Calibrating the Landsat Data Record

The Landsat data record is important for terrestrial remote sensing and global change research because it covers a 30 year time when significant anthropogenic terrestrial change has occurred.  In order to benefit from this data record, steps are needed to ensure that the data are self-consistent and not significantly affected by artifacts of the various Landsat sensors. In anticipation of a successful Landsat 7 mission, renewed efforts were made to ensure radiometric calibration across the Landsat series of sensors and with other Earth observation sensors. A critical step in such a process is sensor radiometric calibration to an absolute scale, yielding image data at the top of the atmosphere in physical units. Additional processing steps to retrieve surface parameters such as reflectance and temperature then become possible.

Consistency between the Landsat sensors starts with sound calibration of the individual sensors, including the development of a stable sensor (i.e. ETM+), detailed prelaunch characterization, and on-orbit calibration. Post-launch radiometric calibrations are based on reference to onboard standards and ground-based test sites. ETM+ cross-calibration with earlier Landsat sensors begins by making use of near-simultaneous imaging of common Earth surface targets. Typically, there is a limited overlap period when more than one of the sensors is operating at the same time. Such an overlap period with Landsat 5 was designed into the initial phases of the Landsat-7 mission. The resulting opportunity for radiometric cross-calibration between ETM+ and Landsat 5's TM is the main subject of this chapter. This material was extracted from a paper that covers the subject in greater detail (Teillet, et. al., 2001).

The Tandem Configuration

The launch of Landsat-7 on April 15, 1999 placed the spacecraft temporarily in an orbit very close to that of the Landsat-5 spacecraft. The mean altitude of Landsat-7 was 699 km, 6 km below the 705-km mean altitude of Landsat-5. At this altitude, the Landsat-7 ground track drifted slowly relative to the nearly fixed Landsat-5 pattern. The key period for the tandem configuration was June 1-4, 1999 when the tracks were almost exactly the same, but with a temporal offset on the order of 10 to 30 minutes. This unusual and valuable opportunity was specifically designed to facilitate the establishment of data consistency between the Landsat ETM+ and TM sensors. During the tandem configuration period when there was useful overlap in coverage between the two sensors, image sequences corresponding to 791 matching scenes were recorded by both the Landsat-7 ETM+ and, in cooperation with Space Imaging EOSAT and international ground stations, the Landsat-5 TM (Table 8.3.1). Subsequently, the Landsat-7 orbit was changed for nominal operations such that its 16-day repeat coverage cycle is now offset from that of Landsat-5 by 8 days. Given cloud cover and possible problems with data reception and recording, the number of useful tandem data scene pairs is roughly estimated to be on the order of 400 scenes.

The cross-calibration methodology documented here is applicable to tandem image pairs and presents specific results for two different pairs of nearly coincident matching scenes from the tandem configuration period. The main results consist of TM responsivities in the six solar reflective spectral bands referenced against well-calibrated ETM+ responsivities in corresponding spectral bands. The formulation includes adjustments for differences in illumination regimes as well as for differences in spectral response profiles between the two sensors.

Attention was focused on two particular tandem image pairs for cross-calibration methodology development and analysis because of the availability of ground reference data. Both Landsat sensors imaged the Railroad Valley Playa (RVPN), Nevada on 1 June 1999, when a team from the University of Arizona made measurements of surface spectral reflectance and atmospheric aerosol optical depth the same day. Similarly, a team from South Dakota State University acquired the same types of ground reference data at a grassland test site in the area of Niobrara, Nebraska (NIOB) on 2 June 1999, the day of the tandem Landsat overpasses for that site.

Table 8.3.2 provides information on the characteristics of the two data sets and Figure 8.3.1 shows both Landsat image pairs. The RVPN test site is a dry-lake playa that is very homogeneous and consists of compacted clay-rich lacustrine deposits forming a relatively smooth surface compared to most land covers. The NIOB test site is characterized primarily by grasslands grazed by cattle and by a smaller proportion of agricultural crops.

The cross-calibration methodology assumes that the Landsat-5 TM calibration is to be updated with respect to the Landsat-7 ETM+ sensor, which serves as a well-calibrated reference sensor with a radiometric calibration uncertainty of ± 3 percent (Barker et al., 1999). Because data acquisitions were only 10 to 30 minutes apart during the tandem configuration period, it is assumed that the surface and atmospheric conditions did not change significantly between the two image acquisitions. Cross-calibration methodologies in general should consider adjustments as appropriate for bi-directional reflectance factor (BRF) effects due to differences in illumination and observation angles. For Landsat sensor image data pairs acquired during the tandem configuration period, the expectation is that such BRF adjustments are not necessary. The solar illumination geometries are very similar (within three degrees), satellite zenith angles are predominantly near-nadir, and relative azimuth angles between solar and satellite directions do not differ significantly from one Landsat overpass to the other.Nevertheless, there are geometric, radiometric, and spectral considerations to be addressed.

Geometric Matching

Geometrically, the Landsat-7 and Landsat-5 sensors differ in their along-track and across-track pixel sampling. Due to wearing of the bumpers used by the Landsat-5 TM scanning mirror, along-track gaps between scans are longer than they are for Landsat-7 ETM+. For the same reason and because the ETM+ scan time is slightly longer than the specification, there are also across-track differences in the ground coverage. In addition, slight mismatches will arise in the imagery because of the altitude difference. In particular, there is variation in the ETM+ scanning pattern and its effect on the scan line corrector due to the lower-than-nominal orbit during the tandem configuration time period. These considerations make it very difficult to establish sufficient geometric control to facilitate radiometric comparisons on a point-by-point and/or detector-by-detector basis. Therefore, the analysis approach was developed to make use of image statistics based on large areas in common between the image pairs.

Radiometric Formulation

Radiometrically raw data are assumed (Level 0 for TM and Level 0R for ETM+). In spectral band i, the image quantized level Q_i (in counts) is related to top-of-atmosphere (TOA) radiance L_i* (in Watts/(m² sr mm)) by

(1)

where:	Gi is band-averaged sensor responsivity (in counts per unit radiance)
	is the zero-radiance bias (in counts) in spectral band i.

Quantized levels of Q = 0 and Q = 255 are excluded to avoid saturation effects. The zero-radiance biases are based on dark current restore values computed on a line-by-line basis. Radiometric detector normalisations based on full-scene statistics are applied in each spectral band, for each particular scene in the case of TM and for many scenes in the case of ETM+. The normalisations are with respect to the band average and the process is not expected to bias the cross-calibration. Normalised and bias-corrected image values are then given by

(2)

Thus, TOA radiances L*_i (in Watts/(m² sr µm)) are related to image data by

(3)

TOA reflectance is related to TOA radiance by

(4)

where:	E0i is the exo-atmospheric solar irradiance in spectral band i (in Watts/(m2 mm)) based on the Modtran-3 spectrum
	is the solar zenith angle
	ds is the Earth-Sun distance in Astronomical Units

A combination of equations (2), (3), and (4) yields

(5)

There are two advantages to using reflectances instead of radiances. One advantage is to remove the cosine effect of different solar zenith angles due to the 10- to 30-minute time difference between data acquisitions. For example, the three-degree difference in solar zenith angles for the RVPN image pair leads to a 2.5 percent effect in the ratio of the cosines of the respective angles. The other advantage is to compensate for different values of exo-atmospheric solar irradiance arising from spectral band differences. If differences in atmospheric conditions are not a factor, then the TOA reflectance comparisons have the potential to yield the best possible calibration comparisons between the TM and ETM+ based on the tandem data sets.

Cross-Calibration

Equation (5) can be defined separately for image data from the Landsat-5 TM ("5") and for image data from the Landsat-7 ETM+ ("7"):

(6)

(7)

The combination of equations (6) and (7) yields

(8)

where the adjustment factor A_i adjusts Landsat-5 TM radiance data for illumination and spectral band difference effects. In particular, Mi is the slope of the linear equation that characterizes as a function of and

(9)

where

(10)

B_i is essentially a spectral band adjustment factor, given that the in equations (6) and (7) are not necessarily the same because of the differences in relative spectral response profiles between corresponding ETM+ and TM spectral bands. Landsat-5 TM responsivity G_i5 is then given in spectral band i (in counts per unit radiance (CPUR)) by

(11)

With this updated value of TM responsivity, users can obtain TOA radiance L_i* (in Watts/(m² sr µm)) from raw image quantized levels Q_i (in counts) using

(12)

where a_i = 1 / G_i and b_i = - Q_0i / G_i . Thus, image pairs from the tandem configuration period make it possible to use well-calibrated Landsat-7 ETM+ image data to update the radiometric calibration of the Landsat-5 TM.

Standard image processing and statistical analysis steps were used to obtain the Mi slopes in equation (8) for use in equation (11). Theand for use in equation (8) were obtained from large areas, depicted in Figure 8.3.1, common to the ETM+ and TM data pairs. As noted before, sub-pixel geometric registration is not critical in this case, but care was taken to capture the common area as accurately as possible.

The image processing steps in each solar-reflective spectral band i were as follows.

1. Set up a 5 by 5 grid of contiguous image windows or cells and extractmeans and standard deviations from each of the 25 grid cells for an area common to both the ETM+ and TM image data.
2. Repeat step 1 for a series of one-pixel shifts in a 5 by 5 pattern, yielding 25 subsets of means and standard deviations per grid cell. This "jitter" pattern makes it possible to assess the sensitivity of grid-cell data to these shifts as an indicator of misregistration effects. The additional sets of values resulting from this jitter exercise are not used for any other purpose.
3. Keep grid-cell mean results only if sensitivity to shifts is low (within one percent). The value retained is the one obtained for the geometric centre of the jitter pattern.
4. Compute from using equations (8) - (10) to adjust for spectral band differences and illumination regime differences between acquisitions.
5. Plot grid-cell and means and obtain the slopes Mi (equation (8)).
6. Use equation (11) to compute Landsat-5 TM responsivity G_i5 .

The jitter exercise revealed low sensitivity to possible misregistration between the sub-scenes selected as areas common to both images in each tandem pair. For the majority of grid cells, the coefficient of variation for the 25 jitter values of is a small fraction of a percent, reaching 0.3 percent in a few cases for the Niobrara scene and just over one percent for one grid cell for the Railroad Valley playa scene. The average coefficient of variation for the RVPN case is 0.24 percent. Therefore, no image cells were excluded on the basis of the jitter exercise.

After preprocessing in accordance with the radiometric formulation described earlier, sub-scene grid-cell means for and were plotted to obtain the slopes Mi (Equation (8)). Figure 8.3.3 shows a plot for the Railroad Valley playa and Table 8.3.4 lists the slope results for the RVPN and NIOB sub-scene pairs analyzed separately and in combination (Figure 8.3.4). Because the quantized levels are bias-subtracted, the linear fits were forced to have zero intercepts. Nevertheless, with the exception of band 4 for the Niobrara case, the unaccounted for variances in percent, 100 (1- R²), with the linear fits are low (Table 8.3.4), where R is the correlation coefficient. No explanation has been found for the greater scatter in spectral band 4. Table 8.3.4 also indicates that the Mi slopes obtained for the two different image pairs generally differ by a few percent only, which provides some degree of confidence in the cross-calibration methodology.

The Mi slopes derived from the two image pairs (RVPN and NIOB) separately and combined were used in equation (11) to generate TM responsivity coefficients. Figure 8.3.5 compares results from the two image pairs with Railroad Valley playa arbitrarily chosen as the reference case. The consistency between results from the two image pairs varies from negligible differences in spectral band 4 to almost four percent difference in band 7. The average difference is 1.6 percent, which, although based on only 12 spectral band cases, is a measure of the repeatability of the cross-calibration approach.

Figure 8.3.5 also shows differences in TM responsivities if spectral band difference adjustments are excluded (B_i = 1). Overall, adjustments for spectral band difference appear to be on the order of two percent or less in the visible and near-infrared bands, but greater than that in the short-wave infrared bands. As noted in an earlier part of the paper, the implication is that cross-calibration comparisons that do not benefit from the surface reflectance spectra and atmospheric optical parameters needed to compute the spectral band difference effect will potentially have an inherent additional uncertainty of several percent.

A starting point for estimating the uncertainty of the tandem-based cross-calibration method is the ± 3 percent uncertainty of the ETM+ radiometric calibration (Barker et al., 1999). Additional sources of uncertainty include residual geometric misregistration, small changes in atmospheric conditions between tandem image pair acquisitions, artifacts in the TM image radiometry, and residual uncertainty from spectral band difference adjustments. The jitter analysis indicated a misregistration effect on the order of 0.24 percent and, although no corroborative analyses have been carried out, experience suggests that the other uncertainties are also well within one percent. If these additional sources of uncertainty amount to a 1-2 percent effect, the overall root-sum-squared uncertainty for the cross-calibration method is approximately ± 3.5 percent. The near-simultaneity of image acquisition and the similarity of imaging geometry afforded by the tandem configuration are definite advantages in this context. If the spectral signature of the common test site surface is unknown and the spectral band difference effect is 5 percent, say, then the overall uncertainty approaches ± 6 percent.

An evaluation of the tandem cross-calibration would be incomplete without a comparison against results obtained from the two TM vicarious calibrations and to pre-launch responsivity coefficients for Landsat 5.

The work described here indicates that the tandem cross-calibration approach provides a valuable "contemporary" calibration update for Landsat-5 TM solar reflective bands based on the excellent radiometric performance of Landsat-7 ETM+. Initial trials of the approach with two different tandem image pairs yielded repeatable results for TM responsivity coefficients. Users, however, should use the Mi slopes derived from the RVPN tandem pair for updating the radiometry for Landsat 5 level 0 data. This work is ongoing and any improved cross-calibration updates will be made in the Handbook as necessary.

REFERENCES

Table of Contents

Last Update: April 19, 2001

NASA Privacy Statement   and   NASA IT Security Warning Banner