TABLE II. Mean Pressure. (Millebars)
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4->
JB M
'S a EJ2
Petrograd
Scotland
Manches- ter
c "u
B
m
TJ C .
"ltd ft/5
u
en
- c
a
P-,
1 J3
C &
C/)
1 3
>
_rt 1
|l
B 3
Sw
Toronto
&
a
3
cr W
20
55-o
55-o
55-2
54-8
54-9
56-0
54-7
55-o
54-8
54-9
53
19
64-0
64-2
64-6
64-0
64-1
65-6
64-0
64-4
64-0
64-1
63
1 8
74-5
74-8
75-4
74-8
75-o
76-6
74-8
75-2
75-o
75-o
75
17
87-0
87-3
88-0
87-4
87-5
89-6
87-6
88-0
87-6
87-8
90
16
IOI
102
103
103
1 02
105
1 02
103
103
102
107
15
118
118
I2O
I2O
I2O
123
120
121
121
1 2O
120
128
H
138
138
I4O
140
140
143
141
142
142
140
142
'52
13
161
161
164
164
I6 4
167
165
165
165
164
167
178
12
187
187
192
192
192
195
193
193
194
192
195
209
II
218
219
224
225
224
228
226
226
227
225
228
244
IO
255
256
261
262
261
266
263
263
264
262
266
283
9
297
299
32
305
303
309
307
306
307
305
309
327
8
346
348
352
354
352
357
355
354
356
353
358
376
7
400
402
407
408
407
412
410
409
412
408
413
430
6
461
464
468
470
469
473
472
471
474
470
475
491
5
529
532
537
538
538
541
54
539
542
538
543
558
4
606
608
613
614
615
617
616
615
618
614
618
632
3
692
694
698
699
699
701
700
700
703
699
73
713
2
787
787
793
795
795
796
794
795
797
794
798
803
I
896
894
898
900
900
900
900
900
901
899
903
903
TABLE III. Density, grammes per cubic metre.
Height km.
England, S.E.
Europe
Canada
Equator
20
87
87
88
96
19
1 02
102
1 02
"3
18
119
119
121
135
17
139
139
144
162
16
162
162
169
191
15
191
191
I 9 8
225
H
223
223
233
261
13
261
26l
268
294
12
305
307
3H <
331
II
355
358
365
374
10
409
411
415
419
9
463
467
470
469
8
524
528
528
522
7
589
590
592
58i
6
658
66 1
662
645
5
735
735
733
7H
4
819
819
8i5
789
3
909
913
90S
871
2
1014
1017
ion
968
I
1128
1128
"34
1067
O
J253
1258
1258
1174
thus renders the connexions between different pairs of events comparable with each other. The velocity of the wind and the steepness of the barometric gradient may be taken as an ex- ample. The actual connexion is obvious from the daily weather charts; on some it is well marked, on others badly, but the fact that there is a connexion is quite apparent from even two or three charts. The correlation coefficient is about -70.
The application of the method of correlation to forecasting can hardly be looked upon as very successful. Two highly correlated events are required happening with a definite time interval between them. A correlation coefficient may be high accidentally if it be founded on too small a number of instances, but genuinely high coefficients between meteorological events occurring with more than a few days' interval betweem them are hard to find. The most suc- cessful instance is perhaps the forecast of the monsoon rain of India by G. T. Walker from the correlation between it and sundry other events occurring in the spring of the same year or earlier. In this case the correlation coefficients on which the forecast is based have values of about -50; if values of -80 or -90 could be obtained very much greater success would be secured. There are a few coefficients of from -70 to -80 between the rainfall at various periods and the subsequent yield of sundry crops. Thus in the eastern counties of England if April and May be wet it is a practical cer- tainty that there will be a large hay crop, and if the autumn be dry there will almost certainly be a large crop of wheat the next year. Mr. R. H. Hooker has calculated a most interesting set of figures relating to the correlation between the weather and the crops. Similar work has been done for the potato crop in America by J. Warren Smith, and many correlation coefficients relating to agricul- tural matters are available from Sweden and elsewhere.
The case is different where correlation is resorted to for the pur- pose of elucidating some physical process in the atmosphere ; here a
small coefficient is just as likely to give information as a large one. But the interpretation of the meaning of the coefficient is often difficult, and in many cases the value obtained is quite different from that which most meteorologists would have expected.
G. T. Walker in addition to his statistical work on the monsoon rain has published several sets of correlation coefficients, and amongst them a set of 100 showing the correlation between the sunspot number and the temperature at 100 stations well dis- tributed over the earth's surface. The correlation is negative and small but it is large enough to be significant and to prove that during the 40 or so odd years considered the temperature of the earth as a whole was lower at the time of the sunspot maxima than at the time of the minima. It is commonly supposed that the sun is giving out most energy when its surface is most disturbed, and this idea has been confirmed by direct observation of the radiant heat. A per- fectly satisfactory explanation is at present wanting. Another case is the low correlation between the direction of the wind and the temperature of the lower air strata (see a paper by Capt. C. K. M. Douglas, Q. J. Met. Soc., Jan. 1921, vol. xlvii., No. ,197), a most unexpected result. Walker also correlated between sunspots and rainfall, and found the coefficient too small to be significant. How- ever, in none of these cases has the work been wasted since important conclusions have been established.
For high correlation coefficients one must take data relating fo the upper air. The relation between pressure and temperature is so remarkable and has such a close relationship to the theory of cyclones and anticyclones that it will be treated separately. The correlation coefficients between the thickness of the troposphere, a height commonly denoted by H , the surface pressure, the tempera- ture of the stratosphere and other variables often exceed -70, and the generally high values show quite plainly that there is an ordered sequence in the processes going on above, which is strikingly absent from the surface phenomena.
Cyclones and Anticyclones. In the meteorological literature of the past no subject has been so much discussed or has had so much attention directed to it as the causes of cyclones and anti- cyclones. When it became possible to obtain observations of temperatures and humidity, and in clear weather of wind direc- tion, from the upper air it was confidently hoped a solution would be found a hope as yet unfulfilled. But the mass of informa- tion collected from Europe, more particularly from the northern and western parts where cyclones are frequent, has given a large amount of detailed information and we have a clear conception of what happens as a cyclone passes over. It is true that we have no simultaneous sets of observations, so that we cannot draw a chart of any one particular cyclone, but we have numerous observations showing the departures from the mean correspond- ing to any observed surface pressure and to any special section of the cyclone.
The facts that stand out are that in a cyclone the troposphere is cold and the stratosphere warm, in an anticyclone the reverse is the case; in a cyclone the tropopause is low, in an anticyclone high. Thus as an area of low pressure passes across the map the following changes occur in the various air strata above. The deficiency of pressure is about the same from the surface up to some 10 km., above which it falls off rapidly until the normal value for the height
