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Solar Illumination and Sensor Viewing Angle Coefficient Files

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Landsat Collection 1 Level-1 products contain radiometrically and geometrically corrected image data for each spectral band and are delivered as fixed point digital numbers (8-bit for Landsat 4-5, and Landsat 7; 16-bit for Landsat 8).  These can be converted to at-sensor radiance or reflectance using the additive and multiplicative scaling parameters contained in the metadata file that is delivered with the products.  The data are precisely registered to a Universal Transverse Mercator (UTM) (or for Antarctica, Polar Stereographic (PS)) map projection grid, making it straightforward to construct pixel ground coordinates from the product corners.

Some applications require additional information about the scene geometry – including elevation, slope / aspect, sensor viewing angles (elevation and azimuth), and/or solar illumination angles.

Landsat 4-5, Landsat 7 and Landsat 8 Level-1 products contain an angle coefficient file (“_.ANG.txt”). This file consists of per-pixel solar (sun) and sensor (satellite, view) azimuth and zenith values to be used in conjunction with the pixel values for each of the Landsat bands in the Level-1 product. The angle coefficient file is used as input into a set of tools that gives users the ability to generate sensor and sun viewing angles. The output files of these tools, termed as “angle bands,” are images that contain the solar and sensor viewing angles.

This page describes the architecture and dependencies of sensor and sun angle viewing angles.  The sensor and sun viewing angle generation tools and documentation can be found at the bottom of the page.

Dependencies

The following technical details determine the outcome of the view angle bands for the product in which they are generated:

  1. The sensor viewing and solar illumination geometry vary with time and location due to the position and movement of the sun; the position, orientation, and movement of the satellite; and the location of the imaged object on the (rotating) Earth’s surface.
  2. The sensor and solar angles are defined with respect to a local coordinate system centered on the imaged point on the surface of the Earth. The z-axis is represented by a vector perpendicular to the Earth ellipsoid at the point, the y-axis is geodetic north, and the x-axis is geodetic east.
  3. The architecture of the imaging instrument, including the focal plane placement and layout, influence the results. The results look significantly different depending on the instrument architecture. For example, the whiskbroom scanner of Landsat 7 Enhanced Thematic Mapper Plus (ETM+), Landsat 4-5 Thematic Mapper (TM), and Landsat 1-5 Multispectral Scanner (MSS) instruments, to Landsat 8’s Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS) pushbroom focal plane.
  4. The angle bands are defined as azimuth and zenith angles for each product’s spectral band. Users may find this information useful in the form of X-Y-Z vector directions. Storing this information as two angles, rather than as three vector components, reduces the size of the data set associated with this information and makes it more manageable from both a storage and distribution standpoint. Figure 1 below shows these relationships (θz = Zenith Angle θA = Azimuth Angle).

Angles and Vectors Associated with Image Bands
Figure 1. Angles and Vectors Associated with Image Bands

Coordinate Systems

The angle bands allow the user to better understand how the sensor viewing geometry and solar illumination geometry affect the object being sensed by the instrument.  This information is important for analyzing effects, such as the Bi-directional Reflectance Distribution Function (BRDF).  

The figures below illustrate the application of the angle band information. Figure 2 shows the local coordinate system in which the view angles are defined, with θ representing zenith angles and ϕ representing azimuth angles. This coordinate system is represented by a z-axis that is perpendicular to the Earth ellipsoid and an x/y axis that is defined by the geodetic directions of east and north.

Local Coordinate System
Figure 2. Local Coordinate System

One impact to the calculated zenith angles is the curvature of the Earth.  Figure 3 demonstrates the curvature by showing how the local vertical axis changes as the object being viewed moves away from nadir with respect to the satellite. The curvature of the Earth causes the z-axis to fall farther away from the nadir viewing vector of the satellite.  This curvature has a measurable effect on the zenith viewing angles.  With respect to the solar zenith viewing band, this is the major source of variation, as the sun’s position changes relatively slowly over the acquisition time of a single scene.

Relationship between Local Vertical and Earth Curvature
Figure 3. Relationship between Local Vertical and Earth Curvature

Sensor Architecture

The sensor focal plane architecture also plays a role in defining the output of the angle bands. Figure 4 below shows the focal plane layouts of both Landsat 8 OLI and the Landsat 7 ETM instruments. The Landsat 8 OLI and TIRS instruments are pushbroom imagers with focal planes that span the full Landsat swath width. Full swath coverage is achieved by using multiple Sensor Chip Assemblies (SCAs) across-track, with sufficient overlap between adjacent SCAs to avoid coverage gaps. This SCA-to-SCA overlap is achieved by displacing alternate SCAs along-track so that adjacent SCAs can cover overlapping portions of the across-track Field of View (FOV). The Landsat 8 OLI uses 14 SCAs to cover the full swath, with the 7 odd SCAs (1 through 13) arranged to point slightly forward of nadir. The 7 even SCAs (2 through 14) are arranged to point slightly aft. For Landsat 8 TIRS, the central SCA-C points forward while the outboard SCAs (A and B) point aft. 

The whiskbroom scanning mirror in the Landsat 7 ETM+ instrument scans bi-directionally in the across track direction of the satellite. The detectors within the focal plane are in parallel rows, one column covering the along track swath width of a single scan, with the odd, even detectors and the bands separated in the along scan direction.  The Landsat 4-5 TM focal plane layout is very similar, minus the set of panchromatic band detectors, and the thermal band would contain 4 detectors rather than 8.

Landsat 8 OLI and Landsat 7 ETM+ Focal Plane Layouts
Figure 4. Landsat 8 OLI and Landsat 7 ETM+ Focal Plane Layouts

A key challenge in analyzing the viewing geometry for the OLI and TIRS sensors is the along-track offset between adjacent SCAs, as this focal plane geometry leads to discontinuities in the viewing geometry at SCA boundaries. The view angle changes by the alternating even/odd SCA geometry. The along-track distribution of the spectral bands causes the viewing angles to be different for each spectral band. The combination of these effects, the along-track offsets for each band, and the along-track and across-track offsets for each SCA, creates a set of azimuth angles that alternate in value per SCA.  

The effect of projecting the sensor Line-of-Sight (LOS) vector into the local coordinate system causes the azimuth angles to change discontinuously for adjacent SCAs (see Figure 5). The alternating fore / aft viewing SCA layout produces a pattern of alternating higher (lighter) and lower (darker) values across the Instrument Field of View (IFOV).

Landast OLI Azimuth Angles for Points Imaged Simultaneously in two OLI SCA's
Figure 5. Landast 8 OLI Azimuth Angles for Points Imaged Simultaneously in two OLI SCA's

Figure 6 below shows the sensor azimuth and zenith angle band for a Landsat 8 image from path/row 163/047 acquired on day 175 of 2014 for Band 6.  The alternating pattern within the azimuth satellite viewing angle band and the light to dark transition at the center of the image are the result of the SCA pushbroom sensor of Landsat 8.  The darker to lighter transition from the center of the zenith angle band to the outer edges is due to the local coordinate system having its z-axis normal to the surface of the Earth ellipsoid.  

Landsat 8 OLI Azimuth (left) and Zenith (right) Sensor Viewing Angle Band for 163/047 Band 6 acquired on 2014 Day 175
Figure 6. Landsat 8 OLI Azimuth (left) and Zenith (right) Sensor Viewing Angle Band for 163/047 Band 6 acquired on 2014 Day 175

As a final demonstration of these effects, sample coordinate profiles display for both the azimuth and zenith angles (see Figure 7).  The y-axis of the profile plots are in units of hundredths of degrees.  Transitions between the SCAs can be seen in both sets of profiles, however, the changes are much more pronounced in the azimuth angle profile. The greatest variability across a scene’s sensor viewing angles is in the azimuth angle. 

Landsat 8 OLI Sample Direction Profiles for Sensor Azimuth and Zenith Angles
Figure 7. Landsat 8 OLI Sample Direction Profiles for Sensor Azimuth and Zenith Angles

Compared to understanding the characteristics of the sensor viewing angles of the Landsat 8 instruments, the Landsat 7 ETM+ and Landsat 4-5 TM sensors are less of a challenge.  For the sensor azimuth angle the effect of projecting the sensor LOS vector into the local coordinate system causes the azimuth angles to change discontinuously only when the mirror transverses the location directly nadir to the spacecrafts position (see Figures 8 and 9). 

Landsat  ETM+ and TM Azimuth Angles for Points Imaged by Consecutive Scans
Figure 8. Landsat 7 ETM+ and Landsat 4-5 TM Azimuth Angles for Points Imaged by Consecutive Scans

Landsat ETM+ Azimuth (left) and Zenith (right) Sensor Viewing Angle Band for 163/047 Band 5 acquired on 2002 Day 294
Figure 9. Landsat 7 ETM+ Azimuth (left) and Zenith (right) Sensor Viewing Angle Band for 163/047 Band 5 acquired on 2002 Day 294

Figure 10 shows sample profiles of the sensor viewing images.  As can be seen from the ETM+ azimuth image, there is only one visible light to dark transition and this change is located along track at the nadir viewing position of the sensor.  The ETM+ zenith viewing angle band is similar to that of the OLI instrument with only a small discontinuity that is present along a scan-to-scan transition, but are much less pronounced effect, but similar to those for the zenith SCA-to-SCA changes within the OLI image.

Landsat ETM+ Sample Direction Profiles for Sensor Azimuth and Zenith Angles
Figure 10. Landsat 7 ETM+ Sample Direction Profiles for Sensor Azimuth and Zenith Angles

Time Dependencies

Time dependencies occur during an acquisition, as both the satellite and sun viewing angles vary within a given scene.  For the same reason that each SCA has its own unique viewing angle, each SCA of each band views the same object on the ground at slightly different times. This time delay between bands of the SCAs causes the sun and satellite viewing angles to differ as a given object is viewed by each band and SCA during an acquisition; therefore, the satellite and sun positions associated with the object are different. 

One way to understand how time affects the sun and sensor viewing angles is to look at the magnitude of change of the time dependencies involved. Figure 11 below lists some of these time dependencies within a given Landsat 8 image acquisition.  Per-scene variabilities that indicated change in the satellite orbit are of much greater magnitude than that of the Earth rotation, which is of much greater magnitude than the orbit of the Earth around the sun.  

Time Dependencies for Sun and Sensor Viewing Bands
Figure 11. Time Dependencies for Sun and Sensor Viewing Bands

The SCAs for each band are also staggered, creating up to a 1.1-second delay between the time when an object is imaged by the leading and trailing bands of a given SCA. Combining this time delay, the rates of change, and the angular offset between the bands for a given SCA shows that the greatest angular variation within an acquisition would be expected in the sensor viewing angles.

Related to the azimuth angle and the local coordinate system, the greatest variability across a scene’s sensor viewing angles is in the azimuth angle.  This is supported in Figure 6 and Figure 7, while also calculating statistics for the angle bands of the 163/047 dataset, shown in the table below. 

Landsat OLI Angle Viewing Band Statistics: 163/047 Band 6, Acquired on 2014 Day 175
Table 1. Landsat 8 OLI Angle Viewing Band Statistics: 163/047 Band 6, Acquired on 2014 Day 175

As a final look at the potential variations in angle bands, consider the solar illumination angle bands. Due to the tilt of Earth’s polar (z) axis with respect to the orbital plane of motion around the sun and the eccentricity associated with this orbit, there is an apparent motion of the sun with respect to the stars. This leads to a change in solar illumination geometry for a given observed location on the Earth’s surface from one acquisition to another.  

When the Earth is tilted toward the Sun for a given observation point on the Earth (local summer), the Sun appears higher above the horizon, and when the Earth is tilted away from the Sun for a given observation point (local winter), the opposite is true—the Sun appears lower in the sky (see Figure 12). 

Earth’s Axial Tilt and Seasonal Effects
Figure 12. Earth’s Axial Tilt and Seasonal Effects

The effects of these variations in the Sun’s position on the solar illumination azimuth and zenith angles for a particular location on the Earth’s surface – the center of the scene at Worldwide Reference System (WRS) path/row 163/047 – are shown in Figure 13 and Figure 14, which show the change in the Sun’s position over the seasons leads to significant changes in the solar illumination angles for this site.

Sun’s Azimuth and Zenith Angles with Respect to the WRS Scene Center of 163/047 Over Time
Figure 13. Sun’s Azimuth and Zenith Angles with Respect to the WRS Scene Center of 163/047 Over Time

Sun’s Geodetic Position for the WRS 163/047 Scene Center Over Time
Figure 14. Sun’s Geodetic Position for the WRS 163/047 Scene Center Over Time

Figure 15 shows the sensor viewing azimuth and zenith angle bands for 163/047 day 319 of 2014 for Band 6. Figure 16 shows the solar illumination azimuth and zenith angle bands for the same band. 

Landsat OLI Azimuth (left) and Zenith (right) Sensor Viewing Angle Band for 163/047 Band 6 Acquired 2014 Day 319
Figure 15. Landsat 8 OLI Azimuth (left) and Zenith (right) Sensor Viewing Angle Band for 163/047 Band 6 Acquired 2014 Day 319

Landsat OLI Azimuth (left) and Zenith (right) Sun Viewing Angle Band for 163/047 Band 6 Acquired 2017 Day 319
Figure 16. Landsat 8 OLI Azimuth (left) and Zenith (right) Sun Viewing Angle Band for 163/047 Band 6 Acquired 2017 Day 319

Table 2 shows the viewing angle band statistics for 163/047 day 319 of 2014 for Band 6. The sensor angles look similar to those in Table 1, while the sun angles show the differences associated with the expected seasonal changes.  

Landsat 8 OLI Angle Viewing Band Statistics: 163/047 Band 6 Acquired 2014 Day 319
Table 2. Landsat 8 OLI Angle Viewing Band Statistics: 163/047 Band 6 Acquired 2014 Day 319

The same logic applies when considering the time dependencies associated with the ETM+ and TM sensors – the sun behaves in exactly the same manner and the satellite orbital dynamics are essentially the same as those for Landsat 8 as Landsats 4-7 are placed and kept within in the same near-polar, sun-synchronous orbit following the WRS-2 global notation.  The difference between the Landsat 8 instruments and ETM+/TM is the difference between acquisition times of the detectors and bands related to the pushbroom and whiskbroom architecture.  Where the OLI instrument has up to a 1.1-second delay between the time when an object is imaged by the leading and trailing bands of a given SCA the time between consecutive scans for the whiskbroom instrument is approximately 71.8 msec.  This produces a very small change within the solar angle bands with respect to the transition between consecutive scans for these angles, especially when compared to the transition between SCAs for the OLI and TIRS instruments.  

Figures 17 and 18 show the ETM+ angle bands for an acquisition also over 163/047, the same as the OLI example, and within three weeks of the OLI example.  As can be seen from Figure 18 the OLI and ETM+ solar angle bands look very similar.  To complete this comparison, Table 3 lists the statistics associated with these angle band files which also helps demonstrate the similarities between these files for the two instruments, especially with respect to the solar viewing bands.

Landsat 7 ETM+ Azimuth (left) and Zenith (right) Sensor Viewing Angle Band for 163/047 Band 5 Acquired 2002 Day 294
Figure 17. Landsat 7 ETM+ Azimuth (left) and Zenith (right) Sensor Viewing Angle Band for 163/047 Band 5 Acquired 2002 Day 294

Landsat 7 ETM+ Azimuth (left) and Zenith (right) Sun Viewing Angle Band for 163/047 Band 5 Acquired 2002 Day 294
Figure 18. Landsat 7 ETM+ Azimuth (left) and Zenith (right) Sun Viewing Angle Band for 163/047 Band 5 Acquired 2002 Day 294

Landsat 7 ETM+ Angle Viewing Band Statistics: 163/047 Band 5 Acquired 2002 Day 294
Table 3. Landsat 7 ETM+ Angle Viewing Band Statistics: 163/047 Band 5 Acquired 2002 Day 294

This information shows that, for the sensor viewing angles, the variability that occurs within an acquisition is much larger than the variability from acquisition to acquisition. Whereas, for the sun angles, the variability is small within an acquisition but changes much more drastically across acquisitions. 

Tools & Documentation 

The Landsat Angles Creation Tools listed below allow users to create angle bands in a LINUX environment.  Future plans include implementing an end-user web-based tool. Until then, users are responsible for creating usable angle bands.

Landsat 4-5 Thematic Mapper (TM) and Landsat 7 Enhanced Thematic Mapper Plus (ETM+) - .tgz (100 KB)  README - .txt (4 KB)
Landsat 8 Operational Land Imager (OLI)/Thermal Infrared Sensor (TIRS) - .tgz (100 KB) README - .txt (2 KB)
 
Landsat TM and ETM+ Solar and View Angle Generation Algorithm Description Document (pdf)
Landsat 8 Solar and View Angle Generation Algorithm Description Document (pdf)

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