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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
JOSEPH H. CASOLA
AND
JOHN M. WALLACE
Department of Atmospheric Sciences, University of Washington, Seattle, Washington
(Manuscript received 1 August 2006, in final form 9 February 2007)
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.
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 upperair 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 De-
Corresponding author address: Joseph H. Casola, Department
of Atmospheric Sciences, University of Washington, P.O. Box
351640, Seattle, WA 98195-1640.
E-mail: [email protected]
DOI: 10.1175/JAM2564.1
© 2007 American Meteorological Society
JAM2564
partment (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
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.
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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 quasistationary 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
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.
VOLUME 46
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
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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 500hPa 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 ␾, 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
60⬚W
2
⫽
d pq
兺 共␾
p
⫺ ␾q兲2.
150⬚E
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
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.
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
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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.
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
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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.
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 con-
tour 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.
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.
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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 540dam 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 552dam 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.
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 540dam contour. For clarity, only one-half of the contours for the
individual pentads in the RR and CR clusters are shown.
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
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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.
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 199pentad 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 limitedcontour 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 227pentad 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.
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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.
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
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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.
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
FIG. 8. As in Fig. 5, but for the pentad maps belonging to the
clusters emerging from the full-field clustering analysis.
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
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.
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7. Discussion
a. Summary of method and results
FIG. 11. Frequency of days of heavy precipitation for each
cluster, as in Fig. 9.
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.
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 ele-
OCTOBER 2007
1629
CASOLA AND WALLACE
vated (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 synopticscale 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 limitedcontour clustering method offers a useful alternative to
the full-field clustering method. Relative to the fullfield 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.
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
TABLE A1. Latitude and longitude of city grid points.
Temperature data
Alaska
Juneau
Fairbanks
Anchorage
Pacific Northwest
Seattle, WA
Portland, OR
Spokane, WA
Boise, ID
California
San Jose
Los Angeles
Sacramento
Southwest
Las Vegas, NV
Phoenix, AZ
Albuquerque, NM
Intermountain west
Salt Lake City, UT
Denver, CO
Casper, WY
Great Falls, MT
Midwest
Omaha, NE
Chicago, IL
Wichita, KS
Lat
(°N)
Lon
(°W)
57.5
65
60
135
147.5
150
47.5
45
47.5
42.5
Precipitation data
Lat
(°N)
Lon
(°W)
122.5
122.5
117.5
115
47.5
45.5
47.75
43.5
122.25
122.5
117.5
116.25
37.5
35
37.5
122.5
117.5
122.5
37.25
34
38.75
122
118.5
121.5
35
32.5
35
115
112.5
107.5
36
33.5
35
115.25
112
106.5
40
40
42.5
47.5
112.5
105
107.5
112.5
40.75
39.75
43
47.5
112
104.75
106.5
111.25
42.5
42.5
37.5
95
87.5
97.5
41.25
42
37.75
96
87.75
97.5
1630
JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
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.
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