RESULTS OBTAINED

For the sake of illustrating the principles involved

in

the method of analysis, the annual m e a n temperatures and annual rainfall amounts at Cape T o w n for periods of

100

and

120

years, respectively, are given

in

Tables

1

and

2.

These data are presented graphically

in

Fig.

1.

For the sake of clarity, the statistical formulae required

in

linear trend analysis are summarized as follows :

If 6

is the regression coefficient with time, t, in a linear equation of the form

y =

a

+ bt,

its value can be determined €rom

- ^{- -}

y€-% yt-yt b = i =

-t2

-

^(t)2

where

y

is temperature or rainfall, a the intercept of the straight line on the

y

axis, ot the standard deviation (root m e a n square) of t (which is always

8.66, 17.32, 25.98

or

34.64,

for t

= 30, 60, 90

or

120

years), and bars signify arithmetic means.

Finally, the standard error of

b,

as given

by

Brooks and Carruthers

(1953)

is

I

-81

Changes of climate

1

Les clzangements de climat

Averages, standard deviations, linear regression coeffi- cients and, in certain cases, standard errors of the regression coefficients of annual mean temperatures and annual rainfall amounts are contained in Table

3

for the given stations and periods.

It

will

be noticed from this table that the results cover a wide range of values for both the analysed elements. Most important was to see whether

valid

conclusions regarding climatic change could

be

arrived at

by

considering the values of

b

for the main stations

in

the chosen periods. F r o m the temperature regression coefficients

in

Table 3 it is noticed that the greatest value of

0.31,

i.e. for Cape Town in

1901-30,

is appre- ciably higher than twice its standard error of

0.008,

which corresponds to

95

per cent significance. This increase is portrayed in the relevant straight dashed line

in

Fig. 1.

But, as no statistical test is absolute, the question

of

the climatic significance of this temperature rise must also be taken into account. In order to decide this issue, use is m a d e of two climatic principles which can be stated as follows:

Climatic changes cannot start or stop abruptly, at least not if they are caused

by

generally accepted long- lasting terrestrial or extra-terrestrial factors. Conse-

and annu4 max.

+

min.

FIG.

1. Annual mean temperature

rainfall variation at Cape Town, and linear regression curves , fitted for 30-year periods.

82

Temperuturc und rainfall trends in South Africa

TABLE

3. Thirty-year averages

(y),

standard deviations (oy), time regression coefficients (b) and regression standard errors (ob) for temperature and rainfall at chosen stations and for given periods.

Temperature (OC.) Rainfall (mm.)

quently a time shift of say five years should not mate- rially affect a regression coefficient relating to a trend over

30

years. Another principle is that for the same reason climatic changes cannot be limited to a small region only. D u e to this, a reasonable space shift

within

the same climatic region should not appreciably affect the regression coefficient.

In accordance

with

these principles, two five-year time shifts were applied on

the 1901-30

temperatures for Cape Town, and, as indicated in Table

3, in

both cases more than

95

per cent significance was maintained.

No

space shift was applied to these temperatures as the time-shift test proved to be very convincing.

Considering the rainfall results for Cape Town in Table

3,

it is observed that the value of

-8.11

for

b in 1901-30

compares very favourably

with

its standard

error of

1.80.

However, backward and forward shifts of five years give fairly but not convincingly significant regression coefficients. Additional proof of the signifi- cance was consequently sought in the results from space shifts to stations Caledon, Worcester, etc.,

up

to George, of which the &st and the last are

90

and

370 km.,

respectively, distant f r o m Cape Town.

Of

these no less than five have clearly significant values for

b

in

1901-30.

It must therefore be concluded that both annual m e a n temperature and annual rainfall at Cape T o w n expe- rienced statistically and climatically significant changes

during 1901-30. Of

added importance is the fact that the trend coefficients of these two elements have opposite signs, as indicated

in

Table

3

and

Fig. 1.

This opposition is in line with the negative correlation coefficients between temperature and rainfall, which have been 83

Changes of climate

/

Les changements de climat

found to be

-0.26,

-0.141,

-0.21,

-0.49, -0.22, -0.42, -0.59, respectively, for the seven main stations

in

Table

3.

Such a n opposite relation, which must be ascribed to either the cooling effect of rain and cloud conditions or to a c o m m o n atmospheric circulatory cause, does

in

fact prove that a significant increase (or decrease) in either of these elements must be associated with an equally significant decrease (or increase)

in

the other.

Only

for one other analysed period, namely

1863-92, did

the annual rainfall experience a pronounced change.

Here

b

is

9.03

(with ab 2.97), but for a backward time shift of five years

b

drops to

1.34

and for a similar forward shift it

drops

to

-0.83.

T h e regression coeffi- cient of 9.03,

in a

period that was chosen b y sight, is therefore climatically non-significant and should warn trend analysts against possible false conclusions from seemingly statistically significant results.

Looking at the indices of the remainder of the main stations, it appears that O’okiep experienced a statisti- cally significant increase of

0.300 C.

per year

in

1901-30, m u c h like Cape Town did in the s a m e period.

On

the other hand, a similar increase at Windhoek, but

in

1931-60, is practically insignificant.

As

for rainfall, a fairly significant increase occurred at Port Elizabeth

in 1871-1900.

B u t at Durban the even greater regression coefficients of

-7.77

and

-8.18

in

1871-1900

and

1901-30

are statistically non-significant, due to the corresponding large standard deviations of rainfall and consequent large standard errors of the

b-

values.

In

this connexion it should be pointed out that rainfalls and their standard deviations tend to increase or decrease together, as borne out

by

the

3

and oy values

in

Table

3.

A t this stage reference must be made to the results obtained for Cape T o w n in the multiple periods, namely in

60, 90

and

120

years.

As

can be expected a

kind

of average effect, as compared to the 30-year analyses, takes place

in

Lhese cases. Therefore no outstandingly

high

regression coefficients appear

in

these longer term analyses.

On

this account. the

b-

values for rainfall completely lose all significance, a result which conforms to that of

de

Loor, w h o analysed a 109-year series of annual rainfall at the same station. Because of this

finding,

some doubt must be attached to the otherwise statistically significant increase of temperature at the rate of

0.0090 C.

per year through

1901

to

1960

and of

0.0080 C.

per year through

1871

to

1960. On

the other hand, these increases are

in

harmony with those men- tioned

by

Callendar for different regions, which fact adds to their signiíìcance in accordance with the space- shift test mentioned above.

In

conclusion it must be pointed out that no time or space-shifl test were applied to stations other than Cape T o w n , since the aim was simply to illustrate their value.

Also, the standard error significance test of regression coefficients for samples of

30

observations is admittedly not ideal. However, in view of the object to examine a speciík approach to the subject of climatic change, it is believed that such tests are sufficiently reliable.

R E S U M E

Les

tendances de la température et de la pluviosité en Afrique du Sud pendant la phiode pour laquelle on possède des données météorologipues

(W. L.

Hofmeyr et

B. R.

Schulze)

Les données présentées illustrent l’évolution des tem- pératures annuelles moyennes et

du

volume annuel des précipitations, par périodes de trente ans ou multiples de trente ans (jusqu’en

1960)

pour sept stations princi- pales et sept stations auxiliaires d‘Afrique

du Sud.

Celles

qui

proviennent de slations auxiliaires, ou

qui

concernent certaines périodes secondaires, servent

à

vérifier la signification climatique des tendances consta- tées. C’est ainsi qu’au Cap (la station

qui

recueille des données depuis le plus longtemps), on constate, aux environs de la période 1901-1930, une hausse des températures moyennes et une baisse des précipitations dans des proportions significatives tant

du

point de vue statistique que

du

point de vue climatique. Pour certains multiples de trente ans, l’augmentation de température se maintient mais la tendance correspondante des

pré-

cipitations cesse d’être significative.

84

Temperature and rainfall trends in South Africa

D I S C U S S I O N

P,.

G. VERYARD.

Have you any ideas regarding a physical explanation of the negative correlation between temperature and rainfall. Could it be a subsidence phenomenon?

W. L.

HOFMEYR. D u e to the limited time for presenting the paper,

I

did not refer in m y talk to the explanation given in the text, namely that the negative correlation must be due to either the cooling effect of rain and cloud or, vice versa, to the heating effect of cloud absence. The latter condition is intimately connected with subsidence in the subtropical high-pressure belt and bordering regions, as mentioned by Mr. Namias in his comment.

J.

NAMIAS.

Regarding the question of negative Correlation between rainfall and temperature-this is a common pheno- menon in the interior of continents during summer. For example, in the Central Plains of the United States, these correlations for monthly values in summer run as high as -80.

The physical explanation must contain the upper level anti- cyclones which dominate dry areas in summer. Through these, dry air from the westerlies (aloft) is flung and this

air is further dried out by subsidence into the core of the upper level anticyclones. This, in turn, inhibits cloud formation and allows insolation to rapidly heat the ground and then the overlying air. Of course, the conditions arc quite the reverse without the upper level anticyclone and thus frequently with convergence, ascent of air, cloud and screeing of insolation.

E. L. DEACON.

The fall in rainfall at Cape T o w n during the earlier part of this century brings to mind a finding of

S. C.

D a s (Aust. J. Phys., no. 9, 1956, p. 394-399) that there has been a southerly shift of the high pressure belt over the period 1909-54. This he derived from the observations at a chain of stations running down the east coast of Australia and statistical tests showed it to be a sigdcant effect.

As

DeLislc in N e w Zealand has also found evidence for such a movement, it would be interesting to consider the implications of the South African results in this connection.

W. L. HOFNEYR.

No corresponding pressure analysis has been made to date in South Africa.

BIB LI0 G R A P H Y / B I B L I O G R A P H I E

BROOKS,

C.

E. P. ;

CARRUTITXIIS,

N.

1953. H a n d b o o k ofstatistical

LOOR, B.

de. 194'8. Die ontleding van ICaapstad se reënval, methods in meteorology. London. 1838-1946, Tijdskrìf Wetenskap Kuns, Pretoria, vol. 8, CALLENDAR,

G. S.

1961. Temperature fluctuations and trends

over the earth, Quart. J. ray. met. Soc., London, vol. 87,

p. 34-46.

p. 1-12.

85

S E C U L A R T R E N D S

IN T H E SOIL T E M P E R A T U R E S AT C O L A B A , B O M B A Y

bY

L. A. RAMDAS

and

N. RAJAGOPALAN

National Physical Laboratory of India, New Delhi

INTRODUCTION

T h e secular variation of climate is a problem of perpetual interest to the meteorologist. For inquiries of this type it is obvious that systematic and reliable observations over a long series of years are required.

In

his paper entitled “Is our Climate changing

? A Study

of Long- T e r m Temperature Trends”, Kincer

(1933)

w h o analysed some of the long series of air temperature data available for a few stations in the United States and elsewhere has arrived at the conclusion that

“with

the exception of a region

in

low latitudes stretching from the W e s t Indies eastwards over northern Africa and the Mediterranean country, there is a general upward trend of temperature”.

T h e problem of climatic changes can also be attacked from the point of view of secular variations in the tem- perature of the earth’s crust, for here w e have the addi- tional advantage of dealing with stationary soil layers, whereas the air temperature at a place comes very much more under the influence of atmospheric circulation.

Systematic records of soil temperature for a long series of years are very rare. A t the Colaba observatory at Bombay, however, the recording of soil temperatures at various depths was taken

up

as early as

1849,

so that a uniquely long series of data is available for discussion.

In

the present paper w e shall summarize the results of an analysis of this series of data

with

particular reference to the secular changes at different depths below the surface of the ground. T h e first indication of the pro- nounced secular change

in

the Colaba soil temperatures was given

in

the Annual Report on Agricultural Meteo- rology in Indiafor the Year ending

21

August

1934l.

SITUATION OF THE OBSERVATORY

Dans le document CHANGEMENTS DE CLIMAT OF CLIMATE (Page 88-93)