Send
requests/inquiries to sjkeihm@gmail.com
MICROWAVE
BRIGHTNESS TEMPERATURES
OF THE MOON: THE APOLLO MODEL
Stephen J. Keihm
This web page provides examples of model-generated
lunar brightness temperatures (TBs) as viewed from the
Earth, including disk
center, disk average, and digital mapping results. The intent of the web page is to alert the
radio telescope and
planetary science community of a free available
resource for using the moon as
a calibration reference as well as a tool for mapping
variations of the
lunar thermal and electrical properties
of the upper ~ 1 meter of regolith. The model
generated brightness
temperatures have been used as calibration references
since the 1980s by a
large number of radio science projects and missions,
including NASA’s Deep
Space Network (1-5), the Cosmic Background Explorer
mission (6,7), the Microwave
Limb Sounder of NASA’s Earth Observing
System (8), and the millimeter wave radiometers on the
European Space Agency’s
Odin and Steam-R satellites (9,10).
The lunar regolith
property model used to generate the
predicted brightness temperatures is based on analyses
of the Apollo 15 and 17
Heat Flow Experiment data (11-15) as well as thermophysical
and electrical property measurements of returned Apollo
samples (16-26).
Validation of the model was provided by extensive
comparisons with Earth-based
microwave measurements of the lunar frontside (27-30).
A recent confirmation of the model was provided by the
Diviner Lunar Radiometer
Experiment (31). Details of the lunar regolith model,
including depth and
temperature dependencies of the relevant thermal and
electrical properties, can
be found in the appendix of reference 32. Analyses of
second order scattering
effects, neglected in the current model, can be found in
references 33 and 34.
The regolith model is
considered regionally uniform
over the lunar front side. Bond albedo contrasts of a
factor of ~ 2 are known
to exist between mare and highland regions, producing
daytime surface
temperature differences of ~ +/-4 K relative to the
uniform model. The
albedo-induced contrasts are lessened at the microwave
wavelengths.
Mare-highland contrasts in electrical absorption
properties have also been inferred
(ref [x]), producing brightness temperature anomalies of
~ +/- 3-4 K at X-band
in regions of the full moon. These regional variations
lie well within the
estimated absolute accuracy (+/- 5%) of the Apollo-based
model predictions.
Sample outputs of the
Apollo-based lunar regolith
model, presented as brightness temperatures (TBs), are
shown below. All TB
values represent Planck black body brightness
temperatures; i.e. the calculations
weighted Planck fluxes over all relevant regolith depths
and the spectral
radiation can be computed from the Planck function for
specified wavelength and
TB values. Libration and
annual effects, less than ~
3 K deviations in the TBs, are neglected. Figure 1 shows
the model-predicted TB
phase variations at the lunar frontside
center over
the 1 mm to 10 cm range. Figure 2 shows the
disk-averaged TB phase variations
over the same wavelength range. Figures 3 and 4 display
digital maps of the
model predicted pencil beam TBs at 1.8 mm wavelength at
the full moon (Fig. 3)
and new moon (Fig. 4) phases.
Similar
data sets and digital maps can be easily generated at
specified wavelengths and
lunar phases upon request. Send requests/inquiries to
sjkeihm@gmail.com
Figure 1.
Model-generated pencil beam brightness
temperatures of the lunar frontside
disk center vs.
lunar phase for wavelengths from 1 mm to 10 cm
Figure 3.
Model-generated digital brightness
temperature map of the full moon at a wavelength of 1.8
mm. The digital pencil
beam TB values are separated by 0.1 lunar disk radii in
the lunar frontside image
plane. Note the north-south (top to bottom)
symmetry (libration effects
neglected) and east-west
(right to left) asymmetry due to the diurnal phase lag.
Figure 4.
Model-generated digital brightness
temperature map of the new moon at a wavelength of 1.8
mm. The digital pencil
beam TB values are separated by 0.1 lunar disk radii in
the lunar frontside image
plane. Note the north-south (top to bottom)
symmetry (libration effects
neglected) and east-west
(right to left) asymmetry due to the diurnal phase lag.
References:
1. Morabito, D.D. (1999), The
Characterization of a 34-Meter
Beam-Waveguide Antenna at Ka-band
(32 GHz) and X-band
(8.4 GHz), IEEE Antennas and Propagation Magazine, vol.
41, no. 4, pp. 23–34.
2. Morabito, D. D., "Lunar
Noise-Temperature Increase
Measurements at S-Band, X-Band, and Ka-Band Using a
34-Meter-Diameter Beam-Waveguide Antenna," IPN PR
42-166, pp. 1-18, Jet
Propulsion Laboratory, August 15, 2006.
3. Imbriale, W. A., "Computing the
Noise Temperature
Increase Caused by Pointing DSS 13 at the Center of the
Moon," IPN PR
42-166, pp. 1-10, Jet Propulsion Laboratory, August 15,
2006.
4. Morabito, D., M. Gatti, and H. Miyatake, "The Moon as a
Calibration Load for the
Breadboard Array," IPN PR 42-172, pp. 1-21, Jet
Propulsion Laboratory, February
15, 2008.
5. Morabito, D. D., "Dynamic
Telemetry Link Advantage
When Tracking a Lunar Orbiter with a 34-m Antenna at 2.3
GHz and 8.4 GHz,"
IPN PR 42-200, pp. 1-17, Jet Propulsion Laboratory,
February 15, 2015.
6.
Collaboration with
COBE Co-I Michael Janssen of the Jet Propulsion
Laboratory, California
Institute of Technology, Pasadena CA.
7.
Jackson, P. et al.
(1991), “COBE DMR Data processing Techniques”, in
Proceedings of the 1st
Annuaol Conference on
Astronomical Data Analyses
Software and Systems, NOAO, Tucson, AZ.
8.
Collaboration with MLS
Co-I Richard Cofield of the Jet Propulsion Laboratory,
California Institute
of Technology,
Pasadena CA.
9.
Collaboration with
Peter Forkman of Chalmers
University of Technology,
Gothenburg, Sweden
10.
Premier-CORSA Final
Report, ESA Contract No.: 4200022848/09/NL/C7, November
2013.
11.
Langseth,
M.G. Jr., S.P. Clark Jr., J.L. Chute Jr., S.J. Keihm,
and A.E. Wechsler (1972),
Heat Flow Experiment, in Apollo 15
Preliminary Science Report, Section 11, NASA
SP-229, U.S. Gov't. Printing
Office,
12.
Langseth,
M.G., S.J. Keihm , and J.L.
Chute Jr., (1973),
Heat-flow experiment. In Apollo 17
Preliminary Science Report, pp. 9-1 to 9-24, NASA
pub. SP330, U.S. Gov't.
Printing Office, Washington D.C.
13.
Keihm, S.J., J.L.
Chute Jr., K. Peters, and M.G. Langseth
Jr. (1973),
Apollo 15 measurement of lunar surface brightness
temperatures: Thermal
conductivity of the upper 1.5 meters of regolith, Earth
and Planet. Sci.
Letters, Vol. 19, pp. 337-351.
14. Keihm,
S.J. and M.G. Langseth
(1973), Surface brightness
temperatures at the Apollo 17 heat flow site: Thermal
conductivity of the upper
15 cm of regolith, Proc. Lun.
Sci. Conf. 4th,
pp. 2503-2513.
15.
Langseth,
M.G., S.J. Keihm, and K. Peters (1976), The revised
lunar heat flow values,
Proc. Lunar Sci. Conf. 7th, Geochimica
et Cosmochimica Acta, Vol. 3, The
Moon and Other Bodies, pp. 3143-3171.
16. Birkebak,
R.C. (1974), Thermophysical
properties of lunar materials from the Apollo missions,
in Advances in Heat Transfer (T.F. Irvine,
Jr., and J.P. Harner, Eds, Vol. 10, pp. 1-37,
Academic Press, New York.
17.
Horai,
K., J.L. Winkler Jr., S.J. Keihm, M.G. Langseth, and
J.A. Fountain (1977), Thermal conductivity of two Apollo
17 drill-core samples
70002 and 70006: A preliminary result, Proc. Lunar Sci.
Conf. 8th, abstract,
pp. 455-456.
18.
Robie,
R.A., B.S. Hemingway, and W.H. Wilson (1970), Specific
heats of lunar surface
materials from 90 to 35 degrees Kelvin, Science 167, pp.
749-750.
19. Carrier,
W.D. III, S.W. Johnson, L.H. Carrasco, and R. Schmidt
(1972), Core sample depth
relationships Apollo 14 and 15, Proc Lunar Sci. Conf. 3rd, pp.
3213-3221.
20. Carrier,
W.D. III, J.K. Mitchel, and A. Mahmood (1973), The
relative density of lunar
soil, Proc. Lunar Sci. Conf. 4th, 2403-2411.
21. Clegg,
P.E., Pandya, S.J., Foster, S.A., and Bastin, J.A.
(1972), Far infrared properties of lunar rock, Proc.
Lunar Sci. Conf. 3rd,
pp. 3035-3045.
22. Katsube,
T.J. and Collett, L.S.
(1973), Electrical characteristics of Apollo 16 lunar
samples, Proc. Lunar Sci.
Conf. 4th, pp. 3101-3110.
23. Bassett,
H.L. and R.G. Shackleford
(1972), Dielectric properties
of Apollo 14 lunar samples at microwave and millimeter
wavelengths, Proc. Lunar
Sci. Conf. 3rd, pp. 3157-3160.
24. Birkebak,
R.C. and C.J. Cremers
(1970), Directional spectral and total reflectance of
lunar material,Proc.
Apollo 11 Lunar Sci. Conf. V. 3, pp. 1993-2000.
25.
Gold, T., F. Bilson,
and R.I. Baron (1976), Electrical of Apollo 17 rock and
soil samples and a
summary of the electrical properties of lunar materials
at 450 MHz frequency,
Proc. Lun. Sci. Conf. 7th,
pp. 2993-2603.
26. Bussey,
H.E. (1979), Microwave dielectric measurements of
lunar soil with a coaxial line resonator method, Proc.
Lunar Sci. Conf. 10th,
pp. 2175-2182.
27.
Keihm, S.J. and M.G. Langseth
(1975), Lunar microwave
brightness temperature observations reevaluated in the
light of Apollo program
findings, Icarus, Vol. 24, pp. 211-230.
28.
Keihm, S.J. and M.G. Langseth
Jr. (1975), Microwave emission spectrum of the
moon: Mean global heat flow and average depth of the
regolith, Science, Vol.
187, pp. 64-66.
29.
Gary,
B.L. and S.J. Keihm (1978), Interpretation of
ground-based microwave
measurements of the moon using a detailed regolith
properties model, Proc.
Lunar Plan. Sci. Conf IX,
pp. 2885-2900.
30.
Keihm, S.J. and B.L.
Gary (1979), Comparison of theoretical and observed l3.55
cm brightness
temperature maps of the full moon, Proc. Lunar Plan.
Sci. Conf. X, pp.
2311-2319.
31.
Vasavada,
A. R., J. L. Bandfield, B.
T. Greenhagen,
P. O. Hayne, M. A. Siegler,
J.-P. Williams, and D. A.
Paige (2012), Lunar
equatorial surface temperatures and
regolith properties from the Diviner Lunar Radiometer
Experiment, J. Geophys.
Res., 117, E00H18, doi:10.1029/2011JE003987.
32.
Keihm, S.J. (1984),
Interpretation of the lunar microwave brightness
temperature spectrum:
Feasibility of orbital heat flow mapping, Icarus, Vol.
60, pp. 568-589.
33.
Keihm, S.J. and J.A. Cutts
(1981), Vertical structure effects on planetary
microwave brightness temperature measurements:
Applications to the lunar
regolith, Icarus, Vol. 48, pp. 201-229.
34.
Keihm, S.J. (1982),
Effects of subsurface volume scattering on the lunar
microwave brightness
temperature spectrum, Icarus, Vol. 52, pp. 570-584.