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Planetary reflectance measurements in the region of planetary thermal emission
[CAaUS 40, 94-103 (1979)
Planetary Reflectance Measurements in the Region of Planetary Thermal Emission R O G E R N. C L A R K Department of Earth and Planetary Sciences, Massachusetts Institute of Technology Cambridge, Massachusetts 02139 and Institute for Astronomy, University of Hawaii at Manoa, 2680 Woodlawn Drive, Honolulu, Hawaii 96822 Received O c t o b e r 30, 1978; revised M a y 22, 1979 As planetary reflectance m e a s u r e m e n t s are extended into the infrared, the emitted thermal radiation b e c o m e s larger t h a n the reflected solar component. This paper describes a m e t h o d for r e m o v a l of the thermal c o m p o n e n t from planetary reflectance m e a s u r e m e n t s and d i s c u s s e s the limitations involved. E x a m p l e s are s h o w n for the case of lunar observations where the t e m p e r a t u r e and emissivity are k n o w n and for M e r c u r y where it is a s s u m e d the t e m p e r a t u r e and emissivity are unknown.
which has been calibrated to an Apollo landing site from telescopic observations and laboratory reflectance spectra of returned lunar samples. The flux received above the Earth's atmosphere from a solar system object at one wavelength is given by the equation
INTRODUCTION
Reflectance spectroscopy is being used successfully for remotely sensing the surface composition of planets and smaller objects in the solar system (e.g., see McCord et al., 1979a). As detectors and instrumentation increase in quality, the spectral coverage of the planets and satellites tend to increase. As measurements are extended into the infrared, the thermal radiation becomes larger than the reflected solar component. If reflectance measurements are needed in a region contaminated by thermal emission, the only action is to try to remove the thermal emission. This paper describes how to remove the thermal component for two cases: (1) the albedo and temperature are known; and (2) the albedo a n d / o r temperature are not known. Examples are shown of both integral disk and small spot measurements.
I = (A/A2r2)RFsu,,
where A is the projected area observed times the cosine of the angle of incidence, A is the o b j e c t - o b s e r v e r distance in the same system of units as A, r is the object Sun distance in AU, R is the reflectance of the object at the particular phase angle observed, and rrFsun is the solar flux at 1.0 AU. The reflectance of an object is found by comparison with a known standard as given by the equation Io = ( I o / L ) R s ,
(2)
where the subscript o refers to object and s to the standard. The result, Io, is the reflectance plus thermal components of the object and standard. Since
REFLECTANCE PLUS THERMAL MEASUREMENTS
Reflectance measurements are made by comparing the flux from the object under observation to that of a known standard. The standard is often an area of the Moon
Io = lo,R + lo,T and 94
0019-1035/79/100094-10502.00/0 Copyright © 1979by AcademicPress, Inc. All rights of reproduction in any form reserved.
(1)
(3a)
PLANETARY THERMAL EMISSION REMOVAL
/S = /s,R + /s,T,
(3b)
where the subscript R refers to reflectance and T refers to the thermal component, we see
Io = [(Io,~ + Io,T)/(&R + Is,T)]gs.
(4)
The thermal component is given by IT = (A/A2)B,
(5)
where B
=
B(h,T,~)
=
ff
A
e(h,O)P(h,T)da.
(6)
In the a b o v e equation, B is the thermal component integrated o v e r the area A observed, ¢ is the emissivity as a function of wavelength, and angle from the normal to the s u r f a c e ~. T h e P l a n c k f u n c t i o n is P(h,T), where T is the temperature o f area element dA. We can now rewrite Eq. 4 I o = [(Ao/Ao2ro2)RoFsun + (Ao/Ao2)Bo]/[(As/Ao2rs2)Rs Fsun + (As/Ao2)Bs]Rs,
95
where the thermal emission becomes important. Note the curves represent planetary thermal emission divided b y incident solar flux/~r (=Fsun). In order to determine the actual ratio multiply the curves in Fig. 1 by ~(h)/R(X), where E(X) is the emissivity and R(h) the reflectance o f the surface. The incident solar flux in Fig. 1 is approximated by a 5995°K Planck blackbody spectrum. Each curve is derived from P.r/Sun = [P(k, Tp)/P(h, /'sun)] [rrr2/(8.34 x 10-~)],
(10)
where PT is the planet thermal emission, Tp is the adopted temperature o f an area on the planet, Tsun is 5995°K, r is the distance of the planet from the Sun in AU, and the constant is a scale factor to scale the Planck blackbody function P(h, Tsu,) to the solar value at 1.0 AU. As the wavelength approaches infinity, the P T / S u n ratio approaches an upper limit o f lim P T / S u n
(7)
where R0 is the true reflectance of the object. If we multiply the numerator and denominator of Eq. 7 by rs2/(RsFs~n) and solve for Ro, we find
= (To/Ts)[r2/(2.65 × 10-5) = 2Tpr2.
(11)
T H E R M A L C O M P O N E N T S IN L U N A R S P E C T R A
Figure 1 indicates that in spectra of the Moon, the thermal componept b e c o m e s a significant fraction of the total observed flux Ro = (AsAo2ro2/AoAs2rs2)lo beginning at about 2.5/~m. Figure 2 shows a reflectance spectrum of an area in Mare + (A~Ao2/AoA~2)(ro2Bs/ Fsu.)(lo/Rs) - roUBo/Fsun. (8) Serentatis (MS2) (McCord et al., 1979b) containing the thermal component (solid Since line) and the resultant data with the thermal removed (data points). The ratio R ~ = (AsAo2roZ/AoAs2rs2)l o MS2/Apollo 16 was derived from telethen scopic data and the Apollo 16 reflectance was measured from returned lunar samples Ro = Rg + (r~2BJFs.n)(R~/R~) (Adams and McCord, 1973). The thermal ro2Bo/Fsun, (9) components were derived using (9) and where R~ is the derived reflectance with some simplifications. It is assumed that the thermal contamination. The values Fsun/rs ~ surface is Lambertian and the emissivity is and Fsun/ro z are the solar fluxes at the stan- independent o f the angle from the normal. dard and object, respectively. Thus the true The emissivity for a Lambert surface is reflectance is found by computing the last = 1 - R , where R is the normal reflectwo terms in (9) and removing them from tance. The areas observed were about Rg. 10-km diameter thus each spot (MS2 and Figure 1 shows a first approximation of Apollo 16) was treated as isothermal rather
96
R O G E R N. C L A R K
4.00
8.00 WRVELENGTH IN MICRONS
12.00
FIG. 1. The ratio of planet thermal/incident solar radiation approximates the wavelengths at which thermal radiation becomes important in planetary reflectance measurements. The assumed temperatures are: Mercury 706°K, Venus cloud tops 210°K, Moon 395°K, Mars 240°K, Jupiter 140°K, Saturn (disk) 120°K, Uranus 89°K, Saturn's rings 89°K, and Neptune 71°K. The reflectance would plot directly on this figure. An object with an albedo of 1.0 is shown. See text.
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w o_ w~ ,
0.80
1.20
1. $ 0
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2.40
WAVELENGTH I N MICRONS
FIG. 2. The reflectance of MS2 plus thermal component (solid line) compared to the reflectance with no thermal component (data points with 1 sigma error bars). The errors represent the error in the observational data and not in the thermal component removal.
PLANETARY THERMAL EMISSION REMOVAL than integrating the Planck function o v e r the small area. T h e t e m p e r a t u r e s for MS2 and Apollo 16 were d e t e r m i n e d f r o m an isothermal atlas o f the Moon as m e a s u r e d b y Saari and Shorthill (1965). The t e m p e r a ture as a function o f angle f r o m the subsolar point was plotted for MS2 (selenographic Long. 21°25'E, Lat. 18°40'N) and Apollo 16 (selenographic Long. 15°20'E, Lat. 8°59'4S). It was found the t e m p e r a t u r e s o f the MS2 and Apollo 16 sites were 394 and 389°K, respectively, when the angles from the subsolar point were 18.73 and 9.68 ° and the p h a s e was - 16° (before full Moon). The a d o p t e d normal albedos are 0.09 for MS2 and 0.151 for Apollo 16 at 0.55 p,m as determined by B a r a b a s h o v (1973). We can now modify (9) to the case o f a L a m b e r t i a n surface with a v e r y small area observed
ponent in this case changes the apparent depth o f the absorption feature f r o m a b o u t 8 to 10% and shifts the band center shortward b y 0.03 /~m. Depending on the relative strengths o f the spot and standard thermal components, an absorption feature can be m a d e to increase or decrease in depth with a shortward or longward shift of band center, can d i s a p p e a r completely, or could a p p e a r where there is actually no feature. The relative strength of the thermal component depends on the t e m p e r a t u r e and albedo o f the spot and standard. The worst case occurs when a very low albedo spot (standard or object) is at the subsolar point and a high albedo spot (standard or object) is far f r o m the subsolar point. In such a case the thermal c o m p o n e n t might be as m u c h two to four times greater than the case shown here.
R0 = R~ + R~(1 - Rs/dps)Ps/
Rs(Fsun/r~ 2) - (1 - Ro/6o)Po/ (Fsun/ro2),
THERMAL EMISSION FROM MERCURY (12)
where P is the Planck function and R/d~ is the normal reflectance where R is the reflectance at p h a s e ~b. Solving for R0 we find
Ro = (R~} + R~(1 - Rs/dps)es/Rs(Fsun/rs 2) Pol(Fsunlrs2)) (1 -- Pol(Fsun/ro2)~po) -'. (13) -
-
For the case o f the Moon rs --- r0. We also assume ~o = ~bs = 1 since the lunar phase function has not been d e t e r m i n e d at these wavelengths. Thus for the e x a m p l e shown here (13) b e c o m e s Ro = (Rfi + Rfi(1 - R~)PJR~F -
P0/F)(1
-
P0 + F) -1,
97
(14)
where F = Fs~n/ro 2 = Fsun/r~ 2. Figure 2 shows the resultant R0 (data points with 1 sigma error bars) and R~ (solid line). The error bars represent the error o f the data, not the error in thermal c o m p o nent removal. The thermal c o m p o n e n t in the MS2 reflectance s p e c t r u m has the effect o f changing the wing o f the v e r y broad 2-/.tm absorption feature. The thermal com-
In the case of reflectance m e a s u r e m e n t s o v e r a large area on a planetary surface, the change in t e m p e r a t u r e o v e r the o b s e r v e d area must be included in the analysis since the sum of two or m o r e Planck functions is not the s a m e as a Planck function at some characteristic wavelength. Thus we must assume a t e m p e r a t u r e function o v e r the area being observed. For the case of the M e r c u r y integral disk m e a s u r e m e n t s reported here we will use T = T0(] cos TM 0 -J- ~), T=]T0,
0 --< 90 °, 0-->90 °
(15) (16)
as suggested b y Peterson (1976). Integrating o v e r the planetary disk, we find
B(X,T(0),~) ~
2
f°lf: du
where
/dU
, ( h , ~ ) P ( X , T ( O ) ) s i n 0 cos y " 1
x dyJ dO,
(17)
y = arc cos ( - c o s a cos O/sin a sin 0), 0 > rr/2, = rr,
0 ---< z r / 2 -
=0,
zr/2-a<0,
a,
98
ROGER
N. CLARK
where O is the angle from the subsolar point (the subsolar colatitude), -y is the subsolar longitude measured from the meridian connecting the sub-Earth to the subsolar point and ot is the phase angle. The angle from the normal to the point (3', 0) is given by = arc cos [cos ot cos/9 + sin~sinOcos3~].
WAVENUMBER (CM-t )
:oooo '' ' ' I '
ISOOO
/
7000
h
I '
(19)
x = C~/~b(ot),
Where ~b(ot) is the phase function and C is an arbitrary constant representing the scaling of the reflectance spectrum to the norWRVENUMBER (CM-t I I0000 7000 6000 I
L
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5000
qO00
L
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~oLc c
• °
,5 ~
"..
~-
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~ tu~, N~
• *" i ° •"
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a
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,°.,"'°"
1.s
2.0
sooo 4ooo ' I"7 .................... r
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,i, ,,'°
~
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,,,°~,°
(18)
For the sample analysis shown on the next few pages, we will assume that the emissivity is independent of wavelength and ~ . Also we will assume that the albedo is not well known so that we can illustrate how we can constrain the solution by the shape of the thermal component. This might be the case needed when observing some asteroids or satellites where the exact radius is not known. Under the assumptions just made, we now have two independent variables: the subsolar temperature and a scale factor
)ISO00
sooo
2.s
~RVELENGTH IN MICRONS
FIG. 3. T h e s p e c t r u m of M e r c u r y on April 21 (a) without the thermal c o m p o n e n t r e m o v e d . C u r v e (b) s h o w s the derived thermal emission of a 731°K blackb o d y divided by the solar s p e c t r u m at M e r c u r y and scaled by a factor of 6.33.
,oo,OO,
N N 1.0
1.5
2.0
2.5
WAVELENGTH IN MICRONS
FIG. 4. A comparison of Mercury (a) and Apollo 16 (b) spectra. The M e r c u r y s p e c t r u m has been displaced 0.1 units above the Apollo s p e c t r u m for clarity. The two spectra m a t c h well within error below 1.5 /~m where the thermal radiation from M e r c u r y is insignificant.
mal reflectance. The Mercury data used in this analysis are reported b y McCord and Clark (1979) and the instrument and observing procedures used are further described by McCord e t a l . (1978). As a first step, the gross shape of the reflected component must be determined. This is accomplished by comparing the thermal component to a b l a c k b o d y / s o l a r flux ratio. Since the two spectra seem relatively similar as in Fig. 3, the reflected component must be generally smooth. That is there is probably not a large slope change from the visible portion to the ir portion of the spectrum. This will be reinforced shortly when the effects of choosing the wrong temperature or scaling factor are discussed. Figure 4 shows a comparison of the Apollo 16 landing site with the Mercury reflectance. The match is close from 0.6 to 1.5 /zm b e y o n d which thermal emission begins to dominate. The match is also very close in the visible region of the spectrum (Vilas and McCord, 1976). Note that these spectra are
99
PLANETARY THERMAL EMISSION REMOVAL scaled to a reflectance of 0.167 at 1.02/~m (the Mercury spectrum has been displaced 0.1 reflectance unit upward from the Apollo 16 spectrum for clarity) indicating that the scaled spectral slope but not necessarily the absolute reflectance are identical. Thus the Apollo 16 spectrum seems to be a good match to M e r c u r y ' s reflectance. As an illustration of the effect of the scaling factor and temperature on the fit, let us examine Figs. 5 and 6. Figure 5 shows the effect o f changing the scaling factor, while the subsolar temperature stays constant at 731°K. As the scaling factor is increased, more o f the thermal radiation is r e m o v e d thus lowering the curve at 2.5 /.~m. The range o f curves shown is from a scale factor o f 5.0 for the b o t t o m curve (f) to 7.5 for the top curve (a). The curves in between the top and b o t t o m each have a scaling factor of 0.5 different from the neighboring curves. The middle two curves ((c) and (d), representing scaling factors o f 6.0 and 6.5) are the closest judged to be the best fit (assuming the Apollo 16 like reflectance). Figure 6 shows the effect of changing the temperature while the scale factor was ad-
15000
WRVENUMBER (CM") 10000 7006 6000
5000
qo00
1.5 2.0 NAVELENGTH IN MICAON$
2.5
¢n~,_
c~ e
u~ ~z
-
c'.6
1.0
FIG. 6. The Mercury spectrum from April 21 with various black body spectra divided by solar removed. The subsolar temperatures and scaling factors are: (a) 850°K, 1.69; (b) 800°K, 2.75; (c) 750°K, 4.81; (d) 700°K, 9.05; (e) 650°K, 20.00; (f) 600°K, 46.91. The scale factor was adjusted to obtain the best fit to Apollo 16. Each curve was displaced 0.05 units upward from the one below it for clarity.
justed to obtain the best fit for that temperature. Note that when the temperature is too low the curve seems to have a relative peak NgVENUMBER (CM-' 1 around 2/~m and then drops off. When the q000 15000 10000 7000 6000 50O0 I I'''' I ' ' I I temperature is too large the curve seems to be level around 2 /,~m and then increases g sharply. Figure 7 shows the residuals after re.2 moval of the thermal component for the three nights Mercury was observed. The ,m o , o c residual Mercury spectra appear different at 8 1.4 and 1.9/zm because the high air mass at g~ which the observations were undertaken provided difficulty in removing the E a r t h ' s atmospheric water bands. The actual ~G m_ spectra are probably smooth through this m region. Other than the differences in the water bands, the spectra appear quite similar to each other and also Apollo 16. Thus , , , I , , ~ , I , , , , I , 2.5 1.0 1.5 2.0 the actual reflectance might contain a slope WAVELENGTH IN MICRONS change beginning about 1.5 /zm. This exFIG. 5. The spectrum of Mercury taken on April 21 with a scaled 73I°K blackbody (subsolar) divided by a ample is insensitive to changes in slope solar spectrum. The various scaling factors are: (a) 5.0; from 1.5 to 2.5/.~m since this is on the same region as the thermal component. This and (b) 5.5; (c) 6.0; (d) 6.5; (e) 7.0; (f) 7.5.
V
100
ROGER WAVENUMBER (CM "~ ) 10000 7000 6000 ' I ~ ' I ' I
N. CLARK
the resulting 2 and 2 . 5 / z m fluxes times the area. The nightside (90-180 °) of Mercury has the largest area but the flux received is far less than any single latitude strip on the 1 day side. The area which contributes the m o s t radiation is between 30 and 70 ° f r o m a~o-~?~!j,,rr7 IT [ the subsolar point giving 72% of the total radiation at 2.0 /xm and 71% at 2.5 /xm. Thus the average t e m p e r a t u r e in this region NN~ o f 640 to 700°K contributes the m o s t radiaz~dtion relative to the other areas. I f we rec o m p u t e the thermal c o m p o n e n t using a t e m p e r a t u r e uniformly distributed o v e r the disk, we find the best fit to be 675°K with a scale factor of 2.75. This is consistent with N the a b o v e average t e m p e r a t u r e . Thus .e ~.0 ~.s 2.o ~.s changing the t e m p e r a t u r e variation to a NQVELENOTH IN MICRONS m o r e uniform distribution o v e r the disk will FIG. 7. T h e M e r c u r y spectra from M c C o r d and lower the subsolar t e m p e r a t u r e and the Clark (1979) with the thermal c o m p o n e n t r e m o v e d , and Apollo 16 as a comparison (c). T h e date, subsolar scale factor. Lowering the night t e m p e r a temperature, and scaling factor for corresponding ture to, say 0.15 To instead of 0.375 To would M e r c u r y s p e c t r a with r e m o v e d thermal are: (a) April result in the scale factor and the subsolar 22,726°K, 6.32; (b) April 21,731°K, 6.33; (d) April 23, 720°K, 6.96. E a c h s p e c t r u m h a s been displaced 0.1 t e m p e r a t u r e increasing slightly. Although unit u p w a r d from the s p e c t r u m below it for better clar- small changes in the t e m p e r a t u r e distribuity. tion or night t e m p e r a t u r e will result in a other limitations will be discussed in the change in the scale factor and subsolar temnext section. perature, one of these two p a r a m e t e r s may The consequences of the assumed tem- be adjusted enough so that a good fit is obperature distribution must be determined. tained while the other p a r a m e t e r need not Table ! shows the area o b s e r v e d on 10° be adjusted at all. This is due to the fact that latitude strips at a phase angle of 82.2 ° and an increase in the scaling factor and an in15000
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TABLE I TEMPERATURE DISTRIBUTION USED IN MERCURY ANALYS1Sa'b
Subsolar colatitude 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-180
Temperature (°K)
Normalized area of latitude strip
725.6 722.0 714.9 703.7 688.0 666.5 637.1 594.1 513.9 272.3
0.0041 0.0145 0.0297 0.0481 0.0673 0.0852 0.0995 0.1084 0.1110 0.4321
Sum
1.000
Q Solar p h a s e angle = 82.2 °. n Subsolar temperature = 726.0°K.
2-/~m flux times area
2.5-/~m flux times area
Percentage of 2.5-/~m flux
0.759 2.541 4.713 6.500 7.205 6.509 4.615 2.222 0.344 5 × 10-~
1.808 6.109 11.560 16.460 19.120 18.473 14.473 8.204 1.852 3 × 10-4
1.0 5.2 10.9 16.3 19.7 19.6 15.8 9.3 2.2 0.0
35.409
98.061
100.0
PLANETARY THERMAL EMISSION REMOVAL crease in t e m p e r a t u r e can produce the s a m e result within the errors of the observational data. This effect could be reduced by increased spectral c o v e r a g e to say 5 /zm which is m u c h nearer to the p e a k in the thermal emission spectrum. The Mercury data were originally scaled to a value o f 0.167 at 1.02/zm which is the a p p r o x i m a t e geometric albedo of 5° p h a s e as determined f r o m data reported in Dollfus and Auriere (1974) and Vilas and McCord (1976). Thus the resultant reflectance should be a first approximation to normal reflectance and the constant C --- 1.0. I f we then c o m p u t e the p h a s e coefficients for Mercury we can c o m p u t e t l ~ emissivity. The results are shown in Table~I along with coefficients for the Moon f r o m L a n e and Irvine (1973) for comparison. The average emissivity is 0.96. This value is s o m e w h a t higher than that reported for the Moon (Murcray et al., 1970; Saari and Shorthill, 1972) and Mercury (Hansen, 1974). I f we assume that Mercury is a L a m b e r t i a n surface then • = 1 - R and we would expect to be 0.82 at 1.4/.tm and 0.65 to 0.82 at 2.5 /.tm. Thus our derived t e m p e r a t u r e a n d / o r scale factor might be slightly wrong or the initial normalization m a y have been incorrect. In a n y case we have illustrated how the thermal analysis can be constrained b y the shape o f the thermal component. H o w ever, the continuum slope is not rigidly constrained, being " c h o s e n " b y the o p e r a t o r performing the analysis. Limitations and methods to constrain the fit further are discussed in the next section. TABLE II
101
LIMITATIONS We h a v e shown two e x a m p l e s o f thermal components in planetary reflectance spectra. I f we k n o w the t e m p e r a t u r e , emissivity, and scattering properties of the surface along with the area o b s e r v e d , we can readily c o m p u t e the thermal components. This is rarely the case. I f the surface is L a m b e r t i a n the reflected c o m p o n e n t I0 is lo(/Xo) = Ro(Fsu,/ro2),
(20)
w h e r e go is the cosine of the angle of reflection and tt is the cosine o f the angle of incidence. The emissivity is then =
1 -
R0.
(21)
I f the surface follows the law of diffuse reflection for isotropic scattering, the reflected intensity is Io(0,g,g0) = ¼&o(Fsun/ro2) ( g o / g + go)H(g)H(g0),
(22)
where H(tt) and H(/~o) are the Chand r a s e k h a r H - f u n c t i o n s for the isotropic case (Chandrasekhar, 1960). The variable &o is the single-scattering albedo. The equivalent normal reflectance is then Ro = &o[/-/~(1,&)/H2(1,1)],
(23)
where the reflectance is normalized to unity at m a x i m u m . The emissivity is e
= 2(1 -
bo)I'2fo~ftH(tx,&o)dlz.
(24)
Such an analysis is quite difficult and is p r o b a b l y not warranted unless the surface is known to follow the isotropic scattering equations. E v e n in the isotropic case the emissivity is
PHASE COEFFICIENTS AND EMISSIVITY OF MERCURY
Date
4/21/76 4/22/76 4/23/76
Phase angle
Phase Phase Scale coeffi- coelfi- factor x cienta cienP
Emissivity
-78.2 ° -82.2 ° -86.0 °
0.165 0.156 0.147 0.147 0.130 0.140
0.99 0.93 0.97
6.33 6.32 6.96
a Lane and Irvine (1973). b This paper: aibedo (a)/albedo (or = 5°).
0.9 ~< • + Ro -- 1.
(25)
In the case of M e r c u r y the emissivity has been shown to be dependent on the angle f r o m the normal (W) b y the equation ~(~) = ~(0) cos ~ ~ ,
(26)
w h e r e / 3 is O. 19 _+ 0.07 at 4 5 / z m (Chase et al., 1976). I f the emissivity and t e m p e r a t u r e
102
R O G E R N. C L A R K
are poorly known we can make a reasonable fit based on the shape o f the thermal component. H o w e v e r , the thermal component could be c o m p u t e d using the wrong models giving an erroneous reflectance. Thus as in the example o f the Mercury analysis presented here there could be a slope change in the reflectance from 1.5 to 2 . 5 / z m relative to 0.6 to 1.5/xm. There could also be a very broad absorption feature extending from 1.5 to 2.5 ~m. Thus the method is insensitive to features which extend over the entire wavelength region of the thermal component. There are two ways to look for large spectral features in the reflectance curve. One is to extend the wavelength coverage so the thermal component coverage is greater than the features sought. This can be accomplished with as little as one data point at a longer wavelength. For instance, in the case of Mercury, a point at 4 or 5 p,m would greatly constrain the fit, although the wavelength coverage is likely to necessitate an analysis where emissivity is wavelength dependent. Another method is to observe the surface
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at two or more different temperatures. If the temperature difference between observations is known or the temperatures at the two observations are known then the reflectance from the two observations can be correlated to constrain the fit. An example of this is shown in Fig. 8. Figure 8 is a simulation o f a planetary reflectance spectrum with thermal components at three different temperatures. If we measured the spectra with the 706 and 395 ° thermal components, we can see the large difference in the long wavelengths. For instance, the spectrum with 395°K thermal is essentially equal to the reflectance at 3 ~m. Thus, since we know the reflectance at 3 /.tm, we have a powerful constraint in the removal of the 706°K component. Of course, the more thermal component we must remove, the more likely we are to have errors in the resultant reflectance spectrum. We must also address the problem of the thermal emission tending to mask absorption features in the reflectance spectrum. Since ~ ~ 1 - Rx, a decrease in reflectivity will tend to cause an increase in emissiv-
I
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I
'
I
'
I
,
+
d d
2. B8
I
, I , I 4.8B S. B8 WRUELEHGTH IH MICROHS
3. OB
,
S. 88
?. 88
FIG. 8. Simulated planetary reflectance plus thermal components. The curves from top to bottom represent reflectance plus 706°K thermal component; reflectance plus 600°K thermal; reflectance plus 395°K thermal; and reflectance with no thermal component.
PLANETARY T H E R M A L EMISSION REMOVAL ity. W h e n the t h e r m a l a n d reflected c o m p o n e n t s are a b o u t e q u a l
103
BARABASHOV, H. P. (1973). Photometric Map o f the Visible Face o f the Moon. Academy of the Ukraine,
Kiev. R~ ~ (1 - R x ) [ P ( h , T ) / ( F s u n ) ] r o "
(27)
t h e n a s m a l l i n c r e a s e (or d e c r e a s e ) in Rx will h a v e the effect o f d e c r e a s i n g (or i n c r e a s i n g ) the e m i s s i v i t y w h i c h will t e n d to "fill i n " a f e a t u r e in the R ' s p e c t r u m , b u t o n l y w h e n the r e f l e c t a n c e a n d e m i s s i v i t y are a b o u t the s a m e . W h e n the r e f l e c t a n c e is n e a r 1.0 the p e r c e n t c h a n g e i n e m i s s i v i t y i s large c o m p a r e d to the p e r c e n t c h a n g e in reflectivity, a n d i n v e r s e l y w h e n the reflectivity is n e a r zero. This filling in o f a n a b s o r p t i o n f e a t u r e occurs only under restricted circumstances a n d c a n be r e m o v e d b y o b s e r v i n g the surface at a different t e m p e r a t u r e . DISCUSSION We h a v e s h o w n t h a t it is p o s s i b l e to rem o v e the t h e r m a l c o m p o n e n t s f r o m p l a n e t a r y r e f l e c t a n c e s p e c t r a t h u s e x t e n d i n g the u s e f u l w a v e l e n g t h c o v e r a g e . This is i m p o r t a n t for s t u d i e s o f M e r c u r y , the M o o n , a n d a s t e r o i d s c l o s e r t h a n a b o u t 1 A U f r o m the S u n w h e r e t h e 2-/xm m i n e r a l b a n d s give c o m p o s i t i o n a l i n f o r m a t i o n a b o u t the surface ( M c C o r d e t al., 1979a). A l t h o u g h s o m e i n f o r m a t i o n a b o u t the t e m p e r a t u r e o f the s u r f a c e is o b t a i n e d , it is p r o b a b l y n o t as acc u r a t e as m e a s u r i n g the b r i g h t n e s s t e m p e r a ture in a region w h e r e the reflected solar c o m p o n e n t is i n s i g n i f i c a n t c o m p a r e d to the thermal emission.
ACKNOWLEDGMENTS I would like to thank Thomas B. McCord, Michael J. Gaffey, Richard Shorthill, Terry Jones, Robert Singer, and Lucy McFadden for reviewing the manuscript. This research was supported by NASA Grants 7323 and 7312. This is contribution no. 212 of the Planetary Sciences Laboratory.
REFERENCES ADAMS, J. B., AND McCORD, T. B. (1973). Vitrification darkening in the lunar highlands and identification of Descartes at the Apollo 16 site. Proc. 4th Lunar Sci. Conf. 1, 163-177.
CHANDRASEKHAR, C. (1960). Radiative
Transfer.
Dover, New York. CHASE, S. C., JR., MINER, E. D., MORRISON, D., MUNCH, G., AND NEUGEBAUER, G. (1976). Mariner
10 infrared radiometer results: Temperatures and thermal properties of the surface of Mercury. Icarus 28, 565-578. DOLLEUS, A., AND AURIER, M. (1974). Optical polarimetry of planet Mercury. Icarus 23, 465-482. HANSE'N, O; (1974); Surface temperature and emissivity of Mercury. Astrophys. J. 190, 715-717. KIEFEER, H. H. (1968). Near infrared spectral reflec-
tance of simulated Martian frosts. Ph.D. thesis, California Institute of Technology, Pasadena. LANE, A. P., AND IRVINE, W. M. (1973). Monochromatic phase curves and albedos for the lunar disk. Astron. J. 78, 267-277. McCORD, T. B., AND CLARK,R. N. (1979). The Mercury soil: Presence of Fe2+. J. Geophys. Res., in press. McCORD, Z. B., CLARK, R. N., AND HUGUENIN, R. L. (1978). Mars: Infrared spectral and compositional implications. J. Geophys. Res. 83, 5433-5441. McCORD, T. B., ADAMS,J. B., AND HUGUENIN, R. L. (1979a). Reflection spectroscopy: A technique for remotely sensing surface mineralogy and composition. Submitted. McCORD, T. B., CLARK, R. N., MCFADDEN,L., PIETERS, C. M., AND ADAMS, J. B. (1979b). Moon:
Near-infrared spectral reflectance. A first good look. To be submitted. MORRISON, D. (1970). Thermophysics of the planet Mercury. Space Sci. Rev. l l , 271-307. MURCRAY, F. H., MURCRAY, D. G., AND WILLIAM,
W. J. (1970). Infrared emissivity of lunar surface features. I. Balloon-borne observations. J. Geophys. Res. 75, 2662-2669. PETERSON, C. (1976). Private communication. PETTIT, E. (1961). Planetary temperature measurements. In Planets and Satellites (G. P. Kuiper and B. M. Middlehurst, Eds.), p. 400. Univ. of Chicago Press, Chicago. SAARI, J. M., AND SHORTHILL, R. W. (1965). Isothermal and isophotic atlas of the Moon. Contours
through a lunation. NASA Cr-855. SAARI, J. M., AND SHORTHIEL, R. W. (1972). The sunlit lunar surface. I. Albedo studies and full Moon temperature distribution. The Moon 5, 161-178. SMITH, B. A., AND BRUCE, T. C. (1971). Ephemeris
for physical observations of Mercury. Department of Astronomy, New Mexico State University, Los Cruces, New Mexico. VILAS, F., AND MCCORD, T. B. (1976). Mercury: Spectral reflectance measurements (0.33-1.06 p,m) 1974/1975. Icarus 28, 593-599.
Planetary Reflectance Measurements in the Region of Planetary Thermal Emission R O G E R N. C L A R K Department of Earth and Planetary Sciences, Massachusetts Institute of Technology Cambridge, Massachusetts 02139 and Institute for Astronomy, University of Hawaii at Manoa, 2680 Woodlawn Drive, Honolulu, Hawaii 96822 Received O c t o b e r 30, 1978; revised M a y 22, 1979 As planetary reflectance m e a s u r e m e n t s are extended into the infrared, the emitted thermal radiation b e c o m e s larger t h a n the reflected solar component. This paper describes a m e t h o d for r e m o v a l of the thermal c o m p o n e n t from planetary reflectance m e a s u r e m e n t s and d i s c u s s e s the limitations involved. E x a m p l e s are s h o w n for the case of lunar observations where the t e m p e r a t u r e and emissivity are k n o w n and for M e r c u r y where it is a s s u m e d the t e m p e r a t u r e and emissivity are unknown.
which has been calibrated to an Apollo landing site from telescopic observations and laboratory reflectance spectra of returned lunar samples. The flux received above the Earth's atmosphere from a solar system object at one wavelength is given by the equation
INTRODUCTION
Reflectance spectroscopy is being used successfully for remotely sensing the surface composition of planets and smaller objects in the solar system (e.g., see McCord et al., 1979a). As detectors and instrumentation increase in quality, the spectral coverage of the planets and satellites tend to increase. As measurements are extended into the infrared, the thermal radiation becomes larger than the reflected solar component. If reflectance measurements are needed in a region contaminated by thermal emission, the only action is to try to remove the thermal emission. This paper describes how to remove the thermal component for two cases: (1) the albedo and temperature are known; and (2) the albedo a n d / o r temperature are not known. Examples are shown of both integral disk and small spot measurements.
I = (A/A2r2)RFsu,,
where A is the projected area observed times the cosine of the angle of incidence, A is the o b j e c t - o b s e r v e r distance in the same system of units as A, r is the object Sun distance in AU, R is the reflectance of the object at the particular phase angle observed, and rrFsun is the solar flux at 1.0 AU. The reflectance of an object is found by comparison with a known standard as given by the equation Io = ( I o / L ) R s ,
(2)
where the subscript o refers to object and s to the standard. The result, Io, is the reflectance plus thermal components of the object and standard. Since
REFLECTANCE PLUS THERMAL MEASUREMENTS
Reflectance measurements are made by comparing the flux from the object under observation to that of a known standard. The standard is often an area of the Moon
Io = lo,R + lo,T and 94
0019-1035/79/100094-10502.00/0 Copyright © 1979by AcademicPress, Inc. All rights of reproduction in any form reserved.
(1)
(3a)
PLANETARY THERMAL EMISSION REMOVAL
/S = /s,R + /s,T,
(3b)
where the subscript R refers to reflectance and T refers to the thermal component, we see
Io = [(Io,~ + Io,T)/(&R + Is,T)]gs.
(4)
The thermal component is given by IT = (A/A2)B,
(5)
where B
=
B(h,T,~)
=
ff
A
e(h,O)P(h,T)da.
(6)
In the a b o v e equation, B is the thermal component integrated o v e r the area A observed, ¢ is the emissivity as a function of wavelength, and angle from the normal to the s u r f a c e ~. T h e P l a n c k f u n c t i o n is P(h,T), where T is the temperature o f area element dA. We can now rewrite Eq. 4 I o = [(Ao/Ao2ro2)RoFsun + (Ao/Ao2)Bo]/[(As/Ao2rs2)Rs Fsun + (As/Ao2)Bs]Rs,
95
where the thermal emission becomes important. Note the curves represent planetary thermal emission divided b y incident solar flux/~r (=Fsun). In order to determine the actual ratio multiply the curves in Fig. 1 by ~(h)/R(X), where E(X) is the emissivity and R(h) the reflectance o f the surface. The incident solar flux in Fig. 1 is approximated by a 5995°K Planck blackbody spectrum. Each curve is derived from P.r/Sun = [P(k, Tp)/P(h, /'sun)] [rrr2/(8.34 x 10-~)],
(10)
where PT is the planet thermal emission, Tp is the adopted temperature o f an area on the planet, Tsun is 5995°K, r is the distance of the planet from the Sun in AU, and the constant is a scale factor to scale the Planck blackbody function P(h, Tsu,) to the solar value at 1.0 AU. As the wavelength approaches infinity, the P T / S u n ratio approaches an upper limit o f lim P T / S u n
(7)
where R0 is the true reflectance of the object. If we multiply the numerator and denominator of Eq. 7 by rs2/(RsFs~n) and solve for Ro, we find
= (To/Ts)[r2/(2.65 × 10-5) = 2Tpr2.
(11)
T H E R M A L C O M P O N E N T S IN L U N A R S P E C T R A
Figure 1 indicates that in spectra of the Moon, the thermal componept b e c o m e s a significant fraction of the total observed flux Ro = (AsAo2ro2/AoAs2rs2)lo beginning at about 2.5/~m. Figure 2 shows a reflectance spectrum of an area in Mare + (A~Ao2/AoA~2)(ro2Bs/ Fsu.)(lo/Rs) - roUBo/Fsun. (8) Serentatis (MS2) (McCord et al., 1979b) containing the thermal component (solid Since line) and the resultant data with the thermal removed (data points). The ratio R ~ = (AsAo2roZ/AoAs2rs2)l o MS2/Apollo 16 was derived from telethen scopic data and the Apollo 16 reflectance was measured from returned lunar samples Ro = Rg + (r~2BJFs.n)(R~/R~) (Adams and McCord, 1973). The thermal ro2Bo/Fsun, (9) components were derived using (9) and where R~ is the derived reflectance with some simplifications. It is assumed that the thermal contamination. The values Fsun/rs ~ surface is Lambertian and the emissivity is and Fsun/ro z are the solar fluxes at the stan- independent o f the angle from the normal. dard and object, respectively. Thus the true The emissivity for a Lambert surface is reflectance is found by computing the last = 1 - R , where R is the normal reflectwo terms in (9) and removing them from tance. The areas observed were about Rg. 10-km diameter thus each spot (MS2 and Figure 1 shows a first approximation of Apollo 16) was treated as isothermal rather
96
R O G E R N. C L A R K
4.00
8.00 WRVELENGTH IN MICRONS
12.00
FIG. 1. The ratio of planet thermal/incident solar radiation approximates the wavelengths at which thermal radiation becomes important in planetary reflectance measurements. The assumed temperatures are: Mercury 706°K, Venus cloud tops 210°K, Moon 395°K, Mars 240°K, Jupiter 140°K, Saturn (disk) 120°K, Uranus 89°K, Saturn's rings 89°K, and Neptune 71°K. The reflectance would plot directly on this figure. An object with an albedo of 1.0 is shown. See text.
'
I
'
'
'
I
,
,
,
I
'
'
'
I
,
,
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I
'
'
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t
i
I
'
'
'
n
a
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o ~N
w ~J tq w
b.
w o_ w~ ,
0.80
1.20
1. $ 0
.
I
2.00
2.40
WAVELENGTH I N MICRONS
FIG. 2. The reflectance of MS2 plus thermal component (solid line) compared to the reflectance with no thermal component (data points with 1 sigma error bars). The errors represent the error in the observational data and not in the thermal component removal.
PLANETARY THERMAL EMISSION REMOVAL than integrating the Planck function o v e r the small area. T h e t e m p e r a t u r e s for MS2 and Apollo 16 were d e t e r m i n e d f r o m an isothermal atlas o f the Moon as m e a s u r e d b y Saari and Shorthill (1965). The t e m p e r a ture as a function o f angle f r o m the subsolar point was plotted for MS2 (selenographic Long. 21°25'E, Lat. 18°40'N) and Apollo 16 (selenographic Long. 15°20'E, Lat. 8°59'4S). It was found the t e m p e r a t u r e s o f the MS2 and Apollo 16 sites were 394 and 389°K, respectively, when the angles from the subsolar point were 18.73 and 9.68 ° and the p h a s e was - 16° (before full Moon). The a d o p t e d normal albedos are 0.09 for MS2 and 0.151 for Apollo 16 at 0.55 p,m as determined by B a r a b a s h o v (1973). We can now modify (9) to the case o f a L a m b e r t i a n surface with a v e r y small area observed
ponent in this case changes the apparent depth o f the absorption feature f r o m a b o u t 8 to 10% and shifts the band center shortward b y 0.03 /~m. Depending on the relative strengths o f the spot and standard thermal components, an absorption feature can be m a d e to increase or decrease in depth with a shortward or longward shift of band center, can d i s a p p e a r completely, or could a p p e a r where there is actually no feature. The relative strength of the thermal component depends on the t e m p e r a t u r e and albedo o f the spot and standard. The worst case occurs when a very low albedo spot (standard or object) is at the subsolar point and a high albedo spot (standard or object) is far f r o m the subsolar point. In such a case the thermal c o m p o n e n t might be as m u c h two to four times greater than the case shown here.
R0 = R~ + R~(1 - Rs/dps)Ps/
Rs(Fsun/r~ 2) - (1 - Ro/6o)Po/ (Fsun/ro2),
THERMAL EMISSION FROM MERCURY (12)
where P is the Planck function and R/d~ is the normal reflectance where R is the reflectance at p h a s e ~b. Solving for R0 we find
Ro = (R~} + R~(1 - Rs/dps)es/Rs(Fsun/rs 2) Pol(Fsunlrs2)) (1 -- Pol(Fsun/ro2)~po) -'. (13) -
-
For the case o f the Moon rs --- r0. We also assume ~o = ~bs = 1 since the lunar phase function has not been d e t e r m i n e d at these wavelengths. Thus for the e x a m p l e shown here (13) b e c o m e s Ro = (Rfi + Rfi(1 - R~)PJR~F -
P0/F)(1
-
P0 + F) -1,
97
(14)
where F = Fs~n/ro 2 = Fsun/r~ 2. Figure 2 shows the resultant R0 (data points with 1 sigma error bars) and R~ (solid line). The error bars represent the error o f the data, not the error in thermal c o m p o nent removal. The thermal c o m p o n e n t in the MS2 reflectance s p e c t r u m has the effect o f changing the wing o f the v e r y broad 2-/.tm absorption feature. The thermal com-
In the case of reflectance m e a s u r e m e n t s o v e r a large area on a planetary surface, the change in t e m p e r a t u r e o v e r the o b s e r v e d area must be included in the analysis since the sum of two or m o r e Planck functions is not the s a m e as a Planck function at some characteristic wavelength. Thus we must assume a t e m p e r a t u r e function o v e r the area being observed. For the case of the M e r c u r y integral disk m e a s u r e m e n t s reported here we will use T = T0(] cos TM 0 -J- ~), T=]T0,
0 --< 90 °, 0-->90 °
(15) (16)
as suggested b y Peterson (1976). Integrating o v e r the planetary disk, we find
B(X,T(0),~) ~
2
f°lf: du
where
/dU
, ( h , ~ ) P ( X , T ( O ) ) s i n 0 cos y " 1
x dyJ dO,
(17)
y = arc cos ( - c o s a cos O/sin a sin 0), 0 > rr/2, = rr,
0 ---< z r / 2 -
=0,
zr/2-a<0,
a,
98
ROGER
N. CLARK
where O is the angle from the subsolar point (the subsolar colatitude), -y is the subsolar longitude measured from the meridian connecting the sub-Earth to the subsolar point and ot is the phase angle. The angle from the normal to the point (3', 0) is given by = arc cos [cos ot cos/9 + sin~sinOcos3~].
WAVENUMBER (CM-t )
:oooo '' ' ' I '
ISOOO
/
7000
h
I '
(19)
x = C~/~b(ot),
Where ~b(ot) is the phase function and C is an arbitrary constant representing the scaling of the reflectance spectrum to the norWRVENUMBER (CM-t I I0000 7000 6000 I
L
'
5000
qO00
L
I
I
[
~oLc c
• °
,5 ~
"..
~-
.'. •-
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°
.
~ tu~, N~
• *" i ° •"
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a
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b 1.o
,°.,"'°"
1.s
2.0
sooo 4ooo ' I"7 .................... r
_
,i, ,,'°
~
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I
,,,°~,°
(18)
For the sample analysis shown on the next few pages, we will assume that the emissivity is independent of wavelength and ~ . Also we will assume that the albedo is not well known so that we can illustrate how we can constrain the solution by the shape of the thermal component. This might be the case needed when observing some asteroids or satellites where the exact radius is not known. Under the assumptions just made, we now have two independent variables: the subsolar temperature and a scale factor
)ISO00
sooo
2.s
~RVELENGTH IN MICRONS
FIG. 3. T h e s p e c t r u m of M e r c u r y on April 21 (a) without the thermal c o m p o n e n t r e m o v e d . C u r v e (b) s h o w s the derived thermal emission of a 731°K blackb o d y divided by the solar s p e c t r u m at M e r c u r y and scaled by a factor of 6.33.
,oo,OO,
N N 1.0
1.5
2.0
2.5
WAVELENGTH IN MICRONS
FIG. 4. A comparison of Mercury (a) and Apollo 16 (b) spectra. The M e r c u r y s p e c t r u m has been displaced 0.1 units above the Apollo s p e c t r u m for clarity. The two spectra m a t c h well within error below 1.5 /~m where the thermal radiation from M e r c u r y is insignificant.
mal reflectance. The Mercury data used in this analysis are reported b y McCord and Clark (1979) and the instrument and observing procedures used are further described by McCord e t a l . (1978). As a first step, the gross shape of the reflected component must be determined. This is accomplished by comparing the thermal component to a b l a c k b o d y / s o l a r flux ratio. Since the two spectra seem relatively similar as in Fig. 3, the reflected component must be generally smooth. That is there is probably not a large slope change from the visible portion to the ir portion of the spectrum. This will be reinforced shortly when the effects of choosing the wrong temperature or scaling factor are discussed. Figure 4 shows a comparison of the Apollo 16 landing site with the Mercury reflectance. The match is close from 0.6 to 1.5 /zm b e y o n d which thermal emission begins to dominate. The match is also very close in the visible region of the spectrum (Vilas and McCord, 1976). Note that these spectra are
99
PLANETARY THERMAL EMISSION REMOVAL scaled to a reflectance of 0.167 at 1.02/~m (the Mercury spectrum has been displaced 0.1 reflectance unit upward from the Apollo 16 spectrum for clarity) indicating that the scaled spectral slope but not necessarily the absolute reflectance are identical. Thus the Apollo 16 spectrum seems to be a good match to M e r c u r y ' s reflectance. As an illustration of the effect of the scaling factor and temperature on the fit, let us examine Figs. 5 and 6. Figure 5 shows the effect o f changing the scaling factor, while the subsolar temperature stays constant at 731°K. As the scaling factor is increased, more o f the thermal radiation is r e m o v e d thus lowering the curve at 2.5 /.~m. The range o f curves shown is from a scale factor o f 5.0 for the b o t t o m curve (f) to 7.5 for the top curve (a). The curves in between the top and b o t t o m each have a scaling factor of 0.5 different from the neighboring curves. The middle two curves ((c) and (d), representing scaling factors o f 6.0 and 6.5) are the closest judged to be the best fit (assuming the Apollo 16 like reflectance). Figure 6 shows the effect of changing the temperature while the scale factor was ad-
15000
WRVENUMBER (CM") 10000 7006 6000
5000
qo00
1.5 2.0 NAVELENGTH IN MICAON$
2.5
¢n~,_
c~ e
u~ ~z
-
c'.6
1.0
FIG. 6. The Mercury spectrum from April 21 with various black body spectra divided by solar removed. The subsolar temperatures and scaling factors are: (a) 850°K, 1.69; (b) 800°K, 2.75; (c) 750°K, 4.81; (d) 700°K, 9.05; (e) 650°K, 20.00; (f) 600°K, 46.91. The scale factor was adjusted to obtain the best fit to Apollo 16. Each curve was displaced 0.05 units upward from the one below it for clarity.
justed to obtain the best fit for that temperature. Note that when the temperature is too low the curve seems to have a relative peak NgVENUMBER (CM-' 1 around 2/~m and then drops off. When the q000 15000 10000 7000 6000 50O0 I I'''' I ' ' I I temperature is too large the curve seems to be level around 2 /,~m and then increases g sharply. Figure 7 shows the residuals after re.2 moval of the thermal component for the three nights Mercury was observed. The ,m o , o c residual Mercury spectra appear different at 8 1.4 and 1.9/zm because the high air mass at g~ which the observations were undertaken provided difficulty in removing the E a r t h ' s atmospheric water bands. The actual ~G m_ spectra are probably smooth through this m region. Other than the differences in the water bands, the spectra appear quite similar to each other and also Apollo 16. Thus , , , I , , ~ , I , , , , I , 2.5 1.0 1.5 2.0 the actual reflectance might contain a slope WAVELENGTH IN MICRONS change beginning about 1.5 /zm. This exFIG. 5. The spectrum of Mercury taken on April 21 with a scaled 73I°K blackbody (subsolar) divided by a ample is insensitive to changes in slope solar spectrum. The various scaling factors are: (a) 5.0; from 1.5 to 2.5/.~m since this is on the same region as the thermal component. This and (b) 5.5; (c) 6.0; (d) 6.5; (e) 7.0; (f) 7.5.
V
100
ROGER WAVENUMBER (CM "~ ) 10000 7000 6000 ' I ~ ' I ' I
N. CLARK
the resulting 2 and 2 . 5 / z m fluxes times the area. The nightside (90-180 °) of Mercury has the largest area but the flux received is far less than any single latitude strip on the 1 day side. The area which contributes the m o s t radiation is between 30 and 70 ° f r o m a~o-~?~!j,,rr7 IT [ the subsolar point giving 72% of the total radiation at 2.0 /xm and 71% at 2.5 /xm. Thus the average t e m p e r a t u r e in this region NN~ o f 640 to 700°K contributes the m o s t radiaz~dtion relative to the other areas. I f we rec o m p u t e the thermal c o m p o n e n t using a t e m p e r a t u r e uniformly distributed o v e r the disk, we find the best fit to be 675°K with a scale factor of 2.75. This is consistent with N the a b o v e average t e m p e r a t u r e . Thus .e ~.0 ~.s 2.o ~.s changing the t e m p e r a t u r e variation to a NQVELENOTH IN MICRONS m o r e uniform distribution o v e r the disk will FIG. 7. T h e M e r c u r y spectra from M c C o r d and lower the subsolar t e m p e r a t u r e and the Clark (1979) with the thermal c o m p o n e n t r e m o v e d , and Apollo 16 as a comparison (c). T h e date, subsolar scale factor. Lowering the night t e m p e r a temperature, and scaling factor for corresponding ture to, say 0.15 To instead of 0.375 To would M e r c u r y s p e c t r a with r e m o v e d thermal are: (a) April result in the scale factor and the subsolar 22,726°K, 6.32; (b) April 21,731°K, 6.33; (d) April 23, 720°K, 6.96. E a c h s p e c t r u m h a s been displaced 0.1 t e m p e r a t u r e increasing slightly. Although unit u p w a r d from the s p e c t r u m below it for better clar- small changes in the t e m p e r a t u r e distribuity. tion or night t e m p e r a t u r e will result in a other limitations will be discussed in the change in the scale factor and subsolar temnext section. perature, one of these two p a r a m e t e r s may The consequences of the assumed tem- be adjusted enough so that a good fit is obperature distribution must be determined. tained while the other p a r a m e t e r need not Table ! shows the area o b s e r v e d on 10° be adjusted at all. This is due to the fact that latitude strips at a phase angle of 82.2 ° and an increase in the scaling factor and an in15000
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TABLE I TEMPERATURE DISTRIBUTION USED IN MERCURY ANALYS1Sa'b
Subsolar colatitude 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-180
Temperature (°K)
Normalized area of latitude strip
725.6 722.0 714.9 703.7 688.0 666.5 637.1 594.1 513.9 272.3
0.0041 0.0145 0.0297 0.0481 0.0673 0.0852 0.0995 0.1084 0.1110 0.4321
Sum
1.000
Q Solar p h a s e angle = 82.2 °. n Subsolar temperature = 726.0°K.
2-/~m flux times area
2.5-/~m flux times area
Percentage of 2.5-/~m flux
0.759 2.541 4.713 6.500 7.205 6.509 4.615 2.222 0.344 5 × 10-~
1.808 6.109 11.560 16.460 19.120 18.473 14.473 8.204 1.852 3 × 10-4
1.0 5.2 10.9 16.3 19.7 19.6 15.8 9.3 2.2 0.0
35.409
98.061
100.0
PLANETARY THERMAL EMISSION REMOVAL crease in t e m p e r a t u r e can produce the s a m e result within the errors of the observational data. This effect could be reduced by increased spectral c o v e r a g e to say 5 /zm which is m u c h nearer to the p e a k in the thermal emission spectrum. The Mercury data were originally scaled to a value o f 0.167 at 1.02/zm which is the a p p r o x i m a t e geometric albedo of 5° p h a s e as determined f r o m data reported in Dollfus and Auriere (1974) and Vilas and McCord (1976). Thus the resultant reflectance should be a first approximation to normal reflectance and the constant C --- 1.0. I f we then c o m p u t e the p h a s e coefficients for Mercury we can c o m p u t e t l ~ emissivity. The results are shown in Table~I along with coefficients for the Moon f r o m L a n e and Irvine (1973) for comparison. The average emissivity is 0.96. This value is s o m e w h a t higher than that reported for the Moon (Murcray et al., 1970; Saari and Shorthill, 1972) and Mercury (Hansen, 1974). I f we assume that Mercury is a L a m b e r t i a n surface then • = 1 - R and we would expect to be 0.82 at 1.4/.tm and 0.65 to 0.82 at 2.5 /.tm. Thus our derived t e m p e r a t u r e a n d / o r scale factor might be slightly wrong or the initial normalization m a y have been incorrect. In a n y case we have illustrated how the thermal analysis can be constrained b y the shape o f the thermal component. H o w ever, the continuum slope is not rigidly constrained, being " c h o s e n " b y the o p e r a t o r performing the analysis. Limitations and methods to constrain the fit further are discussed in the next section. TABLE II
101
LIMITATIONS We h a v e shown two e x a m p l e s o f thermal components in planetary reflectance spectra. I f we k n o w the t e m p e r a t u r e , emissivity, and scattering properties of the surface along with the area o b s e r v e d , we can readily c o m p u t e the thermal components. This is rarely the case. I f the surface is L a m b e r t i a n the reflected c o m p o n e n t I0 is lo(/Xo) = Ro(Fsu,/ro2),
(20)
w h e r e go is the cosine of the angle of reflection and tt is the cosine o f the angle of incidence. The emissivity is then =
1 -
R0.
(21)
I f the surface follows the law of diffuse reflection for isotropic scattering, the reflected intensity is Io(0,g,g0) = ¼&o(Fsun/ro2) ( g o / g + go)H(g)H(g0),
(22)
where H(tt) and H(/~o) are the Chand r a s e k h a r H - f u n c t i o n s for the isotropic case (Chandrasekhar, 1960). The variable &o is the single-scattering albedo. The equivalent normal reflectance is then Ro = &o[/-/~(1,&)/H2(1,1)],
(23)
where the reflectance is normalized to unity at m a x i m u m . The emissivity is e
= 2(1 -
bo)I'2fo~ftH(tx,&o)dlz.
(24)
Such an analysis is quite difficult and is p r o b a b l y not warranted unless the surface is known to follow the isotropic scattering equations. E v e n in the isotropic case the emissivity is
PHASE COEFFICIENTS AND EMISSIVITY OF MERCURY
Date
4/21/76 4/22/76 4/23/76
Phase angle
Phase Phase Scale coeffi- coelfi- factor x cienta cienP
Emissivity
-78.2 ° -82.2 ° -86.0 °
0.165 0.156 0.147 0.147 0.130 0.140
0.99 0.93 0.97
6.33 6.32 6.96
a Lane and Irvine (1973). b This paper: aibedo (a)/albedo (or = 5°).
0.9 ~< • + Ro -- 1.
(25)
In the case of M e r c u r y the emissivity has been shown to be dependent on the angle f r o m the normal (W) b y the equation ~(~) = ~(0) cos ~ ~ ,
(26)
w h e r e / 3 is O. 19 _+ 0.07 at 4 5 / z m (Chase et al., 1976). I f the emissivity and t e m p e r a t u r e
102
R O G E R N. C L A R K
are poorly known we can make a reasonable fit based on the shape o f the thermal component. H o w e v e r , the thermal component could be c o m p u t e d using the wrong models giving an erroneous reflectance. Thus as in the example o f the Mercury analysis presented here there could be a slope change in the reflectance from 1.5 to 2 . 5 / z m relative to 0.6 to 1.5/xm. There could also be a very broad absorption feature extending from 1.5 to 2.5 ~m. Thus the method is insensitive to features which extend over the entire wavelength region of the thermal component. There are two ways to look for large spectral features in the reflectance curve. One is to extend the wavelength coverage so the thermal component coverage is greater than the features sought. This can be accomplished with as little as one data point at a longer wavelength. For instance, in the case of Mercury, a point at 4 or 5 p,m would greatly constrain the fit, although the wavelength coverage is likely to necessitate an analysis where emissivity is wavelength dependent. Another method is to observe the surface
I
'
i
i
I
'
at two or more different temperatures. If the temperature difference between observations is known or the temperatures at the two observations are known then the reflectance from the two observations can be correlated to constrain the fit. An example of this is shown in Fig. 8. Figure 8 is a simulation o f a planetary reflectance spectrum with thermal components at three different temperatures. If we measured the spectra with the 706 and 395 ° thermal components, we can see the large difference in the long wavelengths. For instance, the spectrum with 395°K thermal is essentially equal to the reflectance at 3 ~m. Thus, since we know the reflectance at 3 /.tm, we have a powerful constraint in the removal of the 706°K component. Of course, the more thermal component we must remove, the more likely we are to have errors in the resultant reflectance spectrum. We must also address the problem of the thermal emission tending to mask absorption features in the reflectance spectrum. Since ~ ~ 1 - Rx, a decrease in reflectivity will tend to cause an increase in emissiv-
I
'
I
'
I
'
I
,
+
d d
2. B8
I
, I , I 4.8B S. B8 WRUELEHGTH IH MICROHS
3. OB
,
S. 88
?. 88
FIG. 8. Simulated planetary reflectance plus thermal components. The curves from top to bottom represent reflectance plus 706°K thermal component; reflectance plus 600°K thermal; reflectance plus 395°K thermal; and reflectance with no thermal component.
PLANETARY T H E R M A L EMISSION REMOVAL ity. W h e n the t h e r m a l a n d reflected c o m p o n e n t s are a b o u t e q u a l
103
BARABASHOV, H. P. (1973). Photometric Map o f the Visible Face o f the Moon. Academy of the Ukraine,
Kiev. R~ ~ (1 - R x ) [ P ( h , T ) / ( F s u n ) ] r o "
(27)
t h e n a s m a l l i n c r e a s e (or d e c r e a s e ) in Rx will h a v e the effect o f d e c r e a s i n g (or i n c r e a s i n g ) the e m i s s i v i t y w h i c h will t e n d to "fill i n " a f e a t u r e in the R ' s p e c t r u m , b u t o n l y w h e n the r e f l e c t a n c e a n d e m i s s i v i t y are a b o u t the s a m e . W h e n the r e f l e c t a n c e is n e a r 1.0 the p e r c e n t c h a n g e i n e m i s s i v i t y i s large c o m p a r e d to the p e r c e n t c h a n g e in reflectivity, a n d i n v e r s e l y w h e n the reflectivity is n e a r zero. This filling in o f a n a b s o r p t i o n f e a t u r e occurs only under restricted circumstances a n d c a n be r e m o v e d b y o b s e r v i n g the surface at a different t e m p e r a t u r e . DISCUSSION We h a v e s h o w n t h a t it is p o s s i b l e to rem o v e the t h e r m a l c o m p o n e n t s f r o m p l a n e t a r y r e f l e c t a n c e s p e c t r a t h u s e x t e n d i n g the u s e f u l w a v e l e n g t h c o v e r a g e . This is i m p o r t a n t for s t u d i e s o f M e r c u r y , the M o o n , a n d a s t e r o i d s c l o s e r t h a n a b o u t 1 A U f r o m the S u n w h e r e t h e 2-/xm m i n e r a l b a n d s give c o m p o s i t i o n a l i n f o r m a t i o n a b o u t the surface ( M c C o r d e t al., 1979a). A l t h o u g h s o m e i n f o r m a t i o n a b o u t the t e m p e r a t u r e o f the s u r f a c e is o b t a i n e d , it is p r o b a b l y n o t as acc u r a t e as m e a s u r i n g the b r i g h t n e s s t e m p e r a ture in a region w h e r e the reflected solar c o m p o n e n t is i n s i g n i f i c a n t c o m p a r e d to the thermal emission.
ACKNOWLEDGMENTS I would like to thank Thomas B. McCord, Michael J. Gaffey, Richard Shorthill, Terry Jones, Robert Singer, and Lucy McFadden for reviewing the manuscript. This research was supported by NASA Grants 7323 and 7312. This is contribution no. 212 of the Planetary Sciences Laboratory.
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W. J. (1970). Infrared emissivity of lunar surface features. I. Balloon-borne observations. J. Geophys. Res. 75, 2662-2669. PETERSON, C. (1976). Private communication. PETTIT, E. (1961). Planetary temperature measurements. In Planets and Satellites (G. P. Kuiper and B. M. Middlehurst, Eds.), p. 400. Univ. of Chicago Press, Chicago. SAARI, J. M., AND SHORTHILL, R. W. (1965). Isothermal and isophotic atlas of the Moon. Contours
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