1. Addendum to Exercise 6 and 7 Handling and Processing Satellite (Landsat) Images

2. Error when executing the reflectance calculation using Model Builder

3. All parameters in the Model “menu” have to be set to match YOUR computer system. (How many of you are using an “E” drive and have a folder named “Ex6data”?)

4. When you run the model, it expects you to update all parameters to the correct names and values for YOUR computer Reflectance Model Menu – First part – Define where DN TIF files are coming from

5. When you run the model, it expects you to update all parameters to the correct names and values for YOUR computer Reflectance Model Menu – Second part – Make sure Lmax, Lmin, etc. are correct (from Landsat Header file)

6. When you run the model, it expects you to update all parameters to the correct names and values for YOUR computer. These seven file locations MUST be changed to fit YOUR computer Reflectance Model Menu – Third part – Define where the OUTPUT reflectance files from the Model are GOING TO (On YOUR computer): This is what is causing the error

7. Conversion to Radiance The units for L b are W/m 2 /sr/mm. “sr” stands for ‘sterradian’ and “mm” represents micrometers (1 millionth of a meter). (1) Lb= Spectral radiance at the sensor (satellite) (watt m -2 ster -1 μm -1 ) Lmax= Spectral radiance scaled to Qcalmax (watt m -2 ster -1 μm -1 ) Lmin= Spectral radiance scaled to Qcalmin (watt m -2 ster -1 μm -1 ) Qcal= Quantized calibrated pixel value = DN Qcalmin= Minimum quantized calibrated pixel value corresponding to Lmin Qcalmax= Maximum quantized calibrated pixel value corresponding to Lmax

8. Bits and Bytes Bit Number 76543210 Value represented by bit 2727 2626 2525 2424 23232 2121 2020 1286432168421 Example: Bit settings for 152 10011000 When Satellites “read” the radiation sensors on the satellite, use much precision, for example, 6 bytes x 8 bits/byte = 48 bits. This is done during the “analog to digital” process (A to D). This means converting from a voltage signal on the sensor to a digital number that can be stored and read. However, when they “store” the pixel data on the satellite (temporarily) and when they download it to Earth via radio transmission, they MUST use less memory. Therefore, the “radiance” value from the sensor that is 48 bits (for example), must be “packed” into a smaller space of 16 bits (on Landsat 8) or 8 bits (on Landsat 7) The following is a representation of ONE BYTE (comprised of 8 BITS) Calculation: 1 x 128 + 0 x 64 + 0 x 32 + 1 x 16 + 1 x 8 + 0 x 4 + 0 x 2 + 0 x 1 = 152

10. MTL.TXT (HEADER FILE)

12. Calculate radiance, L, for each band. For example, for band 2 of Landsat 8: LC80350312013171LGN00 LC80350322013171LGN00

13. Step 2. Conversion from radiance to reflectance At-satellite reflectance = Top of Atmosphere (TOA ) r= Planetary reflectance (unitless) L= Spectral radiance at the sensor (satellite) (watt m -2 ster -1 μm -1 ) d 2 = Square of earth-sun distance (in astronomical units, where 1.0 = average Earth-Sun distance) Esun= Mean solar exoatmospheric irradiance (watt m -2 μm -1 Table 2) θ= Solar zenith angle (degree)

14. The definition of solar zenith angle (degree) and sun elevation (degree) Position of Landsat satellite (nadir view) relative to the Earth and Sun.

15. Esun- The energy reaching the surface of the earth per square meter Esun is the energy reaching the surface of the earth per square meter in the specific ‘band’ when there is no atmosphere to absorb any of it. Esun represents energy on a surface that is at a right angle to the solar beam. In other words, if the sun is directly overhead. Band 2Band 3Band 4Band 5Band 6Band 7 2019.61861.11569.3960.4238.880.5 Table 1. Esun for Bands 2 – 7 of Landsat 8, watt m -2 μm -1

16. Drawing showing the earth-sun distance (d). The d is 1.0 on average and changes slightly as season progresses due to rotation of earth around the sun. d 2 = (1 + 0.033 Cos (DOY *2 * 3.141592654)/365)) -1 DOY = day of year = 1 – 365 or 366