Embed Size (px)
Citation preview
VoLuME 1.
DEP ARTMEN'l' OF PHYSICS.
1939.
FORESHADOWING SUMMER RAIN IN QUEENSLAND.
By
NUMBER3.
the late T. RIMMER, M.Sc., and A. W. W. HOSSACK, M.Sc.,
Depm·tmcnt of Physics, Unive?·sity of Queensland.
DATE OJ!' PUBLICATION:
4TH OCTOBER, 1 9 3 9.
l
FORESHADOWING SUMMER RAIN IN
QUEENSLAND.
By the late T. IUIVIMER, M.Sc., and A. W. W. HOSSACK, 1\ti.Sc.
SUMMARY.
Statistical. methods al'e used to study the l'elationship between l'ainfall in seven selected distl'icts in Queensland and wol'ld weather. T'he control of the southe1·n oscillation (JuneAugust) varies from ·56 in the Ipswich district to ·75 in the Roma district. Correlation coefficients with previous pressures, temperatures, and rainfalls in other regions are given. From these coefficients f01·mulre. are derived for foreshadowing the November-January 1ain in five of the districts, the December-February rain in two, the January-April rain and the October-December rain in one each, the total correlation coefficients ranging from •72 to ·81. With predictions limited to those which have a 4 : 1 chance of success, the "performance" of the formulre over eight years beyond the period used in computing the correlation coefficients is satisfactory.
INTRODUCTION.
It i s well known that seasons in different parts of the world are not
independent of one another, but are often closely connected, even at places which are widely separated. With the gradually increasing recognition of the unity of the earth 's atmosphere and of the consequent dependence of localweather sequence on the state of the general circulation , considerable attention has been paid to the relations existing between seasonal features in different
parts of the world.
Sir Gilbe .rt Walker introduced the idea that world weather IS dominated
by three fluctuations or oscillations of pressure, known as the North Atlanti::�
(N.A.O.), the North Pacific (N.P.O.) and the Southern (S.O.) Oscillations. Since the N.A.O. and the N.P.O. exercise their control mainly over regions in the
Northern Hemisphere, we in Australia are more concerned with the S.O., which may be briefly described as a fluctuation of pressure between the Indian andthe Pacific Oceans , low pressure in the former area being usually associated
with an excess of pressure in the latter.
vValker has gradually developed the principal features of this oscilla .. tion, discovering regions over which variations are linked together. The positive
area where high pressure corresponds to an increase in the general circulation
2 FORESHADOWING SUMMER RAIN lN QUEENSLAND.
extends from Bengal across the Pacific to South America, while the· negative area of contemporary low pressure over the Indian Ocean embraces a largeportion of Africa on the one side, and the continent of Australia on the other. Of particular interest is the close relation which exists between pressure,
temperature, and rainfall, high pressures in the Pacific being associated with low temperature and high rainfall ·over large areas in tropical and sub-tropicalregions, the terms ''high'' and ''low '' referring to seasonal deviations from the local ave.rage for the corresponding period.
After finding by a preliminary investigation the most representativestations, Walker has chosen a series of figures to represent the variations of each oscillation for the four quarters of the year, December-February, MarchMay, June-August, September-November, and from these have been obtained the relations of the S .O. with pressure, temperature, and rainfall over wide
regions. Walker's formula (1932) for the June-August S.O. is:-
(Santiago pressure) + (Honolulu pressure) + India ram + (Nile flood) + ·7 ( Manila pressure) - (Batavia pressure)
(Cairo pressure) - (Madras temperature)
·7 ( Darwin pressure) - .7 ( Chile rain )
That conditions in the southern winter exercise greater influence onsubsequent seasons than those in the southern summer is strikingly confirmed by
the correlation coefficient of -84 between 'the June-August S.O. and the following December-February 8.0., while the control of the December-February S.O . on the
following June-Aug·ust S.O. is only -20 ( Walker , 1932). Hence any factor which has a close relationship with the contemporary December-:B�ebruary S .O., should
have a corresponding relation with the S .O. of the previous ,June-August, whichis extremely persistent , i.e. there should be a three month's foreshadowing which is of practical value in seasonal forecasting . After finding centres with which
the season in question varies , a regression equation involving data available atthe beginning of the season is worked out, and from the equation the most probable departure from average of the element considered can be determined.
Sir Gilbert Walker ( 1930) in studying the summer rainfall (OctoberApril) of the Kimb'erley division of West Australia, Northern 'rerritory, and
Queensland found that an abundant monsoon tends to be preceded by highpressure at Honolulu and South America, and· by low pressure in NorthernAustralia. He obtained a formula which had a coefficient of -79 with the summerrainfall of North Australia. H . l\1. 'L'reloar (1934) also obtained formulae with t'oefficients of ·11 , -51, and -54 for the rain in the Darwin, Pine Creek, andVictoria River Downs districts in North Australia.
FORESHADOWING SUMMER RAIN IN QUEENSLAND.
Rain over different parts of such a large area as that investigated by
\Valker may be controlled by various factors, and the object of this research was to find what relationships the rainfall of Queensland bore to the S.O. and,
if possible, to develop formulae which would be directly applicable to foreshadowing the rainfall in restricted districts in Queensland.
1. METHOD OF INVES'fiGA'fiON.To obtain districts homogenous with regard to rainfall, adjacent stations
whose average annual rainfalls were of the same magnitude were selected, the!l
three-�onthly averages were compared. It was intended to represent ead1district, by the average of six stations, but in two instances lack of suitable data
reduced the number of stations to four.
Having obtained three-monthly averages for the summer rainfall in various districts, the departures over a period of forty-five years were corTelated
with the previous June-August S.O. It was found that the November-January
rain in five districts in south-east Queensland gave correlation coefficients with the S.O., ranging from -56 to -75 . The Downs and Roma districts in the southeast appeared to be a local centre or focus, values falling off as we proceed either inland or down the Brisbane Valley through the Ipswich district.
In the north, another centre was found in the Charters Towers and Georgr,town districts, where the December-February rain gave correlations of -71 and
-60 respectively with tl1e previous June-August S.O., while the Charters TowersOctober-December rain also gave a correlation of - 6 9 .
Attempts were made to find relationships vvith the late summer rain,
but only in the Springsure district where the January-April rain had a cor
relation of -62 was any success attained .
Relationship with the S.O. having been esta.blished the various district
rainfalls were correlated with values of pressure, .temperature, or rainfall for selected months, at various centres controlled by the S.O. For convenience in ealculation, ''reduced departures'' for the various elements were used in working
out the ·correlation coefficients and only those coefficients which satisfied Walker's
(1914) criterion for reliability were used in formulae .
As several coefficients satisfied the reliability criterion, they were furthe:· tested by extending the correlations from forty-five to fifty-three years. There was an appreciable falling off in value with some of the coefficients and in selecting the elements to be used in the various formulae, not only the magnitude: of the correlation coefficients was taken into account, but also their consistertcvover the extended period.
"
4 FORESHADOWING SUMMER RAIN IN QUEENSLAND.
T ABLE I.
ANNUAL AND QUARTERLY RAINFALL AVERAGES IN INCHES FOR REPHESENTATIVE STATIONS IN DISTRICTS SELECTED.
Districts. Stations.
Key Key Quarterly Average. No. No. Annual.
Fig. Name. Fig. 1. Name. Average. 1. Quarter. Average.
----- --
I
II
III
IV
v
VI
VII
v
VI
St. George
Downs
Ipswich
Roma ..
Springsure
. .
. .
. .
. .
. .
Charters Towers
Georgetown
Springsure
. .
. .
Charters Towers
. .
. .
. .
. .
..
. .
. .
..
- 1 2 3 4
5 6 7 8 9
lO
ll 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27
28 29 30 31
32 33 34 35 36 37
22 23 24 25 26 27
28 29 30 31
BoHon . .
Dirranbandi .. St. George Well town
Allora Dalby
. .
. .
..
. .
Goondiwindi Inglewood Pittsworth Warwick
Esk . . Ipswich Laidley Mundoohm Nanango
Miles Mitchell Roma Surat Taro om Yeulba
Banana Cam boon Clermont-Duaringa
Emerald Springsure
. .
..
. .
. .
. .
..
. .
..
. .
..
. .
..
..
. .
. .
. .
. .
. .
..
..
Charters Towers Clarke River Pentland . . Ravenswood
Chillagoe Croydon Cumberland Georgetown
. .
. .
Gilbert River Mount Surprise
Banana Cam boon Clermont Duaringa
Emerald Springsure
. .
. .
. .
..
. .
. .
Charters Towers Clarke River Pentland . .
Ravenswood
. .
. .
. .
. .
. . . . ..
. . . . . .
. .
. .
. .
. . . .
. .
. . . .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
..
..
..
. .
. .
..
..
..
. .
. . . .
. .
. .
..
..
. .
..
. .
. .
18 18 20 21
27 26 24 26 28 27
39 33 31 37 31
26 23 23 23 27 25
27 28 27 28 25 26
25 25 26 27
32 28 27 32 31 30
27 28 27 28 25 26
25 25 26 27
Nov .-Jan .. . Nov.-Jan ... Nov.-Jan ... Nov.-Jan ...
Nov.-Jan ... Nov.-Jan ... Nov .-Jan ... Nov.-Jan .. . Nov.-Jan ...
Nov.-Jan .. .
Nov.-Jan ... Nov.-Jan ... Nov.-Jan ... Nov .-Jan .. . Nov.-Jan ...
Nov .-Jan .. . Nov .-Jan ... Nov.-Jan ... Nov.-Jan ... Nov.-Jan ... Nov.-Jan ...
Nov.-Jan ... Nov.-Jan .. . Nov.-Jan ... Nov.-Jan ... Nov.-Jan ... Nov.-Jan ...
Dec.-Feb ... Dec.-Feb ... Dec.-Feb ... Dec.-Feb ...
Dec.-Feb ... Dec.-Feb ... Dec.-Feb ... Dec.-Feb ... Dec.-Feb • . .
Dec.-Feb ...
Jan.-Apr ... Jan.-Apr ... Jan .-Apr . . Jan.-Apr .. . Jan .-Apr .. . Jan.-Apr ...
Oct.-Dec . .. Oct.-Dec . . •
Oct.-Dec ... Oct.-Dec . . .
6 6 6 7
lO 9 8 9
10 10
13 12 13 13 ll
9 8 8 7
10 9
10 10 10 ll
9 9
13 15 14 16
22 20 20 23 23.. 21
12 12 15 16 12 13
6 5 5 6
FORESHADOWING SUMMER RAIN IN QUEENSLAND.
·- .. . . .. ........ . . .. .. . . .
'· ·
I" I! (fto1rn
33 3? 35 37
34 S\
2,9 1'1
CT. 2� 30
24
2? 27
.
.'i)/Sure 22 .
23 ---- 20_._ JV Roma •
FJG. 1.-Location of Representative Stations and Districts. Key in Table I.
5
TA
BL
E
II.
CO
RR
EL
ATI
ON
CO
EF
FIC
IEN
TS
WIT
H Q
UE
EN
SLA
ND
RA
IN.
(AL
L C
OE
�'F
ICIE
NT
S H
AV
E B
EE
N :M
UL
TIP
LIE
D B
Y 1
00
.)
Dis
tric
t:
Pe
rio
d:
Ele
me
nt,
L
oc
ali
ty,
an
d P
er
iod
.
S.O
. J
\me-
Au
gu
st.
Pre
ssur
e-A
lex
an
dri
a
An
tana
rivo
..
. .
Jt
me-
Au
gu
st
Ju
ly-S
epte
mb
er
Ju
ne-A
ug
ust
Ju
ly-S
epte
mb
er
Bu
enos
Air
es J
une
-Au
gu
st
Co c
hin
Col
ombo
Dar
win
Hon
olul
u
Sa
nti
ag
o
Ju
ly-S
epte
mb
er
Ju
ne-
Au
gu
st
Ju
ly-S
epte
mb
er
Jru1e
-Au
gu
st
Ju
ly -S
epte
mb
er
Ju
ne-
Au
gust
J
uly
-Sep
tem
ber
A
ug
ust
-Oct
ob
er
Ma
y-J
uly
. .
J
une
-Au
gu
st
Ju
ly-S
epte
mb
er
June
-Au
gus
t
. .
..
. .
..
. . . .
. .
. .
. .
..
. .
..
. .
. .
. .
..
. .
..
No
. o
f
Yea
rs.
45
42
40
45
415
45
45
44
45
St. G
eo
rge
.
No
v.-
Ja
n.
62
-5
3
-47
-3
8
-3
2
34
1
7
-4
3
-5
0
-4
9
�
52
-4
1
-3
0
. . . . 6
5
43
44
Do
wn
s.
No
v.-
Ja
n.
71
-5
8
-6
1
-3
5
-4
8
48
40
-5
2
-;')
6
-5
7
-6
1
-5
7
-:i
4
. .
. . G
4
5[)
50
Ipsw
ich
.
No
v.-
Ja
n.
56
-5
1
-5
7
-3
6
-4
8
43
29
-4
9
-5
4
-5
3
-5
6
-5
1
-;)
3
. .
61
();)
ij7
:�G
R.o
ma
.
No
v.-
Ja
n.
75
·-5
7 -
52
-5
2
-4
8
47
40
-5
2
-;')
9
-6
0
-6
5
-5
8
-5
6
. .
66
65
54
,;2
Sp
rin
g-� Char
ters
su
re.
To
we
rs.
No
v.-
Ja
n.
67
--
51
-
48
-4
8
-4
5
45
42
-5
3
-6
5
-5
1
-6
0
-5
4
-5
4
. .
. . 63
(j]
48
De
c.-
:Fe
b.
7l
-4
2
-4
0
-4
5
-4
8
43
42
-5
7
-6
4
-5
7
-6
5
-6
4
-(i
7
-6
6
. . 6
1
6:.?
51
..
.
Ge
org
e-
tow
n.
De
c.-
Fe
b.
60
-4
2
-3
7
-4
1
-5
1
31
34
-6
5
-6
3
-6
3
-6
1
-6
0
-6
5
-6
6
. .
40
41
:l[)
Sp
rin
g-
sure
.
Jan
.-A
pr.
62
-4
0
-4
2
-5
5
-61
43
44
-5
1
-5
7
-5
6
-6
2
-6
3
-6
6
-6
8
52
50
48
42
Ch
art
ers
T
ow
ers
.
Pre
vio
us
Oc
t.-D
ec
.
69
-4
0
..
-4
8
..
38
..
-6
5
..
-6
2
..
-6
2
..
..
..
48
..
60
0> "':!
a
�
t::j
Cr.;
1::1
�
tJ
a � <:;':)
V::
<:::i � t::j
�
�
.... ;;; .....
'<:
«:>
<:::i
l::j
t::
'<: � ll-.
'<:
tJ
'l'A
BL
E
II.-
con.
t·im
wd.
CO
RR
EL
A'l'
ION
C
OE
FJ<'I
CIE
N'l'
S
WIT
H
QU
EEN
SLA
ND
RA
IN.
(ALL
CO
EF
FIC
IEN
TS
H
AV
E BE
EN
:i\fU
L'l'I
PLIE
D BY
10
0.)-
cont
inuc
d.
Dis
tric
t:
Per
iod
:
Ele
men
t,
Lo
cali
ty,
an
d
Per
iod
.
---
-
Tem
per
atu
re-
Dar
win
Ju
ne-
Au
gu
st
Au
gu
st-
Octo
ber
..
Ma
dra
s Ju
ne-
Au
gu
st
..
Ju
ly-
Sep
tem
ber
..
Rai
n-
..
..
. .
..
Cap
e Y
ork
Pe
nin
sula
(1
) Ju
ly-
Sep
.
East
In
die
s (2
) Ju
ne-
Au
gu
st
July
-Se
pte
mb
er .
.
Cap
e Y
ork
an
d
Ea
st
Ind
ies
July
-Se
pte
mb
er
No
. o
f Y
ears
.
45
45
42
45
42
St.
Ge
org
e.
No
v.-
Ja
n.
. .
..
-5
1
-4
8
53
59
6
1
66
Do
wn
s.
No
v.-
Ja
n.
. .
. .
-5
0
-5
4
59
55
5
6
68
Ipsw
ich
.
Nov
.-J
an
.
..
. .
-4
2
-4
9
44
47
5
0
55
Ro
ma
.
No
v.-
Ja
n.
. .
. .
-5
3 -
55
63
65
67 75
Sp
rin
g-
sure
.
No
v.-
Ja
n.
. .
. .
-4
5
-4
6
39
62
69
63
------
--
Ch
art
ers
To
wer
s.
Dec
.-F
eb.
. .
. .
-4
8
-5
0
38
63
68
61
Ge
org
e-to
wn
.
Dec
.-F
eb.
36
. .
-5
7
-61
20
60
60
4 5
Sp
rin
g-
sure
.
Ja
n.-
Ap
r.
48
5
5
-4
7
-4
7
24
55
65
51
(1)
Cap
e Y
ork
Pe
nin
sula
ra
in i
s th
e a
ver
ag
e o
f t
he
rain
at
Sta
tio
ns
Coen
, M
ay
tow
n,
Mo
reto
n,
Pa
lmer
vil
le.
(2)
East
In
die
s ra
in i
s th
e a
ver
ag
e o
f t
he
rain
at
Sta
tio
ns
Amb
oin
a, M
eda
n,
Men
ad
o,
Pa
dan
g,
Pon
tia
na
k.
ICh
art
ers
To
wer
s.
Pre
vio
us
Oc
t-D
ec.
--
-- 56
.
.
-5
8
..
..
61
.
.
..
'>;j s;.
t:;j
v, � 1::::1
a � '<;
<;':)
� � t:;j
�
�
� � � <C>
<:::1
t:;j
t:;j
'<;
v,
t:-<
�
'<; � -1
TAB
LE
III.
RE
GR
ES
SIO
N
EQ
UA
TIO
NS
.
(All
co
effici
ents
ha
ve
bee
n m
ult
ipli
ed b
y
10
0.)
Dis
tric
t R
ain
. E
lem
ents
use
d i
n R
egre
ssio
n E
qu
ati
on
s.
Co
effici
ents
bet
wee
n S
elec
ted
Ele
men
ts.
St.
Geo
rge
No
v.
-Jan
.
(St.
G.
) A
lex
an
dri
a
Pres
s. J
un
e-A
ug
. (A
.)
Co
chin
Pr
ess.
Ju
ly-
Sep
t. (C
.)
Ho
no
lulu
Pr
ess.
Ju
ne-
Au
g.
(H.
) .
.
Ca
pe
Yo
rk a
nd
Ea
st
Ind
ies
Ra
in
July
-Se
pt.
(C.
Y.
)
St.
G.
H
. C.
Y.
c.
Do
wn
s N
ov
.-J
an
. (
Do
.)l C
olo
mb
o
Pres
s. J
uly
-Se
pt.
(Co
.)
. ·1 D
o.
H
on
olu
lu
Pres
s. J
un
e-A
ug
. (H
.)
. .
Co
.
Ma
dra
s Te
mp
. J
uly
-Se
pt.
(M
.)
. .
H
.
Ca
pe
Yo
rk a
nd
E
ast
In
die
s R
ain
M
.
July
-Sep
t. (
C.Y
.)
Ipsw
ich
N
ov
.-J
an
. (I.
) I A
lex
an
dri
a
Pres
s. J
uly
-Se
pt.
(A.
) I.
Co
chin
Pr
ess.
Ju
ly-
Sep
t. (C
.)
..
A
.
Da
rwin
Pre
ss.
Ju
ne-
Au
g.
(D
.)
..
c.
Ho
no
lulu
Pr
ess.
Ju
ne-
Au
g.
(H
.)
..
D
.
Ro
ma
N
ov
.-J
an
.
(R.)
I Al
ex
and
ria
Pre
ss.
Ju
ne-
Aug
. (
A.
R.
Coch
in
Pres
s. J
uly
-Sep
t. (C
.)
.. H
. H
on
olu
lu
Pres
s. J
un
e-A
ug
. (H
.)
..
C
.Y
.
Cap
e Y
ork
an
d
East
In
die
s l�
ain
c
. Ju
ly
-Sep
t. (C
.Y.)
H.
C.
Y.
Co
. 5
5
66
66
H.
c. 50
4
7
-5
9
M.
A.
5
3
47
5
0
34
C.
Y.
-
61
64
-
54
6
8
-5
1
66
-
62
-
50
66
5
5
A.
c
. D
. H
.
-5
7
54
5
1
63
28
3
8
-6
3
49
-
47
-
51
H.
C
.Y
.
c.
A.
65
75
-
59
-
57
(]6
-
47
4 7
--
ii!l
50
34
Reg
ress
ion
Eq
ua
tio
ns
bet
wee
n ·P
rop
ort
ion
al
Dep
art
ure
s.
R.
(St.
G.
) =
·1
3 (
H.
) +
·3
8 (
C.Y
.)
-·1
4 (
C.)
-·2
4 (A
.)
·72
(Do
.)
=
-·2
2 (
Co.
) -
·08
(M
.)
+ ·
28
(H.)
+
·3
2 (
C.Y
.)
I ·76
(I.) =
·2
5 (H
.)
-·1
4 (
D.
) -
·27
(C.
) -
·28 (A
.) ·7
3
(R.)
=
·19
5 (H
.)
+ ·
40
5 (C
.Y
.)
-·1
9 (C
.)
-·2
1 (
A.)
I
·81
(fJ
>:::j
0
�
t::j � t;j
0 � �
V:: � t::j
�
�
I:;. � � .0 � t::j
� � I:;.
� �
Dis
tric
t R
ain
.
s p
rin
gsu
re N
ov
.-J
an
.
(S.
)
ba
rter
s To
we
rs D
ec.
-F
eb.
(C
.T.
)
ieo
rge
tow
n D
ec.
-Feb
.
(G.)
pri
ng
sure
J
an
-Ap
r.
(S.
)
:ba
rte
rs
Tow
ers
O
ct.
'l'A
l3L
E
II
l.-
co1L
tinu
ed.
nE
G!t
ES
SIO
N
EQ
UA
'l'IO
NS
-co
nti
nu
ed.
(All
co
eilic
ieu
ts h
ave
bee
n m
ult
ipli
ed h
y 1
00.)
Ele
men
ts u
sed
in
Reg
ress
ion
Eq
ua
tio
ns.
Ea
st I
nd
ies
Ra
in J
uly
-Sep
t. (E
.) .
.
Ho
no
lulu
Pre
ss.
Ju
ne
-Au
g.
(H
.)
..
C
ocb
in P
ress
. J
uly
-Sep
t. (C
.)
Ale
xa
nd
ria
Pre
ss.
Ju
ne-
Au
g.
(A
.)
Ho
no
lulu
Pre
ss J
uly
-Sep
t. (
H.
) C
ocb
in P
ress
. J
uly
-Sep
t. (C
.)
Da
rwin
Pre
ss.
Ju
ly-S
ept.
(D.
)
Da
rwin
Pre
ss.
Ju
ly-S
ep
t. (D
.)
Co
cbin
Pre
ss.
Ju
ly-S
ept.
(C.
) M
ad
ras
Tem
p.
Ju
ly-S
ept.
(M.
)
Ho
no
lulu
Pre
ss.
Ma
y-J
uly
(H.
) D
arw
in P
ress
. A
ug
.-O
ct.
(D.
)
-·
..
.
.
..
..
.
.
..
..
. .
A
nta
na
riv
o P
ress
. J
uly
-Se
pt.
(An
.)
Co
lom
bo
Pre
ss.
Ju
ly-S
ept.
(Co
.)
..
Co
cbin
Pre
ss.
Ju
ne
-Au
g.
(C.
) .
.
Sa
nti
ag
o P
ress
. J
un
e-A
ug
. (S
a.
) .
.
Da
rwin
Te
mp
. J
un
e-A
ug
. (
D.
) E
ast
In
die
s R
ain
Ju
ne
-Au
g.
(E.)
. .
Co
effic
ien
ts b
etw
een
Sel
ecte
d E
lem
ents
.
E.
H
.
c.
A.
s
. 6
9
63
-
65
-
51
E.
6
0
-6
3
-4
6
H.
-
47
-
47
c.
-3
4
H.
c
. D
.
C.
T.
62
-
64
-
67
H
.
-4
7
-5
2
c.
51
D.
c
. M
.
G.
-6
5
-6
3
-6
1
D.
5
1
62
c.
52
H.
D.
A
n.
C
o.
s
. 5
2
-6
8
-6
1
-6
2
H.
-5
2
-3
6
-5
2
D.
6
2
63
An
. 7
4
c.
Sa
.
D.
E
. C
.T.
-
65
6
0
56
6
1
c.
-4
6
-4
8
-5
5
Sa
. 4
2
56
D.
2
9
Reg
ress
ion
Eq
ua
tio
ns
bet
wee
n P
rop
ort
ion
a D
epa
rtu
res.
(S.
) =
·2
75
(E
.)
+ ·
24
(H
.)
-·3
1
(C.
) -
·16
5 (
A.
)
(C.
T.
) =
·2
8
(H.
) -
·33
(C
.)
-·3
6
(D.
)
(G.)
=
-
·34
(D
.)
-·3
4
(C.
) -
·22
(M
.)
. .
. .
(S.
) =
·1
8
(H.
) -
·37
(D
.)
-·2
2
(An
.)
-·1
3 (
Co
.)
(C.
T.)
=
·22
(S
a.
) +
·2
6
(D.
) +
·2
6
(E.
) -
·29
(C
.)
----
..
. .
. .
..
..
R'
---
·79
· 79
·76
·75
·79
�
0
�
t::l
tlo � 1::::1
0 � q'.)
V:; � � � � ......
�
<()
c:::j
t::l � �
� � <0
10 FORESHADOWING SUMMER RAIN IN QUEENSLAND.
2. RELATIONS BETWEEN DISTRICT RAINFALLS AND
WORLD WEATHER.
Fig. 1 shows the location of the districts discussed and the representative stations within them, the key to these being included in Table L
In 'l'able II the relations between Queensland rain and meteorological
elements at other centres are indicated . The correlation coefficients· with Hono
lulu June-August pressure were consistently high, but those with Buenos Aires
and Santiago , the other stations representing conditions in the Pacific, were much lower.
Darwin, Co1chin, and Colombo, thfl last two being too near to be independent, were the stations representing conditions in the Indian Ocean, whose pressure had the closest relationship with Queensland rain.
There was also a relationship between winter rain in the Cape York Peninsula and the East Indies , and the Queensland rain in the following summer. Probably the- winter rain is an index of the same influences that
control the summer rainfall .
3. F ORESHADOWING F ORIVITJLAE.
Table III shows the nine regression equations which wer:e obtained, together with the correlation coefficients from which they were derived and the resultant total correlation coefficient R.
Sir Gilbert Walker (1926) has pointed out that data which indicates a
decidedly abnormal season is not likely to mislead, but an anticipation based on conditions only slightly abnormal has little value . He urges, therefore , that
the issuing of forecasts be restricted to years in which the dflparture foreshadowed is greater than -842 ks, where k2 = 1- R2, R being the total correla
tion coefficient and s the standard deviation of the element foreshadowed . ·walker shows that there is a 4: 1 chance that such departures will have the correct sign, and the formulae obtained for Queensland rain have been tested from that standpoint. This means that only foreshadowed departures which are greater
than the above limit and have the wrong sign are regarded as failures. When the actual rain corresponding to a foreshadowed departure is average, the forecast is considered a partial failure.
Tables IV and V give a detailed comparison of the actual, departure;:; with those calculated from the formulae for the November-January Ipswich rain
and the November-January Springsure rain , these formulae being selected as
those giving the best and worst ''performances'' respectively.
Year. --
188
189
190
191
192
193
c389 '
FORESHADOWING SUMMER RAIN IN QUEENSLAND. 11
TABLE IV. DEPARTURES IN INcHgs FROM AVERAGE NOVEMBER-JANUARY IPSWICH RAIN.
Average 12·4 Inches. Black figures indicate departures greater than ·84ks = 2·8 .. all data not available. - failure. . .. partial failure.
0. 1. 2. 3. 4. 5. 6. 7. 8. I --- --- --- --- --- --- --- ---
(Calc.) (Act.)
(Calc.) (Act.)
(Calc.) (Act.)
(Calc.) (Act..)
(Calc.) (Act.)
(Calc.) (Act .)
. .
. .
..
. .
.. ..
. .
..
..
..
. .
. .
--
--
--
7 8
5 3
2 4
2 1
1 1
. .
--
--
--
- 2 5 1 - 2 2
5 - 1 - 2 5 - 9 - 3
4 - 4 0 6 - 8 - 3
1 1 0 2 3 - 2
4 2 - 1 4 - 1 1
4 6 1 8
1 - 4 - 4 1
-
- 4 - 3 - 4 - 4
- 1 4 - 2 1
0 - 1 3 2
. . -
-
--
-
--
1
0 3
2 1
1 6 3 1
1 3
. . 12
--
-
-
0 0
1 4
6 4
1 8
0 7
Departures from 1931-1938 were added after computing correlations.
\89• I
!89? I
19041 c9Z9 I
. . - 4
3 11
- 5 - 3
8 8 2 3
2 3
1914' •
FIG. 2.-Ipswich Rain, November-January Departures from Average.
9. ---
--
-
--
--
-
2 3
1 2
1 4
6 9
1 1
1Gl9 I
12 FORESHADOWING SUMMER RAIN IN QUEENSLAND.
Only when the calculated departure is greater than 2·8, i.e. lies outside
the lower pair of horizontal lines in Fig. 2, can a prediction be made with 4: 1
chance of success. Out of forty-nine years there are seventeen in which this
condition is satisfied, and out of these there are 16 successes and 1 failure,
14 being the expected number of successes.
TABLE V.
DEPARTURES IN INCHES FROM AVERAGE NOVEMBER-JANUARY SPRINGSURE RAIN.
Year. --
188
189
190
191
192
193
Average 10·8 inches.
Black figures indicate departures greater than ·84ks = 2·6.
all data not available. fail re. partial failure.
o. 1. 2. "· 4. 5. 6.
I --- --- --- --- --- ---
( Calc.) (Act.)
(Calc.) (Act.)
(Calc.) (Act.)
(Calc.) (Act.)
(Calc.) (Act.)
(Calc . ) (Act. )
. . . .
. . . .
. . · -
.. . .
. .
. .
.. . .
7 7
- 5 - 3
2 4
- 3 - 5
- 1 2
.. - 3 4 - 1
- 6 - 2 - 7 - 8
6 - 5 6 - 6
- 3 1 - 1 0
- 4 3 - 6 - 2
-
. . - 6
3 4 6 0 - 2 - 1 4 4 - -
- 3 3 -4 - 3 - 2 1 1 - 2 -
1 - 3 -4 - 1 - 3 - 3 - 5 - 4
0 - 3 5 - 2 1 - 4 6 - 1
- 3 4 1 - 2 0 - 2 1 - 2
-. . .
7. ---
. .
--
-
5
3 3
1 1
10 9
- 1 2
0 - 5
Departures from 1931-1938 were added after computing correlations.
8. ---
. .
-
-
3
2 4
3 2
-
8 20
3 4
2 0
9. ---
- 4 - 5
3 0
0 - 4
- 7 - ().
- 2 0·
Only when the calculated departure is greater than 2·6, i.e. lies outside
the lower pair of horizontal lines in Fig. 3, can a prediction be made with a 4: 1
chance of success. Out of forty-nine years there are thirty in which this con
dition is satisfied, and out of these) there are 23 successes, 6 failures , 1 partial
failure, 24 being the expected number of successes.
FORESHADOWING SUMMER RAIN IN QUEENSLAND.
!899
I 1£119
I •924
I 193�
I
FIG. 3.-Springsure Rain, November-January Departures from Avemge.
13
•939
I
The correlation coefficients used in the formulae were based on data from 1886-1930, the years being those of the January for which rain is foreshadowed. With each of the nine formulae the number of successful forecasts possible during
that period was greater than the number expected on the assumption o£ a 4: 1
ehance of success..
'rhe real test of any formulae is its "performance" over a series of years beyond the period used in its formation. At the time of writing, data as far' as
] 938 is available, so that it is possible to test the formulae for eight years beyond the period used in computing the correlations. With the nine formulae obtained there were two instances-the Springsure November-January rain and the Charters Towers October-December rain-in which the actual number of successes during 1931-1938 did not equal the expected number. This is not
unexpected, as a 4 : 1 chance of success does not mean four successful forecasts out of every five issued, but that these will be the average figures over a long period. Taking ail possible forecasts during the fifty-three year period-
14 FORESHADOWING SUMMER RAIN IN QUEENSLAND.
1886-1938-those for the November-January Springsure rain were the only one,i'n which the number of ·successes (23) was less than the number (24) necessaryfor the 4: 1 ratio to hold.
TABLE VI. " PERFORMANCE " OF FORMULAE.
(a) Used in computing correlation coefficients. (b) Added after computing coefficients.
w ,1j; ,;,
District and Period. R. No. of ��rg �� Years. -. �;:;
O::;l o:; Oow
I z�� z�
� -g � .,; 4-;�e <..,w g�� ��:§ 0�
· o �0� 0�� o� ZH� zr;s �Zr:.r;,.
---- - ---- ---- ---- ---- ---
St. George Nov, .. Jan.
Downs Nov.-Jan.
Ipswich Nov.-Jan.
Roma Nov.-Jan.
Springsure Nov.-Jan.
. .
. .
. .
Charters Towers Dec.-Feb .
Georgetown Dec.-Feb.
Springsure Jan.-Apr .. .
Charters Towers Oct.-Dec.
. .
. .
. .
. .
. .
. .
..
. .
. .
·72
·76
·73
·81
·79
·79
·76
·75
·79
(a) 41 19 (b) 8 1
49 20
(a) 41 25 (b) 8 2
49 27
(a) 41 16 (b) 8 1
49 17
(a) 41 25 (b) 8 3
49 28
(a) 41 26 (b) 8 4
49 30
(a) 44 28 (b) 8 3
52 31
(a) 45 24 (b) 8 2
53 26
(a) 39 19 (b) 8 2
47 21
(a) 45 28 (b) 8 3
53 31
3 0 16 15 0 0 1 1 3 0 17 16
3 1 21 20 0 0 2 2 3 1 23 22
1 0 15 13 0 0 1 1 1 0 16 14
I 2 22 20 0 1 2 2 1 3 24 22
4 0 22 21 2 1 1 3 6 1 23 24
3 2 23 22 1 0 2 2 4 2 25 25
2 1 21 19 0 0 2 2 2 1 23 21
1 1 17 15 0 0 2 2 1 1 19 17
2 0 26 22 0 2 1 2 2 2 27 25
It is recognised that in forming the regression equations from elements which give the higher coefficients, elements are chosen for which the randomvariations tend to be in the same direction as those caused by the correlationssought, . with the result that R, the total correlation coefficient obtained, mayindicate high
.er correlations than actually exist. The effect of reducing R is to
increase the minimum departure which can be forecast with a 4: 1 chance of
FORESHADOWING SUMMER RAIN IN QUEENSLAND. 15
success. 'I'hus, with lower values of R, fewer forecasts would be issued, but thoseomitted would be the ones with least chance of success, so that the tendency
would be for some of the failures to be eliminated.
This is the case with the November-January Springsure rain . Taking the value of R to be -79 as calculated, 30 forecasts were possible in forty-nineyears, and of these only 23 vvere successful, 24 being the expected number of successes . Suppose the actual value of R were lower, e.g . - 75 , then only 25 forecasts would be possible, but of these 21 would be successful, the expectednumber of successes being 20, i .e . out of the 5 forecasts (1897, 1908, 1914, 1932, 1933) eliminated, 3 would be unsuccessful ones. 'rhus, if further tests indicate that the calculated value of R in any formula is too high, it could be replacedby the actual value . This would result in fewer forecasts being possible, butwould make it probable that the 4 : 1 ratio would continue to hold.
There are, of course , occasions on which no forecast can be issued, although
the actual rain is such as to call for one . It must be understood that the
non-issuing of a forecast does not imply average rain . If this limitation i s borne in mind, it is seen from Table VI that seven of the formulae have maintained the 4 : 1 ratio during the eight years it has been possible to test them beyond the period used in calculating the correlation coefficients.
SOURCES OF DATA. A. Queensland Rain-
1. 1885-1935. ' ' Queensland Monthly Rainfall Tables , ' ' compiled by Mr. I. Jonesfrom monthly data issued by the Divisional Meteorologist, Brisbane.
2. 1 9 3 6 - 1 9 3 8 . Monthly rainfall sheets issued by t h e Divisional Meteorologist, Brisbane .
3 . 1930-1938. Exceptions : Welltown and Mundoolun data from MS . received from Commonwealth Meteorological Bureau, Brisbane.
B . Pressures, Temp eratures, and East Indies Rain-
1. 1 8 8 5 - 1 9 3 0 . ' ' World 'Weather Records, ' ' Smithsonian Miscellaneous Collection, Vols.79 and 9 0 .
2 . 1 9 3 1 - 1 9 3 8 . M:SS. received from individual stations.
REFERENCES.
Walker, G. T . ( 1 9 14 ) . , l\'Iem . Incl. Met. Dept. Vol. 2:1 , Pt. 9 .
Walker, G. T. ( 192 6 ) . Quart. J. R. Met. Soc. V o l . 52 .
Walker, G. T . ( 1 9 30 ) . Mem. R. Met . Soc. Vol . 3, No. 24.
Walker, G. T . ( 19 3 2 ) . Mem. R.. Met. Soc. Vol . 4, No. 3 6 .
Treloar, H. M . ( 1 934 ) . Bulletin No. 18, Commonwealth Bureau of Met., Melbourne.
THOMAS GILBERT HoPE, Actir1g G overn1nent Printer, Brisbane.
