REMOTE SENSING OF ENVIRONMENT 12:313-329 (1982)
Survey of Emissivity Variability in Thennography of Urban Areas
DAVID A. ARTIS and WALTER H. CARNAHAN Physics Department, Indiana State University, Terre Haute, Indiana 47809
This study investigates the effects of roof emissivity variation of aerial thermogram images. Thermograms have been used to detect heat loss from residential roofs. Emissivity variation among rooftops, however, can lead to a misrepresentation of the temperatures mapped in a thermogram image. The objectives of this study were (a) to demonstrate the feasibility of a technique to use remotely sensed data to calculate surface emissivities and (b) to apply that technique, to determine the extent of emissivity variation in urban surfaces. In the first part of the experimental approach a passive technique is developed to calculate emissivity from two-band thermal infrared radiance data. Inherent limitations and sources of error associated with the technique are discussed. In the second part of the experimental approach the technique was used to measure the emissivity of 1411 roofs within the city limits of Terre Haute, Indiana. Results of this survey indicated that over 98% of the roofs surveyed were confined to a very narrow range of emissivities. It is concluded that the observed variation in rooftop emissivities has a minimal effect on the temperatures depicted in thermograms.
Introduction With increasing awareness of the need for energy conservation, aerial thermography has become an important tool for the detection of heat loss in residential buildings (Schmer and Hause, 1979; Texas Instruments, 1978). Thermograms are images of the temperatures of a scene which are created from radiance measurements made in the longwave infrared portion of the electromagnetic spectrum. In the specific case of aerial thermograms, these measurements are made by an airborne multispectral line scanner. These data are processed by a computer to create an image indicative of a temperature mapping of a swath of terrain centered beneath the aircraft housing the scanner. Temperature variations are represented as tonal differences in the resulting image, with light and dark tones corresponding to low and high temperatures, respectively. ©Elsevier Science Publishing Co., Inc., 1982 52 Vanderbilt Ave., New York, NY 10017
A problem of aerial thermography is the correlation of thermal infrared radiance measurements with temperatures. It is appropriate to consider the concept of emissivity.
Emissivity Emissivity is a ratio which compares the radiating capability of a surface to that of an ideal radiator, or blackbody (Kruse et al., 1962). A pedect blackbody would absorb all electromagnetic radiant energy incident upon its surface. Such a sudace neither reflects nor transmits radiant energy, and once in thermal equilibrium with its surroundings, emits radiant energy at the same rate at which it is absorbed. Real solids, however, are not ideal. A fraction of the radiant energy striking such a surface is either transmitted or reflected or both. Furthermore, this fraction may be a function of the wavelength of the incident radiation. In 00344257/82/040313-17502.75
order to simplify the calculation for a real solid, it is useflfl to apply a "graybody" approximation. A graybody is a surface with emissivity independent of wavelength. A graybody absorbs the same fraction of the incident radiant energy regardless of the wavelength of that radiation. Thus a graybody, when in thermal eqtfilibrium with its environment, both absorbs and emits less radiant energy than a blackbody under the same conditions. The emissivity (e) of a surface is found by taking the ratio of radiant energy emitted from the surface to the corresponding emission from a blackbody at the same temperature (Wolfe, 1965). Therefore a blackbody has an emissivity of unity, while graybodies have emissivities of less than 1. Emissivity may be conveniently thought of as the emitting "efficiency" of an object.
The emissivity problem in aerial thermography In order to be able to associate a temperature with a measured value of thermal infrared energy radiated by a given object, it is necessary to know the emissivity of that object. The very nature of aerial thermography precludes the possibility of obtaining ground-based measurements of emissivity for all features for which radiance data is recorded. A common approach, therefore, is to generate thermograms based on the assumption that all features have an emissivity of unity (Bartolucci-Castedo et al., 1973; Burch, 1979). The resulting temperatures are commonly referred to as brightness temperatures (also known as apparent or radiant temperatures). Brightness temperature may be defined as the temperature at which a blackbody would need be in
D A. ARTIS AND W. H. CARNAHAN
order to emit the same amount of radiation per unit of surface area as the body being observed (Kruse et al., 1962). While the use of brightness temperatures can be an effective means of locating sources of heat loss, a problem arises if there is a significant amount of variation in the emissivities of the features imaged ill a thermogram. For example, the analysis of thermograms for residential heat loss is often based on comparisons between rooftops (Texas Instruments, 1978). One rooftop may appear warmer than another, evidently indicating insufficient attic insulation, while ill reality both roofs may have the same temperature and different emissivities. This very problem has resulted in controversy within the technical field about the merits of such uses of thennography (Burch, 1979; Bowman and Jack, 1979). The present study was initiated in an attempt to demonstrate the feasibility of a technique to use remotely sensed data to calculate a close approximation of surface emissivities and to apply that technique to determine the extent of emissivity variation ill roofing materials. Theory The Planck radiation formula, which relates the rate at which a surface radiates energy, is usually given as a function of kinetic temperature. In thermography, however, brightness temperatures are generally used. The definition of brightness temperature can be used to derive a relationship between brightness and kinetic temperatures. Brightness temperature is the temperature necessary for a blackbody to emit energy at the same rate as that observed from a graybody. Thus the radiances LBB(T, 2t ) and LC.B(T,X)
URBAN EMISSIVITY VARIABILITY
can be equated if the blackbody has brightness temperature TB and the graybody (with emissivity e) kinectic temperature T. Combining constants such that a = h c / K and fl = 2hc2/f~, the radiances for a blackbody and graybody may be written in the forms:
LB.(TB, X)= LCB(T, X ) =
)~5(e'~/XTB --1) eft ~5(e"/XT--1)
where h = Planck's constant (6.26 × 10 -34 J-see), c--velocity of light (2.998×10 s m/see), ~2= one steradian (dimensionless), ~ = wavelength of emitted radiance (m), K = Boltzman constant (1.38 × 10 -z3 J/K), T = kinetic temperature of observed object (K), L ( T , ~ ) = r a d i a n c e per unit-area per solid-angle per wavelength for body at kinetic temperature T (W/m3), a= h c / K (1.438× 10 -2 mK), r = 2hc2/~ (1.19×10 -16 Wm2), e = surface emissivity. Assuming that the - 1 in the denominators of Eqs. (1) and (2) is negligible the right sides of the two equations may be equated to solve for T:
TB/a)ln e .
and brightness temperature. As previously noted, kinetic temperatures are typically not available from thermographic data sets. Thus T must be eliminated from Eq. (3) to arrive at a relationship in which emissivity is functionally dependent on wavelength and brightness temperature only. The Terre Haute aerial thermography data set can be used to calculate two brightness temperatures for a given pixel, as radiance measurements were recorded by the scanner in two different wavebands. This access to two different brightness temperatures for the same pixel provides a convenient means to eliminate the dependence on kinetic temperature in Eq. (3), using an approach similar to the ratio technique of Vincent and Thomson (1972) as described by Carnahan and Goward (1977). Equation (3) may be thought of as applying to a situation in which a brightness temperature Tn has been calculated from a radiance measurement in wavelength ~ for a pixel with kinetic temperature T. Given another brightnesstemperature for the same pixel, T~, corresponding to radiance in wavelength )V, Eq. (3) may be written in the form
1 + ()VT~/a)ln e" Equations (3) and (4) then represent expressions for the same kinetic temperature. As such, the two may be equated, yielding the following expression for emissivity
Brightness temperature and emissivity Equation (3) provides a relationship among emissivity, kinetic temperature,
e = exp TBT[~(h, - k)
To summarize, Eq. (1) can be used to associate a brightness temperature with a measured value of radiance. Once two brightness temperatures for a given pixel have been calculated, Eq. (5) can be used to calculate an emissivity value for that pixel. It is important to note that in addition to the approximation used in the derivation of Eq. (3), a graybody approximation has been made. In other words, it has been assumed that the emissivity of a pixel is the same for both wavelengths used in Eq. (5). The equations presented in this section incorporate specific wavelengths, or zero bandwidths. The process of implementing these equations in nonzero bandwidth (wideband) situations will be discussed in the following sections.
D. A. ARTIS AND W. H, CARNAHAN
the city and ended with number 24 at the eastern edge of the city limits (run number 21 was not used, as no residential buildings were present in this flight line). The data were collected between 12:09 A.M. and 4:16 A.M. EST under nearly ideal conditions--no cloud cover with little wind, low humidity, and an air temperature just above 0°C. Band radiance measurements were made in two different thermal infrared wavelength bands: 3.5-5.7 and 8-14 /~m (Carnahan and Llewellyn, 1981). The aircraft's altitude was 396 m and the instantaneous field of view of the scanner was 2.5 mrad. Thus, each pixel represents 0.98 m e of ground surface at nadir. To minimize distortion due to parallax only the center 256 pixels on each scan line were used in this study. This corresponds to an area of 1.09 m 2 at the outermost pixel.
Data set The data set used in this investigation consists of 23 computer-compatible magnetic tapes on which thennographic data were recorded. These tapes were created by the Environmental Research Institutes of Michigan (ERIM) as part of the Terre Haute Aerial Thermography Pilot Project, which was sponsored by the Terre Haute Board of Redevelopment in conjtmction with Indiana State University. The purpose of this project was to generate aerial thermograms of the city in order to provide homeowners with heat loss information. The thermographic data were recorded by ERIM's M7 multispectral line-scanner on board a C-47 aircraft in a series of 23 south-to-north flight lines over the city on 13 March 1979. The scanning began with run number one at the western edge of
Calculation of brightness temperatures There are two digitized voltages recorded on magnetic tape for each pixel seen by the M7 scanner. One corresponds to the voltage output of the scanner for radiance in the 3.5---5.7 /~m waveband, while the other is for the 8-14/~m waveband. These voltages must be converted to radiance values as prerequisite to the actual calculation of brightness temperatures of the two bands. The scanner's output voltage is not merely a function of the radiance entering the aperture from the target pixel. It is also functionally dependent on the instantaneous field of view, wavelength bandpass, the area of the collecting aperture, detector responsivity, scanner optics transmission, and the voltage offset in the system due to internal electronics.
URBAN EMISSIVITY VARIABILITY
The effects of these factors are most easily determined using the internal calibration plates. These reference plates had an emissivity of 0.95. The hot plate was kept at a constant temperature of 9.05°C while the cold plate's temperature was maintained at 1.89°C. The temperature of the ambient plate, which indicated the scanner housing temperature, varied for each of the 23 flight lines. These temperatures were available from the multispectral scanner calibration log supplied by ERIM. An expression which makes use of these internal reference plates to calculate the radiance seen by the scanner for any pixel in a specific flight line is e( V o - V n )LBB(Tn ) -- LBB(Tc ) Lsc~ner
( v . - vc) + eLBB(Tn) +
(1 -- e)LBB (TA ),
(6) where e = plate emissivity, Vo = output voltage of scanner for target pixel, V n = output voltage of scanner for hot plate, L BB(Tn) = radiance from blackbody at temperature of hot plate (for a specific waveband), L BB(Tc) = radiance from blackbody at temperature of cold plate (for a specific waveband), L 88(TA) = radiance from blackbody at temperature of ambient plate (for a specific waveband). 3.5-5.7 pm brightness temperatures
Numerical integration of Planck's formula was used to calculate values for L BH(Tn), L 8B(Tc), and L Bs(TA) for the
3.5-5.7/~m waveband. Thus all the variables needed for Eq. (6) were determined, allowing the conversion of scanner output voltage to band radiance for each target pixel in a selected scan line for this waveband. In reality the scanner-detected radiance is not a true indication of the actual target radiance. The radiant energy emitted by a surface-level feature is affected by both scanner and atmospheric characteristics. Absorption by the latter is not only a function of the distance between the object and the scanner aperture, but also atmospheric parameters such as temperature and humidity. Similarly, any radiance emitted by the intervening atmosphere is difficult to determine accurately. Such atmospheric effects were neglected in this study. The scanner alters incoming radiance in two ways. The optics do not transmit 100% of the incoming band radiance, nor are the detectors 100% responsive to the depleted radiance reaching them. Moreover, the relative response and percent transmission of the scanner vary with wavelength (graphs of these variables as a function of wavelength were supplied by ERIM). All of these factors mean that Eq. (1) could not easily have been solved for T to obtain a value for target temperature in terms of the scanner-detected radiance. Thus a brightness temperature versus radiance table was created for the 3.5-5.7 ftm band. The range of temperatures for which these attenuated bandwidth radiances were calculated was from - 2 0 ° to + 20 ° in 0.1 ° increments. Thus a table of a scanner-detected radiance versus target brightness temperature was created, with a resolution of 0.1°C (Fig. 1). The imaging program could then search this
D . A . ARTIS AND W. H. CARNAHAN
1 I" -20
I - 10
TEMPERA TURE ('Celsius) FIGURE 1. Graph of the computer-generated radiance versus temperature table for the 3.5-5.7 gm-waveband. Here the radiance seen by the scanner has been attenuated by scanner response and percent transmission. The radiance of a target pixel is used in this table as an index to locate the associated brightness temperature.
computer-generated table to assign the appropriate brightness temperature of each pixel. 8-14/~m brightness temperatures The same procedure used to calculate brightness temperatures for pixels in the 3.5-5.7 ~tm waveband could have been used for pixels in the 8-14/zm waveband. However, as seen in Fig. 2, the resulting radiance versus temperature table is an approximately linear function. Meyer (personal communication, 1979) has verified that the net band radiance is sufficiently linear in the 8 - 1 4 / z m waveband to make a faster temperature calibration technique feasible.
For temperatures near 0°C in the 8-14 /zm region, scanner-recorded voltage is approximately linearly proportional to brightness temperature. The imaging program made use of this by effectively creating a linear function of temperature versus digitized voltage. This linear function was calibrated to the values of the hot and cold reference plates, for which known temperatures could be associated with the corresponding scanner-recorded values of Vft and Vc for this band. The output voltage of the scanner for a target pixel could then be multiplied by the slope and incremented by the intercept of the linear function, thus obtaining the correct brightness temperature for each
URBAN EMISSIVITY VARIABILITY
TEMPERA TURE ['Celsius) FIGURE 2. Graph of band radiance versus temperature for the 8-14 gm-waveband. The radiance has been attenuated by scanner response and percent transmission. This graph can be seen to approximate a linear function.
pixel within a scan line in a "tlme-emc~ent -" "" done using the following equation: manner.
f bS(X) (X)L(X)XdX
Emissivity calculation Once the two brightness temperatures for a pixel have been calculated, Eq. (5) may be used to find an emissivity value for that pixel. TA is the brightness temperature for the 3.5-5.7 ttm band (k'), while TB is the brightness temperature for the 8 - 1 4 g m band (k). The brightness temperatures calculated by the method described, however, are for wide-band wavelengths rather than a single spectral wavelength. Thus it was necessary to compute a weighted average value for h' and k to be used in equation (5). This was
where R(2~) = relative response as a function of wavelength, r(?t) = percent transmission as a function of wavelength, L(X) = radiance from Planck's formula as a function wavelength. and a and b are the limits of integration - - 3 . 5 - 5 . 7 gm, respectively for ~'av; 8 and
D.A. ARTISAND W . H . CARNAHAN
(a) FIGURE 3. (a) Thermography in the 8-14-p,m window of a scene in the data. This scene shows a number of suburban homes. The cooler brightness temperatures are represented by the darker pixels. Black corresponds to temperatures less than or equal to 271 K and folrr gray values amount to a 1 ° temperature change. With 256 gray values the complete white eorresponds to a temperature greater than or equal to 335 K. (b) An emissivity map of the same scene as shov,ql in Fig. 3(a). The metallic ridge vents, antennas, and air-conditioners are the most notable features with below average emissivity. Only 210 of the gray values are used in the emissivity map with complete black corresponding to 0.65 and every six gray values amolmting to a change of 0.01 in the emissivity.
14/zm for ~ v (the 3.5-5.7/~m band), the integration was done numerically using Simpson's rule. A value of 5.565/~m was obtained. Similarly a value of 13.175/zm was found for ~av" The imaging program could then use these values in Eq. (5) to calculate an emissivity value for all pixels in each scan line to be imaged. Figures 3 and 4 are images generated using the techniques discussed above. Figures 3(a) and 4(a) represent 8 - 1 4 / z m brightness temperature mappings of two scenes selected from the data set, while Figs. 3(b) and 4(b) represent emissivity mappings of the same scenes.
Emissivity survey It was decided to select at random 50 image frames from the Terre Haute aerial thermography data set in order to perform an emissivity survey. This was done by randomly selecting a run number from the 23 possible values. Knowing the number of scan lines contained in that run, a scan line was then selected at random, which represented the first of the 256 lines to be imaged. This process was repeated until 50 nonduplicate run number/scan line combinations were determined.
URBAN EMISSIVITY VARIABILITY
Co) FIGURE 3.
Emissivity statistics were collected for each of the frames in the following manner. The statistics-gathering program placed on the display screen two cursors which the user then positioned by manual control at opposite comers of a roof in the emissivity image quadrant. The program then histogrammed the digitized values of all the pixels in the rectangle defining the roof. These values were stored in a data file, and the value occuring most frequently in that rooftop (the modal value) was stored in another file. This process was repeated for each roof occuring in that image. Then the cursors were placed at the opposite comers of the entire emissivity image frame, for which a histogram was also created and stored in a third data file. In an identical fashion the procedure was repeated for the remaining 49 image frames, resulting in data being accumulated for a total of 1411 residential
roofs, roughly a 5% sampling of all residences within the Terre Haute city limits. Thus three sets of statistics were accumulated. One set represented a histogram of the emissivity values for all pixels contained in rooftops; another a histogram of emissivity values for all pixels contained in the 50 emissivity image frames; and the last a histogram of the number of roofs for which a given emissivity value occured most frequently. The latter set of data was collected in order to minimize the effects of pixels within the roof area corresponding to chimneys, awning, etc., which might have adversely affected an averaging technique. Graphs of the resulting histograms are shown in Fig. 5. Results The histogram curves shown in Fig. 5 graphically depicts the observed emissiv-
D. A. ARTIS AND W. H. CARNAHAN
(a) FIGURE 4. (a) A thermogram from another scene in the data set. These buildings are primarily apartments surrounded by trees. The cooler brightness temperatures are represented by the darker pixels. Black corresponds to temperatures less than or equal to 271 K and four gray vMues amount to a 1 ° temperature change. With 256 gray values the complete white corresponds to a telnperature greater than or equal to 335 K. (b) An emissivity m a p of the scene shown in Fig. 6, The driveway and roof have a slightly lower emissivity than the lawn. Only 210 of the gray values are used in the emissivity m a p with complete black corresponding to 0.65 and every six gray values amounting to a change of 0.01 in the emissivity.
ity distribution in the rooftop survey. Analysis of the three data sets resulted in a mean emissivity of 0.923 for the rooftop pixel data and 0.924 for the modal roof emissivity values. The emissivity frame pixel data resulted in a mean of 0.931. The standard deviation for each data set was found to be 0.021, 0.016, and 0.016, respectively. The larger mean for the emissivity frame pixels is most likely a result of "shine." This is the term used to describe areas which both absorb and reflect some of the electromagnetic radiation emanat-
ing from nearby sources, such as walls and windows. Thus a falsely high temperature is calculated from the radiance of such pixels. The emissivity calculated for these pixels is also affected, often resulting in a value of 1.0. Such areas probably resulted in a slightly higher mean emissivity for the frame pixel data set. Care was taken in the acquisition of roof data to exclude pixels surrounding the roof which had abnormally high temperatures due to shine. A discussion of possible sources of error will be presented prior to drawing conclusions from the survey statistics.
URBAN EMISSIVITY VARIABILITY
go) FIGURE 4.
There is an inherent random error present in the recorded radiance data which results in error in the brightness temperatures calculated from these data. It was thus necessary to determine what effect this propagation of errors had in the emissivity calculations. Previous research indicated a random error measurement of 0.11 K (Meyer, personal communication, 1979) in the 8-14 ptm band temperatures and 0.6 K in the 3.5-5.7 /~m band temperatures, (Hassel, et al., 1977). The resulting error in emissivity calculation (Ae) may be found using Eq. (5). Letting AT represent the error in the 8-14 ftm band temperatures and AT' the error in the 3.5-5.7/~m band temperatures, Ae may be found using the propa-
gation of errors expression (Young, 1962) 0~
Ae= -~-T7AT' + - ~ AT,
where Eq. (5) may be used to find the necessary derivatives. Inserting the proper derivatives and simplifying resulted in the following equation:
Ae---- •,,_ 2~ T~z
Because Eq. (9) requires specific brightness temperatures to obtain a numerical value of Ae, the brightness temperatures in both bands were listed for a total of 30 pixels representing water in the Wabash river. These temperatures
D.A. ARTISAND W.H. CARNAHAN
30000 0 0
(a) FIGURE 5. Histograms of (a) all emissivity image pixels contained in rooftops, (b) all emissivity image pixels contained in the 50 frames, and (c) the modal emissivity values of all roofs contained in the .50 emissivity image frames.
were averaged to find T ~ : 278.5 K and TB : 277.0 K. Using these temperatures in Eq. (5) resulted in an emissivity value of 0.965 for water pixels. The weighted average values of ?~' and ~ were then used in Eq. (9) to generate a value for error in emissivity. It was found that A e : 0.011. Thus a deviation of --+0.011 in any calculated value of emissivity is within the bounds of random error. Systematic error
A number of factors other than propagation of errors could cause an incorrect value of emissivity to be calculated for a pixel. The determination of a correct
emissivity value is dependent on accurate brightness temperatures. As discussed above, several approximations were used in relating radiance data to emissivity. Perhaps most significant was the fact that atmospheric effects on radiance data were ignored. Attenuation of thermal infrared radiance in the 8-14 # m window of the electromagnetic spectntm appears to be negligible. Existing data, however, indicate that atmospheric attenuation of thermal radiance in the 3.5--5.7/~m window may be significant (Wolfe, 1965). Any error in calculating emissivity as a result of this would, however, be consistent for
URBAN EMISSIVITY VARIABILITY
0 400000 0
o W-------t .65 .7
every pixel in the data set, assuming little variation in atmospheric parameters during the data collection mission. Such an error should not significantly affect the spread or distribution of emissivities, which is of primary importance in this study. Furthermore, Haigh and Pritchard (1981) point out that the sky is not a graybody radiator. More thermal infrared energy is radiated by the sky in the 3.55.7/am band than in the 8-14 #m band. This emission of thermal infrared radiation could have the effect of countering the opposite phenomenon of atmospheric absorption. Despite the possibility of systematic error in the emissivity values, those calculated are in close accordance with pub-
.8 .85 EMISSIVITY
lished data. It was found, for example, that pixels representing water had emissivities ranging from 0.96 to 0.98 with an average emissivity of 0.964. In a brief summary of literature concerning water emissivity, Bartolucci-Castedo et al., (1973) reports a typical value for sea or lake water is 0.97, which is within the range of random error of the experimental value. In addition, the mean value of 0.92 for roof emissivities is consistent with existing published data on building material emissivities (Gubareff et al., 1960). Furthermore, recent research at ERIM (Sampson, personal communication, 1980) found emissivities on the order of 0.9 for residential roofs are typical, thus implying empirically no gross systematic errors in
D, A ARTIS AND W. H. CARNAHAN
500 (n tU (.) ;~ 4 0 0 tU
I • T5
EMISSIVITY (c) FIGURE 5. (Continued)
the emissivity calculation technique developed for this study. Discussion
The purpose of this study was to develop and implement a technique to calculate emissivity from remotely sensed thermographic data. As demonstrated, the application of this technique was in the form of a roofing material emissivity survey, the objective of which was to test the following hypotheses: the magnitude of emissivity variation among residential rooftops is such that the use of thermograms to detect heat loss by roof comparison is invalid. The histogram of modal rooftop emissivities was selected for further analysis
because the technique used to histogram these emissivities selected the most frequently occuring value for each roof. Thus stray pixels representing metallic features or chimneys on a roof surface were rejected by this technique. This data set had a mean emissivity of 0.924 and a standard deviation of 0.016. Close inspection of the histogram in Fig. 5c reveals two very small modes below 0.85 on the emissivity scale. Fewer than 1% of the roofs surveyed had an emissivity less than 0.85 (only 14 of the 1411 roofs surveyed had emissivities lower than 0.9). These anomalous roofs are likely to consist of metal sheeting or low-emissivity slate, for which emissivity values of 0.8 have been reported (Gubareff et al., 1960). Such roofs appear colder than they really are
URBAN EMISSIVITY VARIABILITY
due to reflectivity ( 1 - c ) as well as the low emissivities. Because these roofs partially reflect the night sky, they are typically imaged as having temperatures at the lower limit of the range displayed. Therefore it is readily apparent to the analyst that the observed temperature in the thermogram is not an accurate measurement for that feature. For this reason further analysis was restricted to the histogram peak between 0.89 and 0.95, which contained 98.8% of the roofs surveyed. This peak was found to have a rounded mean emissivity of 0.92 and a standard deviation of 0.0086. An approach similar to that used to find the effect of random error on emissivity was used to develop an expression which determines what effect emissivity variation (Ae) has on brightness temperatures ( ATB). Equation (3) may be rewritten by solving for TB:
T hTln e
This equation was used to obtain the necessary derivative needed in the expression for ATe:
0TBAe Thus Ae)tT 2
ATe = ae(1
X Tzl nae )
It was decided to use this equation to determine the effect on emissivity varia-
tion on brightness temperatures in the 8-14 /~m waveband. This is the band most commonly used to generate thermograms because of greater accuracy than in the 3.5-5.7 ttm waveband. Thus the weighted average wavelength from the 8-14/~m band was used for ~. The mean emissivity value was used for e, while the standard deviation of the peak was used for A e. An assumed roof kinetic temperature of 273 K resulted in a value of 0.6 K for ATe . This value is consistent with studies by ERIM, in which an airborne CO 2 laser was used to remotely measure reflectivity ( 1 - e ) with an active technique, as opposed to the passive technique used in this study (Lowe, 1979). Of the roofs surveyed, 88.7% were within the emissivity range of 0.91 to 0.93, which is approximately one standard deviation on either side of the mean within the histogram peak. The above arguments have been presented as a rough approximation only. The standard deviation of the emissivity data set is of the same order as the possible error in emissivity due to propagation of errors. While the modal emissivity histogram technique should minimize the effect of random errors, it is not possible to completely eliminate these errors. As a result, the statistics collected are representative not only of true emissivity variation, but variation due to random error as well. Nevertheless, the null hypothesis has been demonstrated with a reasonable degree of confidence. This study has developed a passive technique to measure emissivity, utilizing remotely sensed measurements of thermal infrared radiance in two wavelength bands. It has been demonstrated that emissivity measurements made by this method are consistent with values mea-
328 sured using an active technique as well as more traditional ground-based approaches. Furthermore this passive technique was implemented in an attempt to resolve any controversy concerning emissivity variation and the use of thermograms to detect heat loss. The magnitude of emissivity variation between roofs has been shown to be not so great as to negate the use of thermograms for such a purpose. With the exception of obviously anomalous features, emissivity variation in common roofing materials has a minimal effect on the brightness temperatures depicted in thermogram images.
The authors wish to thank Ralph Llewellyn and Paul Mausel for their guidance during this project; Dave Meyer for his work on the calibration o f the temperatures; Uwe Hansen and Norman Cooprider for their help with the figures and photography; and Tom Young forohis help with the data gathering. References Bartolucci-Castedo, L. A., Hoffer, R. M., and West, R. T. (1973), Computer-Aided Processing of Remotely Sensed Data for Temperature Mapping of Surface Water front Aircraft Altitudes, Technical Report 042473, Laboratory for Applications of Remote Sensing, Purdue University, W. Lafayette, Indiana. Bowman, R. L., and Jack, J. R. (1979), Feasibility for Determining Flat Roof Heat Losses Using Aerial Thermography, NASA Technical Memorandum 79152, Lewis Research Center, Cleveland, Ohio. Burch, D. M. (1979), The Use of Aerial Infrared Thermography to Compare the Thermal Resistances of Roofs, National Bureau of Standards Technical Note 1107, Washington, D.C.
D.A. ARTISANDW.H. CARNAHAN Carnahan, W. H., and Goward, S. N. (1977), A Method for the Determination of Surface Emissivities from Multi-spectral Data in the 8 tzm to 13 I~m Region, Symposium on Machine Processing of Remotely Sensed Data, Purdue University, W. Lafayette, Indiana, p. 144. Caruahan, W. H., and Llewellyn, R. A. (1981), Terre Haute Infrared Thermography Project--Final Report. Department of Physics, Indiana State University, Terre Haute, Indiana. Gubareff, G. G., Janssen, J. E., and Torborg, R. H. (1960), Thermal Radiation Properties Survey--A Review of the Literature, 2nd. Ed., Honeywell Research Center, Minneapolis, Minnesota. Haigh, G. A., and Pritchard, S. E. (1981), Quantifying heat losses using aerial thermography, in Thermal Infrared Sensing Applied to Energy Conservation in Building Envelopes (7hermosense III), Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, 91-101. Hassell, P. G., Legault, R. R., Braithwaite, J. G., Larsen, L. M., Lampert, S. R., Work, E. A., Levereault, L. A., Stewart, S. R., Lambeck, P. F., Wiseman, J. K., Ladd, J. C., Juodawlkis, W. J., Griffin, N. V., and Kraudelt, E. L. (1977), Michigan Experimental Mapping System--A Description of the M7 Airborne Sensor and its Performance, Environmental Research Institute of Michigan Technical Report 190900-10-T, Ann Arbor, Michigan. Kruse, P. W., McGlauchlin, C. D., and McQuistan, R. B. (1962), Elements' of Infrared Technology: Generation, Transmission, and Detection, Wiley, New York, pp. 13-20. Lowe, D. S. (1979), Effects of emissivity on airborne observation of roof temperature, in First National Conference on the Capabilities and Limitations of Thermal Infrared Sensing Technology in Energy Conservation Programs (Thermosense I),
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