Advanced Remote Sensing: Reflectance Models, Atmospheric Correction, and Sensor Mechanics

Data Availability and Levels of Correction: Space agencies provide satellite products that have already undergone various levels of processing. These levels are indicated by specific designations in the file names: * L0 (Level 0): Raw data. * L1 (Level 1): Radiometrically corrected data (often converted from digital numbers to radiance). * L2 (Level 2): Reflectance products reflecting surface conditions after atmospheric correction.

Importance of Illumination and Viewing Angles: To derive an ideal surface reflectance product, analysts must consider the solar zenith angles and the sensor viewing zenith angles.
Bidirectional Effects: These effects describe how the same object can appear with different contrasts depending on the time of observation and the viewing angle of the sensor. A change in contrast does not necessarily indicate a change in the condition of the vegetation.
Forward Scattering: * Occurs when the sun is in front of the camera (sensor). * The sensor observes in one direction while illumination comes from the opposite direction. * Results in increased brightness due to forward scatter.
Backward Scattering: * Occurs when the sun is behind the camera/sensor. * Results in reduced scatter compared to forward scattering.

Definition: Improved simplified reflectance attempts to improve upon simple reflectance by incorporating additional parameters to increase quality.
Key Parameters: * Solar Irradiance: The amount of energy given out by the sun. This value varies across different bands or wavelengths. * Apparent Reflectance: Also synonymous with simplified reflectance (calculated in previous steps). This is required as an input for the improved formula. * Zenith Angle of Incident Flux ( $\theta$ ): The angle of the irradiance incident on a surface. * Correction Factor ( $d$ ): Used to account for the variation in the distance between the Earth and the Sun.
Top of the Atmosphere (TOA) Reflectance: The final product of the improved simplified reflectance calculation is called TOA reflectance. * It is not the "ideal" reflectance because it does not account for atmospheric effects or sensor viewing angles. * It only improves on simple reflectance by incorporating solar irradiance and Earth-sun distance variations.

Orbital Variations: The Earth's orbit around the sun is not perfectly round; it is described as "egg-shaped." Because the sun stays fixed while the Earth moves along its orbit (taking 365 days), the distance between them changes throughout the year. * Perihelion: The point where the Earth is closest to the sun. * Aphelion: The point where the Earth is farthest from the sun.
Impact on Intensity: These distance changes introduce variations in illumination intensity. The $d$ factor corrected for these variations to ensure images are consistent throughout the year.
The Julian Calendar ( $j$ ): Calendar days are expressed as Julian numbers (e.g., May 23rd or June 7th would correspond to a specific integer in a Julian calendar) which are substituted into the formula.
Mathematical Constraint: In the trigonometric terms of the $d$ factor equation (specifically the sine term), calculators must be set to radians to ensure accuracy.

Components of the Radiance Model: * Downward Irradiance ( $L_0$ ): Irradiance emitted by the sun that passes through the vacuum of space before entering the atmosphere. * Transmission ( $T$ ): As light hits the atmospheric layer, it undergoes transmission. * Scattering and Absorption: Two key processes within the atmosphere that reduce the amount of irradiance that reaches the surface. * Diffuse Irradiance ( $E_d$ ): Irradiance that scatters specifically as it lands or becomes incident on a surface.
Sensor Recorded Signal: The sensor records a combined signal consisting of: 1. The radiance coming directly from the object of interest. 2. Atmospheric reflectance ( $L_A$ ), which represents scattering from the top of the atmosphere.
Correction Process: The goal of atmospheric correction is to isolate and remove the $L_A$ component (atmospheric errors) from the radiance measurements to improve the quality of the reflectance data. Ignoring these effects results in biased results.

Data Conversion: Digital Numbers (DN) in thermal bands must be calibrated as follows: * $\text{DN} \rightarrow \text{Spectral Radiance} \rightarrow \text{Surface Brightness Temperature}$
Units: Surface brightness temperature is measured in Kelvin ( $K$ ) but can be translated to Celsius ( $^{\circ}C$ ).
Surface Profiles: A transect (cross-section) can be drawn across heterogeneous images (containing water, rooftops, soil, and grass) to produce a temperature profile. * Example (Gauteng): A transect across agricultural farms and open soil shows high brightness temperatures. As the transect crosses a water body, the temperature drops significantly.

Whizbroom Scanners: These scanners oscillate back and forth. They have the advantage of covering wider areas (e.g., the MODIS sensor).
Pushbroom Scanners: These scanners record data along the orbital track as the satellite moves.
Orbital Tracks: Satellites move along specific orbits (tracks) in space. Each orbit has a specific number. To achieve global coverage, a satellite moves from the first orbit to the second, third, and so on.
Swath Width: The horizontal size/width of an orbital track. This defines the width of the captured image.

Sensor Dwell Time: The amount of time the sensor spends recording radiance from an individual pixel. * Higher Dwell Time: Leads to a better signal-to-noise ratio. * Lower Dwell Time: Occurs when scanners must move quickly to achieve high temporal resolution (e.g., daily global coverage), often resulting in lower quality or blurrier data.
Orbital Velocity ( $v$ ): Calculated using the formula: * $v = \sqrt{\frac{GM}{r}}$ * Where $r$ is the total distance from the center of mass (the orbital height $h$ plus the radius of the Earth $R$ ). * Landsat 7 Example: The orbital velocity is approximately $7,500\,m/s$ .
Dwell Time Calculation Formula: * $\text{Dwell Time} = \frac{\text{Down track pixel size}}{\text{Orbital Velocity} \times (\frac{\text{Cross track line width}}{\text{Cross track pixel size}})}$ * Landsat Specifications: For Landsat, the pixel resolution is $30\,m \times 30\,m$ . Therefore, the down-track pixel size is $30\,m$ and the cross-track pixel size is $30\,m$ .

Lab 2: Focused on calibrations (DN to radiance to reflectance) and improved surface reflectance.
Lab 3: Scheduled for after the recess, focusing on image correction.
Exercise Task: Calculating simple reflectance for a single pixel across multiple bands and then calculating the improved simplified reflectance for comparison.