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

Error when executing the reflectance calculation using Model Builder

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”?)

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

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)

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

Conversion to Radiance

The units for Lb are W/m2/sr/mm. “sr” stands for ‘sterradian’ and “mm” represents micrometers (1

millionth of a meter).

LMIN)QCALMINDN(QCALMINQCALMAX

LMINLMAXLb

(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

Bits and Bytes

Bit Number 7 6 5 4 3 2 1 0

Value represented by bit

27 26 25 24 23 22 21 20

Value represented by bit 128 64 32 16 8 4 2 1

Example: Bit settings for 152

1 0 0 1 1 0 0 0

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

MTL.TXT (HEADER FILE)

)-62.24319()165535(

)1(*))(-62.24319-753.72913(2

DN

L

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

LMIN)QCALMINDN(QCALMINQCALMAX

LMINLMAXLb

LC80350312013171LGN00

LC80350322013171LGN00

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) d2 = 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)

CosE

dLr

sun*

** 2

The definition of solar zenith angle (degree) and sun elevation (degree)

Position of Landsat satellite (nadir view) relative to the Earth and Sun.

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 2 Band 3 Band 4 Band 5 Band 6 Band 7

2019.6 1861.1 1569.3 960.4 238.8 80.5

Table 1. Esun for Bands 2 – 7 of Landsat 8, watt m-2 μm-1

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.

d2 = (1 + 0.033 Cos (DOY *2 * 3.141592654)/365))-1

DOY = day of year = 1 – 365 or 366