INTERNATIONAL JOURNAL OF CLIMATOLOGY, VOL. 17, 415–426 (1997) THE SPATIAL VARIATION OF LONG-TERM MEAN GLOBAL RADIATION IN FINLAND ARI VENÄLÄINEN* AND MARTTI HEIKINHEIMO Finnish Meteorological Institute, P.O. Box 503, 00101 Helsinki, Finland Received 5 January 1996 Revised 26 August 1996 Accepted 29 August 1996 ABSTRACT 6 In this study, detailed spatial analyses of the long-term mean global radiation in Finland were made using both directly measured and indirectly estimated radiation values. The interpolation on to a 10 km 10 km grid was done using the kriging interpolation method, which can take external forcing, such as the altitude, into account in the interpolation. The time period used was 1961–1990. When inaccuracies due to indirect estimation methods and due to the interpolation method were taken into account the error of the interpolated radiation value at any randomly selected grid-point was found to be less than 5 per cent for most months. During winter the spatial distribution of global radiation was clearly dependent on latitude, the higher latitudes receiving less radiation than the southern parts, and during summer the spatial distribution of global radiation was 1997 by the Royal Meteorological Society, Int. J. Climatol. 17: 415–426 (1997) determined by the variation of cloudiness. # (No. of Figs: 5 KEY WORDS: No. of Tables: 2 No. of Refs: 28) spatial variation; solar energy; global radiation; kriging; Finland. INTRODUCTION The amount of solar radiation (hereafter referred to as global radiation or radiation) received on the Earth’s surface is the driving force for most meteorological, biological, and hydrological processes. Besides meteorology many other sectors need detailed spatial analyses of global radiation. For example, agriculture and forestry in vegetation growth simulations, hydrologists when making evaporation estimates, the construction industry, as well as those making solar power estimates—all could utilize detailed information on the spatial variation of global radiation. There are at present only six stations making year-round direct measurements of global radiation in Finland (Finland’s geographical location is between latitudes 60 N and 70 N and longitudes 20 E and 30 E, Figure 1), and based on only these six stations it is impossible to make a detailed analysis of how radiation varies spatially in such a large country. Sunshine duration measurements and synoptic cloud observations are, however, made on a more dense observation network than radiation measurements, and use of these observations could make detailed spatial analyses meaningful. Besides latitude, variation in cloudiness is the most important factor affecting the spatial variation of global radiation. In Finland, layered clouds are usually connected with synoptic-scale weather disturbances. The tracks of low pressure centres are reflected in areas of dense cloudiness and obviously also areas of negative anomaly in global radiation. During spring or early summer the sea and lakes are colder than the surrounding areas and can inhibit the formation of convective clouds. On the other hand, during the autumn the sea is warmer than the land and convective clouds form more often over the sea than inland. When air experiences forced lifting, e.g. in the case of an airstream flowing over mountains or hills, orographic clouds may be formed. Vegetation and soil type can affect the local energy balance and also the formation of convective clouds. *Correspondence to: A. Venäläinen. # CCC 0899-8418/97/040415-12 $17.50 1997 by the Royal Meteorological Society 416 A. VENÄLÄINEN AND M. HEIKINHEIMO Figure 1. Observing stations, indicating which method was used at each station for the estimation of global radiation The spatial analyses of different climatological parameters have traditionally been carried out manually. These analyses have been based on subjective knowledge of regional geographical features and on an understanding of how those features, such as altitude, lakes or the nearness of the seashore, affect the parameter analysed. In this work objective numerical analysing methods also have been applied to climatology. Kriging is a spatial interpolation method which gives the best linear unbiased predictors of unobserved values. This interpolation method can take into account external forcing factors such as altitude, the sea effect, etc. In Finland the method has been used for the interpolation of July temperature and precipitation sums by Henttonen (1991). Hudson and Wackernagel (1994) used the kriging method for the interpolation of temperature in Scotland, and Bigg (1991) for the interpolation of rainfall in England. In the Finnish Meteorological Institute the kriging method has been used for the interpolation of mean wind speed by Heikinheimo and Hellsten (1992). Owing to the lack of dense radiation observing networks only a few analyses on global radiation are available. Josefsson (1993) has analysed spatial variation of global radiation in Sweden for the normal period 1961–1990. Budyko (1963) (work continued by Ohmura and Gilgen, 1993) has published analyses of global radiation on the continental and global scale. Also the WMO (1981) has published values of global radiation on a global scale. However, many details at a scale of tens or a few hundreds of kilometres can remain unobserved on such a large- LONG-TERM GLOBAL RADIATION, FINLAND 417 scale map. No analysis of the spatial variation in Finland of global radiation on a monthly scale has been published. The number of sites that can be utilized in the estimation of the spatial distribution of global radiation potentially can be increased by using cloud observations made regularly at synoptic weather stations together with a radiation transfer parameterization scheme which utilizes those observations. In the literature there are several parameterization schemes available for solar radiation transfer. Evaluations made between different approaches (Davies and McKay, 1989; Fouquart et al., 1991; Gueymard, 1993b) can help in the selection of the parameterization. Another possibility to increase the number of observing sites to provide estimates of solar radiation is to use sunshine duration measurements together with an experimental parameterization by which sunshine duration is converted into global radiation (Ångström, 1924). The original Ångstöm equation has been used and modified by several researchers, for example by Cowley (1978), for estimation of global solar radiation over Great Britain, and by Gopinathan (1992) for estimation of hourly global and diffuse solar radiation in southern Africa. The aim of this study was to estimate the spatial variation of global radiation in Finland. Analyses were done on to a 10 km 10 km grid using the kriging interpolation method. The analyses were based on long-term mean monthly values, which were obtained either from direct measurements of solar radiation (five stations) or indirectly, based on sunshine duration measurements (17 stations) or synoptic cloud observations (15 stations). The years used for the calculation of mean values were 1961–1990. This article is based on the licentiate thesis presented by Venäläinen (1995). 6 ESTIMATION OF GLOBAL RADIATION Parameterization of clear-sky radiation The parameterization used in this work for the estimation of solar radiation in a cloudless situation is well documented in Iqbal (1983). This parameterization scheme also succeeded well in an evaluation of different parameterization schemes (Gueymard, 1993a). Global radiation is a sum of direct and diffuse radiation. Following Bird and Hulstrom (1981) for the direct radiation we have Rdir 019751R0 sin gt tt tt 1 R g w a o g t where Rdir is the direct radiation on a horizontal surface, R0 is the solar flux on a surface exposed normal to the sun’s rays in the absence of the atmosphere, is the sun’s elevation angle, R is the broadband transmittance by Rayleigh scattering, g is the transmittance by uniformly mixed gases, w is the transmittance by water vapour, a is the transmittance by aerosols, and o is the transmittance by ozone. The factor 019751 is included because the spectral interval considered is 013–310 m. This parameterization was further developed by Iqbal (1983) and Bird and Riordan (1986). The formulae for the calculation of parameters needed in equation (1) were taken from Iqbal (1983). The diffuse radiation Rdif was calculated as the sum of three terms (Iqbal, 1983) t t t m Rdif Rdifr Rdifa Rdifm t 2 where Rdifr is the Rayleigh-scattered and Rdifa is the aerosol-scattered diffuse radiation after the first pass through the atmosphere, and Rdifm is the multiply reflected radiation. Multiply reflected radiation is the component of global radiation reflected from the Earth’s surface to the atmosphere and from the atmosphere back to Earth. Parameterization of clouds t Following the logic of equation (1), the global radiation under a cloudy sky can be estimated by adding one more transmittance factor, the transmittance by clouds, c. Thus the equation for global radiation under a cloudy sky is Rgc tR c g0 3 418 A. VENÄLÄINEN AND M. HEIKINHEIMO where Rg0 is the global radiation under a cloudless sky. Manabe (1964) presented a method of calculating the transmittance function for multiple layers of clouds t Q1 nc c ÿ c i 1 ÿ i 1 c 4 i c where ci is the amount and i the transmittance of each individual cloud layer. The amount and type of each individual cloud layer is not available from a standard synoptic weather observation and thus some assumptions must be made. In this work three layers of clouds were used: low (i 1), medium (i 2) and high (i 3) clouds. Based on Haurwitz (1948) and Kasten and Czeplak (1980), Marshall and Ball (1980) suggested that constant cloud transmittance values could be used. The transmittance ( i) varies from 0115 (stratus, nimbostratus) to 0190 (cirrus, cirrostratus). However, in the case of a partly cloudy sky the amount of radiation reflected from the cloud sides to the Earth’s surface can be large. This is the case especially when the scattered clouds are deep, e.g. cumulus or cumulonimbus. Improved accuracy was sought here by letting the values for i vary depending on the cloud amount (Table I) to mimic this reflection from the sides. The values of i differ from values given, for example, by Marshall and Ball (1980) in the case of low clouds and total cloudiness below 50 per cent. Synoptic cloud codes were translated to the format needed in the parameterization using a formulation explained in Venäläinen and Nordlund (1988). Global radiation was calculated as the sum of direct, Rayleigh-scattered diffuse, aerosol-scattered diffuse and multiply reflected diffuse radiation. Multiple reflected radiation results mainly from the cloud layer in the case of cloudy conditions and thus equation (3) was modified to c c c Rgc Rdir Rdifr Rdifa t c Rdifm 5 t When calculating Rdifm the atmospheric albedo is needed, and in the case of cloudy conditions this was taken as the sum of the clear-sky atmospheric albedo and the cloud transmittance, c (equation 4). Parameterization of global radiation based on measurements of sunshine duration Measurements of sunshine duration need less expensive equipment and also the measuring technique is less demanding than in the case of direct measurements of solar radiation. Measurements of sunshine duration are available from about 20 stations in Finland. Sunshine duration at all stations has been determined using Campbell–Stokes recorders. Table I. Cloud transmittance factors in different synoptic cloud conditions, as used in this work Cloud height Low (cl) Total cloudiness < 015 Cloud type 1, 2, 3, 8, 9 < 01875 < 01875 4 0 75 4 0 75 > 01875 1 4, 5 1 > 0175 Medium (cm) High (ch) a > 0175 0 < ctot < 1 0 < ctot < 1 0 < ctot < 1 0 < ctot < 1 0 < ctot < 1 Transmittance ( i) < 015 019 018 01 6 0145 0136 014 0125 0135 0125 0115 0169 01 4 01 5 01 9 4 4 4 4 4 < 015 < 01875 6, 7 10 1, 2, 7 3, 4, 5, 6, 8, 9 1 < ch < 9 c Cloud amounta 0175 < c1 015 01875 c1 0175 >0 015 > 015 015 > 015 0 < c1 < 1 0 < c1 < 1 0 < c2 < 1 0 < c2 < 1 0 < c3 < 1 c1 amount of low cloud, c2 amount of medium cloud, c3 amount of high cloud (0 corresponds no cloud and 1 to a completely overcast sky). 419 LONG-TERM GLOBAL RADIATION, FINLAND Ångström (1924) proposed a linear expression for the estimation of daily sums of radiation by using the measurements of sunshine duration: RS =R0 a 0 0 b H =N 6 0 0 where RS is the daily global radiation, r0 is the daily global radiation from a cloudless sky, a and b are constants, H is the length of sunshine duration and N is the length of sunshine duration on a cloudless day. This formula has been used very widely all over the world. Constants a and b are dependent on the latitude and season, so that they must be defined locally for each season and place. In this work the constants were defined using 1971–1992 daily radiation sum and sunshine duration data for Jokioinen (60 49 N, 23 30 E) and for Sodankylä (67 22 N, 26 39 E). It was found that instead of a linear regression a logarithmic formula (7) described the dependence between sunshine duration and radiation slightly better. 0 0 0 0 0 0 RS =R0 a b lnf H =N = 2 ÿ 1 a=ag 1 7 Differences in the constants a and b between months and between stations located at different latitudes can be explained by the prevailing cloud type; the average cloud thickness increases during spring towards the summer season because of increased convection. The transition from thinner clouds to thicker convective cloud types occurs on average earlier in the south than in the north. Once the monthly mean values for a and b for Jokioinen and Sodankylä had been calculated, a linear equation was fitted to the data to describe the latitudinal dependence (Table II). SPATIAL INTERPOLATION WITH KRIGING The interpolation program used in this work was developed by Henttonen (1991) based on a rigorous description by Ripley (1981) (see also Hudson and Wackernagel (1991) and Bigg (1991)). As an advantage, kriging can use external forcing variables, such as the mean altitude of terrain above sea-level at grid-squares, in a statistical manner to improve accuracy of estimates at grid-points. Let Z be the monthly mean global radiation with known values Z(Xi) at the weather station locations Xi. The aim is to estimate the values of Z at any arbitrary location X (in our case on a 10 km 10 km grid over Finland). In kriging, the parameter Z at position X is decomposed into a slowly varying ‘drift’ (also called ‘trend’) M(X) and a residual called the ‘fluctuation’ e(X ) so that Z(X ) M(X ) e(X ). Both are unknown at the beginning. Here X is a vector denoting the positions of the grid squares for which the value should be interpolated. The drift M(X ) describes the broad-scale features of the interpolation variable. It is composed of a polynomial of uncorrelated physically meaningful variables, such as the geographical location (x, y), the altitude above sealevel (h), the percentage coverage of lakes (l ) and sea (s), selection of these variables depends on their expected influence on the variable to be interpolated. The functional form of the drift used here was 6 M x; y; h; l; s a0 a1 x a2 y a3 x2 a4 y2 a5 xy a6 h a7 s a8 l 8 For each interpolation run the coefficients a0 . . . a8 were first estimated from the observed data by performing a least-squares fit on the observed radiation values. Table II. Constants a and b as a function of season and latitude defined using Jokioinen and Sodankylä observations Season/month Winter (NOJF) March April Summer (MJJ) August September October a 1115 a 1165ÿ7143 a 4189ÿ5135 a 8114ÿ9166 a 7104ÿ8117 a 3175ÿ3171 a 2110ÿ1149 6 10 6 10 6 10 6 10 6 10 6 10 3 ÿ 2 ÿ 2 ÿ 2 ÿ 2 ÿ 2 ÿ 6 latitude 6 latitude 6 latitude 6 latitude 6 latitude 6 latitude 6 10 6 latitude 6 latitude 6 10 6 latitude 6 10 6 latitude 6 10 6 latitude 6 10 6 latitude b 4130 b ÿ2129 8192 b ÿ6154 01144 b ÿ1144 5120 b ÿ0190 4146 b ÿ3129 8192 b ÿ1169 7143 2 ÿ 2 ÿ 2 ÿ 2 ÿ 2 ÿ 420 A. VENÄLÄINEN AND M. HEIKINHEIMO The fluctuation e(X ) is a spatial stochastic process around the drift surface with a zero mean. With the assumption that the process is isotropic, the spatial covariance between variables at two points depends only on the distance between the two points. A suitable form of covariance function was sought by fitting Whittle’s correlation function (see Ripley, 1981) into the residuals Z(X ) M(X ). The parameters defining the form of Whittle’s covariance were adjusted iteratively by minimizing the error between the interpolated and measured radiation values. For the observing stations the percentage of lake or sea coverage was taken as the value of the grid-square inside which the station was situated. For stations located nearer than 25 km to the coast the percentage of sea cover in a surrounding 50 km 50 km grid-square was calculated. Information on the surface type inside the 10 km 10 km grid squares was based on interpretation of Landsat images and ground verification. 7 6 6 MATERIAL Time series and stations The data used in this study for the estimation of global radiation came from three sources: direct measurements, sunshine duration measurements, and cloud observations (Figure 1). All stations that made pyranometer measurements also made measurements of sunshine duration and synoptic weather observations. All stations making sunshine duration observations also made synoptic weather observations. For any given station the global radiation estimate was made as follows: (i) pyranometer measurements were used, if available; (ii) if there were sunshine duration measurements but no pyranometer measurements, then sunshine duration measurements were used; and (iii) for stations that had neither pyranometer nor sunshine measurements, synoptic weather observations were utilized for the calculation of radiation. In all, 37 stations were used, five stations having pyranometer measurements, 17 having sunshine duration observations, and 15 having synoptic weather observations only. Not all stations had the whole 30 years’ of observations and thus some shorter time series were used. The possible bias due to shorter time series was corrected and short missing periods filled by using data from the nearest station having a complete time series. Summary of factors affecting the accuracy of a grid-point estimate The accuracy of the grid-point estimates of global radiation were dependent on the one hand on the accuracy of the station values and on the other on the accuracy of the spatial interpolation method. For the period 1961–1990 the Moll–Gorczynski (Kipp & Zonen, Holland) type pyranometer has been used at the Finnish observing stations. For secondary standard instruments the World Meteorological Organization (WMO) requires maximum errors in hourly totals not to exceed 3 per cent. If the hourly error is less than 5 per cent and if there is no bias, then a good approximation is that the long-term monthly mean value can be estimated with an accuracy of better than 2 per cent. All data obtained with pyranometers were adjusted to the recommended international WRR Scale (WMO, 1986). Cloud parameterization needs information about the amount of different cloud types at different heights above the surface, and because ordinary synoptic observations do not contain all the information needed, approximations must be made when the synoptic code is translated into appropriate parameters. The parameterization schemes themselves cannot take into account all the processes affecting the radiation transfer in a cloudy sky, even though the clear-sky radiation can be estimated with good accuracy. The cloud observations are very subjective: in the same synoptic conditions two observers can record cloud differently. Also the openness of the observing site has an effect on the observation, so that at a more sheltered site, lower cloudiness values are recorded than at a more open one (Heino, 1994). The observing conditions (such as openness of the horizon) can affect the sunshine duration measurements. The instrument’s recording has been converted subjectively to sunshine hours, and this also may have affected the accuracy of the measurements. Another reason for inaccuracies is the dampness of the card. In a very dry LONG-TERM GLOBAL RADIATION, FINLAND 7 421 6 Figure 2. The difference between estimated and measured long-term (1961–1990) mean monthly global radiation values: (A) absolute error (estimated measured, W m 2) and (B) relative error (100 difference/measured, per cent) at stations making radiation measurements. The estimation was made using the kriging interpolation method and radiation values from 36 stations shown in Figure 1. The station for which error was studied has been excluded from the interpolation input data ÿ weather situation the burn may begin earlier than under very humid conditions. One should also remember that daily sunshine duration cannot completely describe the daily global radiation. If we want to know how accurately a certain grid-point value can be estimated the spatial interpolation method is to be considered an additional source of inaccuracy. A good assumption is that the accuracy of interpolation is not completely independent of inaccuracies in the input data; if the input values vary randomly from one station to another then also the interpolation method cannot work well. On the other hand, interpolation can also smooth out unreal variation and thus improve an estimate that is based on inaccurate station values. To test how accurate a randomly selected grid-point value was, the interpolated radiation values were compared with the measured values at station locations (Figure 2 (A and B)). The error of estimate (estimated value measured value) varied between ÿ11 and 8 W m 2, with the largest errors occurring at stations in northern Finland. The relative error (the error compared with the measured value) was, with some exceptions, for March to September better than 5 per cent. When the sun’s elevation angle was low the relative error reached 7 ÿ 422 A. VENÄLÄINEN AND M. HEIKINHEIMO high values, even though the absolute error is only about 2 W m 2. In the case of the annual mean, the error was greatest at Sodankylä (ÿ4 per cent) and smallest at Vantaa (015 per cent). Estimates of global radiation during the winter were unreliable: the errors in northern Finland can be several tens of per cent. During most of the year, and in the case of annual mean values, the accuracy of a long-term mean estimate at any randomly selected grid-point was better than 5 per cent. ÿ Figure 3. The long-term mean monthly global radiation (W m 2) in January, April, July, and October analysed using the kriging interpolation method and data from 37 stations as shown in Figure 1 ÿ LONG-TERM GLOBAL RADIATION, FINLAND 423 THE SPATIAL FEATURES OF GLOBAL RADIATION IN FINLAND The spatial features of the long-term mean monthly global radiation values are seen in Figure 3. The geographical locations referred in the text can be found in Figure 4. Each season is represented by 1 month’s radiation values characteristic of that season. The difference in global radiation between winter and summer is very large. In January the highest radiation values (about 12 W m 2) are received in southern Finland, whereas in Lapland the sun does not rise above the horizon at all. The most obvious feature is thus the clear north–south gradient. In April the lower elevation angles of the Sun in northern Finland compared with southern Finland are compensated for by the longer days in the north, and the radiation is about the same over the whole of Finland. The highest values (150 W m 2) are observed along the Baltic coast and in south-eastern Finland. The lowest values (140 W m 2) are in Lapland and in the north-eastern part of Finland. An area of negative anomaly covers the southern Ostrobothnia and Suomenselkä Divide regions. In July the lowest values are observed in northernmost Lapland and the highest values along the Baltic coast. The difference between the highest and lowest values is more than 50 W m 2. The pattern of spatial distribution ÿ ÿ ÿ ÿ Figure 4. The climate zones defined by Solantie (1990) 424 A. VENÄLÄINEN AND M. HEIKINHEIMO in July resembles that in April, with a local minimum in the Suomenselkä Divide regions. In northern Finland the north-east–south-west gradient, which can be noticed in all the other maps too, is very clear in July. The negative gradient directed inland from the coast of the Gulf of Bothnia is steep, the radiation decreasing by about 15 W m 2 over a distance of about 100 km. In October the spatial distribution resembles the situation in January. The days are now shorter in northern Finland than in the south, and the northernmost point of Lapland receives less than half the radiation received by southern Finland. There is a slight positive anomaly near the coast of the Gulf of Bothnia. Also in northern Finland the north-east–south-west gradient can be noticed. ÿ DISCUSSION In summary one may say that the spatial distribution of long-term mean monthly global radiation in Finland showed strong latitudinal dependence during the late autumn and winter months, whereas during months of high radiation values more localized patterns could be detected. The reason for longitudinal variations of global radiation is the variation in cloudiness. In April and in July the distribution of total cloudiness resembled the spatial features of global radiation; areas with high cloudiness were correspondingly areas of low radiation. In January and in October the effect of clouds was not so important because the spatial variation of global radiation is predominantly defined by the latitudinal variation caused by Earth’s orbit of the Sun. Solantie (1990) divided Finland into quasi-latitudinal climatic zones mainly on the basis of the conditions during the vegetational period (Figure 4). The border between the middle boreal and the southern boreal zone is characterized by summertime maximum rainfall and minimum air pressure. Solantie explained that the increase in the proportion of bogs and decrease in the volume of growing stands northward across the border between the southern and middle boreal zones affects the energy budget of the Earth’s surface. This change in the Earth’s energy budget can, according to Solantie, be seen as an increase in daily maximum temperatures in summer, occurring around the southern boundary of the middle boreal climatic zone. The corresponding change of sensible heat flux is about 811 W m 2, leading to increased convection and cloudiness and decreased global radiation. Although the variation in convective cloudiness is one obvious reason for the spatial variation of global irradiance, it is hardly, however, the only reason. For example the negative anomaly of radiation in north-east Finland in April, July, and October could be due partly to the cold air flow from the Barents Sea north of Russia. This kind of flow is characterized by a thick stratocumulus cloud cover, which effectively inhibits the solar radiation from reaching the Earth’s surface. The areas of negative anomaly in radiation are also characterized by terrain higher than its surroundings. The forced ascent of an airstream can be one reason for increased cloudiness and decreased solar radiation. The frictional force experienced by the airflow causes convergence and thus an ascent of air and again increased cloudiness. The prevailing wind direction in western Finland is from the southwest; when the wind comes from the Gulf of Bothnia it meets the forests and hills of the Suomenselka Divide, where the friction is increased and at the same time terrain higher than the flat areas of the coastal regions is encountered. According to Josefsson (1993), the local maximum values of radiation in Sweden are measured in eastern Sweden along the Gulf of Bothnia. Josefsson’s explanation is that near the coast there are less clouds than inland due to the cold water surface, which inhibits the formation of convective clouds. Josefsson’s (1993) work for Sweden provides a comparison of the spatial variation of global radiation values. His analysis of the mean annual global radiation in Sweden is based on measurements made at 17 stations. His analysis and the analysis presented in this work (Figure 5) resemble each other: the isolines for annual mean global radiation could be drawn across the border of Finland and Sweden without discontinuity. Ohmura and Gilgen (1993) presented an analysis of the annual mean global radiation for central Europe. Their analysis was based on direct measurements and thus the network is rather sparse. Only the southernmost point of Finland was included in their analysis. For southern Finland they found values of about 110 W m 2, which is about the same as those values obtained in this study. In most of central Europe the annual mean value was 110– 130 W m 2 and only as far south as northern Italy did the values exceed 150 W m 2. Thus the difference in ÿ ÿ ÿ ÿ 425 LONG-TERM GLOBAL RADIATION, FINLAND Figure 5. Mean annual global radiation (W m 2) analysed using the kriging interpolation method and data from 37 stations as shown in Figure 1 ÿ annual global radiation between southern Finland and Lapland is about the same as between southern Finland and northern Italy. In June over large areas of Finland the global radiation exceeds 250 W m 2, which is more than that received in most of western Europe (Ohmura and Gilgen, 1993): only as far south as the Mediterranean region is more solar radiation received. During summer the rather low elevation angles of the Sun in northern Europe are compensated by longer days than in southern latitudes. ÿ CONCLUSIONS According to the results presented above, the number of sites that can be used for the estimation of solar radiation can be increased by using sunshine duration measurements or synoptic cloud observations for this estimation. With the increased spatial density of stations it is then meaningful to spatially interpolate the long-term mean monthly global radiation values on to a 10 km 10 km grid over Finland. The so-called kriging interpolation method offers an opportunity for using an objective scheme and for taking into account in the analysis the effects of landscape in terms of ‘external forcing’. When inaccuracies due to indirect estimation methods and to the interpolation method were taken into account the error of the interpolated radiation value at any randomly selected grid-point was found to be less than 5 per cent for most months. During the winter months the spatial distribution of global radiation was very clearly dependent on latitude, the northern parts of the country receiving less radiation than the southern parts. During summer the minimum values of global radiation were found in north-east Lapland and over the Suomenselkä Divide and southern Ostrobothnia. Maximum values were observed along the coast of the Baltic Sea and in south-eastern Finland. The longitudinal variation in global radiation is caused by variation in cloudiness. The coastal areas represent areas of less cloudiness. Convective clouds, in particular, tend not to be formed over cold water surfaces. Other factors, such as the tracks of synoptic-scale weather phenomena, can also affect the distribution of cloudiness. The longitudinal spatial variation of global radiation in Finland is so large that the spatial analysis would be misleading if it were based only on the measurements made on the few radiation measuring stations. 6 426 A. VENÄLÄINEN AND M. HEIKINHEIMO ACKNOWLEDGEMENTS The authors with to express sincere thanks to Professor Eero Holopainen and Dr Hannu Savijärvi working in the Department of Meteorology, University of Helsinki for their support and scientific revision. Significant financial support was received from the Academy of Finland in the SILMU Programme, Project no, 2031012. REFERENCES Ångström, A. 1924. ‘Report to the international commission for solar research on actinometric investigations of solar and atmospheric radiation’, Q. J. R. Meteorol. Soc., 50, 121–125. Bigg, G. R. 1991. ‘Kriging and interregional rainfall variability in England’, Int. J. Climatol., 11, 663–675. Bird, R. and Hulstrom, R. L. 1981. ‘Direct insolation models’, Trans. ASME J. Solar En. Eng., 103, 182–192. Bird, R. E. and Riordan, C. 1986. ‘Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the earth’s surface for cloudless atmospheres’, J. Clim. Appl. Meteorol., 25, 87–97. Budyko, M. I. (ed.) 1963. Atlas of the Heat Balance of the Earth. Akademiya Nauk SSSR, Moscow. Cowley, J. P. 1978. ‘The distribution over Great Britain of global solar irradiation on a horizontal surface’, Meteorol. Mag., 107, 357–373. Davies, J. A. and McKay, D. C. 1989. ‘Evaluation of selected models for estimating solar radiation on horizontal surfaces’, Solar En., 43, 153– 168. Fouquart, Y., Bonnel B. and Ramaswamy, V. 1991. ‘Intercomparing shortwave radiation codes for climate studies’, J. Geophys. Res., 96(D5), 8955–8968. Gopinathan, K. K. 1992. ‘Estimation of hourly global and diffuse solar radiation from hourly sunshine duration’, Solar En., 48, 3–5. Gueymard, C. 1993a. ‘Analysis of monthly average solar radiation and bright sunshine for different thresholds at Cape Canaveral, Florida’, Solar En., 51, 139–145. Gueymard, C. 1993b. ‘Critical analysis and performance assessment of clear sky solar irradiance models using theoretical and measured data’, Solar En., 51, 121–138. Haurwitz, G. 1948. ‘Insolation in relation to cloud type’, J. Meteorol., 5, 110–113. Heikinheimo, M. and Hellsten, E. 1992. ‘Gridpoint presentation of climatological parameters’, in Tammelin, B., Säntti, K., Peltola, E. and Neuvonen, H. (eds), BOREAS, An International Experts’ Meeting on Wind Power in Icing Conditions, 1, Ilmatieteen laitos, Hetta, pp. 370. Heino, R. 1994. Climate in Finland during the Period of Meteorological Observations, Contributions No. 12, Finnish Meteorological Institute, Helsinki, 209 pp. Henttonen, H. 1991. Kriging in Interpolating July Mean Temperatures and Precipitation Sums, Jyväskylän yliopiston tilastotieteen laitoksen julkaisuja No. 12, Department of Statistics, University of Jyväskylä, Jyväskylä, 41 pp. Hudson, G. and Wackernagel, H. 1994. ‘Mapping temperature using kriging with external drift: theory and example from Scotland, Int. J. Climatol., 14, 77–91. Iqbal, M. 1983. An Introduction to Solar Radiation. Academic Press Canada, Ontario. Josefsson, W. 1993. Normalvärden för perioden 1961–1990 av globaltrålning och solskenstid i Sverige, SMHI Meteorologi, 18, Sveriges meteorologiska och hydrologiska institut, Norrköping, 22 pp. Kasten, F. and Czeplak, G. 1980. ‘Solar and terrestrial radiation dependent on the amount and type of cloud’, Solar En., 24, 177–189. Manabe, S. and Stricler, R. F. 1964. ‘Thermal equilibrium of an atmosphere with convective adjustment’, J. Atmos. Sci., 21, 433–444. Marshall, A. A. and Ball, J. T. 1980. ‘A surface solar radiation model for cloudy atmosphere’, Mon. Wea. Rev., 109, 878–888. Ohmura, A. and Gilgen, H. 1993. ‘Re-evaluation of the global energy balance’, Geophys. Monogr., 75(15), 93–110. Ripley, B. D. 1981. Spatial Statistics, Wiley, New York. Solantie, R. 1990. The Climate of Finland in Relation to its Hydrology, Ecology and Culture, Contributions, No. 2, Finnish Meteorological Institute, Helsinki, 130 pp. Venäläinen, A. and Nordlund, A. 1988. Kasvukauden ilmastotiedotteen sisätö ja käyttö, Raportteja No. 1988:6, Ilmatieteen laitos, Helsinki, 63 pp. Venäläinen, A. 1995. The spatial variation of mean monthly global radiation in Finland. Licentiate thesis. University of Helsinki, 54 pp. WMO 1981. Meteorological Aspects of the Utilization of Solar Radiation as an Energy Source. ANNEX, World Maps of Relative Global Radiation, Technical Note 172, WMO-No 557, World Meteorological Organization, Geneva, 7 pp. WMO 1986. Revised Instruction Manual on Radiation Instruments and Measurements, WCRP Publication series No. 7, WMO/TD-No. 149, World Meteorological Organization, Geneva, 140 pp.