Statistical Analysis of Long Term Trends in Atmospheric CO2 Concentration at Baseline Stations

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W O R K I N G P A P E R

mAl"ISi3CAL ANALYSIS O F LONG TERU TRENDS IN A T W O S P ~ C

CO,

CONCENTRATIONS

AT

BASELINE

STATIONS

M. Ya. Antonovsky

ZM.

Bukhshtaber A.A. Zubenko

December 1980 WP-08-122

I n t e r n a t i o n a l I n s t i t u t e tor Agpliad Systems Analysis

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STATBIXCAL ANALYSIS OF LONG TERM TRENDS

IN

ATMOSPHERIC

CO,

CONCENTRATIONS

AT

BASEWUE STATIONS

M.Ya. A n t o n o v s k y KM. B u k h s h t a b e r A.A. Z u b e n k o

December 1988 WP-88-122

W o r k i n g P a p e r s are interim r e p o r t s o n work of t h e International I n s t i t u t e f o r Applied Systems Analysis a n d h a v e r e c e i v e d only limited review. Views or opinions e x p r e s s e d h e r e i n d o not n e c e s s a r i l y r e p r e s e n t t h o s e of t h e Institute or of its National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS A-2361 Laxenburg, Austria

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Foreword

Carbon dioxide i s one of s e v e r a l greenhouse g a s e s t h a t can modify t h e e a r t h ' s h e a t balance by absorbing outgoing radiation from t h e e a r t h ' s s u r f a c e , t h e r e b y in- creasing t h e amount of h e a t retained by t h e atmosphere (the so-called greenhouse effect). Changes in C02 are t h e r e f o r e of considerable importance.

In t h i s p a p e r , t h e long-term t r e n d s are assessed at f o u r baseline stations

-

Mauna Loa (Hawaii), Barrow (Alaska), American Samoa and South Pole. The a u t h o r s conclude t h a t a parabolic model provides t h e b e s t f i t f o r t h e observed rates of CO, concentration growth o v e r t h e l a s t 20-30 years.

I welcome P r o f . Antonovsky's initiative in tackling t h i s v e r y important problem.

Bo R. Dijijs

Leader, Environment Program

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STATISIJCAL ANALYSIS OF LONG

TERM

TRENDS IN ATMOSPHERIC CO, CONCENTRATIONS

AT

BASEUNE

SPATIONS

M.Ya. Antonovsky,

EM.

Bukhshtaber* a n d A.A. Zubenko*

1.

MTRODUCTION

An assessment of possible f u t u r e climatic changes r e q u i r e s a knowledge of t r e n d s in C0, concentrations in t h e atmosphere. Trend analysis i s difficult because of annual, seasonal and daily fluctuations in C02 concentrations. In t h i s p a p e r we use algorithms t o remove t h e periodic components. Then we assess long-term t r e n d s at f o u r baseline monitoring stations.

2. DATA

SET

The d a t a set consisted of NOAA/GMCC time-series of C0, concentrations o v e r t h e period 1968-82. These d a t a included mean-monthly C02 concentrations f o r a s e t of stations (see Table I ) , but we a r e mainly interested in t h e f o u r monitoring stations: Bar-row, Alaska (1973-82), Mauna-Loa, Hawaii (1974-82), American Samoa (1976-82) and South Pole (1975-82). All f o u r stations a r e located at a n approximately similar longitude of 170". The t o t a l number of d a t a i s 400. These d a t a w e r e obtained on t a p e from t h e Carbon Dioxide Information Center, Oak Ridge National Laboratory, USA. The t a p e also included mean weekly d a t a f o r 1968-82 (11397 readings), and hourly d a t a f o r Mauna-Loa f o r t h e y e a r s 1958-86 (C0, concentrations and meteorological observations of p r e s s u r e , temperature, r e l a t i v e humidi- ty.. .) (254208 d a t a points).

*

All-Union Research I n s t i t u t e o f Physiotechnical and Radiotechnical Measurements, USSR.

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Table 1: Coordinates of s t a t i o n s of d a t e b a s e demonstrations (network of s t a t i o n s NOAA/GMCC)

S t a t i o n Amsterdam Is.

Ascension Is.

St.Croix Is.

Azors Islands B a r r o w Cold Bay Cape Meares Cosmos

Falkland Islands Guam Is.

Key Biscane Kumukahi Mould Bay Mauna Kea Mauna Loa Niwot Ridge Palmer Point S i x S e y c h e l l e s American Samoa Ammundsen Scott

"Charly" Ocean

"M" Ocean

Notation AMS

ASC AVI AZR BRW CBA CMO COS FLK G MI KEY KUM MBC M KO MLO NWR P S A PSM SEY S M O SPO STC STM

Longitude 77"E 14OW 64"N 27" W 156"W 162"W 124"W 75"W 60°W 144"E 80°W 158"W 119"W 155"W 155"W 105"W 64"W 1 1 O 0 W 55"E 170" W 24"W

2"E

Altitude 37"s

7 " s 17"N 38"N 71°N 55"N 45"N 1 2 " s 5 2 " s 13"N 25"N 22"N 76"N 20°N 19"N 40°N 6 4 " s 47"s 4"s 1 4 " s 89"s

66"N

Region Indian Ocean S. Atlantic C a r r i b e a n S e a N. Atlantic Alaska Alaska Oregon P e r u S. Atlantic N. Pacific Florida Hawaii Canada Hawaii Hawaii Colorado Antarctic Montana Indian Ocean S. Pacific Antartic N. Atlantic N. Atlantic

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3. METHOD

W e assume t h a t time s e r i e s of monthly values c a n b e r e p r e s e n t e d in t h e following form:

w h e r e Co i s a t y p i c a l c o n c e n t r a t i o n f o r a given s t a t i o n , C1 i s t h e y e a r l y variation, C2 i s t h e monthly v a r i a t i o n a n d E i s a random fluctuation a s s o c i a t e d with o t h e r fac- t o r s . Equation (1) allows u s t o analyze s e a s o n a l v a r i a t i o n s a n d long-term t r e n d s . To minimize b i a s w e u s e medians r a t h e r t h a n mean values (Huber, 1981).

The p r o c e d u r e i s as follows ( s e e F i g u r e 1):

1. The medians f o r e a c h y e a r are calculated a n d t h e r e s u l t s are s u b t r a c t e d from t h e y e a r l y d a t a . The mcdians themselves are added t o C1, which f o r t h e f i r s t i t e r a t i o n i s assumed t o b e equal t o z e r o .

2. In t h e year-month matrix, medians f o r e a c h month are calculated and t h e r e s u l t s s u b t r a c t e d from t h e data f o r t h e c o r r e s p o n d i n g month. The monthly C2 i s assumed t o b e equal t o z e r o f o r t h e f i r s t i t e r a t i o n .

3. The computed median of y e a r l y e f f e c t s i s s u b t r a c t e d from e a c h y e a r l y C1 and added t o i t s computed value f o r t h e f i r s t i t e r a t i o n .

4. The computed median of monthly e f f e c t s i s s u b t r a c t e d from e a c h monthly C2 a n d added t o i t s computed value f o r t h e f i r s t i t e r a t i o n .

5. This p r o c e s s continues until c h a n g e s in t h e deviation of r e s i d u a l s are less t h a n 1 X of t h e r e s i d u a l s in t h e previous i t e r a t i o n . The deviation is measured by t h e sum of a b s o l u t e values of residuals.

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W e assume t h a t t h e changes of monthly e f f e c t s are a reflection of biospheric seasonal cycling and t h a t fluctuations are caused by local C02 sources. A s p e c t r a l analysis i s used t o study t h e s t r e n g t h s of t h e s e f a c t o r s .

4. RESULTS

4.1. Spectral analysis

A s p e c t r a l analysis of t e n y e a r s of monthly values f o r t h e Barrow s t a t i o n is given in Figure 2. The amplitude of harmonica with given frequency are p r e s e n t e d h e r e f o r e a c h frequency point at t h e abscissa-axis ( t h e module of d i s c r e t e Fourie transformation at a given point). The abscissa point 1/120 c o r r e s p o n d s t o t h e period of oscillation once in 120 months lw

=

l / T ( . This harmonic i s c h a r a c t e r i s t i c of t h e t r e n d , i.e., t h e harmonic is equal t o t h e period of observation.

In Figure 2, t h e r e a l s o e x i s t harmonics with periods equal t o 1 2 , 6, 4 and 3 months. The s u b t r a c t i o n of y e a r l y e f f e c t s from t h e mean monthly concentrations (Figure 3) r e s u l t e d in t h e e x t r a c t i o n of t h e harmonic with t h e 120 month period, i.e, t h e t r e n d component. T h e r e f o r e , t h e long-term t r e n d s in C02 concentrations a r e c h a r a c t e r i z e d by t h e y e a r l y effect.

The amplitude spectrum of t h e monthly e f f e c t s (Figure 5) and residuals (Fig- u r e s 4 a n d 7) show t h e precision of t h e expansion. By t h e c r i t e r i a of t h e maximum entropy, i t a l s o shows t h a t t h e monthly e f f e c t s contain all evident harmonics (with periods of 12, 6 , 4 and 3 months). A comparison of t h e monthly spectrum f o r dif- f e r e n t stations confirms t h e conclusion of previous studies (see, f o r example, Gemon et al., 1986) r e g a r d i n g t h e growth of amplitudes of seasonal oscillations in t h e direction from south to n o r t h , as w e l l as t h e opposite p h a s e of oscillations f o r t h e n o r t h e r n and s o u t h e r n hemispheres. This f a c t suggests t h a t t h e monthly ef- f e c t s r e f l e c t t h e seasonal biosphere cycle, t h e behavior of t h e residuals r e f l e c t t h e local s o u r c e s and sins of C02.

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Consideration of t h e amplitude spectrum of t h e time-series for various stations (see, f o r example, Figures 3 and 6) shows t h a t t h e signal with maximal amplitude always h a s a 12-month period. A l l stations have a 6-month harmonic, and most stations h a v e clear 4- and 3-month harmonics.

4.2. L o n g i t u d i n a l p a t t e r n s

The behavior of

C,

in expansion (1) (Figure 8 ) shows t h e tendency of a d e c r e a s e in value in t h e d i r e c t i o n from n o r t h to south (Figure 10). However, deviations from t h i s tendency h a v e been observed in some cases. I t would a p p e a r t h a t remote stations have t h e lowest values f o r a given latitude and, t h e r e f o r e , provide a n opportunity to consider

C,

as a background level of COZ concentration.

The similarity in behavior of t h e y e a r l y e f f e c t s (Figure 9) f o r d i f f e r e n t stations allow t h e construction of a global model of COZ changes based o n d a t a from a single station.

In c o n t r a s t t o t h e algorithms of t h e time-series analysis, t h e algorithm of t h e two-factor analysis (Tukey, 1977) h a s a p r o p e r t y of statistically s t a b l e expansion into background t r e n d s a n d seasonal components of concentration variations.

4.3. Long-term t r e n d s at Mauna-Lou

An analysis of long-term t r e n d s in annual values of y e a r l y e f f e c t s w a s done on t h e longest time-series (1958-87) for t h e Mauna-Loa Observatory. Evaluation of such t r e n d s h a s been considered in a number of r e s e a r c h e s (Keeling, 1984, 1987;

Gemon et al., 1986; Pearman and Hyson, 1981, and Antonovsky, 1986). F o r t h i s pur- pose, Pearman and Hyson (1981) f o r example, used a cubic spline approximation with a 1 - y e a r time s t e p .

I t i s worth mentioning t h a t t h e presentation of a long-term s e r i e s of observations as some spline i s a way of smoothing of experimental d a t a t h a t are slowly changing. More precisely, let zi

-

mean monthly concentrations in month

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zi , i = l , .

..

,n

.

In t h e c l a s s

c2

of twice differentiated functions u(t ) l e t us consider two functionals:

t h e functional of t h e least s q u a r e method, and

t h e Sobolian functional. I t s minimization c o r r e s p o n d s t o choosing t h e most smoothly changing function a. H e r e ti i s on t h e time a x i s corresponding to t h e month z .

I t i s found t h a t t h e cubic spline u O ( t ) of t h e d a t a (ti , z i ) gives t h e minimum of t h e functional

i-e., u o l ( t )

=

^argmin F ( u ) u E C ~

Thus, in Pearman and Hyson (1981), a combination of quasiparametric and extremal a p p r o a c h e s to t h e construction of a t r e n d is used.

The non-linear r e g r e s s i o n ( f o r functions of a s h a p e ml e x p a2t

+

m3) BMDP3R gives t h e following b e s t approximations:

The RMS deviation of t h e approximation from t h e observed c u r v e is 0.9. The r e s u l t s are shown in Figure 11. An inflexion point on t h e r e s i d u a l s c u r v e (Figure 1 2 ) suggests t h a t a piecewise approximation with two exponents might give a b e t t e r r e s u l t . The inflexion point coincides, approximately. to t h e y e a r 1969. A non- l i n e a r r e g r e s s i o n which was done f o r t h e periods 1958-1969 and 1970-1987 r e s p e c - tively, gives:

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A polynomial regression BMDP5R gives t h e b e s t approximation of all c u r v e s of t h e form a l t 3

+

a 2 t 2

+

^{a 3 t}

+

a4 as t h e following second o r d e r polynomial

The RMS deviation f o r t h e regression (5) is equal to 0.15 (Figure 13). Now t h e residual behavior becomes r a t h e r random (Figure 14). The c h a r a c t e r i s t i c s of a l l t h r e e m o d e l s are given in Figure 15. Thus, t h e parabolic approximation is b e t t e r t h a n t h e exponential f o r t h e whole interval (1958-86).

When w e say t h a t one m o d e l i s b e t t e r than a n o t h e r , w e should clarify in what sense. Suppose t h a t by t h e method of nonparametric estimation o v e r t h e interval [O,T] (in t h e case of Mauna Loa, T

=

30y,,,,), w e have found a t r e n d , i.e., t r e n d

T

=

~ ( t ) i s defined by points r ( t l ) ,

. . .

, ~ ( t , ) . For construction of a parametric model, l e t us choose a family of functions u(t ; a ,

. . .

^,^{a k )}^,where u i s a given functional, and a l ,

. . .

^{, a k}are t h e p a r a m e t e r s estimated during t h e analysis. In o u r case:

u l ( t ; a 1 , . . . , Q n ) = ~ l t 3 + ~ t t 2 + ~ 3 t + a , , a 2 ( t ;al.a2.a3)

=

a l e a g t

+

a3

.

Let us choose T1

<

T and l e t us consider t h e functional of t h e method of least s q u a r e s (MLS):

T1

F(Tl;al.

. . . .

^{a k}

⁼

^(r(t1

-

u(tl ; a l ,

. . . .

^ak⁾¹²

1 =l

L e t u s put:

( a

. . . .

^{a )}

⁼

^a a l . . . ^min

.

^.a)^F(Tl;al,

^{. . .}

^,^ak⁾

^,

i.e., w e find a;,

. . .

^,^a; by t h e method of least squares.

In t h e framework of a given family of functions, w e find t h e optimal number of p a r a m e t e r s k with t h e aid of F - c r i t e r i a as in BMDP.

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A s a r e s u l t , w e g e t a function of t (model):

u ( t ; a l I . . . # a ; ) . The f i r s t method of comparing models.

W e calculate residuals of predictions:

This residual is a function of

TI.

W e s a y t h a t model u l ( t ; a : ,

. . .

,

all)

^{i s}

b e t t e r than model u2(t ;a:,

. . .

,

ai2)

if t h e residuals of predictions by model u l ( ; ) are l e s s than residuals of predictions by model u 2 ( ; ) .

TRe second method of comparing models.

Let u s define t h e residuals of predictions in t h e form:

W e s a y t h a t model u ( t ; a l ,

. . .

, a t ) i s w e l l on t h e level E, if A(TL) S E , where E

i s a given number. Let T; b e t h e f i r s t value for t h a t model uq ( t ; a l ,

. . . .

^akq⁾^,^q=1,2, i s w e l l on t h e level E .

We s a y t h a t model u ( t ;a;.

. . .

, a;) i s b e t t e r t h a n model u2(t ;a;,

. . .

,

a i l )

^on

t h e level E, if T ;

<

T;.

The calculation by both methods h a s shown t h a t t h e long-term t r e n d of s e r i e s of concentration of C02 on o b s e r v a t o r y Mauna-Loa i s b e t t e r d e s c r i b e d by a p a r a - bolic model t h a n a n exponential one.

Let u s consider t h e f o r e c a s t ability of a parabolic model. A s c a n b e s e e n from Figures 1 6 a n d 16', a p a r a b o l a obtained from t h e d a t a for t h e f i r s t 5-year period deviates o v e r t h e complete 28-year period. However, a p a r a b o l a obtained f r o m d a t a for t h e f i r s t 15-years gives a n almost e x a c t forecast f o r t h e next 13-years (Figures 17 and 17'). T h e r e f o r e , t h e observed p r e s e n t C02 concentration w a s

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possible t o predict in 1973 on t h e basis of t h e parabolic model, i.e., t h e observed r a t e s of C02 concentration growth a r e still t h e same as in t h e previous 10-years.

Let us make a n analogous investigation of t h e temperature time-series f o r t h e Mauna-Loa station o v e r t h e period 1958-1986. An amplitude spectrum of t h e tem- p e r a t u r e time-series (Figure 18) shows t h e p r e s e n c e of t r e n d and two harmonics in a period of 12-months and of approximately 3-years. Those harmonics of more than a 12-month period d i s a p p e a r a f t e r subtraction of t h e yearly e f f e c t s (Figure 19).

This means t h a t t h e c u r v e of t h e yearly e f f e c t s contains information on global behavior. The behavior of t h e monthly effects evidently r e f l e c t s seasonal (winter-summer) temperature oscillations (Figure 20). The l a r g e year-to-year variability does not allow construction of a simple analytical m o d e l . Nevertheless, i t i s possible t o say t h a t , o v e r t h e past 1 0 y e a r s , t h e mean annual t e m p e r a t u r e h a s increased. The second o r d e r polynomial which gives t h e b e s t approximation i s a s follows:

The amplitude spectrum f o r t h e yearly temperature effects before and a f t e r subtraction of t h e parabolic c u r v e (6) can b e seen in Figures 22 and 23. The comparison shows t h a t t h e parabola can b e considered as a model of t r e n d because i t s subtraction deletes t h e harmonic with t h e maximal period, leaving all o t h e r harmonics unchanged. A s h i f t in temperature parabola (Figure 21) in comparison with t h e parabola of C02 growth might b e explained as a result of t h e lag between rising COz concentrations and rising global temperatures.

5. CONCLUSIONS

A method was developed f o r finding a long-term tendency in t h e atmospheric concentration of CO2. In p a r t i c u l a r , it w a s shown t h a t on a long-time interval t h e

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polynomial a p p r o a c h is b e t t e r than t h e exponential one, which means t h a t t h e prediction f o r c e of a parabolic model i s s t r o n g e r t h a n a n exponential one. The constancy of t h e rate of growth of t h e statistically s t a b l e c h a r a c t e r i s t i c of t h e main direction of a s e r i e s of concentrations of C02 f o r t h e Mauna Loa station during t h e l a s t 28-years was also shown.

More p a r t i c u l a r r e s u l t s were: t h e amplitude of t h e seasonal oscillation on g r a p h s of t h e monthly e f f e c t considerably i n c r e a s e s from t h e South Pole to t h e North Pole; to obtain t h e e f f e c t s of annual t r e n d s , a 12-month interval i s a statistically s t a b l e interval; oscillation of t h e monthly e f f e c t s f o r t h e n o r t h e r n and south- e r n hemisphere h a s opposite phases.

The main problem of t h e possible existence of a statistically confident c o r r e - lation between long-term t r e n d s in t h e observation s e r i e s of concentrations of CO, and t h e main climatic v a r i a b l e t e m p e r a t u r e remains open.

ACKN(IWLEDGrnENTS

The a u t h o r s wish t o e x p r e s s t h e i r recognition of D. Keeling, S c r i p p s Institu- tion of Oceanography, f o r his pioneer work at Mauna L o a . They would also like t o thank Oak Ridge National Laboratory f o r providing a t a p e of t h e d a t a used in this analysis.

The a u t h o r s would a l s o like to thank P r o f e s s o r s Bo Diias and Ted Munn f o r t h e i r advice and support.

REF%BENCES

Antonovsky, M.Ya. (1986) The modern a s s e s s m e n t of carbon d i o x i d e a n d o t h e r t r a c e g a s roles i n climate v a r i a t i o n s . WMO/TD No.151, December. Env. Poll.

Mon. & Res. Prog. No.45.

BMPD (BioMeDical Package), Statistical Software Manual, 1440 Supulveda Blvd..

Palo Alto, Ca.. USA.

Gemon, R.H.,

J.T.

P e t e r s o n , W.D. Komyr (1986) Atmospheric C02 c o n c e n t r a t i o n s . NOAA, GIMS, Flask and Continuous Network. CDIAC, NDP 005, Oak Ridge N a t . Lab., Tenn., USA.

Huber, P.J. (1981) Robust S t a t i s t i c s , Wiley & Sons, NY.

Keeling, C.D. (1984) Atmospheric a n d oceanic measurement n e e d e d f o r e s t a b l i s h - i n g d a t a base i n the potential effect of CO, i n d u c e d c l i m a t i c changes of Alaska. Proceedings of University of Alaska.

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Keeling, C.D. (1987) Hourly c d i b r a t i o n a t m o s p h e r i c C02 c o n c e n t r a t i o n 1958- 1988. Mauna Loa Observatory. CDIAC NDP 043, Oak Ridge Nat. Lab., Tenn., USA.

Pearman, G., P. Hyson (1981) The annud v a r t a t i o n of atmospheric C 0 2 concen- t r a t i o n observed i n the n o r t h e r n hemtsphere. Journal of Geophysical Research. 86: 40:9839-9843.

Tukey. J.W. (1977) E z p l o r a t o + y Data A n d y s t s . Reading, M.A.: Addison-Wesley.

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Figure 1: Decomposition of matrix of data on effects by method of median smoothing.

c,

-

typical (characteristic) value f o r a given station;

c l

-

year effect (variation);

c

-

month effect (variation);

E

-

random fluctuation associated with other factors.

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F i g u r e 2 : Amplitude s p e c t r u m of mean-monthly c o n c e n t r a t i o n of C O z , B a r r o w sta- t i o n , 1973-1982.

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Figure 4: Amplitude s p e c t r u m of r e s i d u a l s of c o n c e n t r a t i o n s of C02 , Barrow ski- tion, 1973-1982.

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F i g u r e 5 : Amplitude s p e c t r u m of monthly e f f e c t s of c o n c e n t r a t i o n , Barrow sta- t i o n , 1973-1982.

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F i g u r e 6: Amplitude s p e c t r u m of mean monthly e f f e c t s of c o n c e n t r a t i o n , of C 0 2 with s u b t r a c t e d y e a r e f f e c t , NWR (Niwot Ridge).

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F i g u r e 7: Amplitude s p e c t r u m of r e s i d u a l s of c o n c e n t r a t i o n s o f C02, NWR (Niwot R i d g e ) s t a t i o n , 1976-1982.

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Figure 8: Dependence of characteristic value of concentration of COz from altitude of the stations of Global Monitoring of climate change NOAA/GMCC, 1968-1982.

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F i g u r e 9: I n c r e a s e of y e a r e f f e c t s f o r f o u r s t a t i o n s of continuous monitoring:

BRW, MLO, SMO, S P O s t a t i o n s . 1971-1982.

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F i g u r e 1 0 : B e h a v i o r of mean-month e f f e c t s of c o n c e n t r a t i o n of C02 f o r f o u r s t a - t i o n s of c o n t i n u o u s monitoring: BRW, MLO, S M O , SPO, 1971-1982.

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F i g u r e 11: Approximation of a c u r v e of y e a r e f f e c t s of c o n c e n t r a t i o n of C02 (o- o b s e r v e d ) by exponential function ( p - p r e d i c t i o n ) o n i n t e r v a l of time 1958-1985.

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Figure 12: Behavior of r e s i d u a l s of exponential approximation of c u r v e of year e f f e c t s of c o n c e n t r a t i o n s of C o p during 1958-1985.

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Figure 1 3 : Approximation of c u r v e of y e a r e f f e c t s of c o n c e n t r a t i o n of C 0 2 (o- o b s e r v e d ) by polynomial function (p-predicted) o n time i n t e r v a l 1958- 1985.

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Figure 1 4 : Behavior of r e s i d u a l of polynomial approximation of c u r v e of y e a r ef- f e c t s of c o n c e n t r a t i o n s of COz d u r i n g 1958-1985.

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SHAPE OF THE MODEL STANDARD DEVIATIONS

I

^c^(t)

⁼

^0.02t2

⁼

^0.55t

⁺

^317.74

i

Figure 15: The models of the behavior of year effects of concentrations of COz Mouna-Loa station, 1958-1985.

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F i g u r e 16: P r e d i c t i o n of t h e b e h a v i o r of y e a r e f f e c t s of c o n c e n t r a t i o n of C O E b y polynomial model, c o n s t r u c t e d by d a t a f o r t h e f i r s t 5 - y e a r s .

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p l = 3 1 4 . L 9 5 2 1 2 pi?

=

^{0 .}Q O L 5 6 1 p 5 = 0. U O O i 3 2

Figure 16': G r a p h of o b s e r v e d a n d p r e d i c t e d functions al e x p a2t

+

a g f o r 28 y e a r s . P r e d i c t i o n of t h e b e h a v i o r of y e a r e f f e c t s of c o n c e n t r a t i o n of C02 with e x p o n e n t i a l model, c o n s t r u c t e d by d a t a f o r f i r s t 5 y e a r s .

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Figure 17: P r e d i c t i o n of t h e b e h a v i o r of y e a r e f f e c t s of c o n c e n t r a t i o n of COz polynomial model, c o n s t r u c t e d by d a t a f o r f i r s t 15 y e a r s .

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Figure 17': G r a p h of o b s e r v e d a n d p r e d i c t e d functions of al e x p a2t

+

a g for 28 y e a r s . P r e d i c t i o n of t h e b e h a v i o r of y e a r e f f e c t s of c o n c e n t r a t i o n of COz with exponential model, c o n s t r u c t e d by d a t a for f i r s t 15 y e a r s .

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F i g w e 18: Amp!itude s p e c t r u m of mear,-monthly t e m p e r a t n r e s . !fauna-50a S ~ Z -

tiofis, 1958-1 985.

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r e 9 Arnp!itude s p e c t r u n : of mean-monthly t e m p e r a t u r e s with s ~ b s t r u c t e c y e a r e f f e c t , Yanna L o a . 1958-1985.

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F i g u r e 20: B e h a v i o r of mean-monthly e f f e c t s of t h e t e r n p e ~ a t u r e Y a 3 ~ n a - L o a s t z - t i o n , 1350-1-985.

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-. : : c u r e 21: S e h a v i o r of y e z r e f f e c t s cf x e z ~ - r c n t h l y te,r,perat;lre. Ya2r.z 1.02 s t ? - t i o n , 1958-1985.

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F i g u r e 22: Amp!itude s 2 e c t r u m of y e a r e f f e c t s of t e m p e r a t u r e . Vaur,a Loz statior., 1958-1985.

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F i g u r e 23: A ~ p l i t u d e s p e c t r u m o f y e a r e f f e c t s of t e m p e r a t u r e with s u b s t r u c t e d

;arabo!ic trend, Mauna 30a statior,, 'L958-1985.