Landsat-7 and Landsat-5 Thermal Band Calibration Updates Julia A. Barsi*a, Brian L. Markhamb, John R. Schottc, Simon J. Hookd, Nina G. Raquenoc a SSAI, NASA/GSFC, Greenbelt, MD USA 20771; b NASA/GSFC Greenbelt, MD, 20771; cCenter for Imaging Science, Rochester Institute of Technology, Rochester NY, 14623; dNASA/JPL, Pasadena CA, 91109 ABSTRACT Landsat-7 ETM+, launched in April 1999, and Landsat-5 TM, launched in 1984, both have a single thermal band. Both instruments’ thermal band calibrations have been updated: ETM+ in 2001 for a pre-launch calibration error and TM in 2007 for data acquired since the current era of vicarious calibration has been in place (1999). This year, the vicarious calibration teams have made regular collects of very hot targets, and have been able to make use of archived buoy data to extend the TM calibration back in time. The new data has made it clear that both instruments require slight adjustments in their thermal calibration coefficients. These new coefficients will be generated and put into the operational processing system to remove the calibration errors. The JPL vicarious calibration team has long operated automated buoys on Lake Tahoe for the purpose of vicarious calibration. This year, the Salton Sea station came on line. Salton Sea, located in southern California, gets far hotter than Lake Tahoe. Vicarious calibration results of the Salton Sea for both instruments added to the understanding of a small gain error that the Tahoe data had suggested. With the Salton Sea data, an ETM+ gain error became statistically significant. Though it causes errors as large as 1.2K at high temperatures (35C), at more usual earth temperatures (420C) the calibration error is within the noise of the calibration methodology (+/-0.6K). With an ETM+ calibration update, the RMSE will be +/-0.6K for all temperatures. The RIT vicarious calibration team mined the archive of the NOAA National Data Buoy Center for sites on the Great Lakes and in the Atlantic Ocean where buoy data was regularly available between 1984 and 2007 and there were radiosonde data within close proximity to allow for atmospheric correction. Four Landsat scenes were chosen and the study made use of almost 200 separate acquisitions of these scenes. The technique was first tested with Landsat-7 data, and was shown to be as reliable as the standard RIT vicarious calibration methods. The TM calibration was largely unmonitored for most if it’s lifetime. The buoy results suggest a lifetime error in gain and a change in the offset after 1997. The 2007 TM calibration update accounted for much of the offset error but was only implemented for data acquired after 1999. With the additional buoy data, the calibration will be corrected for the earlier time period and the result will be a consistent calibration to within +/-0.6K for the lifetime of the TM. Keywords: Landsat, radiometry, calibration, thermal
1. INTRODUCTION The Landsat instruments, the Thematic Mapper (TM) and the Enhanced Thematic Mapper Plus (ETM+), have been acquiring coverage of the earth’s surface since 1984. Landsat-7 was launched in April 1999 and its ETM+ sensor has been used to acquire data nearly continuously since July 1999. The ETM+ has 6 reflective spectral bands with 30 meter spatial resolution, one panchromatic band at 15 meter spatial resolution and one 60 meter thermal band (Band 6; 10.3112.36 μm). This scanner uses silicon detectors on an uncooled focal plane for Bands 1-4 and 8; InSb detectors for Bands 5 and 7 and HgCdTe detectors for Band 6 on a 91K radiatively cooled focal plane. Two gain states are available for each band; the high gain state is 1.5 times higher than low gain state in the reflective bands. The data are quantized to 8 bits. The scan-line corrector mirror assembly stopped working in 2003, which affects the spatial coverage of the *
[email protected] Earth Observing Systems XIV, edited by James J. Butler, Xiaoxiong Xiong, Xingfa Gu Proc. of SPIE Vol. 7452, 74520S · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.828501
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scanner, but has not affected the radiometric performance1. In 2007, the scan mirror and shutter flag were unable to maintain synchronization and the instrument was switched to an alternate scanning mode, called Bumper Mode (BM). This also has affected the geometric performance of ETM+ but not the radiometric performance. Landsat-5 launched in 1984 and the Thematic Mapper (TM) has been operating for well over its predicted lifespan of three years. Privately run for most of its lifetime, the spacecraft and the data archive reverted to government control in 2001. The TM has a similar suite of bands as the ETM+, though TM does not have a panchromatic band and the spatial resolution of the thermal band is 120 meters. The instrument only has one gain state and the data are quantized to 8 bits. A technical failure of one of the transmitters in 1987 means that only data acquired within an acquisition circle of a ground station can be downlinked. The US archive, therefore, primarily contains data acquired over North America. However, international ground stations hold years of global TM data as well. The TM scanner was switched to BM in 2002 due to the loss of synchronization between the mirrors. As with ETM+, the switch has not affected the radiometric performance of the instrument.
2. INTERNAL CALIBRATION The TM and ETM+ internal calibration systems consist of a single on-board cavity blackbody and a black highly emissive shutter2. The blackbody sits off the optical axis at one of three temperatures. The shutter, which carries the calibration lamps across the optical axis for calibration of the visible bands, has on it a toroidal mirror. As the shutter sweeps onto the optical axis, the mirror reflects the radiation from the blackbody onto the optics and through to the cooled focal plane. The non-mirror part of the shutter is coated with a high-emissivity paint and sits at the instrument ambient temperature. Outputs from thermistors located within TM and ETM+ monitoring temperatures of individual components are included in the downlinked data. 2.1 Landsat-5 equations The instrument gain is calculated from the blackbody and the shutter, i.e.,
Gin = and
Qbb − Qsh Lbb − Lsh
Gext = aGin
(1) (2)
where Qbb is the average digital number of the internal blackbody (calibration pulse), Qsh is the average digital number of the shutter, Lbb is the spectral radiance of the blackbody as calculated from the blackbody temperature, Lsh is the spectral radiance of the shutter as calculated from the shutter temperature, and a is the per-detector pre-launch determined gain ratio between the gain determined by the calibration system, Gin, and the gain of the full system, Gext. The offset, Q0, or the response of the system to zero radiance, was modeled during pre-launch testing. The final model relied on constant coefficients rather then including any dependency on instrument temperatures, unlike the Landsat-7 ETM+ thermal model. The offset is calculated from these coefficients, the shutter, and the internal gain:
Q0 = Qsh − Gin (bLsh − c )
(3)
where b and c are per-detector pre-launch determined constants. The Landsat processing system calculates the gain and offset on a per-scan and per-scene basis and records these to a database. Radiance images are generated using the perscene gains and per-scan offsets:
Lλ = (Q − Q0 ) /Gext where Lλ is the spectral scene radiance and Q is the raw digital count from the scene.
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(4)
TM Band 6 Offset
TM Band 6 External Gain 40
26 24
20
22 0
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18
5
10
15
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25
-20
16 -40
14 12
-60
10 0
5
10
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time since launch (years)
time since launch (years)
Fig. 1. Internal calibrator data of TM Band 6 as calculated by the processing system. The band is affected by the build-up of ice on the dewar window, which attenuates the incoming energy. When the ice is melted off, the detectors return to full responsivity These gains and offsets are used in the processing system; thus the variation is fully accounted for in the calibration.
The cold focal plane of Landsat-5 is affected by the build up of a contaminant, presumably ice, on the Dewar window. This slow build up of ice affects the transmission of the window, decreasing the amount of energy reaching the Band 6 detectors as the layer gets thicker (Bands 5 and 7 are affected differently than the thermal band). Figure 1 is a plot of the on-board calibrator gain, Gext, and offset, Q0. The thermal band gain has traditionally been used as the bellwether for when to perform the operation to melt off the ice (known as outgassing). The occurrence of this procedure can be clearly seen in Figure 1; the responsivity drops slowly while the ice layer is building, then jumps when the layer of ice is suddenly removed. The calibration gain and offset of TM Band 6 have never been stable as a result of the ice build-up, but these internal calibrator gains and offsets are used in the calibration of the data, so the variation in responsivity is fully accounted for by the calibration process. 2.2 Landsat-7 equations For ETM+ Band 6, the gain is calculated in the same manner as for Landsat-5 (Equations 1 and 2), although the coefficient is known as GR, instead of a. However, for the offset, rather than rely solely on temperature independent coefficients to account for the contribution of the internal components, which change temperature as the instrument warms up, the effect of the components was empirically derived3. Five components were analytically determined to have a significant effect on the overall calibration: the scan-line corrector, the central baffle, the secondary mirror, the primary mirror and the scan mirror. Their contribution is based on their temperature, their emissivity and the extent to which they emit into the optical path. Thus, the temperatures (by way of their radiances) of the components are included in the calculation of the offset term: 5 ⎛V ⎞ sh ⎟ ⎜ Q0 = Qsh − GR Gin ⎜ Lsh + ∑ a j (Lsh − L j )⎟ j=1 ⎠ ⎝ GR
(5)
where Lj is the spectral radiance from optical element j; and aj is the view factor associated with optical element j. The gain and offset of the ETM+ Band 6 are shown in Figure 2. Landsat-7 does not suffer from the build-up of ice on the dewar window, so the gain and offset have remained stable for the lifetime; the gain is stable to within 0.5%, the offset to with 1.5%.
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ETM+ Band 6 External
ETM+ Band 6 Offset
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32 31.5
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12.2
28
0
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Fig. 2. Internal calibrator data of ETM+ as trended by the processing system. Landsat-7 does not suffer from the build-up of ice so the gain and offset have remained stable. The steps and gaps seen in the plots are due to operational or processing changes and are either not significant or are accounted for by the processing system.
3. VICARIOUS CALIBRATION Water is the primary target for thermal calibration because it is uniform in composition, has a high and known emissivity, and often exhibits low surface temperature variation (less than or equal to 1C) over large areas. Land targets can provide a higher range of temperatures, but they are generally more difficult to characterize. The Landsat vicarious calibration teams perform their work on water, though early in the lifetime of Landsat-7, a very flat land target was used for high temperature verification. The NASA/Jet Propulsion Laboratory (JPL) has operated four buoys on Lake Tahoe on the California/Nevada boarder since 1999 for the purpose of thermal calibration4. The high altitude lake is an ideal thermal calibration target; there is little atmosphere above the lake, the lake is extremely deep so doesn’t freeze in the winter, and it has a fairly broad annual temperature range from about 4C to 20C. The four buoys acquire surface radiance and temperature measurements every few minutes and send the data to JPL via cell phone. The JPL team has also installed a similar station on the Salton Sea which has reliably been collecting data for the past two years. Though not the ideal water body – the sea is below sea level and the atmosphere is generally quite thick – it does get up to 35C in the summer, so provides a hot target without having to use land. In 1999 and 2000, JPL made several collects on a hot desert, Railroad Valley in Nevada. However, regular collects have not been made since due to the difficulty of the collection and the uncertainty in the measurements. The Rochester Institute of Technology (RIT) team makes use of the local Great Lakes for their targets5. They deploy in boats on the lakes and bays around Rochester, NY and Buffalo, NY to measure surface temperatures. The lakes do freeze, but RIT collects data from about 4 to 25C. Recently, RIT has begun using the National Data Buoy Center (NDBC)archive to expand their reach, both in space and time6. Using water temperatures collected by open water buoys in Lake Huron, Lake Superior and off the coast of Delaware and corresponding atmospheric data acquired near shore, the same techniques are used to predict satellite reaching radiance for the NDBC buoys as for the manually collected temperatures. The buoy method has been found to be as accurate as their traditional method (not statistically different at the 99% CI level). Since the water temperature archive is available for the lifetime of Landsat-5, the team was able to extend the calibration back to years before rigorous calibration monitoring started.
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Fig. 3. JPL vicarious calibration data broken down by site. The slope suggested by early data collected on Railroad Valley (RRV) was discounted as error in the measurements. The recent addition of the Salton Sea data provides a stronger argument for a gain error.
Fig. 4. Vicarious calibration results for ETM+ Band 6 using the current calibration coefficients. In a perfectly calibrated system, the data will fall on the 1:1 line.
Fig. 5. ETM+ Band 6 residual error vs target radiance. The dependence of the error on target radiance indicates an error in gain that has been present since launch.
Fig. 6. ETM+ Band 6 residual error over time. The error has been random about zero since launch with the current calibration coefficients.
3.1 Landsat-7 Shortly after the launch of Landsat-7, vicarious calibration efforts discovered a calibration error in the thermal band, a offset error of 0.31 W/m2 sr μm7. It was corrected in 2000 for all ETM+ data acquired since launch by modifying the Vsh calibration coefficient in the processing system. In the first two years of the post-launch vicarious calibration program, JPL made measurements of hot desert pavement (40-55C) at Railroad Valley (RRV) (Figure 3). These data were considered in the initial calibration correction but because the uncertainty on the hottest points was high enough that the slope was not statistically different than unity, only an offset correction was implemented in the 2000 correction. Regular monitoring has continued since, and the addition of the warm Salton Sea data from the past two years has made the gain error apparent (Figure 4). All data here are processed including the 2000 correction. The Tahoe data have always been in agreement with the RITG data, but over a relatively narrow temperature range. Because uncertainty in the Salton Sea data is smaller than the uncertainty in the RRV measurements, the slope is now statistically different than 1. The gain error is apparent in the collected data (Figure 4) but more apparent in the residual error plots. The residual error shows a strong dependence on target radiance (Figure 5) but is not time dependent (Figure 6). This indicates that
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neither the gain nor offset have changed since the 2000 update, but the gain error has been present since launch. Table 1 lists the gain and offset errors as estimated by the teams. The slope is statistically different than unity in all cases. The error in offset, though small, is significant and can be corrected at the same time. The calibration error is small at normal earth temperatures (0-20C) and has been difficult to discern in the Tahoe and RITG data for years. With the with the addition of the hot Salton Sea data, the error became apparent. The effect to the data product is similarly difficult to discern; the calibration error amounts to less then 1C between 0 and 20C but at 35C is 1.2C (Table 2).
Table 1. ETM+ vicarious calibration statistics. A slope significantly different than unity indicates a calibration error in gain. A residual offset significantly different than zero indicated a calibration offset error. The three methods agree that there is gain error of between 4 and 9%. The residual offset is also statistically significant, though small.
Team JPL RITG RITB Combined, all data taken together Combined, team average
N 189 49 38 276
Slope ± 95% CI 0.936 ± 0.009 0.955 ± 0.019 0.918 ± 0.030 0.943 ± 0.008
Residual Offset ± 95% CI -0.013 ± 0.014 -0.028 ± 0.016 -0.038 ± 0.029 -0.019 ± 0.010
0.936 ± 0.037 (RSS)
-0.026 ± 0.036 (RSS)
Table 2. ETM+ Band 6 estimated effect of the calibration error on top-of-atmosphere brightness temperature for different temperature targets and the team-combined error estimate. A positive error indicates the satellite is predicting too hot, a negative indicates too a cold prediction.
Team Combined, all data taken together
0C [C] 0.7
Target Temperature 10C 20C 35C [C] [C] [C] 0.1 -0.4 -1.2
50C [C] -2.0
3.2 Landsat-5 Early in the lifetime of Landsat-5, RIT performed the first verification of the thermal band calibration. Conclusions were that TM Band 6 was calibrated to within ±0.9K8. Unfortunately, the calibration was not monitored between 1985 and 2001. In 2001, the Landsat-7 vicarious calibration teams began monitoring Landsat-5 as well. RIT deployed regularly under Landsat-5 in the lakes and bays but could only calibrate current data. JPL team was able to carry the calibration back to 1999, the beginning of the Lake Tahoe buoy archive. By 2007, enough evidence had accumulated to indicate that there was a calibration error9. Both teams’ data indicated an offset error, both saying that Landsat-5 was reporting cooler than it should be. In 2007, an update was made to the c calibration coefficient to account for a 0.092 W/m2 sr μm offset, but only for data acquired since 1999. As there was no vicarious calibration data before 1999, it was felt that the prelaunch calibration should be maintained until otherwise invalidated. Since 2007, the RIT buoy method and the JPL Salton Sea station have become reliable sources of calibration data. These data expand the temporal and thermal range of the vicarious calibration far beyond the data used to make the calibration update in 2007. While the JPL Tahoe data and the RIT Traditional data (RITG) both suggested that the instrument had a gain error, the slope was not statistically significant. The hotter Salton Sea data increases the temperature range, to provide greater confidence in the dependence on target radiance of the calibration. The RIT Buoy data (RITB) added 95 points before 1999, allowing a check of the calibration status for a period of time when there was previously no data.
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Fig. 7. Vicarious calibration results for TM Band 6 acquired after 1999 using the prelaunch calibration coefficients (the 2007 correction has been removed). In a perfectly calibrated system, the data will fall on the 1:1 line. All data here are below the 1:1 line, indicating an offset error. The high temperature Salton Sea data also contribute to the indication of the gain error.
Fig. 9. TM Band 6 residual error vs target radiance. The dependence of the error on radiance indicates an error in gain that has been present since launch.
Fig. 8. TM RITB vicarious calibration data broken down by date. Difference in offset is apparent between the data acquired before 1997 and after 1999. Analysis is ongoing to determine when between 1997 and 1999 the change in offset occurred.
Fig. 10. TM Band 6 residual error over time. The error was random about zero until about 12 years after launch with the prelaunch calibration coefficients. After year 15, there is a significant offset error; the data generally lie below zero. Between 12 and 15 years since launch, there is a transition from one state to the other.
All the data presented here are processed using the prelaunch calibration, meaning the 2007 calibration correction has not been applied. Figure 7 shows the vicarious radiance vs. image radiance for all data acquired after April 1999, including JPL Tahoe and Salton, RIT Traditional and Buoy. The gain error is apparent in Figure 7, as evidenced by a non-unity slope, particularly with the recent Salton Sea data (points above 9 W/m2 sr μm) but the slopes in the two RIT data sets are also statistically different than unity (Table 3). The methods are predicting between 5 and 10% gain error after 1999. Looking at just RITB in Figure 8, the data is split by date of acquisition. Data after 1999 (duplicated from Figure 7) sits below the 1:1 line, while the data acquired before 1997 is scattered about the 1:1 line. The gain error exists in both cases, but the offset error is only in the data after 1999. The data collected between 1997 and 1999 is plotted separately, as work is ongoing to determine when the offset change occurred. The errors are more apparent in the residual error plots. In Figure 9, the error is dependent on target temperature. In Figure 10, the residual offset error is
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time dependent. The RITB data show that the residual error changes from being random about zero from launch until about 1997, when it drops below zero (Table 3). The RITG and JPL data, only being collected after 1999, are in agreement as to their being a residual negative error of between -0.10 and -0.16 W/m2 sr μm . Taken altogether, the data indicate there has been a gain error since the launch of Landsat-5, and sometime between 1997 and 1999, the offset changed. No cause has been established for the change in offset, but it appears that it happened independently of the launch of Landsat-7 in 1999. Table 4 gives an estimate of the effect of the calibration error on top-of-atmosphere (TOA) temperatures for the historical RIT Buoy data error estimates, for the two time periods. For targets between 0 and 20C, a “normal” surface temperature, the, the error is between -1.0 and 1.0C for the older data, where a negative indicates the instrument is predicting too cold and a positive is too hot. For data acquired after 1999, the errors in this table are all negative because of the offset error, but over the 0-20C range, the error is within 1.5C. Note that the 2007 correction, which is removed in these data, served to eliminate the offset error in the data acquired since 1999, so the temperature error estimates presented here for scenes acquired after 1999 don’t actually reflect the calibration of the products being distributed currently. Since there is little reason to believe the gain should be different before and after 1999, the slopes of the teams’ vicarious data will be combined to generate a new lifetime gain coefficient, a from Equation 2. Once a definitive date has been established for the offset change, a new bias coefficient, c, will be determined as well. Once new calibration coefficients have been calculated, they will be presented to the Landsat Calibration Working Group for approval. Once approved, they can be updated in the CPF and put into production immediately.
Table 3. TM vicarious calibration statistics. A slope significantly different than unity indicates a calibration error in gain. A residual offset significantly different than zero indicated a calibration offset error. The RITB data indicate that before 1999, there was a gain error, but no offset error. The post-1999 data are in agreement that there is both a gain and offset error. Team RITB (19841997) JPL (>1999) RITG (>1999) RITB (19992008) Combined, all data taken together (>1999) Combined, team average (>1999) combined (1984-2008)
N 95
Slope ± 95% CI 0.895 ± 0.020
Residual Offset ± 95% CI 0.006 ± 0.020
Table 4. TM Band 6 estimated effect of the calibration error on top-of-atmosphere brightness temperature for different temperature targets and for the worst case of the error estimates (RITB). The errors are estimated relative to the prelaunch calibration. A positive error indicates the satellite is predicting too hot, a negative indicates too cold a prediction.
Year of Data Acquisition 1984 – 1997 > 1999
118 23 76
0.964 ± 0.020 0.978 ± 0.041 0.916 ± 0.018
-0.104 ± 0.015 -0.124 ± 0.025 -0.160 ± 0.022
217
0.948 ± 0.014
-0.126 ± 0.012
0.953 ± 0.049 (RSS)
-0.129 ± 0.037 (RSS)
0.952 ± 0.049 (RSS)
n/a
352
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0C [C] 1.0 -0.5
TOA Target Temperature 10C 20C 35C 50C [C] [C] [C] [C] 0.0 -1.0 -2.4 -3.8 -1.0 -2.0 -2.5 -4.0
4. CONCLUSIONS The vicarious calibration results for both TM and ETM+ thermal bands indicate calibration errors. This is a result of new data available from the calibration teams; warm data from the Salton Sea and historical data from NDBC buoys. The Landsat-5 results indicate a gain error that has been present since the launch of the instrument in 1984 and an offset error after 1999. Over the range of normal Earth temperatures (0-20C), the gain error causes between 1.0 and -1.0C in the temperature prediction before 1997. However, the error is more significant in extreme temperatures. The change in offset between 1997 and 1999 adds an offset error, so the errors range between -0.5 and -2.0 for normal Earth temperatures after 1999. Most of this offset error has been corrected for in the processing system since 2007, but an update to the calibration coefficients will correct for both. Landsat-7 vicarious calibration results are similar; recent Salton Sea data has made a gain error apparent. The error has been present since launch but difficult to detect in the relatively cool data from Tahoe and RIT. Errors in predicted topof-atmosphere temperature range from between 0.7 and -0.4C for targets between 0 and 20C. New calibration coefficients will correct for this error. Landsat data are now distributed for free by the US Geological Survey Center for Earth Resources Observation and Science (USGS/EROS). The data are generally processed in advanced to a radiometrically and geometrically calibrated product for immediate download by the user. With this product delivery model, it is not guaranteed that the user will receive data processed with the latest calibration updates. Please check the Calibration Notice website for the latest information on when the thermal band calibration is implemented how to tell is downloaded data has been processed with the update: http://landsat.usgs.gov/science_calibration.php.
REFERENCES [1]
[2] [3] [4]
[5] [6] [7] [8] [9]
Markham, B.L., K.J. Thome, J.A. Barsi, E. Kaita, D.L. Helder, J.L. Barker, and P. Scaramuzza, “Landsat-7 ETM+ on-orbit reflective-band radiometric stability and absolute calibration,” IEEE Trans. Geoscience and Remote Sensing, 42(12), 2810-2820 (2004). Markham, B.L., Boncyk, W.C., Helder, D.L., Barker, J.L., “Landsat Enhanced Thematic Mapper plus radiometric calibration,” Canadian Journal of Remote Sensing, 23(4), 318-332 (1997) Turtle, R.R., “ETM+ band 6 calibration report” (PL2807E-T06298), SBRS (1999) Hook, S.J., Chander, G., Barsi, J.A., Alley, R.E., Abtahi, A., Palluconi, F.D., Markham, B.L., Richards, R.C., Schladow, S.G., Helder, D.L., “In-flight validation and recovery of water surface temperature with Landsat-5 thermal infrared data using an automated high-altitude lake validation site at Lake Tahoe,” IEEE Trans Geoscience and Remote Sensing, 42(12), 2767-2776 (2004) Schott, J.R., Barsi, J.A., Nordgren, B.L., Raqueno, N.G., de Alwis, D., “Calibration of Landsat thermal data and application to water resource studies,” Remote Sensing Environment, 78(1/2), 108-117 (2001) Padula, F.P., Schott, J.R., “Historic Thermal Calibration of Landsat 5 TM”, submitted to Photogrammetric Engineering and Remote Sensing (2009) Barsi, J.A., Schott, J.R., Palluconi, F.D., Helder, D.L., Hook, S.J., Markham, B.L., Chander, G., O’Donnell, E.M., “Landsat TM and ETM+ thermal band calibration,” Canadian Journal of Remote Sensing, 29(2), 141-153 (2003) Schott, J.R., “Thematic Mapper band 6, radiometric calibration and assessment,” Proc SPIE 924, 72-88 (1988) Barsi, J.A., Hook, S.J., Schott, J.R., Raqueno, N.G., Markham, B.L., “Landsat-5 Thematic Mapper Thermal Band Calibration Update,” IEEE Geoscience and Remote Sensing Letters, 4(4), 552-555 (2007).
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