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Section 5 - Conversion of DNs to Physical Units
5.1 OLI and TIRS at Sensor Spectral Radiance
Images are processed in units of absolute radiance using 32-bit floating-point calculations. These values are then converted to 16-bit integer values in the finished Level-1 product. These values can then be converted to spectral radiance using the radiance scaling factors provided in the metadata file:
Lλ = ML*Qcal + AL
Lλ = Spectral radiance (W/(m2 * sr * μm))
ML = Radiance multiplicative scaling factor for the band (RADIANCE_MULT_BAND_n from the metadata).
AL = Radiance additive scaling factor for the band (RADIANCE_ADD_BAND_n from the metadata).
Qcal = L1 pixel value in DN
5.2 OLI Top of Atmosphere Reflectance
Similar to the conversion to radiance, the 16-bit integer values in the L1 product can also be converted to TOA reflectance. The following equation is used to convert Level-1 DN values to TOA reflectance:
ρλ' = Mρ*Qcal + Aρ
ρλ' = TOA Planetary Spectral Reflectance, without correction for solar angle. (Unitless)
Mρ = Reflectance multiplicative scaling factor for the band (REFLECTANCE_MULT_BAND_n from the metadata).
Aρ = Reflectance additive scaling factor for the band (REFLECTANCE_ADD_BAND_n from the metadata).
Qcal = L1 pixel value in DN
Note that ρλ' is not true TOA Reflectance, because it does not contain a correction for the solar elevation angle. This correction factor is left out of the L1 scaling at the users' request; some users are content with the scene-center solar elevation angle in the metadata, while others prefer to calculate their own per-pixel solar elevation angle across the entire scene. Once a solar elevation angle is chosen, the conversion to true TOA Reflectance is as follows:
ρλ = TOA Planetary Reflectance. (Unitless)
θ = Solar Elevation Angle (from the metadata, or calculated)
5.3 TIRS Top of Atmosphere Brightness Temperature
TIRS data can also be converted from spectral radiance (as described above) to brightness temperature, which is the effective temperature viewed by the satellite under an assumption of unity emissivity. The conversion formula is as follows:
T = TOA Brightness Temperature, in Kelvin.
Lλ = Spectral radiance (Watts/(m2* sr * μm))
K1 = Thermal conversion constant for the band (K1_CONSTANT_BAND_n from the metadata)
K2 = Thermal conversion constant for the band (K2_CONSTANT_BAND_n from the metadata)
5.4 Unpacking Quality Assessment Band Bits
The pixel values in the QA band file must be translated to 16-bit binary form to be used effectively. The gray shaded areas in Table 5‑1 show the bits that are currently being populated in the L1 QA Band, and the conditions each describe. None of the currently populated bits is expected to exceed 88 percent accuracy in their reported assessment at this time.
Table 5-1 . Bits Populated in the Level-1 QA Band
For the single bits (0, 1, 2, and 3):
- 0 = No, this condition does not exist
1 = Yes, this condition exists.
The double bits (4-5, 6-7, 8-9, 10-11, 12-13, and 14-15), read from left to right, represent levels of confidence that a condition exists:
- 00 = "Not Determined" = For Cloud or Cirrus, the algorithm did not run. For the other confidence classifications this is a "No", the Algorithm has no confidence that this condition exists
- 01 = "No" = Algorithm has low to no confidence that this condition exists (0-33 percent confidence)
- 10 = "Maybe" = Algorithm has medium confidence that this condition exists (34-66 percent confidence)
11 = "Yes" = Algorithm has high confidence that this condition exists (67-100 percent confidence)
For example, a pixel with a value "58384" translates to the 16-bit binary string "1110 0100 0001 0000." Reading the binary string from right to left and using Table 5-1 as an interpretation legend, this pixel is as follows:
- Bit 0 = 0 = not fill
- Bit 1 = 0 = not a dropped frame
- Bit 2 = 0 = not terrain occluded
- Bit 3 = 0 = not determined
- Bit 4-5 = 01 = not water
- Bit 6-7 = 00 = not determined
- Bit 8-9 = 00 = not determined
- Bit 10-11 = 01 = not snow/ice
- Bit 12-13 = 10 = could be cirrus cloud
- Bit 14-15 = 11 = cloudy
Certain values occur regularly and can be interpreted without unpacking them into 16-bit strings and using Table 5‑1 as a reference. Table 5‑2 includes some common pixel values and their meanings. A no-cost tool is available for user download that will extract the bit-packed information in the OLI QA band for easy interpretation. Details are provided on the Landsat QA Tools web page.
Table 5-2. A Summary of Some Regularly Occurring QA Bit Settings
5.5 LandsatLook Quality Image (.png)
The 8-bit LandsatLook Quality Image (.png) is available to download when downloading L8 data products. This file provides a quick view of the quality of the pixels to determine which scene would work best for each user's application. Only the highest confidence conditions are used to create the LandsatLook Quality image. Similar as stated above, this image may not be useful to all users.
Table 5-3 gives the bits and colors associated with the LandsatLook Quality Image:
Table 5-3 . Bits and Colors Associated with LandsatLook Quality Image
Figure 5-1. Landsat Look "Quality" Image (QA.png) displayed as .jpg, for reference only. Landsat 8 Path 45 Row 30 Acquired April 23, 2013