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Adjustment factors for the ASHRAE

clear-sky model based on

solar-radiation measurements in Riyadh

Sami A. Al-Saneaa,*, M.F. Zedana, Saleh A. Al-Ajlanb

aDepartment of Mechanical Engineering, College of Engineering, King Saud University,

P.O. Box 800, Riyadh 11421, Saudi Arabia

bEnergy 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: sanea@ksu.edu.sa (S.A. Al-Sanea).

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

doi:10.1016/j.apenergy.2003.11.005

www.elsevier.com/locate/apenergy

Applied Energy 79 (2004) 215–237

APPLIED

ENERGY

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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 many

applications. 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 and

wind, 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 for

the 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.

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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=Hclear¼ a þ ð1 ? aÞS;

where Hclearis the value of H when the averaging is done over clear days only, and a

is a location-based empirical constant (a ¼ 0:25 for Stockholm); note that 06S 61.

This correlation was later modified by Prescott and others by replacing Hclearwith

the average extraterrestrial solar radiation H0. The modified correlation is known as

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

ð1Þ

H=H0¼ a þ bS;

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 Hclear

for most locations while H0can be calculated for any location. The disadvantage of

this modified equation is that the local transmittance of solar radiation (due to water

vapor), which was considered by Angstr€ om through the local Hclear, 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 a

and b for Niamey, Niger. They showed that the yearly averages of these coefficients

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

ð2Þ

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217

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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 hybrid

model 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 these

methods. 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.

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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 cm3and 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 an

influence 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 these

factors 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 the

unavailability 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 the

clearness 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 cloud

cover. 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,

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