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David M. Le Vine and Saji Abraham 

Goddard Space Flight Center, Greenbelt, MD 20771 


The spectral window at L-band (1.4 GHz) is important for passive remote sensing 
of soil moisture and ocean salinity from space, parameters that are needed to understand 
the hydrologic cycle and ocean circulation. At this frequency, radiation from 
extraterrestrial (mostly galactic) sources is strong and, unlike the constant cosmic 
background, this radiation is spatially variable. This paper presents a modern radiometric 
map of the celestial sky at L-band and a solution for the problem of determining what 
portion of the sky is seen by a radiometer in orbit. The data for the radiometric map is 
derived from recent radio astronomy surveys and is presented as equivalent brightness 
temperature suitable for remote sensing applications. Examples using orbits and antennas 
representative of those contemplated for remote sensing of soil moisture and sea surface 
salinity from space are presented to illustrate the signal levels to be expected. Near the 
galactic plane, the contribution can exceed several Kelvin. 


The spectral window 1.400-1.427 GHz (L-band) reserved for passive use only is 
important for measuring parameters of the Earth surface such as soil moisture and ocean 
salinity that are needed for understanding the hydrological cycle and energy exchange 
with the atmosphere. Being able to make observation at the long wavelength end of the 
microwave spectrum is critical to these measurements. In the case of soil moisture, long 
wavelengths increase penetration into the soil and mitigate effects of attenuation through 
the vegetation canopy and the effects of surface roughness. In the case of sea surface 
salinity, long wavelengths increase the sensitivity to salinity and minimize the 
dependence on surface temperature and roughness. 

However, at L-band radiation from extraterrestrial sources is not negligible. For 
example, one needs to know the brightness temperature of the celestial sky to correct for 
down-welling radiation that is reflected from the surface into the receiver [1, 2]. This 
contribution is of particular concern for remote sensing of sea surface salinity because the 
surface is a good reflector and the salinity signal itself is relatively small [3, 4, 5], The 
problem is exacerbated by the fact the down-welling radiation is not a constant across the 
celestial sky, being significantly stronger in the galactic plane [4, 6]. This is a particular 
concern in the case of remote sensing from space because the portion of the celestial sky 
that contributes radiation changes rapidly as the sensor moves through its orbit. In 
addition, the orbit itself may change its orientation with respect to the celestial sky as is 

the case with sun-synchronous orbits that precess as the Earth rotates around the Sun (to 
keep the orientation of the orbit with respect to the sun constant). 

Previous estimates of the magnitude and distribution of galactic radiation for use 
in remote sensing [4, 6, 7] have been rather course. However, recent surveys of the radio 
sky at 1.4 GHz [8, 9, 10, 11, 12, 13] have made it possible to produce maps with 
sufficient spatial and radiometric accuracy to be relevant to remote sensing applications. 
This paper present a modern map of the radiometric sky at L-band and a solution to the 
problem of determining the portion of the sky seen by a down-looking radiometer in 
orbit. The data is presented as equivalent brightness temperature for remote sensing 
applications. Examples using orbits and antennas representative of those contemplated 
for remote sensing of soil moisture and sea surface salinity from space are presented to 
illustrate the signal levels to be expected. 


There are three important sources of radiation within the L-band window at 1.413 
GHz that originate outside of our solar system: The cosmic microwave background 
(CMB), discrete line emission from (mostly) neutral hydrogen and continuum emission 
such as is emitted by thermal sources. The latter two are the subject of this paper but all 
three are discussed for completeness. 

A. Cosmic Background: 

The cosmic microwave background radiation is a remnant of the origin of the 
universe in a "big bang". Although the recent cosmological research has focussed on 
details of its spatial distribution [14], these variations (milli-Kelvin) are not important for 
applications such as remote sensing of soil moisture or ocean salinity from space. For 
remote sensing applications, the cosmic background radiation is essentially constant in 
both space and time with a value of about 2.7 K. This background radiation can 
contribute to a measurement with a down-looking radiometer in a direct manner if, for 
example, the radiometer antenna has side lobes above the horizon. It also can contribute 
via reflection of down-welling radiation off the surface [1]. The latter is especially 
important in remote sensing of the ocean surface where the reflection coefficient is 
relatively large. The cosmic background will be included in the examples to be presented 
here; but, since it is uniform and constant over the spectral window, it is relatively easily 
included in radiometer retrieval algorithms [1,7]. 

B. Line Emission: 

The window at 1.413 GHz was protected for passive use because of the interest in 
emission from a hyperfine transition in neutral hydrogen that occurs in this window. The 
original proposal that such radiation could be detected from neutral hydrogen in our 
galaxy is attributed to Oort and van de Hulst, and the first observations were made by 
Ewen and Purcell in 1951 [12]. This radiation provides information on the temperature, 
density and motion of hydrogen. The radiation is concentrated around the plane of the 

galaxy, but clouds of hydrogen are widespread and no direction is observed without some 
such radiation. 

Several surveys of this source of radiation have been made [15, 16, 17, 18, 19, 
20]. Recently, Hartman and Burton [12] motivated by the high quality, all-sky surveys 
being made at other wavelengths, reported a new survey. The Leiden/Dwingeloo survey 
(Table I) used a 25-meter radio telescope and covered the sky above declination of -30°. 
This survey was recently complemented by data collected with the 30 meter dish antenna 
at the Instituto Argentino de Radioastronomia (lAR) and reported by Arna! et al [13]. The 
lAR survey (Table I) covered declinations south of -25 degrees filling in the missing 
portions of the southern sky. The result is data with sufficient spatial resolution (0.5° x 
0.5°) and radiometric resolution (AT < 0.1 K) to be applicable to remote sensing at L- 
band from space, including high-resolution sensors proposed for the future (e.g. a spatial 
resolution of 0.5° x 0.5° corresponds to an aperture of about 25 meters). 

C. Continuum Radiation 

In addition to the discrete spectra associated with atomic transitions as in 
hydrogen above, there is a continuum of radiation from extra-terrestrial sources. This 
radiation can be divided into thermal and non-thermal sources. Thermal sources have a 
spectrum (amplitude versus frequency) similar to that of blackbody radiation. At L-band, 
the Rayleigh- Jeans law applies and the power increases with frequency as f . Non- 
thermal sources are sources whose spectra behave differently. An example is 
synchrotron radiation from relativistic electrons, in which case the spectrum at L-band 
decreases with frequency roughly as F^''^ [21]. The source of continuum radiation may 
be localized in space (discrete sources) or may be of a spatially continuous nature (diffuse 
or unresolved discrete sources). The source of the radiation is mostly galactic because 
these sources are closest, but there are also strong extra-galactic sources such as the 
"radio galaxy" Cygnus A [21]. 

There have been several surveys of the continuum radiation at 1 .4 GHz [22, 23, 
24, 25, 26, 27]. None of these surveys covered the entire sky and they use different 
bandwidths and the measurements were made with differing sensitivity. For the most 
part, they consist of a map of discrete sources. However, for applications to remote 
sensing of the Earth, it is desirable to have the integrated signal from a particular 
direction in the sky (i.e. power from all sources, discrete and continuous), because 
antennas likely to be employed in space in the foreseeable future will not resolve 
individual sources. The recent survey with the Stockert telescope at Bonn University [8], 
[9] provides data in this format. The antenna had a half-power beam width of about 0.5 
degrees. The sensitivity of these measurements is about 0.05 K and the absolute 
calibration (zero level accuracy) is 0.5 K. This survey (Stockert survey; Table I) covers 
all of the northern sky and the southern sky to -19° declination. The data includes all 
sources except for a region around Cassiopia A which was too strong. Recently, the 
survey of the southern sky was completed using the 30-m radio telescope of the Instituto 
Argentino de Radioastronomia [10], [11]. The lAR continuum survey (Table I) covers the 

southern sky for declination below -10° with spatial resolution and sensitivity similar to 
that of the Stockert survey. 

III. DATA in Remote Sensing Format 

It is common practice in passive microwave remote sensing to treat the scenes as 
thermal sources and the receivers as narrow bandwidth devices [7, 21]. In the Rayleigh- 
Jeans limit, this permits one to describe the measurements and scenes in terms of an 
equivalent "brightness" temperature. For sources that are not blackbodies, the brightness 
temperature is the product of the physical temperature and emissivity of the surface. The 
emissivity is a function of the properties of the surface, hopefully including the 
parameters of interest. This is the approach proposed to measure soil moisture and sea 
surface salinity [4, 28, 29] in which case water and salt change the emissivity sufficiently 
that the resulting changes in brightness temperature can be detected. 

In the sections below, the data from the radio astronomy surveys will be presented 
in the form of an equivalent blackbody temperature. The data will be presented as an 
equivalent thermal source normalized such that total power is P = kTaAB. For this 
purpose, a bandwidth, AB = 20 MHz, has been assumed. This represents a reasonable 
maximum for the window at 1 .41 3 GHz after allowances for filter shape. 

A. Line Emission 

The line emission has a relatively narrow spectrum [21]. For hydrogen at rest, it 
occurs at the frequency associated with the hyperfine transition at 21.106 cm. However, 
the line is shifted by motion of hydrogen relative to the observer (doppler shift) and 
spread by thermal energy of the gas (collisions and vibrations). But, even with large 
Doppler shift and thermal broadening, the spectrum of this radiation is relatively narrow. 
For example, the Leiden/Dwingeloo sui-vey [12] and lAR survey [13] cover the velocity 
range from ^50 to +400 km/s (Table I) which corresponds to a frequency range of less 
than ±2.2 MHz about the center (at rest) frequency of 1 .42 GHz. The two surveys both 
report power integrated over the spectrum of the line. The integrated power is given in K- 

To convert into a format useful for remote sensing, this data was first converted to 
K-MHz using the standard form for Doppler shift: v = Vo (1 - v/c) where v is velocity. 
Then, this value was divided by 20 MHz to convert it into an effective brightness 
temperature. The brightness temperature, Tb, is the temperature of a blackbody that 
observed with an ideal receiver with a bandwidth of AB = 20 MHz, will give the power 
(P = kTfiAB) reported in the radio astronomy surveys. The data can be converted for use 
with receivers with other bandwidth with the obvious re-normalization. (Of course, this 
only makes sense if the receiver bandwidth is centered on the line and is greater than ±2.2 

The data in the above form is shown in Figure 1 (top). The units are Kelvin and 
the plot is in celestial coordinates. The "U' shape region of high brightness temperature 

is the plane of the galaxy (which is tilted with respect to an observer in the celestial 
coordinate system). The effective brightness temperature is small almost everywhere 
except in the galactic plane where equivalent blackbody temperatures on the order of 3 K 
can occur. 

B. Continuum Radiation 

For the continuum radiation, the data used here was the Stockert survey [9] for the 
northern sky together with the more recent lAR survey [10] for the southern sky (Table 
I). In both cases, the data are in the form of total power over the bandwidth of the 
receiver with the exception that the line emission from hydrogen was excluded (removed 
with a narrow filter at the line center). The power represents radiation from all sources 
within the beam, discrete and unresolved and includes thermal and non-thermal sources. 
However, Cassiopeia A, which was too strong to be included in the Stockert survey, and 
a small region of the sky around Cassiopeia A is excluded from the data. 

For both surveys, the data are in the form of power integrated over the pass-band 
of the radiometer receiver. The effective bandwidth was about 18 MHz and 13 MHz for 
the Stockert and Villa Elisa surveys, respectively (after correction for the filter to remove 
line emission). The Villa Ellisa antenna (30 m) was under-illuminated to match the 
resolution of 25 m antenna used in the Stockert survey [10, 11]. 

The data from the Stockert survey [9] normalized to a bandwidth of 20 MHz is 
shown in celestial coordinates in bottom panel of Figure 1 . (All of data in Figure 1 has 
been converted to celestial coordinates using the J2000 epoch [21, 32]). As in the case of 
the line emission from hydrogen, the strongest radiation tends to lie along the plane of the 
galaxy as is evident on the far right hand side. Also notice the white spot at the upper 
right (Declination 60° and Right Ascension 355°) which is the data missing around 
Cassiopeia A. Data exists for the portion of the southern sky missing in Figure 1. 
However, this data (LAR continuum survey; Reich, 2001) has not been released at the 
resolution shown in Figure 1. The data has been provided for use in this paper at lower 
resolution [30] and is presented and discussed in Sections IV-V. 

C. Examples 

Figure 2 shows examples of the magnitude and spatial distribution of the data in 
more detail. The data shown are cuts through the color-coded maps in Figure 1 at fixed 
declination of 0°, 20° and 40°. On the left side of Figure 2 is shown the effective 
brightness temperature due to line emission from hydrogen (from Figure 1; top) as a 
function of right ascension and on the right side is shown the effective brightness 
temperature for the continuum radiation (from Figure 1 ; bottom). The peaks in these 
curves are associated with crossing the galactic plane. Notice that the contribution from 
the continuum is considerably larger than from the line emission from hydrogen. In 
particular, peak values of effective brightness temperature from line emission are on the 
order of 2 K whereas the peak value due to continuum radiation is nearly 20 K. Also, 

notice that the distribution is quite complex with the obvious peak at the galactic plane 
but with levels that depend on where the intersections with the galactic plane occur. 

IV. Effect of Antenna Beam 

The apparent brightness temperature actually seen in a remote sensing application 
will depend on the antenna employed. The antenna smoothes (integrates) the incident 
radiation and, as a result, the observed value can be significantly different from the peak 
values in Figure I. This is especially true in the vicinity of the galactic plane, which is 
relatively narrow. 

In order to understand the effect of the antenna, one could integrate over the 
portion of the celestial sky contributing to the measurement. That is, take the convolution 
with the power pattern of the antenna (e.g. Section 3.4 of [21]). However, it is equivalent 
to perform the convolution over the entire sky first and then locate the portion of the sky 
contributing to the measurement. This approach has the advantage of presenting the 
smoothed data in its entirety independent of the particular application. This has been 
done here. 

The data is presented in Figure 3 for an antenna with a Gaussian beam with a full 
width at half maximum (FWHM) of 10°. The details of the integration are presented in 
Appendix A. The choice of 1 0° beam width was made to indicate the effect of smoothing 
but to remain conservative and not overly smooth the data for remote sensing 
applications. Figure 3 (top) shows the smoothed data for line emission and Figure 3 
(bottom) is the smoothed data for the continuum radiation. In the case of the continuum 
radiation, the data from the Stockert survey (Table I) was smoothed as outlined in 
Appendix A and the data for the southern sky (lAR continuum survey) was provided to 
us with the 10 degree smoothing (courtesy of P. Reich [30]). Notice that the general 
features of the high-resolution maps remain in the smoothed data. 

Figure 4 shows detail for cuts through the data at fixed declination of 0°, 20° and 
40°. The smoothed line emission is shown on the left and the continuum radiation is on 
the right. Notice that the general features evident in the high-resolution data (Figure 2) 
remain, although the large difference in the peak value between line emission and 
continuum at 40 degrees is much reduced. This reflects the very narrow nature of the 
peak in the continuum radiation on the galactic plane. Also, notice that away from the 
galactic plane, the continuum radiation (~ 1 K) is greater than from line emission (~ 0.05 

Figure 5 is an example at 20 degrees declination of the total from the three 
contributions: Cosmic background, line emission and continuum. Shown at the top is the 
original and smoothed data for the line emission. In the middle is the original and 
smoothed data for the continuum radiation. The bottom panel shows each of the 
components (smoothed line emission, smoothed continuum and the cosmic background) 
together with the sum. Notice that the plane of the galaxy is evident and that the 
contribution of the continuum and line emission is clearly important and comparable to 

the CMB. The peak around the galactic plane depends on declination and, for example, 
would be much larger if a declination of 40 degrees were shown (see Figures 2 and 4). 

It is clear from Figures 1-5 that the background radiation is spatially complex. 
Large values are possible along the galactic plane. On the other hand, there are regions 
near the galactic pole where the line emission and continuum radiation are small (< 1 K) 
and the cosmic background dominates. Clearly, it is important to know what portion of 
the "sky" is contributing to a particular measurement. This problem is addressed in 
Section V. 


The data from the radio astronomy surveys indicates that the background 
radiation can be significant and highly variable. Consequently, for remote sensing 
applications it is important to know what portion of the celestial sky is contributing to a 
particular measurement. To address this problem, imagine a radiometer at L-band in 
orbit circling the Earth with its antenna pointing down. The goal is to determine the 
contribution from the radio sky (down-welling radiation that is reflected into the 
antenna), which must be taken into account at each position in this orbit. The input is the 
data given in Figure 1 (or Figure 3) normalized to the radiometer bandwidth, plus a 
constant of 2.7 K that is added to account for the cosmic microwave background. 

The solution can be found by tracing rays from the antenna to the surface and 
computing how they are reflected toward the sky. For example, a flat, specular surface 
behaves like a mirror and the solution can be obtained by placing the antenna at its 
conjugate point behind the surface and looking out in the direction of the specularly 
reflected ray. The antenna pattern is unchanged, but it does undergo a mirror image 
change of symmetry (i.e. right hand symmetry becomes left hand). One computes the 
power reflected into the antenna by integrating the mirrored antenna pattern over the sky. 

One can follow a similar procedure to solve the problem for a curved earth. The 
solution is outlined in Appendix B and solved for an ideal case (spherical earth, circular 
orbit and specular surface). Examples are shown in Figure 6 for the case of an antenna 
that looks to the side in a plane perpendicular to the orbit (e.g. as in a cross track scan). 
At the left are the smoothed data describing the radio sky at L-band in celestial 
coordinates (sum of line emission and continuum) seen by the antenna (Gaussian power 
pattern with a 10 degree beam width). Shown on the smoothed data is the locus traced by 
the reflected ray at bore-sight for an antenna looking to the right at 6, = 30 degrees in a 
circular orbit with inclination angle is 95 degrees (angle y in Equations 4B). It is possible 
to plot orbits on the original data and then integrate over the antenna beam. However, as 
mentioned above, it is more efficient to integrate first and then plot the orbits. This what 
has been done in creating Figure 6. The panels on the right show the brightness 
temperature along this locus as a function of declination. Four values are plotted: The 
line emission, continuum emission, CMB (the straight line) and the total. 

The shape of the loci in Figure 6 depends on the incidence angle of the antenna 
and the inclination of the orbit. The position of the locus (i.e. center of the curve) is 
determined by the intersection of the plane of the orbit with the plane of the equator. This 
is illustrated by the two examples shown in Figure 6 that differ only in that the 
intersection of the plane of the orbit has been rotated by 90 degrees. These two examples 
show that keeping track of changes in the orbit, for example due to precession, can be 
important for determining the background radiation. This is illustrated further in the 
section below using the orbit for a mission proposed several years ago to measure soil 
moisture from space. The problem of relating the orbit as seen in an earth-centered 
coordinate system (e.g. equatorial intersection as a function of longitude and local time) 
to celestial coordinates is discussed in Appendix C. 


An example is presented here for a sun-synchronous orbit with a 6am/6pm 
equatorial crossing. This is an orbit commonly selected for remote sensing of soil 
moisture [28], [31] and was the orbit for a sensor proposed to measure soil moisture from 
space called HYDROSTAR [28]. A sun-synchronous orbit is one oriented such that all 
observers on the Earth sees the satellite pass overhead at the same local time. It is the 
orbit of choice for many remote sensing applications because the local time of 
observation is constant. In practice, this orbit generally has a high inclination (passes 
close to the pole) and the equatorial crossing time precesses a bit about the nominal 

In order to remain in the same local orientation with respect to the sun, the orbit 
must precess in celestial coordinates as the earth rotates about the sun. The change is 
about 1 degree per day. As a result of the precession, the position of the locus of the 
reflected rays in celestial coordinates (Figure 6) will drift across the sky going through a 
change of 360 degrees in right ascension each year. The problem of locating the orbit in 
celestial coordinates given the local time of equatorial crossing is the problem in 
astronomy of transforming local time into sidereal time. The solution used here is given 
in Appendix C. Once the orbit is located in celestial coordinates, the procedure outlined 
in Section V above is followed to plot the locus of the reflected rays on the sky. (This 
amounts to neglecting changes of the orbital plane during one period, about 90 minutes.) 

Figure 7 shows examples with the HYDROSTAR orbit for several times of the 
year starting with March 15, 2002. The calculation is for the antenna described above 
(10° Gaussian beam) looking right at 5 degrees (0i = 5). The orbit inclination is 95 
degrees. The curves on the left show the orbit in celestial coordinates. The curves on the 
right show the total effective background radiation, the sum of the three terms, line 
emission, continuum and CMB. Notice that the total varies from a little less than 4 K to 
nearly 1 1 K. The values change over the orbit (i.e. in one period). Also, the distribution 
over the orbit varies seasonally (i.e. with the time of year). The values would also change 
if the incidence angle, Gj, where changed. 


In addition to the uniform cosmic background radiation (CMB), there is additional 
radiation (line emission from hydrogen and a continuum background) that must be taken 
into account for remote sensing at L-band. In contrast to the CMB, this additional 
radiation is spatially varying and strongest in the direction of the plane of the galaxy. 
The effective brightness temperature of down-welling radiation from these sources that is 
reflected from the surface into the radiometer depends on the antenna beam width and 
surface conditions. For, a perfectly reflecting surface (reflectivity of unity) and an 
antenna with a beam width on the order of 10 degrees, the peak contribution from sources 
other than the CMB is on the order of 1 - 6 K, varying with the orientation of the sensor 
and orbit. The fact that this signal can change both seasonally and with the location of 
the sensor in its orbit makes its presence an important issue for remote sensing of the 
Earth. The importance of the background radiation depends on the applications and 
surface conditions. For example, it is less an issue for applications such as the remote 
sensing of soil moisture where the signal is large and the reflectivity at the surface small 
(on the order of 0.3). However, it is more important for remote sensing applications such 
as the measurement of sea surface salinity where the reflectivity of the surface is large 
(on the order of 0.7) and the signal is small (on the order of 0.5 K per psu). In the latter 
case, careful mapping of the down-welling radiation will be an important issue. 


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Goutoule, C. Tabard and A. Lannes, "The soil moisture and ocean salinity mission: 
an overview," in Microwave Radiometry and Remote Sensing of the Earth's Surface 
and Atmosphere. (Pampaloni P. and S. Paloscia, Eds.), VSP, The Netherlands, pp. 
467-475, 2000. 

[32] D. A. Vallado and W. D. McClain, Fundamentals of Astrodynamics and 
Applications. McGraw.Hill, 1997. 

Table I: Summary of the survey parameters 







Hydrogen Survey 


Hydrogen Survey 




5 > -30° 

0°< a < 360° 

HPBW (effective) 






50 mK 

-50 mK 

70 mK 

70 mK 

Velocity range 



-450< vlsr < 400 km/s 

-450< vlsr < 400 km/s 

Velocity resolution 



1 .03 km/s 

1.27 km/s 



13 MHz 

Antenna diameter 

25 m 

30 m 

25 m 

30 m 

Notes: a is right ascension and 5 is declination. 


Integration Over The Antenna Beam 

The objective is to compute the effective brightness temperature, Tb, of the 
background radiation when observed with an antenna representative of those one might 
use for remote sensing from space. In particular, if Pn(0) is the normahzed power pattern 
of the antenna, it is desired to compute: 

TbCQo) = (l/Qa)lT(Q)Pn(Qo-f^)sin(0)d(pd0 lA 

Where, Q. denotes a direction (point in the celestial sky) with spherical coordinates ((p,0), 
dQ = sin(6) dcp d9 and Qa is the beam solid angle: 

Qa = jPn(Q)dQ 2A 

The calculations will be done here for an antenna with a Gaussian power pattern with full 
width at half-maximum (FWHM) of 6b: 

Pn(e) = exp{-a(2e/eb)^} 3 A 

where a = ln(2) = 0.6931. 

Since the data is presented at discrete points in celestial coordinates, this suggests 
doing the integration (Equation lA) in celestial coordinates: a = cp; 8 = 7r/2 - 9. One 

TB(ao,6o) = (l/Qa) 2T(ai,5.)Pn(0.)cos(5,) AaA6 4A 

The sum is over all data points within the beam. The major issue is to determine the 
angle ©i from antenna boresight at (ao,5o) to the data at point (0Cj,6i). The angle needed is 
the polar angle in spherical coordinates (Equation 3A). This angle can be found by 
rotating coordinates from the original system (z-axis toward the north pole) into one with 
the z-axis aligned with the antenna boresight. (See Appendix B.) One obtains: 

cos(0i) = cos(8o) cos(5,) cos(0Co - oci) + sin(8o) sin(Si) 5A 

The calculations in the text (Figure 3) have been carried out for the case 9b = 10°. This 
was done with a simple search in which each ©i is computed for each point (ai,5i). The 
sum should be over all space, but the antenna beam decreases very quickly and it was 
found that an integration out to about ©, = 1.5 6b was adequate. Also, to reduce the 
computational time, the antenna bore sight (oCo, So) was stepped across the map in 1° x 1° 


Appendix B 

Location of Antenna Bore Sight on Celestial Sky 

Imagine a satellite in orbit about Earth. Assume that the plane of the orbit is fixed 
and independent of rotation of Earth about its axis. Also imagine a sensor on this satellite 
with an antenna that looks down toward the Earth surface. It is desired to determine the 
radiation from the celestial sky that is reflected from the surface into the antenna. The 
objective of this appendix is to determine where on the celestial sphere this radiation 
originates and to trace the locus of this spot as the satellite rotates in its orbit. 

The solution is found by, tracing rays from the antenna to the surface and 
computing how they are reflected toward the sky. To solve the problem, make the 
following assumptions: 

1. The Earth is spherical; 

2. The orbit is circular; 

3. The Earth surface is specular. 

In actuality the power received by the radiometer will depend on the properties of the 
surface (roughness, dielectric constant, etc.), but since these are specific to each 
application, they are being ignored here. The ideal case will be an upper bound. 

First consider the case when the antenna looks across track (i.e. perpendicular to 
the orbit) at an angle 9i. The geometry is given in Figure IB where Re is the radius of the 
Earth and h is the altitude of the satellite above the surface. The specular angle is 0s and 
is given by: 

Bs = sin-'{ [(Re + h)/Re]sin(e,) } IB 

Obviously there is an upper limit, 9, = sin''(Re/(Re + h)), above which rays no longer 
encounter the Earth. For larger angles, the antenna receives radiation directly from the 
sky in the direction of the antenna beam. However, when this limit is not exceeded, the 
radiation incident on the antenna comes from the direction of the specularly reflected 
rays. Since, the celestial sources are very far away, these rays can be assumed to come 
from the center of the Earth (or Sun) with negligible error. The curvature of the Earth 
will cause slight divergence of the rays and a mirror-image change in rotational 
symmetry. To a first approximation, the divergence will be neglected. Also, only 
antennas with rotationally symmetric antenna patterns, for which the change in symmetry 
is unimportant, will be considered. With these assumptions, the radiation can be 
calculated by translating the antenna to the center of the Earth and imagining that it looks 
out in the direction of the reflected ray (i.e. 0s). 

Now consider the motion of the satellite in orbit. The plane of the orbit is defined 
by its normal, the vector ON in Figure IB, using the right hand rule with respect to the 
direction of rotation of the satellite. As the satellite rotates, the ray in the direction Oj 
traces a cone with interior angle, Q, with respect to the normal: 


Q = 90 - 265 + e,. 2B 

The last step is to plot this ray in celestial coordinates. This is done in the 
following steps. First imagine an earth-centered coordinate system with the z-axis in the 
direction of the north pole and the x-axis pointing in the direction of the vernal equinox 
(zero right ascension). Standard spherical coordinates (6,(p) are related to celestial 
coordinates "declination", 5, and "right ascension", a, as follows: 

a = (p 3B 

6 =90-6 

Now, rotate coordinates to a new system with the z'-axis in the direction of the normal to 
the orbit. Rotate as follows: 

1 . About the z-axis through an angle, i// 

2. About the new y'-axis through an angle, y 

In the new, spherical coordinate system {9',(p'), the desired ray traces a cone. This ray is 
given by, 6' = constant = H, and with (p' rotating through 360 degrees as the satellite 
traces it orbit (i.e. < ^' < 2%). The path in celestial coordinates is obtained by 
transforming back to the original (unrotated) coordinate system. The transformation is: 

(p = tan" 

sine [sin \|/ cosy cos (p -I- cos\|/ sincp]-!- cos 9 sinvj/ siny 
sin0 [cos\(/ cosy cos(p - sin\|/ sincp]-!- cos9 cos\|/ siny 

e = tan ■ 

Isin^O [cos^y cos'cp'-f-sin^cp'] -f- cos^O' sin'y -H 0.5 sin(2B') sin(2y)cos(p' 
[cosG' cosy - sin0'cos(p'sin y]^ 


Substituting Equations 4B into Equations 3B, locates the locus of the ray from the 
antenna bore sight in celestial coordinates. The orbit itself is in a plane perpendicular to 
z' (z-axis in the rotated system) and is defined by the rotation angles y/ and y. In 
particular, yh the "inclination" of the plane of the orbit with respect to the z-axis (north 
pole), and ^determines the equatorial crossing. Because of the choice (definition) made 
for \j/, this occurs on the y'-axis. Since, right ascension is measured from the x-axis in 
celestial coordinates, one has that the right ascension of equatorial crossing of the orbit is: 
0.= y/- Till. 

The case of a sensor with an antenna employing a conical scan is treated in the 
same manner as described above (for a cross track scan). In the case of a conical scan, a 
ray from the center of the Earth through the satellite identifies defines "nadir" (the vector 
OC in Figure 2B). It also identifies a point in celestial coordinates "above" the satellite 
that moves as the sensor rotates in its orbit. At each point along this orbit the antenna is 


imagined to do a conical scan about nadir (i.e. about OC). If the motion of the satellite 
can be neglected during each conical scan, then the problem is again identical to the 
problem above, except that in this case the cone is formed about the vector OC (rather 
than the normal to orbit, ON, as before). That is, as the antenna does a conical scan with 
the satellite frozen in space, the reflected ray for the antenna bore sight traces a cone 
about the nadir, OC, with interior angle Q = 20s - 6i as shown in Figure 2B. 

Figure IB: Geometry for calculation the specular ray at bore sight with cross track scan. 

Figure 2B: Geometry for calculation the specular ray at bore sight with conical 



Locating Orbits in Celestial Coordinates 

As illustrated in Appendix B, the idealized orbit can be described by the vector 
perpendicular to its plane (e.g. ON in Figure IB) and therefor by two angles that describe 
this vector. In a celestial coordinate system, by judicious choice, these angles can be 
declination and right ascension or perhaps their complements. Both geographic and 
celestial coordinate systems are Earth centered with their axis aligned at the vernal 
equinox. Latitude and declination are nearly equal. But the relationship between 
longitude and right ascension is complicated by the rotation of the Earth about its axis 
and around the Sun. 

The relationship between longitude and right ascension is equivalent to the 
problem of converting from local time at a point on the Earth to sidereal time (time 
measured in celestial coordinates). This is a problem with nuances caused by fluctuations 
in the Earth orbit and solved in astronomy [14]. Given a location on the Earth with 
longitude, X., at universal time, Ut, the solution can be written as follows [32]: 

©L = ©GO + COeUt + l IC 

where ©l is sidereal time at this point (defines right ascension), ©go is sidereal time at 
Greenwich at midnight of the day on which this calculation is being made (i.e. hr min 
s), and co is the rate of rotation of the Earth (in the same units as Uy). If the units for © 
and X are degrees and Ut is in minutes, then [32]: 

coe = 0.250 684 6 deg/min 

©GO = 100.46062 + 36000.77 Uo + 0.000388 Uo^ - 2.6 X 10'^ Uo^ 

Uo = (JD-2 451 544.5)/36 525 2C 

JD = 367 Y - INT{ 1 .75 INT[(M + 9)/l 2] } + INT[275 M/9] + D + Co 

Co = 1721013.5 

where Y is the current year (e.g. 2002), M is the month, D is the day of the month, and 
INT[«] is the lower nearest integer. Also, JD is the Julian date (number of days at the 
beginning of the current day since January 1, 4713) and Uq is the number of Julian 
centuries since the reference epoch, January 1, 2000. The expressions above are given in 
"mean" sidereal time. 

When the units in Equation IC are in degrees, ©l is equivalent to right ascension. 
For example, at midnight Ut on January 1, 2000, the Greenwich meridian {X = 0) is 
100.46 degrees east of the mean vernal equinox (the reference for right ascension). Also, 


if the Earth didn't rotate, ©l and X (right ascension and longitude, respectively) would 
differ by a constant (which could be set to zero). 

When an orbit is specified in an Earth centered (geological) coordinate system, 
Equations 1C-2C can be used to describe it in celestial coordinates. For example, given 
the equatorial crossing (date, time and longitude) of the orbit (assumed to be in a plane), 
the expressions above can be used to locate the right ascension of the orbit in celestial 
coordinates. In the examples presented in this paper (Figures 6-7), it is assumed that the 
plane of the orbit is frozen in this orientation during one rotation. 


100 20D 300 


100 200 300 


Figiire 1 : Line emission (top) and continuum background (bottom) as equivalent brightness 
temperature in 20 MHz bandwidth. 


100 150 200 250 300 

50 100 150 200 250 300 


100 150 200 250 300 

100 150 200 250 

100 150 200 250 300 

50 100 150 200 250 


Figure 2: Line emission (left) and continuum background (right) at constant declination of 0, 20 
and 40 degrees (bottom to top). Notice that the vertical scale of the upper right panel is 0-20 K. 


100 200 300 


100 200 300 


>0.0 0.05 0.1 0.25 0.5 1.0 2.0 3.0 4.0 >5.0 K 

Figure 3: Smoothed data. Line emission (top) and continuum background (bottom) as 
equivalent brightness temperature in 20 MHz bandwidth as seen by an antenna with a 
Gaussian beam with a 10 degree beam width (full width at half maximum). 


100 150 200 250 300 

50 100 150 200 250 300 


50 100 150 200 260 300 


50 100 150 20C 250 300 


50 100 150 200 250 300 

50 100 150 200 250 


Figure 4: Smoothed data. Line emission (left) and continuum background (right) from Figure 
3 but at constant declination of 0, 20 and 40 degrees (bottom to top). 



UJ 16 


UJ 12 

UJ 10 






50 100 150 200 250 300 350 



50 100 150 200 250 300 350 


IDO 150 200 250 3O0 


Figure 5: Total background radiation at a constant declination of 20 degrees. The line 
emission is shown at the top and continuum background in the middle. Each of the 
components (smoothed) and the CMB is shown at the bottom together with the total. 




100 200 





Net Emission 


Continuum Emission^^ 
+ -' 1 

Line Emission / • 

-20 D 20 



100 200 










1 — _ij«_ 

Continuum Emission 
Line Emission 

-20 20 


Figure 6: Examples of the background radiation seen by a sensor at look angle 30 degree in a circular, 
polar orbit with inclination 95 degrees. The two cases are identical except for a change of 90 degrees 
in the equatorial crossing. The data on the left is the net background (line emission plus continuum) as 
smoothed with a Gaussian beam with a 10 degree beam width (FWHM). The two panels on the right 
show the brightness temperature along the locus of the projected beam (solid line) shown on the left. 


MARCH 15, 2002, 00:00:00 

100 200 MO 

RIGHT WCENSON (0<i9r»e] 

-80 -60 

-40 -20 20 40 60 


JULY 15, 2002, 00:00:00 




100 200 


-80 -60 

-40 -20 20 40 

60 80 

NOVEMBER 15, 2002, 00:00:00 


100 200 



-80 -60 -40 -20 20 40 60 

Figvire 7: Examples using the HYDROSTAR orbit. The antenna points at 5 degree look angle. The 
projection of the beam on celestial coordinates is shown on the left. On the right are the values of 
brightness temperature (the total contribution from line and continuum emission together with the 
CMB). The values are for a sensor with 20 MHz bandwidth and a 10 degree Gaussian beam.