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The longwave radiative environment around buildings
Building and Environment, Vol. 11, pp. 3-13. Pergamon Press 1976. Printed in Great Britain
REVIEW PAPER
The Longwave Radiative Environment Around Buildings R. J. COLE* Although the impact of solar radiation on the thermal performance of buiMings is well documented, the longwave radiative environment is generally little understood. Several relationships have been proposed in the literature which describe the incoming atmospheric radiation componentfor both clear and cloudy sky conditions but their inclusion in thermal design models is still relatively unexplored. This review discusses the nature of the longwaveradiative environment and explains the origins and characteristics of equations whichquantify it.
NOMENCLATURE A~ c e E~ EA EAo EAc E(z) h, L Lb R, R,t R.d, R.4c p u t T~ T. T~ u z
absorptivity of surface to longwave radiation cloud cover surface water vapour pressure emissivity of surface effective emissivity of atmosphere effective emissivity of atmosphere for clear sky condition effective emissivity of atmosphere for cloud cover c effective emissivity of atmosphere at zenith angle z surface coefficient of radiative heat transfer nett longwave radiation exchange nett longwave radiation exchange between the atmosphere and a black body radiator longwave radiation emitted by a surface atmospheric emission atmospheric emission from a clear sky atmospheric emission from a cloudy sky reflectivity of surface to longwave radiation Stefan-Boltzmann constant temperature of radiating surface absolute temperature of radiating surface absolute screen height air temperature absolute temperature of cloud base optical path depth zenith angle. 1. I N T R O D U C T I O N
TO produce successful results from a mathematical model describing the thermal performance of buildings it is necessary to identify the variability of the energy balance at the external surface of the building envelope. This energy balance results from the simultaneous interaction of solar radiative, convective and longwave radiative components. Solar radiation only occurs during the daytime and always represents a heat gain to the building. As a result of the incidence of summertime overheating problems in buildings and its more recent application of wintertime heating, considerable research and documentation has been undertaken and is available on the nature and variability of solar radiation[I-3]. Convective heat exchange generally leads to a heat loss
*Welsh School of Architecture, UWIST.
from buildings and, again, the literature is reasonably comprehensive in this field[4, 5]. However, the third component, the longwave radiation exchange between the surface and its surroundings, is less well defined and the relationships currently used in thermal design models are correspondingly overly simplified. Until approximately twenty years ago, the effects of nett longwave radiation exchange between the building and its surroundings were considered minimal in comparison with the solar radiation absorbed by the building surfaces. Roux[6], and Parmelee and Aubele[7], however, presented experimental evidence which indicated the fallacy of this supposition. Recent studies comparing the predicted heat flow through elements with measured values[8, 9], illustrate that significant errors may be introduced into the calculation of heat flow through building elements if the longwave radiation exchange at the outside surface is neglected. 1.1 Longwave radiation All surfaces above absolute zero emit radiation. The temperatures of building surfaces are sufficiently low that they emit energy as longwave radiation. This radiation lies within the wavelengths 3-100/zm with a maximum occurring at approximately 10/an. The amount of the radiation is dependent upon the emissivity of the surface and the fourth power of its absolute temperature in accordance with the StefanBoltzmann Law:
Rs = e~oTs4,
(I)
where, R~ is the radiation emitted by surface (W/m2); E, is the emissivity of surface ;~ris the Stefan-Boltznaann constant [5-67x10-s(W/m2°K4)]; and T, is the absolute temperature of surface (°K). Radiation exchange in the built environment may be treated as a surface-to-surface phenomenon, and the nett radiation exchange is determined by the difference between the radiation emitted by the surface and that emitted by the surfaces 'seen' by it. The physical relationship between the surface and the surroundings involves the mathematical development of a con-
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figuration factor. These standard relationships are well established [10--12]. This paper will examine the nature and variability of the longwave radiation environment in which buildings are situated. Because of the importance of atmospheric radiation in this context, a large section of the paper is devoted to the method of predicting atmospheric radiation during both clear and cloudy sky conditions. 1.2 The longwave radiation balance at a surface The longwave radiation, L, exchange at a surface of emissivity, E,, is given by:
(2)
L = R , - pR,- E,~T~,
where Rs is the longwave radiation incident on the surface from the surroundings, p is the reflectivity of the surface to longwave radiation. Now, p = (1-As), where As is the absorptivity of surface to longwave radiation, which by Kirchoff's Law is equal to E,. Therefore equation (2) may be rewritten:
L = E,(R,-aT~).
(3)
The radiation incident upon the envelope, (R,), originates from the atmosphere, the ground and the surrounding buildings. Whereas a horizontal surface, not overshadowed by other buildings or natural features, receives radiation from the atmospheric constituents only, vertical surfaces receive radiation from the combination of atmospheric, ground and surrounding surfaces in the ratio of their respective configuration factors. 2. A T M O S P H E R I C RADIATION Atmospheric radiation originates from constituents within the atmosphere (Fig. 1). The intensity of the
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Wavelength, 15 I
p.m 20 I
25
~ ~°
COa
H~O
03
HzO
C0z
HzO
Fig. 1. Spectral distribution of long wave radiation for black bodies at 288 and 2630K. Dark grey areas show the emission from atmospheric gases at 263°K. The light grey area therefore shows the nett loss of radiation from a surface at 288°K to a cloudless atmosphere at a uniform temperature of 263°K (after Gates[36]). radiation emitted at any wavelength is dependent upon the partial pressure of the constituents, their temperature and their thickness. Since the partial pressure and temperature vary with altitude, the energy received at ground level is the sum of that emitted by the lowest layer of the atmosphere and radiation transmitted by this layer originating from layers at greater altitude,
although it is generally considered that the majority of atmospheric radiation originates from the lowest few hundred meters of the atmosphere. Water vapour and carbon dioxide are the principle constituents with respect to atmospheric radiation, the former being by far the most important. Both of these constituents show absorptive (and emissive) characteristics at selected wavelengths over the entire spectrum. In the wavelengths from 8.5 to 13-0/tm, atmospheric water vapour is largely transparent to longwave radiation, but at all other wavelengths it can be considered practically opaque[13]. As would be expected, clouds are powerful sources of atmospheric radiation and, in general, the effect of clouds is to 'close the atmospheric window' of transparency in the 8.5-13.0/tm region. Clouds will therefore always increase the amount of radiation relative to the clear sky condition. 2. I Variations in atmospheric radiation
The nature of the parameters on which atmospheric radiation is dependent indicate that it is subject to both diurnal and seasonal variations. The diurnal pattern is more pronounced with clear sky conditions which generally lead to the lowest nighttime and the maximum daytime values[14, 15]. During clear, dry nights atmospheric radiation can reach extremely low values causing what is generally termed the 'cold sky' effect. Bliss[13], however, indicates that this effect is also common during the daytime. The presence of clouds significantly modifies the availability of atmospheric radiation throughout the twenty-four hour period, the overall value being higher and more stable than that with the clear sky condition. A seasonal variation in atmospheric radiation was observed by Dines[16] who measured the effective radiant temperature of the sky vault just after senset on a number of occasions during the period December 1919-December 1920. The results are reproduced in Fig. 2 and shows the maximum, minimum and mean values of atmospheric radiation received throughout the period. The curves are similar in shape to those of the general seasonal air temperature pattern, the maximum values occurring in July and the minimum in February. The observed range between maximum and minimum values is seen to vary between 25-50°C depending upon the amount of atmospheric water and cloud. 3. RELATIONSHIPS GOVERNING THE AVAILABILITY OF A T M O S P H E R I C RADIATION Since a numerical value of the atmospheric radiation is required in the energy balance between the building envelope and its surroundings it is necessary to determine its value with some reliability. Essien[17] mentions that measurements of atmospheric radiation are scarce; the one such series of measurements that is most often quoted were those by Dines and Dines[18]. There are however several methods currently available to predict the amount of radiation emitted by the atmosphere. These fall into three main groups. 1. Radiation charts, for clear sky radiation, having either a theoretical or an empirical background.
The Longwave Radiative Environment Around Buildings 2. Empirical formulae for clear sky radiation. 3. Empirical formulae for cloudy sky radiation. 3.1 Radiation charts Theoretically based radiation charts have been derived from the emission spectra of the radiating gases. These, however, can only be used confidently if the vertical distribution of temperature and water vapour are known up to a height of approximately 7 km. There are a number of theoretical radiation charts available for computing the longwave radiation both within the atmosphere and at the earth's surface. In general, these differ in relatively minor details concerning the assumptions necessary to simplify the complex transfer process. Probably the most widely quoted are the Elsasser Chart[19] which was later improved by Elsasser[20]. 40
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conditions, a process which can be both time consuming and laborious. In many cases, the necessary meteorological data are not in any case available to plot the imposing conditions on the chart. 3.2 Empiricalformulae for clear sky conditions The empirical methods are statistical summaries of the correlation between the observed radiation and parameters such as screen-height air temperature and water vapour pressure[23]. A n analysis of observed results shows that with a clear sky condition there is relatively good correlation between atmospheric radiation and the air temperature and water pressure at a height of 1.5-2.0m[23]. Reifsnyder and Lull[24] indicate that this is due to the fact that the majority of the atmospheric radiation from a clear sky comes from the lowest few hundred meters and that the value at ground level can be assumed to be representative. This correlation makes it possible to determine the atmospheric emission from a clear sky, Rao, by means of the following general equation:
RAo = aTe'f (e), 20
(4)
max
IG
P ~. c
mean
-IC
rain
-EC
where f(e) is a function of the water vapour pressure, e, and the absolute screen height air temperature, To. By transforming equation (4) such that f(e)= RAo[ aT 4, f(e) can be defined as the Effective Emissivity of the atmosphere, that is the ratio of the incoming longwave radiation Rao to the black body radiation at screen height air temperature, aTa 4. Among the rather numerous methods using this type of equation, the most frequently used are those by Angstr6m[25] and Brunt[26]. (i) Angstr~m's equation. AngstriSm's equation for the effective emissivity, Eao, from a clear sky has the form: Eao = Rao/aT~ =
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D
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M o n t h of year
Fig. 2. Effective radiant temperature of the sky vault after sunset (after Dines[16]). Empirical radiation charts have also been constructed on the basis of experimental measurements of atmospheric radiation, temperature and vapour pressure. These methods assume that the amount of radiation emitted by a layer of water is a function of temperature and the corrected optical depth of water vapour. The corrected optical depth is the product of the vapour pressure density and the average distance from points in the vapour layer to the receiving surface in terms of the standard sea level pressure. The most commonly used charts of this form are those by Brooks[21] and the Kew Radiation Charts of Robinson[22]. Radiation charts tend to give more information than is generally required for the thermal design of buildings and do not lend themselves to simple computation. In using the charts, the radiation exchange is obtained from the area of the chart defined by the atmospheric
(A+B-10-c'~),
(5)
where e is the water vapour (mb) and A, B and C are subject to variation from place to place. The mean figures usually quoted are: A = 0-25; B = 0.32; C = 0.052. Angstr6m's formula is more reliable in estimating nocturnal i.r. radiation, but it can be used to estimate day-time values with less precision. The decline in reliability during the day can be partly due to the errors introduced in the aT~ term (27). The temperature used might be expected to be less representative of the emitting air temperature at ground level. (ii) Brunt's equation. The empirical equation suggested by Brunt has the form, E:,o = Rao/aT ~ = (a+b'e~).
(6)
Using the radiation figures of Dines and Dines[18] taken at Benson, Oxfordshire, and vapour pressures from Kew, Brunt obtained the values: a = 0.52; b = 0.065. Although Brunt correlated the data from other workers, the Dines's values appear to be a better basis for comparison with recorded data in that they are monthly means of systematic observations extending over a period of about 6 yr. Goss and Brooks[28]
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emphasise that unreliable estimates can be expected for day-time usage of Brunt's formula. Attempts have been made to give theoretical justification for the Angstrfm and Brunt formulae (29), but the empirical nature of these relationships is evident when the vapour pressure is taken as zero. This result would infer that an absolutely dry atmosphere is capable of radiating half the blackbody radiation at the same temperature. Although carbon dioxide could contribute some of this, the upper limit would be approximately 0"2aT~ (29). Radiation originating from water vapour at heights which are not affected by surface variations in vapour pressure may account for this apparent anomaly. Montieth[30] provides a review of Brunt's constants using L6nnqvist's[31] radiation measurements at Kew Observatory and indicate that the effective emissivity of the atmosphere can be related to the optical path u(cm), by:
EAo = 0"7 + 0"22"1og (u).
(7)
The optical depth (or effective length of the water vapour path), u, is defined as the pressure corrected precipitable water depth. The pressure correction is necessary to allow for the narrowing of the water vapour absorption bands with decrease in atmospheric pressure. The relationship between 'u' and the vapour pressure found by Belasco's[32] air mass analysis was used: log (u) = 0.29.e * - 0'8.
(8)
Combining these equations gives;
E.4o = 0.53 +0-065e ~,
(9)
which agrees well with Brunt's original formula. The constants in both Angstr6m and Brunt equations are subject to considerable variation with location. As M611er[33] mentions, numerous authors have derived constants for these formulae but the scattering of the constants given by the different authors is as great as the scattering of the individual measurements around the curves plotted by each author. The scattering of the relative atmospheric radiation is indicated in Fig. 3 after Bolz and Falkenberg[34]. Although the Brunt and/~ngstr6m relationships give fairly good regressions for most localities, their empirical coefficients are subject to quite large variations. In an attempt to overcome this local specificity Swinbank [35] re-examined this subject area. Swinbank initially established the relationship between R~ and trT~ alone, exclusive of vapour pressure, from data for Benson, Oxfordshire. Then, from observations made in the Indian Ocean, he related the clear sky atmospheric radiation to the sixth power of screen height air temperature.
Rao = 5.31 × 10-1aT6 W/m 2.
(10)
Since the regression on R A and T~ extrapolated the origin and since the slope of the Benson data agreed closely with this equation, it appeared that Swinbank's relationship provided the universality that the Brunt and .&ngstrfm equations lacked. Although Swinbank did not provide a theoretical
1.0
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Fig. 3. Scattering of the effective emissivity of the atmosphere~ Rao/trT,,4 (after Bolz and Falkenberg[34]). justification for the T~ dependence of atmospheric emissivity implied in his equation, that has since come from Deacon[37]. In addition to the empirical methods involving vapour pressure as a surface predictor, several equations have been presented in the literature which have a stronger theoretical justification and involve other parameters. LOnnqvist[38] for example, presents a theoretical formula of the form;
RAo
=
a T ~ [ ( 1 - A ) + D'log(u)],
(11)
where, RAo is the radiation emitted by a clear sky; Ta is the screen height air temperature; u is the vertical depth of water vapour millimeters, corrected for the pressure dependence of the absorption coefficients of water vapour; D is the constant. The term A in the equation, varies slightly with temperature and the stratification of the atmosphere. LOnnqvist therefore, related A to the temperature, the lapse rate and the humidity of the air. To establish the numerical value of A it is necessary to make soundings above the point of observation and the method is therefore not generally applicable. Idso and Jackson[39] indicate that the effective emissivity of the atmosphere is a minimum at 273°K (i.e. at 0°C) and that it increases symmetrically to approach unity exponentially at higher and lower temperatures. Starting with the effective emissivity of the atmosphere, EAo, from the basic Brunt equation, Eao = 0.527 + 0.065e ~,
(12)
and assuming that the actual vapour pressure varies with temperature in a manner similar to the saturation vapour pressure, the Osbourne-Meyer equation, as quoted by Dorsey[40], was used to determine EA in terms of T~. Considering the first two dominating factors of the Osbourne-Meyer equation gives: In (e) = A + (B/Ta), where A and B are constants.
(13)
The Longwave Radiative Environment Around Buildings Idso and Jackson subsequently derived that, e = 6"11 exp [16.9 (1-273/To)].
(14)
adjustment to the clear sky condition by considering the height of the cloud base to be an indicator of the cloud temperature. Their equation has the form,
Substitution of this expression for e in the Brunt equation [equation (12)] gives,
EAo = 0.527+0.161 exp [8.45 (1-273/Ta)].
(15)
A comparison of calculated values of radiations using this expression of atmospheric emissivity and measured values led Idso and Jackson to postulate that atmospheric radiation can be presented by,
R,, t = a T e - F ( a T ~ - R,4o),
F = 0.17 at 2 k i n = 0.38 at 5 km
(16)
RAo = 5"5ta+213,
(17)
where Rao is the incoming atmospheric radiation (W/m 2) and to is the screen air temperature (°C). This result was obtained by the linearisation of the empirical relationship
RAo = p+q.trT~
= 0.45 at 8 km. Equation (19) indicates that during overcast conditions the amount of radiation emitted by the cloud base approaches that of a black body radiator at screen height temperature. Parmelee and Aubele[7] indicate that a representative value of this fraction would be 0.96. i.e. R,~c = 0.9&rT:. (20) (ii) Partially overcast sky. Although observations have shown that the total amount of cloud cover is probably the most important factor[14], the dependence of atmospheric radiation on cloud cover is non-linear. The relationships available for predicting the atmospheric radiation emitted by a partially overcast sky generally involve the multiplication of a clear sky radiation by an empirical cloud cover modifier. Few of these methods actually allow for the non-linearity between atmospheric radiation and cloud amount. Of these, the works by Bolz[44] and Kreitz[45] are the most often quoted. The experimental results of Bolz are reproduced in Fig. 4. The abscissa scale shows the cloud amount
No. of readings, t76 176 L~05 184 158 165 I
(18)
where p and q are constants. For measurements at Sutton Bonnington, England, the value of p was - 1 1 9 _+ 16W/m 2 ' a n d q was 1.06 _+ 0.04, with an uncertainty in a single estimate of RAo of + 30 W/m 2. 3.3 Empirical formulae for cloudy sky conditions Both common experience and scientific investigation show the influence of clouds on the reduction of heat loss by radiation from the earth. However, since clouds are powerful sources of atmospheric radiation, in practice it is difficult to take account of all the various factors which affect the availability of radiation under cloudy conditions[7]. For simplicity it is necessary to distinguish between overcast and partially overcast skies. (i) Overcast sky. The amount of radiation emitted by a completely overcast sky depends upon the emissivity and temperature of the lower surface of the cloud base. Angstr6m and Asklof[43] developed an empirical
(19)
where Rac is the atmospheric radiation from overcast sky; Rao is the atmospheric radiation from clear sky; a is the screen height air temperature and F i s the parameter which depends upon the height of the cloud base and takes the values:
RAo = ate{1 - 0.261 exp [ - 7.77 x 10- 4(273 - T~)=]} In their theoretical paper, Idso and Jackson demonstrated that this relationship describes atmospheric radiation from a clear sky with a high degree of accuracy. Idso[41 ] indicates that the relative success of equations involving only a temperature term results from two hypotheses. (i) That the depth of the surface atmospheric layer necessary to contain sufficient water vapour to provide effectively full emission in the long wavebands may always be so shallow that the surface screen temperature is representative. (ii) Screen air temperature is correlated to the amount of water vapour and thereby removes the necessity to consider water vapour explicitly. For a detailed comparison of the Swinbank and Idso and Jackson equations see Idso[41]. Unsworth and Monteith[42] have recently derived relationships giving the incoming atmospheric radiation from the sky vault during clear sky conditions as
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Z 1,55 164 280 1027
~jy,S
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,~..o...a..~'~RA/RAe 0+z.2d51 I
t
0.2
I
I 0,4
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I 0.6
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l OB
Cloudamount
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Fig. 4. Dependence of atmospheric emission on cloud amount (after Bolz[44]).
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(as a fraction of unity) and the lower scale the number (Z) readings for each of the cloud amounts. Bolz describes the results of his measurements by the following relationship: R,t = Rao(1 + U'c2"5),
(21)
where, RA is the radiation emitted by a partially overcast sky; U is the empirical coefficient dependent upon cloud type and c is the cloud amount expressed as a fraction. Bolz pointed out that satisfactory results could also be obtained by using the simpler relationship; Ra = Rao(1 + U'c2).
(22)
Table 1 gives the values of the coefficient, U, determined by Bolz for various types of cloud. The coefficient N is the number of days on which observations were made and the figures on the last line of Table 1 represent the mean curve plotted in Fig. 3. Table 1. Dependence of atmospheric emission on type of cloud. At n= 10 tenths (After Bolz[44]) III
Cloud type
U
Z
N
Cirrus Cirro-stratus Alto-cumulus Alto-stratus Cumulus Stratus
0-04 0"08 0.17 0.20 0.20 0-24
302 59 140 43 82 59
53 23 63 20 21 15
Average cloud conditions
0-22
2711
253
This data indicates that, on average, the emission of a cloud sky exceeds that of a clear sky by 22 %. The greatest increase in atmospheric emission is observed with stratus cloud and the least with cirrus clouds. The relationship developed by Kreitz has the same formulation as Bolz's equation with the exception that the average value of U is 0.27. The remaining methods describing the atmospheric radiation available from a partially overcast sky assume a linear relationship. The two methods of this type that are commonly referred to are those by Angstr6m[25] and Roach[46]. Angstr6m's equation has the simple form; Rac = Rao(1 + k . c ) ,
(23)
where k is an empirically derived factor and c is the cloud amount. Roach started with the basic relationship, R,i c = (1 - c)Rao + c" a T e ,
(24)
where Tb is the temperature of the cloud base which is assumed to have unit emissivity. Due to the difficulty of measuring T~, the assumption was made that the cloud base temperature equals the screen air temperature, and by defining the emissivity of the atmosphere, EAo, as E.,o = R,o/OT.'.
equation (24) can be simplified to, Rac = [E~o + c(1 - Eao)]oT~4.
(25)
By comparing measured and calculated values of Ra, Roach established a mean difference of 15.8 W/m 2. This difference corresponded to an over estimation of the cloud base temperature by 1.7°C at 10°C surface air temperature. This is equivalent to a difference between black body radiation at cloud and screen air temperature of AR = 8.75 W/m 2. Roach assumed that there was no seasonal variation in AR and subsequently corrected his equation to, Rac = [Eao+C(1-E~o)]aT~+c'AR.
(26)
Unsworth and Monteith[42] suggest that beneath a cloudy sky, the atmospheric radiation has two components. (i) That emitted by water vapour and carbon dioxide beneath the cloud base. (ii) That emitted by water droplets constituting the cloud base. Since atmospheric radiation originates from constituents within the lowest few hundred meters the gaseous component can be considered as that for a clear sky and that (1 --EAo) can be regarded as the apparent transmissivity of the atmosphere between the ground and the cloud base. The atmospheric radiation from the cloud base of an overcast sky therefore given by ( 1 - E a o ) a T ~ where Tc is the radiative temperature of the cloud base. These authors examined the records of Dines and Dines[18] for overcast conditions and indicate the following points. (i) The angular distribution is the same as for clear sky. (ii) The mean temperature of the cloud base at the Dines and Dines site was l l ° K below screen air temperature. (iii) The apparent emissivity during partially cloudy conditions is given by: Eao = (1 - 0"84c)EAo + 0"84c.
(26)
4. RADIATION F R O M D I F F E R E N T PARTS O F T H E SKY VAULT The formulae described in Section 3 predict the atmospheric radiation originating from the total hemispherical sky vault. However, because the relative depth of water vapour in the atmosphere varies with path length, the intensity of atmospheric radiation varies over the sky vault. The depth of atmosphere is thinnest vertically above the absorption point and therefore the atmospheric radiation from the zenith is at a minimum[24]. The radiation originating from the relatively thicker layer of the atmosphere at angles approaching the horizon emit at correspondingly greater amount of energy than from overhead. This relationship is common to both clear and overcast sky conditions[42]. This effect was first quantified by Brunt[26]. Brunt determined values of the hemispherical emissivity, providing values of the constants in his general formula for incident radiation at various angles above the horizon. These values are reproduced in Table 2.
The Longwave Radiative Environment Around Buildings Table 2. Coefficients for Brunt's equation Angle of elevation
a
b
Correlation
0-15 15-30 30--45 45-60 60-75 75-90 Hemisphere
0.498 0.508 0.522 0.548 0.581 0-774 0"551
0.057 0.056 0.055 0.055 0.059 0.050 0-056
0.94 0.94 0.94 0.93 0.92 0.91 0.91
Brunt suggested that b can be considered as a constant and variations in a are given by: a = 0 . 6 4 - 0 . 1 4 cos (z),
(27)
where, z is the zenith angle. This empirical relationship, not surprisingly, fitted the data with a high degree of accuracy except for the zone near the horizon. This, Brunt considered, was due to the effect of objects, such as buildings, projecting above the horizon. In their study, Unsworth and Monteith[42] showed that the flux density at the zenith angle z is given by:
R(z) = [ a + b . l n (u.sec (z))]aT~.
(28)
Where u is the pressure corrected depth of precipitable water (cm). F o r a set of 46 scans at Sutton Bonnington, England, the mean values of a and b were determined experimentally to be 0.70 + 0.05 and 0.09 + 0.002 respectively. These workers show that the variation in a and b can be attributed partly to vertical and partly to horizontal temperature gradients of particulate material (that is, pollution or haze near the ground or water droplets in high cloud). The total atmospheric radiation incident upon a horizontal surface is given by the integration of equation (26):
R a = S 2~ d(~ ~/2 (R(z)/n) cos z sin z dz = aTria+ b(0"5 + In (u))].
(29) (30)
Therefore, as these workers identify, the atmospheric radiation on a horizontal surface equals the equivalent flux density at zenith angle z given by sec z = 0.5 or z = 52.5 °, a value which is independent of a and b and dependent upon the existence of a linear relationship between R(z) and In [sec (z)]. 5. L O N G W A V E R A D I A T I O N I N C I D E N T U P O N VERTICAL SURFACES Vertical surfaces receive radiation from the atmosphere, the ground and any surrounding buildings, in the ratio of their respective configuration factors. Although it is possible to predict the longwave radiation originating from the atmosphere, there is very little information available regarding the magnitude of the ground radiation. The ground radiates in accordance with the temperature attained by its surface and its
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spectral emissivity. This temperature is dependent upon the nature of the surface, the prevailing climatic conditions and the heat gains and losses during the previous days. Because of the lack of knowledge about the time variability of ground surface temperatures, the assumption is generally made that the ground radiates with unit emissivity at screen height air temperature. It is difficult to assess the error involved in making this assumption when one considers the non-uniformity of the ground surfaces surrounding any building and the temperature gradients that exist near the surface of the ground. The surface temperature characteristics of pavement or concrete characteristics are markedly different from those of grass, the former attaining generally higher temperatures during periods of high solar radiation and lower during the night-time. In addition, the surface temperature of the ground is subject to a much wider diurnal variation than the screen height air temperature. However, the daily mean values will tend to approach one another. 6. NETT L O N G W A V E R A D I A T I O N EXCHANGE The literature covering nett longwave radiation exchange generally only refers to the radiation exchange between black body radiators at air temperature and the atmosphere, or between the ground and the atmosphere. However, the nett radiation exchange between building surfaces and the surrounding follow the same principles. There is generally always a longwave radiation loss from the earth to the atmosphere, even under overcast conditions. Because of the higher surface temperatures during the day, the outward longwave radiation from a surface is normally higher in the day than at night. Frost conditions on clear dry nights thus result from lower values of atmospheric radiation and subsequent excessive outward radiation from the earth. A n analysis of radiation measurements made in Canada led Polvarapu[47] to conclude that the nett longwave radiation loss and subsequent overall nett radiation increase with latitude during summer months. This conclusion was based on the premise that the decrease in air temperature and precipitable water vapour at higher results in a decrease in atmospheric radiation. In addition Idso and Blad[48] indicate that the converse of this would generally occur in the winter months. On a more local scale, the nett loss of heat by longwave radiation is largely dependent upon the amount of exposed sky above the site under construction Angstrfim[25], in an extensive study of the radiative environment, examined the radiation exchange between the earth and various parts of the sky vault. The results indicated that the nett radiation loss to a constant area of sky decreases with an increase in zenith distance, approaching zero near the horizon. The reasons for this are evident from the anisotropic characteristics of the hemispherical radiation discussed previously. In addition, Angstrfm concluded that an increase in the water vapour pressure would cause a decrease in the nett radiation exchange to every point of the sky vault and that this decrease would be more significant for larger
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zenith angles than for smaller ones. Geiger[49] also indicates that this effective outgoing radiation is roughly inversely proportional to the relative humidity. Bailey[50] reproduces the findings of Lauscher[51 ] to the effective outgoing radiation at various elevations as a percentage of the outgoing radiation at the zenith. Using this data, Bailey was able to specify the effective outgoing radiation for a number of different topographic and building forms. These relationships are reproduced in Figs. 5 (i and ii) and described numerically in Table 3.
,.0
0
--
1926 on days of either clear or totally overcast skies. These results are shown in Fig. 6 and indicate that the average nett longwave radiation from a black surface at air temperature to clear and overcast skies remained fairly constant throughout the year. Loudon[52] accepts these findings in developing an 'equivalent outdoor temperature'. During the heating season, the radiation loss from a black surface at air temperature averaged 101-5 W/m 2 for a clear sky and 14.5 W/m 2 for an overcast sky.
,,oi
0
1
I00
e~
d~
6,9
9o/ 69
51
T E
5~
Loss 1o clear sky
/
80
7O
(i)
(a)
m
o c o
60
P
50
(b)
g 3O
(el
(d)
(e)
(ii) I0
Fig. 5 (i). Effective outgoing radiation to a clear sky for different angles of elevation, measured only in the direction shown by the lines (after Bailey[50]). (ii) Influence of topography, buildings and other physical features on outgoing radiation. Possible amount of exposed sky is shown diagrammatically by semi circle. Tinted area represents extent to which this is partially obscured in each case. This drawing should be read in conjunction with Table 3. The above results are defined for clear sky conditions. With overcast conditions, radiation returned from the cloud bases to earth increases and thereby decreases the nett outgoing radiation. Lauscher calculated the relationship of nett longwave exchange to cloudiness and indicated a rapid decrease in outgoing radiation at heavier cloud covers. Measurements of longwave radiation exchange were made by Dines and Dines[18] during the years 1922-
/
d
I
I
F
L
M A
I
I
M J
1
J
I
A
I
S
I
0
I
I
r~ D
I
Month of year
Fig. 6. Average monthly means longwave radiation losses from a black horizontal surface at air temperature to clear and overcast skies (after Dines and Dines[18]). By making the assumption that the average radiation loss is linearly related to the fraction of the sky covered by cloud, Loudon quotes the loss from a horizontal surface at air temperature as being, Lb = 14"5c+101"5 (I--c) = 101"5-- 87c W/m 2,
(32)
where, Lb is the mean longwave radiation loss from a
Table 3. Ratio (parts per thousand) of effective outgoing radiation from sheltered or inclired surfaces to radiation from a completely open horizontal surface. To be read in conjunction with Fig. 5(ii) Angle (°) Basic (ct) Slope (,8) Rise (y) Surface of street (5) Middle of street (e)
A B C D E
0
5
10
15
20
30
45
60
75
90
1000 1000 1000 1000 1000
996 996 997 930 993
982 986 992 862 984
995 970 988 797 976
915 951 979 737 958
793 900 951 622 902
549 796 877 452 754
282 667 772 296 544
79 528 639 143 279
0 396 500 0 0
The Longwave Radiative Environment Around Buildings horizontal surface, and c is the mean cloudiness (angular fraction of hemisphere covered with cloud). Monteith[30] proposed a similar equation; L = 97.2- 86.4c W/m 2
heat transfer coefficient. Several workers[9, 54] develop the approximation as follows: Let dT= T,-TR,
(33)
for calculating the yearly mean values of longwave radiation from the ground surface. The slight difference between this and Loudon's equation arises from the fact that Monteith was considering annual mean losses from ground surfaces, whereas Loudon's equation is intended to apply only to the heating season and to surfaces at air temperature.
11
and Tm = time average of TR and T+ =
(T~+TR)/2.
Substituting the values of dT and T. in equation (36) gives; h, = 2Tm'E+a(T, + dT/2) 2 + (Tin- dT/2) 2 = 2Tm.E~a2T~+2dT2/+.
7. THE RADIATION COEFFICIENT Since the radiation exchange between the building envelope and its surroundings involves fourth power absolute temperature terms, this mode of heat transfer is generally reduced to a simple linear expression. It is usual to represent the longwave radiation exchange by a coefficient such that when it is multiplied by the temperature difference between the surface and ambient air, it would give the radiative component of heat transfer. The longwave radiation exchange at the building surface is given by the Stefan-Boltzmann Law; L = E,'a(T,4- T~), (34) where, L is the nett longwave radiation exchange at the surface (W/m2); TR is the effective temperature of surroundings (temperature of a black body radiation which would produce the same radiation as that emitted by the surroundings) (°K); and T, is the absolute temperature of surroundings (°K). This nett longwave radiation exchange may be represented in terms of a unit coefficient, h,; L = h,(t+- tR),
If dT is small, then (dT) 2 can be considered negligible, and therefore, h, = 4e, aT3m. (38) There is no indication in the literature as to how Tm should be estimated. The variation in h, with Tm is shown in Fig. 7. 70
I
I
I
I
1
J
6.0-
o o
5.0
.~
4.0
3.0
2q£o
The value of h, is therefore given by:
-
I,
-5
I
o
I
5
I
Io
I
15
1
2o
]
z5
3o
Tm, *C
Es~r(T:- T~)/(t s - tR),
Fig. 7. Surface coctIicient of radiation heat transfer as a function of temperature.
which simplifies to: h, = E,a(T: + T~)'(Ts+ TR) ,
I
/
(°c). =
I
(35)
where, h, is the surface coefficient of radiative heat transfer (W/m 2 °C); t~ is the temperature of surface (°C) and tR is the effective temperature of surroundings
h,
(37)
(36)
and is thus dependent upon the temperature of the surface, the effective radiating temperature of the surroundings and the nature of the surface as determined by its emissivity. The I.H.V.E. Guide[53] leaves the emissivity term, Es, as a variable and treats the remainder as constant, i.e. Esh,; and quotes the radiative resistance for high (0-9) and low (0.05) emissivities. 7.1 Simplifications o f the surface coefficient o f radiative heat transfer Because the effective temperature of the surroundings and the surface temperature are not commonly measured and therefore not available at the design stage, it is necessary to approximate the value of the radiative
A further assumption commonly made, is that the surroundings radiate as a black body at air temperature, and the mean temperature in equation (38) replaced by the temperature of the air (8). Both Ogunlesi and Ran and Ballantyne[55] give an analysis of the error in making the assumption that the mean temperature is equal to the mean temperature difference. The error in h, is strongly dependent upon the temperature difference between the surface and air, being approximately 6 ~ for a temperature of 12°C and rising to 40~0 when the difference is 50°C. 8. DISCUSSION AND CONCLUSION This paper has described the nature and variability of the longwave radiative heat exchange between the
12
R. J. Cole
building envelope and its surroundings. important points emerge from this review;
Several
(i) Level o f understanding In comparison with solar radiation, there is relatively little published information concerning the effect of this mode of heat transfer on the thermal performance of buildings. This has probably resulted from a combination of the following. (a) The difficulty in measuring the longwave component within the radiative balance. This is confirmed by the fact that virtually all of the relationships presented in the literature relate to nocturnal readings of atmospheric radiation. (b) The belief that this mode of heat transfer is of secondary importance compared with solar radiation and convection exchange. This has been subsequently disapproved by recent investigations. (ii) Surface coefficient The radiative surface coefficient generally adopted in thermal design models is a gross over-simplification of the radiative heat exchange process. Although the coefficient would approach a reasonably constant value if defined in terms of the temperatures of the surface and the surroundings, the assumption that the surroundings radiate at air temperature renders the definition unrepresentative of the real situation. It is unlikely that any linear representation of the longwave radiation exchange will significantly improve the situation. If Computer Models representing the thermal performance of buildings are capable of treating this mode of heat transfer in terms of fourth power absolute temperatures, then the only basic requirement is a closer specification of the incoming longwave radiation as a function of its dependent variables. (iii) Predictive techniques The majority of the techniques available for describing the availability of atmospheric radiation relate to the clear sky condition. These can be grouped into two parts. (a) Those which express the atmospheric emissivity as a function of vapour pressure alone (Brunt, Angstr6m). (b) Those in which vapour pressure is represented by temperature function (Swinbank, Idso and Jackson).
The first of these groups assumes that the majority of the atmospheric radiation during clear sky condition originates from the lowest few hundred metres of water vapour and that the vapour pressure at screen height is representative of this quality. The second type relies on the relationships between vapour pressure and temperatures; in that the higher the temperature the greater amount of atmospheric water vapour. Considerable variation appears between these methods; in particular the Brunt and Angstr6m relationships show a marked lack of universality. However, as already indicated, clear skies are the exception rather than the rule. The relationships, describing the availability of atmospheric radiation during this condition involve the multiplication of the clear sky value by some modifier. The premise that the clear sky radiation is known introduces one source of error and the empirically derived cloud cover modifier introduces a second. The combination of these two terms therefore introduces a compound error. (iv) Radiation on vertical surface The longwave radiation exchange between vertical surfaces and the surroundings 'seen' by it is even less well defined. At present the radiation impinging upon the surface is defined as that emitted by a black body at air temperature. The value of this radiation is dependent upon the nature of the ground surfaces surrounding it. Surfaces such as pavement, tarmac etc., follow quite wide temperature variations and consequently the radiation emitted by such surfaces is difficult to quantify. In terms of its application to thermal design of buildings there is a need for relationships which describe the dynamic longwave radiation income for use in the more sophisticated mathematical models. These relationships must be able to be developed from commonly recorded climatic elements and of a simple format to avoid the application of complex configuration factors. Until such relationships are available, building scientists concerned with the transformation of weather data into longwave radiation data in the U.K. are advised to use the atmospheric radiation data presented by Unsworth and Monteith and continue to assume that the longwave radiation incident on a vertical surface is equivalent to that emitted by a black body at screen air temperature.
REFERENCES 1. N. Robinson (Editor), Solar Radiation. Elsevier, Amsterdam (1966). 2. D.G. Stephenson, Equations of solar heat gain through windows, Sol. Energy 9, 81-85 (1965). 3. Building Research Station, Library Communication, Utilisation of Solar Energy, No. 220 July (1970). 4. M. Lokmanhekim, Procedure for determining heating and cooling loads for computerised energy calculations--algorithms for building heat transfer subroutines, ASHRAE, New York (1971). 5. N. Ito, K. Kimura & J. Oka. A field study on the convective heat exchange on the external surface of a building. ASHRAEBi-Annual Meeting. New Orleans. LA. (1972). 6. A. J. A. Roux, The effect of weather conditions on heat transfer through building elements, Building Research Congress. Div. 3, 82-87 (1951). 7. G. V. Parmelce & W. W. Aubele, Radiant energy emission of atmosphere and ground. Trans. ASHRAE58, 85-106 (1952). 8. •. •gun•esi• S••ar radiati•n and therma• gradients in bui•ding units. Build. S•i. • •-2• (•965). 9. B. L. Hoglund, C. P. Mitalas & D. G. Stephenson, Surface temperatures and heat fluxes for flat roofs. Build. Sci. 2, 29-36 (1967).
The Longwave Radiative Environment Around Buildings 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.
H.L. Hackforth, Infra-red Radiation. McGraw-Hill (1960). E. M. Sparrow & R. D. Cess, Radiation Heat Transfer. Brooks-Cole, CA. (1966). N. S. Billington, Building Physics Heat. Pergamon Press, London (1967). R. W. Bliss, Atmospheric radiation near the surface of the ground. A summary for engineers. SoL Energy 5, 3 (1961). K. Ya. Kondratyev, Radiative Heat Exchange in the Atmosphere. Hydro Meteorological, Leningrad. Translated from Russian (1956). D. L. Morgan, W. O. Pruitt & F. J. Laurence, Estimation of atmospheric radiation. J. appl. Alet. 10, 463--468 (1971). W.H. Dines, Observations in radiation from the sky. Geophys. Mem. 18 (1921). F. Essien, An investigation of free convection and low temperature radiation from surfaces of building elements. Ph.D. Thesis, Univ. Newcastle-upon-Tyne (1972). W. H. Dines & L. H. G. Dines, Monthly mean values of radiation from various parts of the sky at Benson, Oxfordshire. Mere. R. met. Soc. 2, 11 (1927). W. M. Elsasser, An atmospheric radiation chart and its use. Q. Jl R. met. Soc. 66, 41 (1940). W. M. Elsasser, Atmospheric radiation tables, Monographs, ARCRL-TR-60-236, U.S. Dept. Commerce (1960). F. A. Brooks, Observations of atmospheric radiation, Paper. Phys. Ocean, Met., M.LT. Woods Ocean Inst. 8, 2 (1941). C.D. Robinson, Notes on the measurement and estimation of atmospheric radiation. II. Q. JI R. met. Soc. 76, 37-51 (1950). M.E. Beryland, Kondratyev (1956). W. Reifsnyder & H. Lull, Radiant energy in relation to forests. U.S.D.A. For Set. Tech. Bull. No. 1344 (1965). A. Angstr6m, A study on radiation of the atmosphere. Smithsonian Misc. Coll. 65, 57-69 (1915). D. Brunt, Notes on radiation in the atmosphere. Q. Jl R. met. Soc. 58, 389-420 (1932). E. M. Agee, Equations for estimating solar and infra-red radiation at the earth-atmosphere interface. Msc. Thesis, University of Missouri, Columbia, U.S.A. (1966). J. R. Goss & F. A. Brooks, Constants for empirical expressions for down-coming atmospheric radiation, J. Met. 13, 482-488 (1956). J. R. Goss & F. A. Brooks, Radiant energy, its reception and disposal, Agricultural meteorology. Met. Mono. 28, 1-26 (1956). J. G. Charney, Radiation, Section 4, Handbook of Meteorology. McGraw-Hill, New York (1945). J. L. Monteith, An empirical method for estimating longwave exchange in the British Isles. Q.J. R. met. Soc. 87,171-179 (1961). O. L6nnqvist, Theoretical verification of the logarithmic formula for relative net radiation to a cloudless sky. Arkiv. Geofysik 151-159 (1954). J.E. Belasco, Geophys. memoirs. Met. Office No. 87 (1952). F. Moiler, Longwave radiation, compendium of meteorology, Boston, Amer. Meteor. Soc. 3449 (1951). H. M. Bolz & G. Falkenberg, Neubestimmung der Kinstanten der Angrom'schen Strahumgsformer. Z. Meteor 3, 367-368 (1949). W.C. Swinbank, Longwave radiation from clear skies. Q. Jl R. met. Soc. 89, 339-348 (1963). D. M. Gates, Energy Exchange in the Biosphere Harper and Row Monograph New York (1962). E. Deacon, The derivation of Swinbank's longwave radiation formula. Q. Jl R. met. Soc. 96, 313-319 (1970). O. Lonnqvist, A general method and a simplified formula for calculating effective radiation. Arkiv Geofysik 79-115 (1950). S.B. Idso & R. D. Jackson, Thermal radiation from the atmosphere, J. Geophys. Res. 74, 53975403 (1969). N.E. Dorsey, Properties of Ordinary Water Substance. Reinhold, New York (1940). S.B. Idso, On the use of equations to estimate atmospheric thermal radiation Arch. Met. Geophys. Biokl. Set. B. 22, 287-299 (1974). M.H. Unsworth & J. L. Monteith, Longwave radiation at the ground (i) Angular distribution of incoming radiation. Q. Jl R. met. Soc. 101,1-13 (1975). A. Angstr6m & S. Asklof, S. Ann. Stockholm Vol., 253 [In Gates (1962)]. H. M. Bolz, Die abhangigkeit der infraroten Gegenstrahlung yon der Bewolkung. Z. Met. 7 (1949). E. Kreitz, Reglstrienungen der langweUigen Gegenstrahuing in Frankfurt, Geof Pura. HapL 28 (1954). In. Kondratsyev (1956). W.T. Roach, Measurements of atmospheric radiation and the heat balance at the ground at Kew, May 1953--May 1954. Air Ministry. Met. Res. Commun. M.R.P. 936(1955). R. J. Polvarapu, A comparative study of global and nett radiation measurements at Guelph, Toronto and Ottawa. J. appl. Met. 9, 809-814 (1970). S.B. Idso & B. L. Blad, The effect of air temperature upon nett and solar radiation relationships. J. appl. Met. 10, 604-605 (1971). R. Geiger, The Radiation Near the Ground. Harvard U.P., Connecticutt (1965). R. Bailey, The A.J. EnvironmentalHandbook--Climate Section. A.J. (1968). F. Lauscher, Bericht u. mess. d. nachtl: Ausstrahlung aufd. Stolzalpe. Meteorolgis. Zeitschrift 45, 371-375 (1928). A. G. Loudon, Heat transmission through roofs of buildings. L Instn Heat. Vent. Engrs 31, 273-291 (1963). I.H.V.E. Guide, Book A--Design Data. Institute of Heating and Ventilating Engineers, London (1970). A. Aittomaki, A model for calculating heat balance of room and building. The state inst. Tech res. Finland. Pub. 0968). K. R. Rao & E. R. Ballantyne, Some investigations on the sol-air temperature concept. D.B.R. Tech.paper No. 27 C.S.I.R.O. Melbourne, Australia (1970).
13
REVIEW PAPER
The Longwave Radiative Environment Around Buildings R. J. COLE* Although the impact of solar radiation on the thermal performance of buiMings is well documented, the longwave radiative environment is generally little understood. Several relationships have been proposed in the literature which describe the incoming atmospheric radiation componentfor both clear and cloudy sky conditions but their inclusion in thermal design models is still relatively unexplored. This review discusses the nature of the longwaveradiative environment and explains the origins and characteristics of equations whichquantify it.
NOMENCLATURE A~ c e E~ EA EAo EAc E(z) h, L Lb R, R,t R.d, R.4c p u t T~ T. T~ u z
absorptivity of surface to longwave radiation cloud cover surface water vapour pressure emissivity of surface effective emissivity of atmosphere effective emissivity of atmosphere for clear sky condition effective emissivity of atmosphere for cloud cover c effective emissivity of atmosphere at zenith angle z surface coefficient of radiative heat transfer nett longwave radiation exchange nett longwave radiation exchange between the atmosphere and a black body radiator longwave radiation emitted by a surface atmospheric emission atmospheric emission from a clear sky atmospheric emission from a cloudy sky reflectivity of surface to longwave radiation Stefan-Boltzmann constant temperature of radiating surface absolute temperature of radiating surface absolute screen height air temperature absolute temperature of cloud base optical path depth zenith angle. 1. I N T R O D U C T I O N
TO produce successful results from a mathematical model describing the thermal performance of buildings it is necessary to identify the variability of the energy balance at the external surface of the building envelope. This energy balance results from the simultaneous interaction of solar radiative, convective and longwave radiative components. Solar radiation only occurs during the daytime and always represents a heat gain to the building. As a result of the incidence of summertime overheating problems in buildings and its more recent application of wintertime heating, considerable research and documentation has been undertaken and is available on the nature and variability of solar radiation[I-3]. Convective heat exchange generally leads to a heat loss
*Welsh School of Architecture, UWIST.
from buildings and, again, the literature is reasonably comprehensive in this field[4, 5]. However, the third component, the longwave radiation exchange between the surface and its surroundings, is less well defined and the relationships currently used in thermal design models are correspondingly overly simplified. Until approximately twenty years ago, the effects of nett longwave radiation exchange between the building and its surroundings were considered minimal in comparison with the solar radiation absorbed by the building surfaces. Roux[6], and Parmelee and Aubele[7], however, presented experimental evidence which indicated the fallacy of this supposition. Recent studies comparing the predicted heat flow through elements with measured values[8, 9], illustrate that significant errors may be introduced into the calculation of heat flow through building elements if the longwave radiation exchange at the outside surface is neglected. 1.1 Longwave radiation All surfaces above absolute zero emit radiation. The temperatures of building surfaces are sufficiently low that they emit energy as longwave radiation. This radiation lies within the wavelengths 3-100/zm with a maximum occurring at approximately 10/an. The amount of the radiation is dependent upon the emissivity of the surface and the fourth power of its absolute temperature in accordance with the StefanBoltzmann Law:
Rs = e~oTs4,
(I)
where, R~ is the radiation emitted by surface (W/m2); E, is the emissivity of surface ;~ris the Stefan-Boltznaann constant [5-67x10-s(W/m2°K4)]; and T, is the absolute temperature of surface (°K). Radiation exchange in the built environment may be treated as a surface-to-surface phenomenon, and the nett radiation exchange is determined by the difference between the radiation emitted by the surface and that emitted by the surfaces 'seen' by it. The physical relationship between the surface and the surroundings involves the mathematical development of a con-
4
R . J . Cole
figuration factor. These standard relationships are well established [10--12]. This paper will examine the nature and variability of the longwave radiation environment in which buildings are situated. Because of the importance of atmospheric radiation in this context, a large section of the paper is devoted to the method of predicting atmospheric radiation during both clear and cloudy sky conditions. 1.2 The longwave radiation balance at a surface The longwave radiation, L, exchange at a surface of emissivity, E,, is given by:
(2)
L = R , - pR,- E,~T~,
where Rs is the longwave radiation incident on the surface from the surroundings, p is the reflectivity of the surface to longwave radiation. Now, p = (1-As), where As is the absorptivity of surface to longwave radiation, which by Kirchoff's Law is equal to E,. Therefore equation (2) may be rewritten:
L = E,(R,-aT~).
(3)
The radiation incident upon the envelope, (R,), originates from the atmosphere, the ground and the surrounding buildings. Whereas a horizontal surface, not overshadowed by other buildings or natural features, receives radiation from the atmospheric constituents only, vertical surfaces receive radiation from the combination of atmospheric, ground and surrounding surfaces in the ratio of their respective configuration factors. 2. A T M O S P H E R I C RADIATION Atmospheric radiation originates from constituents within the atmosphere (Fig. 1). The intensity of the
I~) I
Wavelength, 15 I
p.m 20 I
25
~ ~°
COa
H~O
03
HzO
C0z
HzO
Fig. 1. Spectral distribution of long wave radiation for black bodies at 288 and 2630K. Dark grey areas show the emission from atmospheric gases at 263°K. The light grey area therefore shows the nett loss of radiation from a surface at 288°K to a cloudless atmosphere at a uniform temperature of 263°K (after Gates[36]). radiation emitted at any wavelength is dependent upon the partial pressure of the constituents, their temperature and their thickness. Since the partial pressure and temperature vary with altitude, the energy received at ground level is the sum of that emitted by the lowest layer of the atmosphere and radiation transmitted by this layer originating from layers at greater altitude,
although it is generally considered that the majority of atmospheric radiation originates from the lowest few hundred meters of the atmosphere. Water vapour and carbon dioxide are the principle constituents with respect to atmospheric radiation, the former being by far the most important. Both of these constituents show absorptive (and emissive) characteristics at selected wavelengths over the entire spectrum. In the wavelengths from 8.5 to 13-0/tm, atmospheric water vapour is largely transparent to longwave radiation, but at all other wavelengths it can be considered practically opaque[13]. As would be expected, clouds are powerful sources of atmospheric radiation and, in general, the effect of clouds is to 'close the atmospheric window' of transparency in the 8.5-13.0/tm region. Clouds will therefore always increase the amount of radiation relative to the clear sky condition. 2. I Variations in atmospheric radiation
The nature of the parameters on which atmospheric radiation is dependent indicate that it is subject to both diurnal and seasonal variations. The diurnal pattern is more pronounced with clear sky conditions which generally lead to the lowest nighttime and the maximum daytime values[14, 15]. During clear, dry nights atmospheric radiation can reach extremely low values causing what is generally termed the 'cold sky' effect. Bliss[13], however, indicates that this effect is also common during the daytime. The presence of clouds significantly modifies the availability of atmospheric radiation throughout the twenty-four hour period, the overall value being higher and more stable than that with the clear sky condition. A seasonal variation in atmospheric radiation was observed by Dines[16] who measured the effective radiant temperature of the sky vault just after senset on a number of occasions during the period December 1919-December 1920. The results are reproduced in Fig. 2 and shows the maximum, minimum and mean values of atmospheric radiation received throughout the period. The curves are similar in shape to those of the general seasonal air temperature pattern, the maximum values occurring in July and the minimum in February. The observed range between maximum and minimum values is seen to vary between 25-50°C depending upon the amount of atmospheric water and cloud. 3. RELATIONSHIPS GOVERNING THE AVAILABILITY OF A T M O S P H E R I C RADIATION Since a numerical value of the atmospheric radiation is required in the energy balance between the building envelope and its surroundings it is necessary to determine its value with some reliability. Essien[17] mentions that measurements of atmospheric radiation are scarce; the one such series of measurements that is most often quoted were those by Dines and Dines[18]. There are however several methods currently available to predict the amount of radiation emitted by the atmosphere. These fall into three main groups. 1. Radiation charts, for clear sky radiation, having either a theoretical or an empirical background.
The Longwave Radiative Environment Around Buildings 2. Empirical formulae for clear sky radiation. 3. Empirical formulae for cloudy sky radiation. 3.1 Radiation charts Theoretically based radiation charts have been derived from the emission spectra of the radiating gases. These, however, can only be used confidently if the vertical distribution of temperature and water vapour are known up to a height of approximately 7 km. There are a number of theoretical radiation charts available for computing the longwave radiation both within the atmosphere and at the earth's surface. In general, these differ in relatively minor details concerning the assumptions necessary to simplify the complex transfer process. Probably the most widely quoted are the Elsasser Chart[19] which was later improved by Elsasser[20]. 40
I
I
i
l
I
I
I
1
I
I
I
3c
5
conditions, a process which can be both time consuming and laborious. In many cases, the necessary meteorological data are not in any case available to plot the imposing conditions on the chart. 3.2 Empiricalformulae for clear sky conditions The empirical methods are statistical summaries of the correlation between the observed radiation and parameters such as screen-height air temperature and water vapour pressure[23]. A n analysis of observed results shows that with a clear sky condition there is relatively good correlation between atmospheric radiation and the air temperature and water pressure at a height of 1.5-2.0m[23]. Reifsnyder and Lull[24] indicate that this is due to the fact that the majority of the atmospheric radiation from a clear sky comes from the lowest few hundred meters and that the value at ground level can be assumed to be representative. This correlation makes it possible to determine the atmospheric emission from a clear sky, Rao, by means of the following general equation:
RAo = aTe'f (e), 20
(4)
max
IG
P ~. c
mean
-IC
rain
-EC
where f(e) is a function of the water vapour pressure, e, and the absolute screen height air temperature, To. By transforming equation (4) such that f(e)= RAo[ aT 4, f(e) can be defined as the Effective Emissivity of the atmosphere, that is the ratio of the incoming longwave radiation Rao to the black body radiation at screen height air temperature, aTa 4. Among the rather numerous methods using this type of equation, the most frequently used are those by Angstr6m[25] and Brunt[26]. (i) Angstr~m's equation. AngstriSm's equation for the effective emissivity, Eao, from a clear sky has the form: Eao = Rao/aT~ =
I
M
I
d
r
d
I
A
I
S
I
0
I
N
I
D
I
d
I
F
1
M
A
M o n t h of year
Fig. 2. Effective radiant temperature of the sky vault after sunset (after Dines[16]). Empirical radiation charts have also been constructed on the basis of experimental measurements of atmospheric radiation, temperature and vapour pressure. These methods assume that the amount of radiation emitted by a layer of water is a function of temperature and the corrected optical depth of water vapour. The corrected optical depth is the product of the vapour pressure density and the average distance from points in the vapour layer to the receiving surface in terms of the standard sea level pressure. The most commonly used charts of this form are those by Brooks[21] and the Kew Radiation Charts of Robinson[22]. Radiation charts tend to give more information than is generally required for the thermal design of buildings and do not lend themselves to simple computation. In using the charts, the radiation exchange is obtained from the area of the chart defined by the atmospheric
(A+B-10-c'~),
(5)
where e is the water vapour (mb) and A, B and C are subject to variation from place to place. The mean figures usually quoted are: A = 0-25; B = 0.32; C = 0.052. Angstr6m's formula is more reliable in estimating nocturnal i.r. radiation, but it can be used to estimate day-time values with less precision. The decline in reliability during the day can be partly due to the errors introduced in the aT~ term (27). The temperature used might be expected to be less representative of the emitting air temperature at ground level. (ii) Brunt's equation. The empirical equation suggested by Brunt has the form, E:,o = Rao/aT ~ = (a+b'e~).
(6)
Using the radiation figures of Dines and Dines[18] taken at Benson, Oxfordshire, and vapour pressures from Kew, Brunt obtained the values: a = 0.52; b = 0.065. Although Brunt correlated the data from other workers, the Dines's values appear to be a better basis for comparison with recorded data in that they are monthly means of systematic observations extending over a period of about 6 yr. Goss and Brooks[28]
6
R . J . Cole
emphasise that unreliable estimates can be expected for day-time usage of Brunt's formula. Attempts have been made to give theoretical justification for the Angstrfm and Brunt formulae (29), but the empirical nature of these relationships is evident when the vapour pressure is taken as zero. This result would infer that an absolutely dry atmosphere is capable of radiating half the blackbody radiation at the same temperature. Although carbon dioxide could contribute some of this, the upper limit would be approximately 0"2aT~ (29). Radiation originating from water vapour at heights which are not affected by surface variations in vapour pressure may account for this apparent anomaly. Montieth[30] provides a review of Brunt's constants using L6nnqvist's[31] radiation measurements at Kew Observatory and indicate that the effective emissivity of the atmosphere can be related to the optical path u(cm), by:
EAo = 0"7 + 0"22"1og (u).
(7)
The optical depth (or effective length of the water vapour path), u, is defined as the pressure corrected precipitable water depth. The pressure correction is necessary to allow for the narrowing of the water vapour absorption bands with decrease in atmospheric pressure. The relationship between 'u' and the vapour pressure found by Belasco's[32] air mass analysis was used: log (u) = 0.29.e * - 0'8.
(8)
Combining these equations gives;
E.4o = 0.53 +0-065e ~,
(9)
which agrees well with Brunt's original formula. The constants in both Angstr6m and Brunt equations are subject to considerable variation with location. As M611er[33] mentions, numerous authors have derived constants for these formulae but the scattering of the constants given by the different authors is as great as the scattering of the individual measurements around the curves plotted by each author. The scattering of the relative atmospheric radiation is indicated in Fig. 3 after Bolz and Falkenberg[34]. Although the Brunt and/~ngstr6m relationships give fairly good regressions for most localities, their empirical coefficients are subject to quite large variations. In an attempt to overcome this local specificity Swinbank [35] re-examined this subject area. Swinbank initially established the relationship between R~ and trT~ alone, exclusive of vapour pressure, from data for Benson, Oxfordshire. Then, from observations made in the Indian Ocean, he related the clear sky atmospheric radiation to the sixth power of screen height air temperature.
Rao = 5.31 × 10-1aT6 W/m 2.
(10)
Since the regression on R A and T~ extrapolated the origin and since the slope of the Benson data agreed closely with this equation, it appeared that Swinbank's relationship provided the universality that the Brunt and .&ngstrfm equations lacked. Although Swinbank did not provide a theoretical
1.0
I
i
I
I
I
I
I
I
I
0.9
0.8
~_o b i1::~0 ?
0.6-
/ /
0.5 0
I
I
I
I
I
[
I
I
4
6
8
I0
12
14
r6
18
Vapour pressure,
20
mb
Fig. 3. Scattering of the effective emissivity of the atmosphere~ Rao/trT,,4 (after Bolz and Falkenberg[34]). justification for the T~ dependence of atmospheric emissivity implied in his equation, that has since come from Deacon[37]. In addition to the empirical methods involving vapour pressure as a surface predictor, several equations have been presented in the literature which have a stronger theoretical justification and involve other parameters. LOnnqvist[38] for example, presents a theoretical formula of the form;
RAo
=
a T ~ [ ( 1 - A ) + D'log(u)],
(11)
where, RAo is the radiation emitted by a clear sky; Ta is the screen height air temperature; u is the vertical depth of water vapour millimeters, corrected for the pressure dependence of the absorption coefficients of water vapour; D is the constant. The term A in the equation, varies slightly with temperature and the stratification of the atmosphere. LOnnqvist therefore, related A to the temperature, the lapse rate and the humidity of the air. To establish the numerical value of A it is necessary to make soundings above the point of observation and the method is therefore not generally applicable. Idso and Jackson[39] indicate that the effective emissivity of the atmosphere is a minimum at 273°K (i.e. at 0°C) and that it increases symmetrically to approach unity exponentially at higher and lower temperatures. Starting with the effective emissivity of the atmosphere, EAo, from the basic Brunt equation, Eao = 0.527 + 0.065e ~,
(12)
and assuming that the actual vapour pressure varies with temperature in a manner similar to the saturation vapour pressure, the Osbourne-Meyer equation, as quoted by Dorsey[40], was used to determine EA in terms of T~. Considering the first two dominating factors of the Osbourne-Meyer equation gives: In (e) = A + (B/Ta), where A and B are constants.
(13)
The Longwave Radiative Environment Around Buildings Idso and Jackson subsequently derived that, e = 6"11 exp [16.9 (1-273/To)].
(14)
adjustment to the clear sky condition by considering the height of the cloud base to be an indicator of the cloud temperature. Their equation has the form,
Substitution of this expression for e in the Brunt equation [equation (12)] gives,
EAo = 0.527+0.161 exp [8.45 (1-273/Ta)].
(15)
A comparison of calculated values of radiations using this expression of atmospheric emissivity and measured values led Idso and Jackson to postulate that atmospheric radiation can be presented by,
R,, t = a T e - F ( a T ~ - R,4o),
F = 0.17 at 2 k i n = 0.38 at 5 km
(16)
RAo = 5"5ta+213,
(17)
where Rao is the incoming atmospheric radiation (W/m 2) and to is the screen air temperature (°C). This result was obtained by the linearisation of the empirical relationship
RAo = p+q.trT~
= 0.45 at 8 km. Equation (19) indicates that during overcast conditions the amount of radiation emitted by the cloud base approaches that of a black body radiator at screen height temperature. Parmelee and Aubele[7] indicate that a representative value of this fraction would be 0.96. i.e. R,~c = 0.9&rT:. (20) (ii) Partially overcast sky. Although observations have shown that the total amount of cloud cover is probably the most important factor[14], the dependence of atmospheric radiation on cloud cover is non-linear. The relationships available for predicting the atmospheric radiation emitted by a partially overcast sky generally involve the multiplication of a clear sky radiation by an empirical cloud cover modifier. Few of these methods actually allow for the non-linearity between atmospheric radiation and cloud amount. Of these, the works by Bolz[44] and Kreitz[45] are the most often quoted. The experimental results of Bolz are reproduced in Fig. 4. The abscissa scale shows the cloud amount
No. of readings, t76 176 L~05 184 158 165 I
(18)
where p and q are constants. For measurements at Sutton Bonnington, England, the value of p was - 1 1 9 _+ 16W/m 2 ' a n d q was 1.06 _+ 0.04, with an uncertainty in a single estimate of RAo of + 30 W/m 2. 3.3 Empirical formulae for cloudy sky conditions Both common experience and scientific investigation show the influence of clouds on the reduction of heat loss by radiation from the earth. However, since clouds are powerful sources of atmospheric radiation, in practice it is difficult to take account of all the various factors which affect the availability of radiation under cloudy conditions[7]. For simplicity it is necessary to distinguish between overcast and partially overcast skies. (i) Overcast sky. The amount of radiation emitted by a completely overcast sky depends upon the emissivity and temperature of the lower surface of the cloud base. Angstr6m and Asklof[43] developed an empirical
(19)
where Rac is the atmospheric radiation from overcast sky; Rao is the atmospheric radiation from clear sky; a is the screen height air temperature and F i s the parameter which depends upon the height of the cloud base and takes the values:
RAo = ate{1 - 0.261 exp [ - 7.77 x 10- 4(273 - T~)=]} In their theoretical paper, Idso and Jackson demonstrated that this relationship describes atmospheric radiation from a clear sky with a high degree of accuracy. Idso[41 ] indicates that the relative success of equations involving only a temperature term results from two hypotheses. (i) That the depth of the surface atmospheric layer necessary to contain sufficient water vapour to provide effectively full emission in the long wavebands may always be so shallow that the surface screen temperature is representative. (ii) Screen air temperature is correlated to the amount of water vapour and thereby removes the necessity to consider water vapour explicitly. For a detailed comparison of the Swinbank and Idso and Jackson equations see Idso[41]. Unsworth and Monteith[42] have recently derived relationships giving the incoming atmospheric radiation from the sky vault during clear sky conditions as
7
I
I
L
i
i
[
I
/
//
// /////'/ //// /
12
//i I.C
I
Z 1,55 164 280 1027
~jy,S
I
,~..o...a..~'~RA/RAe 0+z.2d51 I
t
0.2
I
I 0,4
I
I 0.6
I
l OB
Cloudamount
I
I 1.0
Fig. 4. Dependence of atmospheric emission on cloud amount (after Bolz[44]).
8
R . J . Cole
(as a fraction of unity) and the lower scale the number (Z) readings for each of the cloud amounts. Bolz describes the results of his measurements by the following relationship: R,t = Rao(1 + U'c2"5),
(21)
where, RA is the radiation emitted by a partially overcast sky; U is the empirical coefficient dependent upon cloud type and c is the cloud amount expressed as a fraction. Bolz pointed out that satisfactory results could also be obtained by using the simpler relationship; Ra = Rao(1 + U'c2).
(22)
Table 1 gives the values of the coefficient, U, determined by Bolz for various types of cloud. The coefficient N is the number of days on which observations were made and the figures on the last line of Table 1 represent the mean curve plotted in Fig. 3. Table 1. Dependence of atmospheric emission on type of cloud. At n= 10 tenths (After Bolz[44]) III
Cloud type
U
Z
N
Cirrus Cirro-stratus Alto-cumulus Alto-stratus Cumulus Stratus
0-04 0"08 0.17 0.20 0.20 0-24
302 59 140 43 82 59
53 23 63 20 21 15
Average cloud conditions
0-22
2711
253
This data indicates that, on average, the emission of a cloud sky exceeds that of a clear sky by 22 %. The greatest increase in atmospheric emission is observed with stratus cloud and the least with cirrus clouds. The relationship developed by Kreitz has the same formulation as Bolz's equation with the exception that the average value of U is 0.27. The remaining methods describing the atmospheric radiation available from a partially overcast sky assume a linear relationship. The two methods of this type that are commonly referred to are those by Angstr6m[25] and Roach[46]. Angstr6m's equation has the simple form; Rac = Rao(1 + k . c ) ,
(23)
where k is an empirically derived factor and c is the cloud amount. Roach started with the basic relationship, R,i c = (1 - c)Rao + c" a T e ,
(24)
where Tb is the temperature of the cloud base which is assumed to have unit emissivity. Due to the difficulty of measuring T~, the assumption was made that the cloud base temperature equals the screen air temperature, and by defining the emissivity of the atmosphere, EAo, as E.,o = R,o/OT.'.
equation (24) can be simplified to, Rac = [E~o + c(1 - Eao)]oT~4.
(25)
By comparing measured and calculated values of Ra, Roach established a mean difference of 15.8 W/m 2. This difference corresponded to an over estimation of the cloud base temperature by 1.7°C at 10°C surface air temperature. This is equivalent to a difference between black body radiation at cloud and screen air temperature of AR = 8.75 W/m 2. Roach assumed that there was no seasonal variation in AR and subsequently corrected his equation to, Rac = [Eao+C(1-E~o)]aT~+c'AR.
(26)
Unsworth and Monteith[42] suggest that beneath a cloudy sky, the atmospheric radiation has two components. (i) That emitted by water vapour and carbon dioxide beneath the cloud base. (ii) That emitted by water droplets constituting the cloud base. Since atmospheric radiation originates from constituents within the lowest few hundred meters the gaseous component can be considered as that for a clear sky and that (1 --EAo) can be regarded as the apparent transmissivity of the atmosphere between the ground and the cloud base. The atmospheric radiation from the cloud base of an overcast sky therefore given by ( 1 - E a o ) a T ~ where Tc is the radiative temperature of the cloud base. These authors examined the records of Dines and Dines[18] for overcast conditions and indicate the following points. (i) The angular distribution is the same as for clear sky. (ii) The mean temperature of the cloud base at the Dines and Dines site was l l ° K below screen air temperature. (iii) The apparent emissivity during partially cloudy conditions is given by: Eao = (1 - 0"84c)EAo + 0"84c.
(26)
4. RADIATION F R O M D I F F E R E N T PARTS O F T H E SKY VAULT The formulae described in Section 3 predict the atmospheric radiation originating from the total hemispherical sky vault. However, because the relative depth of water vapour in the atmosphere varies with path length, the intensity of atmospheric radiation varies over the sky vault. The depth of atmosphere is thinnest vertically above the absorption point and therefore the atmospheric radiation from the zenith is at a minimum[24]. The radiation originating from the relatively thicker layer of the atmosphere at angles approaching the horizon emit at correspondingly greater amount of energy than from overhead. This relationship is common to both clear and overcast sky conditions[42]. This effect was first quantified by Brunt[26]. Brunt determined values of the hemispherical emissivity, providing values of the constants in his general formula for incident radiation at various angles above the horizon. These values are reproduced in Table 2.
The Longwave Radiative Environment Around Buildings Table 2. Coefficients for Brunt's equation Angle of elevation
a
b
Correlation
0-15 15-30 30--45 45-60 60-75 75-90 Hemisphere
0.498 0.508 0.522 0.548 0.581 0-774 0"551
0.057 0.056 0.055 0.055 0.059 0.050 0-056
0.94 0.94 0.94 0.93 0.92 0.91 0.91
Brunt suggested that b can be considered as a constant and variations in a are given by: a = 0 . 6 4 - 0 . 1 4 cos (z),
(27)
where, z is the zenith angle. This empirical relationship, not surprisingly, fitted the data with a high degree of accuracy except for the zone near the horizon. This, Brunt considered, was due to the effect of objects, such as buildings, projecting above the horizon. In their study, Unsworth and Monteith[42] showed that the flux density at the zenith angle z is given by:
R(z) = [ a + b . l n (u.sec (z))]aT~.
(28)
Where u is the pressure corrected depth of precipitable water (cm). F o r a set of 46 scans at Sutton Bonnington, England, the mean values of a and b were determined experimentally to be 0.70 + 0.05 and 0.09 + 0.002 respectively. These workers show that the variation in a and b can be attributed partly to vertical and partly to horizontal temperature gradients of particulate material (that is, pollution or haze near the ground or water droplets in high cloud). The total atmospheric radiation incident upon a horizontal surface is given by the integration of equation (26):
R a = S 2~ d(~ ~/2 (R(z)/n) cos z sin z dz = aTria+ b(0"5 + In (u))].
(29) (30)
Therefore, as these workers identify, the atmospheric radiation on a horizontal surface equals the equivalent flux density at zenith angle z given by sec z = 0.5 or z = 52.5 °, a value which is independent of a and b and dependent upon the existence of a linear relationship between R(z) and In [sec (z)]. 5. L O N G W A V E R A D I A T I O N I N C I D E N T U P O N VERTICAL SURFACES Vertical surfaces receive radiation from the atmosphere, the ground and any surrounding buildings, in the ratio of their respective configuration factors. Although it is possible to predict the longwave radiation originating from the atmosphere, there is very little information available regarding the magnitude of the ground radiation. The ground radiates in accordance with the temperature attained by its surface and its
9
spectral emissivity. This temperature is dependent upon the nature of the surface, the prevailing climatic conditions and the heat gains and losses during the previous days. Because of the lack of knowledge about the time variability of ground surface temperatures, the assumption is generally made that the ground radiates with unit emissivity at screen height air temperature. It is difficult to assess the error involved in making this assumption when one considers the non-uniformity of the ground surfaces surrounding any building and the temperature gradients that exist near the surface of the ground. The surface temperature characteristics of pavement or concrete characteristics are markedly different from those of grass, the former attaining generally higher temperatures during periods of high solar radiation and lower during the night-time. In addition, the surface temperature of the ground is subject to a much wider diurnal variation than the screen height air temperature. However, the daily mean values will tend to approach one another. 6. NETT L O N G W A V E R A D I A T I O N EXCHANGE The literature covering nett longwave radiation exchange generally only refers to the radiation exchange between black body radiators at air temperature and the atmosphere, or between the ground and the atmosphere. However, the nett radiation exchange between building surfaces and the surrounding follow the same principles. There is generally always a longwave radiation loss from the earth to the atmosphere, even under overcast conditions. Because of the higher surface temperatures during the day, the outward longwave radiation from a surface is normally higher in the day than at night. Frost conditions on clear dry nights thus result from lower values of atmospheric radiation and subsequent excessive outward radiation from the earth. A n analysis of radiation measurements made in Canada led Polvarapu[47] to conclude that the nett longwave radiation loss and subsequent overall nett radiation increase with latitude during summer months. This conclusion was based on the premise that the decrease in air temperature and precipitable water vapour at higher results in a decrease in atmospheric radiation. In addition Idso and Blad[48] indicate that the converse of this would generally occur in the winter months. On a more local scale, the nett loss of heat by longwave radiation is largely dependent upon the amount of exposed sky above the site under construction Angstrfim[25], in an extensive study of the radiative environment, examined the radiation exchange between the earth and various parts of the sky vault. The results indicated that the nett radiation loss to a constant area of sky decreases with an increase in zenith distance, approaching zero near the horizon. The reasons for this are evident from the anisotropic characteristics of the hemispherical radiation discussed previously. In addition, Angstrfm concluded that an increase in the water vapour pressure would cause a decrease in the nett radiation exchange to every point of the sky vault and that this decrease would be more significant for larger
10
R. J. Cole
zenith angles than for smaller ones. Geiger[49] also indicates that this effective outgoing radiation is roughly inversely proportional to the relative humidity. Bailey[50] reproduces the findings of Lauscher[51 ] to the effective outgoing radiation at various elevations as a percentage of the outgoing radiation at the zenith. Using this data, Bailey was able to specify the effective outgoing radiation for a number of different topographic and building forms. These relationships are reproduced in Figs. 5 (i and ii) and described numerically in Table 3.
,.0
0
--
1926 on days of either clear or totally overcast skies. These results are shown in Fig. 6 and indicate that the average nett longwave radiation from a black surface at air temperature to clear and overcast skies remained fairly constant throughout the year. Loudon[52] accepts these findings in developing an 'equivalent outdoor temperature'. During the heating season, the radiation loss from a black surface at air temperature averaged 101-5 W/m 2 for a clear sky and 14.5 W/m 2 for an overcast sky.
,,oi
0
1
I00
e~
d~
6,9
9o/ 69
51
T E
5~
Loss 1o clear sky
/
80
7O
(i)
(a)
m
o c o
60
P
50
(b)
g 3O
(el
(d)
(e)
(ii) I0
Fig. 5 (i). Effective outgoing radiation to a clear sky for different angles of elevation, measured only in the direction shown by the lines (after Bailey[50]). (ii) Influence of topography, buildings and other physical features on outgoing radiation. Possible amount of exposed sky is shown diagrammatically by semi circle. Tinted area represents extent to which this is partially obscured in each case. This drawing should be read in conjunction with Table 3. The above results are defined for clear sky conditions. With overcast conditions, radiation returned from the cloud bases to earth increases and thereby decreases the nett outgoing radiation. Lauscher calculated the relationship of nett longwave exchange to cloudiness and indicated a rapid decrease in outgoing radiation at heavier cloud covers. Measurements of longwave radiation exchange were made by Dines and Dines[18] during the years 1922-
/
d
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I
F
L
M A
I
I
M J
1
J
I
A
I
S
I
0
I
I
r~ D
I
Month of year
Fig. 6. Average monthly means longwave radiation losses from a black horizontal surface at air temperature to clear and overcast skies (after Dines and Dines[18]). By making the assumption that the average radiation loss is linearly related to the fraction of the sky covered by cloud, Loudon quotes the loss from a horizontal surface at air temperature as being, Lb = 14"5c+101"5 (I--c) = 101"5-- 87c W/m 2,
(32)
where, Lb is the mean longwave radiation loss from a
Table 3. Ratio (parts per thousand) of effective outgoing radiation from sheltered or inclired surfaces to radiation from a completely open horizontal surface. To be read in conjunction with Fig. 5(ii) Angle (°) Basic (ct) Slope (,8) Rise (y) Surface of street (5) Middle of street (e)
A B C D E
0
5
10
15
20
30
45
60
75
90
1000 1000 1000 1000 1000
996 996 997 930 993
982 986 992 862 984
995 970 988 797 976
915 951 979 737 958
793 900 951 622 902
549 796 877 452 754
282 667 772 296 544
79 528 639 143 279
0 396 500 0 0
The Longwave Radiative Environment Around Buildings horizontal surface, and c is the mean cloudiness (angular fraction of hemisphere covered with cloud). Monteith[30] proposed a similar equation; L = 97.2- 86.4c W/m 2
heat transfer coefficient. Several workers[9, 54] develop the approximation as follows: Let dT= T,-TR,
(33)
for calculating the yearly mean values of longwave radiation from the ground surface. The slight difference between this and Loudon's equation arises from the fact that Monteith was considering annual mean losses from ground surfaces, whereas Loudon's equation is intended to apply only to the heating season and to surfaces at air temperature.
11
and Tm = time average of TR and T+ =
(T~+TR)/2.
Substituting the values of dT and T. in equation (36) gives; h, = 2Tm'E+a(T, + dT/2) 2 + (Tin- dT/2) 2 = 2Tm.E~a2T~+2dT2/+.
7. THE RADIATION COEFFICIENT Since the radiation exchange between the building envelope and its surroundings involves fourth power absolute temperature terms, this mode of heat transfer is generally reduced to a simple linear expression. It is usual to represent the longwave radiation exchange by a coefficient such that when it is multiplied by the temperature difference between the surface and ambient air, it would give the radiative component of heat transfer. The longwave radiation exchange at the building surface is given by the Stefan-Boltzmann Law; L = E,'a(T,4- T~), (34) where, L is the nett longwave radiation exchange at the surface (W/m2); TR is the effective temperature of surroundings (temperature of a black body radiation which would produce the same radiation as that emitted by the surroundings) (°K); and T, is the absolute temperature of surroundings (°K). This nett longwave radiation exchange may be represented in terms of a unit coefficient, h,; L = h,(t+- tR),
If dT is small, then (dT) 2 can be considered negligible, and therefore, h, = 4e, aT3m. (38) There is no indication in the literature as to how Tm should be estimated. The variation in h, with Tm is shown in Fig. 7. 70
I
I
I
I
1
J
6.0-
o o
5.0
.~
4.0
3.0
2q£o
The value of h, is therefore given by:
-
I,
-5
I
o
I
5
I
Io
I
15
1
2o
]
z5
3o
Tm, *C
Es~r(T:- T~)/(t s - tR),
Fig. 7. Surface coctIicient of radiation heat transfer as a function of temperature.
which simplifies to: h, = E,a(T: + T~)'(Ts+ TR) ,
I
/
(°c). =
I
(35)
where, h, is the surface coefficient of radiative heat transfer (W/m 2 °C); t~ is the temperature of surface (°C) and tR is the effective temperature of surroundings
h,
(37)
(36)
and is thus dependent upon the temperature of the surface, the effective radiating temperature of the surroundings and the nature of the surface as determined by its emissivity. The I.H.V.E. Guide[53] leaves the emissivity term, Es, as a variable and treats the remainder as constant, i.e. Esh,; and quotes the radiative resistance for high (0-9) and low (0.05) emissivities. 7.1 Simplifications o f the surface coefficient o f radiative heat transfer Because the effective temperature of the surroundings and the surface temperature are not commonly measured and therefore not available at the design stage, it is necessary to approximate the value of the radiative
A further assumption commonly made, is that the surroundings radiate as a black body at air temperature, and the mean temperature in equation (38) replaced by the temperature of the air (8). Both Ogunlesi and Ran and Ballantyne[55] give an analysis of the error in making the assumption that the mean temperature is equal to the mean temperature difference. The error in h, is strongly dependent upon the temperature difference between the surface and air, being approximately 6 ~ for a temperature of 12°C and rising to 40~0 when the difference is 50°C. 8. DISCUSSION AND CONCLUSION This paper has described the nature and variability of the longwave radiative heat exchange between the
12
R. J. Cole
building envelope and its surroundings. important points emerge from this review;
Several
(i) Level o f understanding In comparison with solar radiation, there is relatively little published information concerning the effect of this mode of heat transfer on the thermal performance of buildings. This has probably resulted from a combination of the following. (a) The difficulty in measuring the longwave component within the radiative balance. This is confirmed by the fact that virtually all of the relationships presented in the literature relate to nocturnal readings of atmospheric radiation. (b) The belief that this mode of heat transfer is of secondary importance compared with solar radiation and convection exchange. This has been subsequently disapproved by recent investigations. (ii) Surface coefficient The radiative surface coefficient generally adopted in thermal design models is a gross over-simplification of the radiative heat exchange process. Although the coefficient would approach a reasonably constant value if defined in terms of the temperatures of the surface and the surroundings, the assumption that the surroundings radiate at air temperature renders the definition unrepresentative of the real situation. It is unlikely that any linear representation of the longwave radiation exchange will significantly improve the situation. If Computer Models representing the thermal performance of buildings are capable of treating this mode of heat transfer in terms of fourth power absolute temperatures, then the only basic requirement is a closer specification of the incoming longwave radiation as a function of its dependent variables. (iii) Predictive techniques The majority of the techniques available for describing the availability of atmospheric radiation relate to the clear sky condition. These can be grouped into two parts. (a) Those which express the atmospheric emissivity as a function of vapour pressure alone (Brunt, Angstr6m). (b) Those in which vapour pressure is represented by temperature function (Swinbank, Idso and Jackson).
The first of these groups assumes that the majority of the atmospheric radiation during clear sky condition originates from the lowest few hundred metres of water vapour and that the vapour pressure at screen height is representative of this quality. The second type relies on the relationships between vapour pressure and temperatures; in that the higher the temperature the greater amount of atmospheric water vapour. Considerable variation appears between these methods; in particular the Brunt and Angstr6m relationships show a marked lack of universality. However, as already indicated, clear skies are the exception rather than the rule. The relationships, describing the availability of atmospheric radiation during this condition involve the multiplication of the clear sky value by some modifier. The premise that the clear sky radiation is known introduces one source of error and the empirically derived cloud cover modifier introduces a second. The combination of these two terms therefore introduces a compound error. (iv) Radiation on vertical surface The longwave radiation exchange between vertical surfaces and the surroundings 'seen' by it is even less well defined. At present the radiation impinging upon the surface is defined as that emitted by a black body at air temperature. The value of this radiation is dependent upon the nature of the ground surfaces surrounding it. Surfaces such as pavement, tarmac etc., follow quite wide temperature variations and consequently the radiation emitted by such surfaces is difficult to quantify. In terms of its application to thermal design of buildings there is a need for relationships which describe the dynamic longwave radiation income for use in the more sophisticated mathematical models. These relationships must be able to be developed from commonly recorded climatic elements and of a simple format to avoid the application of complex configuration factors. Until such relationships are available, building scientists concerned with the transformation of weather data into longwave radiation data in the U.K. are advised to use the atmospheric radiation data presented by Unsworth and Monteith and continue to assume that the longwave radiation incident on a vertical surface is equivalent to that emitted by a black body at screen air temperature.
REFERENCES 1. N. Robinson (Editor), Solar Radiation. Elsevier, Amsterdam (1966). 2. D.G. Stephenson, Equations of solar heat gain through windows, Sol. Energy 9, 81-85 (1965). 3. Building Research Station, Library Communication, Utilisation of Solar Energy, No. 220 July (1970). 4. M. Lokmanhekim, Procedure for determining heating and cooling loads for computerised energy calculations--algorithms for building heat transfer subroutines, ASHRAE, New York (1971). 5. N. Ito, K. Kimura & J. Oka. A field study on the convective heat exchange on the external surface of a building. ASHRAEBi-Annual Meeting. New Orleans. LA. (1972). 6. A. J. A. Roux, The effect of weather conditions on heat transfer through building elements, Building Research Congress. Div. 3, 82-87 (1951). 7. G. V. Parmelce & W. W. Aubele, Radiant energy emission of atmosphere and ground. Trans. ASHRAE58, 85-106 (1952). 8. •. •gun•esi• S••ar radiati•n and therma• gradients in bui•ding units. Build. S•i. • •-2• (•965). 9. B. L. Hoglund, C. P. Mitalas & D. G. Stephenson, Surface temperatures and heat fluxes for flat roofs. Build. Sci. 2, 29-36 (1967).
The Longwave Radiative Environment Around Buildings 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.
H.L. Hackforth, Infra-red Radiation. McGraw-Hill (1960). E. M. Sparrow & R. D. Cess, Radiation Heat Transfer. Brooks-Cole, CA. (1966). N. S. Billington, Building Physics Heat. Pergamon Press, London (1967). R. W. Bliss, Atmospheric radiation near the surface of the ground. A summary for engineers. SoL Energy 5, 3 (1961). K. Ya. Kondratyev, Radiative Heat Exchange in the Atmosphere. Hydro Meteorological, Leningrad. Translated from Russian (1956). D. L. Morgan, W. O. Pruitt & F. J. Laurence, Estimation of atmospheric radiation. J. appl. Alet. 10, 463--468 (1971). W.H. Dines, Observations in radiation from the sky. Geophys. Mem. 18 (1921). F. Essien, An investigation of free convection and low temperature radiation from surfaces of building elements. Ph.D. Thesis, Univ. Newcastle-upon-Tyne (1972). W. H. Dines & L. H. G. Dines, Monthly mean values of radiation from various parts of the sky at Benson, Oxfordshire. Mere. R. met. Soc. 2, 11 (1927). W. M. Elsasser, An atmospheric radiation chart and its use. Q. Jl R. met. Soc. 66, 41 (1940). W. M. Elsasser, Atmospheric radiation tables, Monographs, ARCRL-TR-60-236, U.S. Dept. Commerce (1960). F. A. Brooks, Observations of atmospheric radiation, Paper. Phys. Ocean, Met., M.LT. Woods Ocean Inst. 8, 2 (1941). C.D. Robinson, Notes on the measurement and estimation of atmospheric radiation. II. Q. JI R. met. Soc. 76, 37-51 (1950). M.E. Beryland, Kondratyev (1956). W. Reifsnyder & H. Lull, Radiant energy in relation to forests. U.S.D.A. For Set. Tech. Bull. No. 1344 (1965). A. Angstr6m, A study on radiation of the atmosphere. Smithsonian Misc. Coll. 65, 57-69 (1915). D. Brunt, Notes on radiation in the atmosphere. Q. Jl R. met. Soc. 58, 389-420 (1932). E. M. Agee, Equations for estimating solar and infra-red radiation at the earth-atmosphere interface. Msc. Thesis, University of Missouri, Columbia, U.S.A. (1966). J. R. Goss & F. A. Brooks, Constants for empirical expressions for down-coming atmospheric radiation, J. Met. 13, 482-488 (1956). J. R. Goss & F. A. Brooks, Radiant energy, its reception and disposal, Agricultural meteorology. Met. Mono. 28, 1-26 (1956). J. G. Charney, Radiation, Section 4, Handbook of Meteorology. McGraw-Hill, New York (1945). J. L. Monteith, An empirical method for estimating longwave exchange in the British Isles. Q.J. R. met. Soc. 87,171-179 (1961). O. L6nnqvist, Theoretical verification of the logarithmic formula for relative net radiation to a cloudless sky. Arkiv. Geofysik 151-159 (1954). J.E. Belasco, Geophys. memoirs. Met. Office No. 87 (1952). F. Moiler, Longwave radiation, compendium of meteorology, Boston, Amer. Meteor. Soc. 3449 (1951). H. M. Bolz & G. Falkenberg, Neubestimmung der Kinstanten der Angrom'schen Strahumgsformer. Z. Meteor 3, 367-368 (1949). W.C. Swinbank, Longwave radiation from clear skies. Q. Jl R. met. Soc. 89, 339-348 (1963). D. M. Gates, Energy Exchange in the Biosphere Harper and Row Monograph New York (1962). E. Deacon, The derivation of Swinbank's longwave radiation formula. Q. Jl R. met. Soc. 96, 313-319 (1970). O. Lonnqvist, A general method and a simplified formula for calculating effective radiation. Arkiv Geofysik 79-115 (1950). S.B. Idso & R. D. Jackson, Thermal radiation from the atmosphere, J. Geophys. Res. 74, 53975403 (1969). N.E. Dorsey, Properties of Ordinary Water Substance. Reinhold, New York (1940). S.B. Idso, On the use of equations to estimate atmospheric thermal radiation Arch. Met. Geophys. Biokl. Set. B. 22, 287-299 (1974). M.H. Unsworth & J. L. Monteith, Longwave radiation at the ground (i) Angular distribution of incoming radiation. Q. Jl R. met. Soc. 101,1-13 (1975). A. Angstr6m & S. Asklof, S. Ann. Stockholm Vol., 253 [In Gates (1962)]. H. M. Bolz, Die abhangigkeit der infraroten Gegenstrahlung yon der Bewolkung. Z. Met. 7 (1949). E. Kreitz, Reglstrienungen der langweUigen Gegenstrahuing in Frankfurt, Geof Pura. HapL 28 (1954). In. Kondratsyev (1956). W.T. Roach, Measurements of atmospheric radiation and the heat balance at the ground at Kew, May 1953--May 1954. Air Ministry. Met. Res. Commun. M.R.P. 936(1955). R. J. Polvarapu, A comparative study of global and nett radiation measurements at Guelph, Toronto and Ottawa. J. appl. Met. 9, 809-814 (1970). S.B. Idso & B. L. Blad, The effect of air temperature upon nett and solar radiation relationships. J. appl. Met. 10, 604-605 (1971). R. Geiger, The Radiation Near the Ground. Harvard U.P., Connecticutt (1965). R. Bailey, The A.J. EnvironmentalHandbook--Climate Section. A.J. (1968). F. Lauscher, Bericht u. mess. d. nachtl: Ausstrahlung aufd. Stolzalpe. Meteorolgis. Zeitschrift 45, 371-375 (1928). A. G. Loudon, Heat transmission through roofs of buildings. L Instn Heat. Vent. Engrs 31, 273-291 (1963). I.H.V.E. Guide, Book A--Design Data. Institute of Heating and Ventilating Engineers, London (1970). A. Aittomaki, A model for calculating heat balance of room and building. The state inst. Tech res. Finland. Pub. 0968). K. R. Rao & E. R. Ballantyne, Some investigations on the sol-air temperature concept. D.B.R. Tech.paper No. 27 C.S.I.R.O. Melbourne, Australia (1970).
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