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  • View in gallery

    Climatology and variance of the pentad 500-hPa geopotential height field during the winters (DJFM) of 1958–99. The thick black line corresponds to the 540-dam contour; gray lines correspond to the 522-, 528-, 534-, 546-, and 552-dam contours. Thin black lines represent variance; contour lines for the variance begin at 6000 m2, and the contouring interval is 3000 m2.

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    Limited-contour clustering results for all 1008 pentad records for the winters (DJFM) of 1958–99. Acronyms for the named clusters appear in the upper left: OT, AR, CR, and RR. The number of pentad records contained in each cluster map is indicated in the lower left. Contours range from 552 to 510 dam; intervals are 6 dam. The thick contour corresponds to the 540-dam contour, which has been used to calculate the distance between pentad records in the clustering algorithm.

  • View in gallery

    Anomaly maps for the named clusters emerging from the limited-contour clustering analysis. Contour interval is 2 dam. Dashed contours indicate negative anomalies; solid contours indicate positive anomalies.

  • View in gallery

    Geopotential height field values at 500-hPa for each cluster pattern along 45°N between 150°E and 60°W. Cluster geopotential height is indicated by the dotted line, and climatology is indicated by the solid line. Areas where the cluster has higher heights than climatology have light shading; areas where the cluster has lower heights than climatology have dark shading.

  • View in gallery

    Ridge locations for the pentad maps belonging to the OT, AR, CR, and RR clusters emerging from the limited-contour clustering analysis. Each circle represents the most poleward position of the 540-dam contour occurring in a single pentad map. The thick, solid black line indicates the 540-dam contour for the particular cluster; the thin gray lines indicate the 540-dam contours for individual pentads included in the cluster. The dashed black line indicates the climatological mean position of the 540-dam contour. For clarity, only one-half of the contours for the individual pentads in the RR and CR clusters are shown.

  • View in gallery

    Full-field clustering results for all 1008 pentad records for the winters (DJFM) of 1958–99. The number of pentad records contained in each cluster map is indicated in the lower left. Contours range from 552 to 510 dam; intervals are 6 dam.

  • View in gallery

    Anomaly maps for the patterns produced from the last several steps of the full-field clustering algorithm. Contour interval is 2 dam. Dashed contours indicate negative anomalies; solid contours indicate positive anomalies. The number of pentad records contained in each cluster map is indicated in the lower left.

  • View in gallery

    As in Fig. 5, but for the pentad maps belonging to the clusters emerging from the full-field clustering analysis.

  • View in gallery

    Frequency of occurrence of each cluster pattern for the full dataset (“All Years”), the El Niño composite (“Warm ENSO”), and the La Niña composite (“Cold ENSO”). The frequency of occurrence of the RR (OT, AR, CR) pattern during the El Niño years is significantly greater (less) than the frequency of occurrence of the same pattern in the full dataset.

  • View in gallery

    Frequency of extreme cold days for each cluster. Extremes have been defined as the coldest 3% of the days in the records (∼150 days). The frequencies are calculated as the number of extreme cold days divided by the number of cluster days. Several grid points have been chosen to represent cities in a region—the average number of extreme cold days at these grid points is used to calculate the frequency for that region. The solid line corresponds to a frequency of 0.03; the dotted lines represent frequencies of 0.01 and 0.09.

  • View in gallery

    Frequency of days of heavy precipitation for each cluster, as in Fig. 9.

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Identifying Weather Regimes in the Wintertime 500-hPa Geopotential Height Field for the Pacific–North American Sector Using a Limited-Contour Clustering Technique

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  • 1 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
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Abstract

A hierarchical clustering algorithm using Ward’s method has been applied to the 500-hPa geopotential height field in the Pacific–North American sector. In contrast to previous clustering studies that measure distance between records by using all the grid points within the domain (full-field method), the procedure outlined here, referred to as the limited-contour method, focuses on the coordinates of the 540-dam contour as the distance measure. Comparison between the regimes emerging from the two methods shows that the limited-contour method is more efficient than the full-field method with respect to grouping maps with ridges located at similar longitudes. The four regimes emerging from the limited-contour clustering analysis have been named as follows: Off-Shore Trough, Alaskan Ridge, Coastal Ridge, and Rockies Ridge. The frequencies of occurrence of the regimes have a significant relationship with the phase of the El Niño–Southern Oscillation. El Niño winters exhibit a strong preference for the Rockies Ridge pattern; La Niña winters exhibit a greater diversity of regimes. The frequencies of occurrence of extreme cold outbreaks and episodes of heavy precipitation in the Pacific Northwest show a relatively strong connection to the regime type. For other regions in the western portion of the United States, only the frequency of occurrence of cold outbreaks exhibits a significant relationship to regime type.

Corresponding author address: Joseph H. Casola, Department of Atmospheric Sciences, University of Washington, P.O. Box 351640, Seattle, WA 98195-1640. Email: jcasola@atmos.washington.edu

Abstract

A hierarchical clustering algorithm using Ward’s method has been applied to the 500-hPa geopotential height field in the Pacific–North American sector. In contrast to previous clustering studies that measure distance between records by using all the grid points within the domain (full-field method), the procedure outlined here, referred to as the limited-contour method, focuses on the coordinates of the 540-dam contour as the distance measure. Comparison between the regimes emerging from the two methods shows that the limited-contour method is more efficient than the full-field method with respect to grouping maps with ridges located at similar longitudes. The four regimes emerging from the limited-contour clustering analysis have been named as follows: Off-Shore Trough, Alaskan Ridge, Coastal Ridge, and Rockies Ridge. The frequencies of occurrence of the regimes have a significant relationship with the phase of the El Niño–Southern Oscillation. El Niño winters exhibit a strong preference for the Rockies Ridge pattern; La Niña winters exhibit a greater diversity of regimes. The frequencies of occurrence of extreme cold outbreaks and episodes of heavy precipitation in the Pacific Northwest show a relatively strong connection to the regime type. For other regions in the western portion of the United States, only the frequency of occurrence of cold outbreaks exhibits a significant relationship to regime type.

Corresponding author address: Joseph H. Casola, Department of Atmospheric Sciences, University of Washington, P.O. Box 351640, Seattle, WA 98195-1640. Email: jcasola@atmos.washington.edu

1. Introduction

For over a century, meteorologists have attempted to categorize and catalog frequently observed, persistent, regional and/or hemispheric atmospheric circulation patterns in terms of “weather types.” One of the earliest mentions of weather types is the paper by Blandford (1897), which defined the weather of the North American Pacific Northwest as arising from one of six weather types, each with its characteristic surface pressure map and a preferred route for steering storms eastward across the continent. Exploiting newly available upper-air observations, the meteorologists of the midtwentieth century expanded their characterizations of weather types to include circulations aloft: Baur (1951) detailed seven fundamental weather types (Grosswetterlagen) that prevail over the Northern Hemisphere midlatitudes; Elliott (1951) discussed efforts, especially at the California Institute of Technology Meteorology Department (1943; see also Blewitt et al. 1942) that resulted in the definition of a multitude of North American weather types; and Rex (1950) characterized blocking events in the Pacific–North American (PNA) sector using criteria that could be considered a weather-typing template.1

As the language of nonlinear systems analysis has gained prevalence in the meteorological lexicon, and in order to highlight the role of large-scale circulations aloft, the term weather types has been replaced by “weather regimes” and “circulation regimes.” Michelangeli et al. (1995) categorize studies on regimes into three groups—studies that focus on recurrent spatial structures within the atmosphere (Molteni et al. 1990; Cheng and Wallace 1993, hereinafter CW; Kimoto and Ghil 1993a, b; Toth 1993; Michelangeli et al. 1995; Smyth et al. 1999; Robertson and Ghil 1999; Monahan et al. 2003; Straus and Molteni 2004; Wu and Straus 2004); studies that focus on anomalies that persist for a number of days (Dole and Gordon 1983; Horel 1985); and, studies that focus on patterns that are quasi-stationary in a dynamical sense (the time derivatives of the atmospheric state variables are nearly equal to zero; see Charney and DeVore 1979; Toth 1992).2

The work presented here fits into the first category. Previous studies in this category have applied a variety of objective methods [e.g., clustering, probability density function (PDF) methods, and nonlinear principal component analysis] to observations or model output of the upper-level geopotential height field in order to define the spatial structure of the regimes. The resulting patterns tend to be separated by a large distance in the phase space spanned by the data, while accounting for a large number of the records and/or a large portion of the variability of the dataset. The studies have typically found between two and seven regime patterns, depending on whether the domain is hemispheric or sectoral. The hemispheric patterns found by CW and Kimoto and Ghil (1993a), which are similar to one another, are robust and have served as benchmarks for subsequent studies of recurrent hemispheric patterns (Michelangeli et al. 1995; Smyth et al. 1999; Monahan et al. 2003; Straus and Molteni 2004; Wu and Straus 2004). The clusters identified for sectoral domains vary significantly from one study to the next. In studies that yield two or three regime patterns for the Pacific sector (CW; Michelangeli et al. 1995; Smyth et al. 1999), the patterns are similar to the opposing polarities of the Pacific–North American pattern, and often identify just two types of flow orientations, one zonal and one meridional. Such a simple dichotomy fails to represent the variety of circulation patterns observed in the Pacific sector. In studies in which a greater number of regional regimes are found (Kimoto and Ghil 1993b; Robertson and Ghil 1999; Straus and Molteni 2004; Straus et al. 2007), the flow patterns tend to be more diverse. However, with the exceptions of Robertson and Ghil (1999) and Stan and Straus (2007), none of the studies relate the frequency of occurrence of the regime patterns to the occurrence of anomalous or extreme surface weather. In all studies, a framework for understanding distinctions among the different regimes is lacking.

In this study, we derive weather regimes for the Pacific–North American sector using a variant of the hierarchical clustering method employed in CW. In contrast to CW, this study focuses on a single limited contour from each data record. This methodological choice has been made in hopes of simplifying the differences among the resulting regime patterns, making them recognizable and meaningful to operational weather forecasters. Use of ridge and trough position as a basis for categorizing the larger-scale circulation is commonplace in synoptic forecast discussions. The utility of “spaghetti diagrams,” which have been some of the most popular products of the National Centers for Environmental Prediction (NCEP) ensemble forecasts (Toth et al. 1997), is predicated on this relationship.

The results of this clustering technique are four weather regimes for the Pacific–North American sector, and we compare the regimes with those derived from a traditional full-field clustering algorithm. We demonstrate that the contour method is more efficient than the full-field method with respect to grouping maps with ridges located at similar longitudes. Thus, the resulting regime patterns can be visually classified by their distinctive ridge positions. Additionally, we present two applications of the regime patterns. We show that the relative frequency of occurrence of these regime patterns has a statistically significant relationship with the phase of ENSO, and we demonstrate how the patterns are associated with an increased (decreased) probability of extreme cold air outbreaks and heavy precipitation episodes for some regions of the North American west.

In contrast to the previously cited works, our goal is not to establish that the atmospheric circulation is fundamentally multimodal, or to specify the precise number of regimes that exist in the data space. Rather, the primary goal of this study is to provide a forecaster with easily recognizable patterns that have a significant relationship to ENSO and to incidences of extreme weather, thereby serving as a basis for improving the skill of long-term (two weeks to seasonal) predictions of severe weather.

2. Data

Daily values for the 500-hPa geopotential height field and the surface temperature during December–March (DJFM) for the period January 1958–December 1999 were taken from the NCEP–National Center for Atmospheric Research reanalysis (Kalnay et al. 1996). Resolution is 2.5° latitude by 2.5° longitude. Data have been calculated as 5-day averages (pentads). Winter is defined as the 120-day period beginning on 2 December.

Daily precipitation data during DJFM for the period January 1958–December 1998 were taken from the NCEP/Climate Prediction Center unified precipitation historical reanalysis for the contiguous United States (Higgins et al. 2000). Resolution is 0.25° latitude by 0.25° longitude. Precipitation pentad values were calculated in the same manner as described above.

The “cold-tongue index” (CTI) was used to classify winters within the dataset with respect to the phase of ENSO. The CTI represents the difference between global mean sea surface temperature (SST) and the SST anomalies (relative to the 1950–79 climatology) averaged over the area 6°N–6°S, 90°W–180° and is based on the Comprehensive Ocean–Atmosphere Dataset (COADS) described in Woodruff (2001a, b).

3. Limited-contour clustering method

A hierarchical clustering algorithm based on Ward’s method was applied to the pentad 500-hPa geopotential height data. The algorithm iteratively combines similar pentad records to form clusters, minimizing the increase in the “error sum of squares” (Ward 1963; Wishart 1969) occurring in each step, as described in CW.

The domain for the clustering analysis is limited to the Pacific–North American sector, defined here as 20–90°N, 150°E–60°W. In contrast to previous hierarchical clustering studies (CW; Wu and Straus 2004), the distance measure is not based on the entire height field in the sector. Rather, the coordinates of the 540-dam 500-hPa geopotential height contour within the sector are calculated for each data record or cluster. For records where the 540-dam contour crossed a single meridian at multiple latitudes, as in bent-back ridges and troughs or cutoff lows and highs, the most equatorward latitude value was used.

Distance in the limited-contour analysis is defined as the difference in latitude between contour coordinates at each longitude ϕ, summed over all the longitudes in the sector of interest. The distance d between records (or clusters) p and q can be expressed mathematically as
i1558-8432-46-10-1619-eq1

The choice of the 540-dam contour is based on two factors. First, in a climatological sense, this contour passes through the variance maximum in the 500-hPa geopotential height field over the North Pacific Ocean, and it traces out the configuration of the planetary waves in the climatological mean flow in the Pacific–North American sector during the winter (Fig. 1). Second, the 540-dam contour can be conveniently rendered as a smooth function of latitude. In all 1008 pentads, the 540-dam contour had at least one value for each longitude meridian in the Pacific–North American sector. By comparison, the 528-dam contour had 22 records lacking meridional intersections, corresponding to ∼2% of the data record.

Note that the limited-contour clustering method segregates the pentad records based on the shape of the 500-hPa flow. We consider this aspect of the circulation the most important factor for forecasters attempting to diagnose the advection of air masses and the surface weather. However, other aspects of the circulation may not be well segregated by our method, such as the strength of the 500-hPa flow, or whether the westerlies, when averaged over the Pacific–North American sector, are poleward or equatorward of their climatological mean position.

4. Limited-contour clustering results

Figure 2 shows plots of the 500-hPa field for the clusters emerging from the last several steps of the clustering algorithm. Each panel within the cluster “pyramid” represents the circulation pattern associated with a particular cluster; the number of records contained in each cluster appears in the lower-left corner of each panel. The top map in the pyramid is the result of the last step of clustering: the overall climatology of the dataset, a map representing the mean of all 1008 pentad records. The clusters of primary interest emerge in the preceding steps (shown in the underlying levels of the pyramid), in which large numbers of maps are included in a small number of clusters. An abbreviated but similar cluster pyramid showing the anomalies relative to the DJFM seasonal mean is shown in Fig. 3.

Labels assigned to the four clusters appearing one level above the base of the pyramid in Fig. 2 identify the distinguishing ridge or trough in the Pacific–North American sector associated with each circulation pattern. We focus on the clusters arising at this particular step in the algorithm because of the disproportionately large jump in the increase in the sum-of-squares error that occurs at the next step of the clustering algorithm, in which four clusters merge into three (not shown). The 138-pentad cluster termed the Off-Shore Trough (OT), exhibits a ridge near the Bering Sea and a trough just to the west of the North American west coast. The 107-pentad cluster that exhibits a high-amplitude ridge centered in the Gulf of Alaska is called the Alaskan Ridge (AR). The 278-pentad cluster labeled the Coastal Ridge (CR) exhibits a ridge aligned with the North American west coast. Last, the 485-pentad cluster named the Rockies Ridge (RR) exhibits a ridge aligned with the Rocky Mountains.

Progressing from OT to AR to CR to RR on the 540-dam contour (left to right in Fig. 2), the ridge position shifts from west to east. Figure 4 illustrates the progression, comparing the 500-hPa geopotential height values for the named clusters with the climatological mean geopotential height values along 45°N between 150°E and 60°W. The OT pattern exhibits a ridge centered at ∼160°W, well to the west of the climatological mean ridge along 120°W. The AR ridge is centered at ∼140°W, also to the west of the climatological ridge. The AR ridge is more pronounced than the ridge associated with the OT pattern. The CR pattern exhibits a relatively lower amplitude ridge along 130°W, just to the west of the climatological ridge. The RR cluster, which contains nearly one-half of the pentads in the dataset, exhibits a broad, relatively low amplitude ridge extending from 120°W, near the climatological mean ridge, to 60°W, which is the eastern boundary of the sector. The distinctions between the ridge positions are more clearly apparent in the anomalies (Fig. 3) than in the total field (Fig. 2).

Figure 5 shows the ridge locations along the 540-dam contour among the pentad records contained within each cluster, giving a sense of 1) the similarity among the ridge locations of the constituent maps; 2) the relationship between the ridge positions in individual records and the ridge position in the climatological mean; and 3) the diversity of the flow patterns that belong to the same cluster. For the pentads in the OT and AR clusters, most of the ridges are situated far to the north and west of the climatological mean ridge. Most of the ridges belonging the CR records are located to the west of the climatological mean ridge and most of those belonging to the RR records are located to the east of the climatological mean ridge.

In a number of the pentad charts, the 540-dam contour becomes detached from the main stream of the westerlies as it passes around the poleward flank of a narrow, high-amplitude blocking ridge. These charts correspond to the widely scattered points over high latitudes in Fig. 5. A disproportionate fraction of these points occur in pentads belonging to the RR cluster.

We can further characterize the patterns in terms of their similarity to the PNA pattern. Following Wallace and Gutzler (1981), we constructed a pentadal PNA index using the 500-hPa geopotential height values at four grid points within the Pacific–North American sector (20°N, 160°W; 45°N, 165°W; 55°N, 115°W; and 30°N, 85°W). The pentadal 500-hPa geopotential height anomaly fields over the domain of the study were regressed onto the standardized index to create our own version of the PNA pattern. Pattern correlations between this PNA pattern and each of the four clusters shown in Fig. 3 are used as a measure of the similarity between the respective clusters and the PNA pattern. The OT and AR patterns resembled the negative polarity of the PNA pattern, with pattern correlation values of −0.703 and −0.569, respectively. The RR pattern projects positively on the PNA pattern, with a pattern correlation of 0.651. The CR pattern exhibits a low pattern correlation (0.052) with the PNA pattern.

To test the reproducibility of the clusters, 50 randomly chosen halves of the dataset were selected and subjected to the clustering algorithm based on the 540-dam contour. Pattern correlation values were calculated between the four named clusters (OT, AR, CR, and RR) and the four clusters arising at the same step in the clustering of the random halves. The pattern correlation values were based on the entire 500-hPa fields within the North Pacific sector, not just the 540-dam contour. Thus, for each of the named clusters, 50 “best analogs” were created, and the average pattern correlation value from the analogs serves as a measure of the regime’s reproducibility. The RR and CR patterns were highly reproducible, with pattern correlations of 0.97 and 0.93, respectively. The OT and AR patterns were less robust, displaying pattern correlation values of 0.65 and 0.83, respectively. Considering the relatively smaller sizes of the OT and AR clusters (13.7% and 10.6% of the data records, respectively), their relatively lower pattern correlation values are not surprising. In CW, pattern correlation values are calculated using the patterns that arise in earlier steps of the clustering algorithm for the half-length data (i.e., more cluster patterns with fewer maps are compared with the named clusters). When this is done, the pattern correlation values for the OT and AR patterns increase: comparing the four named clusters with the five clusters emerging from the half-sets, pattern correlations increase to 0.78 for OT and 0.88 for AR.

To test the sensitivity of the results, the clustering algorithm was applied to the 528-, 534-, 546-, and 552-dam contours and was repeated using three alternative longitude domains (150°E–90°W; 180°–60°W; and 180°–90°W). The results (not shown) are generally similar to those presented here; they are more sensitive to choice of contour than to choice of domain.

5. Comparison with full-field clustering results

A full-field clustering algorithm, following CW, was applied to the 500-hPa geopotential height field of the 1008-pentad dataset in order to determine how the distance criterion affected the clusters produced. Rather than calculating the distance between contour coordinates, the full-field method is based on the difference in geopotential height values at all grid points within the Pacific–North American sector. To ensure that grid points are weighted in accordance with the area that they represent, geopotential height values are multiplied by the square root of the cosine of the respective latitude prior to clustering.

The results of the full-field clustering are shown in Fig. 6, the corresponding anomaly patterns are shown in Fig. 7, and the individual ridges for each cluster are shown in Fig. 8. The 293-pentad cluster and the 199-pentad cluster, shown in the left side of the diagram, are analogs of the CR and AR and patterns, respectively. These analogs exhibit geopotential height anomalies with a similar spatial orientation to the patterns produced by the limited-contour clustering method; however, the amplitudes and the number of pentads in the clusters are not the same. In the 293-pentad pattern produced by the full-field clustering method, the trough in the western portion of the sector is of larger amplitude than in the CR pattern produced by the limited-contour clustering method. The 199-pentad pattern produced by the full-field clustering method shows a markedly smaller amplitude ridge in the Gulf of Alaska than the AR pattern produced by the limited-contour clustering method. Although the location and tightness of individual ridges for the 293-pentad cluster (Fig. 8) is comparable to the individual ridges for the CR cluster (Fig. 5), the 199-pentad cluster exhibits a much looser collection of ridges than the AR pattern. The remaining patterns formed by the full-field clustering method bear little resemblance to the clusters produced by the limited-contour clustering method. The geopotential height anomalies associated with the 289- and 227-pentad clusters (Fig. 7) are centered farther poleward than the anomalies observed in the regimes shown in Fig. 3. The individual ridges (Fig. 8) for these two clusters are scattered over a wide geographical range, with the majority located near the axis of the climatological mean ridge. From a comparison of Figs. 5 and 8, it is evident that the limited-contour clustering method is more effective than the full-field method in grouping together patterns with similar ridge locations.

The full-field clustering results also demonstrate how the expansion of the latitudinal extent of the clustering domain affects the patterns. In the contour clustering results, the geopotential height fields for all four clusters exhibit a polar circulation that is almost identical to the climatological pattern: a “kidney bean” shape circulation extending from the pole southward over Hudson Bay. In contrast, the full-field method is sensitive to differences that occur both in the midlatitudes and in the polar regions, and its clusters show more diversity in their polar circulations.

6. Applications of the limited-contour cluster patterns

a. Effect of ENSO on the relative frequencies of the four clusters

It has been established that ENSO has a significant impact on the structure of the variability of the extratropical winter atmosphere (Renwick and Wallace 1996; Chen and van den Dool 1997, 1999; Robertson and Ghil 1999; Compo et al. 2001; Straus and Molteni 2004). In particular, La Niña winters exhibit a higher frequency of blocking events in the North Pacific and a greater level of intraseasonal variability than El Niño winters.

For the full dataset, the CR and RR patterns are observed more frequently than the relatively high amplitude ridges and troughs associated with the OT and AR patterns. To determine if the frequency of occurrence of the various clusters (indicated by the number of maps in each cluster) is significantly different among the phases of ENSO, we have partitioned the dataset into thirds (El Niño, neutral, and La Niña winters) based on seasonal values of the CTI. Results are shown in Fig. 9. For the El Niño composite, the RR pattern occurs more frequently while the OT, AR, or CR patterns occur less frequently when compared with the full dataset or the La Niña composite. The La Niña composite displays the opposite tendencies—the OT, AR, and CR patterns occur more frequently and the RR pattern occurs less frequently than in the full dataset.

The statistical significance of each frequency of occurrence value was estimated using a Monte Carlo test. One thousand Monte Carlo subsets were created, each containing 336 randomly selected pentads. The distribution of the frequency of occurrence values for the 1000 Monte Carlo subsets was compared with the frequency of occurrence values associated with the El Niño and La Niña composites. For a particular cluster and a particular composite, significance is attributed to a relatively high (low) frequency of occurrence value when it exceeds (is exceeded by) the frequency of occurrence values for at least 950 of the Monte Carlo subsets. All four (OT, AR, CR, and RR) of the frequency of occurrence values for the El Niño composite are significantly different from the frequency of occurrence values for the full dataset; for the La Niña composite only the RR and OT frequency of occurrence values are significant.

b. Frequencies of extreme events

The relationship between the four weather regimes and the frequency of occurrence of days of extreme cold and extreme wet weather was also explored. Figures 10 and 11 show the frequency of extreme weather days for each cluster pattern, calculated from an average of the number of extreme days for several grid points corresponding to the locations of major cities in the western United States (see the appendix). Extreme days have been defined as the 3% coldest, and separately, the 3% wettest winter days (∼150 days) in the records at those data points. Hence, the values of interest in Fig. 10 are the ones that depart significantly from 0.03 (solid line). The dotted lines indicate a frequency of 0.01 (1/3 less frequent than climatology) and a frequency of 0.09 (3 times as frequent as climatology).

Relationships are strongest for the Pacific Northwest, which shows an elevated probability of extreme cold days during the occurrence of the AR pattern, a lowered probability of extreme cold days during occurrence of the RR pattern, and a lowered probability of extreme wet days during the occurrence of both the AR and CR patterns. With regard to temperature, many of the continental United States’ regions exhibited the same relationship with the AR pattern (increased incidence of cold extremes) and the RR pattern (decreased incidence of cold extremes) as the Pacific Northwest. In contrast, Alaska exhibited a reduced number of extreme cold days during the occurrence of the AR pattern. In general, the occurrence of warm extremes exhibited an inverse relationship to that of the cold extremes (not shown).

These temperature and precipitation relationships are consistent with the flow orientation of the respective regime patterns. The AR pattern brings warmer air from the Pacific to the Alaskan coast while bringing cold, dry continental air to the contiguous western United States. It follows that the Alaskan areas would be prone to warm spells while the other western regions experience cold outbreaks, and the Pacific Northwest in particular experiences cold and dry conditions. Similarly, the RR pattern advects marine air over most of the western United States, reducing the frequency and severity of cold outbreaks. It should be noted that the RR regime contains a relatively large number of records—a frequency of occurrence of 10−2 for the RR records corresponds to 38 extreme days, as compared with 5–14 days for the other regimes. From Figs. 10 and 11, it is clear that the 500-hPa regime patterns identified in the study have a much weaker effect upon precipitation extremes than on temperature extremes, and that their influence is largely restricted to the Pacific Northwest.

7. Discussion

a. Summary of method and results

In this study, we have applied a limited-contour clustering algorithm to the pentad 500-hPa geopotential height field data for the Pacific–North American sector in order to isolate weather regimes. In contrast to previous clustering studies that utilize all grid points in the sector when computing the distance among records (full-field methods), the limited-contour method focuses more narrowly on the latitudinal coordinates, and thus the shape of the 540-dam 500-hPa geopotential height contour.

Four regimes emerge from the limited-contour clustering method: Off-Shore Trough, Alaskan Ridge, Coastal Ridge, and Rockies Ridge. These patterns can be distinguished from one another based on the magnitude and longitudinal location of their respective ridges. The OT and AR patterns exhibit relatively large amplitude ridges in the western portion of the sector and occur relatively less frequently than the other patterns. The CR and RR patterns exhibit relatively lower amplitude ridges in the eastern portion of the sector and together account for over 75% of the pentad records.

Although no formal test of regime patterns’ significance has been performed, the clustering algorithm has been applied to randomly selected, half-length portions of the data in order to assess the reproducibility of the regime patterns. The patterns produced from these half-length datasets bear a strong resemblance to AR, CR, and RR patterns. The OT pattern is less robust, but closer analogs are detected when smaller clusters emerging in earlier steps of the half-length clustering algorithm are examined. Thus, we contend that the patterns are reproducible.

Comparisons between the frequency of occurrence of the clusters and the phase of ENSO have been made. El Niño winters exhibit a high frequency of occurrence of the RR pattern relative to the other regime patterns. This preference suggests that during El Niño winters the planetary-wave ridge over the Pacific–North American sector tends to be displaced east of its climatological-mean position, while the higher-amplitude patterns that exhibit ridges located to the west of the climatological mean occur less frequently. La Niña winters, on the other hand, exhibit a greater diversity of cluster patterns.

The frequency of occurrence of the clusters has also been compared with the frequency of occurrence of extreme weather. Across much of the western United States, the AR (RR) pattern is related to an elevated (lowered) probability of extreme cold outbreaks. In the Pacific Northwest in particular, the AR and CR patterns are rarely associated with extreme wet conditions.

b. Caveats for future application of the limited-contour clustering method

Our experience with the limited-contour clustering method has brought to light two limitations with respect to its further application:

  1. The method is not as effective when applied to other seasons or other sectors, where factors such as the strength or meridional position of the jet play a larger role in determining the variance of the geopotential height field than the position of the ridge in the planetary wave. For example, our attempts to cluster the geopotential height contours in the North Pacific during the summer, as well as the contours in the North Atlantic during the winter, did not yield particularly interesting or distinctive patterns (i.e., the Northern Annular Mode could not be detected using the limited-contour clustering method).

  2. With the exception of the Pacific Northwest, the clustering method performs poorly in segregating incidences of extreme precipitation. We speculate that precipitation is inherently dependent on synoptic-scale events that are associated with patterns smaller in spatial scale and shorter in time scale than the patterns captured here.

c. Advantages of the limited-contour clustering method

Despite the aforementioned caveats, the limited-contour clustering method offers a useful alternative to the full-field clustering method. Relative to the full-field method, the limited-contour clustering method more consistently groups together individual records with similar ridge locations. This provides a simple framework for differentiating the clusters. The clusters derived from the 540-dam contour exhibit a simpler and more straightforward relationship to the phase of ENSO than those derived from the full-field cluster analysis. For the full-field clusters, a frequency of occurrence plot for the ENSO phases (as in Fig. 9) shows only small differences among the cluster patterns (plot not shown). The relationships between the clusters derived from the 540-dam contour, the phase of ENSO, and the frequency of occurrence of extreme weather, especially cold outbreaks, may allow forecasters in the western United States to assess better the likelihood of extreme weather threats in long-term winter forecasts.

Acknowledgments

This research was supported by the National Science Foundation under Grant ATM 0318675. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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APPENDIX

Calculating the Frequency of Occurrence of Extreme Cold Outbreaks and Episodes of Heavy Precipitation

Temperature and precipitation data from specific grid points have been selected to represent cities in the western United States, listed in Table A1. To calculate frequencies of occurrence for the regions, the mean of the number of days of extreme cold and, separately, of extremely heavy precipitation amongst all locations in a region was used. The frequency of occurrence is equal to the mean number of days of extreme cold and heavy precipitation divided by the number of days during which the cluster pattern was observed (i.e., the number of cluster maps multiplied by 5). Table A1 lists the selected cities that constituted each region as well as the latitude and longitude coordinates of the grid points used to represent the cities. Separate columns are listed for the temperature and precipitation because each dataset has its own resolution (see section 2). Also, the precipitation data are only available for the continental United States.

Fig. 1.
Fig. 1.

Climatology and variance of the pentad 500-hPa geopotential height field during the winters (DJFM) of 1958–99. The thick black line corresponds to the 540-dam contour; gray lines correspond to the 522-, 528-, 534-, 546-, and 552-dam contours. Thin black lines represent variance; contour lines for the variance begin at 6000 m2, and the contouring interval is 3000 m2.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 2.
Fig. 2.

Limited-contour clustering results for all 1008 pentad records for the winters (DJFM) of 1958–99. Acronyms for the named clusters appear in the upper left: OT, AR, CR, and RR. The number of pentad records contained in each cluster map is indicated in the lower left. Contours range from 552 to 510 dam; intervals are 6 dam. The thick contour corresponds to the 540-dam contour, which has been used to calculate the distance between pentad records in the clustering algorithm.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 3.
Fig. 3.

Anomaly maps for the named clusters emerging from the limited-contour clustering analysis. Contour interval is 2 dam. Dashed contours indicate negative anomalies; solid contours indicate positive anomalies.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 4.
Fig. 4.

Geopotential height field values at 500-hPa for each cluster pattern along 45°N between 150°E and 60°W. Cluster geopotential height is indicated by the dotted line, and climatology is indicated by the solid line. Areas where the cluster has higher heights than climatology have light shading; areas where the cluster has lower heights than climatology have dark shading.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 5.
Fig. 5.

Ridge locations for the pentad maps belonging to the OT, AR, CR, and RR clusters emerging from the limited-contour clustering analysis. Each circle represents the most poleward position of the 540-dam contour occurring in a single pentad map. The thick, solid black line indicates the 540-dam contour for the particular cluster; the thin gray lines indicate the 540-dam contours for individual pentads included in the cluster. The dashed black line indicates the climatological mean position of the 540-dam contour. For clarity, only one-half of the contours for the individual pentads in the RR and CR clusters are shown.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 6.
Fig. 6.

Full-field clustering results for all 1008 pentad records for the winters (DJFM) of 1958–99. The number of pentad records contained in each cluster map is indicated in the lower left. Contours range from 552 to 510 dam; intervals are 6 dam.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 7.
Fig. 7.

Anomaly maps for the patterns produced from the last several steps of the full-field clustering algorithm. Contour interval is 2 dam. Dashed contours indicate negative anomalies; solid contours indicate positive anomalies. The number of pentad records contained in each cluster map is indicated in the lower left.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 8.
Fig. 8.

As in Fig. 5, but for the pentad maps belonging to the clusters emerging from the full-field clustering analysis.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 9.
Fig. 9.

Frequency of occurrence of each cluster pattern for the full dataset (“All Years”), the El Niño composite (“Warm ENSO”), and the La Niña composite (“Cold ENSO”). The frequency of occurrence of the RR (OT, AR, CR) pattern during the El Niño years is significantly greater (less) than the frequency of occurrence of the same pattern in the full dataset.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 10.
Fig. 10.

Frequency of extreme cold days for each cluster. Extremes have been defined as the coldest 3% of the days in the records (∼150 days). The frequencies are calculated as the number of extreme cold days divided by the number of cluster days. Several grid points have been chosen to represent cities in a region—the average number of extreme cold days at these grid points is used to calculate the frequency for that region. The solid line corresponds to a frequency of 0.03; the dotted lines represent frequencies of 0.01 and 0.09.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Fig. 11.
Fig. 11.

Frequency of days of heavy precipitation for each cluster, as in Fig. 9.

Citation: Journal of Applied Meteorology and Climatology 46, 10; 10.1175/JAM2564.1

Table A1. Latitude and longitude of city grid points.

i1558-8432-46-10-1619-ta01

1

In more recent studies, the term “weather typing” typically refers to statistical groupings of surface weather conditions, with less emphasis on the circulation patterns that accompany the weather. See Sheridan (2002) and references therein for descriptions of contemporary weather typing studies.

2

Some more recent studies actually fit into more than one category—Stan and Straus (2007) and Straus et al. (2007) filter the data using quasi-stationarity criteria prior to applying a clustering algorithm that isolates recurrent spatial patterns.

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