Analysis of the Thermal Dome Effect from Global Solar

Current Optics and Photonics

Vol. 1, No. 4, August 2017, pp. 263-270

- 263 -

I. INTRODUCTION

To evaluate the performance of radiometric devices, both

in a laboratory setting and in the field, it is necessary to

have accurate knowledge of the luminous radiation that

stimulates the equipment [1]. Pyrheliometers, pyranometers,

and pyrgeometers are used to obtain solar and infrared

radiation data from observatories worldwide [2]. Typical

solar radiometers measure the entire optical range of the

electromagnetic spectrum emitted by the sun, including

certain parts of the ultraviolet (UV - A, B; 0.285-0.4 µm),

visible (VIS; 0.4-0.7 µm), and near-infrared regions (NIR;

0.7-2.8 µm). The pyrheliometer was invented by Pouillet

in 1837, and he observed a TSI (Total Solar Irradiance) of

1,227 W m-2, which is within 10% of the current standard

TSI of 1,366 W m-2 [3]. In addition, the Smithsonian

Institution began surface solar radiation observation in

1890, while the US National Weather Service contributed

to the improvement of meteorological observation capability

and the development of agrometeorology by beginning

observations in 1901 [4]. The Kimball-Hobbs pyranometer,

developed in 1923, became the prototype of the Eppley

pyranometer. Meanwhile, the Moll-Gorczynski radiometer,

which was based on the first model developed by Kipp

Analysis of the Thermal Dome Effect from Global Solar Radiation

Observed with a Modified Pyranometer

Ilsung Zo1, Joonbum Jee2, Buyo Kim1,3, and Kyutae Lee1,3*

1Research Institute for Radiation-Satellite, Gangneung-Wonju National University, Gangneung 25457, Korea2Weather Information Service Engine, Hankuk University of Foreign Studies, Yongin 17035, Korea

3Department of Atmospheric & Environmental Sciences, Gangneung-Wonju National University,

Gangneung 25457, Korea

(Received March 21, 2017 : revised June 5, 2017 : accepted June 19, 2017)

Solar radiation data measured by pyranometers is of fundamental use in various fields. In the field of

atmospheric optics, the measurement of solar energy must be precise, and the equipment needs to be

maintained frequently. However, there seem to be many errors with the existing type of pyranometer, which

is an element of the solar-energy observation apparatus. In particular, the error caused by the thermal dome

effect occurs because of the thermal offset generated from a temperature difference between outer dome

and inner casing. To resolve the thermal dome effect, intensive observation was conducted using the method

and instrument designed by Ji and Tsay. The characteristics of the observed global solar radiation were

analyzed by classifying the observation period into clear, cloudy, and rainy cases. For the clear-weather

case, the temperature difference between the pyranometer’s case and dome was highest, and the thermal

dome effect was 0.88 MJ m-2 day-1. Meanwhile, the thermal dome effect in the cloudy case was 0.69

MJ m-2 day-1, because the reduced global solar radiation thus reduced the temperature difference between

case and dome. In addition, the rainy case had the smallest temperature difference of 0.21 MJ m-2 day-1.

The quantification of this thermal dome effect with respect to the daily accumulated global solar radiation

gives calculated errors in the cloudy, rainy, and clear cases of 6.53%, 6.38%, and 5.41% respectively.

Keywords : Modified pyranometer, Thermal offset, Global solar radiation, TDE (Thermal dome effect),

Dome temperature

OCIS codes : (010.1290) Atmospheric optics; (010.1615) Cloud; (010.3920) Meteorology; (010.5630)

Radiometry

*Corresponding author: [email protected]

Color versions of one or more of the figures in this paper are available online.

*

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Copyright 2017 Current Optics and Photonics

ISSN: 2508-7266(Print) / ISSN: 2508-7274(Online)

DOI: https://doi.org/10.3807/COPP.2017.1.4.263

Current Optics and Photonics, Vol. 1, No. 4, August 2017264

and Zonen, was developed in 1924 [5]. In 1930, the Eppley

Laboratory began production of commercialized pyrano-

meters, leading to their worldwide installation and operation.

Nowadays the significant growth of the photovoltaic

industry has led to an increase in the use of pyranometers,

which are often used to select a development site, and

help to develop models for predicting solar radiation [6, 7].

The amount of generated solar power increases as the

solar radiation reaching the surface of the earth becomes

stronger, and thus accurate solar radiation observations are

considered to be a very important tool for solar power

generation [8].

Solar radiation is observed according to WMO (World

Meteorological Organization) and WRC (World Radiation

Center) regulations [9, 10]. The pyranometers used are

classified based on performance, using the WMO and ISO

9060 pyranometer classification standards. The WMO standard

classifies pyranometers as High Quality, Good Quality, and

Moderate Quality, while the ISO classifies them as Secondary

Standard, First Class, and Second Class. Such an instrument

must be carefully managed and handled because pyrano-

meters are affected by uncertainties resulting from their

sensitivity function, thermal offset, other spectral effects, and

geometrical, environmental, and instrumental factors [11].

Although most of the uncertainty factors have already been

studied, the problem related to thermal offset has not been

solved [12-14].

Thermal offset refers to errors generated because the

thermopile in the pyranometer is affected not only by solar

energy, but also by the ambient temperature [15]. This

effect generates a larger error when the sky is clear during

the night, compared to cloudy conditions [16]. One study

attempted to decrease the error by reducing the increase of

case temperature using a fan [17]. Analysis has also been

performed of the correlation of thermal effect with the

difference between long-term observation data (BSRN obser-

vations) and model results from the GCM (Global Circu-

lation Model), and the MODTRAN (Moderate resolution

atmospheric Transmission) radiative transfer model [18, 19].

Ji and Tsay [20] calculated the temperature difference

between outer and inner domes of a pyranometer using

pressure observations and the ideal gas equation. The thermal

offset was calculated using the TDE (Thermal Dome Effect),

and the change in solar radiance was determined using the

calculated temperature and the temperature observed at the

inner pyranometer case. In this study the thermal offset

difference was calculated and the change in solar radiation

due to the TDE was analyzed, using solar radiation data

classified into clear, cloudy, and rainy days, from intensive

observations at Gangneung-Wonju National University.

II. RESEARCH METHODS AND MATERIALS

2.1. Research Methods

For a general pyranometer, the global solar radiation (I, in

units of W m-2) is determined by multiplying the calibration

constant (c, in units of W m-2 mV-1) of each pyranometer

by the voltage measurement from the pyranometer (V, in

units of mV), as shown in Eq. (1). In the night case without

solar radiation, the observation is 0 W m-2. However, most

pyranometers actually show a negative (-) value, such as the

result of Carnicero [21]. This is because the temperature of

the case (Tc) was higher than the temperature of the dome

(Td), opposite the daytime situation. Thus the TDE can be

found using Eq. (2) as the energy difference generated by

the temperature difference between dome and case.

I cV (1)

Thermal of fset ∝

(2)

where σ denotes the Stefan-Boltzmann constant (5.6697 ×

10-8 W m-2 K-4).

Similarly, Ji and Tsay [20] built a modified pyranometer

to study the thermal offset, as illustrated in Fig. 1. Unlike

for a general pyranometer, the Tc and Pd (dome pressure)

between outer and inner dome were also observed. Smith

[11] directly attached a temperature sensor to the dome to

observe Td, but because this can cause an error in the

pyranometer’s measurements, the Ji and Tsay method was

used in this study.

Using Eqs. (1) and (2), the equation for global solar

radiation of Ji et al. [22] can be deduced as:

I cV f

(3)

Here the dome factor f accounts for the optical and

radiative properties of the domes and detector surface [23],

and Ts is the thermopile temperature calculated from Tc

using Hickey’s method [24], while Td is calculated using

Pd and the ideal gas equation. Thus, to observe an accurate

value from the pyranometer, the energy generated by the

first general term and the temperature difference between

the pyranometer case and dome must be considered.

Table 1 shows the TDE calculation procedure of Ji and

Tsay, consisting of 4 steps. In step 1, Tdnight is estimated

FIG. 1. Schematic diagram of a modified pyranometer.

Analysis of the Thermal Dome Effect from Global Solar Radiation Observed with … - Ilsung Zo et al. 265

during the night (2000 LST to 0400 LST) when the solar

radiation becomes 0 W m-2, by setting the left side of

Eq. (3) to zero. To compensate for the small pressure loss

generated around the pressure observation hose, Pd is

defined by 2 terms, as in Eq. (4), and each term can be

expressed as in Eqs. (5) and (6).

(4)

(5)

(6)

Here P0 is the dome pressure without pressure loss using

the state equation in Eq. (5), δPd is the pressure difference

between inner and outer domes with pressure loss, and k

is the dome factor. Combining these gives

(7)

where Pd and Pa are the measurements. r0 (y-intercept) and

k (slope) are calculated with the first equation form in

Step 2, by dividing both sides of Eq. (7) by the Td calculated

in Step 1. In Step 2, the dome temperature during daytime

can be calculated by substituting the calculated r0 and k

into Eq. (7) and arranging the Pd-related equation into the

Td-related equation, as given in Step 3. The daytime Tdnight

is calculated with the obtained r0 and k, using the daytime

dome pressure (Pd), atmospheric pressure (Pa), and night

data. The Td (Tdnight + Td

daytime) calculated in Steps 1 and 3

is substituted into Eq. (3), and the irradiance including the

TDE can be calculated.

2.2. Research Materials

This study used a modified Eppley PSP (Precision Spectral

Pyranometer) device, as illustrated in Fig. 1. The c and f

values of the modified pyranometer required for Eq. (3)

were determined by experiment [25]. In addition to the usual

observation data, Tc and Pd were observed. In addition,

measurements were made of the solar radiation (direct, global,

and diffuse), temperature, relative humidity, and pressure

on the rooftop of Life Science Building 2nd, Gangneung-

Wonju National University, Gangneung, Republic of Korea

(Lat.: 37.77°E, Lon.: 128.87°N, Alt.: 63.50 m). This obser-

vation site was chosen because there was no impinging

shade from other buildings. However, shading occurred

between 1600 LST and 1700 LST due to a hill to the

west, and varied depending on the altitude and azimuth of

the sun. Thus the observation data from these times were

omitted from the study. Table 2 shows the three classifi-

cations for sky and weather conditions (clear, cloudy, and

rainy) during the intensive observation period from 9 October

until 7 November 2011, which was in collaboration with

NASA. The observation period consisted of 5 clear days,

16 cloudy days, and 9 rainy days [26]. In addition, Fig. 2

presents the time series for solar radiation (in units of MJ

m-2) with the pyranometer and the total cloud amount (in

units of tenths) per day [27], as observed with a sky viewer.

The maximum irradiance was found to be higher than 2.0

MJ m-2 at noon on a clear day, but less than 1.0 MJ m-2

on a cloudy or rainy day. The rainfall accumulated during

the corresponding day is summarized in Table 2.

TABLE 1. Procedure for obtaining the solar radiation

corrected thermal dome effect

Step Action Equation

1Calculation of Td

night

during night timeTd

night = (Ts4 + cV/fσ)1/4

2Calculation of r0 and k

using Tdnight

Pd/Tdnight =

r0 + k(Pd-Pa)/ Tdnight

3 Calculation of Tddaytime Td

daytime =

[(1-k)Pd + kPa)]/ r0

4calculation of solar radiation

corrected thermal effectI = cV + fσ(Ts

4-Td4)

TABLE 2. The cases were classified as clear, cloudy, and

rainy according to sky and weather conditions during an

intensive observation period in 2011 (from 9 October to 7

November, 2011)

Case Date (Month/Day)

Clear

(5 days)10/13, 10/17, 10/18, 10/19, 10/31

Cloudy

(16 days)

10/09, 10/10, 10/11, 10/12, 10/16, 10/20,

10/23, 10/24, 10/25, 10/26, 10/27, 10/28,

11/01, 11/02, 11/03, 11/04

Rainy

(in units of mm)

(9 days)

10/14(4.0), 10/15(4.5), 10/21(4.5),

10/22(37.5), 10/29(9.0), 10/30(0.5),

11/05(6.0), 11/06(28.0), 11/07(2.0)

FIG. 2. Time series of hourly solar radiation and daily mean

total cloud amount at Gangneung-Wonju National University

during an intensive observation period in 2011 (from 9

October to 7 November, 2011).


III. RESULTS

3.1. Clear Case

The global solar radiation data from 18 October 2011,

which is among the selected clear days, is shown in Fig. 3.

The global solar radiation was observed using the modified

pyranometer (PSP, EPPLEY), while the direct and diffuse

solar radiation were observed at 1 minute intervals using

the Kipp & Zonen instrument (direct: CHP1, diffuse: CMP

21, sun-tracker: 2AP). The direct (red dots) and diffuse

(blue dots) solar radiation observations could be considered

accurate because the effect of atmospheric components

such as aerosols, including clouds in the optical path, was

insignificant [28, 29]. From about 1620 LST, the majority

of direct solar radiation was shaded by a mountain, and a

value close to 0 W m-2 was observed. Accordingly the total

solar radiation and diffuse solar radiation were observed to

have a very similar. Figure 3(b) shows the magnification

of the solar radiation change at night. As stated before, the

observation during the night should be 0 W m-2; however,

a negative (-) energy was observed, due to the TDE error.

The TDE in the clear case was determined according to

the procedure in Table 2. Figure 4 presents the graphs of

Tdnight during the night as a function of time from the

observed Tc and Step 1 in Table 2. As shown in Fig. 4(b),

Td was lower than Tc during the night. The difference

between these two values resulted in a small current being

generated, and an error in the observation data.

The calculated dome factor (k = 0.064) and r0 (3.457 g

m-2 K-1) were obtained using the equation and the night

observation data from Fig. 5(a) for the calculation in Step

2 of Table 1. The R² and standard error were 0.889 and

FIG. 3. Time series of hourly solar radiation at Gangneung-

Wonju National University on 18 October 2011: (a) solar

radiation (global, direct, and diffuse), and (b) global radiation

captured at night.

FIG. 4. Same as Fig. 3, except for case temperature (Tc, black

dots) and dome temperature at night (Tdnight, blue dots).

(a)

(b)

FIG. 5. (a) Estimation of r0 and k from nighttime mea-

surement in Step 2 from Table 1. (b) Time series of case

temperature and dome temperature at daytime in Step 3

from Table 1.


0.0008 MJ m-2 respectively. The dome factor and r0

calculated in Step 2 were implemented in Step 3 and are

presented in Fig. 5(b), which shows both Tc and Tddaytime.

It can be seen that the case temperature was higher than

the dome temperature, in a similar situation to that at

night. Hence, because of the difference between the two

temperatures, the actual daytime irradiance was lower than

the observation from the pyranometer. It can be concluded

that the reduction of global solar radiation during daytime

was larger than the reduction that occurred at night,

because the temperature difference was higher in the

daytime than the nighttime.

After the daytime temperature of the inner dome was

calculated per Step 3, the global solar radiation in one day

could be calculated using Eq. (3) to compensate for the

pyranometer temperature. Figure 6 shows the change of

pyranometer thermal offset for 18 October 2011, while

Fig. 6(a) shows the global solar radiation before (red dots)

and after (blue dots) correction with the pyranometer thermal

offset. Additionally, Fig. 6(b) presents the global solar

radiation change at nighttime after sunset, without global

solar radiation. The global solar radiation at night without

sunlight must be 0 W m-2, but in Fig. 6(b), the pyrano-

meter showed a negative (-) global solar radiation at night.

Thus, as has been mentioned previously, the compensation

for pyranometer temperature is needed since a negative (-)

global solar radiation was found during the night due to

the difference between the dome temperature and case

temperature. The corrected irradiances by pyranometer (blue

dots) give a value much closer to 0 W m-2.

3.2. Cloudy Case

The cloudy cases in this study were the case with upper

and middle clouds (15 October 2011; Fig. 7(a)), and the

case with the rainfall until morning and clouds in the

afternoon (30 October 2011; Fig. 7(b)). The case on October

2011, which same season as the clear case, was selected.

The temperature difference between Tdnight and Tc before

sunrise is shown in Fig. 8 using the analysis method in

Table 1, in a similar manner as for the clear case. The red

color indicates data from the clear case on 18 October

2011, while blue and black indicate data from the cloudy

and rainy cases on 15 and 30 October 2011 respectively.

The clear case data exhibited the highest temperature

difference of 0.3 K, while the temperature difference for

the rainy day was less than 0.05 K. Hence, the temperature

of the inner pyranometer during the night was higher than

0900

LST

1200

LST

1500

LST

(a) (b)

FIG. 7. Total sky images for (a) cloudy (15 October 2011) and

(b) rainy (30 October 2011) cases, observed from Gangneung-

Wonju National University.

FIG. 8. Temperature difference between Tc and Tdnight during

the night (from 2000 LST to 0400 LST) for all cases.

FIG. 6. Same as Fig. 3, except for observed global solar

radiation (black dots) and modified global solar radiation

(blue dots) corrected for the thermal effect.


the dome’s temperature, whereas the largest difference was

found for a day with a higher temperature difference.

The calculated Tdnight from Fig. 8 was used to calculate

Tddaytime, and then inserted into Eq. (3) to produce the results

in Fig. 9. First, the maximum value of the cloudy case on

15 October 2011 was consistent with the clear day (18

October 2011). However, the global solar radiation change

was significant, due to the effect of clouds. Especially at

1400 LST and 1500 LST, the global solar radiation that

reached the surface of the earth was significantly reduced,

owing to the clouds. The global solar radiation for the

rainy day (30 October 2011) was also highly reduced. In

addition, negative (-) global solar radiation was found for

the cloudy case before sunrise and after sunset, as shown

by the black line. Correction of the offset reduced the

negative (-) global solar radiation, producing a measured

global solar radiation close to 0 W m-2, as shown in blue.

As the negative (-) global solar radiation before sunrise

was very small owing to the rain, the difference between

Tc and Tdnight was also very small (Fig. 8, black points; 30

October 2011). Moreover, because the difference between

Tc and Tdnight becomes larger after sunset for the rainy

case, the negative (-) error was decreased by the offset

correction.

The daily accumulated TDE during the observation

period is quantitatively presented in Fig. 10. The gray bar

represents the daily accumulated global solar radiation, the

red bar shows the daily accumulated TDE, and the line

indicates the total cloud amount. The TDE was proportionally

larger for days with high daily accumulated global solar

radiation. The maximum daily accumulated TDE of 1.16

MJ m-2 was calculated for 31 October 2011. Moreover, the

lowest TDE of 0.02 MJ m-2 was found on 6 November

2011, when clouds and rain occurred all day. When the

FIG. 10. Same as Fig. 2, except for daily accumulated solar

radiation (gray bars), daily accumulated thermal dome effect

(red bars), and daily mean total cloud amount (blue dots).

TABLE 3. Daily accumulated solar radiation (DSR, in units

of MJ m-2), thermal dome effect (TDE, in units of MJ m-2) and

ratio (%) of TDE to daily accumulated solar radiation

CaseDSR

(MJ m-2)

TDE

(MJ m-2)

Ratio of TDE

(%)

Clear 16.29 0.88 5.41

Cloudy 10.56 0.69 6.53

Rainy 3.35 0.21 6.38

(a) (b)

FIG. 9. Same as Fig. 6, except for the cases with (a) cloudy (15 October 2011) and (b) rainy (30 October 2011).


surface-reaching global solar radiation became stronger, the

temperature increased. Thus, the temperature difference of

the inner and outer pyranometer cases became larger,

resulting in the TDE. Table 3 shows the average TDE for

the clear, cloudy, and rain cases, with the highest value

found for the clear case. These maximum differences can

also be stated for the cloudy, rainy, and clear cases as

percentages: 6.53%, 6.38%, and 5.41%.

IV. CONCLUSION

Pyranometers for the observation of global solar radiation

have been developing, into their present form since the

19th century. However, studies are still being conducted to

solve the problems related to thermal offset, owing to the

temperature difference between case and dome. In this

study, intensive observations were performed and the TDE

was analyzed using the Ji and Tsay (2010) method [20]

and a modified pyranometer at Gangneung-Wonju National

University, in collaboration with NASA. The analysis

involved classifying the observation period into clear,

cloudy, and rainy cases using observations of the total

cloud amount. The difference between Tc and Td was large

for clear days, leading to an increase of the TDE, and a

value of 0.88 MJ m-2 day-1 was found. For the cloudy

case, the temperature difference between case and dome

was reduced and the TDE increased to a value of 0.69 MJ

m-2 day-1, while the rainy case showed only 0.21 MJ m-2

day-1. However, when these were expressed as a daily

accumulated global solar radiation percentage ratio, the

cloudy case day exhibited the highest percentage difference

(6.53%), followed by the rainy case (6.38%), and clear case

(5.41%).

As a result, even though the TDE strongly affected the

measured global solar radiation on a clear day, the TDE

had a relatively higher effect on cloudy or rainy day. Thus,

the TDE must be considered in all weather conditions.

Correcting for the TDE in a solar observation instrument

should be considered necessary for global solar radiation

observations and the study of its application. In particular,

the observation of the TDE in the field of atmospheric

optics could provide an error range for the utilization of

global solar radiation data. However, the data used in this

study resulted from the analysis of intensive observation

data over only one month, and thus a generalization for all

global solar radiation instruments is problematic. Hence the

quantification of TDE should be considered as a prerequisite

for long-term observations and analysis.

ACKNOWLEDGMENT

This work was funded by the Korea Meteorological

Administration Research and Development Program under

Grant KMIPA 2014-21080.

This research was supported by Basic Science Research

Program through the National Research Foundation of

Korea (NRF) funded by the Ministry of Education (NRF-

2017R1D1A3B03034467).

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