a) b)

c) d)

Figure 3.8: Standard deviation of time-¬ltered 500 hPa geopotential height (in m) during winter.

Courtesy V. Kharin.

a) Variability of the original time series Xt (contour interval: 10 m),

b) ˜Slow™ variability of Xs (longer than about 10 days; contour interval: 10 m),

t

c) ˜Baroclinic™ variability of Xb (between 2.5 and 6 days; contour interval: 5 m),

t

f

d) ˜Fast™ variability of Xt (between one and two days; contour interval: 2 m).

daily Northern Hemisphere 500 hPa geopotential in the subtropics. Two centres of action, with

heights. After subtracting the annual cycle at standard deviations of about 175 m, are located

each grid point (by calculating the ¬rst four over the Northeast Paci¬c, the Northeast Atlantic

harmonics of the annual cycle) he calculated ¬rst and North-Central Asia.

the overall standard deviation, and then separated In order to determine how much of the

the data into three components, each of which variability depicted in Figure 3.8a comes from

low-frequency11 variability (10 days and longer)

represents a different time scale. We repeated

these calculations using 1979“87 analysis from

11 The term ˜low-frequency™ is not de¬ned in absolute

the European Centre for Medium Range Weather

terms. Instead the meaning depends on the context. In the

Forecasts (ECMWF).

present variations on time scales of 10 and more days are

The overall standard deviation shown in ˜slow™ compared to the baroclinic and fast components. Slow

Figure 3.8a is largest at about 50—¦ N and smallest variations are de¬ned differently in [3.1.7].

3.1: Atmospheric Variables 59

Figure 3.9: The teleconnection patterns that represent a substantial part of the month-to-month

variability of 500 hPa height during winter (Wallace and Gutzler [409]). Teleconnection patterns display

correlations between a base point (given by a 1.0 in the maps) and all other points in the Northern

Hemisphere extratropics. A maximum is marked by an ˜H™ and a minimum by an ˜L™. The patterns are

named (a) Eastern Atlantic Pattern, (b) Paci¬c/North American Pattern, (c) Eurasian Pattern, (d) West

Paci¬c Pattern, and (e) West Atlantic Pattern. See also [13.5.5].

3: Distributions of Climate Variables

60

or from baroclinic activity on a shorter time

scale, the data are time ¬ltered. That is,

the original time series, say Xt , is split up

f

into Xt = Xt + Xb + Xs , with X f , Xb ,

t t

and Xs representing fast, baroclinic, and slow

components. The ˜fast™ component varies on time

scales between one and two days, the ˜baroclinic™

time scale covers the medium range between 2.5

and 6 days, and the ˜slow™ component contains

all variability longer than about 10 days. The

technical details of the separation are explained in

Section 17.5.

The three components vary independently, as

a result of the time scale separation. Thus the

variance of the complete time series is distributed

to the variances of the three components: Var(Xt )

f

≈ Var Xt + Var Xb + Var Xs .

t t

Figure 3.10: Distribution of the skewness γ1 of

The spatial distributions of the standard de-

the low-pass ¬ltered daily Northern Hemisphere

viations of the three components are shown in

500 hPa geopotential height. All variability on

Figure 3.8. The largest contribution to the overall

time scales longer than six days was retained.

standard deviation in Figure 3.8a originates from

Positive contours are dashed. The stormtracks

the low-frequency variations (Figure 3.8b). In the

are indicated by the stippling (compare with Fig-

North Paci¬c, the standard deviation due to low

ure 3.8b). From Nakamura and Wallace [287].

frequency variations is 145 m compared with

175 m in the un¬ltered data, that is, about 70% of

the total variance stems from the slow variations. 3.1.7 Extratropical 500 hPa Height: Charac-

An important contributor to this pool of variability teristic Low-Frequency Patterns. Wallace and

is the process of ˜blocking,™ which often occurs Gutzler [409] examined the month-to-month vari-

on the west coast of continents and over eastern ability of the 500 hPa height ¬eld during winter

oceans. Another characterization of the low fre- in the Northern Hemisphere extratropics. They

quency variability 500 hPa height ¬eld is given in calculated teleconnection patterns, that is, spatial

[3.1.7]. distributions of the correlations at a base point with

the height ¬eld everywhere else. The concept of

The baroclinic component (Figure 3.8c) is

teleconnection patterns and their identi¬cation is

considerably less energetic than the slow processes

explained in some detail in Section 17.4. Wallace

with maximum standard deviations of about 70 m

and Gutzler™s study is further discussed in [17.4.2]

(representing about another 25% of the total

and [17.4.3].

variance). These variations may be traced back to

Five reproducible12 patterns were identi¬ed

the baroclinic waves, that is, extratropical storms.

(Figure 3.9). They were named after the regions

The regions of large variability in Figure 3.8c

they affect: Eastern Atlantic (EA) Pattern, Pa-

over the western and central part of the Paci¬c

ci¬c/North American (PNA) Pattern, Eurasian

and Atlantic Ocean are called ˜stormtracks.™ (The

(EU) Pattern, West Paci¬c (WP) Pattern and West

same stormtracks are displayed by the shaded

Atlantic (WA) Pattern. Each pattern represents

regions in Figure 3.10; there is a large circumpolar

a ¬xed structure whose amplitude and sign are

stormtrack in the Southern Hemisphere.)

controlled by a time varying coef¬cient. The coef-

The ˜fast™ component has small standard

¬cient time series can be determined by projecting

deviations, with maxima of the order of only

the monthly mean height ¬elds onto the patterns.

20 m (which is about 1“2% of the total variance;

The coef¬cients for the ¬ve patterns are more or

Figure 3.8d). Blackmon [47] argued that most of

less statistically independent; that is, variations in

this variance is due to ˜a spurious high-frequency

one mode are not related to those in another. In

component in the ¬nal analyses map.™ However,

space, the patterns have a wave-like appearance

the similarity of the structure of Figure 3.8d to

Figure 3.8c, and the comparable results from the 12 Reproducible means that essentially the same result is

EOF analyses, suggest that at least some of the obtained when another independent data set is analysed with

˜fast™ variability is natural. the same technique.

3.1: Atmospheric Variables 61

Relative Frequency (%)

Standardized Height Anomaly

Figure 3.12: Estimated probability density dis-

Figure 3.11: Frequency distributions of the low-

tribution f Z of the ˜wave-amplitude indica-

pass ¬ltered daily 500 hPa geopotential height at