Errata for: Statistical Methods in the Atmospheric Sciences, 2nd Edition.

Last Update: 14 May 2015

p. 19, end if line 4 "...having neither –25˚C"

p. 28, Eq, 3.10: Denominators should be "IQR"

p. 63, Figure 3.24:

(a) (b) (c) (d)

p. 66, Figure 3.26:

p. 78, second line above (4.7). ... right-hand side of Equation 4.6 ...

p. 81, Eq. 4.11. Comma ahead of x = 0, 1, 2, . . .

p. 83, 6th line below Eq. 4.13 should refer to Equation 4.13.

p. 90, first line after (4.24), PDF, not CDF

p. 90 end of second line after (4.24), z, not x

p. 94, line 6, µzx = µzy = 0 and σzx = σzy = 1

p. 94, last line. 27.0˚F — substantially lower

p. 95, Figure 4.6:

20 25 30 35 40 45 5015

Conditional distribution, !=27.0˚F, "=2.28˚F

Unconditional distribution, !=31.8˚F, "=7.86˚F

f(x)

p. 95, line 13, (32–27.0)/2.28 = 2.19

p. 95, line 14 a probability of .986.

p. 99, Figure 4.8:

p. 104, Eq. 4.54:

€

f (x) =1β

1+κ(x −ζ)

β

⎡

⎣ ⎢ ⎤

⎦ ⎥

−1− 1κ

exp − 1+κ(x −ζ)

β

⎡

⎣ ⎢ ⎤

⎦ ⎥

−1κ

⎧

⎨ ⎪

⎩ ⎪

⎫

⎬ ⎪

⎭ ⎪ , 1+κ(x −ζ) /β > 0

p. 105, line 14: Zheng et al. 1997, not Zhang et al. 2004

p. 119, left-hand side of Eq. 4.76c:

€

ˆ σ 1 , not

€

ˆ µ 2

p. 135, line 7. (1 – α/2) % p. 143, line 16 from bottom. Equation 3.30 p. 147, Table 5.1, Gaussian probability for 2—2.5" should be 0.178 p. 151. Line 11, Ka, not Ca, = 1.358

p. 173. 6th line from bottom should refer to Figure 5.11b.

p. 181, Eq. 6.3:

€

yi = ˆ y i + ei = a + bxi + ei

p. 183, second line from bottom: which is proved in most regression texts.

p. 186, Figure 6.3:

y

y

y

y(a) (b)

x x p. 190, Figure 6.4:

p. 190, Figure 6.5:

p. 194, Figure 6.9:

p. 199, Figure 6.11:

p. 204, first line of 2nd para, ". . . single (K=1) predictor is . . . "

p.204, last line above Fig 6.12, b0 = –0.0645

p 205, lines 2 and 5, –0.0645, rather than –0.645

page 215, 22 from bottom, Zhang (1993)

p. 218, line 24. Barnston et al. 1999a.

p. 219, Table 6.6 Intercept value is –2709.5

p. 247, line 39. Barnston et al. 1999b.

p. 252, 6.4b. 95% prediction, not confidence, interval.

p. 275, Fig 7.4b. s2,3 and s3,2 should be –.49, not –.98

p. 276, Eq. 7.26b = –0.49, not –0.98

p. 276, 10th line after Eq. 7.26, replace “almost as” with “moderately”

p. 276, 16th line after Eq. 7.26, replace “–.98” with “–.49” (twice)

p. 276, 17th line after Eq. 7.26, replace “0.54” with “0.57”.

p. 281, line 14. Add reference to Juras (2000) after “not be reflected”.

p. 288, Fig. 7.8a:

p. 292, Fig. 7.10:

o

(.062)

(.183)

(.099)

Forecast probability, yi

No resolution

Perfect reliability

1.0

0.8

0.6

0.4

0.2

(.411) (.067)

(.037)

(.030)(.028)

(.024)(.022)

(.017)(.020)

0.0

Obse

rved

relat

ive fr

eque

ncy,

o j

1.00.80.60.40.20.0

No skill

p. 293, Fig. 7.11:

Forecast probability, i

Likeli

hood

, p( i

| oj)

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0

p(yi | o2)

p(yi | o1)

p(o1) = 0.162p(o2) = 0.838

y

y

d

p. 294, lines 1–2: "d = | 0.567 – 0.101 | = 0.466, "

p. 297, line 3: , c / n = p(y2, o1) = 0.045, and d / n = p(y2, o2) = 0.255

p. 310, Figure 7.18:

Longitude

Geop

oten

tial a

nom

aly, z

’

Forecast, y’’

Obse

rved

, o’

(c)

(a)

FcstObs

Longitude

Forecast, y’

(d)

(b)

FcstObs

1:1b > 1

b = 1

1:1

p. 310, second line after Eq. 7.58: b < 1

p. 310, third line after Eq. 7.58: b > 1

p. 310, fifth line after Eq. 7.58: b > 1

p. 330, 6th line from end of Example: U = (51)(2752)(1–.761) = 33544

p. 410, last line, cos–1(0)=90˚

p. 417, Eq. 9.36:

€

R[ ] =1

n −1z iz i

T

i=1

n

∑

p. 426, second line after Eq. 9.70: (n–1)–1[X']T[X']

p. 426, last paragraph of Section 9.3.5: all five instances of [X] should be [X']

p. 427, Eq. 9.74:

€

σk,l = (xk − µk )(xl − µl ) fk,l (xk,xl )dxldxk−∞

∞

∫−∞

∞

∫

p. 428, Eq. 9.77b, should have

€

σ1.2 in the first row, not

€

σ 2,1.

p. 428, Eq. 9.77c:

€

= [Σ1,1] [Σ1,2][Σ2,1] [Σ2,2]⎡

⎣ ⎢

⎤

⎦ ⎥

p. 438, Eq. 10.8b:

€

Σ11 | x2[ ] = Σ11[ ] − Σ12[ ] Σ22[ ]−1 Σ21[ ]

p. 441, Eq. 10.10,

€

= (x i − x )T [S]−1(x j − x )

p. 444, second line of text from bottom: unchanged correlation structure, not covariance structure

p. 450, line 8: "Since

€

x is subject to sampling variations, a continuum ..."

p. 484, Eq. 11.14:

€

T(m) =1jj=m

K

∑

p. 487, Eq. 11.16b:

€

ˆ λ k ~ N λk, 2nλk

2⎛

⎝ ⎜

⎞

⎠ ⎟

p. 490, line 2, true eigenvalues

p. 490, line 3. sample eigenvalues

p. 498, end of line ahead of Eq. 11.30: rotated eigenvectors

p. 498, Eq. 11.33,

€

˜ E [ ]T ˜ E [ ] = E[ ] Λ[ ]−1/ 2 T[ ]( )T

E[ ] Λ[ ]−1/ 2 T[ ]

= T[ ]TΛ[ ]−1/ 2 E[ ]T E[ ] Λ[ ]−1/ 2 T[ ]

= T[ ]TΛ[ ]−1/ 2 I[ ] Λ[ ]−1/ 2 T[ ] = T[ ]T

Λ[ ]−1 T[ ]

p. 500, first para. of 11.6.2: (n–1)–1/2[X'] (three instances)

p. 503, Figure 11.13:

p. 502, 4th line after Eq. 11.38, γ0 = σ2

x ≈ 2.29

p. 503, 6th line after Eq. 11.38, γ1 ≈ 1.29

p. 503, 7th line after Eq. 11.38, γ2 ≈ –0.21

p. 513 Eq. 12.11a:

€

Sx,x[ ] =1

n −1[X ']T [X '] = [ ˜ A ]−1([ ˜ A ]−1)T = ˜ a m ˜ a m

T

m=1

I

∑

p. 513 Eq. 12.11b

€

Sy,y[ ] =1

n −1[Y ']T [Y '] = [ ˜ B ]−1([ ˜ B ]−1)T = ˜ b m ˜ b m

T

m=1

J

∑

p. 515, line 15: rC2 = 0.770

p. 519, Eq. 12.22.

€

ˆ β 0,m = w m − ˆ β 1,mv m = bmT E(y ' ) + ˆ β 1,mam

T E(x ' ) = 0

p. 520, line 20 from bottom. Barnston et al. 1999b.

p. 525, Eq. 12.36(a)–(c):

€

f1 =.8781 .1788.0185 .8531⎡

⎣ ⎢

⎤

⎦ ⎥ .719.695⎡

⎣ ⎢

⎤

⎦ ⎥

.8781 .1788

.0185 .8531⎡

⎣ ⎢

⎤

⎦ ⎥ .719.695⎡

⎣ ⎢

⎤

⎦ ⎥ =

.780

.626⎡

⎣ ⎢

⎤

⎦ ⎥ (12.36a)

€

f2 =.8781 .1788.0185 .8531⎡

⎣ ⎢

⎤

⎦ ⎥ −.695.719

⎡

⎣ ⎢

⎤

⎦ ⎥

.8781 .1788

.0185 .8531⎡

⎣ ⎢

⎤

⎦ ⎥ −.695.719

⎡

⎣ ⎢

⎤

⎦ ⎥ =

−.626.780

⎡

⎣ ⎢

⎤

⎦ ⎥ , (12.36b)

€

Sy,y[ ]−1/2

Sy,x[ ] Sx,x[ ]−1/2=

.1960 −.0930−.0930 .1699⎡

⎣ ⎢

⎤

⎦ ⎥

58.070 81.63351.697 110.800⎡

⎣ ⎢

⎤

⎦ ⎥

.1788 −.0522−.0522 .0917⎡

⎣ ⎢

⎤

⎦ ⎥

=.8781 .1788.0185 .8531⎡

⎣ ⎢

⎤

⎦ ⎥

(12.36c)

p. 528, Eq 12.44: [ECan] =

€

.657 .327 .679

.688 .107 −.718

.308 −.939 .155

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

, λCan =

€

1.904.925.171

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

p. 528, Eq. 12.45: [RCan-Ith] =

€

.957 .762 .076

.761 .924 .358

.166 .431 .904

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

p. 532, Eq. (13.8b) [S2] =

€

2.01 0.060.06 0.17⎡

⎣ ⎢

⎤

⎦ ⎥

p. 532, Eq. (13.9)

€

a =1.73 0.370.37 0.84⎡

⎣ ⎢

⎤

⎦ ⎥

−1 80.65.67⎡

⎣ ⎢

⎤

⎦ ⎥ −

78.73.57⎡

⎣ ⎢

⎤

⎦ ⎥

⎛

⎝ ⎜

⎞

⎠ ⎟

=.640 −.283−.283 1.309⎡

⎣ ⎢

⎤

⎦ ⎥

1.92.10⎡

⎣ ⎢

⎤

⎦ ⎥ =

0.622.21⎡

⎣ ⎢

⎤

⎦ ⎥

p. 533, Fig 13.1:

Temperature , ˚F

4

5

6

7

76 78 80 823

!1

AtlantaAugusta

m̂

xx

xxx

x

x

xx

p. 533.

€

ˆ m = 59.59; δ1 = 59.18 for Atlanta, =59.70 for Augusta, =65.78 for New Orleans

p. 534. δ1 = 53.76 for Columbus < 59.59

p. 542, Eq. 13.30

€

ln(pg ) −12ln Sg[ ] − 12 x0 − x g( )

TSg[ ]

−1x0 − x g( )

p. 548, 13.2b. Add: assuming BVN distributions with common covariance matrices.

p. 536, Figure 14.4:

–1

0

1

2

–2 –1 0 1

Standardized Temperature

G1 G2

G3

G4

G5

G6

2

p. 556, first line of text, 378 distances

p. 557, Figure 14.5:

–1

0

1

2

–2 –1 0 1

Standardized Temperature

22520151051Stage Number

(a) (b)

++++ + +

+

++ xxx x

xxxxx

1.00

0.75

0.50

0.25

0.00

p. 579, 2.1c,

€

Pr{A∩ BC} = 0.1

p. 579, 2.1d,

€

Pr{AC ∩ BC} = 0.3

p. 579, 3.2, s = 0.880 mb

p. 579, 3.4 (not 3.3)

€

γYK = 0.158, ...

p. 580, 4.10a and b, ξ’s should be ζ’s

p. 580, 5.1b: [1.10 ˚C, 2.56 ˚C]

p. 580, 5.3: z = –4.00

p. 580, 5.3a, p = .000063

p. 580, 5.3b, p = .000032

p. 580 5.5b: χ2 = 0.33

p. 580, 5.7b: z = –3.18, p = .0007

p. 581, 7.3e, 0.407

p. 583, 10.2a,

€

4.96 0.150.15 27.12⎡

⎣ ⎢

⎤

⎦ ⎥

p. 584, 11.2b: 1, 1, 1

p. 584, 11.3b λ2 and λ3 may be entangled

p. 584, 12.3a:

€

1.883 0 1.838 −0.2120 0.927 0.197 0.791

1.838 0.197 1.904 0−0.212 0.791 0 0.925

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

p. 584, 12.3b: a1 =

€

.728

.032⎡

⎣ ⎢

⎤

⎦ ⎥ , a2 =

€

−.0231.038⎡

⎣ ⎢

⎤

⎦ ⎥ , b1 =

€

.718−.142⎡

⎣ ⎢

⎤

⎦ ⎥ , b2 =

€

.0991.030⎡

⎣ ⎢

⎤

⎦ ⎥ , rC1=.984, rC2=.867

p. 584, 14.1:

€

03.59 02.29 1.59 03.12 0.82 0.89 00.71 4.27 2.89 3.75 01.64 2.24 0.71 1.59 2.20 0

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

p. 585, 14.2a. 1967+1970, d = 0.71; 1965+1969, d = 0.71; 1966+1968, d = 0.82;

(1967+1970) + (1966+1968), d = 1.59; all, d = 1.64

b. 1967+1970, d = 0.71; 1965+1969, d = 0.71; 1966+1968, d = 0.82;

(1967+1970) + (1966+1968), d = 2.24; all, d = 4.27

c. 1967+1970, d = 0.71; 1965+1969, d = 0.71; 1966+1968, d = 0.82;

(1967+1970) + (1966+1968), d = 1.58; all, d = 2.97

p. 588, Barnston, Glantz and He, 1999a

p. 588, Barnston, Leetmaa, Kousky, Livezey O'Lenic van den Dool, Wagner, and Unger, 1999b

p. 599. Add: Lorenz, E.N. 1993. The Essence of Chaos. Univ. of Washington Press, 227 pp.