NASA Technical Memorandum 104566, Vol. 2

SeaWiFS Technical Report Series

Stanford B. Hooker and

Elaine R. Firestone, Editors

Volume 2, Analysis of Orbit Selection for SeaWiFS:

Ascending vs. Descending Node

Watson W. Gregg

September 1992
NASA Technical Memorandum 104566, Vol. 2

SeaWiFS Technical Report Series

Stanford B. Hooker, Editor

NASA Goddard Space Flight Center

Greenbelt, Maryland

Elaine R. Firestone, Technical Editor

General Sciences Corporation

Laurel, Maryland

Volume 2, Analysis of Orbit Selection for SeaWiFS:

Ascending vs. Descending Node

Watson W. Gregg

NASA Goddard Space Flight Center

Greenbelt, Maryland

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

1992
Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

Author’s Note

This Technical Memorandum is a re-release of NASA TM 104546, originally published in September 1991, under

the same title. It is being re-released here to provide completeness for the SeaWiFS Technical Report Series.

However, some aspects of the SeaWiFS mission have changed since the original printing. The Pegasus will not

be carried aloft by a B-52, but rather by a refitted Lockheed L-1011. A daytime launch, however, with its

consequent decending node orbit, is still the preferred option due to increased visibility at launch time. The

remainder of this TM analyzes the consequences of descending node orbits in relation to ascending node orbits,

and remains an applicable analysis.

Greenbelt, Maryland — W. W. G.

August 1992

ii
W. Gregg

Abstract

Due to range safety considerations, the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean color instrument

may be required to be launched into a near-noon descending node, as opposed to the ascending node used

by the predecessor sensor, the Coastal Zone Color Scanner (CZCS). The relative importance of ascending

versus descending near-noon orbits was assessed here to determine if descending node will meet the scientific

requirements of SeaWiFS. Analyses focused on ground coverage, local times of coverage, solar and viewing

geometries (zenith and azimuth angles), and sun glint. Differences were found in the areas covered by individual

orbits, but were not important when taken over a 16 day repeat time. Local time of coverage was also different:

for ascending node orbits the Northern Hemisphere was observed in the morning and the Southern Hemisphere

in the afternoon, while for descending node orbits the Northern Hemisphere was observed in the afternoon and

the Southern in the morning. There were substantial differences in solar azimuth and spacecraft azimuth angles

both at equinox and at the Northern Hemisphere summer solstice. Negligible differences in solar and spacecraft

zenith angles, relative azimuth angles, and sun glint were obtained at the equinox. However, large differences

were found in solar zenith angles, relative azimuths and sun glint for the solstice. These differences appeared to

compensate across the scan, however, an increase in sun glint in descending node over that in ascending node on

the western part of the scan was compensated by a decrease on the eastern part of the scan. Thus, no advantage

or disadvantage could be conferred upon either ascending node or descending node for noon orbits. Analyses

were also performed for ascending and descending node orbits that deviated from a noon equator crossing time.

For ascending node, afternoon orbits produced the lowest mean solar zenith angles in the Northern Hemisphere;

and morning orbits produced the lowest angles for the Southern Hemisphere. For descending node, morning

orbits produced the lowest mean solar zenith angles for the Northern Hemisphere; afternoon orbits produced

the lowest angles for the Southern Hemisphere.

1. INTRODUCTION

The purpose of this report is to investigate the importance of ascending versus descending node orbits for the

Sea-viewing Wide Field-of-view Sensor (SeaWiFS), due for

launch in the latter part of August, 1993. SeaWiFS is designed to make global observations of ocean color. The

sensor will be carried by the spacecraft SeaStar, which is

in turn carried by the launch vehicle, Orbital Sciences Corporation’s Pegasus. Unlike traditional launch vehicles, the

Pegasus must be carried to high altitude before launch,

usually by a NASA B-52 fromEdwards Air Force Base in

California.

The issue of ascending versus descending node orbits

arises due to launch considerations for the Pegasus vehicle. Specifically, range safety requires a launch to the south

fromthe western United States. A noon ascending node

orbit requires a night launch of the Pegasus fromEdwards

Air Force Base in California. The NASA B-52 carrier vehicle is poorly equipped for night launches and chase planes

are less effective at night. A noon descending node orbit

may be launched during the daytime. Thus discussion has

turned to the scientific need for an ascending node orbit

and whether a descending node orbit might accomplish the

scientific purposes of SeaWiFS. The predecessor sensor to

SeaWiFS, the Coastal Zone Color Scanner (CZCS), was in

a noon ascending node orbit.

The analyses here attempt to clarify this issue by focusing on solar geometry (solar zenith and azimuth), viewing

geometry (spacecraft zenith and azimuth), and the derived

parameters relative azimuth (sun-sensor angle) and sun

glint (specular reflection by the sun off the ocean surface).

Sun glint is a major contaminant of ocean observations

and is calculable fromthe solar and viewing geometries.

Solar zenith is defined as the angle fromlocal nadir to the

sun and spacecraft zenith is the angle to the spacecraft.

The zenith angles determine the path length of irradiance

and radiance through the atmosphere and the effectiveness

of the atmospheric correction algorithm. Solar azimuth

is defined as the angle fromTrue North to the sub-solar

point, measured relative to the pixel. Spacecraft azimuth

is defined similarly with respect to the sub-satellite point.

These parameters are most important with respect to sun

glint, but also determine the contribution of scattering to

the total signal received by the sensor.

2. METHODS

Computations were performed using orbital dynamics

and Earth location code derived fromWilson et al. (1981).

The code was modified to correct the computation of spacecraft azimuth angle and several quadrant ambiguities in

the computation of azimuth, longitude and latitude. Most

of these corrections were important only near the poles

and the dateline. The SeaStar orbit is assumed circular

and coverage is calculated for global area coverage (GAC)

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Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

for which the scan period is 0.667 sec and the swath width

is ±45◦. Other orbit and sensor parameters are described

in Table 1.

Table 1. SeaStar orbital simulation parameters

and SeaWiFS instrument characteristics.

SeaStar Orbital Parameters

Altitude 705 km

Orbital Repeat Time 16 days (233 orbits)

Period 98.9 minutes

Inclination 98.25◦

Equatorial Crossing Time Noon (local time)

SeaWiFS Instrument Characteristics (GAC)

Scan Width ±45◦

Ground IFOV at nadir 1.13 km

Pixels Along Scan 981

Scan Period 0.667 seconds

Tilt ±20◦

Ground Coverage along 1487 km

Scan

Successive Orbit Equatorial −24.721◦

Crossing Longitude

Computations were performed for Julian Day 80, the

vernal equinox, and Julian Day 182, the Northern Hemisphere summer solstice. In both cases the sensor is assumed to scan from west to east. The tilt strategy for

both ascending and descending nodes is designed to minimize sun glint. Generally, the sensor tilts away from the

sub-solar point (defined by the solar declination). The

strategy used here is shown in Table 2.

Table 2. Tilt strategy used for computation of

importance of ascending or descending node orbits

for SeaWiFS. Fore is defined as along the direction

of motion of the spacecraft, aft is backward to the

direction of motion, and Ψ is the solar declination

latitude.

Sub-satellite Point Tilt

>60◦ south of Ψ 0◦ (nadir)

>60◦ north of Ψ 0◦ (nadir)

60◦ south of Ψ to Ψ 20◦ aft for ascending

20◦ fore for descending

60◦ north of Ψ to Ψ 20◦ fore for ascending

20◦ aft for descending

Sun glint was computed from these geometric parameters using the Cox and Munk (1954) theory. A global mean

wind speed of 6 ms−1 was chosen.

3. RESULTS

3.1 Ground Coverage

Fig. 1 shows the ground coverage for noon ascending

and descending node orbits for a full day. The effects of the

tilt strategy are apparent in Fig. 1 by the gap in equatorial

coverage, where the tilt changes from −20◦ (aft) to 20◦

(fore). The major differences are: 1) areas covered for a

given day, 2) the angle the swaths make with respect to

latitude, and 3) the local time of coverage. Regarding the

latter point, ascending node orbits travel fromafternoon in

the South Pole through noon to morning in the North Pole,

while descending node orbits travel fromafternoon in the

North Pole to morning in the South Pole. Thus descending

node noon orbits will observe the Northern Hemisphere in

the afternoon, as opposed to morning for ascending node.

These local times encountered by the two nodes are shown

in Fig. 2.

3.2 Zenith Angles at Equinox

The solar zenith angles encountered by ascending and

descending nodes at the vernal equinox are identical (Fig.

3), as are spacecraft zenith angles (Fig. 4). Thus the path

lengths of irradiance travelling through the atmosphere

and into the ocean and the radiance travelling back to the

spacecraft should be the same. The path length has important ramifications for radiative transfer in the atmospheric

correction algorithms.

3.3 Azimuth Angles at Equinox

Solar azimuth angles encountered by ascending and descending nodes are substantially different (Fig. 5). The angles may be verified by analyzing the coverage plots (Fig. 1)

and noting that for noon orbits at the equinox the sub-solar

point is at the equator and along-track. The differences result fromthe different approaches to the equator taken by

ascending and descending nodes. A difference plot is also

shown in Fig. 5 for solar azimuth angle. Positive difference means that descending node produced a larger solar

azimuth angle at a given point in the scan. Differences

ranged from0 to 360◦. Note that these are not the smallest difference, i.e., a difference of 360◦ is really a difference

of zero.

Differences are also apparent in spacecraft azimuth angle (Fig. 6), however, they are not as extreme. A difference

plot (Fig. 6) shows that the ranges are between 0 and 120◦.

Differences in spacecraft azimuth are due to the difference

in the angle made between the cross-track scan and latitude.

Despite large differences in solar and spacecraft azimuth angles, relative azimuth angles are remarkably similar for ascending and descending nodes (Fig. 7). A difference plot (Fig. 7) shows that the differences are between

−4◦ and 5◦. This range also only occurs near the equator and most of the orbit contains negligible (less than 1◦)

differences. Note that for relative azimuth, the minimum

angle between sun and spacecraft are shown, such that the

maximum possible difference is 180◦. Since it is the relative

azimuth that is used in radiative transfer calculations and

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W. Gregg

Fig. 1. a) Ground coverage of a SeaWiFS sensor in ascending node, with GAC coverage (scan of ±45◦) for a

full day. b) Descending node.

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Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

Fig. 2. Distribution of local time for ascending and descending noon orbits. The noon local time is only achieved

at the equator. Note that the sub-satellite point is denoted on the ordinate, but that the actual location of the

pixel in the scan is usually much different due to inclination and the tilting strategy. a) Ascending node. In

ascending node the spacecraft travels from afternoon in the Southern Hemisphere to morning in the Northern

Hemisphere. b) Descending node. In descending node the spacecraft travels fromafternoon in the Northern

Hemisphere to morning in the southern hemisphere.

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Fig. 3. a) Solar zenith angle distribution encountered for an ascending node, noon orbit, for the vernal equinox.

b) Descending node.

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Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

Fig. 4. Spacecraft zenith angles encountered by ascending and descending node orbits, for the vernal equinox.

The tilting strategy is described in the text and may be noted in the figure by discontinuities at 60◦ N and S,

where the tilt changes fromnadir-pointing to ±20◦. a) Ascending node. b) Descending node.

6
W. Gregg

Fig. 5. a) Solar azimuth angle distribution encountered for an ascending node, noon orbit, for the vernal

equinox. b) Descending node. c) Difference plot of solar azimuth angles for descending and ascending nodes.

A positive difference indicates the descending node had a larger solar azimuth angle, while a negative difference

indicates descending node had a smaller angle. Note these angles are not the smallest difference.

7
Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

Fig. 6. a) Spacecraft azimuth angle distribution encountered for an ascending node, noon orbit, for the vernal

equinox. b) Descending node. c) Difference plot of spacecraft azimuth angles for descending and ascending

nodes. A positive difference indicates the descending node had a larger spacecraft azimuth angle, while a negative

difference indicates descending node had a smaller angle. Note these angles are not the smallest difference.

8
W. Gregg

Fig. 7. a) Relative azimuth angle (angle between sun and spacecraft) distribution encountered for an ascending

node, noon orbit, for the vernal equinox. b) Descending node. c) Difference plot of relative azimuth angles for

descending and ascending nodes.

9
Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

in the calculation of sun glint and not the solar and spacecraft azimuth angles individually, these plots show that

there is little difference between ascending and descending

nodes.

3.4 Sun Glint at Equinox

Sun glint radiance is a good indicator of the importance

of solar and viewing geometries on radiative transfer for atmospheric correction and is also important in and of itself.

This is because sun glint is determined by the solar and

viewing geometries in a manner nearly identical to aerosol

and Rayleigh scattering. Maximum sun glint occurs at the

forward scattering area (where relative azimuth is 180◦)

and where solar and spacecraft zenith angles are identical.

Maximum scattering also occurs in the forward direction

for most aerosols. Sun glint at 500 nm was computed since

this represents a spectral maximum. This wavelength is

near the SeaWiFS 490 nmband.

As may be expected from the relative azimuth and

zenith angle plots, there is an indistinguishable difference

in sun glint between ascending and descending nodes (see

Fig. 8). The maximum occurs near the equator, which is

expected for the equinox. The small sun glint radiance

near 60◦ N and 60◦ S is where the tilt changes from0◦ to

±20◦.

A sun glint difference plot more clearly shows the relative importance of ascending versus descending node (Fig.

8). While descending node obtains slightly higher sun glint

just north of the equator, it obtains less below. Thus over

the entire orbit there can be considered to be no difference.

The absolute magnitude of the differences is small in any

event, not exceeding approximately 0.1 m W cm−2 μm−1

sr−1.

3.5 Zenith Angles at Solstice

The solar zenith angles encountered by ascending and

descending nodes at the Northern Hemisphere summer solstice are different, but symmetrical (Fig. 9). On this day,

an ascending orbit passes to the west of the sub-solar point,

while a descending orbit passes to the east. Thus minimum solar zenith angles are obtained on the right (east)

side of the ascending scan and on the left (west) side of the

descending scan. Spacecraft zenith angles do not change

substantially fromthe equinox case.

3.6 Azimuth Angles at Solstice

Only relative azimuth angles are shown for the solstice

case, since they are the important parameter for atmospheric correction. Also, it is important to note that spacecraft azimuth angles do not change substantially as a function of node.

Unlike the equinox case, relative azimuth angles are

quite different for ascending and descending orbits (Fig.

10). A difference plot (Fig. 10) shows that the angles are

smaller for descending node, reaching −50◦. This is an

asymmetry due to the Equation of Time: the sub-solar

point is not always exactly overhead at noon (Iqbal 1983).

In fact, the sub-solar point is usually a small distance east

or west of directly overhead at noon. For the summer

solstice it is slightly east.

3.7 Sun Glint at Solstice

As might be expected from the difference in the solar

zenith angles and relative azimuth angles in ascending and

descending orbits at noon, sun glint radiance is also different (Fig. 11). The location of the maximum is shifted

slightly east for ascending node and slightly west for descending node. This is a consequence of the fact that, at

the solstice, the sub-solar point is located east of the ascending node sub-satellite track and west of the descending

node.

Differences in sun glint are plotted in Fig. 11. The

magnitude of the differences is relatively large—up to approximately 0.5 m W cm−2 μm−1 sr−1. This has important consequences for ocean observations and atmospheric

correction. However, the differences are symmetrical. An

increase in sun glint on the western part of the scan for

descending orbits is compensated by a reduction on the

eastern part. Thus, taken as an entire orbit, there appears

to be no loss of quality of ocean observations by descending

node.

3.8 Importance of Equator Crossing Time

To evaluate the importance of deviations from a noon

equator crossing time (ECT), a one year simulation was

performed, which also diminishes the importance of the

Equation of Time. ECTs of noon ±1.5 hours were assessed,

for both ascending and descending orbits. At the outset

it must be emphasized that exact noon ECTs provide the

minimum mean solar zenith angle for both Northern and

Southern Hemispheres.

For ascending node, lowest mean solar zenith angles are

obtained in the Northern Hemisphere for 12:30 ECT and

in the Southern Hemisphere for an 11:30 ECT (Fig. 12).

The worst (largest) solar zenith angles are obtained for a

10:30 ECT in the Northern Hemisphere and a 1:30 ECT

in the Southern. Maximum departures occurred near the

equator and amounted to approximately 10◦. Generally,

morning orbits are preferred to obtain smaller zenith angles

in the Southern Hemisphere and afternoon orbits for the

Northern Hemisphere.

For descending node, lowest mean solar zenith angles

are obtained for 11:30 ECT in the Northern Hemisphere

and 12:30 ECT in the southern (Fig. 12). The largest

angles are obtained for a 1:30 ECT in the northern hemisphere and a 10:30 ECT in the Southern. Again the maximum departure is approximately 10◦. In contrast to ascending orbits, afternoon orbits are preferred for the Southern Hemisphere and morning for the Northern Hemisphere

10
W. Gregg

Fig. 8. a) Relative azimuth angle (angle between sun and spacecraft) distribution encountered for an ascending

node, noon orbit, for the vernal equinox. b) Descending node. c) Difference plot of relative azimuth angles for

descending and ascending nodes.

11
Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

Fig. 9. a) Solar zenith angle distribution encountered for an ascending node, noon orbit, for the Northern

Hemisphere summer solstice. The smallest angles are located to the east because in ascending node the subsatellite track crosses the sub-solar point to the west. b) Descending node. The smallest angles are located to

the west because in ascending node the sub-satellite track crosses the sub-solar point to the east.

12
W. Gregg

Fig. 10. a) Relative azimuth angle distribution encountered for an ascending node, noon orbit, for the Northern

Hemisphere summer solstice. b) Descending node. c) Difference plot of relative azimuth angles for descending

and ascending nodes.

13
Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

Fig. 11. a) Sun glint radiance distribution at 500 nmencountered for an ascending node, noon orbit, for

the Northern Hemisphere summer solstice. b) Descending node. c) Difference plot of sun glint radiance for

descending and ascending nodes.

14
W. Gregg

Fig. 12. a) Mean solar zenith angles encountered for ascending nodes at different equator crossing times. This

analysis was performed for an entire year to minimize the effect of the Equation of Time. The smallest solar

zenith angles are obtained in the Northern Hemisphere for afternoon ascending orbits, while the smallest angles

are obtained in the Southern Hemisphere for morning ascending orbits. b) Descending node. The smallest solar

zenith angles are obtained in the Northern Hemisphere for morning descending orbits, while the smallest angles

are obtained in the Southern Hemisphere for afternoon descending orbits.

15
Analysis of Orbit Selection for SeaWiFS: Ascending vs. Descending Node

for descending orbits. These conclusions are summarized

in Table 3.

Table 3. Lowest mean solar zenith angles for ascending and descending node orbits.

Hemisphere Ascending Node Descending Node

Northern Afternoon Morning

Southern Morning Afternoon

4. DISCUSSION

Simulations of the solar and viewing geometries encountered by noon ascending and descending node orbits

revealed substantial differences in solar azimuth and spacecraft azimuth angles both at equinox and at the Northern

Hemisphere summer solstice. Negligible differences in solar

and spacecraft zenith angles, relative azimuth angles and

sun glint were obtained at the equinox. However, large

differences were found in solar zenith angles, relative azimuths and sun glint for the solstice. These differences

evened out across the scan, however, an increase in sun

glint in descending node over that in ascending node on

the western part of the scan was compensated by a decrease on the eastern part of the scan. Thus, no advantage

or disadvantage could be conferred upon either ascending

or descending node for noon orbits.

Differences occurred for ascending and descending node

orbits that deviated froma noon equator crossing time.

To obtain the lowest mean solar zenith angles, afternoon

orbits are preferred for ascending node in the Northern

Hemisphere and morning for the Southern Hemisphere.

Concerning the descending node, morning orbits are preferred for the Northern Hemisphere, and afternoon for the

Southern Hemisphere.

Glossary

CZCS Coastal Zone Color Scanner

ECT Equator Crossing Time

GAC Global Area Coverage

IFOV Instantaneous Field-Of-View

SeaWiFS Sea-viewing Wide Field-of-view Sensor

References

Cox, C., and W. Munk, 1954: Measurement of the roughness

of the sea surface from photographs of the sun’s glitter. J.

Mar. Res., 44, 838-850.

Iqbal, M., 1983: An Introduction to Solar Radiation. Academic

Press, 390 pp.

Wilson, W.H., R.C. Smith, and J.W. Nolten, 1981: The CZCS

geolocation algorithms. SIO Ref. 81-32, Scripps Institute

of Oceanography, 37 pp.

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13. ABSTRACT (Maximum 200 words)

National Aeronautics and Space Administration

Washington, D.C. 20546–0001 TM–104566, Vol. 2

Laboratory for Hydrospheric Processes

Goddard Space Flight Center 92B00122

Greenbelt, Maryland 20771

6. AUTHOR(S)

 Watson W. Gregg

 Series Editors: Stanford B. Hooker and Elaine R. Firestone

Due to range safety considerations, the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean color instrument may be required to

be launched into a near-noon descending node, as opposed to the ascending node used by the predecessor sensor, the Coastal Zone

Color Scanner (CZCS). The relative importance of ascending versus descending near-noon orbits was assessed here to determine if

descending node will meet the scientific requirements of SeaWiFS. Analyses focused on ground coverage, local times of coverage,

solar and viewing geometries (zenith and azimuth angles), and sun glint. Differences were found in the areas covered by individual

orbits, but were not important when taken over a 16 day repeat time. Local time of coverage was also different: for ascending node

orbits the Northern Hemisphere was observed in the morning and the Southern Hemisphere in the afternoon, while for descending node

orbits the Northern Hemisphere was observed in the afternoon and the Southern in the morning. There were substantial differences in

solar azimuth and spacecraft azimuth angles both at equinox and at the Northern Hemisphere summer solstice. Negligible differences

in solar and spacecraft zenith angles, relative azimuth angles, and sun glint were obtained at the equinox. However, large differences

were found in solar zenith angles, relative azimuths and sun glint for the solstice. These differences appeared to compensate across the

scan, however, an increase in sun glint in descending node over that in ascending node on the western part of the scan was compensated by a decrease on the eastern part of the scan. Thus, no advantage or disadvantage could be conferred upon either ascending node

o descending node for noon orbits. Analyses were also performed for ascending and descending node orbits that deviated from a noon

equator crossing time. For ascending node, afternoon orbits produced the lowest mean solar zenith angles in the Northern Hemisphere;

and morning orbits produced the lowest angles for the Southern Hemisphere. For descending node, morning orbits produced the lowest

mean solar zenith angles for the Northern Hemisphere; afternoon orbits produced the lowest angles for the Southern Hemisphere.