power spectrum analysis of the time-series of annual mean surface air temperatures

P O W E R S P E C T R U M A N A L Y S I S OF T H E T I M E - S E R I E S OF

A N N U A L M E A N S U R F A C E AIR T E M P E R A T U R E S

R. P. K A N E andN. R. T E I X E I R A

Instituto de Pesquisas Espaciais- INPE, C.P. 515, 12201 Sdo JosO dos Carnpos, SP, Brasil

Abstract. Maximum Entropy Spectral Analysis of the annual mean surface temperature series for land masses and sea in the northern and southern hemispheres indicated long-term linear warming trends of (0.12 to 0.56) ~ with superposed significant periods in the ranges T= 5-6 yr, 10-11 yr, 15 yr, 20 yr, 28-32 yr, and 55-80 yr. Extrapolation in future indicated for 2 0 0 0 - 2 0 3 0 a departure of (+0.4 ~ above the 1950-70 level. However, for the 1980s, the observed values are above the expected level, probably indicating large greenhouse effects due to human intervention. In that case, our predictions would be underestimates.

1. Introduction

Surface air temperatures for several thousand locations are given in the World Weather Records (WWR) and are available in digitized form from the National Center for Atmospheric Research (NCAR) (Jennes 1975). Bradley et al. (1985) and Jones et al. (1985) have supplemented these with additional data from meteorological archives, thus improving the spatial coverage significantly. From these, Jones et al. (1986a) have compiled a new gridded hemispheric dataset for the Northern hemisphere for 1851-1984, considered superior to their earlier compilation (Jones et al., 1982) from the point of view of spatial and temporal coverage as well as homogeneity. These data refer mainly to the land masses and are almost similar to the earlier compilations by Hansen et al. (1981) and Jones et al. (1982) who used only WWR records, but differ from the marine air temperature data of Folland et al. (1984). For the Southern Hemisphere, Jones et al. (1986b) have given a new compilation for 1851-1984 which refers mainly to the land masses and com- pares reasonably well with the earlier compilation of Hansen et al. (1981) but not so well with the marine data of Folland et al. (1984) who used the UK Meteorologi- cal Office (UKMO) data bank. The marine data have problems of inhomogeneities resulting from non-climatic factors. Folland et al. (1984) tried to overcome these by identifying specific sources of errors; but their corrections have inherent uncertainties. Recently, Jones et al. (1986c) used the more copious Comprehensive Ocean Atmosphere Data Set (COADS) compilation up to 1979 and data from Climate Analysis Center, NOAA for 1980-84, homogenized the same, made due corrections for the Marine Air Temperature (MAT) data and produced Globa l and H e m i s p h e r i c annual mean variation series for 186 l - 1984.

A striking feature of all these series is a long-term warming trend amounting to

Climatic Change 17:121-130, 1990. �9 1990 Kluwer Academic Publishers. Printed in the Netherlands.

122 R. E Kane and N. R. Teixeira

about 0.5 ~ over the past 100 years. However, these also seem to have superposed wavy structures. Folland et al. (1984) have mentioned the possibility of a dominant peak at a period of 83 yr and minor peaks in the range 3-5 yr. Currie (1974) mentioned the possibility of a solar cycle signal. In this communication, we report the results of a power spectrum analysis of some of the series mentioned above.

2. M e t h o d o f A n a l y s i s

The method used is the Maximum Entropy Spectral Analysis (MESA) developed by Burg (1967) and critically reviewed by Ulrych and Bishop (1975). MESA is superior to the Blaekman and Tukey (1958) method based on autocorrelatiota. However, the amplitude estimation in MESA is unreliable. Hence, Kane (1977) suggested the alternative approach viz. using MESA only for detecting the possible periodicities T k (k = 1 to n) and then using these in the expression:

f(t) Ao+~--~ [aksin2ar t +bkcos2ar t 1 = - - - - + E

(1)

= A o + rksin 2 : r - -+~bk + E , k = l Tk

where f(t) = the observed time-series and E = Error factor. The parameters A0, (ak, bk) and their standard errors aak , abg are then estimated by a Multiple Regres- sion Analysis (MRA) (Johnston, 1960; Bevington, 1969) using the least-square fit. From these, (rk, Ok) and the standard error ark can be calculated. Amplitudes r k exceeding 2ark would be significant at a 95% a priori confidence level.

3. D a t a a n d R e s u l t s

Figure la shows a plot of the annual Surface Air Temperature series for the Northern Hemisphere land masses (NHLAND) (Jones et al., 1986a) for 1851- 1984 (134 years). The values are departures, in degrees Celsius, from a reference period (1951-1970) mean. The results of a Maximum Entropy Spectrum Analysis of this series are shown in Figure 2. In MESA, the choice of the Length of the Pre- diction Error Filter is not straightforward. Akaike's (1969) final prediction error (FPE) criterion often falls to give a clear minimum (see Kane and Trivedi, 1982). From a study of artificial samples, Kane (1977, 1979) suggested that spectra may be obtained for several LPEF and periods up to roughly 1/10th of the data length may be searched in the small LPEF plots and larger periods in the larger LPEF plots. Figure 2 shows the MESA results for LPEF = 45, 67, 89 and 107. corre- sponding to 33%, 50%, 66% and 80% of the data length 134. From these T= 2.14, 2.21, 2.37, 2.85, 3.1, 3.9, 4.6, 5.3, 6.5, 7.5, 9.7 and 11.8 years were selected from the plot for LPEF = 45, T = 14.6, 20.9, 28.2 years from the plot for LPEF = 67 and

Climatic Change August 1990

Power Spectrum Analysis of Annual Mean Surface Air Temperature 123

U o v

I.- rr

W

W n~

n~ W O_

W

n~

W 0 ,,< er"

U)

1850 60 70 80 90 1900 I0 20 50 40 50 60 70 80 90

0.4 0.2 0.0

-0.2 -0.4 -0.6

!

' I ' ] ' I ' I ' T ~ - q ' ! r ~ I ' I ' I ' I ' I T R E N D

A , A A X ' 1 0 3 ~ ~ 3 . 3

0.4 0.2 0.0

-0.2 -0.4 -0.6

YR (a)

NH LAND-

O.4 o2i o 2

-0.2 -0.4 -0.6

0.4 0.2 0.0 ,o,.2 ( c )

-0.2 SIR LAND- -0.4 -0.6

0.4 (d) 1 0.2 ~ 2.8 0.0 SH MAT-

-O2 -0.4

0.4 0 . 2 / A . ~ ~ f ~ ~ 41 (e) 0.0 ~" NH _:

-0.2 ~ ~ LV ~'/m/~ V ' LAND SEA -0.4 -0.6 !

( f )

LAND SEA

!

(b) NH MAT-

J,

4.7 GLOBAL

LAND SEA

0.4 0.2 ~ �9 �9 ,,. �9 �9 �9 0.0 ~- ,,.

-0.4 ~ v v v v v v v ] ,7 v v v v ]

1850 60 70 80 90 1900 IO 20 50 40 50 60 70 80 90

YEAR Fig. 1. Annual mean surface temperature departures for: (a) Northern Hemisphere land masses (NHLAND) (Jones et al., 1986a), (b) Northern Hemisphere nighttime Marine Air temperature (NHMAT) (Folland et aL, 1984), (c) Southern Hemisphere land masses (SHLAND) (Jones et al., 1986b), (d) Southern Hemisphere nighttime Marine Air Temperature (SHMAT) (Folland et aL, 1984), (e) Northern Hemisphere land and sea (NHLANDSEA) (Jones et al., 1986c), (f) Southern Hemi- sphere land and sea (SHLANDSEA) (Jones et al., 1986c), (g) Global land and sea (GLOBALLAND- SEA) (Jones et al., 1986c). Full and open triangles mark years of sunspot maxima and minima, respectively. The straight lines represent linear uptrends with trend coefficients as indicated.


124 R. R Kane and N. R, Teixeira

0.4

0.3

0.2

0.1

la.I 0 .4

0 0 .3

0 .2

~ Q 0 .1 0 ._1

0 .3

0 .2

0.1

L O G T 0 .3 0 . 4 0 . 5 0 .6 0 .7 0 .8 0 .9 1.0 I.I I .Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 .0

L . ~ . . . . . . . . . . . . . . ' . ~ , - ~ - ~ - 0 . 4 ,~..;,~ zss 4 s .~3 v - . e 0.3 . 6.5 �9 0,7 - -

0 .2 �9 �9 11.6 ~ . . . . . . . . . . . . . . .

T=55 YEAR8 - 4 .7 I I . I I 20 .9 2E .2 .

6.2 6 .8 77 8.8 I0 .0 14 6 T 69

- 2e .8 - ' ' ' - ' - - . . . . 21,4 . . . . . "

LPEF = ( ~ = 6 6 % - , , , - - , . . . . . , / 20 .4 27.5 T �9 65

4.7 66 "~311-1 9.1 10.2 4:5

6"2 12.9 15,9 T 78

44 " " " " i , , , . - - -

/ ~ , - . / ~ ' - - - ' / LPEF " @ " 80%

11,8 20 .9 2Z9 43 T �9 67

9.1 10,2 127 15.9 , '~

�9 4 5 �9

15.9 ++x / " , ~ - . _ . ~ -

L O G I o T r 014 01~. O~ 0'.7 ole o11) IiO Ill I12 1'.3 1'.4 I'.'~ I',6 117 I'.e I=.9 Z'.O 1 I I I I I I i I i i , i I I I '1 I I z J I

T= 2 2 .5 3 4 5 6 7 8 I 0 if3 2 0 Z5 3 0 4 0 5 0 7 0 I 0 0

P E R I O D T ( Y E A R S )

Fig. 2. Maximum Entropy Spectra for the Northern Hemisphere land masses annual mean surface temperature series 1851-1984 (NHLAND) (Jones et al., 1986a) for LPEF = 45, 67, 89 and 107 cor- responding to 33%, 50%, 66% and 80% of the data length 134. Full lines - spectra of original data. Dashes - spectra for series corrected for linear trend (vertical scale shifted down). The abscissa scale is Log T.

T - 4 3 , 65 years from the plot for LPEF = 89. All these periods were used in Equation (1). A Multiple Regression Analysis showed that only T= 2.14, 5.3 and 28.2 years with amplitudes of 0.06 ~ 0.07 ~ and 0.08 ~ respectively with a standard error of + 0.03 ~ were significant at a 2 o a priori level. Since these amplitudes are very small and the long-term warming trend was comparable, there was a possibility that this trend may distort the spectra, specially in the large periodicity region. Hence, the original data were corrected for linear trend by a simple procedure as follows. The deviations for the first 5 years 1851, 1852, 1853, 1854, 1855 were -0.08, -0.26, -0.22, +0.01 and -0.39 ~ respectively having an average value of -0.188 ~ centered at 1853. The deviations for the last 5 years 1980, 1981, 1982, 1983 and 1984 were +0.19, +0.48, +0.07, +0.43 and +0.01 having an average value of +0.236 ~ centered at 1982. Thus, from 1853 to 1982 (129 years), there was an increase of 0.424 ~ yielding a trend coefficient of 0.0033 ~ The original series was corrected for this linear trend and the corrected values were subjected to MESA. In Figure 2, the dashed curves represent spectra for this trend-corrected series, with the ordinate scale shifted. As can be seen, low periods remain un- changed; but larger periods are affected by the trend by about + 5%. This is in


Power Spectrum Analys& of Annual Mean Surface Air Temperature 125

agreement with similar results reported earlier by Courtillot et al. (1977) and Kane and Trivedi (1986). An attempt was also made to obtain the linear trends by a linear regression on all values. The resulting trend values were slightly lower than those indicated in Figure 1 but the results shown in Figure 2 did not change appre- ciably. Hence, linear trends for all the series were obtained by the simple procedure. A Multiple Regression Analysis was carried out using the periods T = 2.14, 2.21, 2.37, 2.85, 3.1, 3.9, 4.6, 5.3, 6.5, 7.5, 9.7, 11.6, 15.0, 21.4, 28.8, 44and 78 years. The periods itafised were significant at a 2a a priori level where a was + 0.021 ~ Amongst these, T = 5.3 years was significant at a 3a level and T= 79 years was significant at a 5a level. Thus, periods of 5 years and 78 years seem to be the main characteristics of the Northern Hemisphere land masses surface temperature series. In Figure 3, the first row (Figure 3a) depicts the peaks significant at a 2o a priori level. The black portion encloses the 2a limit and the horizontal dashed line indicates the 3 a limit. It is good to remember, however, that in MESA, frequen- cy estimates of large periodicities (exceeding half the data length) can have errors as large as + 10% (Chen and Stegan, 1974). Hence, for physical interpretation, values like T= 78 years should be considered as roughly ifi the range T= 75-85 years.

Figure lb shows a plot of the Northern Hemisphere nighttime Marine Air Tem- perature (NHMAT) (Folland et aL, 1984) expressed as departures, in degrees Celsius, from a reference period (1951-1960) mean. The long-term linear trend (obtained by the simple procedure) was not large (only 0.0012 ~ The data were corrected for such a trend and MESA was performed for the corrected values. The periods T= 7.4, 8.7, 11.1, 20.0, 28.5 and 60 years were significant at a 2 a a priori level, where a was _ 0.021 ~ Amongst these, T= 20 years was significant at a 3a level. The most prominent period was T = 60 years, significant at a 9a level. Figure 3b shows the various significant peaks.

Figure lc shows a plot of the Southern Hemisphere land masses temperature series (SHLAND) (Jones et al., 1986b). The long-term trend was 0.0042 ~ After correcting for the same, MESA showed periods T= 3.24, 6.2, 14.6, 20.4 and 78 years significant at a 2 0 a priori level, where a was + 0.018 ~ The period T= 14.6 years was significant at a 3 a level. Figure 3c shows the various significant peaks.

Figure ld shows a plot of the Southern Hemisphere nighttime Marine Air Tem- perature (SHMAT) (Folland et al., 1984). The long-term linear trend was 0.0028 *C/yr. After correcting for the same, MESA showed periods T = 19.7, 25.4 and 55 years significant at a 3o a priori level, where a was +0.028 ~ T = 19.7 years was significant at a 5a level. Figure 3d shows the peaks.

Using the land data mentioned above (Jones et al., 1986a, 1986b) and marine data in the COADS compilation and applying due corrections, Jones et al. (1986c) prepared homogenized near-surface temperature series. Figure lc shows a plot for the Northern Hemisphere (NHLANDSEA) series for 1861-1984. There was a linear trend of 0.0041 *C/yr. After correcting for the same, MESA showed periods


126 R. E Kane and N. R. Teixeira

LOGT 0.3 0 .4 Q 5 0 .6 0.7 0.8 0.9 I.O I.I 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

I 0

5 (a) O 15 T "I(~) "~eS JO N H M A T ? . . . . . [ ~ 1 1 5 . . . . . . . . . . . . . . .

o ( b )

" ~ I0 SH LANO . . . . . . ~22 . . . . . . . _6.=_ . . . . . . . . . ~ _ _ _ _zo.. . . . . . . . . . . . . . . . "r ._',.e ','~A_RS_ _.

o s I I / I- I Cc) • 0

r..) o 15

IO u3 W 5 r-, �9 - , O

.- .I ck 5 ~ 0

I0 5

0 I0 5

0

T=2

__:"_'_'\ . . . . . . . . . . . . . . . . . . . . . . .

T - I - ~ YEARS

( d )

SH ( LANO SEA) ~ [ ~ T = r i i 4 l YEARS 3.9 6, I 10.5 41 ,

GLOBAL (LAddO SEA)

m m l I I I ~'10

I k J i _ I m I i i - i t i I I I I i i l i = l 2.5 3 4 5 6 7 8 I0 15 20 25 30 40 50 70 I 0 0

P E R I O D T ( Y E A R S )

( e )

( f )

(g)

Fig. 3. Amplitudes of the various peaks for the various surface temperature series. The black portion encloses the 2 0 a priori level. The dashed line indicates the 30 a priori level. Numbers in rectangles represent periods significant at a 30 level and numbers in circles represent periods significant at levels exceeding 4~r.

t = 2.14, 5.3, 6.1, 7.5, 9.2, 20.7, 29.5 and 69 years, significant at a 20 apriori level, where o was _+ 0.014 ~ T= 5.3 and 9.2 years were significant at a 3o level. T= 29.5 years was significant at a 4o level and T = 69.0 years was significant at a 6 o level. Figure 3e shows these peaks.

Figure I f shows a plot of the Southern Hemisphere (SHLANDSEA) series for 1861-1984. The linear trend was 0.0056 ~ and MESA of the trend-corrected valuesgave periods T = 3.9, 6.1, 10.5, 15.0, 21.4, 41 and 64 years significant at a 20 a priori level, where o was _+ 0.0014 ~ T= 21.4 and 64 years were significant at a 3 0 level. T = 15.0 was significant at a 4 o level. Figure 3f shows these peaks.

Figure lg shows a plot of the Global Surface Air Temperature series for 1861- 1984. The linear trend was 0.0047 *C/yr and, after correcting for the same, MESA gave periodicities T = 3.8, 4.2, 4.7, 5.3, 6.1, 10.5, 15.3, 20.9, 32, 41 and 69 years, significant at a 20 apriori level, where owas + 0.012 ~ T = 6.1, 10.5, 20.9, 32 and 41 years were significant at a 30 level and T= 69 years was significant at a 50 level. Figure 3g shows these peaks.

In Figure lg, the full triangles indicate sunspot maxima and the open triangles indicate sunspot minima. In almost all cycles, temperature maxima seemed to have occured 0-2 years before sunspot minima.



4. Conclusions and Discussion

From the data and analysis presented here, the following conclusions may be drawn:

(1) The temperature variations in the land masses and the marine areas are not alike. Also, these are different in the northern and southern hemispheres.

(2) All these have a long-term warming trend. If assumed linear, the gradients are different for them all but are in the range (0.0012 to 0.0056) *C/yr.

(3). Superposed on these linear trends are wavy structures with periods ranging from 2 to 80 years. Many of the low periods (2 to 5 years) are significant only on a 20 a priori level and may still be just a manifestation of random noise. However, some are significant at a 3 o or better level. Such periods extend to high period range too.

(4) Some periods seem to be significant in all the series, e.g. T = 5-6 years, 10- 11 years, 15 years, 20 years, 28-32 years and 55-80 years.

The reliability of the above time series has been discussed in detail by Jones et al. (1986a, 1986b, 1986c). The spatial coverage is less than 75%, is better in the Northern Hemisphere and changes with time, being <35% before 1900 and <20% in the 1860's. Probably, some inaccuracies and uncertainties still remain. Neverthe- less, periods significant at a 3 ~ or better a priori level are likely to be genuine rather than spurious. Periods T= 20-22 years seem to match the 22 year Hale magnetic sunspot cycle, T = 10-11 years the sunspot cycle and T= 5-6 years its second harmonic. A superposed epoch analysis using years of sunspot minima as zero epochs showed that the global surface temperature was maximum at epoch (-1) i.e. one year before the sunspot minima. The larger periods are similar to those observed in other geophysical parameters like geomagnetic field variations (Currie, 1976; Kane, 1986, 1988), length of the day (L.O.D.) fluctuations (Currie, 1973) etc. and in sunspot numbers (Kane and Trivedi, 1985).

The above gradients and periods are obtained from data for the past 130 years. There is no guarantee that these will persist in future with the same magnitud.es. These changes are usually attributed to external forcing factors such as solar out- put, explosive volcanic eruptions and changes in concentration of CO 2 and other radiatively active gases. The last item probably has a large man-made contribution, radically different in this century as compared to the last century. The next century may have an altogether different pattern depending upon new combustion technol- ogies and/or new energy sources. Nevertheless, assuming that the above magnitudes persist in future, Figure 4 (a) shows an extrapolation for the next few decades. In all the three rows, the full lines represent the observed values (same as in Figure lg). To check validity of predictions, only the first 104 yearly values (1861-1964) were used for spectrum analysis. The periods obtained were slightly differelit from those obtained with 124 years data and shown in Figure 3g. In particular, in place of the strongest period T= 69 years, we now had twb strong periods, T= 38 and 68 years, of comparable amplitudes. In Figure 4 (a), the new expected values


128 R. R Kane and N. R, Teixeira

1650 6 0 70 8 0 90 2 0 0 0 t0 20 80 , , , , , , , , , , , , , , , ,

�9 x x x E X P E C T E D V A L U E S , G R A D I E N T 6 . 0 0 4 7 � 9 YR - I 0.6 " A N D , T = 3 . 9 , 5 . 3 , 6 . 2 , I 0 . 6 , 1 5 . 3 , 1 6 . 7 , 3 4 , 6 8 V E & R S

,; o, iGR o , "

M

,~ 0.6 T = 1 5 . 3 , 3 4 , 6 8 Y E A R S ( ; = 3 o ' ) 0.4 *** '*~ , ,~x ,o~ ,~ , , , , ,~ '

-0.2

ILl I-- 6.6 e,,,. [ T = 3 4 6 8 Y E A R S ( ~ 4 o - ) w 04 t "~ " ~- G R ~ I I ~ = ~ ' = = ~ , , ~ , r ,~,'~ �9 6 . z l - ~ _ ~ ~,,'=

~ -6.2

,J

+6,1 oOR2"gO, E O.O0 ',6. (b) �9 / t 4 PAIRS, + 0 . 6 0 x tG8t t 9 6 5 - 8 4

/ § 0.2 ~- X 1980

i~ii~4" 6 I �9

io �9 �9 ~974

�9 , ~0~ o +6.1 -I-0.2 [~

m o . 4 1 J �9 I J O N E S E T A L E X P E C T E D ( G R O U P t )

o t A -J 0.3 , , ~,~ , / ~ C 6.=~ j \ Z i \ / ,~ '4 . . . . . ( ~ m ) �9 , , o., ~ . . . . 2~.,'.-,-'~'-~ ." I . . . . . .ED,~T,ON

6 I" i ' - ' ~ - i ; ,- , , " . . , - , " , , I ( Q ~ , U P I I

Fig. 4. (a) Observed and expected values for the Global surface air temperature departures (GLOBALLANDSEA) (Jones et al., 1986c, 1988) for 1950 onwards. In all the three rows, full lines represent the observed values shown with bigger dots for 1965-84. The crosses represent the expected values, using a linear warming trend of 0.0047 ~ and periods of various significance levels as indicated. The vertical bars represent _+ 2a i.e. 95% confidence limits. (b) A plot of observed versus expected values for Group 1 (8 periodicities, top plot of Figure 4a) for the 20 years 1965-84. The regression line is a 45 ~ slope line, representing equal observed and expected values. Crosses represent the 6 years (1974, 1975, 1976, 1980, 1981, 1983) when values deviated considerably from the general pattern. (c) Observed values of global temperature in recent years. Full lines are for Jones et al. (1986c) and big dots connected with dashed fines are for their revised values (Jones et al., 1988). Crosses and dashed lines are our prediction as in Figure 4 (a), Group 1.

(crosses and dashes) are obtained by using a linear uptrend of 0.0047 ~ and periods T = 3.9, 5.3, 6.2, 10.6, 15.3, 19.7, 34 and 68 years (all significant at a 20 a priori level) in row 1 as Group 1, periods T= 15.3, 34 and 68 years (all significant at a 30 apriori level) in row 2 as Group 2, and period T= 34 and 68 years (significant at a 4 a a priori level) in row 3 as Group 3. Only data for 1950 onwards are plotted. Observed values for 1965-84 (20 years) are independent data (not used for spectral analysis) and are shown as big dots. A comparison with the expected values (crosses) shows that the matching is not very good. Figure 4 (b) shows a plot of observed versus expected values for these 20 pairs (1965-84). The 45 ~ slope line represents the expected regression line (observed values equal to expected values). The scatter is very large and the correlation coefficient for the 20 pairs is zero. However, this seems to be largely due to the values for years 1974, 1975, 1976 when observed values were abnormally low and for 1980, 1981, 1983 when the observed values were abnormally high. If these 6 years are omitted, the correlation coefficient for the remaining 14 pairs is quite good (+0.60). The reason for these discrepancies is not clear. In the earlier solar cycles, the sunspot minima in



years 1867, 1878, 1889, 1901, 1923, 1933, 1944, 1954, 1964 were all preceded by temperature maxima within 0-2 years. (The solar minimum of 1913 was not preceded by temperature maximum). For the solar minimum of 1976, the temperature values were abnormally low during 1974, 1975, 1976 but were high 3 years earlier in 1973. (See Figure lg). For the recent solar minimum (1986) too, the temperature maximum seems to have occurred 3 years earlier (1983). If these discrepancies are ignored, Figure 4 (a) shows that, apart from variations of the order of 0.1 ~ which occur from year to year or over short periods, the basic trend indicates large posi- tive departures throughout the early decades of the next century (+0.4 ~ relative to the 1950-1970 mean). The vertical bars are + 2 cr i.e. 95% confidence limits. In a recent publication, Jones et aL (1988) have extended their earlier analysis (Jones et al., 1986c) to include 1985-87 and to improve ocean and land coverage for the 1980s. Figure 4 (c), shows their earlier values (full lines) and the new values (big dots and dashes). The two differ only slightly. In particular, older values for 1981 and 1983 were different but the new values are alike. The crosses represent our prediction as in row 1 (group 1) of Figure 4 (a). Jones et al. (1988) emphasize that 1987 is the warmest year recorded, 0.05 ~ above the next warmest, 1981 and 1983 (new values). In general, the observed values are larger than our predicted values (crosses) during the 1980s so far. This could be partly due to the E1 Nifio/ Southern Oscillation events of 1982-83 and 1986-87. But it may also be an indi- cation of the consequences of increased concentration of CO2 and other radiatively active atmospheric gases due to human intervention in the last few decades. It is not quite clear, however, why changes on this count should be so large during the last few years only, while CO 2 concentration is on the increase for the last 2-3 decades. A sort of threshold effect might be operating. Whether the recent temperature increases will continue or accentuate in future to give - 5 ~ temperature rise in the next 100 years (Hansen et al., 1986) and whether these will cause dangerous sea-level rising due to melting of polar ice caps as also due to thermal expansion of the oceans (Titus, 1986) are controversial questions, beyond the scope of the present analysis. If these do occur, our predictions of Figure 4 (a) will certainly be underestimates.

Acknowledgements

This work was partially supported by FNDCT, Brazil under contract FINEP-537/ CT.

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i 3 0 R. E Kane and N. R. Teixeira

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(Received 22 February, 1989; in revised form 24 August, 1989) Climatic Change August 1990

power spectrum analysis of the time-series of annual mean surface air temperatures

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