ridge over the eastern North Pacific. The EOF patterns associated with the collection of ensemble members from the 96- to 78-h forecasts initialized on 5 September (Figs. 4c,d) define similar patterns of zonal variability (EOF 1, see Fig. 4c) and amplitude variability (EOF 2, see Fig. 4d) associated with the upper-level ridge over the western North Pacific. Whereas EOF 1 from 4 September (Fig. 4a) only represents a zonal shift in the circulation over the western and central North Pacific, the first EOF from 5 September (Fig. 4c) also includes centers of variability that ring the periphery of the eastern North Pacific ridge. Although the amplitudes of these centers are much smaller than the amplitudes associated with the variability over the western North Pacific, the EOF patterns from forecasts initialized on 5 September begin to define an increase in variability downstream of the ET from that based on forecasts initialized from 4 September. This downstream spread in variability is consistent with the organization of plumes of increased standard deviation across the North Pacific defined in Figs. 3b,c. The centers of variability contained in EOFs 1 and 2 based on forecasts from 6 September (Figs. 4e,f) continue to be located in regions similar to the EOF patterns based on forecasts from 4 (Figs. 4a,b) and 5 (Figs. 4c,d) September. However, the amplitudes of the centers over the western North Pacific in the patterns from 6 September are much smaller than the centers from the EOF patterns based on earlier forecasts. The amplitudes of the centers of variability in EOFs 1 and 2 over the central and eastern North Pacific based on forecasts from 6 September are similar to patterns from forecasts initiated on 4 and 5 September. The location of the centers of variability along 170 and 125 W in EOFs 1 and 2 is consistent with the centers of standard deviation that begin to increase at those longitudes after 9 September (Fig. 3d). Several characteristic changes occurred in the collection of h ensemble member forecasts from 7 September. There is an increase in amplitude and coverage of a center of variability near Japan in EOF 1 (Fig. 4g) that is related to the location of the TC, but multiple centers of variability are found elsewhere. Also, a center of variability northwest of the Kamchatka Peninsula indicates that other midlatitude features are beginning to influence the variability in ensemble forecasts. In both EOFs based on forecasts initiated on 7 September (Figs. 4g,h), the centers of variability associated with the FIG. 6. The first and second principal components for the (a) two-, (b) three-, and (c) four-cluster solution based on principal components from ensemble members generated on 4 Sep and verified at 0000 UTC 9 Sep. Symbols define the model initial time as defined by the legend in the lower-right portion of each panel. Cluster centers are defined by the circled number. Small light gray points define principal components that do not belong to any cluster.

9 SEPTEMBER 2008 H A R R E T A L FIG. 7. Sea level pressure (contour intervals of 4 hpa) and potential temperature (shaded, K) on the 2-PVU surface for (a) cluster 1 of the two-cluster solution, and (b) cluster 2 of the two-cluster solution, based on PCs of forecasts from 4 Sep that are verified at 0000 UTC 9 Sep. trough over the central North Pacific are similar in amplitude to the corresponding centers associated with forecasts initiated on 6 September (Figs. 4e,f). This is consistent with the local maximum in ensemble standard deviation over the central North Pacific in Fig. 3e in that there is only a small reduction in amplitude between forecasts from 1200 UTC 6 September (Fig. 3d) and 1200 UTC 7 September (Fig. 3e) that are verified at 0000 UTC 9 September. Additionally, the number of centers in EOF 2 based on forecasts from 7 September (Fig. 4h) is smaller than the number of centers in EOF 2 from the forecasts of 6 September. Therefore, as the forecast period to the investigation time of 0000 UTC 9 September decreases, there is less variability associated with the ET because the number of cluster centers and their amplitudes decrease as the forecast interval becomes shorter (Figs. 4e h). To examine the sensitivity of the results of the EOF analysis to the choice of the investigation time of 0000 UTC 9 September, the procedure was repeated for an investigation time of 0000 UTC 10 September. At this time, the extratropical cyclone that resulted from the ET of TY Nabi was located near 50 N, 175 E (Fig. 2f). For the collection of ensemble members from 4 September (Figs. 5a,b), the high-amplitude centers of variability defined by EOFs 1 and 2 are concentrated around the eastern portion of the ridge over the western North Pacific and the trough over the central North Pacific. Similar patterns are found for EOFs 1 and 2 from the ensemble members of 5 September (Figs. 5c,d). Therefore, the variability in ensemble member forecasts from 4 5 September that are verified at 0000 UTC 10 September (Figs. 5a d) has shifted downstream from the locations defined in the EOFs for forecasts that are verified at 0000 UTC 9 September (Figs. 4a d). Similar comparisons (not shown) were found for the variability among ensemble members for forecasts initiated on 6 7 September and verified on 10 September. b. Cluster analysis The fuzzy cluster analysis was applied to the PCs associated with the leading two EOFs for each 24-h period. As defined in section 2, the cluster analysis for each 24-h period was repeated by specifying an increasing number of clusters. As the number of clusters increases, clusters split to form new groups. The creation of additional clusters can be considered an increase in

10 3214 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 FIG. 8. As in Fig. 7, but for clusters (a) 3 2 and (b) 3 3 of the three-cluster solution based on forecasts initiated on 4 Sep and verified at 0000 UTC 9 Sep. These two clusters result from the split of cluster 2 2 in Fig. 7b. precision or detail with respect to the identification of synoptic-scale patterns. In a statistical sense, an optimal number of population clusters exists. However, it is often very difficult to determine this number objectively (Everitt 1979; Hartigan 1985). Typically, valid statistical tests used to determine the true number of clusters suffer from sampling problems or null hypotheses that are not informative. For example, significance tests for identifying differences among groups (e.g., analysis of variance, F tests) are not valid because cluster analysis is designed to maximize separation. Other tests have been based on probability models such that the null hypothesis is based on a mixture of probability distributions that represent different clusters (Lee 1979; Fraley and Raftery 1998). In this context, measures such as the Bayesian information criterion have been applied to determine the number of model parameters (i.e., clusters). However, the null hypothesis associated with an underlying probability distribution is often not valid when samples are small, as is the case in this group of ensemble members. Often, the purpose of a cluster analysis is to not determine the true number of population groups, but to partition the data into an adequate subdivision of similar groups. In this case, the number of clusters is based on the level of detail desired. In this study, the final cluster number is defined when no significant differences were identified in the synoptic patterns associated with new clusters defined by the split of the previous cluster. Individual clusters will be represented by two numbers such that the first number defines the total number of clusters and the second is the individual cluster number. Symbols are used to identify the initial time of the EPS run that generated that cluster member, to verify that a cluster is not defined by all the members from the same EPS run (e.g., all at 0600 UTC), which would signify that the grouping was based on an EPS run and not the common features of the forecast sequence. 1) ENSEMBLE FORECASTS FROM 4 SEPTEMBER For the ensemble forecasts from 4 September that are verified at 0000 UTC 9 September, the two-cluster solution (Fig. 6a) defines groups that are divided along a line roughly equal to the negative diagonal. Therefore, the groups contain elements of the patterns of variability in both EOFs (Figs. 4a,b). The sea level pressure pattern and the distribution of potential temperature (Fig. 7) on the dynamic tropopause for the cluster

11 SEPTEMBER 2008 H A R R E T A L FIG. 9. As in Fig. 7, but for the four-cluster solution based on forecasts from 4 Sep that are verified at 0000 UTC 9 Sep. Clusters 4 3 and 4 4 result from the split of cluster 3 3 in Fig. 8.

12 3216 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 TABLE 1. Summary of the four-cluster solution for ensemble forecasts initiated on 4 Sep and verified at 0000 UTC 9 Sep. The ET type is based on the amplitude of the sea level pressure cyclone that results from the ET. A strong ridge extends farther northward than a weak ridge. Cluster PC 1 sign PC 2 sign ET Type Downstream ridge amplitude Downstream ridge zonal shift 4 1 Moderate Weak East 4 2 Weak Weak West 4 3 Moderate Strong East 4 4 Strong Strong West means indicate that the differences between the two clusters are due to the forecast positions of the extratropical cyclone that results from the ET of TY Nabi. Ensemble forecasts contained in cluster 2 1 (Fig. 7a) resulted in a 990-hPa extratropical cyclone at the very southern tip of the Kamchatka Peninsula near 51 N, 157 E, while forecasts in cluster 2 2 (Fig. 7b) resulted in a 992-hPa cyclone farther west near 51 N, 148 E. Furthermore, it is evident in Figs. 7a,b that the ridge over the western North Pacific in cluster 2 2 is forecast to be farther west and extends farther north than in forecasts contained in cluster 2 1. These differences in zonal and meridional extent of the upper-level ridge over the western North Pacific are consistent with the distribution of PCs in the two clusters such that each cluster represents portions of the two leading EOFs (Fig. 6a). Because of the rather large differences in the twocluster solution (Fig. 6a), the analysis was repeated by solving for three clusters (Fig. 6b). Cluster 2 2 (Fig. 7b) split to form clusters 3 2 (Fig. 8a) and 3 3 (Fig. 8b). Cluster 2 1 remained intact, although a few members became boundary points. Therefore, the synoptic pattern associated with cluster 3 1 (not shown) is essentially identical to cluster 2 1. The split of cluster 2 2 (Fig. 6b) indicates that a group of ensemble forecasts resulted in a very weak ET of TY Nabi, such that cluster 3 2 (Fig. 8a) has a weak, elongated extratropical cyclone that is oriented from the southwest to northeast from northern Japan to the Kamchatka Peninsula. The westward shift in the position of the upper-level ridge FIG. 10. Differences between the mean analyzed 500-hPa height of all 40 ensemble members from 4 Sep and each cluster mean analyzed 500-hPa height (shaded in m). Difference between the mean analyzed sea level pressure of all 40 ensemble members from 4 Sep and each cluster mean analyzed sea level pressure (hpa, contoured at an interval of 0.5 hpa with the zero contour omitted).

13 SEPTEMBER 2008 H A R R E T A L FIG. 11. Cluster mean 500-hPa height contours (m at 120-m intervals) for each of the final clusters in the four-cluster solution for all forecasts that were initiated from 0000 to 1800 UTC 4 Sep and verified at (a) 0000 UTC 9 Sep and (b) 0000 UTC 10 Sep. The ellipses identify regions where the standard deviations among the ensemble members is greater than 60 m, as defined in Fig. 3b. over the western North Pacific in cluster 3 2 would have reduced the interaction of TY Nabi and the upstream midlatitude trough such that only a weak ET resulted. Cluster 3 3 (Fig. 8b) contains forecasts that result in a cyclone similar in intensity to cluster 2 2 but broader and farther north than the cyclone in cluster 2 2. A four-cluster solution (Fig. 6c) resulted primarily from the split of cluster 3 3 (Fig. 8b) into cluster 4 3 (Fig. 9c) and cluster 4 4 (Fig. 9d). Again, the original cluster 2 1 remained intact and the mean pattern of cluster 4 1 (Fig. 9a) is essentially identical to clusters 2 1 and 3 1. Because the location of cluster 4 2 remained nearly identical to cluster 3 2, cluster 4 2 (Fig. 9b) also contains the set of ensemble members that forecast a weak ET event. The split of cluster 3 3, which contains a moderately deep cyclone centered in the Sea of Okhotsk (Fig. 9b), resulted in two clusters that each have a deeper cyclone but with a northeast shift toward the Kamchatka Peninsula in cluster 4 3 (Fig. 9c) and a shift to the southwest toward northern Japan in cluster 4 4 (Fig. 9d). A five-cluster solution resulted in the split of cluster 4 3 such that a new cluster was formed that only contained two members from the upper-left portion of cluster 4 3 in Fig. 6c. Based on the small size of that cluster, and because the synoptic pattern of the new cluster (not shown) did not differ much from cluster 4 3, the cluster procedure was stopped at the fourcluster solution. In summary, the clustering of the ensemble forecasts from 4 September resulted in a cluster center in each quadrant of the PC 1 and PC 2 phase space (Fig. 6c). These clusters represent forecast scenarios defined by zonal shifts and amplitude variations in the upper-level ridge over the western North Pacific (Table 1). The relationships of these forecasts to the initial conditions

14 3218 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 associated with the forecast sequences in each cluster are examined by taking differences between the sea level pressure and 500-hPa heights for the analysis field of each cluster and the average of all ensemble member analyses for 4 September (Fig. 10). The largest differences were associated with different representations and locations of the TC (Fig. 10), and they appear to be consistent with the characteristics of perturbations generated by the breeding method (Toth and Kalnay 1997). For clusters 4 1 and 4 3 (Figs. 10a,c), which resulted in a forecast extratropical cyclone that was deeper and farther east near the Kamchatka Peninsula, the analysis differences indicate that these forecast sequences began with the TC closer to the midlatitude trough (i.e., negative sea level pressure differences ahead of the TC center). The negative differences in sea level pressure for cluster 4 1 (Fig. 10a) are larger and extend farther into the midlatitudes than the negative differences of cluster 4 3 (Fig. 10c), which is consistent with the more eastward placement of the forecast position of the extratropical cyclone at 0000 UTC 9 September in cluster 4 1. Furthermore, the shifted TC in the set of cluster 4 1 members is deeper than the overall average, while the members in cluster 4 3 contained a shifted center without a change in amplitude. The sea level pressure and 500-hPa height differences for cluster 4 2 (Fig. 10b), which contains forecasts of a weak ET, began with the TC shifted away from the midlatitude trough and is also weaker than the average TC from all ensemble members. This contributed to the reduced interaction between the poleward-moving TC and the midlatitude trough (Klein et al. 2002; Ritchie and Elsberry 2007), which may have reduced outflow into the midlatitudes and contributed to less development of the downstream ridge. For cluster 4 4, which contains forecasts that resulted in the deepest extratropical cyclone and the least amount of translation downstream, the sea level pressure and 500-hPa height differences (Fig. 10d) also define a southeast shift in the TC that would seemingly delay the interaction with the midlatitude trough. The interaction between the TC and midlatitude trough was enhanced such that the ET resulted in a deep extratropical cyclone and the deeper trough may have resulted in less downstream movement of the extratropical cyclone resulting from a more meridional trough ridge pattern. This pattern in cluster 4 4 is consistent with the cluster center being in the positive PC 1 and positive PC 2 quadrant (Fig. 6c), which indicates that this cluster is composed of forecasts of a strong northward extension (positive EOF 2) and a westward shift (positive EOF 1) of the warm air or upper-level ridge. FIG. 12. As in Fig. 6, but for principal components from ensembles generated on 5 Sep that are verified at 0000 UTC 9 Sep. The four clusters are summarized by overlaying 500- hpa height contours for each cluster mean forecast with verifying times of 0000 UTC 9 September (Fig. 11a) and 0000 UTC 10 September (Fig. 11b). At a verifying time

15 SEPTEMBER 2008 H A R R E T A L FIG. 13. As in Fig. 7, but for the three-cluster solution from the ensembles generated on 5 Sep. of 0000 UTC 9 September (Fig. 11a), cluster 4 2 (i.e., weak ET) resulted in a 500-hPa height pattern with a much smaller wave amplitude across the western and central North Pacific than the other three clusters. By 0000 UTC 10 September (Fig. 11b), cluster 4 2 continues to be associated with a smaller-amplitude wave that has shifted to the east of the date line. Alternately, cluster 4 4 (strong ET and a shift to the west) at 0000 UTC 9 September (Fig. 9a) resulted in a highamplitude height pattern with the trough over the central North Pacific shifted to the west. At 0000 UTC 10 September (Fig. 9b), the forecasts in cluster 4 4 evolve downstream to contain a trough over the central North Pacific that is deeper than the other three clusters. Clusters 4 1 and 4 3 lie between the extremely weak ET forecast of cluster 4 2 and the strong ET of cluster 4 4. It is clear that as the forecast interval increases, the four forecast scenarios diverge with respect to their representation of the trough over the central North Pacific and the eastern periphery of the downstream ridge over the eastern North Pacific. Therefore, the four-cluster solution associates the standard deviation plumes between 180 E and 120 W in Fig. 3b with different forecast scenarios that are related to the impact of the ET

16 3220 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 TABLE 2. Summary of the three-cluster solution for ensemble forecasts initiated on 5 Sep and verified at 0000 UTC 9 Sep. The ET type is based on the amplitude of the sea level pressure cyclone that results from the ET. Cluster PC 1 sign PC 2 sign ET type Weak 3 2 Moderate 3 3 Moderate of TY Nabi on downstream predictability or increased variability. 2) ENSEMBLE FORECASTS FROM 5 SEPTEMBER FIG. 14. As in Fig. 10, but for the three-cluster solution from ensemble members generated on 5 Sep and verifying at 0000 UTC 9 Sep. The two-cluster solution (Fig. 12a) based on the PCs associated with EOFs from the ensemble forecasts from 5 September (Figs. 4c,d) resulted in clusters divided by positive and negative representations of EOF 2. The primary differences (not shown) between these two clusters was that the upper-level ridge over the western North Pacific in cluster 2 1 extends farther north than in cluster 2 2, which is consistent with the EOF 2 patterns in Fig. 4d. The three-cluster solution (Fig. 12b) resulted from a split of cluster 2 2 into clusters with positive and negative values of PC 1. Based on the EOF 1 pattern (Fig. 4c), this split accounts for either an eastward or westward shift in the upper-level ridge over the western North Pacific. In the cluster mean maps (Figs. 13), the extratropical cyclone from the ET of TY Nabi is similarly shifted east in cluster 3 2 (negative PC 1) and west in cluster 3 3 (positive PC 1). The mean central pressure in the two clusters of the forecasts that are verified at 0000 UTC 9 September is essentially the same. Cluster 3 1 (Fig. 13a) represents the weak ET scenario. Although the character of the downstream ridge over the western North Pacific is nearly the same among the three clusters, there are differences in forecast locations and central pressures of the cyclone that result from the ET of TY Nabi and in the cyclone over the Aleutian Islands. Cluster 3 3 split to form the four-cluster solution (Fig. 12c). It is clear that the centers of clusters 4 3 and 4 4 are not well separated. Furthermore, the center of cluster 4 3 is very near the origin of the PC 1 and PC 2 phase space. The synoptic-scale patterns of clusters 4 3 and 4 4 (not shown) were found to be very similar. Therefore, the final representation of the forecast groups among the ensemble members from 5 September was defined by the three-cluster solution (Table 2). The differences among the three clusters are primarily defined by the ET amplitude, rather than a combination of ET amplitude and downstream ridge amplitude, and shift as in the four clusters from 4 September (Table 1). As for the ensembles from 4 September, the differ-

17 SEPTEMBER 2008 H A R R E T A L FIG. 15. As in Fig. 11, but for the three-cluster solution for forecasts from 5 Sep that verify at (a) 0000 UTC 9 Sep and (b) 0000 UTC 10 Sep. The ellipses identify regions where the standard deviation among the ensemble members is greater than 60 m as defined in Fig. 3c. ences in the initial conditions (Fig. 14) among the three clusters are primarily associated with the representation of TY Nabi in the initial conditions. The weaker ET in the forecasts of cluster 3 1 (Fig. 13a) is associated with the smallest changes between the cluster mean initial conditions and the 40-member mean (Fig. 14a). A small shift of the TC to the south may have adversely impacted the phasing of TY Nabi and the midlatitude trough. In cluster 3 2, which resulted in a stronger ET and an eastward shift of the resulting extratropical cyclone toward the Kamchatka Peninsula (Fig. 13b), the initial TC is shifted to the north (Fig. 14b) and the 500-hPa heights to the northeast of the TC are higher than the mean. The analyzed 500-hPa pattern at 1200 UTC 5 September (Fig. 2a) contains a trough along the East Asian coast near 45 N, 140 E, northeast of TY Nabi. The increased heights in the initial conditions of the forecasts of cluster 3 2 over this region (Fig. 14b) are associated with either a weakened trough or more zonal flow that contributes to the more rapid translation of the decaying TY Nabi to the east and places the extratropical cyclone farther east to be south of the Kamchatka Peninsula (Fig. 13b). The ET associated with the forecasts in cluster 3 3 also resulted in a deeper extratropical cyclone, but it was shifted west toward northern Japan (Fig. 13c). The differences in the initial conditions (Fig. 14c) indicate that the TC was shifted south and the 500-hPa heights to the northeast were lower than the mean. Therefore, the trough over the East Asian coast was deeper and the combination of the deeper trough and the southward shift of the TC contributed to a slower translation speed and less downstream movement during the ET process. Examination of the 500-hPa patterns for the threecluster means (Fig. 15) reveals that the increased variability that is just east of the date line at 0000 UTC 9 September (Fig. 3c) is due to differences in forecasts of the extratropical cyclone over the Aleutian Islands

18 3222 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 (Fig. 15a). Differences among the three cluster means are larger for the ensemble forecasts that are verified at 0000 UTC 10 September (Fig. 15b); note especially the variations on the trough along 170 W. To the west of 180 E, variability increases over the region of the extratropical cyclone that resulted from the ET of TY Nabi. The plume of increased standard deviation along 130 W is due to differences in the representation of the eastern extension of the ridge over the eastern North Pacific in the three forecast clusters that are verified on 10 September. 3) ENSEMBLE FORECASTS FROM 6 SEPTEMBER The two-cluster solution based on the PCs of the EOFs from 6 September (Figs. 4e,f) is split around PC 1 (Fig. 16a). The two cluster centers represent solutions with small east west shifts in the location of the upperlevel ridge over the western North Pacific and the extratropical cyclone that results from the ET of TY Nabi (Figs. 17a,b). The three-cluster solution (Fig. 16b) results primarily from a split of cluster 2 2 and two members from cluster 2 1. Therefore, the synoptic pattern associated with cluster 3 1 (not shown) is nearly identical to the pattern of cluster 2 1. Recall that the differences among the four clusters from 4 September were defined in sea level pressure and in the character of the upper-level downstream ridge. The differences among the three clusters from 5 September were primarily in the sea level pressure pattern. In the two clusters from 6 September, differences in sea level pressure pattern also become small. Differences among the three mean 500-hPa height patterns for the forecasts in the three clusters that are verified at 0000 UTC 9 September (Fig. 18a) and 0000 UTC 10 September (Fig. 18b) are also small over the western North Pacific. This similarity between the three sets indicates that predictability associated with the evolution of the ET event in that region increased from 4 September when four clusters exhibited large variability in the upper-level ridge and sea level pressure over the western North Pacific (Figs. 9 and 11). The three forecast clusters from 6 September that are verified at 0000 UTC 9 September contain a significant amount of variability along the west coast of North America for the verification time of 0000 UTC 10 September, which is consistent with the plume of increased standard deviation west of 120 W in Fig. 3d. Because the evolution and 500-hPa heights as defined in Fig. 18 indicate that clusters 3 2 and 3 3 are very similar over the western North Pacific, the forecasts of the ET associated with the ensemble members from 6 September are partitioned into only two clusters. FIG. 16. As in Fig. 6, but for principal components from ensembles generated on 6 Sep that are verified at 0000 UTC 9 Sep. 5. Discussion and conclusions Three representations of the variability among forecasts produced by the NCEP EPS during the ET of TY Nabi have been examined to establish the predictability associated with extratropical transition. In this analysis, predictability is measured by the spread among forecast members, and various representations of spread have been examined. These representations are given at 24-h intervals because of the necessity to combine ensemble members in the EOF analysis. The standard deviation in 500-hPa heights among ensemble members (Fig. 3) exhibited systematic patterns of forecast spread with respect to the ET event. TY Nabi was declared extratropical at 0600 UTC 8 September, and the variability among ensemble members began to increase shortly thereafter at 0000 UTC 9 September.

19 SEPTEMBER 2008 H A R R E T A L FIG. 17. As in Fig. 7, but for the two-cluster solution solutions from the ensembles generated on 6 Sep. Two important characteristics in the distribution of ensemble standard deviation were identified. The standard deviation among ensemble forecasts in the region of the ET do not increase dramatically until after TY Nabi has completed its transition to an extratropical cyclone. For the forecasts through 1200 UTC 6 September, this timing is independent of the forecast interval prior to this transition. Therefore, the increase in variability is tied to the ET event and not to the forecast interval. The downstream standard deviations decreased in the forecasts after 1200 UTC 6 September, which suggests that the spread of ensemble variability depends on the ET event. The principal patterns of variability were identified with an EOF analysis of ensemble forecasts (Figs. 4 and 5). The EOF analyses identified coherent structures of variability that were tied to physical characteristics of the atmosphere during the ET of TY Nabi. Although the maximum amplitudes of the variability in the EOF analysis decreased with the decrease in forecast intervals, the spatial distribution of the centers remained largely consistent with the synoptic-scale features associated with the ET. These characteristics were consistently diagnosed through the collection of ensemble forecasts from 6 September. Following that time, the centers of variability became smaller in scale and amplitude with less connection to synoptic-scale features, which was consistent with the decrease in the organization of the time longitude distribution of ensemble standard deviation following 1200 UTC 6 September. The final examination of ensemble variability grouped ensemble forecast sequences according to similar forecast scenarios associated with the ET of TY Nabi. The number of forecast scenarios is representative of the variability among ensemble members. Four clusters or forecast scenarios were found for the ensemble forecasts initialized for the 24 h of 4 September. These clusters differed in representation of the upperlevel downstream ridge and sea level pressure pattern of the cyclone resulting from the ET of TY Nabi. The number of clusters decreased to three for the forecasts from 5 September. The differences among the clusters from 4 and 5 September forecasts were primarily associated with the ET of TY Nabi, and variability associated with the downstream ridge was reduced in the forecasts from 5 September. The ensemble forecasts in the two- and three-cluster solutions from 6 September had small differences in the ET of TY Nabi. Rather, the differences between clusters from 6 September occurred downstream of the ET event over the eastern North Pacific. Typically, the skill in the deterministic forecasts by

20 3224 M O N T H L Y W E A T H E R R E V I E W VOLUME 136 FIG. 18. As in Fig. 11, but for the three-cluster solution for forecasts from 6 Sep that are verified at (a) 0000 UTC 9 Sep and (b) 0000 UTC 10 Sep. The ellipse identifies the region where the standard deviations among the ensemble members are greater than 60 m, as defined in Fig. 3d. an operational global numerical weather prediction model decreases during ET events. Based on the results of this study, the decrease in skill could be defined as the errors associated with the amplitude and/or phase of the wave patterns that occur in conjunction with an ET event. In a companion study (Anwender et al. 2008), the methodology in this case study is used with the ECMWF ensemble system to examine the impact of additional ET events. Tropical cyclones with varying characteristics such as intensity and size over the North Pacific and North Atlantic are examined. Downstream impacts in that study are examined with respect to midlatitude flow patterns, errors in deterministic forecasts, and variability among ensemble members. Acknowledgments. This study was sponsored in part by the Office of Naval Research, Marine Meteorology Program. The authors acknowledge the constructive comments from two reviewers. REFERENCES Agusti-Panareda, A., C. D. Thorncroft, G. C. Craig, and S. L. Gray, 2004: The extratropical transition of hurricane Irene (1999): A potential vorticity perspective. Quart. J. Roy. Meteor. Soc., 130, Anwender, D., P. A. Harr, and S. C. Jones, 2008: Predictability associated with the downstream impacts of the extratropical transition of tropical cyclones: Case studies. Mon. Wea. Rev., 136, Bosart, L. F., and G. M. Lackmann, 1995: Postlandfall tropical cyclone reintensification in a weakly baroclinic environment: A case study of Hurricane David (September 1979). Mon. Wea. Rev., 123, Buizza, R., 1997: Potential forecast skill of ensemble prediction and spread and skill distribution of the ECMWF Ensemble Prediction System. Mon. Wea. Rev., 125, Evans, J. L., J. M. Arnott, and F. Chiaromonte, 2006: Evaluation of operational model cyclone structure forecasts during extratropical transition. Mon. Wea. Rev., 134, Everitt, B. S., 1979: Unresolved problems in cluster analysis. Biometrics, 35,