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A field method for measuring the thermal infrared emissivity
ISPRS Journal of Photogrammetry and Remote Sensing
24
Jos6 A. Sobrino 1 and Vicente Caselles i
A field method for measuring the thermal infrared emissivity In this work, a field m e t h o d for measuring thermal infrared emissivities is proposed which is based on the box method, initially developed by B u e t t n e r and Kern (1965) for laboratory measurements. A theoretical analysis was m a d e of the m e a s u r e m e n t carried out using the box and a correcting factor to Buettner and Kern's technique has been determined. Buettner and K e r n ' s m e t h o d has been modified to use radiative temperatures measured with a r a d i o t h e r m o m e t e r instead of radiance m e a s u r e m e n t s . The walls of the box used and the cold lid was m a d e of polished aluminium and the hot lid was m a d e of black-painted anodized aluminium and it was heated in the field by solar radiation. With this m e t h o d m e a s u r e m e n t s of the thermal infrared emissivity of ground and vegetation can be obtained with a relative error not larger than 0.6%.
1. Introduction
The radiance measurement obtained by a sensor placed on board a satellite is made assuming that the observed surface is a black-body, but this is not true for natural objects (or surfaces), and therefore to obtain accurate measurements of surface temperature by infrared radiometry a good determination of the surface emissivity is necessary (Becker, 1987; Sobrino et al., 1990). This is due to the fact that an uncertainty in emissivity of 1% may lead to an error in temperature of 0.5°C when the surface temperature is around 300 K (Sobrino and Caselles, 1989). The emissivity measurement is generally dillicult to make in natural surfaces because the observed radiance is the result of a double contribution: the ground emission itself and the reflection on it of the radiance coming from its surroundings (atmosphere, walls, trees, etc.). Thus assuming that the thermal equilibrium is reached and that the surroundings are characterized by a black-body equivalent temperature Ta, the observed radiance coming from the ground LA(TBB), considered as a Lambertian surface, can be written as: LA(TBB) = ~AL°~(T) + (1 - cA)LA(Ta)
(1)
where L°~(T) is Planck's radiation function; the first term on the right is the radiance emitted by 1 D e p a r t m e n t of Thermodynamics, Faculty of Physics, University of Valencia, 50, Dr. Moliner, 46100 Burjassot, Spain.
the ground itself and the second one represents the fraction of the ambient radiance LA (Ta) which is reflected by the target. Therefore it will be necessary to solve an equation with three unknown quantities: the surface emissivity, cA, the ground temperature, T, and the surroundings equivalent temperature, Ta. This problem can be simplified by making a separation between the contributions corresponding to the system and its surroundings. In order to solve this problem two methods are frequently used: the reflection method in active radiometry and the box method in passive radiometry. The first one obtains the emissivity from the knowledge of the hemispherical reflectivity, PA, by applying Kirchhoff's law to opaque surfaces: cA = 1 - PA
(2)
Spectral emissivity has been determined in the laboratory using this method by Lyon and Burns (1963), Wong and Blevin (1967), Robinson and Davies (1972) and more recently by Becker et al. (1986) and Salisbury and Milton (1988). The hemispherical reflectivity is the result of integrating, in the upper hemisphere, the bidirectional reflectivity weighted by cos 0', where 0' is the angle defined by the beam reflected and the normal to the surface. The bidirectional reflectivity is obtained by irradiating the surface in the (0, ¢) direction and measuring the reflected radiance in the (0', ¢') direction. A modulated laser source associated with a synchronized detec-
ISPIL7 Journal of Photogrammetry and Remote Sensing, 48(3): 24-31 0924-2716/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 48, number 3, 1993
2fi
tion system is used in order to eliminate both the proper emission of the sample and the reflection of the radiance coming from its surroundings. A good calibration panel is also necessary and the noise is very important due to the fact that this method works with the reflected radiance instead of the emitted radiance and therefore the signal received is small. All of these reasons mean that the reflection method is only applicable in the laboratory. The box method eliminates the surroundings radiance, isolating the sample by means of a perfectly reflecting surface, so eq. 1 becomes:
the use of these solutions for field measurements necessitates the use of heavy equipment. In addition, eq. 5 is only strictly valid for an "ideal" box with perfectly reflecting and emitting materials. Therefore the aim of this paper is to propose a simpler method, consisting of a modification of the box method, which accounts for these drawbacks and can be used in field conditions to allow agronomists, geologists, oceanographers, etc., to obtain the thermal infrared emissivity of natural samples in a precise, easy and quick way.
L~°X(TBB) = z;~L°A(T) + (1 -¢A)L°~(T)
Like Buettner and Kern (1965) the influence of the surroundings has been eliminated using a bottomless box with reflecting interior sides and having two exchangeable lids, both provided with a hole through which the infrared radiometer views the sample (see Fig. la). One is the cold lid which is made with a reflecting material (ec ~ 0) and the other is the hot lid made with an emitting material (eh ~ 1). In the following, the subscript 's' refers
(3)
= L°~(T) Combining eqs. 1 and 3 and assuming that the ground temperature does not change during the measurement period, one obtains: L
(TBB) -
L;,(T.)
E;~ = L~ox(ri3B) _ LA(Ta)
(4)
This equation proposed by Combs et al. (1965), and modified by Lorenz (1966) and Fuchs and Tanner (1966, 1968), has been used by Davies et al. (1971) and Taylor (1979) for obtaining field determinations of soil and water emissivities. The main difficulty of this method is the determination of the surroundings radiance (Chen and Zhang, 1989). To avoid the measurement of the surroundings radiance, Buettner and Kern (1965) add to the box a second lid made of an emitting material (the hot lid). Buettner and Kern's method, with alternatives proposed by Conaway and Van Bavel (1967) and Dana (1969), determines the emissivity from the relationship: cA -
LA3 -- LA1
2. Proposed method
(a)
ES Is F
SAMPLE RADIOMETER
(5)
LA3 -- LA2
where LA1 and LA2 are the radiances measured with the emitting and reflecting lids, respectively, and LA3 is the radiance emitted by the hot lid. For obtaining the sample emissivity from eq. 5 the emitting lid temperature must be higher than the sample temperature and constant during the measurements. Buettner and Kern (1965) solve this problem in the laboratory with water flowing through channels into the hot lid, and Nerry (1988) by using heating resistances. Nevertheless,
:::::::
........
\
(b) Figure 1. (a) Box geometry and (b) main factors composing the radiance reflected by the sample.
26
ISPRS Journal of Photogrammetry and Remote Sensing
to the sample material, 'w' refers to the box walls, and 'c' and 'h' refer, respectively, to the cold and hot lids of the box. In this way, the radiance coming from the sample, when the box is placed over it and considering that the radiometer only views the sample, can be written as: L~ = Rs + (1 - es) Gs
(6)
where Rs is the radiance emitted by the sample itself, and G~ is the radiance striking the sample. R~ is given by: e~ =
ff
e~;~L°(Ts) q(A) dk = esB~
(7)
1
where Bs is the integrated value of the black-body spectral radiance at the sample temperature, Ts, over the spectral transfer function of the instrument q(A), A1 and A2 are the wavelengths at which q(A) goes to zero, and e~ is the averaged sample emissivity. If we consider that the materials used to construct the box do not possess emissivities exactly equal to 1 or 0 and if we neglect the hole influence (its size being much smaller than the lid), Gs is composed primarily of four terms: (1) the radiance emitted by the lid itself, (2) the radiance emitted by the side itself, (3) the radiance from the lid that is reflected by the sides, and (4) the upward radiance, Ls, which is reflected following the same paths (1) and (3) (see Fig. lb). Then:
the hot lid, L1, (b) using the cold lid, L2, and (c) using the hot lid when the sample is replaced by the cold lid, L3: L1 = esBs + (1 - es) [eeBcF +
ehBh
(1 - F e c )
+ LI(1 - eh) (1 -- F ec)]
(9)
L2 = esBs + (1 - es) (ecBc [1 + F (1 - ec)] + L2(1 - ¢c) (1 - F ec)}
(10)
L3 = ecBc + (1 - ec) [e~B~F + ehBh (1 -- F ec)
+ L3(1 - eh) (1 -- F ee)l
(11)
where eh and ec are the hot and cold lid emissivities, and Bh and B~ are, respectively, the integrated values of the black-body spectral radiance at temperatures Th and T¢. In these equations ew = ec, because the same material has been used for the box walls and the cold lid. The above equations mean a clear improvement of the description made in the ideal case (ew = e¢ = 0, and eh = 1), situation in which L 1 = e s L 2 -t- (1 - e s ) L 3 , L 2 = Bs and L3 = Bh. Subtracting eqs. 9 and 10, the sample emissivity is obtained as: G = 1 -
L1 - L2 (1 - F ec)[(L1 - L2)
+ ec(L2
-
Bc)
"st" e h ( B h
L1)] (12)
Gs = etBt (1 - F ) + e w B w F + etBt (1 - ew)F + Ls(1 - st) [(1 - F ) + F (1 - ew)]
i
(8)
where st and ew are the lid and wall emissivities, Bt and Bw are, respectively, the integrated values of the black-body spectral radiance at temperatures Tt and Tw, and F is a geometrical factor which accounts for the proportion of radiation leaving the box walls and reaching the observed sample. This factor can be easily evaluated following the procedure proposed by Siegel and Howell (1981). Then, the procedure for determining the sample emissivity is described. Like in the ideal case (see eq. 5), this procedure is based on the measurement of the change in energy received from the sample when the temperature of the lid above sample is altered. To accomplish this, eq. 6 has been rewritten for the measurements made with three different configurations of the box; (a) using
Equation 12 can be given in a more convenient form if eqs. 10 and 11 are rewritten as: L2 = a B e
(13)
L3 = /3Bh
(14)
where a and ¢/are two effective emissivities, which can be deduced from eqs. 10 and 11: es (Bs/Bc) + (1 - e~) e~ I1 +
=
1 - (1 - es) (1 - s o ) ( 1
F (1 - e~)]
(15)
- Fee)
and: ec ( B c / B h ) [1 + F (1 - ec)] 1 - (1 - eh) (1 -- e~) (1 -- F e ~ ) Ch (1 -- ec) (1 -- F e c )
+ 1 - (i -- -c~ (-1--- -eT)( i - ~ Fee)
}
(16)
Volume 48, number 3, 1993
27
In this way and taking into account the fact that L2 is measured when the thermal equilibrium is achieved (Bs = Bc and therefore a = 1), eq. 12 after its combination with eqs. 13 and 14 can be rewritten as: L 1 -- L 2 Cs=l
(l -- F Cc)[(L1 - L2) + ~h(kL3 - L1)]
(17) where k = 1//3. Equation 17 represents the novel extension of the box method proposed for obtaining the sample emissivity, which will be analyzed in the next section. The more important points to make about this equation is that, against what happens with eq. 5, it takes into account the box geometry (through F), the cold and hot lid temperatures (through k), and the fact that the emissivity values of the materials used to construct the box are not exactly equal to 1 and 0 (through eh and e~). On the other hand and for a given box (that is, if F, c~ and ec are known) the emissivity is obtained from a simple procedure that consist in making the L2 measurement first, when the thermal equilibrium is achieved, followed rapidly by the L1 and L3 measurements. Finally it can be seen that for an ideal box (eh = 1, ec = 0) eq. 17 is identical to eq. 5.
3. Analysis In this section a detailed analysis of eq. 17 has been made as a function of its different parameters: k, cold and hot lid emissivities and box geometry, in order that it can be applied in an operational way. Thus, in the first place, the influence of cold and hot lid emissivities and box geometry have been evaluated, when for simplicity it was assumed that k = 1. According to this, Table 1 (see column 3) gives the hot lid influence in the sample emissivity when ~ = 0 for a box with F = 0.9 (this is our case). In the same way this table (see column 4) accounts for the cold lid influence in the sample emissivity when eh = 1. It can be observed that for each increase (decrease) of 1% in the cold lid (hot lid) emissivity the sample emissivity decreases approximately by 0.1%. At this point it should be noted that data in columns 3 and 4 have been computed considering 7"1 = 302 K, 7"2 = 300 K a n d T3 = 320 K.
TABLE 1 Effects of the hot lid emissivity, eh, in the sample emissivity when ec = 0 (column 3) and of the cold lid emissivity, ec, when eh = 1 (column 4)
eh
e~
~ (e¢ = O)
e~ (eh = 1)
1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.90
0.00 0,01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.907 0.906 0.905 0.905 0.904 0.903 0.902 0.901 0.900 0.899 0.897
0.907 0.906 0.905 0.905 0.904 0.903 0.902 0.901 0.900 0.899 0.897
These three radiative temperatures represent, respectively, the upgoing temperature obtained when the radiometer views the sample, covered by the box, through a small hole in the hot lid, the upgoing temperature obtained for the fully reflecting box (using the cold lid), and the upgoing temperature obtained with the hot lid when the sample is replaced by the cold lid. It is important to consider that the hot lid temperature, Th, must be higher than the sample temperature, Ts, and remain constant during the time necessary for making the Tx and T3 measurements. This can be achieved in the field by exposing the hot lid to direct solar radiation, making the hot lid temperature 20-30°C higher than the sample temperature. Moreover, Fig. 2 accounts the effect of the box geometry in the sample emissivity. It can be seen that this effect depends on the sample emissivity, which becomes higher when the box height increases. Lastly, Table 2 gives some values obtained for real box (co ~ 0 and Ch ~ 1). In this case, the sample emissivity values are always lower than that determined for an ideal box (ec = 0 and Cn = 1). Likewise, it can be observed that this difference increases when the hot (cold) emissivity decreases (increases) and when the difference between the temperatures T2 (measurement with the cold lid) and T1 (measurement with the hot lid) increases. Nevertheless, another analysis of eq. 17 can be made when k ~ 1. It is necessary to know the relationship between the cold (To) and hot (Th) lid temperatures. In the field experiments, it was observed that 20°C < Th -- Tc < 30°C. Tc can
ISPRS Journal of Photogrammetry and Remote Sensing
28
0.006
0.015 F(O)-F(
,.v 0
0.005
k
I< 0.004 ~ __ __z
0.003
~,
0.002
~
1
""•
~.
F(O)-F(0.4)
"~
---
""
"
-
~.
0 h,< 0 . 0 1 0 I.k.
- . - F(O)-F(0.6)
~'~ ~. ~ .
"..,•
j--.-
F(O)-F(0.8)
---
~
I)
•
D,FFC:30"C~ I DIFF. c2o°c>I
~" DIFF. (30°C) T3=340 K L ~ D I F F . (20°C)
~
\
F(O)-F(0.2) -
T3 =3:30 K L
\
Z i I--
~
e., e.¢
".
0.005
(.,J
0.001
""--
--.N
"" • ~"~
~
0.80
0 0.80
0.85
0.90
0.95
1.00
SAMPLE EMISSIVITY Figure 2. Effect of the box geometry in the emissivity determination. The correcting factor is determined as the difference between the ideal case (F = 0, in eq. 17) and a real case in which 0 < F < 1 for different values of the sample emissivity. In this calculation it is assumed that k = 1, ec = 0.03 and eh = 0.98.
TABLE 2 Effect of the hot and cold lid emissivities in the emissivity determination ec
0.00 0.03 0.03 0.05 0.05
eh
1.00 0.98 0.95 0.98 0.95
T1 -- T2 (°C)
0.85 SAMPLE
0.90
0.95
1.00
EMISSIVITY
Figure 3. Correcting factor which must be added to the emissivity when eq. 5 is used instead of eq. 17. The calculation is made for three values of T3 and two differences Th -- To.
7"3 increases, being more important for Th - Tc = 30°C. It is also interesting to see that if T3 = 340 K and Th -- Tc = 20°C the correcting factor is null. It can be concluded that eq. 5 can be used for calculating the sample emissivity if a correcting factor is added. 4. Simplification of the method
3.0
2.0
1.0
0.5
0.877 0.871 0.868 0.869 0.865
0.915 0.911 0.908 0.909 0.907
0.956 0.954 0.952 0.953 0.951
0.977 0.976 0.976 0.976 0.975
be estimated using two reflecting lids, one as a lid and the other as the bottom. The Narcissus effect is avoided using a surface having a little diffusing effect. However, from a practical viewpoint the best solution for obtaining the p a r a m e t e r k is to use the T2 and T3 measurements instead of the T~ and Th measurements. This procedure that does not introduces significant errors in the sample emissivity determination (lower to 0.001 for the measurements m a d e with our box) requires a sensible choice of the box building materials (that is, e¢ ~ 0 and Eh ~' 1). Then, Fig. 3 gives the correcting factor which must be introduced as a function of the sample emissivity and for different T3 values when eq. 5 is used for determining emissivities with our box (ec = 0.03, eh = 0.98 and F = 0.95). It is seen that the correcting factor decreases when
Now another simplification that consists of taking L ,,~ a T b can b e considered (Slater, 1980). In this way, using temperatures - - the data directly obtained by our field radiometer - - instead of radiance measurements a more practical equation for determining the emissivity will result. Table 3 gives a and b values for different wavebands and for the most usual field temperatures (from 300 to 340 K) (Badenas and Caselles, 1992). Thus, the associated error for the ideal case (eq. 5) can be studied when the sample emissivity is written as:
TABLE 3 Values of a and b for different wavebands and for the most usual field temperatures (from 300 to 340 K) Waveband ( # m )
a (W m - z K - b )
b
A T (K)
8-14 10.5-12.5 10.5-11.5
3.0783 × 10 - 9 6.5850 × 10 - 9 1.4159 × 10 - 9
4.3400 4.0161 4.1697
0.16 0.17 0.17
11.5-12.5
8.2751 × 10 - 9
3.8486
0.17
A T is the error made when the simplification L ,,~ aT b is used (after Badenas and Caselles, 1992).
Volume 48, number 3, 1993
29
0.010 0
--
T3=320 K
0.008
~"
0.006
~
x ~
------'Z~-
Z
h~
0.004
ew
0.002 0 0.80
0.85
0.90
0.95
1.00
SAI'IPLE E H I S S I V I T ¥
Figure 4. Correcting factor which must be added to the emissivity when eq. 18 is used instead of eq. 5. It is assumed that Tz = 3 0 0 K .
T3b - T~
(18)
In this way a second correcting factor can be obtained by subtracting eqs. 5 and 18. Figure 4 shows the mean correcting factor that must be added to the results of eq. 18 as a function of the sample emissivity and for a radiometer working in the 8-14 # m waveband (the interval more frequently utilized by the field radiometers). It can be observed that the correcting factor is higher when T3 increases and that it decreases when the emissivity increases. Using eq. 18 and the correcting factors given in Figs. 3 and 4, the sample emissivity will be obtained. At this point it is interesting to analyze the capacity of eq. 18 to distinguish between samples with emissivities which are different. To accomplish this, a sensitivity analysis has been made. Thus, according to eq. 18:
Equation 20 shows that the relative error in emissivity is a function of the temperature differences between the sample and the cold lid. Thus, for a difference of 20 degrees (T3 = 320 K and T2 = 300 K) the relative error on emissivity is (A¢/E) ~ 0.6%. Another source of error are the systematic errors due to the instrumental errors which can reach 2 K. However, this error, which is constant during the short time necessary for making the/'1, T2 and T3 measurements, does not alter the final result because eq. 18 is a quotient of temperature differences. As an example of this, it can be seen that considering the following combinations: (a) T1 = 302 K, 7"2 = 300 K and T3 = 320 K; (b) T/ = (Ti + 2) K, with i = 1, 2, 3; and (c) Tf = (Ti - 2) K, the emissivity values only yield a maximum difference of 2 × 10 -4. In this way it is possible with this method to know the sample emissivity with a relative error not larger than 0.6%, which is sufficient in most oceanographical, geological and agronomical applications. 5. E x p e r i m e n t a l
results
(20)
The box used in this work was 30 cm long x 30 cm wide x 70 cm high, and weighted 1.2 kg (permitting easy utilization in the field). Polished aluminium has been used as a perfect reflector of emissivity 0.03 for the inside walls and cold lid, and anodized corrugated aluminium painted with Parson's black (~ ~ 0.98) as a perfect emitter for the hot lid. The measurement of radiometric temperature was made with an infrared thermometer A G A T H E R M O P O I N T 80", which operates in the 8-14 # m waveband, has an instantaneous field of view of 2 ° and measures temperatures with a sensitivity of 0.1 K. A control of the performance was made by means of a calibration source E V E R E S T Model 1000", which has an accuracy of 0.5°C. Although eq. 18 shows that the sample emissivity, es, can be obtained from only three simple temperature measurements 7"1, T2 and T3 (see Sect. 4), the following precautions must be taken in order that the method gives reliable results: (a) Due to the fact that small variations in the
To obtain this equation, the temperatures measured with the hot and cold lids have been assumed to be approximately equal.
* Use of trade and company n a m e s is for benefit of the reader and does not imply any e n d o r s e m e n t by the University of Valencia.
A~
--
AT
= 6 ~ -
T
(19)
where A T is the temperature error of the radiometer 0.1 K, and ¢5 is a function of the hot lid and sample temperatures, given by: =
(T2) TM (T3)4.34 _ (T2)4.34
30
ISPRS Journal of Photogrammetry and Remote Sensing
weather conditions (as for example presence of clouds and wind) can alter the reliability of the T1 and T3 measurements, these measurements must be made quickly and preferably during cloudless, calm days. In the same way, it is necessary to construct the hot lid with a considerable thickness and weight ( ~ 1 cm and 1 kg) providing it with a large thermal capacity (900 J/K for the hot lid used in this experience). (b) The radiative state of the sample should be the same in both measurements T1 and 7"2. A good procedure involves making the T2 measurement first, when the thermal equilibrium is achieved, followed rapidly by the T1 and T3 measurements. (c) In order that the hot lid temperature can be higher than the sample temperature (20-30°C), the emissivity measurements must be made in daytime and it is best during the central hours of the day (10 to 15h GMT). (d) To avoid systematic errors, it is necessary to made a control of the performance of the method. This can be achieved by measuring a sample of known emissivity (in our case we have used a quartz sand whose emissivity is 0.87) before and after the measurement of the sample of interest. (e) To reduce the effect of noise in the final result, the sample emissivity should be obtained through averaging over 20 successive measurements. To test the field method developed, the emissivities in two orange orchards were measured; one with orange trees of the Thompson variety and a brown loamy soil (Torrent) and the other with orange trees of the Navel variety and a red clay soil (Rafelguaraf). More details of these experiments have been described by Caselles et al. (1988) and Caselles and Sobrino (1989). The experimental results are given in Table 4. Green and yellow grass emissivities are also included. These results, which agree with those given by different authors (Buettner and Kern, 1965; Fuchs and Tanner, 1966, 1968; Lorenz, 1966; Gorodetskiy and Filippov, 1968; Klaassen and Nieuwenhuis, 1978; Becker et al., 1986; Chen and Zhang, 1989) confirm the good sensitivity of the method.
TABLE 4 Emissivities of different samples and their standard deviations, in the 8-14 #m waveband
6. Conclusion
The authors wish to express their gratitude to the Comision Interministerial de Ciencia y Tecnologia (Project No. ESP89-0436) for financial support. Constructive discussions with M.R Stoll (University of Strasbourg) are also acknowl-
In this article, the question on the feasibility of the field measurements of effective surface emissivity and the attainable accuracy have been
Samples
Emissivity
Red clay Brown loam Orange tree (Navel) Orange tree (Thompson) Green grass Yellow grass
0.957 :t: 0.006 0.925 -4-0.006 0.985 -t- 0.005 0.983 -4-0.005 0.972 -t- 0.008 0.945 -t- 0.012
Each value corresponds to the average of 20 measurements. addressed. To accomplish this, a novel extension of the box method that uses radiative temperatures instead of radiance measurements has been developed. This extension also permits evaluating the influence of the box configuration in the sample emissivity retrievals. The discussion regarding the different parameters (emissivity of the cold and hot lids, box geometry and use of radiative temperatures) has led to correction factors which should be considered in order to obtain accurate values of the sample emissivity. The method has several advantages in comparison with other methodologies used in field conditions: (1) the equipment is of simple construction, a box made of light materials (anodized and polished aluminium); (2) the measurements are carried out quickly (less than 5 min) and easily (only three radiant temperature measurements) in the laboratory or the field; (3) the emissivity is derived from a ratio of radiometric temperature differences which do not require high absolute accuracy; (4) the emissivity is measured with a good relative error of 0.6%; and (5) it only uses direct solar radiation as a heating system (avoiding the use of heavy equipment). As a result the method can constitute a powerful tool for measuring the spatial variability of land surface emissivity. The authors consider that this method is very practical for field measurement and that it can be used by anybody. Acknowledgements
Volume 48, number 3, 1993
edged. We also thank the reviewers for comments and suggestions. References Badenas, C. and Caselles, V., 1992. A simple technique for estimating surface temperature by means of a thermal radiometer. Int. J. Remote Sensing, 13: 2951-2956. Becker, E, 1987. The impact of spectral emissivity on the measurement of land surface temperature from a satellite. Int. J. Remote Sensing, 8: 1509-1522. Becker, E, Nerry, E, Ramanantsizehena, P. and Stoll, M.P, 1986. Mesures d'6missivit6 angulaire par r~flexion dans l'infrarouge thermique - - implications pour la t616d6tection. Int. J. Remote Sensing, 7: 1751-1762. Buettner, K.J.K. and Kern, C.D., 1965. The determination of infrared emissivities of terrestrial surfaces. J. Geophys. Res., 70: 1329-1337. Caselles, V. and Sobrino, J.A., 1989. Determination of frosts in orange groves from NOAA-9 AVHRR data. Remote Sensing Environ., 29: 135-146. Caselles, V., Sobrino, J.A. and Becker, E, 1988. Determination of the effective emissivity and temperature under vertical observation of a citrus orchard. Application to frost nowcasting. Int. J. Remote Sensing, 9: 715-727. Chen, J.-M. and Zhang, R.-H., 1989. Studies on the measurements of crop emissivity and sky temperature. Agric. For. Meteorol., 49: 23-34. Combs, A.C., Weickmann, H.K., Mader, C. and Tebo, A., 1965. Application of infrared radiometers to meteorology. J. Appl. Meteorol., 4: 253-262. Conaway, J. and van Bavel, C.H.M., 1967. Evaporation from a wet surface calculated from radiometrically determined surface temperatures. J. Appl. Mcteorol., 6: 650-655. Dana, R.W., 1969. Measurement of 8-14 micrometer emissivity of igneous rocks and mineral surfaces. NASA Sci. Rep. NSG-632, GSFC, Greenbelt, MD. Davies, J.A., Robinson, P.J. and Nufiez, M., 1971. Field determinations of surface emissivity and temperature for lake Ontario. J. Appl. Meteorol., 10: 811-819. Fuchs, M. and Tanner, C.B., 1966. Infrared thermometry of vegetation. Agron. J., 58: 596-601. Fuchs, M. and Tanner, C.B., 1968. Surface temperature measurements of bare soils. J. Appl. Meteorol., 7: 303-305. Gorodetskiy, A.K. and Filippov, G.E, 1968. Terrestrial mea-
31 surements of the radiation of the atmosphere and of the underlying surface in the spectral region of 8-12 mm. Atmos. Ocean. Phys., 4: 228-232. Klaassen, W. and Nicuwenhuis, G.J.A., 1978. Estimation of the regional evapotranspiration from remotely sensed crop surface temperatures, Part II. Arable land. Nota 1057 of the Instituut voor Cultuurtechniek en Waterhuishouding, Wageningcn. Lorenz, D., 1966. The effect of the long-wave reflectivity of natural surfaces on surface temperature measurements using radiometers. J. Appl. Meteorol., 5: 421-430. Lyon, R.J.P. and Burns, E.A., 1963. Analysis of rocks and minerals by reflected infrared radiation. Econ. Geol., 58: 274. Nerry, E, 1988. Contribution ~ l'6tude exp6rimentale et th6orique de l'6missivit6 et de la r6flectivit6 des milieux naturels terrestres dans l'infrarouge thermique dans le contexte de la t616d6tection spatiale, Doctoral thesis, University of Strasbourg. Robinson, P.J. and Davies, J.A., 1972. Laboratory determination of water surface emissivity. J. Appl. Meteorol., 11: 1391-1393. Salisbury, J.W. and Milton, N.M., 1988. Thermal infrared (2.5- to 13.5-/zm) directional hemispherical reflectance of leaves. Photogramm. Eng. Remote Sensing, 54 (9): 13011304. Siegel, R. and Howell, J.R., 1981. Thermal Radiation Heat Transfer. McGraw-Hill, New York, pp. 822-831. Slater, P.N., 1980. Remote Sensing: Optics and Optical Systems. Addison-Wesley, Reading (U.S.A.), pp. 242-243. Sobrino, J.A. and Caselles, V., 1989. Medida mediante el m6todo de la caja de la emisividad en la banda espectral de los 8-14 /tm de algunos suelos agrfcolas y de la vegetaci6n. An. Ffs., Ser. B, 85: 220-227. Sobrino, J.A., Caselles, V.. and Becker, E, 1990. Significance of the remotely sensed thermal infrared measurements obtained over a citrus orchard. ISPRS J. Photogramm. Remote Sensing, 44: 343-354. Taylor, S.E., 1979. Measured emissivity of soils in the Southeast United States. Remote Sensing Environ., 8: 359-364. Wong, C.U and Blevin, W.R., 1967. Infrared reflectances of plant leaves. Aust. J. Biol. Sci., 20: 501-508. (Received January 22, 1992; revised and accepted October 20, 1992)
24
Jos6 A. Sobrino 1 and Vicente Caselles i
A field method for measuring the thermal infrared emissivity In this work, a field m e t h o d for measuring thermal infrared emissivities is proposed which is based on the box method, initially developed by B u e t t n e r and Kern (1965) for laboratory measurements. A theoretical analysis was m a d e of the m e a s u r e m e n t carried out using the box and a correcting factor to Buettner and Kern's technique has been determined. Buettner and K e r n ' s m e t h o d has been modified to use radiative temperatures measured with a r a d i o t h e r m o m e t e r instead of radiance m e a s u r e m e n t s . The walls of the box used and the cold lid was m a d e of polished aluminium and the hot lid was m a d e of black-painted anodized aluminium and it was heated in the field by solar radiation. With this m e t h o d m e a s u r e m e n t s of the thermal infrared emissivity of ground and vegetation can be obtained with a relative error not larger than 0.6%.
1. Introduction
The radiance measurement obtained by a sensor placed on board a satellite is made assuming that the observed surface is a black-body, but this is not true for natural objects (or surfaces), and therefore to obtain accurate measurements of surface temperature by infrared radiometry a good determination of the surface emissivity is necessary (Becker, 1987; Sobrino et al., 1990). This is due to the fact that an uncertainty in emissivity of 1% may lead to an error in temperature of 0.5°C when the surface temperature is around 300 K (Sobrino and Caselles, 1989). The emissivity measurement is generally dillicult to make in natural surfaces because the observed radiance is the result of a double contribution: the ground emission itself and the reflection on it of the radiance coming from its surroundings (atmosphere, walls, trees, etc.). Thus assuming that the thermal equilibrium is reached and that the surroundings are characterized by a black-body equivalent temperature Ta, the observed radiance coming from the ground LA(TBB), considered as a Lambertian surface, can be written as: LA(TBB) = ~AL°~(T) + (1 - cA)LA(Ta)
(1)
where L°~(T) is Planck's radiation function; the first term on the right is the radiance emitted by 1 D e p a r t m e n t of Thermodynamics, Faculty of Physics, University of Valencia, 50, Dr. Moliner, 46100 Burjassot, Spain.
the ground itself and the second one represents the fraction of the ambient radiance LA (Ta) which is reflected by the target. Therefore it will be necessary to solve an equation with three unknown quantities: the surface emissivity, cA, the ground temperature, T, and the surroundings equivalent temperature, Ta. This problem can be simplified by making a separation between the contributions corresponding to the system and its surroundings. In order to solve this problem two methods are frequently used: the reflection method in active radiometry and the box method in passive radiometry. The first one obtains the emissivity from the knowledge of the hemispherical reflectivity, PA, by applying Kirchhoff's law to opaque surfaces: cA = 1 - PA
(2)
Spectral emissivity has been determined in the laboratory using this method by Lyon and Burns (1963), Wong and Blevin (1967), Robinson and Davies (1972) and more recently by Becker et al. (1986) and Salisbury and Milton (1988). The hemispherical reflectivity is the result of integrating, in the upper hemisphere, the bidirectional reflectivity weighted by cos 0', where 0' is the angle defined by the beam reflected and the normal to the surface. The bidirectional reflectivity is obtained by irradiating the surface in the (0, ¢) direction and measuring the reflected radiance in the (0', ¢') direction. A modulated laser source associated with a synchronized detec-
ISPIL7 Journal of Photogrammetry and Remote Sensing, 48(3): 24-31 0924-2716/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 48, number 3, 1993
2fi
tion system is used in order to eliminate both the proper emission of the sample and the reflection of the radiance coming from its surroundings. A good calibration panel is also necessary and the noise is very important due to the fact that this method works with the reflected radiance instead of the emitted radiance and therefore the signal received is small. All of these reasons mean that the reflection method is only applicable in the laboratory. The box method eliminates the surroundings radiance, isolating the sample by means of a perfectly reflecting surface, so eq. 1 becomes:
the use of these solutions for field measurements necessitates the use of heavy equipment. In addition, eq. 5 is only strictly valid for an "ideal" box with perfectly reflecting and emitting materials. Therefore the aim of this paper is to propose a simpler method, consisting of a modification of the box method, which accounts for these drawbacks and can be used in field conditions to allow agronomists, geologists, oceanographers, etc., to obtain the thermal infrared emissivity of natural samples in a precise, easy and quick way.
L~°X(TBB) = z;~L°A(T) + (1 -¢A)L°~(T)
Like Buettner and Kern (1965) the influence of the surroundings has been eliminated using a bottomless box with reflecting interior sides and having two exchangeable lids, both provided with a hole through which the infrared radiometer views the sample (see Fig. la). One is the cold lid which is made with a reflecting material (ec ~ 0) and the other is the hot lid made with an emitting material (eh ~ 1). In the following, the subscript 's' refers
(3)
= L°~(T) Combining eqs. 1 and 3 and assuming that the ground temperature does not change during the measurement period, one obtains: L
(TBB) -
L;,(T.)
E;~ = L~ox(ri3B) _ LA(Ta)
(4)
This equation proposed by Combs et al. (1965), and modified by Lorenz (1966) and Fuchs and Tanner (1966, 1968), has been used by Davies et al. (1971) and Taylor (1979) for obtaining field determinations of soil and water emissivities. The main difficulty of this method is the determination of the surroundings radiance (Chen and Zhang, 1989). To avoid the measurement of the surroundings radiance, Buettner and Kern (1965) add to the box a second lid made of an emitting material (the hot lid). Buettner and Kern's method, with alternatives proposed by Conaway and Van Bavel (1967) and Dana (1969), determines the emissivity from the relationship: cA -
LA3 -- LA1
2. Proposed method
(a)
ES Is F
SAMPLE RADIOMETER
(5)
LA3 -- LA2
where LA1 and LA2 are the radiances measured with the emitting and reflecting lids, respectively, and LA3 is the radiance emitted by the hot lid. For obtaining the sample emissivity from eq. 5 the emitting lid temperature must be higher than the sample temperature and constant during the measurements. Buettner and Kern (1965) solve this problem in the laboratory with water flowing through channels into the hot lid, and Nerry (1988) by using heating resistances. Nevertheless,
:::::::
........
\
(b) Figure 1. (a) Box geometry and (b) main factors composing the radiance reflected by the sample.
26
ISPRS Journal of Photogrammetry and Remote Sensing
to the sample material, 'w' refers to the box walls, and 'c' and 'h' refer, respectively, to the cold and hot lids of the box. In this way, the radiance coming from the sample, when the box is placed over it and considering that the radiometer only views the sample, can be written as: L~ = Rs + (1 - es) Gs
(6)
where Rs is the radiance emitted by the sample itself, and G~ is the radiance striking the sample. R~ is given by: e~ =
ff
e~;~L°(Ts) q(A) dk = esB~
(7)
1
where Bs is the integrated value of the black-body spectral radiance at the sample temperature, Ts, over the spectral transfer function of the instrument q(A), A1 and A2 are the wavelengths at which q(A) goes to zero, and e~ is the averaged sample emissivity. If we consider that the materials used to construct the box do not possess emissivities exactly equal to 1 or 0 and if we neglect the hole influence (its size being much smaller than the lid), Gs is composed primarily of four terms: (1) the radiance emitted by the lid itself, (2) the radiance emitted by the side itself, (3) the radiance from the lid that is reflected by the sides, and (4) the upward radiance, Ls, which is reflected following the same paths (1) and (3) (see Fig. lb). Then:
the hot lid, L1, (b) using the cold lid, L2, and (c) using the hot lid when the sample is replaced by the cold lid, L3: L1 = esBs + (1 - es) [eeBcF +
ehBh
(1 - F e c )
+ LI(1 - eh) (1 -- F ec)]
(9)
L2 = esBs + (1 - es) (ecBc [1 + F (1 - ec)] + L2(1 - ¢c) (1 - F ec)}
(10)
L3 = ecBc + (1 - ec) [e~B~F + ehBh (1 -- F ec)
+ L3(1 - eh) (1 -- F ee)l
(11)
where eh and ec are the hot and cold lid emissivities, and Bh and B~ are, respectively, the integrated values of the black-body spectral radiance at temperatures Th and T¢. In these equations ew = ec, because the same material has been used for the box walls and the cold lid. The above equations mean a clear improvement of the description made in the ideal case (ew = e¢ = 0, and eh = 1), situation in which L 1 = e s L 2 -t- (1 - e s ) L 3 , L 2 = Bs and L3 = Bh. Subtracting eqs. 9 and 10, the sample emissivity is obtained as: G = 1 -
L1 - L2 (1 - F ec)[(L1 - L2)
+ ec(L2
-
Bc)
"st" e h ( B h
L1)] (12)
Gs = etBt (1 - F ) + e w B w F + etBt (1 - ew)F + Ls(1 - st) [(1 - F ) + F (1 - ew)]
i
(8)
where st and ew are the lid and wall emissivities, Bt and Bw are, respectively, the integrated values of the black-body spectral radiance at temperatures Tt and Tw, and F is a geometrical factor which accounts for the proportion of radiation leaving the box walls and reaching the observed sample. This factor can be easily evaluated following the procedure proposed by Siegel and Howell (1981). Then, the procedure for determining the sample emissivity is described. Like in the ideal case (see eq. 5), this procedure is based on the measurement of the change in energy received from the sample when the temperature of the lid above sample is altered. To accomplish this, eq. 6 has been rewritten for the measurements made with three different configurations of the box; (a) using
Equation 12 can be given in a more convenient form if eqs. 10 and 11 are rewritten as: L2 = a B e
(13)
L3 = /3Bh
(14)
where a and ¢/are two effective emissivities, which can be deduced from eqs. 10 and 11: es (Bs/Bc) + (1 - e~) e~ I1 +
=
1 - (1 - es) (1 - s o ) ( 1
F (1 - e~)]
(15)
- Fee)
and: ec ( B c / B h ) [1 + F (1 - ec)] 1 - (1 - eh) (1 -- e~) (1 -- F e ~ ) Ch (1 -- ec) (1 -- F e c )
+ 1 - (i -- -c~ (-1--- -eT)( i - ~ Fee)
}
(16)
Volume 48, number 3, 1993
27
In this way and taking into account the fact that L2 is measured when the thermal equilibrium is achieved (Bs = Bc and therefore a = 1), eq. 12 after its combination with eqs. 13 and 14 can be rewritten as: L 1 -- L 2 Cs=l
(l -- F Cc)[(L1 - L2) + ~h(kL3 - L1)]
(17) where k = 1//3. Equation 17 represents the novel extension of the box method proposed for obtaining the sample emissivity, which will be analyzed in the next section. The more important points to make about this equation is that, against what happens with eq. 5, it takes into account the box geometry (through F), the cold and hot lid temperatures (through k), and the fact that the emissivity values of the materials used to construct the box are not exactly equal to 1 and 0 (through eh and e~). On the other hand and for a given box (that is, if F, c~ and ec are known) the emissivity is obtained from a simple procedure that consist in making the L2 measurement first, when the thermal equilibrium is achieved, followed rapidly by the L1 and L3 measurements. Finally it can be seen that for an ideal box (eh = 1, ec = 0) eq. 17 is identical to eq. 5.
3. Analysis In this section a detailed analysis of eq. 17 has been made as a function of its different parameters: k, cold and hot lid emissivities and box geometry, in order that it can be applied in an operational way. Thus, in the first place, the influence of cold and hot lid emissivities and box geometry have been evaluated, when for simplicity it was assumed that k = 1. According to this, Table 1 (see column 3) gives the hot lid influence in the sample emissivity when ~ = 0 for a box with F = 0.9 (this is our case). In the same way this table (see column 4) accounts for the cold lid influence in the sample emissivity when eh = 1. It can be observed that for each increase (decrease) of 1% in the cold lid (hot lid) emissivity the sample emissivity decreases approximately by 0.1%. At this point it should be noted that data in columns 3 and 4 have been computed considering 7"1 = 302 K, 7"2 = 300 K a n d T3 = 320 K.
TABLE 1 Effects of the hot lid emissivity, eh, in the sample emissivity when ec = 0 (column 3) and of the cold lid emissivity, ec, when eh = 1 (column 4)
eh
e~
~ (e¢ = O)
e~ (eh = 1)
1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.90
0.00 0,01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.907 0.906 0.905 0.905 0.904 0.903 0.902 0.901 0.900 0.899 0.897
0.907 0.906 0.905 0.905 0.904 0.903 0.902 0.901 0.900 0.899 0.897
These three radiative temperatures represent, respectively, the upgoing temperature obtained when the radiometer views the sample, covered by the box, through a small hole in the hot lid, the upgoing temperature obtained for the fully reflecting box (using the cold lid), and the upgoing temperature obtained with the hot lid when the sample is replaced by the cold lid. It is important to consider that the hot lid temperature, Th, must be higher than the sample temperature, Ts, and remain constant during the time necessary for making the Tx and T3 measurements. This can be achieved in the field by exposing the hot lid to direct solar radiation, making the hot lid temperature 20-30°C higher than the sample temperature. Moreover, Fig. 2 accounts the effect of the box geometry in the sample emissivity. It can be seen that this effect depends on the sample emissivity, which becomes higher when the box height increases. Lastly, Table 2 gives some values obtained for real box (co ~ 0 and Ch ~ 1). In this case, the sample emissivity values are always lower than that determined for an ideal box (ec = 0 and Cn = 1). Likewise, it can be observed that this difference increases when the hot (cold) emissivity decreases (increases) and when the difference between the temperatures T2 (measurement with the cold lid) and T1 (measurement with the hot lid) increases. Nevertheless, another analysis of eq. 17 can be made when k ~ 1. It is necessary to know the relationship between the cold (To) and hot (Th) lid temperatures. In the field experiments, it was observed that 20°C < Th -- Tc < 30°C. Tc can
ISPRS Journal of Photogrammetry and Remote Sensing
28
0.006
0.015 F(O)-F(
,.v 0
0.005
k
I< 0.004 ~ __ __z
0.003
~,
0.002
~
1
""•
~.
F(O)-F(0.4)
"~
---
""
"
-
~.
0 h,< 0 . 0 1 0 I.k.
- . - F(O)-F(0.6)
~'~ ~. ~ .
"..,•
j--.-
F(O)-F(0.8)
---
~
I)
•
D,FFC:30"C~ I DIFF. c2o°c>I
~" DIFF. (30°C) T3=340 K L ~ D I F F . (20°C)
~
\
F(O)-F(0.2) -
T3 =3:30 K L
\
Z i I--
~
e., e.¢
".
0.005
(.,J
0.001
""--
--.N
"" • ~"~
~
0.80
0 0.80
0.85
0.90
0.95
1.00
SAMPLE EMISSIVITY Figure 2. Effect of the box geometry in the emissivity determination. The correcting factor is determined as the difference between the ideal case (F = 0, in eq. 17) and a real case in which 0 < F < 1 for different values of the sample emissivity. In this calculation it is assumed that k = 1, ec = 0.03 and eh = 0.98.
TABLE 2 Effect of the hot and cold lid emissivities in the emissivity determination ec
0.00 0.03 0.03 0.05 0.05
eh
1.00 0.98 0.95 0.98 0.95
T1 -- T2 (°C)
0.85 SAMPLE
0.90
0.95
1.00
EMISSIVITY
Figure 3. Correcting factor which must be added to the emissivity when eq. 5 is used instead of eq. 17. The calculation is made for three values of T3 and two differences Th -- To.
7"3 increases, being more important for Th - Tc = 30°C. It is also interesting to see that if T3 = 340 K and Th -- Tc = 20°C the correcting factor is null. It can be concluded that eq. 5 can be used for calculating the sample emissivity if a correcting factor is added. 4. Simplification of the method
3.0
2.0
1.0
0.5
0.877 0.871 0.868 0.869 0.865
0.915 0.911 0.908 0.909 0.907
0.956 0.954 0.952 0.953 0.951
0.977 0.976 0.976 0.976 0.975
be estimated using two reflecting lids, one as a lid and the other as the bottom. The Narcissus effect is avoided using a surface having a little diffusing effect. However, from a practical viewpoint the best solution for obtaining the p a r a m e t e r k is to use the T2 and T3 measurements instead of the T~ and Th measurements. This procedure that does not introduces significant errors in the sample emissivity determination (lower to 0.001 for the measurements m a d e with our box) requires a sensible choice of the box building materials (that is, e¢ ~ 0 and Eh ~' 1). Then, Fig. 3 gives the correcting factor which must be introduced as a function of the sample emissivity and for different T3 values when eq. 5 is used for determining emissivities with our box (ec = 0.03, eh = 0.98 and F = 0.95). It is seen that the correcting factor decreases when
Now another simplification that consists of taking L ,,~ a T b can b e considered (Slater, 1980). In this way, using temperatures - - the data directly obtained by our field radiometer - - instead of radiance measurements a more practical equation for determining the emissivity will result. Table 3 gives a and b values for different wavebands and for the most usual field temperatures (from 300 to 340 K) (Badenas and Caselles, 1992). Thus, the associated error for the ideal case (eq. 5) can be studied when the sample emissivity is written as:
TABLE 3 Values of a and b for different wavebands and for the most usual field temperatures (from 300 to 340 K) Waveband ( # m )
a (W m - z K - b )
b
A T (K)
8-14 10.5-12.5 10.5-11.5
3.0783 × 10 - 9 6.5850 × 10 - 9 1.4159 × 10 - 9
4.3400 4.0161 4.1697
0.16 0.17 0.17
11.5-12.5
8.2751 × 10 - 9
3.8486
0.17
A T is the error made when the simplification L ,,~ aT b is used (after Badenas and Caselles, 1992).
Volume 48, number 3, 1993
29
0.010 0
--
T3=320 K
0.008
~"
0.006
~
x ~
------'Z~-
Z
h~
0.004
ew
0.002 0 0.80
0.85
0.90
0.95
1.00
SAI'IPLE E H I S S I V I T ¥
Figure 4. Correcting factor which must be added to the emissivity when eq. 18 is used instead of eq. 5. It is assumed that Tz = 3 0 0 K .
T3b - T~
(18)
In this way a second correcting factor can be obtained by subtracting eqs. 5 and 18. Figure 4 shows the mean correcting factor that must be added to the results of eq. 18 as a function of the sample emissivity and for a radiometer working in the 8-14 # m waveband (the interval more frequently utilized by the field radiometers). It can be observed that the correcting factor is higher when T3 increases and that it decreases when the emissivity increases. Using eq. 18 and the correcting factors given in Figs. 3 and 4, the sample emissivity will be obtained. At this point it is interesting to analyze the capacity of eq. 18 to distinguish between samples with emissivities which are different. To accomplish this, a sensitivity analysis has been made. Thus, according to eq. 18:
Equation 20 shows that the relative error in emissivity is a function of the temperature differences between the sample and the cold lid. Thus, for a difference of 20 degrees (T3 = 320 K and T2 = 300 K) the relative error on emissivity is (A¢/E) ~ 0.6%. Another source of error are the systematic errors due to the instrumental errors which can reach 2 K. However, this error, which is constant during the short time necessary for making the/'1, T2 and T3 measurements, does not alter the final result because eq. 18 is a quotient of temperature differences. As an example of this, it can be seen that considering the following combinations: (a) T1 = 302 K, 7"2 = 300 K and T3 = 320 K; (b) T/ = (Ti + 2) K, with i = 1, 2, 3; and (c) Tf = (Ti - 2) K, the emissivity values only yield a maximum difference of 2 × 10 -4. In this way it is possible with this method to know the sample emissivity with a relative error not larger than 0.6%, which is sufficient in most oceanographical, geological and agronomical applications. 5. E x p e r i m e n t a l
results
(20)
The box used in this work was 30 cm long x 30 cm wide x 70 cm high, and weighted 1.2 kg (permitting easy utilization in the field). Polished aluminium has been used as a perfect reflector of emissivity 0.03 for the inside walls and cold lid, and anodized corrugated aluminium painted with Parson's black (~ ~ 0.98) as a perfect emitter for the hot lid. The measurement of radiometric temperature was made with an infrared thermometer A G A T H E R M O P O I N T 80", which operates in the 8-14 # m waveband, has an instantaneous field of view of 2 ° and measures temperatures with a sensitivity of 0.1 K. A control of the performance was made by means of a calibration source E V E R E S T Model 1000", which has an accuracy of 0.5°C. Although eq. 18 shows that the sample emissivity, es, can be obtained from only three simple temperature measurements 7"1, T2 and T3 (see Sect. 4), the following precautions must be taken in order that the method gives reliable results: (a) Due to the fact that small variations in the
To obtain this equation, the temperatures measured with the hot and cold lids have been assumed to be approximately equal.
* Use of trade and company n a m e s is for benefit of the reader and does not imply any e n d o r s e m e n t by the University of Valencia.
A~
--
AT
= 6 ~ -
T
(19)
where A T is the temperature error of the radiometer 0.1 K, and ¢5 is a function of the hot lid and sample temperatures, given by: =
(T2) TM (T3)4.34 _ (T2)4.34
30
ISPRS Journal of Photogrammetry and Remote Sensing
weather conditions (as for example presence of clouds and wind) can alter the reliability of the T1 and T3 measurements, these measurements must be made quickly and preferably during cloudless, calm days. In the same way, it is necessary to construct the hot lid with a considerable thickness and weight ( ~ 1 cm and 1 kg) providing it with a large thermal capacity (900 J/K for the hot lid used in this experience). (b) The radiative state of the sample should be the same in both measurements T1 and 7"2. A good procedure involves making the T2 measurement first, when the thermal equilibrium is achieved, followed rapidly by the T1 and T3 measurements. (c) In order that the hot lid temperature can be higher than the sample temperature (20-30°C), the emissivity measurements must be made in daytime and it is best during the central hours of the day (10 to 15h GMT). (d) To avoid systematic errors, it is necessary to made a control of the performance of the method. This can be achieved by measuring a sample of known emissivity (in our case we have used a quartz sand whose emissivity is 0.87) before and after the measurement of the sample of interest. (e) To reduce the effect of noise in the final result, the sample emissivity should be obtained through averaging over 20 successive measurements. To test the field method developed, the emissivities in two orange orchards were measured; one with orange trees of the Thompson variety and a brown loamy soil (Torrent) and the other with orange trees of the Navel variety and a red clay soil (Rafelguaraf). More details of these experiments have been described by Caselles et al. (1988) and Caselles and Sobrino (1989). The experimental results are given in Table 4. Green and yellow grass emissivities are also included. These results, which agree with those given by different authors (Buettner and Kern, 1965; Fuchs and Tanner, 1966, 1968; Lorenz, 1966; Gorodetskiy and Filippov, 1968; Klaassen and Nieuwenhuis, 1978; Becker et al., 1986; Chen and Zhang, 1989) confirm the good sensitivity of the method.
TABLE 4 Emissivities of different samples and their standard deviations, in the 8-14 #m waveband
6. Conclusion
The authors wish to express their gratitude to the Comision Interministerial de Ciencia y Tecnologia (Project No. ESP89-0436) for financial support. Constructive discussions with M.R Stoll (University of Strasbourg) are also acknowl-
In this article, the question on the feasibility of the field measurements of effective surface emissivity and the attainable accuracy have been
Samples
Emissivity
Red clay Brown loam Orange tree (Navel) Orange tree (Thompson) Green grass Yellow grass
0.957 :t: 0.006 0.925 -4-0.006 0.985 -t- 0.005 0.983 -4-0.005 0.972 -t- 0.008 0.945 -t- 0.012
Each value corresponds to the average of 20 measurements. addressed. To accomplish this, a novel extension of the box method that uses radiative temperatures instead of radiance measurements has been developed. This extension also permits evaluating the influence of the box configuration in the sample emissivity retrievals. The discussion regarding the different parameters (emissivity of the cold and hot lids, box geometry and use of radiative temperatures) has led to correction factors which should be considered in order to obtain accurate values of the sample emissivity. The method has several advantages in comparison with other methodologies used in field conditions: (1) the equipment is of simple construction, a box made of light materials (anodized and polished aluminium); (2) the measurements are carried out quickly (less than 5 min) and easily (only three radiant temperature measurements) in the laboratory or the field; (3) the emissivity is derived from a ratio of radiometric temperature differences which do not require high absolute accuracy; (4) the emissivity is measured with a good relative error of 0.6%; and (5) it only uses direct solar radiation as a heating system (avoiding the use of heavy equipment). As a result the method can constitute a powerful tool for measuring the spatial variability of land surface emissivity. The authors consider that this method is very practical for field measurement and that it can be used by anybody. Acknowledgements
Volume 48, number 3, 1993
edged. We also thank the reviewers for comments and suggestions. References Badenas, C. and Caselles, V., 1992. A simple technique for estimating surface temperature by means of a thermal radiometer. Int. J. Remote Sensing, 13: 2951-2956. Becker, E, 1987. The impact of spectral emissivity on the measurement of land surface temperature from a satellite. Int. J. Remote Sensing, 8: 1509-1522. Becker, E, Nerry, E, Ramanantsizehena, P. and Stoll, M.P, 1986. Mesures d'6missivit6 angulaire par r~flexion dans l'infrarouge thermique - - implications pour la t616d6tection. Int. J. Remote Sensing, 7: 1751-1762. Buettner, K.J.K. and Kern, C.D., 1965. The determination of infrared emissivities of terrestrial surfaces. J. Geophys. Res., 70: 1329-1337. Caselles, V. and Sobrino, J.A., 1989. Determination of frosts in orange groves from NOAA-9 AVHRR data. Remote Sensing Environ., 29: 135-146. Caselles, V., Sobrino, J.A. and Becker, E, 1988. Determination of the effective emissivity and temperature under vertical observation of a citrus orchard. Application to frost nowcasting. Int. J. Remote Sensing, 9: 715-727. Chen, J.-M. and Zhang, R.-H., 1989. Studies on the measurements of crop emissivity and sky temperature. Agric. For. Meteorol., 49: 23-34. Combs, A.C., Weickmann, H.K., Mader, C. and Tebo, A., 1965. Application of infrared radiometers to meteorology. J. Appl. Meteorol., 4: 253-262. Conaway, J. and van Bavel, C.H.M., 1967. Evaporation from a wet surface calculated from radiometrically determined surface temperatures. J. Appl. Mcteorol., 6: 650-655. Dana, R.W., 1969. Measurement of 8-14 micrometer emissivity of igneous rocks and mineral surfaces. NASA Sci. Rep. NSG-632, GSFC, Greenbelt, MD. Davies, J.A., Robinson, P.J. and Nufiez, M., 1971. Field determinations of surface emissivity and temperature for lake Ontario. J. Appl. Meteorol., 10: 811-819. Fuchs, M. and Tanner, C.B., 1966. Infrared thermometry of vegetation. Agron. J., 58: 596-601. Fuchs, M. and Tanner, C.B., 1968. Surface temperature measurements of bare soils. J. Appl. Meteorol., 7: 303-305. Gorodetskiy, A.K. and Filippov, G.E, 1968. Terrestrial mea-
31 surements of the radiation of the atmosphere and of the underlying surface in the spectral region of 8-12 mm. Atmos. Ocean. Phys., 4: 228-232. Klaassen, W. and Nicuwenhuis, G.J.A., 1978. Estimation of the regional evapotranspiration from remotely sensed crop surface temperatures, Part II. Arable land. Nota 1057 of the Instituut voor Cultuurtechniek en Waterhuishouding, Wageningcn. Lorenz, D., 1966. The effect of the long-wave reflectivity of natural surfaces on surface temperature measurements using radiometers. J. Appl. Meteorol., 5: 421-430. Lyon, R.J.P. and Burns, E.A., 1963. Analysis of rocks and minerals by reflected infrared radiation. Econ. Geol., 58: 274. Nerry, E, 1988. Contribution ~ l'6tude exp6rimentale et th6orique de l'6missivit6 et de la r6flectivit6 des milieux naturels terrestres dans l'infrarouge thermique dans le contexte de la t616d6tection spatiale, Doctoral thesis, University of Strasbourg. Robinson, P.J. and Davies, J.A., 1972. Laboratory determination of water surface emissivity. J. Appl. Meteorol., 11: 1391-1393. Salisbury, J.W. and Milton, N.M., 1988. Thermal infrared (2.5- to 13.5-/zm) directional hemispherical reflectance of leaves. Photogramm. Eng. Remote Sensing, 54 (9): 13011304. Siegel, R. and Howell, J.R., 1981. Thermal Radiation Heat Transfer. McGraw-Hill, New York, pp. 822-831. Slater, P.N., 1980. Remote Sensing: Optics and Optical Systems. Addison-Wesley, Reading (U.S.A.), pp. 242-243. Sobrino, J.A. and Caselles, V., 1989. Medida mediante el m6todo de la caja de la emisividad en la banda espectral de los 8-14 /tm de algunos suelos agrfcolas y de la vegetaci6n. An. Ffs., Ser. B, 85: 220-227. Sobrino, J.A., Caselles, V.. and Becker, E, 1990. Significance of the remotely sensed thermal infrared measurements obtained over a citrus orchard. ISPRS J. Photogramm. Remote Sensing, 44: 343-354. Taylor, S.E., 1979. Measured emissivity of soils in the Southeast United States. Remote Sensing Environ., 8: 359-364. Wong, C.U and Blevin, W.R., 1967. Infrared reflectances of plant leaves. Aust. J. Biol. Sci., 20: 501-508. (Received January 22, 1992; revised and accepted October 20, 1992)