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Finnish Meteorological Institute, P.O. Box 503, 00101 Helsinki, Finland
Received 5 January 1996
Revised 26 August 1996
Accepted 29 August 1996
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
No. of Tables: 2
No. of Refs: 28)
spatial variation; solar energy; global radiation; kriging; Finland.
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
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-
scale map. No analysis of the spatial variation in Finland of global radiation on a monthly scale has been
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
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).
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
019751R0 …sin
gt tt tt
… †
R g w a o
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
The diffuse radiation Rdif was calculated as the sum of three terms (Iqbal, 1983)
Rdifr ‡ Rdifa ‡ Rdifm
… †
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
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
c g0
… †
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
c i …1 ÿ
i ˆ1
i †Š
… †
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 ˆ 1),
medium (i ˆ 2) and high (i ˆ 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
ˆ …
Rdir ‡ Rdifr ‡ Rdifa †
… †
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
4, 5
> 0175
Medium (cm)
High (ch)
> 0175
0 < ctot < 1
0 < ctot < 1
0 < ctot < 1
0 < ctot < 1
0 < ctot < 1
Transmittance ( i)
< 015
01 6
01 4
01 5
01 9
4 4
< 015
< 01875
6, 7
1, 2, 7
3, 4, 5, 6, 8, 9
1 < ch < 9
Cloud amounta
0175 < c1 015
01875 c1 0175
> 015
> 015
0 < c1 < 1
0 < c1 < 1
0 < c2 < 1
0 < c2 < 1
0 < c3 < 1
c1 ˆ amount of low cloud, c2 ˆ amount of medium cloud, c3 ˆ amount of high cloud (0 corresponds no cloud and 1 to a completely overcast
Ångström (1924) proposed a linear expression for the estimation of daily sums of radiation by using the
measurements of sunshine duration:
RS =R0
b …H =N †
… †
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.
RS =R0
a b
lnf‰…H =N
ˆ … = † 2
1† ‡ aŠ=ag ‡ 1
… †
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).
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 ) ˆ 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
M …x; y; h; l; s† ˆ a0 ‡ a1 x ‡ a2 y ‡ a3 x2 ‡ a4 y2 ‡ a5 xy ‡ a6 h ‡ a7 s ‡ a8 l
… †
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
Winter (NOJF)
Summer (MJJ)
a ˆ 1115
a ˆ 1165ÿ7143
a ˆ 4189ÿ5135
a ˆ 8114ÿ9166
a ˆ 7104ÿ8117
a ˆ 3175ÿ3171
a ˆ 2110ÿ1149
6 10
6 10
6 10
6 10
6 10
6 10
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 ˆ 4130
b ˆ ÿ2129 ‡ 8192
b ˆ ÿ6154 ‡ 01144
b ˆ ÿ1144 ‡ 5120
b ˆ ÿ0190 ‡ 4146
b ˆ ÿ3129 ‡ 8192
b ˆ ÿ1169 ‡ 7143
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.
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
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
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
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.
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
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
Figure 4. The climate zones defined by Solantie (1990)
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.
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
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
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
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
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.
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.
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.
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