Estimation of Local Values of Monthly Mean Temperature, Effective Temperature Sum and Precipitation Sum in Europe

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

ESTIMATION OF LOCAL VALUES OF MONTHLY MEAN TEMPERATURE, EFFECTWE TEMPERATURE SUM

AND PRECIPITATION SUM IN EUROPE

Helena R e n t t o n e n A nnikki Makela

July 1988 WP-88-061

I n l e r n a t ~ o n a l l n s t ~ t u t e for A p p l ~ e d Systems Analys~s

ESTIMATION OF LOCAL VALUES OF MONTHLY MEAN TEMPERATURE, EFFECTIVE TEMPERATURE SUM

AND PRECIPITATION SUM IN EUROPE

Helena Henttonen A nnikki Makela

July 1988 WP-88-061

Working Papers are interim reports on work of the International Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute or of its National Member Organizations.

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

Preface

This study c o n t r i b u t e s to t h e c o n s t r u c t i o n of t h e environmental d a t a b a s e of t h e Regional Acidification INformation and Sfmulatin (RAINS) m o d e l . I t u s e s long- t e r m d a t a from E u r o p e a n w e a t h e r s t a t i o n s f o r calculating local values of tempera- t u r e , p r e c i p i t a t i o n a n d t h e e f f e c t i v e sum of y e a r l y t e m p e r a t u r e . The method p r e s e n t e d in t h i s p a p e r involves t h r e e dimensions; latitude, longitude, and a l t i t u d e , t h u s accounting f o r t h e l a p s e rates of t e m p e r a t u r e and t h e v a r i a t i o n of p r e c i p i t a - tion with altitude. This f e a t u r e i s p a r t i c u l a r l y a t t r a c t i v e f o r applications in Cen- t r a l E u r o p e w h e r e t h e topography i s marked with high altitudinal g r a d i e n t s .

The method i s c u r r e n t l y available to all models included in t h e RAINS system, and i t h a s a l r e a d y been used in t h e d i r e c t f o r e s t impact submodel. A s t h e calcula- tions of local values of t h e meteorological v a r i a b l e s are not r e s t r i c t e d to a p a r t i c - u l a r g r i d size, t h e method h a s also wider applicability independent of t h e RAINS system.

R.W. Shaw

L e a d e r , Acid Rain P r o j e c t

Acknowledgements

The authors a r e indebted t o Timothy Carter, Pekka Kauppi and Roderick Shaw for their constructive comments on the manuscript.

Abstract

The p r e s e n t p a p e r p r e s e n t s a method f o r estimating t h e local values of meteorological v a r i a b l e s from measurements in t h e vicinity of t h e s u b j e c t point.

Two interpolation methods are considered: t h e moving a v e r a g e s method, which cal- c u l a t e s a weighted a v e r a g e of o b s e r v a t i o n s in t h e neighbourhood of t h e s u b j e c t point, and t h e combined method, which improves t h e moving a v e r a g e s estimate by utilizing t h e s t a t i s t i c a l d e p e n d e n c e on latitude and a l t i t u d e of t h e v a r i a b l e s .

The methods are applied t o t h e estimation of t h e local values of monthly mean t e m p e r a t u r e , monthly p r e c i p i t a t i o n sum, and t h e e f f e c t i v e t e m p e r a t u r e sum in Eu- r o p e . The input d a t a consists of 30-year time s e r i e s of monthly values from a net- work of meteorological s t a t i o n s , comprising 666 s t a t i o n s f o r monthly mean tem- p e r a t u r e and 517 f o r precipitation.

The methods are t e s t e d by s u b t r a c t i n g o n e s t a t i o n at a time from t h e o b s e r v a - tion network and calculating t h e values of t h e climatic v a r i a b l e s from t h e rest of t h e d a t a . The r o o t mean s q u a r e e r r o r (RMSE) of t h e smoothed mean t e m p e r a t u r e in t h e period May-August i s approximately 0 . 7 "C, and t h a t of t h e p r e c i p i t a t i o n sum in t h e o r d e r of 70mm. In areas with a d e n s e r network of observations, t h e RMSE i s lower.

-

vii

-

T a b l e o f C o n t e n t s

MTRODUCTION U T E R I A L METHODS

Mean T e m p e r a t u r e and Precipitation E f f e c t i v e T e m p e r a t u r e Sum

RESULTS

CONCLUDING RJmAF2KS REFERENCES

APPENDIX

Estimation ot Local Values of Monthly Mean Temperature. Etrective Temperature

Sum

and Precipitation

Sum

in Europe

Helena Henttonen a n d A n n i k k i Ma" k e l h

INTRODUCTION

One of t h e most c r i t i c a l components of l a r g e s c a l e ecological models, such as t h o s e included in t h e Regional Acidification INformation and Simulation System (IIAINS) (Alcamo et a l . , 1987), is t h e availability of r e l i a b l e input d a t a in t h e re- gional s c a l e . Even if regional d a t a a r e available, t h e y are not always in a form d i r e c t l y applicable t o t h e model. In t h e c a s e of meteorological d a t a , i t is o f t e n a question of converting t h e information from a network of s t a t i o n s t o a systematic grid-based d a t a system.

Ojansuu and Henttonen (1983) p r e s e n t e d a method which aims at efficient and r e l i a b l e prediction of local values of climatological v a r i a b l e s from o b s e r v a t i o n s at neighbouring w e a t h e r stations. The method utilizes t h e s t a t i s t i c a l dependence of t e m p e r a t u r e on both latitude and altitude. I t s potential applications involve meteorological time s e r i e s as well as long-term a v e r a g e s . The method was t e s t e d using d a t a from meteorological s t a t i o n s in Finland, and i t h a s now b e e n i n c o r p o r a t - ed in t h e Finnish f o r e s t inventory and management system.

The o b j e c t i v e of t h e p r e s e n t study is t o assess t h e applicability of t h e method in a l l E u r o p e , as r e g a r d s calculating local values of monthly mean t e m p e r a t u r e and p r e c i p i t a t i o n , and t h e e f f e c t i v e t e m p e r a t u r e sum

(ETS,

d e g r e e days). In p a r t i c u - l a r , w e focus on t h e applications w e envisage in connection with t h e RAINS model.

This sets t h e emphasis on predicting monthly mean values, b u t we a l s o briefly con-

- 2 - s i d e r examples on applications t o time s e r i e s .

MATERIAL

F o r t h e mean v a l u e calculations, w e used 30-year means of t h e monthly mean values of t h e meteorological v a r i a b l e s . These were obtained from s e v e r a l s o u r c e s , as explained in Table 1. A t o t a l of 666 s t a t i o n s were used f o r o b s e r v a t i o n s of long- t e r m a v e r a g e t e m p e r a t u r e a n d 517 f o r t h o s e of p r e c i p i t a t i o n .

In addition to long-term mean values, time s e r i e s of t h e monthly means were available. The Austrian Meteorological Institute provided measurements of monthly mean t e m p e r a t u r e a n d p r e c i p i t a t i o n from 6 3 s t a t i o n s o v e r t h e p e r i o d 1950-1984, a n d t h e British Meteorological Office t h o s e from 1 0 1 s t a t i o n s o v e r t h e p e r i o d 1959-1984. The y e a r b o o k s of t h e Finnish Meteorological I n s t i t u t e w e r e used t o s e l e c t 88 s t a t i o n s f o r values of monthly mean t e m p e r a t u r e a n d p r e c i p i t a t i o n o v e r 1950-1982. Note t h a t t h e s e s t a t i o n s were not used in t h e mean value a n a l y s i s un- l e s s t h e s e r i e s c o v e r e d more t h a n 15 y e a r s . The information on t h e s t a t i o n s comprises l a t i t u d e , longitude a n d altitude. A l i s t of t h e s t a t i o n s a n d t h e i r locations i s p r e s e n t e d in Appendix 1.

METHODS

Mean Temperature and Precipitation

The simplest method of smoothing i s t o c a l c u l a t e a weighted a v e r a g e of o b s e r - vations in t h e neighbourhood of t h e s u b j e c t point (method of m o v i n g a v e r a g e ) (0 jansuu a n d Henttonen, 1983).

The r e l a t i v e weights are c a l c u l a t e d using t h e formula

wi=l

^{0. zi} o t h e r w i s e

^-

^z

^<

^500m

Table

1.

Number of o b s e r v a t i o n s from d i f f e r e n t s o u r c e s by c o u n t r y .

1

Albania 1 1 1

I 1 I I I 1 1 1

S o u r c e of

I

c o u n t r y r e f e r e n c e

Austria Belgium

(9)

(2) (5)

(1)

Bulgaria

Czechoslovakia

1

^Denmark

(

^{E i r e}

5 2

I I Fed. Rep. of Germany Finland

I

F r a n c e

Luxembourg , I /

1 1 1

(6) (3)

4 3 5 5

!

German Dem. Rep.

I G r e e c e

/

Hungary

1

i

Iceland

I

Netherlands 1 3 3 1

1 1 I l / I I

(4)

2

18 8 2 1

/

^Norway

1

¹⁵⁴

(7)

4 2

4 8

(8)

I

1 9

15

9

I

1

^{1taly i 16}

M I f l l e r (1982), rnean values o v e r 1931-1960

Kllmadaten von Europa (1980), monthly mean values o v e r 1931-1960 Klimadaten von Europa (1982), monthly rnean v a l u e s o v e r 1931-1960 Kllmadaten von Europa (1981), monthly mean values o v e r 1931-1960 Bruun (1962). monthly mean t e m p e r a t u r e s o v e r 1931-1960

T a e s l e r (1972), mean v a l u e s o v e r 1931-1960

Meteorological y e a r b o o k of Finland, volumes 51-80, P a r t 1 , monthly mean v a l u e s o v e r 1951-1980

British Meteorological Office, monthly mean values o v e r 1956-1984 (digital) Austrlan Meteorological I n s t i t u t e , monthly rnean values o v e r 1951-1980 (digital)

37

56

I I

I

^{Rumania 5 5}

Spain

1 Sweden Switzerland USSR

I United Kingdom Yugoslavia

1 3 1 ⁱ 3

I 14

11 4 29 17 6

3 I

9

9

19

I

80

43

where

wi

=

weight f o r t h e o b s e r v a t i o n a t s t a t i o n i

4 ⁼

t h e d i s t a n c e between t h e s t a t i o n a n d t h e s u b j e c t point

zi

=

a l t i t u d e of s t a t i o n i

z

=

a l t i t u d e of t h e s u b j e c t point max

=

maximum d i s t a n c e

-

p a r a m e t e r Q

=

p a r a m e t e r

If t h e r e are no measurements within t h e r a d i u s ^dm,,, t h e n e a r e s t o b s e r v a t i o n i s s e a r c h e d and given t h e weight 1. The p a r a m e t e r s d

,,,

and q are determined by t r i a l and e r r o r to give t h e b e s t estimates. The c h o i c e of t h e s e p a r a m e t e r s depends on t h e density of t h e d a t a network.

The method d o e s not a c c o u n t f o r s i t e d i f f e r e n c e s in t o p o g r a p h y and location among t h e s t a t i o n s a n d t h e s u b j e c t points. The reliability of t h e smoothed r e s u l t can b e i n c r e a s e d by utilizing t h e s t a t i s t i c a l dependence on l a t i t u d e and a l t i t u d e of t h e v a r i a b l e s involved (Combined method) (Ojansuu and Henttonen, 1983).

The combined method w a s applied t o t h e monthly mean t e m p e r a t u r e . A l i n e a r r e g r e s s i o n model w a s f i r s t formulated f o r d e s c r i b i n g t h e s t a t i s t i c a l dependence of a v e r a g e t e m p e r a t u r e on t h e a b o v e v a r i a b l e s . This t u r n e d o u t t o b e s t r o n g l y biased with r e s p e c t t o t h e a l t i t u d e term. The bias d i s a p p e a r e d upon t h e introduction of a t e r m non-linear in t h e altitude:

where

yi

=

l a t i t u d e of s t a t i o n i

zi

=

a l t i t u d e of s t a t i o n i

t k i

=

a v e r a g e t e m p e r a t u r e of month k at s t a t i o n i

& k i

=

estimation e r r o r

The dependent v a r i a b l e w a s t h e long-term a v e r a g e t e m p e r a t u r e . The parame- t e r s

BOB.. .

,

O3

of model (2) were estimated f o r e a c h month s e p a r a t e l y , using t h e

method of l e a s t s q u a r e s . The AR p r o g r a m (Derivative-Free Nonlinear Regression, Dixon et al., 1985) of t h e BMDP l i b r a r y was used in t h e estimation.

The a b o v e s t a t i s t i c a l d e p e n d e n c e (Equation 2) and t h e moving a v e r a g e smooth- ing method (Equation 1 ) are combined as follows:

(1) The estimates of monthly mean t e m p e r a t u r e s at t h e meteorological s t a t i o n s and at t h e s u b j e c t point are calculated using r e g r e s s i o n model (2).

(2) The d i f f e r e n c e s between t h e measured values and t h e estimates obtained with t h e model are smoothed with t h e weights given by Equation (1) in t h e neigh- bourhood of t h e s u b j e c t point.

(3) The r e s u l t given by t h e r e g r e s s i o n model i s c o r r e c t e d with t h e smoothed d i f f e r e n c e s at t h e s u b j e c t point.

E f f e c t i v e T e m p e r a t u r e Sum

The f f e c t i v e t e m p e r a t u r e sum (ETS) i s defined as follows:

where Ti

=

daily mean t e m p e r a t u r e To

=

t h r e s h o l d t e m p e r a t u r e

The calculation of t h e e f f e c t i v e t e m p e r a t u r e sum from t h e monthly mean tem- p e r a t u r e s comprises estimating t h e annual c o u r s e of mean t e m p e r a t u r e (daily a v e r a g e s ) a n d summing u p t h e a v e r a g e t e m p e r a t u r e s t h a t e x c e e d t h e t h r e s h o l d t e m p e r a t u r e chosen (Ojansuu a n d Henttonen, 1983).

In smoothing t h e annual c o u r s e of t e m p e r a t u r e , a smoothed c u r v e i s f i r s t cal- culated which p a s s e s t h r o u g h t h e monthly mean t e m p e r a t u r e at t h e c e n t r e of t h e month. The smoothing employs a spline function, which i s found using t h e subpro-

gram ICSICU of t h e IMSL p r o g r a m l i b r a r y (TMSL L i b r a r y 2 , 1977). The d i f f e r e n c e between t h e monthly mean t e m p e r a t u r e obtained from t h i s smoothing function, and t h e original mean t e m p e r a t u r e , i s f u r t h e r smoothed with a spline function, and t h e d i f f e r e n c e i s used f o r c o r r e c t i n g t h e smoothing function f o r t h e annual c o u r s e of t e m p e r a t u r e .

The resulting spline function gives t h e c o u r s e of t h e daily t e m p e r a t u r e as a v e r a g e d o v e r t h e 30-year p e r i o d in question. When calculating t h e a v e r a g e ETS o v e r t h e p e r i o d , t h e between-year v a r i a n c e of t h e daily t e m p e r a t u r e s i s a l s o ac- counted f o r . This p r o c e d u r e i s e s s e n t i a l f o r t h o s e days when t h e 30-year a v e r a g e t e m p e r a t u r e i s n e a r t h e t h r e s h o l d , 5 "C. The p r o g r a m only u s e s t w o values of vari- a n c e , however; o n e f o r t h e e a r l i e r and o n e f o r t h e l a t e r half of t h e y e a r . A s no o t h e r daily d a t a were available, t h e v a r i a n c e s were estimated from t h e Finnish d a t a .

Figures 1 a n d 2 i l l u s t r a t e t h e year-to-year variation in t h e e f f e c t i v e tempera- t u r e sum f o r locations in Finland and Austria.

RESULTS

The methods were t e s t e d by s u b t r a c t i n g o n e s t a t i o n at a time from t h e o b s e r - vation network and calculating t h e values of t h e climatic v a r i a b l e s of t h a t s t a t i o n from t h e rest of t h e d a t a . This p r o c e d u r e underestimates t h e reliability of t h e smoothing, as t h e o b s e r v a t i o n network i s actually more d e n s e t h a n t h e o n e used f o r testing.

Table 2 shows t h e root mean s q u a r e e r r o r (RMSE) of t h e smoothed mean tem- p e r a t u r e and p r e c i p i t a t i o n sum in May-August f o r t h e methods p r e s e n t e d above.

When using t h e combined method f o r t h e areas of dense network, with q

=

2 a n d dm,, = 250 km in Equation (I), t h e values of RMSE and t h e corresponding l a r g e s t errors of mean t e m p e r a t u r e in May-August were as shown in Table 3.

8 0 0 :

! . . . . I . " ' I r

. ' . , . . . . , . . . . , . . . . ,

1950 1955 1960 1965 1970 1975 1980 1985

Y E A R

Figure 1. Effective t e m p e r a t u r e sum in 1950-1982 and as c a l c u l a t e d f o r t h e 'mean y e a r ' with r e s p e c t t o monthly mean t e m p e r a t u r e s in t h e period (horizontal line). Location: latitude 63" N, longitude 24" E , altitude 130 m. Threshold t e m p e r a t u r e w a s 5 "C.

In Sweden, Finland and Norway, a l l t h e s t a t i o n s with e r r o r s g r e a t e r t h a n o n e d e g r e e were located o n t h e c o a s t .

Table 4 displays t h e reliability f i g u r e s f o r t h e whole d a t a set by month, ob- tained with t h e combined method with q = 2 and d,,,=250 km in Equation (1). Figure 3 shows t h e e r r o r of t h e estimate of mean t e m p e r a t u r e in May-August as a function of t h e a l t i t u d e of t h e s t a t i o n , using t h e same method. Figure 4 shows t h e same er- r o r s in r e l a t i o n to latitude.

CONCLUDING REMARKS

The comparison between t h e combined method (Equations 1 and 2) and t h e mov- ing a v e r a g e s method (Equation 1) (Table 2) shows c l e a r l y t h a t t h e combined method i s more r e l i a b l e , f o r t h e monthly mean t e m p e r a t u r e . F o r f u r t h e r improving t h e re- liability, t h e number of explaining v a r i a b l e s should b e i n c r e a s e d (e.g. vicinity of

Y E A R

Figure 2. Effective t e m p e r a t u r e sum in 1950-1984 and as calculated f o r t h e 'mean y e a r ' with r e s p e c t t o monthly mean t e m p e r a t u r e s in t h e period (horizontal line). Location: latitude 48" N , longitude 15" E, altitude 300 m. Threshold t e m p e r a t u r e was 5 "C.

s e a and direction of t h e slope). Some new smoothing methods could a l s o b e con- s i d e r e d (e.g., 'universal kriging', Ripley, 1981). If t h e combined method i s applied t o precipitation also, a d e n s e r measurement network should b e used in o r d e r t o im- p r o v e t h e p r e s e n t results.

The p r e s e n t a p p r o a c h i s applied t o a s p a r s e network of d a t a f o r most of Eu- r o p e , and a d e n s e r network f o r Austria, Britain, Finland, Norway and Sweden.

Comparing t h e root mean s q u a r e e r r o r s of Table 2 and Table 3, i t i s a p p a r e n t t h a t increasing t h e number of observation stations improves t h e reliability of t h e results. E a r l i e r work shows, however, t h a t t h e r e i s a limit to decreasing t h e esti- mation e r r o r t h i s way. Ojansuu and Henttonen (1983) concluded t h a t in t h e case of Finland, about 30 stations were sufficient to stabilize t h e root mean s q u a r e error.

if f u r t h e r d a t a are i n c o r p o r a t e d , t h e question of changing t h e p a r a m e t e r values a r i s e s . The b e s t choice of t h e p a r a m e t e r s q and dm,, in t h e weighting func-

Table 2. The root mean square e r r o r (RMSE) of the smoothed mean tempera- ture and precipitation in May-August.

Average temperature (OC)

moving averages 0.5 2.16 1.98 1.69 1.69 1.66 1.66

1.0 2.19 2.02 1.71 1.68 1.67 1.65

2.0 2.25 2.09 1.78 1.71 1.68 1.66

0.5 0.73 0.69 0.68 0.69 0.71 0.74

1.0 0.73 0.69 0.67 0.68 0.69 0.71

2.0 0.73 0.69 0.67 0.66 0.67 0.68

combined method

Precipitation (mm) moving averages

Table 3. RMSE and the corresponding largest e r r o r s of mean temperature in May-August ( q

=

2, dm,,

=

250).

RMSE. "C number of abs (maximum e r r o r ) , ^{O C ,} and station stations (station number in parentheses)

Sweden and Finland 0.44 143 1.7

Svenska Hogarna (456)

Norway 0.56 163 2.9

Jan Mayen ( 4 )

United Kingdom 0.38 4 9 0.9

Lerwick (48)

Austria 0.51 42 1.3

Vils (815)

tion (Equation I), in principle, depends on the density of the measurement network.

As shown by the results in Table 2, however, the RMSE is not very sensitive to these parameters. The most important requirement seems to be that the radius dm,, is not considerably smaller than the average distance between the observa-

Table 4. Bias a n d r o o t mean s q u a r e e r r o r (RMSE) of t h e smoothed e s t i m a t e s of monthly mean t e m p e r a t u r e a n d p r e c i p i t a t i o n by month. Combined method ( d

,,, ⁼

^{250 km, q}

⁼

^2).

J a n u a r y F e b r u a r y March April May June

I

Mean t e m p e r a t u r e

b i a s -.02 0.00 0.00 0.00 -.01 -.03

RMSE 1.54 1.32 0.91 0.58 0.65 0.74

P r e c i p i t a t i o n

b i a s -1.3 -1.1 -1.0 -1.6 -1.7 -2.3

RMSE 27.1 23.5 19.9 18.9 16.8 18.6

8

I

^{July August} S e p t e m b e r O c t o b e r November December ^I

(

I

I Mean t e m p e r a t u r e

I

i

b i a s -.02 -.02 -.OO 0.00 -.01 -.02

RMSE 0.84 0.69 0.61 0.87 1.12 1.44

P r e c i p i t a t i o n

bias -2.9 -2.2 -0.8 -0.0 -0.5 -0.6 1

RMSE 21.6 18.9 21.1 24.1 27.1 _30.4

I

_I

tion points, to make s u r e t h a t t h e c i r c l e always c o v e r s some points. From t h e n o n , t h e r e s u l t s are n o t v e r y s e n s i t i v e t o f u r t h e r i n c r e a s i n g t h e r a d i u s , b e c a u s e of t h e efficiency of t h e r e l a t i v e weighting by d i s t a n c e .

A s r e g a r d s t h e r e g r e s s i o n equation (Equation 2), o u r e x p e r i e n c e i n d i c a t e s t h a t if t h e additional d a t a merely s e r v e s t o make t h e network d e n s e r , t h e n t h e same p a r a m e t e r s as b e f o r e c a n b e s a f e l y used f o r both t h e r e g r e s s i o n a n d t h e weighting of t h e points. However, if e n t i r e l y new areas are included, t h e r e g r e s - sion p a r a m e t e r s may h a v e to b e r e c a l c u l a t e d . d u e to possible d i f f e r e n c e s in t h e macroclimate of t h e newly i n c o r p o r a t e d area.

The improvements indicated a b o v e may b e n e c e s s a r y if t h e system i s a p p l i e d t o small s c a l e s t u d i e s with high r e q u i r e m e n t of a c c u r a c y . F o r a l a r g e scale model,

4

E R 3 R 0 R

2 I N D E G E 0 E S C

-

¹

E L S - 2

I U S

-3

0 500 1000 1500 2000 2500 3000

A L T I T U D E I N METRES

Figure 3. Estimation errors of the mean temperature f o r the period May-August a s a function of altitude. The figures indicate number of station.

Figure 4. Estimation errors of the mean temperature f o r t h e period May-August a s a function of latitude. The figures indicate number of station.

4

-

R E 3 - R 0 R

2

-

I N D l - E C

E 0 E S

- I - C E L

s -2

-

u

I ^' S -3

-

115

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192 ? 161 159

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3 5 40 4 5 5 0 55 60 65 7 0 75

L A T l TUDE

however, t h e p r e s e n t l e v e l of a c c u r a c y seems sufficient in m o s t of t h e f o r e s e e a b l e situations.

REFERENCES

Alcamo, J., M. Amann, J.-P. Hettelingh, M. Holmberg, L. Hordijk, J . Kamari, L.

Kauppi, P . Kauppi, G . Kornai a n d A. Makela (1988). Acidification in E u r o p e : A simulation model f o r evaluating c o n t r o l s t r a t e g i e s . IIASA R e s e a r c h R e p o r t RR-88-2. R e p r i n t e d f r o m Ambio, 16(5).

Austrian Meteorological I n s t i t u t e . Monthly m e a n v a l u e s of air t e m p e r a t u r e a n d m o n t h l y v a l u e s o f p r e c i p i t a t i o n over 1951-1980. Magnetic t a p e .

British Meteorological Office. Monthly m e a n v a l u e s of air temperature a n d m o n t h l y v a l u e s o f p r e c i p i t a t i o n o v e r 1956-1984. Magnetic t a p e .

Bruun, I. (1962). The A i r Temperature i n Norway 1931-1960. Climatological Sum- m a r z e s f o r Norway. Det N o r s k e Meteorologiske Institutt. Oslo 1962.

Dixon, W.J., M.B. Brown, L. Engelman, J.W. F r a n e , M.A. Hill, R.I. J e n n r i c h a n d J . D . Toporek (1985). BMDPStatistical Soptware. University of California P r e s s . IMSL-Library 2, R e f e r e n c e Manual, Edition 6 (1977). I n t e r n a t i o n a l Mathematical

a n d S t a t i s t i c a l L i b r a r y , Inc. Houston, Texas.

Klimadaten von E u r o p a . Teil I: Nord-, West- und Mitteleuropa (Climatic d a t a f o r Eu- r o p e . Volume I: N o r t h , West, a n d C e n t r a l E u r o p e . In German) (1980). Compiled by M a r g r e t Kalb a n d Hermann Noll. D e u t s c h e r Wetterdienst.

Kilmadaten von E u r o p a . Teil 11: Sudwesteuropa und Mittelmeerlander (Climatic d a t a f o r E u r o p e . Volume 11: Southwest E u r o p e a n d t h e M e d i t e r r a n e a n c o u n t r i e s . In German). (1981). Compiled by B a r b a r a Hanle a n d M a r g r e t Kalb. D e u t s c h e r Wetterdienst.

Klimadaten von E u r o p a . Teil 111: Sudost- und O s t e u r o p a (Climatic d a t a f o r E u r o p e . Volume 111: S o u t h e a s t a n d E a s t E u r o p e . In German). (1982). Compiled by Mar- g i t t a Baucus a n d M a r g r e t Kalb. D e u t s c h e r Wetterdientst.

Meteorological Yearbook of Finland. Volumes 50-80. P a r t 1. Finnish Meteorological I n s t i t u t e .

Miiller, M.J. (1982). Selected Climatic Data f o r a Global Set of S t a n d a r d S t a t i o n s for Vegetation Science. D r . W. Junk P u b l i s h e r s .

Ojansuu, R., a n d H. ja Henttonen (1983). Kuukauden keskilampotilan, lamposumman ja s a d e m a i k a n p a i k a l l i s t e n a r v o j e n johtaminen ilmatieteen l a i t o k s e n mittaus- t i e d o i s t a (Derivation of t h e local v a l u e s of monthly mean t e m p e r a t u r e , e f f e c - t i v e t e m p e r a t u r e sum, a n d p r e c i p i t a t i o n , f r o m o b s e r v a t i o n s of t h e Finnish Meteorological I n s t i t u t e . In Finnish). S i l v a Fennica 17(2),143-160.

Ripley, B.D. (1981). S p a t i a l S t a t i s t i c s . John Wiley.

T a e s l e r , R. (1972). Klimadata f 6 r S v e r i g e (Climatic d a t a f o r Sweden. I n Swedish).

Ed: Ann-Kristin Nord. ISBN 91-540-2012-3.

Appendix

1.

Location of the meteorological stations and sources of information (A) = number of station,

(B)

= latitude,

(C)

= longitude,

(D)

= altitude, m.

The number after station name refers to the source (see p. 2).

(E)

after station name refers to stations out of use.

(F)

after station name refers to stations lacking data on mean temperature or precipitation

( A ) ( 8 ) ( C ) ( D )

1 65.41-18.15 7. A K U R E Y R I ( 1 ) 2 65.05-14.39 40. H A L L O R M S T A D U R ( 1 ) 3 64.08-21.56 1 8 . R E Y K J A V I K ( 1 ) 4 70.59 -8.20 23. J A N M A Y E N ( 1 ) 5 70.22 31.06 10. V A R D O ( 1 ) 6 69.36 18.57 115. T R O M S O ( 1 ) 7 66.21 14.08 20. M O I R A N A ( 1 ) 8 63.25 10.27 133. T R O N D H E I M ( 1 ) 9 62.04 .9.07 643. D O M B A A S ( 1 ) 1 0 61.06 10.26 226. L I L L E H A M M E R ( 1 ) 1 1 60.12 5.19 45. B E R G E N ( 1 ) 1 2 59.56 10.44 96. O S L O ( 1 ) 1 3 59.27 8.00 7 7 . D A L E N ( 1 ) 14 58.10 7.59 23. K R I S T I A N S A N D ( 1 ) 1 5 65.50 24.09 7. H A P A R A N D A ( 1 ) 1 6 65.04 17.10 330. S T E N S E L E ( 1 ) 1 7 63.10 14.40 328. O S T E R S U N D ( 1 ) 1 8 62.28 17.57 8. H A R N O S A N D ( 1 ) 1 9 59.22 13.28 47. K A R L S T A D ( 1 ) 2 0 59.21 18.04 44. S T O C K H O L M ( 1 ) 21 57.46 14.11 9 2 . J O N K O P I N G ( 1 ) 2 2 5 7 . 4 2 11.58 31. G O T E B O R G ( 1 ) 23 57.39 18.18 28. V I S B Y ( 1 ) 2 4 56.39 16.23 12. K A L M A R ( 1 ) 2 5 55.26 1 3 . 0 3 8. M A L M O ( 1 ) 26 67.22 26.36 1 7 8 . S O D A N K Y L A ( 1 ) 2 7 65.01 25.29 17. O U L U ( 1 ) 28 64.17 27.41 1 3 4 . K A J A A N I ( 1 ) 29 63.03 21.46 6. V A A S A ( 1 ) 3 0 61.48 29.17 88. P U N K A H A R J U ( 1 ) 3 1 61.28 23.46 84. T A M P E R E ( 1 ) 32 60.12 24.55 45. H E L S I N K I ( I L M A L A ( 1 ) 33 60.07 19.54 4. M A A R I A N H A M I N A ( 1 ) 34 62.02 -6.45 20. H O Y V I K ( 1 ) 3 5 57.11 9.57 13. T Y L S T R U P ( 1 ) 36 56.05 8.55 54. S T U D S G A A R D ( 1 ) 3 7 55.41 12.33 9 . K O B E N H A V N ( 1 ) 3 8 55.17 14.47 1 1 . S A N D V I G ( 1 ) 39 60.09 -1.10 8 2 . L E R W I K ( 1 ) 4 0 58.13 -6.20 3. S T O R N O W A Y ( 1 ) 4 1 57.37 -1.50 26. R A T T R A Y H E A D ( 1 ) 4 2 57.29 -5.16 67. A C H N A S H E L L A C H ( 1 ) 4 3 56.56 -4.14 359. D A L W H I N N I E ( 1 ) 4 4 55.19 -3.12 242. E S K D A L E M U I R ( 1 ) 4 5 55.01 -1.25 33. T Y N E M O U T H ( 1 ) 46 54.39 -6.13 67. B E L F A S T ( 1 ) 4 7 54.10 -4.28 87. D O U G L A S ( 1 ) 4 8 53.45 -0.16 2. K I N G S T O N - U P O N - H ( 1 ) 4 9 52.56 1.17 54. C R O M E R ( 1 ) 50 52.29 -1.56 1 3 6 . B I R M I N G H A M ( 1 )

~ B E R S T W Y T H ( 1 )

KEW ( 1 )

D O V E R ( 1 )

P L Y M O U T H ( 1 )

ST. MARY'S ( 1 )

M A L I N H E A D ( 1 ) B E L M U L L E T ( 1 ) D U B L I N ( 1 ) K I L K E N N Y ( 1 ) V A L E N T I A ( 1 )

E E L D E ( 1 )

D E N H E L D E R ( 1 ) D E B I L T ( 1 ) B R U X E L L E S ( 1 ) B O T R A N G E - R O B E R T ( 1 ) L E L U X E M B O U R G - C I T Y ( 1 ) H E L G O L A N D ( 1 ) H A M B U R G ( 1 L U C H O W ( 1 ) B E R L I N - D A H L E M ( 1 ) H A N N O V E R - L A N G E N ( 1 ) E N

E S S E N ( 1 )

K A S S E L ( 1 ) B A D E M S ( 1 )

H O F ( 1 )

P R A N K F U R T / M A I N ( 1 ) R P O R

T R I E R ( 1 )

N U R N B E R G ( 1 ) N E U S T A D T / W E I N S T ( l ) S E R E G E N S B U R G ( 1 ) S T U T T G A R T ( 1 ) M U N C H E N ( 1 ) F R I E D R I C H S H A F E N ( 1 ) Z U G S P I T Z E ( 1 ) G R E I P S W A L D ( 1 ) B R O C K E N ( 1 ) D R E S D E N ( 1 ) E R F U R T ( 1 ) G D Y N I A ( 1 ) S U W A L K I ( 1 ) P O Z N A N ( 1 ) W A R S Z A W A ( 1 ) W R O C L A W ( 1 ) Z A M O S C ( 1 ) K R A K O W ( 1 )

P R A H A ( 1 )

P R E S O V ( 1 ) C E S K E B U D E J O V I C ( 1 )

C H E R B O U R G ( 1 )

R E I M S ( 1 )

P A R I S I L E B O U R G E ( 1 ) 1 5 8 36.06 -5.21 27.

S T R A S B O U R G ( 1 ) 1 5 9 46.30 11.21 2 7 1 .

B R E S T ( 1 ) 1 6 0 45.39 13.46 11.

R E N N E S ( 1 ) 161 45.28 9.11 147.

T O U R S ( 1 1 6 2 45.27 12.19 1.

DI J O N ( 1 ) 1 6 3 44.25 8.55 54.

N A N T E S ( 1 164 43.46 11.15 76.

L I M O G E S ( 1 ) 1 6 5 43.37 13.31 17.

C L E R M O N T - F E R R A N ( 1 ) 1 6 6 41.54 12.29 46.

L Y O N ( 1 ) 1 6 7 41.28 15.33 74.

G R E N O B L E ( 1 ) 168 40.51 14.15 25.

B O R D E A U X ( 1 ) 1 6 9 40.38 15.48 8 2 6 . T O U L O U S E ( 1 ) 1 7 0 40.28 17.13 16.

M A R S E I L L E ( 1 ) 171 39.13 9.06 75.

PIC-DU-MIDI ( 1 ) 1 7 2 38.12 15.33 54.

P E R P I G N A N ( 1 ) 1 7 3 38.07 13.21 7 1 . B A S T I A ( 1 1 7 4 37.29 14.04 570.

M O N A C O ( 1 ) 1 7 5 35.54 14.31 70.

L E S E S C A L D E S ( 1 ) 1 7 6 45.49 15.58 163.

Z U R I C H ( 1 ) 1 7 7 44.48 20.27 132.

S A N T I S ( 1 ) 178 43.52 18.26 537.

G E N E V E ( 1 ) 1 7 9 43.31 16.26 128.

L U G A N O ( 1 ) 1 8 0 43.20 1 7 . 4 9 9 9 .

W I EN ( 1 ) 181 42.00 21.06 245.

S A L Z B U R G ( 1 ) 1 8 2 43.36 24.35 110.

I N N S B R U C K ( 1 ) 1 8 3 43.12 27.55 3.

S O N N B L I C K ( 1 ) 1 8 4 42.42 23.20 550.

G R A Z ( 1 ) 1 8 5 42.09 24.45 160.

D E B R E C E N ( 1 ) 1 8 6 41.18 1 9 . 4 8 114.

B U D A P E S T ( 1 ) 1 8 7 40.51 25.53 7.

P E C S ( 1 ) 1 8 8 40.39 23.07 2.

I AS1 ( 1 ) 1 8 9 39.53 25.04 2.

C L U J ( 1 1 9 0 39.37 19.55 25.

T I M I S O A R A ( 1 ) 1 9 1 39.33 21.46 149.

S I B I U ( 1 ) 1 9 2 37.58 23.43 1 0 7 . B U C A R E S T I ( 1 1 9 3 37.31 22.21 6 6 1 . B R A G A N C A ( 1 ) 1 9 4 37.06 25.25 3.

P O R T 0 ( 1 ) 1 9 5 35.21 25.08 29.

C O I M B R A ( 1 1 9 6 35.09 33.17 218.

C A M P O H A J O R ( 1 ) 2 1 5 68.58 33.03 46.

L I S B O A ( 1 ) 216 66.05 32.59 94.

P O N T A D E G A D A ( 1 2 1 7 65.00 34.48 10.

P R A I A D A R O C H A ( 1 ) 2 1 8 61.49 34.16 40.

S A N T A N D E R ( 1 ) 2 1 9 64.30 40.30 4.

L A C O R U N A ( 1 ) 2 2 0 59.17 39.52 118.

V A L L A D O L I D ( 1 ) 2 5 5 54.42 20.37 27.

Z A R A G O Z A ( 1 ) 256 41.14 44.57 4 9 0 . B A R C E L O N A ( 1 ) 2 5 7 59.25 24.48 44.

M A D R I D ( 1 ) 2 5 8 56.58 24.04 3.

P A L M A ( B A L E A R I C ( 1 ) L . ) 2 5 9 54.53 23.53 75.

V A L E N C I A ( 1 ) 2 6 0 48.38 22.16 1 1 8 . C I U D A D R E A L ( 1 ) 261 53.52 27.32 234.

M U R C I A ( 1 ) 2 6 2 47.01 28.52 9 5 . S E V I L L A ( 1 ) 2 6 3 59.58 30.18 4.

G R A N A D A ( 1 ) 2 6 4 50.24 30.27 1 7 9 . A L M E R I A ( 1 2 6 5 55.45 37.34 1 5 6 . L A S P A L M S ( C A N ( 1 ) ( E ) 266 49.56 36.17 1 5 2 .

G I B R A L T A R T O W N ( 1 ) B O L Z A N O ( 1 ) T R I E S T E ( 1 M I L A N 0 ( 1 ) V E N E Z I A ( 1 ) G E N O V A ( 1 ) P I R E N Z E ( 1 ) A N C O N A ( 1 )

R O M A ( 1 )

P O G G I A ( 1 ) N A P O L I ( 1 ) P O T E N Z A ( 1 ) T A R A N T O ( 1 ) C A G L I A R I ( 1 ) M E S S I N A ( 1 ) P A L E R M O ( 1 ) C A L T A N I S S E T T A ( 1 ) V A L E T T A ( 1 ) ( E ) Z A G R E B ( 1 ) B E O G R A D ( 1 ) S A R A J E V O ( 1 )

S P L I T ( 1 )

M O S T A R ( 1 ) S K O P J E ( 1 ) P L E V E N ( 1 )

V A R N A ( 1 )

S O F I J A ( 1 ) P L O V D I V ( 1 ) T I R A N E ( 1 ) A L E X A N D R O P O U L I S ( 1 ) T H E S S A L O N I K I ( 1 ) L I M N O S ( 1 ) K E R K I R A ( 1 ) T R I K K A L A ( 1 ) A T H I N A I ( 1 ) T R I P O L I S ( 1 )

N A X O S ( 1 )

I R A K L I O N ( 1 ) ( E ) L E V K O S I A ( 1 ) ( E ) M U R H A N S K ( 1 ) L O U C H I ( 1 )

K E M ( 1 )

P E T R O Z A V O D S K ( 1 ) A R C H A N G E L S K ( 1 )

V O L O G D A ( 1 ) K A L I N I N G R A D ( 1 )

T B I L I S I ( 1 ) T A L L I N N ( 1 )

R I G A ( 1 )

K A U N A S ( 1 ) U Z G O R O D ( 1

M I N S K ( 1 )

K I S H I N E V ( 1 L E N I N G R A D ( 1 )

KI J E V ( 1 )

H O S K V A ( 1 ) C H A R K O V ( 1 )

P E N Z A ( 1 ) 4 1 8 57.47 14.17 99.

K A Z A N ( 1 ) 4 1 9 64.16 19.38 179.

O D E S S A ( 1 ) 4 2 0 68.27 22.30 327.

S I M P E R O P O L ( 1 ) 4 2 1 58.31 14.32 94.

Z A P O R O Z JE ( 1 ) 4 2 2 56.10 14.52 5.

ROSTOV-NA-DONU ( 1 ) 423 67.51 20.14 505.

P A T I G O R S K ( 1 ) 4 2 4 60.09 13.48 198.

V O L G O G R A D ( 1 ) 4 2 5 56.02 14.09 6.

K R A S N O D A R ( 1 ) 426 56.18 12.27 72.

S O C I ( 1 ) 4 2 7 58.21 13.08 80.

K U T A I S I ( 1 ) 4 2 8 59.18 11.56 125.

Z O N G U L D A K ( 1 ) ( E ) 4 3 0 58.25 15.38 64.

S A M S U N ( 1 ) ( E ) 431 56.05 13.14 43.

B U R S A ( 1 ) ( E ) 4 3 3 65.33 22.08 10.

A N K A R A ( 1 ) ( E ) 4 3 4 55.43 13.12 73.

E R Z U R U M ( 1 ) ( E ) 4 3 5 67.11 20.42 366.

S I V A S ( I ) (El 436 60.41 13.43 308.

U R F A ( 1 ) ( E ) 4 3 7 61.01 14.31 170.

A D A N A ( 1 ) ( E ) 4 3 8 58.33 15.05 94.

A N T A L Y A ( 1 ) ( E ) 4 3 9 63.34 19.30 6.

H A L A B ( A L E P P 0 ) ( 1 ) ( E ) 4 4 0 58.36 16.13 3.

D I M A S H Q ( 1 ) ( E ) 4 4 2 59.46 18.43 10.

B A Y R U T ( 1 ) ( E ) 4 4 3 58.46 17.00 25.

J E R U S A L E M ( 1 ) ( E ) 4 4 4 57.39 1 4 . 4 2 305.

E L A T ( 1 ) ( E ) 4 4 5 63.09 17.46 27.

C A S A B L A N C A ( 1 ) ( E ) 446 67.12 23.25 176.

R A B A T ( 1 ) ( E ) 4 4 7 68.26 18.08 5 0 8 . T A N G E R ( 1 ) ( E ) 4 4 8 60.22 15.31 152.

O U J D A ( 1 ) ( E ) 4 5 0 58.24 13.27 1 1 6 . M A R R A K E C H ( 1 ) ( E ) 4 5 1 63.19 12.06 595.

O R A N ( 1 ) ( E ) 4 5 2 62.48 13.04 5 7 5 . A L G E R ( 1 ) ( E ) 453 58.56 11.12 17.

T A R A B U L U S ( 1 ) ( E ) 4 5 4 62.31 17.26 4.

S U R T ( 1 ) ( E ) 4 5 5 62.02 14.22 360.

B A N G H A Z I ( 1 ) ( E ) 456 59.27 19.30 12.

D A R N A H ( 1 ) ( E ) 4 5 7 58.26 12.42 50.

AL-SALLUM ( 1 ) ( E ) 4 5 8 61.41 13.08 441.

A L E X A N D R I A ( 1 ) ( E ) 4 5 9 61.16 17.06 25.

C A I R O ( 1 ) ( E ) 4 6 0 57.43 11.47 4.

A L N A R P ( 6 ) 4 6 2 59.11 17.55 45.

A S K E R S U N D ( 6 ) 463 63.50 2 0 . 1 7 11.

B A R K A B Y ( 6 ) 4 6 4 59.53 17.36 18.

B I S P G A A R D E N ( 6 ) 4 6 5 59.52 17.38 13.

B J U R O K L U B B ( 6 ) 466 55.57 15.42 6.

B J O R K E D E T ( 6 ) 4 6 7 57.38 1 1 . 3 7 19.

B O R A A S ( 6 ) 4 6 9 58.23 12.20 49.

B R E D A A K R A ( 6 ) 4 7 0 57.47 16.36 5.

B R O M M A P L Y G P L A T ( 6 ) 471 59.36 16.39 3.

E D S B Y N ( 6 ) 4 7 3 56.52 14.48 168.

E G G E G R U N D ( 6 ) 4 7 4 55.26 13.50 32.

P A L U N ( 6 ) 476 59.03 12.42 60.

P R O S O N ( 6 ) 4 7 7 58.25 13.46 300.

G I S S E L A A S ( 6 ) 4 7 8 56.12 16.24 4.

G A D D E D E ( 6 ) 4 7 9 59.15 15.13 51.

G A V L E ( 6 ) 4 8 0 42.41 26.19 265.

H A G S H U L T S P L Y G P ( 6 )S 4 8 1 51.44 19.24 184.

H A L M S T A D ( 6 ) 4 8 2 50.44 15.441603.

H U S K V A R N A ( 6 ) H A L L N A S - L U N D ( 6 ) K A R E S U A N D O ( 6 ) K A L S B O R G ( 6 ) K A R L S H A M N ( 6 ) K I R U N A ( 6 )

K N O N ( 6 )

K R I S T I A N S T A D ( 6 ) K U L L E N ( 6 )

L A N N A ( 6 )

L E N N A R T S P O R S ( 6 ) L I N K O P I N G ( 6 ) L J U N G B Y H E D ( 6 ) L U L E A A P L Y G P L A T ( 6 )

L U N D ( 6 )

M A L M B E R G E T ( 6 ) M A L U N G ( 6 )

M O R A ( 6 )

M O T A L A ( 6 ) N O R D M A L I N G ( 6 ) N O R R K O P I N G ( 6 ) N O R R T A L J E ( 6 ) N Y K O P I N G ( 6 ) N A S S J O ( 6 )

O F F E R ( 6 )

P A J A L A ( 6 R I K S G R A N S E N ( 6 R O M M E H E D ( 6 ) S K A R A ( 6 ) S T O R L I E N ( 6 ) S T O R S J O ( 6 ) S T R O M S T A D ( 6 ) S U N D S V A L L P L Y G P ( 6 ) S

S V E G ( 6 1

S V E N S K A H O G A R N A ( 6 ) S A A T E N A S ( 6 )

S A R N A ( 6 )

S O D E R H A M N ( 6 ) T O R S L A N D A P L Y G P ( 6 ) S T U L L I N G E ( 6 )

U M E A A ( 6 )

U P P S A L A ( 6 ) U P P S A L A ( 6 ) U T K L I P P A N ( 6 1

V I N G A ( 6 )

V A N E R S B O R G ( 6 ) V A S T E R V I K ( 6 ) V A S T E R A A S ( 6 ) V A X J O ( 6 ) Y S T A D ( 6 ) A A M A A L ( 6 ) A A S A B O R G ( 6 ) O L A N D S S U D D E ( 6 ) O R E B R O ( 6 ) S L I V E N ( 3 ) L O D Z - L U B L I N E K ( 3 ) S N I E Z K A ( 3 )