Adjustment factors for the ASHRAE clear-sky model based on solar-radiation measurements in Riyadh

APPLIED

www.elsevier.com/locate/apenergy

Applied Energy 79 (2004) 215–237ENERGY

Adjustment factors for the ASHRAEclear-sky model based on

solar-radiation measurements in Riyadh

Sami A. Al-Sanea a,*, M.F. Zedan a, Saleh A. Al-Ajlan b

a Department of Mechanical Engineering, College of Engineering, King Saud University,

P.O. Box 800, Riyadh 11421, Saudi Arabiab Energy Research Institute, King Abdulaziz City for Science and Technology, P.O. Box 6086,

Riyadh 11442, Saudi Arabia

Accepted 22 November 2003

Available online 5 February 2004

Abstract

The solar-radiation variation over horizontal surfaces calculated by the ASHRAE clear-sky

model is compared with measurements for Riyadh, Saudi Arabia. Both model results and

measurements are averaged on an hourly basis for all days in each month of the year to get a

monthly-averaged hourly variation of the solar flux. The measured data are further averaged

over the years 1996–2000. The ASHRAE model implemented utilizes the standard values of

the coefficients proposed in the original model. Calculations are also made with a different set

of coefficients proposed in the literature. The results show that the ASHRAE model calcu-

lations generally over-predict the measured data particularly for the months of Octo-

ber!May. A daily total solar-flux is obtained by integrating the hourly distribution. Based

on the daily total flux, a factor U (<1) is obtained for every month to adjust the calculated

clear-sky flux in order to account for the effects of local weather-conditions. When the

ASHRAE model calculations are multiplied by this factor, the results agree very well with the

measured monthly-averaged hourly variation of the solar flux. It is recommended that these

adjustment factors be employed when the ASHRAE clear-sky model is used for solar radia-

tion calculations in Riyadh and localities of similar environmental conditions. Instantaneous,

daily and yearly solar-radiation on various surfaces, such as building walls and flat-plate solar

collectors, can then be conveniently calculated using the adjusted model for different orien-

tations and inclination angles. The model also allows the beam, diffuse and ground-reflected

*Corresponding author. Tel.: +966-1-4676682; fax: +966-1-4676652.

E-mail address: [email protected] (S.A. Al-Sanea).

0306-2619/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.apenergy.2003.11.005

mail to: [email protected]

216 S.A. Al-Sanea et al. / Applied Energy 79 (2004) 215–237

solar-radiation components to be determined separately. Sample results characterizing the

solar radiation in Riyadh are presented by using the ‘‘adjusted’’ ASHRAE model.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Solar radiation in Riyadh; ASHRAE clear-sky model

1. Introduction

Accurate estimation of solar radiation on the Earth�s surface is needed in manyapplications. These include calculation of air-conditioning loads in buildings, design

and performance evaluation of passive building-heating systems as well as solar-

energy collection and conversion systems. Such data are also beneficial in areas of

agriculture, water resources, day-lighting and architectural design, and climate

change studies. In fact, solar radiation provides energy for photosynthesis and

transpiration of plants and is, therefore, one of the most important parameters in

estimating potential crop-yields and crop water consumption.

Compared to meteorological parameters such as precipitation, temperature andwind, irradiance measurements are scarce, and are not available except at limited

geographical locations around the world. Even in developed countries, daily mea-

surements of solar radiation are too dispersed location-wise to use in simulation

models. Alternatives such as the use of average values, spatial interpolation, esti-

mates from remote-sensing data, and estimates obtained from models based on

climatic variables have been suggested. However, to use interpolation, the maximum

distance between observing stations and the location of interest should not exceed 30

km in order to account for most of the spatial variation of global radiation [1]. As forthe use of average values, it is not adequate in the analysis of energy systems which

usually require hour-by-hour values.

Because of the previous needs and the scarce nature of solar radiation measure-

ments, a number of models with varying degrees of complication, detail and accu-

racy have been developed. Some of these models are either empirical and therefore

are site-dependent or semi-empirical of a more general nature when local parameters

are input to them. Recent and more relevant among these models are discussed later

in the section on previous studies.Saudi Arabia is no exception to other parts of the world where available mea-

surements are limited. Moreover the solar-radiation intensity is among the highest in

the world. This high solar intensity can be put to good use via collection and thermal

storage, while its adverse effects can be reduced if we have accurate models for

calculating the temporal and spatial variations of solar radiation. This points to the

need for a robust model to achieve these requirements. The ASHRAE clear-sky

model [2] appears to be general enough for the above objectives; however, one of its

drawbacks is that it is for �clear skies� as the name implies and was developed for a‘‘basic atmosphere’’. In Saudi Arabia, the sky is far from clear over a good portion

of the year, mainly because of suspended dust in the air and sometimes because of

the presence of clouds.

S.A. Al-Sanea et al. / Applied Energy 79 (2004) 215–237 217

In this paper, the ASHRAE clear-sky model is used to estimate the monthly-

average hourly global solar-radiation on horizontal surfaces in Riyadh. Monthly

adjustment factors are obtained by comparing model results with the corresponding

averaged measurements. The measured data cover 5 years from 1996 to 2000. The

model is then used with these adjustment factors to obtain the beam, diffuse and

global radiations on vertical surfaces with different orientations in Riyadh.

2. Previous studies

Most of the extensive literature available on estimating surface solar-radiation

can be classified into two broad categories: monthly-averaged daily irradiation and

monthly-averaged hourly irradiation.

2.1. Monthly-averaged daily irradiation

Measured monthly-averaged values of daily irradiation H are a good source of

information and provide the starting point of many calculation schemes. At a par-

ticular location, the long-term average of H is generally constant. Angstr€om, as early

as 1924, proposed a correlation relating H and the monthly average of the instru-

ment-recorded daily time fraction of bright sunshine S in the form [3]:

H=H clear ¼ aþ ð1� aÞS; ð1Þ
where H clear is the value of H when the averaging is done over clear days only, and ais a location-based empirical constant (a ¼ 0:25 for Stockholm); note that 06 S6 1.
This correlation was later modified by Prescott and others by replacing H clear with

the average extraterrestrial solar radiation H 0. The modified correlation is known as

the Angstr€om–Prescott equation [3] and has the form:

H=H 0 ¼ aþ bS; ð2Þ
where a and b are empirical local constants. This equation proved to be more
beneficial than the original Angstr€om equation because of the unavailability of H clear

for most locations while H 0 can be calculated for any location. The disadvantage of

this modified equation is that the local transmittance of solar radiation (due to watervapor), which was considered by Angstr€om through the local H clear, is now con-

sidered through the introduction of an additional empirical constant. Many papers

were published reporting the values of the empirical constants in the Angstr€om–

Prescott equation for various locations around the world. Some of these papers are

reviewed below.

Kuye and Jagtap [4] used measured solar data at Port Harcourt, Nigeria for the

years 1977–1989 and determined the regression constants a and b for each year by a

least-squares fitting technique. They showed no systematic variation in the coeffi-cients from one year to another. Frangi et al. [5] determined the monthly values of aand b for Niamey, Niger. They showed that the yearly averages of these coefficients

are in line with corresponding published values for neighboring African towns.


Using measurements from 10 stations in Europe with latitudes between 60�N and

70�N, Gopinathan and Soler [6] obtained the constants a and b through regression

analyses. When they tested the Angstr€om–Prescott relation with their constants

against measurements, they found excellent agreement for all locations within the

above latitudes. Kamel et al. [7] presented measurements of global solar-irradiance

on horizontal surfaces at five meteorological stations in Egypt for the years 1987–1989 and obtained the a and b coefficients in the Angstr€om–Prescott correlation for

these locations through regression analyses. Comparisons of predicted and measured

data are generally acceptable. Srivastava et al. [8] compared measured global radi-

ation in Uttar Pradesh (India) with calculations based on the Angstr€om–Prescott

equation with constants a and b from work by others for the same location, and

showed acceptable agreement. Also, they obtained new values for these constants

based on their measurements giving a maximum deviation of 7.5% in the global

radiation.Recently, the Angstr€om–Prescott equation was revisited by Suehrcke [3] who

developed a new correlation that does not contain empirical constants and only

requires the monthly average clear-sky transmittance to account for the climate of a

particular location. Other efforts in the literature suggested additional empirical

modifications to the Angstr€om–Prescott equation. For example, Rietveld (see [3])

suggested that the coefficients a and b could be linearly regressed versus �S and 1=�S,respectively, where �S is the (annual) average of the mean monthly values of S. Yang

et al. [9] extended the Angstr€om correlation to develop what they called a hybridmodel with four constants. The model relates the monthly-averaged daily global

radiation to the time fraction of bright sunshine, the effective beam-radiation and the

effective diffuse-radiation. The last two parameters are dependent on latitude, ele-

vation and season. Power [10] developed a correlation to estimate the clear-sky beam

radiation from the observed beam-irradiation time fraction of bright sunshine for

use in turbidity studies.

Supit and van Kappel [1] developed a simple method to estimate the daily global

radiation from mean daytime cloud-cover and maximum and minimum tempera-tures. The method is particularly beneficial when sunshine duration observations are

not available and therefore the methods discussed previously cannot be used. Sayigh

[11] developed a model to predict monthly global radiation from temperature, hu-

midity, relative sunshine hours, length of the day in hours and geographical factors

such as latitude and altitude. Telahun [12] used this approach to estimate the global

radiation in the Addis Ababa region but with a new set of model constants to achieve

better agreement with the measurements.

2.2. Monthly-averaged hourly irradiation

The second category of methods deals with the prediction of the monthly-aver-

aged hourly solar-radiation. The ASHRAE clear-sky model [2] is among thesemethods. In this model, the direct normal irradiation is calculated by means of a

simple equation containing two constants A and B while the diffuse irradiation is

given as a fraction C of the direct normal component.


The constants A, B, C are tabulated by ASHRAE [2] for each month of the year,

giving 12 sets of these constants. The model was developed for a ‘‘basic atmosphere’’

containing 200 dust particles per cm3 and a specific value of ozone concentration.

The amount of precipitate water varies for different months and is therefore ac-

counted for via the different sets of constants. Thus the 12 sets of coefficients reflect

the annual variation of the absolute atmospheric humidity. Because humidity had aninfluence on particle size of aerosols, the variations of the constants B and C indicate

a variation in turbidity as well. The constant A is related to the solar constant. The

tabulated values of A are based on work dating back to 1940, which assumes a solar

constant of 1332 W/m2. Recent accurate measurements yield an agreed-upon value

of 1367 W/m2. To account for regional variations of humidity and turbidity,

ASHRAE published maps for a parameter called ‘‘clearness number’’, for both

summer and winter, for different regions in the USA. This parameter is used to

modify the radiation values obtained from the model. The unavailability of thesefactors for other regions of the world prevented the use of this model for these re-

gions. The present work to develop adjustment factors to the ASHRAE clear-sky

model for Saudi Arabia is in the same spirit of these ‘‘clearness numbers’’.

The ASHRAE model was examined by Powell [13], by using data collected at 31

NOAA (National Oceanographic and Atmospheric Administration, USA) moni-

toring stations in the year 1977. The results confirmed the general validity of the

model in estimating solar radiation under cloudless conditions. The author reported

that the model results were inaccurate for Canadian sites mainly because of theunavailability of the clearness number, which was assumed to be unity at these sites.

Powell modified the basic ASHRAE model using elevation corrected optical air-

mass instead of seasonal clearness numbers. The author claims that his modifications

made the model generally more accurate.

Machler and Iqbal [14] recognized the above shortcomings of the ASHRAE

model and revised the constants A, B, and C in view of the advancement in solar

radiation research up to the 1980s. Further, they developed an algorithm that uses

horizontal visibility at ground level as a parameter for turbidity instead of theclearness numbers used in conjunction with the monthly constants. Also, they

modified the model by introducing a correction humidity term that accounts for

variable water-vapor absorption. Galanis and Chatigny [15] presented a critical re-

view of the ASHRAE model. They pointed out some inconsistencies in the way the

model is presented and formulated; they suggested including the clearness number in

the expressions of the direct and more importantly in the diffuse irradiation under

cloudless conditions. Also, they suggested to re-write expressions for cloudy-sky

conditions in a way that they reduce to the cloudless formulation for zero cloudcover. The authors also pointed out that the results of the model were acceptable

when compared with actual data in the USA while they were not for Canadian lo-

cations. They also showed that model results are sensitive to the clearness numbers

which unfortunately are only available for US locations.

Recently, Maxwell [16] developed a solar radiation model (called METSTAT

model) based on quality-assessed data collected from 1978 to 1980 at 29 US National

Weather Service sites. The model calculates hourly values of direct normal, diffuse,


and global solar radiation. The model input includes total and opaque cloud cover,

aerosol optical depth, precipitable water vapor, ozone, surface albedo, snow depth,

days-since-last snowfall, atmospheric pressure, and present weather. Although this

model appears to be comprehensive, its application is limited to locations where the

above input data are available.

Rigollier et al. [17] presented another clear-sky model developed in the frameworkof the new digital European Solar Radiation Atlas (ESRA). The model has explicit

expressions for both beam and diffuse radiation components. The parameters in the

model have been empirically adjusted by fitting techniques using hourly measure-

ments over several years for a number of European locations. Gueymard [18] pre-

sented two new models to predict the monthly-average hourly global irradiation

distribution from its monthly-averaged daily counterpart. He found that a quadratic

expression in the sine of the solar elevation angle fits the data very well at all lo-

cations considered. Other parameters in these models include mean monthly clear-ness index, average day-length, and daily average solar elevation. Using a large data

set from 135 stations covering diverse geographic locations (82.5�N to 67.5�S), theauthor assessed the performance of those models showing better relative accuracy

compared to other published models.

Yang and Koike [19] developed a numerical model to estimate the hourly-mean

global solar-irradiance in which the upper-air humidity is considered. The authors

defined a sky-clearness indicator as a function of the relative humidity profiles in the

upper atmosphere; then they used this indicator to relate global solar radiation undercloudy skies to that under clear skies.

3. Solar radiation calculations

The following calculations of the solar radiation on horizontal and vertical sur-

faces are based on the ASHRAE clear-sky model [2]. The latitude and longitude of

the location of interest, and the standard meridian for the local time-zone are specificinputs to the model and, hence, are the only parameters that need to be specified by

the user. Values of other parameters used in the model are of a more general nature

and are summarized in tables given later.

3.1. Horizontal surfaces

The global solar radiation on horizontal surfaces qh is composed of the following

two components:(1) Beam (direct) radiation qbh given by

qbh ¼ DNcoshh; ð3Þ
where DN is the direct normal radiation (W/m2) and hh is the angle of incidence
(zenith angle), and

(2) Diffuse sky radiation qdh given by

qdh ¼ CDN; ð4Þ


where C is the diffuse-sky factor.

Therefore, the global radiation on horizontal surfaces is

qh ¼ DNcoshh þ CDN: ð5Þ

The direct normal radiation DN is calculated from:

DN ¼ Ae�B= sin b; ð6Þ
where A is the apparent solar-radiation constant, B is the atmospheric extinction
coefficient, and b is the solar altitude angle above the horizontal.

The value of sin b is calculated from:

sin b ¼ sin/ sin dþ cos/ cos d cosx; ð7Þ
where / is the latitude of the location, d is the solar declination angle, and x is the
solar hour angle.The solar hour angle x, in degrees, is given by the local solar time (tsol) as

x ¼ 15ð12 : 00� tsolÞ; ð8Þ
with the solar noon as zero and each hour equivalent to 15� of longitude with
morning (+) and afternoon ()).The local solar-time is calculated from the local standard-time (tstd) and the

equation of time (Et), given later, by

tsol ¼ tstd þ Et þ 4ðLstd � LlocÞ; ð9Þ
where Lstd is the standard meridian for the local time zone (longitude of the time
zone) and Lloc is the longitude of the location in degrees west (0� < Lloc < 360�).The angle of incidence hh is the angle between the incoming solar rays and the

normal to the surface. For a horizontal surface:

cos hh ¼ sin b: ð10Þ

3.2. Vertical surfaces

The global solar radiation on vertical surfaces qv is composed of the following

three components:

(1) Beam (direct) radiation qbv given by

qbv ¼ DNcoshv; ð11Þ
where hv is the angle of incidence on vertical surfaces.(2) Diffuse sky radiation qdv given by
qdv ¼ CDNFws; ð12Þ
where Fws is the shape (view) factor between the surface and the sky; for a vertical
surface, Fws ¼ 1=2:(3) Ground reflected radiation qrv given by

qrv ¼ qhqgFwg; ð13Þ


where qh is the rate at which the global radiation (beam plus diffuse) strikes the

ground (horizontal surface) in front of the target surface, qg is the reflectance of the

ground, and Fwg is the shape factor between the surface and the ground; for a vertical

surface, Fwg ¼ 1=2.Therefore, the global radiation on vertical surfaces is

Table

ASHR

Mo

Jan

Feb

Mar

Apr

May

Jun

July

Aug

Sep

Oct

Nov

Dec

qv ¼ qbv þ qdv þ qrv ¼ DNcoshv þ CDNFws þ qhqgFwg: ð14Þ

The values of qh and DN are already given by Eqs. (5) and (6), respectively. The

angle of incidence hv is the angle between the incoming solar rays and the normal to

the surface. For a vertical surface:

cos hv ¼ � sin d cos/ cos cþ cos d sin/ cos c cosxþ cos d sin c sinx; ð15Þ

in which all the angles are known except c, which is the surface azimuth angle

measured east or west from the south. Hence, the value of c changes according to the

vertical surface orientation; the zero value is being due south, with east positive andwest negative. Accordingly, c ¼ 180�, 0�, 90� and )90� for vertical surfaces facing

north, south, east and west, respectively. It is noted that Eq. (15) is a simplified form

of a more general equation, given for inclined surfaces, relating the angle of inci-

dence of beam radiation on a surface (h) to other angles, see Duffie and Beckman

[20].

The input to the ASHRAE clear-sky model is, thus, complete by specifying values

for nine parameters, namely: A, B, C, Et, d, /, Lstd, Lloc and local standard-time (tstd).The ASHRAE model solar data [2] for each month are given in Table 1 for the firstfive parameters. The following three parameters are specific to the location of in-

terest; their values for Riyadh are given in Table 2. The ninth and final parameter;

namely the local standard time (tstd) is now the only varying parameter which is input

for calculations at any required time in the day.

It is interesting to note that the solar parameters given in Table 1 are for the 21st

day of each month. In the present investigation, the ASHRAE clear-sky model is run

1

AE clear-sky-model data for 21st day of each month [2]

nth A (W/m2) B C Equation of Time Et

(min)

Declination d(deg)

1230 0.142 0.058 )11.2 )20.01215 0.144 0.060 )13.9 )10.81186 0.156 0.071 )7.5 0.0

1136 0.180 0.097 1.1 11.6

1104 0.196 0.121 3.3 20.0

e 1088 0.205 0.134 )1.4 23.45

1085 0.207 0.136 )6.2 20.6

1107 0.201 0.122 )2.4 12.3

t 1151 0.177 0.092 7.5 0.0

1192 0.160 0.073 15.4 )10.51221 0.149 0.063 13.8 )19.81233 0.142 0.057 1.6 )23.45

Table 2

Particular data pertinent to the city of Riyadh

Latitude (/) Standard meridian (Lstd) Longitude (Lloc)

24.72� )45� )46.72�


for every day in the year and solar radiation data are produced every 15 min.

Therefore, the values of the solar parameters (A, B and C) for days other than the

21st day in each month are obtained by linear interpolation. Also, in the ‘‘modified’’ASHRAE model, which is used here just for comparison purposes, the values of A, Band C are different from those given in Table 1 and are as proposed by Machler and

Iqbal [14].

The equation of time (Et) and the declination (d) are obtained for any day of the

year (N ) from available sinusoidal-fit formulae given by Duffie and Beckman [20] as

Et ¼ 9:87 sinð2BNÞ � 7:53 cosðBNÞ � 1:55 sinðBNÞ; ð16Þ

where

BN ¼ 360ðN � 81Þ=365 ð17Þ

and

d ¼ 23:45 sin½360ð284þ NÞ=365�; ð18Þ

with N ¼ 1 for January the 1st and N ¼ 365 for December 31st.

The values of the solar parameters; namely, A, B, C, Et and d, change very slightly

from day-to-day. Therefore, their variations with time during the day are neglected

and, hence, they take constant values for each day of the year. Accordingly, at thebeginning of the solar-radiation calculations, the values of these five parameters

must first be determined for each day of the year. The ASHRAE model is run to

calculate the clear-sky solar-flux for each day of the year with a time increment of 15

min over the 24-h period. The solar flux is then averaged for each month on a

quarter-hourly basis. This gives a monthly mean solar flux for each quarter-hour of

the day. From this, the following quantities are also calculated: the daily mean flux

(in W/m2), the daily maximum flux (in W/m2) and its time of occurrence, and the

daily total flux (in MJ/m2 day).

4. Results and discussion

Solar measurements for the city of Riyadh are available for horizontal surfaces on

an hourly basis and are provided by King Abdulaziz City for Science and Tech-

nology (KACST). Such data are used here with permission [21] for comparison with

the ASHRAE clear-sky model. In the present investigation, the raw measured dataare averaged over each month of the year. The averaging is done at each hour of the

day over the whole month to produce a monthly-averaged hourly variation. This

process is found to eliminate large variations in the measured hourly solar flux from


day-to-day within each month due to local weather conditions. These monthly-

averaged hourly values are then averaged again over the years 1996–2000 to further

smooth out other, but smaller, variations from year-to-year.

4.1. Qualification of data

As mentioned above, the solar data used in this paper were obtained from

KACST. Such data were originally acquired through the Joint Solar Radiation

Resource Assessment project between KACST and the US National Renewable

Energy Laboratory (NREL). In that project, NREL assisted KACST with the design

of a 12-station solar-radiation-monitoring network including the selection of sen-sors, data loggers, instrument platform design, data collection, quality assessment,

and management [22]. The data used here were acquired at the Solar Village station

near Riyadh.

Measurements included the total (global) solar radiation, direct-beam radiation

and diffuse-sky radiation on a horizontal surface, ambient temperature and relative

humidity [22]. The data were sampled at a rate of 0.1 Hz (i.e. once every 10 s) and the

digitized data were averaged over 5-min records. All radiometers were calibrated

against a Reference Absolute Cavity Pyrheliometer. This reference device was ac-quired by KACST, which participated in the World Meteorological Organization

(WMO) 1995 International Pyrheliometric Comparison (IPC) in order to obtain

traceability to the WMO World Radiometric Reference (WRR). Further NREL

developed Radiometer Calibration and Characterization software to automatically

collect calibration data, generate calibration reports and archive calibration results.

The collected data were first examined by the network manager in order to find

obvious problems such as failed sensors. Faulty data were always excluded. Then,

the data were processed through a Data Quality Management System that per-formed checks on the relative partitioning of the radiometric data and whether it

exceeded physical limits. This was done by checking the balance of the following

equation:

IGH ¼ IDN cosðzÞ þ IDF; ð19Þ
where IGH is the global horizontal, IDN is the direct-beam, IDF is the diffuse-sky ra-
diation and z is the zenith angle. The latter equals the incidence angle for a direct

beam on a horizontal surface. Quality assessment flags were assigned to various

readings depending on the deviations from the balance of Eq. (19). The investigators

[22] have found that more than 80% of network data fell within the quality limit of�5% from the correct partitioning of the three radiation components.

4.2. Comparison with ASHRAE clear-sky model

Fig. 1(a) and (b) present and compare the monthly-averaged hourly variation ofthe measured global (beam plus diffuse) solar radiation on horizontal surfaces in

Riyadh for January and July, respectively. The symbols signify different years and

the solid line is the average over these years. Predictions of the ASHRAE clear-sky

Fig. 1. Monthly-averaged hourly global-solar-radiation variations on horizontal surfaces in Riyadh;

comparison between measurements and ASHRAE clear-sky-model calculations using original and mod-

ified sets of coefficients: (a) January; (b) July.


model with the original set of coefficients [2] and with a modified set of coefficients

[14] are also presented as dashed lines for comparison. The latter model will be called

from now on the ‘‘modified’’ ASHRAE model. The ASHRAE calculations presented

are also produced on a monthly-averaged hourly basis by the same averaging process

as used for measurements. This is done as follows: the model is run for every day of

the year and the results are generated at 15-min intervals. These are then averaged

over all the days in the month at each time level (quarter-hourly basis), and the

process is repeated for all months in the year as explained earlier.The results presented for January in Fig. 1(a) show that the ASHRAE model

consistently over-predicts the measurements at all times. This is expected since the

model does not account for local weather conditions such as the presence of clouds


and dust. Also, it is noted that there are discernible differences between the mea-

surements for different years. This is mainly attributed to local cloud formations in

this wintry month which obviously vary from year-to-year. However, on a monthly-

averaged hourly basis, these variations have actually been reduced quite substan-

tially. In contrast, the results presented for July in Fig. 1(b) show that both the

measurements and ASHRAE model predictions differ only slightly. In fact, there is areasonably close agreement between the results of the ASHRAE model and the mean

values of the measurements.

Results for the other months, which are not presented here to conserve space,

follow a similar trend and agree with the above conclusion, i.e. some differences exist

among the measurements for different years and with the predictions for the cloudy

months, namely, October!May. These differences decrease noticeably for the

months of June! September for which the sky is relatively clearer.

The results obtained from the modified ASHRAE model slightly over-predictthose obtained with the standard values of coefficients proposed in the original

model. Therefore, the modified ASHRAE model produces results that generally fall

farther away from the measurements compared with those of the standard model.

Fig. 2(a) and (b) present the variations of the monthly-averaged hourly global-

solar-radiation measured on horizontal surfaces in Riyadh for each month of the

year averaged over the years 1996! 2000. The corresponding monthly-averaged

hourly results using the ASHRAE clear-sky model with the original set of coeffi-

cients are presented in Fig. 3(a) and (b).The striking similarities between the measured and calculated solar-flux variations

with time suggest that monthly factors can be worked out such that when multiplied

by the ASHRAE model calculations, the resulting values are brought closer to the

measurements. The ‘‘adjustment’’ factors are worked out, for each month, based on

the monthly-averaged hourly global-solar-radiation integrated over one full-day.

These integrated daily global solar-fluxes are displayed in Fig. 4. Fig. 5 shows the

adjustment factor U calculated to bring the daily integrated ASHRAE (using the

original set of coefficients) and the daily-integrated measured global solar-fluxes intoagreement. The values of U are also summarized in Table 3, for each month.

Monthly adjustment factors for the modified ASHRAE model could have also

been worked out by using the results presented in Fig. 4. Bigger adjustments would

have been needed, i.e. corresponding values of U would have been smaller still than

those shown in Fig. 5. So far, the modified ASHRAE model has been used mainly

for validation and comparison purposes. From this point on, emphasis is given to the

standard ASHRAE model calculations and the adjustment factors.

Fig. 6(a) and (b) present three curves for the monthly-averaged hourly global-solar-radiation variation on horizontal surfaces in Riyadh for January and July,

respectively. The first curve (solid line) shows the averaged measured values as

presented earlier, the second (short dashed line) is the ASHRAE model result cal-

culated with the original set of coefficients while the third (long dashed line), des-

ignated ‘‘adjusted’’ ASHRAE, is the ASHRAE result when multiplied by the

adjustment factors U. It is noted that the adjusted ASHRAE distribution is very

close to the averaged measured data. Of course the total areas under the adjusted


measurements averaged over the years 1996–2000: (a) January–June; (b) July–December.


ASHRAE and measurement curves agree exactly since the adjustment factors arebased on obtaining equal daily global solar radiations for the adjusted ASHRAE

and measurement values. It is also interesting to note that only a slight adjustment is

needed for July (Fig. 6(b)) for the reasons discussed earlier.

Similar results and trends of variations are obtained for the other months. Thus, it

is concluded that the ASHRAE clear-sky model, coupled with monthly adjustment

factors, produces realistic solar-flux distributions that can be applied in solar ap-

plications in general and in building energy analyses. This conclusion is particularly

valuable in estimating solar-flux distributions and daily integrated values for verticaland tilted surfaces, facing different directions, from actual data on a horizontal

surface. Also, the ground-reflected radiation on such surfaces is accounted for


calculations by the ASHRAE clear-sky model using original set of coefficients: (a) January! June; (b)

July!December.


separately in the model; different ground reflectivity values can be investigated too.

The diffuse and beam radiation components can also be studied as separate parts of

the global radiation. Such information is usually lacking in the literature and is not

so convenient to obtain by measurement. Besides, measurements are usually ex-

pensive, time consuming and limited to specific locations.

4.3. Adjusted ASHRAE-model results for Riyadh

In the remaining part of the paper, the main emphasis is given to calculated solar-

radiation information for the city of Riyadh for both horizontal and vertical surfaces

Fig. 4. Monthly-averaged daily integrated global-solar-radiations on horizontal surfaces in Riyadh for

each month: comparison between measurements averaged over the years 1996–2000 and ASHRAE clear-

sky-model calculations using original and modified sets of coefficients.

Fig. 5. Monthly adjustment factors for the ASHRAE clear-sky model based on solar measurements in

Riyadh averaged over the years 1996! 2000.


of different orientations. These results are produced by the ASHRAE clear-sky

model, with the original set of coefficients, multiplied by the monthly adjustment

factors proposed in the present study (Table 3); from this point on, this is referred to

as the ‘‘adjusted ASHRAE model’’. Depending upon a particular surface absorp-

tivity for solar radiation, the results presented in the following figures and tables canbe used in practical applications for estimating the solar radiation absorbed by

different surfaces. In accordance with common practice, these data are produced for

the 21st day of each month.

Table 3

Monthly adjustment factors for the ASHRAE clear-sky model based on solar measurements in Riyadh

averaged over the years 1996–2000

Month

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

/ 0.825 0.766 0.843 0.879 0.907 0.978 0.965 0.962 0.949 0.928 0.852 0.880


comparison between measurements averaged over the years 1996–2000 and ASHRAE clear-sky-model

calculations before and after adjustment using original set of coefficients: (a) January; (b) July.


The daily variations of the diffuse and beam components as well as the global

solar-radiation over horizontal surfaces, as calculated from the adjusted ASHRAE

model, are displayed in Fig. 7(a) and (b) for January and July, respectively. The

Fig. 7. Diffuse, beam and global solar-radiation variations on horizontal surfaces in Riyadh calculated by

the adjusted ASHRAE clear-sky model for the 21st day of: (a) January; (b) July.


breakdown of the global radiation on horizontal surfaces into beam and diffuse

components is necessary for evaluating the global radiation on vertical and inclined

surfaces facing different directions. Fig. 8(a)–(d) present the adjusted ASHRAE

model results in January for vertical surfaces facing north, south, east and west,

respectively, including the ground-reflected component employing a ground reflec-

tivity of 0.2 (as appropriate for a crushed rock surface). The corresponding results

for July are given in Fig. 9(a)–(d).The daily global solar radiations calculated by the adjusted ASHRAE model are

compared for all months and surface orientations in Fig. 10. The yearly global solar-

radiations on these surfaces are given in Fig. 11 before and after adjustment. It is

evident from the results that, in Riyadh, a unit area of a horizontal surface receives

Fig. 8. Diffuse, beam, ground reflected and global solar-radiation variations in Riyadh calculated by the

adjusted ASHRAE clear-sky model for the 21st day of January on vertical surfaces facing: (a) north; (b)

south; (c) east; (d) west. Ground reflectivity¼ 0.2.


the largest amount of yearly global solar radiation, followed by the south-facing

vertical surface, then followed equally by the east- and west-facing vertical surfaces,

and finally the north-facing vertical surface receives the smallest solar flux. Nor-

malized by the horizontal surface value, the vertical surfaces receive about the fol-

lowing percentages: 20%, 56%, 53% and 53% for the north, south, east and westorientations, respectively.

It is also interesting to note that the south-facing vertical surface has the largest

solar radiation swing throughout the year, as can be seen in Fig. 10. However,

having the highest solar radiation in winter and the lowest in summer makes the

south-facing wall (in buildings in Riyadh and localities of similar environmental

conditions) the most favourable orientation with regard to energy consumption by

Fig. 9. Diffuse, beam, ground reflected and global solar-radiation variations in Riyadh calculated by the

adjusted ASHRAE clear-sky model for the 21st day of July on vertical surfaces facing: (a) north; (b) south;

(c) east; (d) west. Ground reflectivity¼ 0.2.


reducing the heating and cooling loads of the air-conditioning equipment. On the

other hand, the east-facing wall is much favoured over the west-facing wall with

regard to building orientation under these environmental conditions and, yet, the

results in Fig. 10 confirm that both the east and west orientations receive the same

amount of daily solar radiation. This apparent disparity should not be attributed to

solar radiation but to other factors such as the daily swing in ambient temperature,

energy storage and time lag effects. At the other extreme, the north-facing wall is theleast favourable in winter, since it receives very little solar radiation (diffuse and

ground reflected only, as shown in Fig. 8(a)).

Based on the yearly global solar radiation calculated by the ASHRAE clear-sky

model before and after the monthly adjustment, a yearly adjustment factor of about

Table 4

Daily solar radiation on horizontal surfaces in Riyadh (MJ/m2 day) calculated by the adjusted ASHRAE

clear-sky model for the 21st day of each month

Month


Beam 13.46 15.32 19.48 21.56 22.59 24.18 23.34 22.46 20.62 17.85 13.69 12.99

Diffuse 1.491 1.550 2.099 2.955 3.767 4.444 4.355 3.832 2.855 2.173 1.637 1.498

Global 14.95 16.87 21.58 24.51 26.36 28.63 27.69 26.29 23.48 20.02 15.32 14.49

Fig. 10. Daily global-solar-radiations calculated by the adjusted ASHRAE clear-sky model for the 21st

day of each month for different surface orientations in Riyadh. For vertical surfaces, ground

reflectivity¼ 0.2.

Fig. 11. Yearly global-solar-radiation calculated by the ASHRAE and adjusted ASHRAE clear-sky

models for different surface-orientations in Riyadh. For vertical surfaces, ground reflectivity¼ 0.2.


Table 5

Daily solar radiations on vertical surfaces in Riyadh (MJ/m2 day) calculated by the adjusted ASHRAE clear-sky model for the 21st day of each month; ground

reflectivity¼ 0.2

Month


North-

facing

vertical

surface

Beam 0.0 0.0 0.0 0.4736 2.130 3.516 2.340 0.5418 0.0 0.0 0.0 0.0

Diffuse 0.7453 0.7749 1.050 1.477 1.884 2.222 2.177 1.916 1.427 1.086 0.8183 0.7492

Ground

reflected

1.495 1.687 2.158 2.451 2.636 2.863 2.769 2.629 2.348 2.002 1.532 1.449

Global 2.240 2.462 3.208 4.402 6.649 8.600 7.286 5.087 3.775 3.088 2.351 2.198

South-

facing

vertical

surface

Beam 15.87 12.38 8.970 3.656 0.8063 0.1200 0.6812 3.515 9.495 14.19 15.99 17.50

Diffuse 0.7453 0.7749 1.050 1.477 1.884 2.222 2.177 1.916 1.427 1.086 0.8183 0.7492

Ground

reflected

1.495 1.687 2.158 2.451 2.636 2.863 2.769 2.629 2.348 2.002 1.532 1.449

Global 18.11 14.85 12.18 7.584 5.326 5.204 5.628 8.060 13.27 17.28 18.34 19.69

East-facing

vertical

surface

Beam 6.275 6.922 8.392 8.735 8.741 9.153 8.926 8.924 8.718 7.928 6.329 6.122

Diffuse 0.7453 0.7749 1.050 1.477 1.884 2.222 2.177 1.916 1.427 1.086 0.8183 0.7492

Ground

reflected

1.495 1.687 2.158 2.451 2.636 2.863 2.769 2.629 2.348 2.002 1.532 1.449

Global 8.515 9.385 11.60 12.66 13.26 14.24 13.87 13.47 12.49 11.02 8.679 8.320

West-

facing

vertical

surface

Beam 6.270 6.923 8.393 8.734 8.739 9.152 8.927 8.927 8.719 7.928 6.332 6.125

Diffuse 0.7453 0.7749 1.050 1.477 1.884 2.222 2.177 1.916 1.427 1.086 0.8183 0.7492

Ground

reflected

1.495 1.687 2.158 2.451 2.636 2.863 2.769 2.629 2.348 2.002 1.532 1.449

Global 8.510 9.385 11.60 12.66 13.26 14.24 13.87 13.47 12.49 11.02 8.683 8.322

S.A.Al-S

anea

etal./Applied

Energ

y79(2004)215–237

235


0.9 is obtained for the horizontal as well as the vertical surfaces. This factor can also

be inferred from the results presented in Fig. 11.

Finally, Table 4 summarizes the daily integrated radiation components and global

radiation (in MJ/m2 day) on horizontal surfaces as calculated by the ASHRAE

model with adjustment for each month. The corresponding values for vertical sur-

faces are summarized in Table 5.

5. Summary and concluding remarks

Solar-radiation measurements on a horizontal surface in Riyadh, which were

available on an hourly basis, were processed to obtain a monthly-averaged hourly

variation of the solar flux. These were further averaged over the years 1996–2000 to

get an hourly variation for a representative year. The ASHRAE clear-sky model wasused to produce solar-radiation data on a horizontal surface in Riyadh on a quarter-

hourly basis for all days in each month of the year. These were also processed to

obtain a monthly-averaged hourly variation of the solar flux. The ASHRAE model

implemented utilized the standard values of the coefficients proposed in the original

model. The results showed that the ASHRAE model calculations generally over-

predicted the measured data. Based on the daily total solar-flux, a factor was ob-

tained for every month to adjust the calculated clear-sky flux in order to account for

the effects of local dust and cloud conditions. When these factors were accounted forin the ASHRAE model calculations, the results agreed very well with the measured

monthly-averaged hourly variation of the solar flux.

In the present study, the adjusted ASHRAE clear-sky model was used to generate

instantaneous, daily and yearly solar radiation values for horizontal as well as ver-

tical surfaces facing north, south, east and west, in Riyadh. Of course, the same

model can be used to produce solar data for any locality by merely changing the

values of three parameters; namely, /, Lstd and Lloc in Table 2. It is recommended

that all future solar-energy applications, such as building energy analyses, employingthe climatic conditions of Riyadh, be carried out using the solar flux produced by the

ASHRAE model corrected by the adjustment factors proposed in the present study.

Hence, the solar flux can be calculated directly at any time of day without having to

approximate the flux daily variation by a sinusoidal fit. An added advantage is that

this solar model can be made as an integral part of the whole heat-transfer analysis

model to supply required boundary conditions.

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Documents

Adjustment factors for the ASHRAE clear-sky model based on solar-radiation measurements in Riyadh