Asia-Pacific J. Atmos. Sci., 48(4), 423-431, 2012
DOI:10.1007/s13143-012-0038-y
Parameterization and Mapping of Solar Radiation in Data Sparse Regions
Ji-Long Chen1,2 and Guo-Sheng Li 1
1
Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing, China
Graduate University of Chinese Academy of Sciences, Beijing, China
2
(Manuscript received 29 October 2011; revised 7 June 2012; accepted 18 June 2012)
© The Korean Meteorological Society and Springer 2012
Abstract: Knowledge of temporal and spatial variation of solar
radiation is essential for many applications. In this work, a simple
and feasible procedure is conducted to map the daily solar radiation
for Liaoning province, one of the most important agricultural areas in
China, but with sparsely measured solar radiation data. The daily
sunshine duration are interpolated to the whole area, subsequently,
solar radiation are calculated by Ångström-Prescott model, the
generic parameters of which are determined by least square to
minimize the overall fitting residual between the ratio of actual to
potential sunshine duration and the ratio of actual to extra-terrestrial
solar radiation of the sites where solar radiation are available. In
other local regions with sparse data, mapping of the solar radiation
could be done following the simple procedure. In the present study area,
using the interpolated daily sunshine duration data by ANUSPLIN,
Ångström-Prescott model with the generic parameters (a = 0.505,
and b = 0.204) returns reasonable results, with the overall RMSE of
2.255 MJ m−2, and RRMSE of 16.54%. The daily solar radiation
varies between 5.26 in December and 22.74 MJ m−2 in May, and
shows an obviously spatial variation which is mainly contributed to
the climate and topography. The substitution of solar radiation from
nearby station is preferred to estimation by Ångström-Prescott model
if the distance between the stations falls below the threshold of
135 ± 15 km. The RMSE of such substitution increases by approximately 0.157 MJ m−2 per 10 km.
Key words: Solar radiation, mapping, variation, substitution
1. Introduction
Solar radiation is the principal and fundamental energy for
many physical, chemical and biological processes, and it is also
an essential and important variable to many simulation models,
such as agriculture, environment, hydrology and ecology. A
good knowledge of the temporal and spatial distribution and
variation is essential for such applications. To map the spatial
variation of solar radiation, sufficient stations with solar radiation measurement equipment are needed for the desired area,
this is practically impossible due to the cost and difficulty of
maintenance and calibration of the measurement equipment
(Hunt et al., 1998). The station measuring solar radiation is very
sparse. For example, in USA, less than 1% of meteorological
Corresponding Author: Guo-Sheng Li, Institute of Geographic
Sciences and Natural Resources Research, Chinese Academy of
Sciences, No.11A, Datun Rd., Beijing 100101, China.
E-mail: [email protected]
stations are recording solar radiation (NCDC, 1995). In China,
more than 2000 stations have records of meteorological data;
only 122 stations are recording solar radiation (Chen and Li,
2012). The ratio of stations recording solar radiation to those
recording temperature is about 1:500 around the world (Thorton
and Running, 1999). Therefore, developing method to estimate
solar radiation for the site where no solar radiation is readily
available has been the focus of many studies.
Major methods including satellite-based model (Pinker et
al., 1995; Schillings et al., 2004; Janjai et al., 2009), stochastic
weather generation (Richardson and Wright, 1984; Hansen,
1999; Wilks and Wilby, 1999), spatial interpolation (Bechini et
al., 2000; Xia et al., 2000; Ertekin and Evrendilek, 2007) and
substitution from nearby station (Hunt et al., 1998; Trnka et
al., 2005) have been developed to parameterize solar radiation
over the desired area. Satellite can provide data continuously
in space, and thus the satellite-based model is promising for
estimation and parameterization of solar radiation over large,
remote area, but the satellite data series are relatively short (De
and Stewart, 1993) and may suffer from discontinuities associated with changes in sensor degradation (Podestá et al., 2004);
moreover, many satellite-based models have difficulties to
produce accurate results, the deviations between the results
and the observation are up to 40% (Vignola et al., 2007; Janjai
et al., 2009). Stochastic method may be useful for generating
the average theoretical simulations. However, the generated data
cannot be used for model validation and simulation analysis
during a particular period since it cannot generate extreme
weather condition and the day-to-day variations (Wallis and
Griffiths, 1995; Liu and Scott, 2001). Spatial interpolation
technique can predict values at unknown locations and create
surface from the surrounding measured points. However, the
principal problem is that it requires sufficient points and it is
therefore limited since the stations of solar radiation measurement are spatially very sparse. Solar radiation data could also
be substituted from nearby stations (Hunt et al., 1998; Trnka et
al., 2005). It was proposed by Allen et al. (1998) as a possible
alternative to obtain the solar radiation for the site where no
solar radiation is available. The precision of this method
decreases with the increase of the distance between the two
stations, and the acceptable distance depends on the intended
use of solar radiation. Some authors investigated the threshold
distance below which the substitution from nearby station is
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superior to empirical models, and showed that the threshold
distances varied largely from 100-200 km in Central Europe
(Vanícek, 1984) to 385-400 km in Ontario of Canada (Hunt et
al., 1998). However, the study carried out by Trnka et al. (2005)
claimed that it was better to use Ångström-Prescott model (A-P)
model rather than substitution of solar radiation from nearby
station, even where such data are available from a station as
close as 17 km away. In other regions, such threshold distance
should be studied and re-computed before the consideration of
this method.
Liaoning province with an area of 145,900 km2, situated in
the southern part of the Northeast china, is a leading province
in respect of agricultural productivity in China. The topography
and soils and even climate in the province are quite favorable
to agriculture, and hence the eco-environmental models and
crop growth simulation are widely studied. However, the
meteorological stations recording solar radiation are very
sparse; only 3 meteorological stations provide solar radiation
recorders. Moreover, no literature reported the study on solar
radiation estimation for this region, and the knowledge of the
temporal and spatial distribution and variation of solar radiation
is limited. Therefore, the objectives of the present study are (1)
to estimate and parameterize daily solar radiation over the
province; (2) to map the temporal distribution and spatial
variation of daily solar radiation; and (3) to study the threshold
ê
Fig. 1. Study area and the distribution of the study sites.
distance below which the substitution from nearby station is
superior to empirical models.
2. Materials and method
a. Study area
Liaoning province lies between longitude 118o53' and
125o46'E, and latitude 38o43' and 43o26'N (Fig. 1). It consists
of the three approximate geographical regions; the mountain
regions in the east which is dominated by Changbai Shan and
Qianshan ranges; the Liaohe Plain in the middle, as a part of
the Northeastern China Plain, has sedimentary deposits from
the Liaohe River and other tributaries, the plain has abundant
water and fertile soil, and is the main farming area and commodity grain base in the province; and the highlands in the
west which is connected with Inner Mongolian plateau. Liaoning
has a continental monsoon climate, with a hot, rainy summer;
and a short, windy spring. The mean annual temperature is
4~10oC. The rainfall is rather concentrated, with a mean annual
precipitation of 400-1,000 mm. The east mountainous region
of Liaoning is the humid area with abundant rainfall, while the
northwest part of the province is frequently attacked by
drought in spring, since the rainfall is comparatively limited in
this area.
30 November 2012
terrestrial Ra and potential sunshine duration Ho are calculated
using the equations detailed by Allen et al. (1998).
b. Site
There are only 3 meteorological stations (Dalian, Chaoyang
and Shengyang, Fig. 1) measuring solar radiation in Liaoning
province. On the contrary, sunshine duration is routinely measured at most meteorological stations. A total of 39 stations
with long-term available records of sunshine duration covering
the period between 2005 and 2009 are used in this study. 27
stations, 3 of which simultaneously measuring solar radiation
and sunshine duration, are located in Liaoning province, and
the reminder in the adjoining Jilin (6 sites) and Hebei (2 sites)
provinces and Inner Mongolia Autonomous Region (4 sites) are
involved in order to avoid the misestimates in margin areas
caused interpolation. The mapping of stations roughly ranges
from latitude 38o to 52oN, from longitude 116o to 130oE, and
from 49 to 910 m altitude. Figure 1 shows distribution of the
study meteorological stations.
c. Data collection and check
Daily solar radiation and sunshine duration data of the study
stations from 2005 to 2009 are used in the present study. The
data were obtained from the National Meteorological Information Center (NMIC), China Meteorological Administration
(CMA). Sunshine duration is measured by Jordan sunshine
recorder for all stations, and solar radiation is measured using
pyranometer (Chen et al., 2011). Preliminary quality control
tests were conducted by the suppliers. We further checked the
data according to the following criterions: (a) Records with
missing data which were replaced by 32766 were removed
from the data set, (b) Daily solar radiation larger than the daily
extra-terrestrial solar radiation, or daily sunshine duration larger
than daily potential sunshine duration were removed from the
data set. Omission of data varied from 0 to 0.28% (average
0.05%) due to criterion b.
d. A-P model and calibration
Many empirical models have been developed to estimate
solar radiation using other easily available meteorological
variables, such as sunshine duration, maximum and minimum
temperatures. It is generally recognized that the sunshinebased models, in particular the Ångström-Prescott (A-P) model
(Ångström, 1924; Prescott, 1940), perform best (Iziomon and
Mayer, 2002; Podestá et al., 2004; Trnka et al., 2005). A-P
model was proposed by Ångström (1924) and further modified
by Prescott (1940). The original form of this model is:
Rs
H- + b
-----= a -----Ra
Ho
425
Ji-Long Chen and Guo-Sheng Li
(1)
Where Rs is daily actual global radiation (MJ m−2), Ra is daily
extra-terrestrial solar radiation (MJ m−2), H is daily actual
sunshine duration (h), Ho is daily potential sunshine duration
(h), a and b are empirical parameters which are calibrated from
regression analysis between H/Ho and Rs/Ra. The extra-
Ra = 37.6d ( ω sin ϕ sin δ + cos ϕ cos δ sin ω )
(2)
2π- n⎞
d = 1 + 0.033 cos ⎛⎝ -------365 ⎠
(3)
2π- n – 1.39⎞
δ = 0.4093 sin ⎛⎝ -------⎠
365
(4)
ω = arc cos ( – tan ϕ tan δ )
(5)
Ho = 24ω ⁄ π
(6)
Where d is the relative distance between the sun and the earth,
ω is sunset hour angle (rad), ϕ is latitude (rad), δ is solar declination angle (rad), n is the number of the day of year starting
from the first of January.
A-P model is widely used for its simplicity and significant
performance. The principal limitation is that it requires calibration using the measured solar radiation data and it is therefore
open to question how to determine the parameters for other
locations where no solar radiation is available, this is especially
difficult in data sparse regions. Lots of literatures reported the
calibrated parameters for different places, and showed that
they varied from location to location. While in a local extent,
Richardson and Wright (1984) found that the spatial variations
of these parameters were very small, so they averaged them to
come up with generic values. In the present study area, each site
(grid) is assigned the same parameters which are determined by
least square regression to minimize the overall fitting residual
between H/Ho and Rs/Ra of the 3 sites (Dalian, Chaoyang and
Shengyang) where solar radiation are available, and the final
generic parameters (a = 0.505, and b = 0.204) and calibrated
parameters at the single site are presented in Table 1. Two
metrics, root mean square error (RMSE) and relative root mean
square error (RRMSE) (%), are used to assess the performance
of the A-P model (Table 1). The smaller the value, the better is
the model’s performance. The scatter plots of the observed solar
radiation and the estimated by A-P model using the generic
parameters show that there is a good agreement between the
observation and the estimation as shown in Fig. 2, where the
points tend to line up around the 1:1 line, indicating that the
observation are close to the estimation. The overall accuracy
(RMSE = 2.159 MJ m−2, and RRMSE = 15.84%) and the scatter
Table 1. The generic parameters and calibrated parameters at the single
site and the prediction residuals of the A-P model.
Stations
a
b
RMSE
RRMSE
Dalian
Chaoyang
Shengyang
Overall
0.509
0.481
0.498
0.505
0.173
0.232
0.215
0.204
1.760
2.415
1.964
2.159
13.10%
17.29%
14.64%
15.84%
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ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES
Fig. 2. Scatter plots of the solar radiation observation vs. estimation by the A-P model using the generic parameters.
plots suggest that the A-P model using the generic parameters
can return reasonable results in the study area.
e. Interpolation of sunshine duration
The direct interpolation of solar radiation is not a viable
approach as the stations measuring solar radiation are spatially
very sparse. On the contrary, the satiations of sunshine duration
observation are much denser, and therefore, alternatively, we
can interpolate sunshine duration from these stations and then
use the A-P model to compute solar radiation for the whole area.
In the present work, we generated the historical (2005-2009)
daily sunshine duration girds with the resolution of 5 km × 5
km using the thin-plate smoothing splines with ANUSPLIN
software (Hutchinson 2002), which is well suited to interpolating noisy climate data, and has performed well in comparisons to other interpolation techniques (Hutchinson and Gessler,
1994; Price et al., 2000; Jarvis and Stuart, 2001). ANUSPLIN
is based on plate smoothing splines as described by Hutchinson
(1984) and Wahba (1990), it enables more than two independent
variables to be incorporated into the spline functions. The variables most commonly included in ANUSPLIN specifications
are latitude and longitude, additional independent variables or
co-variates can be any factors associated to geographic variation of climate.
f. Accuracy assessment
Although the A-P model using the generic parameters can
return reasonable results in the study area. The error of the
sunshine duration interpolation will be transferred into solar
radiation estimation at the grid where sunshine duration is not
measured, but interpolated from nearby stations. To assess the
final accuracy of solar radiation estimation by A-P model with
the interpolated sunshine duration, 3 stations (Dalian, Chaoyang
and Shengyang) which simultaneously measure solar radiation
and sunshine duration were excluded from the sunshine duration interpolation data. The measured against the interpolated
sunshine duration, and the measured solar radiation against the
estimated by A-P model with the interpolated sunshine duration
30 November 2012
Ji-Long Chen and Guo-Sheng Li
427
Table 2. Precision of the substitution of solar radiation from the
remaining stations.
Stations
Dalian
Chaoyang
Shengyang
RMSE RRMSE RMSE RRMSE RMSE RRMSE
Dalian
-
-
5.077
36.35%
4.971
37.10%
Chaoyang
5.077
37.82%
-
-
4.399
32.83%
Shengyang
4.971
37.03%
4.399
31.50%
-
-
Table 3. Interpolation and the integrated Precision.
Stations
Interpolation
Integrateda
RMSE
RRMSE
RMSE
RRMSE
Dalian
1.781
25.20%
2.154
16.03%
Chaoyang
1.514
22.38%
2.522
18.12%
Shengyang
1.336
20.21%
2.068
15.42%
Overall
1.561
22.91%
2.255
16.54%
a
Final accuracy of solar radiation estimation by A-P model with the
interpolated sunshine duration
are compared, the results are presented in Table 3. When the
interpolated sunshine duration is used, A-P model returns the
overall RMSE of 2.255 MJ m−2 and the RRMSE of 16.54%,
suggesting that Å-P model with the generic parameters (a =
0.505, and b = 0.204) and the interpolated sunshine duration
can return reasonable results. Although the sunshine duration
interpolation returns the overall RMSE of 1.561 h and the
RRMSE of 22.91%, the error caused by interpolation only accounts for 4.23% of the final error of solar radiation estimation.
3. Result and discussion
a. Temporal distribution of sunshine duration and solar
radiation
Figure 3 shows the temporal distribution of daily solar radiation and sunshine duration for the study area. These figures
are based on the averaged daily data of 2005-2009 of the
whole study area. The daily sunshine duration varies between
1.57 and 10.93 h, with the annual mean daily value of 6.82 h.
The monthly mean daily sunshine duration varies between 5.55
and 7.96 h, with two peaks observed in May and September,
and the lowest in December. Actual sunshine duration decrease
in June while the potential sunshine duration increases to the
maximum value, the actual sunshine duration in July and
August are also lower than those in May, this is attributed to
the increase in rainy days from June to August, coinciding
with the rainy season in the study area. Under the influence of
the continental monsoon climate, the rain mainly clusters in
summer (June to August), which could account for 60-75% of
the total annual precipitation in Liaoning province. Daily solar
radiation varies between 5.26 and 22.74 MJ m−2, and the monthly mean daily values varies between 7.55 and 19.01 MJ m−2,
with the highest peak observed in May, and the lowest in
Fig. 3. Temporal distribution of daily sunshine duration (a) and solar
radiation (b).
December, yielding a pattern similar to that of daily extraterrestrial solar radiation. However, the actual solar radiation
decreases in June due to more attenuation of the solar radiation
in the rainy days, while extra-terrestrial increases to its maximum value.
b. Variation of solar radiation
The map of the daily solar radiation should be presented to
illustrate the spatial variation of the daily solar radiation. However, we only present the spatial distribution of the monthly
mean daily solar radiation in Fig. 4. Solar radiation shows an
obviously spatial variation. It generally decreases from south
to north in January, February, March, November and December, this is mainly due to the change of the suns declination,
causing a decrease of the extraterrestrial horizontal radiation
from south to north. During June to September, the eastern part
receive less solar radiation than the rest part of the province,
this is probably because most parts of the east are mountain
and forest areas. Under the influence of the warm-humid
monsoon and topography, the rain extensively clusters in this
area, and causes more cloud formation, thus reducing solar
radiation. While higher solar radiation occur in northwest part
which is connected with Inner Mongolian plateau where is
frequently attacked by drought and presents a climate with low
precipitation and cloud cover, thus causing clearer skies, and,
therefore, less attenuation of the total solar radiation.
The coefficient of variation, calculated as the ratio of standard
deviation to arithmetic mean, is adopted to measure the
variation of solar radiation, and coefficient of spatial variation
of the whole study area for each day is presented in Fig. 5. The
coefficient of variation ranges from a minimum of 2.29% in
March to a maximum of 20.64% in July. It is noted that the
coefficient of variation shows a generally opposite change trend
to sunshine duration. The sunshine duration is lower in summer
and winter and higher in spring and autumn, while the vari-
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ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES
Fig. 4. Spatial distribution of the monthly mean daily solar radiation.
the warm-humid south-east monsoon starting from the pacific
reaches to the area, and gradually becomes to the strongest in
July, causing large precipitation in the eastern mountain area,
while the low precipitation and cloud cover in the northwest
part. Such climate pattern increases the spatial difference of the
solar radiation, and, therefore, the larger spatial variation. While
the solar radiation in spring and autumn are more stable in
space, with the lower coefficient of variation.
Fig. 5. Coefficient of spatial variation of the whole study area for each
day of the year.
Fig. 6. Relation between coefficient of variation and sunshine duration.
ation is larger in summer and winter and lower in spring and
autumn, the correlation between them are statistically significant
(Fig. 6, r = −0.593, p < 0.001). In general, at the end of May
c. Substitution of solar radiation from nearby stations
It is an alternative to substitute daily solar radiation from
nearby stations. In the present work, if the measured solar radiation at each of the stations is replaced by the data at the
remaining stations, the returned RMSE and RRMSE are very
large, with the average RMSE of 4.816 MJ m −2, and the
RRMSE of 35.44% (Table 2). As the solar radiation data are
spatially very sparse in the study area, it is difficult to plot the
precision versus distance relationship. The studies carried out
by Hunt et al. (1998) and Trnka et al. (2005) showed that the
RMSE between the substitution and measured values could be
described as a function of distance in a curvilinear manner.
However, within a moderate distance, the relationship could
also be well described as a linear function, which was reported
by Podestá et al. (2004) in Pampas of central-eastern Argentina.
In the present study, we assume that the relationship can be
described in a linear manner within the moderate distance, the
RMSE increases by approximately 0.157 MJ m−2 day−1 per 10
km, which is similar to 0.15 MJ m−2 d−1 per 10 km in Czech
30 November 2012
Ji-Long Chen and Guo-Sheng Li
and Austrian (Trnka et al., 2005). The threshold distance point
at which the substitution of solar radiation from a nearby
station gives the same precision with that of the A-P equation
is calculated, substitution from the nearby station within the
threshold distance is preferred to A-P model. The distance is
approximately 135 ± 15 km. The threshold distance in our study
area is much smaller than 385-400 km in Ontario of Canada
(Hunt et al., 1998), while within the range of 100-200 km in
Central Europe (Vanícek, 1984).
ê
d. Variation of clearness index
The clearness index, which is defined as the ratio of the
daily actual solar radiation to the extra-terrestrial irradiation
following the notations of the European Solar Radiation Atlas
(ESRA, 2000), is used as the criterion for sky conditions in this
study, and the daily clearness index curve is presented in Fig.
429
7. The index varies between 0.261 in July and 0.711 in December, with an average of 0.499. This means that about half of the
extraterrestrial irradiation reaches the ground. The smaller
indexes occur in summer, corresponding to the rainy season in
the study area. The cloud coverage and the optical thickness of
the atmosphere, including the turbidity of the air mass, cause
higher fraction of the solar radiation attenuation, including the
absorbed and scattered by the atmosphere, thus reducing that
reaching the surface. In winter, the northwest wind is prevailing
due to the influence of the northern high pressure. It brings dry
and cold air to the province, the precipitation is low, and thus
causing higher clearness index.
Although the clearness index strongly depends on latitude,
to the local extent, it shows a seasonal behavior as shown in
Fig. 8. The clearness index generally decreases from south to
north in winter; this means that the latitude is dominated. In
summer and autumn, lower clearness index occur in the eastern
part where most parts of which are mountains, while higher
clearness index are observed in the northwest part which is
connected with Inner Mongolian plateau, this indicates that the
topography and climate are dominated.
4. Conclusion
Fig. 7. Clearness index of the study area for each day of the year.
Fig. 8. Variation of the monthly mean daily clearness index.
Knowledge of temporal and spatial variation of solar radiation is essential for many applications, such as ecological and
crop growth models, evapotranspiration estimation. In spite of
its significance, such information is limited, especially in data
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ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES
Acknowledgments. The work was supported by the Geological
Survey program of China Geological Survey (GZH201200503,
1212010611402) and Special Fund for Land and Resources
Research in the Public Interest (201111023). We thank the
National Meteorological Information Center, China Meteorological Administration for providing the long-term data records.
Many thanks go to the anonymous reviewers for the comments
on the manuscript.
Edited by: Tadahiro Hayasaka
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ê
sparse regions. A simple and feasible procedure is conducted in
this work to map the daily solar radiation in local extent with
sparse data. Daily sunshine duration are interpolated to the
whole area, consequently, daily solar radiation are calculated by
A-P model using the generic parameters which are determined
by least square regression to minimize the overall fitting
residual between H/Ho and Rs/Ra of the sites where solar
radiation are available. Admittedly, the limitation is that the
validation is constrained by the availability of the solar radiation
measurement, and hence the overall fitting residual and the selfvalidation are employed for evaluation. In the present study
area, the A-P model with the generic parameters (a = 0.505, and
b = 0.204) and interpolated sunshine duration returns reasonable results, with the overall RMSE of 2.255 MJ m−2, and
RRMSE of 16.54%. In other local regions with sparse data, the
study on mapping of the solar radiation could be carried out
following the simple procedure, and the validation should be
investigated in other regions with greater availability of solar
radiation measurement.
In the present study area, substitution of solar radiation from
nearby station is preferred to estimation by A-P model if the
distance between the stations falls below the threshold of 135 ±
15 km. The RMSE of such substitution increases by approximately 0.157 MJ m−2 per 10 km. The daily solar radiation
varies between 5.26 in December and 22.74 MJ m−2 in May.
Under the influence of the monsoon, the large precipitation
during June to August causes higher fraction of solar radiation
attenuation, and thus causing lower clearness index in summer.
The solar radiation shows an obviously spatial variation. It
generally decreases from south to north in January, February,
March, November and December. During June to September, it
is mainly influenced by warm-humid monsoon and topography,
the eastern part receive less solar radiation than the rest part of
the province, while higher solar radiation occur in northwest
part, such pattern results in the larger spatial variation with
higher coefficient of variation.
30 November 2012
Ji-Long Chen and Guo-Sheng Li
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