Figure 1: This shows how the thermal bar forms, causing water at 4 degrees C, shown here in yellow, to sink.
The surface temperature on the left is greater than 4 degrees C and the surface temperature on the right is less
than 4 degrees C(1).
The progression of the thermal bar is different in each of the Great Lakes. This progression will depend on the size and depth of the lake. This results in the selection of images from different lakes during different times in the spring. However the thermal bar forms in all the lakes between March and June. So image selection is restricted to these months. Image selection was also limited to the days where there wasn't any cloud coverage on the lake. The known temperatures surrounding the thermal bar will be the reference to which this research will radiometrically calibrate images.
Equation 1:
Equation 2: bias = LMIN
Sensor reaching radiance, has to be converted using a linear transformation into ground leaving radiance, Lground, because the atmosphere effects the radiance reaching the sensor and the reference temperatures are on the ground. Once we have ground leaving radiance this is to be converted into planckian radiance, Lplanck, which will mimic a black body radiator. This is important because there is a known relationship, equation 3 between black body radiators and temperature. Since the data is extracted from the lake, the emissivity of water has to be accounted for to convert Lground into Lplanck. Downwelled radiance, Ldownwelled, is backround noise that also contributes to the ground radiance. Equation 4 converts ground radiace to planckian radiance utilizing emissivity of water, a known value of .98, and downwelled radiance.
Equation 3:
Equation 4:
Then the radiance values are put through a look up table that utilizes equation 4, to obtain temperatures.
Then this research used various IDL programs written by Julia Barsi (1). Her radiosonde program was used, it inputs radiosonde and weather data and creates a MODTRAN carddeck. Radiosonde data had to be obtained from the closet radiosonde station to each individual lake. Radiosonde and weather information was obtained form stations closest to the scenes that were being examined. This data was needed for each day at the time Landsat 5 was imaging the area. Another program by Julia Barsi (1), make_modtranprofile inputs the carddeck and temperatures, runs MODTRAN and returns a gain and bias. MODTRAN is a radiative transfer, atmospheric propagation model. This gain and bias is applied to sensor reaching radiance and converts it into ground leaving radiance.
Downwelled radiance was obtained by running a Digital Imaging and Remote Sensing Image Generation Model, DIRSIG, component called make_adb. This also ran MODTRAN using the carddeck created previously which is slightly modified, integrates over the visible hemisphere and outputs a spectral array. The carddeck is modifie4d to work with make_adb instead of just Julia's code. This array had to be spectrally integrated across the Landsat 7 bandpass, 10.40-12.50 micrometers, to produce downwelled radiance. The carddeck was modified by filling in the wildcards which were put in using Julia's code that only work when MODTRAN is run using her code. Once the downwelled radiance was determined all the parameters needed for equation 4 were known and planckian radiance was calcuclated. After putting these values through a look up table temperatures were determined. The difference between the planckian temperature and the estimated temperature of the region of interest was considered to be the bias.
Equation 5:
Landsat 7's calibration for that day had to be adjusted because the calibration was done for the sensor just after it was in orbit. However, the cross calibration occurred while the sensor was still achieving orbit and the sensor's shutter had still not completely cooled (which effects the calibration.) The adjustment for the shutter was done by obtaining radiance bias data and temperature for the shutter from a separate calibration effort on various days that the sensor was achieving orbit. The bias versus shutter temperature was plotted and a linear regression, shown by figure 2 was done. Then the equation was applied to the known shutter temperature for the day of the cross calibration, the resulting bias, -0.30841W/(m2 sr um), is the amount that the calibration was off from the orbiting stable Landsat 7 calibration.
Figure 2: The blue points represent the various days during orbital
insertion. The red
point is the value derived from the regression for the day of the cross
calibration.
Figure 3: This image of Lake Ontario and a small section of Lake
Erie is representative of the
scenes selected for this study. The green region of interest
was taken in the area appearing to
be the coldest on the lake that isn't ice or clouds. This region
of interest is similar to those taken
for all the scenes used in this study.
Calibration Bias' versus Year
Figure 4: This graph represent the resulting bias determined
for the calibration for that particular year.
Figure 5: This image of Lake Michigan shows the common coverage
of the two sensors on June 3, 1999.
The regions shown in color are the common regions selected that were
compared for the cross calibration.
The result of this cross calibration is shown in figure 6. This is the bais determined after adjusting the Landsat 7 calibration. The error bars here are the total error representing the intrinsic error Landsat 7 and Landsat 5.
Calibration Bias' versus Year
Figure 6: The resultant cross calibration bias is shown here
in purple.
Calibration Bias' versus Year
Figure 7: This graph shows the calibration done in 1985 and the
cross calibration.
The line represents the assumption of how the sensor has been behaving
over the years.
After applying the additional dates to this chart, figure 8, it shows that there is a possibility that this is how the sensor has been behaving because most of the points agree with the line within error. However, two of the data points do not fall near the line. These two points are scenes, shown in figure 9, that are considered to be bad data. After comparing these scenes with an average scene, as shown in figure 10, a difference in the quality of the data was obvious.
Calibration Bias' versus Year
Figure 8: This graph shows all the data points involved in this
study. The black points are the
historical data points. The two circled in yellow show the two
scenes that appear to be bad data.
Figure 9: These two images are the scenes that correspond to
the two data point that are considered to obtain bad data.
Figure 10: This is an average scene. After comparing this
scene to
those in figure 9 there is an obvious difference in the quality of
the images.
In an attempt to explain why these two scenes had bad data, outgassing data was obtained (3). These scenes were assumed to be collected around an outgassing period. Outgassing is a procedure that burns off the built up ice crystals that form on the sensor. However after looking at the outgassing dates and comparing them to the scenes' dates it was determined that there was no connection between the two.
This research shows that the linear assumption is not the only possible line that can be drawn encompassing this data. To improve the estimated behavior of the sensor more points can now be used to perform a regression on the data. The trustworthy data points can be weighted more to improve the result of the regression.
The historical calibration can be improved by looking at more scenes and improving the estimated temperature of the region of interest. There was one estimate for all the scenes. All that was considered was that it was the coldest spot in the lake. A refined estimate can be made by considering the time of year, the particular lake and the weather conditions for the season. For example, the coldest spot in Lake Superior in June 1987 is probably much different from the coldest spot in Lake Ontario in March 1999. This would also reduce the error associated with the calibration.