1. AMwww.Remote-Sensing.info Ch 6. Electromagnetic Radiation Principles and Radiometric Correction www.Remote-Sensing.info

2. Remote sensing systems do not function perfectly. Also, the Earth’s atmosphere, land, and water are complex and do not lend themselves well to being recorded by remote sensing devices that have constraints such as spatial, spectral, temporal, and radiometric resolution. Consequently, error creeps into the data acquisition process and can degrade the quality of the remote sensor data collected. Remote sensing systems do not function perfectly. Also, the Earth’s atmosphere, land, and water are complex and do not lend themselves well to being recorded by remote sensing devices that have constraints such as spatial, spectral, temporal, and radiometric resolution. Consequently, error creeps into the data acquisition process and can degrade the quality of the remote sensor data collected. The two most common types of error encountered in remotely sensed data are radiometric and geometric. Electromagnetic Radiation Principles and Radiometric Correction Radiometric correction attempts to improve the accuracy of spectral reflectance, emittance, or back-scattered measurements obtained using a remote sensing system. Geometric correction is concerned with placing the reflected, emitted, or back-scattered measurements or derivative products in their proper planimetric (map) location so they can be associated with other spatial information in a geographic information system (GIS) or spatial decision support system (SDSS). Radiometric correction attempts to improve the accuracy of spectral reflectance, emittance, or back-scattered measurements obtained using a remote sensing system. Geometric correction is concerned with placing the reflected, emitted, or back-scattered measurements or derivative products in their proper planimetric (map) location so they can be associated with other spatial information in a geographic information system (GIS) or spatial decision support system (SDSS).

3. Radiometric Correction of Remote Sensor Data Radiometric correction requires knowledge about electromagnetic radiation principles and what interactions take place during the remote sensing data collection process. To be exact, it also involves knowledge about the terrain slope and aspect and bi-directional reflectance characteristics of the scene. Therefore, this chapter reviews fundamental electromagnetic radiation principles. It then discusses how these principles and relationships are used to correct for radiometric distortion in remotely sensed data caused primarily by the atmosphere and elevation.

4. Electromagnetic Energy Interactions Energy recorded by remote sensing systems undergoes fundamental interactions that should be understood to properly preprocess and interpret remotely sensed data. For example, if the energy being remotely sensed comes from the Sun, the energy: is radiated by atomic particles at the source (the Sun), is radiated by atomic particles at the source (the Sun), travels through the vacuum of space at the speed of light, travels through the vacuum of space at the speed of light, interacts with the Earth’s atmosphere, interacts with the Earth’s atmosphere, interacts with the Earth’s surface, interacts with the Earth’s surface, interacts with the Earth’s atmosphere once again, and interacts with the Earth’s atmosphere once again, and finally reaches the remote sensor, where it interacts with various finally reaches the remote sensor, where it interacts with various optics, filters, film emulsions, or detectors. optics, filters, film emulsions, or detectors. Energy recorded by remote sensing systems undergoes fundamental interactions that should be understood to properly preprocess and interpret remotely sensed data. For example, if the energy being remotely sensed comes from the Sun, the energy: is radiated by atomic particles at the source (the Sun), is radiated by atomic particles at the source (the Sun), travels through the vacuum of space at the speed of light, travels through the vacuum of space at the speed of light, interacts with the Earth’s atmosphere, interacts with the Earth’s atmosphere, interacts with the Earth’s surface, interacts with the Earth’s surface, interacts with the Earth’s atmosphere once again, and interacts with the Earth’s atmosphere once again, and finally reaches the remote sensor, where it interacts with various finally reaches the remote sensor, where it interacts with various optics, filters, film emulsions, or detectors. optics, filters, film emulsions, or detectors.

5. Jensen 2004 How is Energy Transferred? Energy may be transferred three ways: conduction, convection, and radiation. a) Energy may be conducted directly from one object to another as when a pan is in direct physical contact with a hot burner. b) The Sun bathes the Earth’s surface with radiant energy causing the air near the ground to increase in temperature. The less dense air rises, creating convectional currents in the atmosphere. c) Electromagnetic energy in the form of electromagnetic waves may be transmitted through the vacuum of space from the Sun to the Earth.

6. Electromagnetic Radiation Models To understand how electromagnetic radiation is created, how it propagates through space, and how it interacts with other matter, it is useful to describe the processes using two different models: the wave model and the particle model.

7. Wave Model of Electromagnetic Radiation In the 1860s, James Clerk Maxwell (1831–1879) conceptualized electromagnetic radiation (EMR) as an electromagnetic wave that travels through space at the speed of light, c, which is 3 x 10 8 meters per second (hereafter referred to as m s -1 ). The electromagnetic wave consists of two fluctuating fields—one electric and the other magnetic. The two vectors are at right angles (orthogonal) to one another, and both are perpendicular to the direction of travel.

8. Radiometric Quantities The relationship between the wavelength ( ) and frequency ( ) of electromagnetic radiation is based on the following formula, where c is the speed of light:

9. How is Electromagnetic Radiation Created? Electromagnetic radiation is generated whenever an electrical charge is accelerated. The wavelength ( ) of the electromagnetic radiation depends upon the length of time that the charged particle is accelerated. Its frequency ( ) depends on the number of accelerations per second. Wavelength is formally defined as the mean distance between maximums (or minimums) of a roughly periodic pattern and is normally measured in micrometers (  m) or nanometers (nm). Frequency is the number of wavelengths that pass a point per unit time. A wave that sends one crest by every second (completing one cycle) is said to have a frequency of one cycle per second, or one hertz, abbreviated 1 Hz.

10. Sources of Electromagnetic Energy Thermonuclear fusion taking place on the surface of the Sun yields a continuous spectrum of electromagnetic energy. The 5770 – 6000 kelvin (K) temperature of this process produces a large amount of relatively short wavelength energy that travels through the vacuum of space at the speed of light. Some of this energy is intercepted by the Earth, where it interacts with the atmosphere and surface materials. The Earth reflects some of the energy directly back out to space or it may absorb the short wavelength energy and then re-emit it at a longer wavelength

11. Solar and Heliospheric Observatory (SOHO) Image of the Sun Obtained on September 14, 1999 Solar and Heliospheric Observatory (SOHO) Image of the Sun Obtained on September 14, 1999

12. Blackbody Radiation Curves Blackbody radiation curves for several objects including the Sun and the Earth which approximate 6,000 K and 300 K blackbodies, respectively. Blackbody radiation curves for several objects including the Sun and the Earth which approximate 6,000 K and 300 K blackbodies, respectively. The area under each curve may be summed to compute the total radiant energy (M ) exiting each object. Thus, the Sun produces more radiant exitance than the Earth because its temperature is greater. As the temperature of an object increases, its dominant wavelength ( max ) shifts toward the shorter wavelengths of the spectrum.

13. Wein’s Displacement Law In addition to computing the total amount of energy exiting a theoretical blackbody such as the Sun, we can determine its dominant wavelength ( max ) based on Wien’s displacement law: where k is a constant equaling 2898  m K, and T is the absolute temperature in kelvin. Therefore, as the Sun approximates a 6000 K blackbody, its dominant wavelength ( max ) is 0.48  m: Where s is the Stefan-Boltzmann constant, 5.66697 x 10-8 W m-2 K-4. In addition to computing the total amount of energy exiting a theoretical blackbody such as the Sun, we can determine its dominant wavelength ( max ) based on Wien’s displacement law: where k is a constant equaling 2898  m K, and T is the absolute temperature in kelvin. Therefore, as the Sun approximates a 6000 K blackbody, its dominant wavelength ( max ) is 0.48  m: Where s is the Stefan-Boltzmann constant, 5.66697 x 10-8 W m-2 K-4.

14. Radiant Intensity of the Sun Radiant Intensity of the Sun The Sun approximates a 6,000 K blackbody with a dominant wavelength of 0.48  m (green light). Earth approximates a 300 K blackbody with a dominant wavelength of 9.66  m. The 6,000 K Sun produces 41% of its energy in the visible region from 0.4 - 0.7  m (blue, green, and red light). The other 59% of the energy is in wavelengths shorter than blue light ( 0.7  m). Eyes are only sensitive to light from the 0.4 to 0.7  m. Remote sensor detectors can be made sensitive to energy in the non-visible regions of the spectrum.

15. Radiometric Quantities All objects above absolute zero (–273°C or 0 K) emit electromagnetic energy, including water, soil, rock, vegetation, and the surface of the Sun. The Sun represents the initial source of most of the electromagnetic energy recorded by remote sensing systems (except RADAR, LIDAR, and SONAR). We may think of the Sun as a 5770 – 6,000 K blackbody (a theoretical construct that absorbs and radiates energy at the maximum possible rate per unit area at each wavelength ( ) for a given temperature). The total emitted radiation from a blackbody (M ) measured in watts per m -2 is proportional to the fourth power of its absolute temperature (T) measured in kelvin (K). This is known as the Stefan-Boltzmann law and is expressed as Where o is the Stefan-Boltzmann constant, 5.66697 x 10-8 W m-2 K-4. All objects above absolute zero (–273°C or 0 K) emit electromagnetic energy, including water, soil, rock, vegetation, and the surface of the Sun. The Sun represents the initial source of most of the electromagnetic energy recorded by remote sensing systems (except RADAR, LIDAR, and SONAR). We may think of the Sun as a 5770 – 6,000 K blackbody (a theoretical construct that absorbs and radiates energy at the maximum possible rate per unit area at each wavelength ( ) for a given temperature). The total emitted radiation from a blackbody (M ) measured in watts per m -2 is proportional to the fourth power of its absolute temperature (T) measured in kelvin (K). This is known as the Stefan-Boltzmann law and is expressed as Where o is the Stefan-Boltzmann constant, 5.66697 x 10-8 W m-2 K-4.

16. Electromagnetic Spectrum The Sun produces a continuous spectrum of energy from gamma rays to radio waves that continually bathe the Earth in energy. The visible portion of the spectrum may be measured using wavelength (measured in micrometers or nanometers, i.e.,  m or nm) or electron volts (eV). All units are interchangeable.

17. Niels Bohr (1885–1962) and Max Planck recognized the discrete nature of exchanges of radiant energy and proposed the quantum theory of electromagnetic radiation. This theory states that energy is transferred in discrete packets called quanta or photons, as discussed. The relationship between the frequency of radiation expressed by wave theory and the quantum is: where Q is the energy of a quantum measured in joules, h is the Planck constant (6.626  10 -34 J s), and is the frequency of the radiation. Niels Bohr (1885–1962) and Max Planck recognized the discrete nature of exchanges of radiant energy and proposed the quantum theory of electromagnetic radiation. This theory states that energy is transferred in discrete packets called quanta or photons, as discussed. The relationship between the frequency of radiation expressed by wave theory and the quantum is: where Q is the energy of a quantum measured in joules, h is the Planck constant (6.626  10 -34 J s), and is the frequency of the radiation. Quantum Theory of EMR

18. Creation of Light from Atomic Particles A A photon of electromagnetic energy is emitted when an electron in an atom or molecule drops from a higher-energy state to a lower- energy state. The light emitted (i.e., its wavelength) is a function of the changes in the energy levels of the outer, valence electron. For example, yellow light is produced from a sodium vapor lamp. Matter can also be subjected to such high temperatures that electrons, which normally move in captured, nonradiating orbits, are broken free. When this happens, the atom remains with a positive charge equal to the negatively charged electron that escaped. The electron becomes a free electron, and the atom is called an ion. If another free electron fills the vacant energy level created by the free electron, then radiation from all wavelengths is produced, i.e., a continuous spectrum of energy. The intense heat at the surface of the Sun produces a continuous spectrum in this manner.

19. Atmospheric Refraction Refraction in three nonturbulent atmospheric layers. The incident energy is bent from its normal trajectory as it travels from one atmospheric layer to another. Snell’s law can be used to predict how much bending will take place, based on a knowledge of the angle of incidence (  ) and the index of refraction of each atmospheric level, n 1, n 2, n 3.

20. Index of Refraction The index of refraction (n) is a measure of the optical density of a substance. This index is the ratio of the speed of light in a vacuum, c, to the speed of light in a substance such as the atmosphere or water, c n (Mulligan, 1980): The speed of light in a substance can never reach the speed of light in a vacuum. Therefore, its index of refraction must always be greater than 1. For example, the index of refraction for the atmosphere is 1.0002926 and 1.33 for water. Light travels more slowly through water because of water’s higher density. The index of refraction (n) is a measure of the optical density of a substance. This index is the ratio of the speed of light in a vacuum, c, to the speed of light in a substance such as the atmosphere or water, c n (Mulligan, 1980): The speed of light in a substance can never reach the speed of light in a vacuum. Therefore, its index of refraction must always be greater than 1. For example, the index of refraction for the atmosphere is 1.0002926 and 1.33 for water. Light travels more slowly through water because of water’s higher density.

21. Snell’s Law Refraction can be described by Snell’s law, which states that for a given frequency of light (we must use frequency since, unlike wavelength, it does not change when the speed of light changes), the product of the index of refraction and the sine of the angle between the ray and a line normal to the interface is constant: From the accompanying figure, we can see that a nonturbulent atmosphere can be thought of as a series of layers of gases, each with a slightly different density. Anytime energy is propagated through the atmosphere for any appreciable distance at any angle other than vertical, refraction occurs. Refraction can be described by Snell’s law, which states that for a given frequency of light (we must use frequency since, unlike wavelength, it does not change when the speed of light changes), the product of the index of refraction and the sine of the angle between the ray and a line normal to the interface is constant: From the accompanying figure, we can see that a nonturbulent atmosphere can be thought of as a series of layers of gases, each with a slightly different density. Anytime energy is propagated through the atmosphere for any appreciable distance at any angle other than vertical, refraction occurs.

22. Atmospheric Scattering Type of scattering is a function of: 1)the wavelength of the incident radiant energy, and 2)the size of the gas molecule, dust particle, and/or water vapor droplet encountered. Type of scattering is a function of: 1)the wavelength of the incident radiant energy, and 2)the size of the gas molecule, dust particle, and/or water vapor droplet encountered.

23. RayleighScatteringRayleighScattering The intensity of Rayleigh scattering varies inversely with the fourth power of the wavelength ( -4 ).

24. Absorption of the Sun's Incident Electromagnetic Energy in the Region from 0.1 to 30  m by Various Atmospheric Gases window

25. ReflectanceReflectance

26. Typical spectral reflectance curves for urban–suburban phenomena in the region 0.4 – 0.9  m.

27. Spectral Bandwidths of Landsat and SPOT Sensor Systems

28. Radiometric quantities have been identified that allow analysts to keep a careful record of the incident and exiting radiant flux. We begin with the simple radiation budget equation: Terrain Energy-Matter Interactions

29. Hemispherical Reflectance, Absorptance, and Transmittance The Hemispherical reflectance (  ) is defined as the dimensionless ratio of the radiant flux reflected from a surface to the radiant flux incident to it: Hemispherical transmittance (  ) is defined as the dimensionless ratio of the radiant flux transmitted through a surface to the radiant flux incident to it: Hemispherical absorptance (  ) is defined by the dimensionless relationship: The Hemispherical reflectance (  ) is defined as the dimensionless ratio of the radiant flux reflected from a surface to the radiant flux incident to it: Hemispherical transmittance (  ) is defined as the dimensionless ratio of the radiant flux transmitted through a surface to the radiant flux incident to it: Hemispherical absorptance (  ) is defined by the dimensionless relationship:

30. Correcting Remote Sensing System Detector Error Ideally, the radiance recorded by a remote sensing system in various bands is an accurate representation of the radiance actually leaving the feature of interest (e.g., soil, vegetation, water, or urban land cover) on the Earth’s surface. Unfortunately, noise (error) can enter the data-collection system at several points. For example, radiometric error in remotely sensed data may be introduced by the sensor system itself when the individual detectors do not function properly or are improperly calibrated. Several of the more common remote sensing system–induced radiometric errors are: random bad pixels (shot noise), random bad pixels (shot noise), line-start/stop problems, line-start/stop problems, line or column drop-outs, line or column drop-outs, partial line or column drop-outs, and partial line or column drop-outs, and line or column striping. line or column striping. Ideally, the radiance recorded by a remote sensing system in various bands is an accurate representation of the radiance actually leaving the feature of interest (e.g., soil, vegetation, water, or urban land cover) on the Earth’s surface. Unfortunately, noise (error) can enter the data-collection system at several points. For example, radiometric error in remotely sensed data may be introduced by the sensor system itself when the individual detectors do not function properly or are improperly calibrated. Several of the more common remote sensing system–induced radiometric errors are: random bad pixels (shot noise), random bad pixels (shot noise), line-start/stop problems, line-start/stop problems, line or column drop-outs, line or column drop-outs, partial line or column drop-outs, and partial line or column drop-outs, and line or column striping. line or column striping.

31. Sometimes an individual detector does not record spectral data for an individual pixel. When this occurs randomly, it is called a bad pixel. When there are numerous random bad pixels found within the scene, it is called shot noise because it appears that the image was shot by a shotgun. Normally these bad pixels contain values of 0 or 255 (in 8-bit data) in one or more of the bands. Shot noise is identified and repaired using the following methodology. It is first necessary to locate each bad pixel in the band k dataset. A simple thresholding algorithm makes a pass through the dataset and flags any pixel (BV i,j,k ) having a brightness value of zero (assuming values of 0 represent shot noise and not a real land cover such as water). Once identified, it is then possible to evaluate the eight pixels surrounding the flagged pixel, as shown below: Random Bad Pixels (Shot Noise)

32. The mean of the eight surrounding pixels is computed using the equation and the value substituted for BV i,j,k in the corrected image:

33. Shot Noise Removal a) Landsat Thematic Mapper band 7 (2.08 – 2.35  m) image of the Santee Delta in South Carolina. One of the 16 detectors exhibits serious striping and the absence of brightness values at pixel locations along a scan line. b) An enlarged view of the bad pixels with the brightness values of the eight surrounding pixels annotated. c) The brightness values of the bad pixels after shot noise removal. a) Landsat Thematic Mapper band 7 (2.08 – 2.35  m) image of the Santee Delta in South Carolina. One of the 16 detectors exhibits serious striping and the absence of brightness values at pixel locations along a scan line. b) An enlarged view of the bad pixels with the brightness values of the eight surrounding pixels annotated. c) The brightness values of the bad pixels after shot noise removal.

34. Line or Column Drop-outs An entire line containing no spectral information may be produced if an individual detector in a scanning system (e.g., Landsat MSS or Landsat 7 ETM + ) fails to function properly. If a detector in a linear array (e.g., SPOT XS, IRS-1C, QuickBird) fails to function, this can result in an entire column of data with no spectral information. The bad line or column is commonly called a line or column drop-out and contains brightness values equal to zero. For example, if one of the 16 detectors in the Landsat Thematic Mapper sensor system fails to function during scanning, this can result in a brightness value of zero for every pixel, j, in a particular line, i. This line drop-out would appear as a completely black line in the band, k, of imagery. This is a serious condition because there is no way to restore data that were never acquired. However, it is possible to improve the visual interpretability of the data by introducing estimated brightness values for each bad scan line.

35. Line or Column Drop-outs It is first necessary to locate each bad line in the dataset. A simple thresholding algorithm makes a pass through the dataset and flags any scan line having a mean brightness value at or near zero. Once identified, it is then possible to evaluate the output for a pixel in the preceding line (BV i – 1,j,k ) and succeeding line (BV i + 1,j,k ) and assign the output pixel (BV i,j,k ) in the drop-out line the average of these two brightness values: This is performed for every pixel in a bad scan line. The result is an image consisting of interpolated data every nth line that is more visually interpretable than one with horizontal black lines running systematically throughout the entire image. This same cosmetic digital image processing procedure can be applied to column drop-outs produced by a linear array remote sensing system. It is first necessary to locate each bad line in the dataset. A simple thresholding algorithm makes a pass through the dataset and flags any scan line having a mean brightness value at or near zero. Once identified, it is then possible to evaluate the output for a pixel in the preceding line (BV i – 1,j,k ) and succeeding line (BV i + 1,j,k ) and assign the output pixel (BV i,j,k ) in the drop-out line the average of these two brightness values: This is performed for every pixel in a bad scan line. The result is an image consisting of interpolated data every nth line that is more visually interpretable than one with horizontal black lines running systematically throughout the entire image. This same cosmetic digital image processing procedure can be applied to column drop-outs produced by a linear array remote sensing system.

36. Line-start Problems Occasionally, scanning systems fail to collect data at the beginning of a scan line, or they place the pixel data at inappropriate locations along the scan line. For example, all of the pixels in a scan line might be systematically shifted just one pixel to the right. This is called a line-start problem. Also, a detector may abruptly stop collecting data somewhere along a scan and produce results similar to the line or column drop-out previously discussed. Ideally, when data are not collected, the sensor system would be programmed to remember what was not collected and place any good data in their proper geometric locations along the scan. Unfortunately, this is not always the case. For example, the first pixel (column 1) in band k on line i (i.e., BV i,1,k ) might be improperly located at column 50 (i.e., BV i,50,k ). If the line-start problem is always associated with a horizontal bias of 50 columns, it can be corrected using a simple horizontal adjustment. However, if the amount of the line-start displacement is random, it is difficult to restore the data without extensive human interaction on a line-by-line basis. A considerable amount of MSS data collected by Landsats 2 and 3 exhibit line-start problems.

37. Line-start Problems P.197

38. N-line Striping Sometimes a detector does not fail completely, but simply goes out of radiometric adjustment. For example, a detector might record spectral measurements over a dark, deep body of water that are almost uniformly 20 brightness values greater than the other detectors for the same band. The result would be an image with systematic, noticeable lines that are brighter than adjacent lines. This is referred to as. The maladjusted line contains valuable information, but should be corrected to have approximately the same radiometric scale as the data collected by the properly calibrated detectors associated with the same band. Sometimes a detector does not fail completely, but simply goes out of radiometric adjustment. For example, a detector might record spectral measurements over a dark, deep body of water that are almost uniformly 20 brightness values greater than the other detectors for the same band. The result would be an image with systematic, noticeable lines that are brighter than adjacent lines. This is referred to as n-line striping. The maladjusted line contains valuable information, but should be corrected to have approximately the same radiometric scale as the data collected by the properly calibrated detectors associated with the same band. To repair systematic n-line striping, it is first necessary to identify the miscalibrated scan lines in the scene. This is usually accomplished by computing a histogram of the values for each of the n detectors that collected data over the entire scene (ideally, this would take place over a homogeneous area, such as a body of water). If one detector’s mean or median is significantly different from the others, it is probable that this detector is out of adjustment. Consequently, every line and pixel in the scene recorded by the maladjusted detector may require a bias (additive or subtractive) correction or a more severe gain (multiplicative) correction. This type of n-line striping correction a) adjusts all the bad scan lines so that they have approximately the same radiometric scale as the correctly collected data and b) improves the visual interpretability of the data. It looks better. Sometimes a detector does not fail completely, but simply goes out of radiometric adjustment. For example, a detector might record spectral measurements over a dark, deep body of water that are almost uniformly 20 brightness values greater than the other detectors for the same band. The result would be an image with systematic, noticeable lines that are brighter than adjacent lines. This is referred to as. The maladjusted line contains valuable information, but should be corrected to have approximately the same radiometric scale as the data collected by the properly calibrated detectors associated with the same band. Sometimes a detector does not fail completely, but simply goes out of radiometric adjustment. For example, a detector might record spectral measurements over a dark, deep body of water that are almost uniformly 20 brightness values greater than the other detectors for the same band. The result would be an image with systematic, noticeable lines that are brighter than adjacent lines. This is referred to as n-line striping. The maladjusted line contains valuable information, but should be corrected to have approximately the same radiometric scale as the data collected by the properly calibrated detectors associated with the same band. To repair systematic n-line striping, it is first necessary to identify the miscalibrated scan lines in the scene. This is usually accomplished by computing a histogram of the values for each of the n detectors that collected data over the entire scene (ideally, this would take place over a homogeneous area, such as a body of water). If one detector’s mean or median is significantly different from the others, it is probable that this detector is out of adjustment. Consequently, every line and pixel in the scene recorded by the maladjusted detector may require a bias (additive or subtractive) correction or a more severe gain (multiplicative) correction. This type of n-line striping correction a) adjusts all the bad scan lines so that they have approximately the same radiometric scale as the correctly collected data and b) improves the visual interpretability of the data. It looks better.

39. N-line Striping

40. a) Original band 10 radiance (W m -2 sr -1 ) data from a GER DAIS 3715 hyperspectral dataset of the Mixed Waste Management Facility on the Savannah River Site near Aiken, SC. The subset is focused on a clay-capped hazardous waste site covered with Bahia grass and Centipede grass. The 35-band dataset was obtained at 2  2 m spatial resolution. The radiance values along the horizontal (X) and vertical (Y) profiles are summarized in the next figure. b) Enlargement of band 10 data. c) Band 10 data after destriping. d) An enlargement of the destriped data a) Original band 10 radiance (W m -2 sr -1 ) data from a GER DAIS 3715 hyperspectral dataset of the Mixed Waste Management Facility on the Savannah River Site near Aiken, SC. The subset is focused on a clay-capped hazardous waste site covered with Bahia grass and Centipede grass. The 35-band dataset was obtained at 2  2 m spatial resolution. The radiance values along the horizontal (X) and vertical (Y) profiles are summarized in the next figure. b) Enlargement of band 10 data. c) Band 10 data after destriping. d) An enlargement of the destriped data

41. N-line Striping a) The radiance values along the horizontal (X) profile of the original band 10 radiance values in the previous figure. b) The radiance values along the vertical (Y) profile of the original band 10 radiance values in the previous figure. c) The radiance values along the vertical (Y) profile of the destriped band 10 radiance values. Note the reduction of the saw-toothed pattern in the destriped data

42. Types of Atmospheric Correction There are several ways to atmospherically correct remotely sensed data. Some are relatively straightforward while others are complex, being founded on physical principles and requiring a significant amount of information to function properly. This discussion will focus on two major types of atmospheric correction: Absolute atmospheric correction, and Relative atmospheric correction. There are various methods that can be used to achieve absolute or relative atmospheric correction. The following sections identify the logic, algorithms, and problems associated with each methodology. There are several ways to atmospherically correct remotely sensed data. Some are relatively straightforward while others are complex, being founded on physical principles and requiring a significant amount of information to function properly. This discussion will focus on two major types of atmospheric correction: Absolute atmospheric correction, and Relative atmospheric correction. There are various methods that can be used to achieve absolute or relative atmospheric correction. The following sections identify the logic, algorithms, and problems associated with each methodology.

43. Absolute Atmospheric Correction Solar radiation is largely unaffected as it travels through the vacuum of space. When it interacts with the Earth’s atmosphere, however, it is selectively scattered and absorbed. The sum of these two forms of energy loss is called. Atmospheric attenuation may 1) make it difficult to relate hand-held in situ spectroradiometer measurements with remote measurements, 2) make it difficult to extend spectral signatures through space and time, and (3) have an impact on classification accuracy within a scene if atmospheric attenuation varies significantly throughout the image. Solar radiation is largely unaffected as it travels through the vacuum of space. When it interacts with the Earth’s atmosphere, however, it is selectively scattered and absorbed. The sum of these two forms of energy loss is called atmospheric attenuation. Atmospheric attenuation may 1) make it difficult to relate hand-held in situ spectroradiometer measurements with remote measurements, 2) make it difficult to extend spectral signatures through space and time, and (3) have an impact on classification accuracy within a scene if atmospheric attenuation varies significantly throughout the image. The general goal of absolute radiometric correction is to turn the digital brightness values recorded by a remote sensing system into values. These values can then be compared or used in conjunction with scaled surface reflectance values obtained anywhere else on the planet. The general goal of absolute radiometric correction is to turn the digital brightness values recorded by a remote sensing system into scaled surface reflectance values. These values can then be compared or used in conjunction with scaled surface reflectance values obtained anywhere else on the planet. Solar radiation is largely unaffected as it travels through the vacuum of space. When it interacts with the Earth’s atmosphere, however, it is selectively scattered and absorbed. The sum of these two forms of energy loss is called. Atmospheric attenuation may 1) make it difficult to relate hand-held in situ spectroradiometer measurements with remote measurements, 2) make it difficult to extend spectral signatures through space and time, and (3) have an impact on classification accuracy within a scene if atmospheric attenuation varies significantly throughout the image. Solar radiation is largely unaffected as it travels through the vacuum of space. When it interacts with the Earth’s atmosphere, however, it is selectively scattered and absorbed. The sum of these two forms of energy loss is called atmospheric attenuation. Atmospheric attenuation may 1) make it difficult to relate hand-held in situ spectroradiometer measurements with remote measurements, 2) make it difficult to extend spectral signatures through space and time, and (3) have an impact on classification accuracy within a scene if atmospheric attenuation varies significantly throughout the image. The general goal of absolute radiometric correction is to turn the digital brightness values recorded by a remote sensing system into values. These values can then be compared or used in conjunction with scaled surface reflectance values obtained anywhere else on the planet. The general goal of absolute radiometric correction is to turn the digital brightness values recorded by a remote sensing system into scaled surface reflectance values. These values can then be compared or used in conjunction with scaled surface reflectance values obtained anywhere else on the planet.

44. Absolute Atmospheric Correction Much research has been carried out to address the problem of correcting images for atmospheric effects. These efforts have resulted in a number of atmospheric radiative transfer codes (models) that can provide realistic estimates of the effects of atmospheric scattering and absorption on satellite imagery. Once these effects have been identified for a specific date of imagery, each band and/or pixel in the scene can be adjusted to remove the effects of scattering and/or absorption. The image is then considered to be atmospherically corrected. Unfortunately, the application of these codes to a specific scene and date also requires knowledge of both the sensor spectral profile and the atmospheric properties at the same time. Atmospheric properties are difficult to acquire even when planned. For most historic satellite data, they are not available. Even today, accurate scaled surface reflectance retrieval is not operational for the majority of satellite image sources used for land-cover change detection. An exception is NASA's Moderate Resolution Imaging Spectroradiometer (MODIS), for which surface reflectance products are available. Nevertheless, we will proceed with a general discussion of the important issues associated with absolute atmospheric correction and then provide examples of how absolute radiometric correction is performed. Much research has been carried out to address the problem of correcting images for atmospheric effects. These efforts have resulted in a number of atmospheric radiative transfer codes (models) that can provide realistic estimates of the effects of atmospheric scattering and absorption on satellite imagery. Once these effects have been identified for a specific date of imagery, each band and/or pixel in the scene can be adjusted to remove the effects of scattering and/or absorption. The image is then considered to be atmospherically corrected. Unfortunately, the application of these codes to a specific scene and date also requires knowledge of both the sensor spectral profile and the atmospheric properties at the same time. Atmospheric properties are difficult to acquire even when planned. For most historic satellite data, they are not available. Even today, accurate scaled surface reflectance retrieval is not operational for the majority of satellite image sources used for land-cover change detection. An exception is NASA's Moderate Resolution Imaging Spectroradiometer (MODIS), for which surface reflectance products are available. Nevertheless, we will proceed with a general discussion of the important issues associated with absolute atmospheric correction and then provide examples of how absolute radiometric correction is performed.

45. Radiance (L T ) from paths 1, 3, and 5 contains intrinsic valuable spectral information about the target of interest. Conversely, the path radiance (L p ) from paths 2 and 4 includes diffuse sky irradiance or radiance from neighboring areas on the ground. This path radiance generally introduces unwanted radiometric noise in the remotely sensed data and complicates the image interpretation process.

46. The total radiance reaching the sensor is: This may be summarized as:

47. Atmospheric Correction Based on Radiative Transfer Modeling Most current radiative transfer-based atmospheric correction algorithms can compute much of the required information if a) the user provides fundamental atmospheric characteristic information to the program or b) certain atmospheric absorption bands are present in the remote sensing dataset. For example, most radiative transfer-based atmospheric correction algorithms require that the user provide: latitude and longitude of the remotely sensed image scene, latitude and longitude of the remotely sensed image scene, date and exact time of remote sensing data collection, date and exact time of remote sensing data collection, image acquisition altitude (e.g., 20 km AGL) image acquisition altitude (e.g., 20 km AGL) mean elevation of the scene (e.g., 200 m ASL), mean elevation of the scene (e.g., 200 m ASL), an atmospheric model (e.g., mid-latitude summer, mid-latitude winter, tropical), an atmospheric model (e.g., mid-latitude summer, mid-latitude winter, tropical), radiometrically calibrated image radiance data (i.e., data must be in the form W m 2 mm - 1 sr -1 ), radiometrically calibrated image radiance data (i.e., data must be in the form W m 2 mm - 1 sr -1 ), data about each specific band (i.e., its mean and full-width at half-maximum (FWHM), and data about each specific band (i.e., its mean and full-width at half-maximum (FWHM), and local atmospheric visibility at the time of remote sensing data collection (e.g., 10 km, obtained from a nearby airport if possible). local atmospheric visibility at the time of remote sensing data collection (e.g., 10 km, obtained from a nearby airport if possible). Most current radiative transfer-based atmospheric correction algorithms can compute much of the required information if a) the user provides fundamental atmospheric characteristic information to the program or b) certain atmospheric absorption bands are present in the remote sensing dataset. For example, most radiative transfer-based atmospheric correction algorithms require that the user provide: latitude and longitude of the remotely sensed image scene, latitude and longitude of the remotely sensed image scene, date and exact time of remote sensing data collection, date and exact time of remote sensing data collection, image acquisition altitude (e.g., 20 km AGL) image acquisition altitude (e.g., 20 km AGL) mean elevation of the scene (e.g., 200 m ASL), mean elevation of the scene (e.g., 200 m ASL), an atmospheric model (e.g., mid-latitude summer, mid-latitude winter, tropical), an atmospheric model (e.g., mid-latitude summer, mid-latitude winter, tropical), radiometrically calibrated image radiance data (i.e., data must be in the form W m 2 mm - 1 sr -1 ), radiometrically calibrated image radiance data (i.e., data must be in the form W m 2 mm - 1 sr -1 ), data about each specific band (i.e., its mean and full-width at half-maximum (FWHM), and data about each specific band (i.e., its mean and full-width at half-maximum (FWHM), and local atmospheric visibility at the time of remote sensing data collection (e.g., 10 km, obtained from a nearby airport if possible). local atmospheric visibility at the time of remote sensing data collection (e.g., 10 km, obtained from a nearby airport if possible).

48. Atmospheric Correction Based on Radiative Transfer Modeling These parameters are then input to the atmospheric model selected (e.g., mid-latitude summer) and used to compute the absorption and scattering characteristics of the atmosphere at the instance of remote sensing data collection. These atmospheric characteristics are then used to invert the remote sensing radiance to scaled surface reflectance. Many of these atmospheric correction programs derive the scattering and absorption information they require from robust atmosphere radiative transfer code such as MODTRAN 4+ or Second Simulation of the Satellite Signal in the Solar Spectrum (6S). Examples include: ACORN ACORN ATCOR ATCOR ATREM ATREM FLAASH FLAASH These parameters are then input to the atmospheric model selected (e.g., mid-latitude summer) and used to compute the absorption and scattering characteristics of the atmosphere at the instance of remote sensing data collection. These atmospheric characteristics are then used to invert the remote sensing radiance to scaled surface reflectance. Many of these atmospheric correction programs derive the scattering and absorption information they require from robust atmosphere radiative transfer code such as MODTRAN 4+ or Second Simulation of the Satellite Signal in the Solar Spectrum (6S). Examples include: ACORN ACORN ATCOR ATCOR ATREM ATREM FLAASH FLAASH

49. Radiometric Correction Using the ATmosphere REMoval (ATREM) Program Radiometric Correction Using the ATmosphere REMoval (ATREM) Program ATREM calculates scaled surface reflectance values from hyperspectral radiance data using an approximate atmospheric radiative transfer modeling technique. Radiative transfer modeling is used to calculate the atmospheric transmittance of gases and molecular and aerosol scattering. The water vapor amount is derived on a pixel by pixel basis using the 0.94  m and 1.14  m water absorption bands and a three channel ratioing technique where several bands in the water absorption feature are averaged and ratioed against two sets of averaged window channels adjacent to the water absorption feature. Additional inputs: - Select up to 7 atmospheric gases that may be modeled and removed during the reflectance calculation - An aerosol model. - Visibility conditions during the overflight (e.g., 10 km) - Standard atmospheric model - Average surface elevation (km) - Scene center latitude and longitude - Aircraft altitude above sea level (km) ATREM calculates scaled surface reflectance values from hyperspectral radiance data using an approximate atmospheric radiative transfer modeling technique. Radiative transfer modeling is used to calculate the atmospheric transmittance of gases and molecular and aerosol scattering. The water vapor amount is derived on a pixel by pixel basis using the 0.94  m and 1.14  m water absorption bands and a three channel ratioing technique where several bands in the water absorption feature are averaged and ratioed against two sets of averaged window channels adjacent to the water absorption feature. Additional inputs: - Select up to 7 atmospheric gases that may be modeled and removed during the reflectance calculation - An aerosol model. - Visibility conditions during the overflight (e.g., 10 km) - Standard atmospheric model - Average surface elevation (km) - Scene center latitude and longitude - Aircraft altitude above sea level (km)

50. Atmospheric Correction Using ATCOR a) Image containing substantial haze prior to atmospheric correction. b) Image after atmospheric correction using ATCOR (Courtesy Leica Geosystems and DLR, the German Aerospace Centre).

51. Comparison of Various Atmospheric Correction Methods a) Forty-six in situ ASD spectroradiometer (400 – 2500 nm) measurements were obtained on the Savannah River Site Mixed Waste Management Facility near Aiken, SC. b) The relationship between the 46 in situ spectroradiometer measurements and pixel spectral reflectance after processing using empirical line calibration (ELC) and ACORN. The ELC and ACORN with the single spectrum enhancements provided the most accurate atmospheric correction of the GER DAIS 3715 hyperspectral data. a) Forty-six in situ ASD spectroradiometer (400 – 2500 nm) measurements were obtained on the Savannah River Site Mixed Waste Management Facility near Aiken, SC. b) The relationship between the 46 in situ spectroradiometer measurements and pixel spectral reflectance after processing using empirical line calibration (ELC) and ACORN. The ELC and ACORN with the single spectrum enhancements provided the most accurate atmospheric correction of the GER DAIS 3715 hyperspectral data.

52. Radiometric Correction Using Empirical Line Calibration Radiometric Correction Using Empirical Line Calibration Absolute atmospheric correction may also be performed using empirical line calibration (ELC), which forces the remote sensing image data to match in situ spectral reflectance measurements, hopefully obtained at approximately the same time and on the same date as the remote sensing overflight. Empirical line calibration is based on the equation: where BV k is the digital output value for a pixel in band k, p equals the scaled surface reflectance of the materials within the remote sensor IFOV at a specific wavelength ( ), A k is a multiplicative term affecting the BV, and B k is an additive term. The multiplicative term is associated primarily with atmospheric transmittance and instrumental factors, and the additive term deals primarily with atmospheric path radiance and instrumental offset (i.e., dark current).

53. In Situ Radiometric Data Collection a) Field crew taking a spectroradiometer measurement from a calibrated reflectance standard on the tripod. b) 8  8 m black and white calibration targets at the Savannah River Site

54. Field spectra Band 1 Band 2 Band 3 One Bright Target 4849 4847 5048 5554 5754 5655 4040 3940 4142 Radiance image (e.g., Band 1) Band 1 Band 2 Band 3 One Dark Target 910 1110 1012 54 56 64 00 40 12 Wavelength, nm Radiance Field spectra Paired Relationship: Band 1 Band 2 Band 3 DarkTarget DarkTarget BrightTarget BrightTarget Remotemeasurement Field spectra = 55 Remote Measurement  = 49  = 55 F = 59  = 41 F = 48 Field spectra = 13 Remote Measurement  = 11  = 5 F = 7  = 3 F = 4

55. Empirical Line Calibration a) Landsat Thematic Mapper image acquired on February 3, 1994 was radiometrically corrected using empirical line calibration and paired NASA JPL and Johns Hopkins University spectral library beach and water in situ spectroradiometer measurements and Landsat TM image brightness values (BV i,j,k ). b) A pixel of loblolly pine with its original brightness values in six bands (TM band 6 thermal data were not used). c) The same pixel after empirical line calibration to scaled surface reflectance. Note the correct chlorophyll absorption in the blue (band 1) and red (band 3) portions of the spectrum and the increase in near-infrared reflectance. a) Landsat Thematic Mapper image acquired on February 3, 1994 was radiometrically corrected using empirical line calibration and paired NASA JPL and Johns Hopkins University spectral library beach and water in situ spectroradiometer measurements and Landsat TM image brightness values (BV i,j,k ). b) A pixel of loblolly pine with its original brightness values in six bands (TM band 6 thermal data were not used). c) The same pixel after empirical line calibration to scaled surface reflectance. Note the correct chlorophyll absorption in the blue (band 1) and red (band 3) portions of the spectrum and the increase in near-infrared reflectance.

56. Relative Radiometric Correction of Atmospheric Attenuation -- Single Image Normalization Using Histogram Adjustment Relative Radiometric Correction of Atmospheric Attenuation -- Single Image Normalization Using Histogram Adjustment

57. Relative Radiometric Correction of Atmospheric Attenuation -- Multiple Date Image Normalization Using Regression Relative Radiometric Correction of Atmospheric Attenuation -- Multiple Date Image Normalization Using Regression Example based on SPOT imagery obtained over Water Conservation 2A in South Florida

58. Cosine Correction for Terrain Slope Cosine Correction for Terrain Slope where: L H = radiance observed for a horizontal surface (i.e., slope-aspect corrected surface (i.e., slope-aspect corrected remote sensor data). remote sensor data). L T = radiance observed over sloped terrain (i.e., the raw remote sensor data) (i.e., the raw remote sensor data)  0 = sun’s zenith angle i = sun’s incidence angle in relation to the i = sun’s incidence angle in relation to the normal on a pixel normal on a pixelwhere: L H = radiance observed for a horizontal surface (i.e., slope-aspect corrected surface (i.e., slope-aspect corrected remote sensor data). remote sensor data). L T = radiance observed over sloped terrain (i.e., the raw remote sensor data) (i.e., the raw remote sensor data)  0 = sun’s zenith angle i = sun’s incidence angle in relation to the i = sun’s incidence angle in relation to the normal on a pixel normal on a pixel