#### Transcript lecture-6 Atmospheric effects and corrections1

Lecture 6 Atmospheric Effects and Corrections Terminology •Radiant flux •Irradiance •Radiance •Reflection •Transmittance Radiance received at a remote sensor Radiance (LT) from paths 1, 3, and 5 contains intrinsic valuable spectral information about the target of interest. Conversely, the path radiance (Lp) 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. Radiance received at a remote sensor •Path 1 contains spectral solar irradiance ( Eo) that was attenuated very little before illuminating the terrain within the IFOV. •We are interested in the solar irradiance from a specific solar zenith angle ( θo) •The amount of irradiance reaching the terrain is a function of the atmospheric transmittance at this angle (Tθo). •If all of the irradiance makes it to the ground, then the atmospheric transmittance equals one. If none of the irradiance makes it to the ground, then the atmospheric transmittance is zero. Radiance received at a remote sensor •Path 2 contains spectral diffuse sky irradiance ( Ed ) that never reaches the the target study area because of scattering in the atmosphere. • This energy is often scattered into the IFOV of the sensor system. • Rayleigh scattering of blue light contributes much to this diffuse sky irradiance. Hence blue band image produced by a remote sensor system is often much brighter than any of the other bands and contains much unwanted diffuse sky irradiance that was scattered into the IFOV of the sensor system. • Therefore, if possible, we want to minimize its effects. This quantity is referred to as the upward reflectance of the atmosphere (Edu). Radiance received at a remote sensor •Path 3 contains modified energy from the Sun that has undergone some Rayleigh, Mie, and/or nonselective scattering and perhaps some absorption and reemission before illuminating the study area. • Its spectral composition and polarization may be somewhat different from the energy that reaches the ground from path 1. • This quantity is also referred to as the downward reflectance of the atmosphere (Edd). Radiance received at a remote sensor • Path 4 contains radiation that was reflected or scattered by nearby terrain covered by snow, concrete, soil, water, and/or vegetation into the IFOV of the sensor system. • The energy does not actually illuminate the study area of interest. Therefore, if possible, we would like to minimize its effects. •Path 2 and Path 4 combine to produce what is commonly referred to as Path Radiance, Lp. Radiance received at a remote sensor Path 5 is energy that was also reflected from nearby terrain into the atmosphere, but then scattered or reflected onto the study area. Generally insignificant. Radiance received at a remote sensor Images are arrays of pixels, where each pixel is represented by a brightness value or grey level, generally between 0 and 255. These values are called DNs. We can determine the radiance at the sensor for any pixel from its DN value, between 0 and 255: L pxl ( DN pix k ) L min where k L max L min DN max Lmax and Lmin are maximum and minimum measurable radiances of the sensor. k and Lmin are also called gain and offset of the detector. This information is provided by the sensor manufacturer. Radiance received at a remote sensor BAND 1 2 3 4 5 7 Lmin (W/m2/sr/μm) -1.5 -2.8 -1.2 -1.5 -0.37 -0.15 Lmax (W/m2/sr/μm) 152.1 296.8 204.3 206.2 27.19 14.38 Preflight TM-4 and TM-5 spectral range values (from NASA, 1986, Table C-8) DN value of a pixel in bands 1 and 7 is 100 For band 1, k = (152.1+1.5)/255 = 0.602353 Maximum DN value in both bands is 255 2 L pix = (100 x 0.602353 ) – 1.5 = 58.73 W/m /sr/μm Radiance at the pixel in band In 7,band 7?? For 1? band k = (14.38+0.15)/255 = 0.05698 Lpix = (100 x 0.05698) – 0.15 = 5.54 W/m2/sr/μm The irradiance (Esunλ) of the sun in a specific length (λ) at a solar zenith angle of θ is E sun cos 0 Remote sensing systems sense wavebands, rather than specific wavelengths. The available irradiance (Eo) in a specific wave band between λ1 and λ2 in the area of interest is 2 E sun cos 0 d E sun cos 0 or or E sun cos 0 d 1 2 where Δλ = λ2- λ1 is very small and Esun Δ λ is the average irradiance in the band Δλ. d2 (in AU)accounts for varying distance of earth from the Sun. If the reflectance of the pixel of interest is R, then the radiant exitance of the pixel is: E Pxl E sun cos 0 d 2 R We know that 2 / 2 E Pxl L Pxl cos .Sin .d .d L Pxl L Pxl 0 0 L Pxl E sun cos 0 R d 2 E Pxl Radiance received at a remote sensor However the atmosphere scatters and absorbs a proportion of the solar irradiance. If the downward scattered or diffused sky irradiance is Edd and Tθo is the atmospheric transmission, i.e., the proportion of radiance transmitted by the atmosphere, in the direction θo, then the total irradiance at the pixel = Radiance received at a remote sensor E cos 0 E ( incident ) sun 2 T o E dd d The radiance from the pixel due to this irradiance = L Pxl E ( incident ) R E sun cos 0 T o E dd d 2 R d L Sensor 2 E sun L Path R is the reflectance. If the atmospheric transmission in the direction θv is Tθv , then the radiance Lsensor arriving at the sensor after traversing the atmosphere is: R 2 L Sensor E sun cos 0 T o E dd d 2 d L path Where Lpath is path radiance T v L Pxl 2 L Sensor E sun cos 0 T o E dd d T L path 2 d R OR Radiance received at a remote sensor L Sensor L path R 2 E cos T E d sun 0 o dd 2 d T v L pxl L L pxl L Sensor L path T v 2 E sun cos 0 T o E dd d pxl L Sensor L path R 2 d T v L Sensor E sun L Path Assume .... E dd negligible R L Sensor L path T Assume .... T R v d 2 E sun cos 0 T o 1 ( is it justified? ) v ( L Sensor L path ) d 2 E sun cos 0 T o L sensor Known , E sun Known , 0 Known , d Known 2 T o , L path ?? Atmospheri c correction involves estimation of T o , L path L Pxl Objectives of atmospheric corrections The high goal of remote sensing: To identify the composition of objects on ground from remote sensing data Spectral reflectance curves are used for this purpose However, radiance-at-the-sensor is contaminated by path radiance due to the atmosphere, hence spectral reflectance estimated from remote sensing data are incorrect We have to correct the radiance-at-the-sensor to remove atmospheric effects When is the atmospheric correction really required?? • Mono-temporal data : NO • Classification: NO • Change monitoring and detection: YES • Composition mapping, spectral analysis: YES Radiometric calibration DN Sensor calibration • gain and offset Radiance at sensor Atmospheric correction Radiance at ground Solar and topographic correction Surface reflectance • image measurement • ground measurements • atmospheric models • sensor view path atmospheric radiance • sensor view path atmospheric transmittance • solar exo-atmospheric spectral irradiance • solar path atmospheric transmittance • down-scattered radiance • solar angle, DEM Atmospheric corrections: Techniques • Histogram minimum method aka dark object subtraction – the bootstrap approach • Empirical line method • Radiative transfer models – Physical-based approach Estimation of LP : Dark object subtraction •Dark-object subtraction techniques derive the corrected DN (digital number) values solely from the digital data with no outside information. •This type of correction involves subtracting a constant DN value from the entire digital image. •The assumption is that there is a high probability that at least a few pixels within an image which should be black (0% reflectance). If there are no pixels with zero values, that is the effect of atmospheric scattering •For example, there are about 45 million pixels in a single TM band – so there very high probability that at least one of them should be black. Estimation of LP : Dark object subtraction Estimation of LP : Dark object subtraction Water bodies have 0% reflectance in the IR region, hence zero DN Water absorption Water absorption Non-zero values over water bodies in the IR consequence of path radiance. 2090-2350 nm Band 7 1550-1750 nm Band 5 775-900 nm Band 4 LANDSAT ETM+ BANDS 450-515 nm Band 1 525-605 nm Band 2 630-690 nm Band 3 Subtract the non-zero value over water bodies from all pixels. That would make water body perfectly non-reflecting. In Visible bands, shadows should be black in absence of path radiance. Hence non-zero values over shadowed areas can be used for dark pixel correction. Estimation of LP : Dark object subtraction • Histograms of pixel values in all bands • pixel values of low reflectance areas near zero • exposures of dark colored rocks • deep shadows • clear water • Lowest pixel values in visible and near-infrared are approximation to atmospheric path radiance • Minimum values subtracted from image Estimation of LP : Dark object subtraction How will you calculate path radiance for all bands ?? For example, calculate reflectance for a pixel whose DN value is 53 in band 1. Estimation of LP : Dark object subtraction How will you calculate path radiance for all bands ?? For example, calculate reflectance for a pixel whose DN value is 53 in band 1. BAND 1 2 3 4 5 7 Lmin (W/m2/sr/μm) -1.5 -2.8 -1.2 -1.5 -0.37 -0.15 Lmax (W/m2/sr/μm) 152.1 296.8 204.3 206.2 27.19 14.38 Estimation of LP : Dark object subtraction How will you calculate path radiance for all bands ?? For example, calculate path radiance for a pixel whose DN value is 53 in band 1. Day of Year Distance Day of Year Distance Day of Year Distance Day of Year Distance Day of Year Distance 1 .98331 74 .99446 152 1.01403 227 1.01281 305 .99253 15 32 46 60 .98365 .98536 .98774 .99084 91 106 121 135 .99926 1.00353 1.00756 1.01087 166 182 196 213 1.01577 1.01667 1.01646 1.01497 242 258 274 288 1.00969 1.00566 1.00119 .99718 319 335 349 365 .98916 .98608 .98426 .98333 R ( L Sensor L path ) d E sun cos 0 T o 2 ETM+ Solar Spectral Irradiances Band watts/(m2 * μm) 1 1997 2 1812 3 1533 4 1039 5 230.8 7 84.90 8 1362. Estimation of LP : Dark object subtraction Regression technique • DN values of correlated bands are plotted • Least square line fit using standard regression methods • Resulting offset is approximation for the atmospheric path radiance offset subtracted from image Empirical line method One dark (X1) and one bright (X2) object selected on the image which can be clearly identified on the ground also Ground reflectance of X1 and X2 measured using field radiometer (R X1 and R X2). Radiance-at-the-sensor of X1 and X2 calculated from the image (L X1 and L X2). The two points plotted on a graph, joined by a line, and the slope (s) and intercept (a) of the line measured. Equation of the line derived, used for converting all radiance values into reflectance values Ri = Lis - a R - Reflectance a - Offset s - Slope = (Rx1-Rx2)/(Lx1-Lx2) a Estimation of LP : Dark object subtraction Regression technique Does it always work? The key criterion of atmospheric correction algorithm ….. Quantify atmospheric influences on satellite image radiometry but at the same time insensitive to surface reflection effects Estimation of LP : Dark object subtraction Regression technique So how to correct this image? Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) Y. Zhang et al., 2002 (RSE) Manually select several clear and hazy area pixels in the image Two spectral bands are selected based on the following criteria: • The spectral responses of different land cover types, under clear atmospheric conditions, should be highly correlated in the two bands. This will result in a well-defined surface response vector in spectral space called “clear line” (CL) • The effect of haze should be markedly different in the two bands so that increased atmospheric contamination manifests in increased shift away from the CL • Typically we would select blue and red bands Apply a transformation whose coefficients define a direction orthogonal to the CL and whose response magnitude is proportional to the deviation from this line Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) Y. Zhang et al., 2002 (RSE) Schematic diagram of the TM1 – TM3 spectral space illustrating the conceptual components of the HOT. Under clear sky conditions, radiances of common surface cover types, coded as A – K, exhibit high correlation and define a ‘clear line’ (CL). The effect of haze of increasing optical depth, illustrated by the numerical sequences 1 – 18, is to pixels to ‘migrate’ away from the CL. The HOT quantifies the atmospheric contamination level at a pixel location by its perpendicular distance, in spectral space, from the CL. Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) Y. Zhang et al., 2002 (Rem Sens Env) Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) 1. Select two correlated bands (bands showing similar reflectance characteristics for all objects) but affected by scattering due to atmospheric components to different degrees. Example: Bands 1 (Blue) and 3 (Red) of ETM/TM Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) 2. Mask out areas with obvious haze 3. Select some very clear areas that are unaffected by clouds/haze) Band 3 (Red) Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) 4. Plot DN (Blue band – X axis) vs DN (Red band – Y axis) of pixels from clear area 5. Fit the pixel DNs to the clear line generated by linear regression (slope = α and offset β on x axis. 6. Haze vector is orthogonal to clearline Band 1 (Blue) Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) 7. Plot clear line 10. Calculate HOT for all pixels as the offset of a pixel from the clear line in the haze vector direction ( DN blue offset ) Sin DN Or DN blue Sin DN red red Cos Band 3 (Red) 8. Plot all DN (Blue) v/s DN(Red) for all pixels on the image 9. Haze vector is orthogonal to clear line, hence you can identify haze pixels Cos (disregard ing the offset) β . .. . ........... .. ........................ . ........................ ................................. .......................... . ............................ .. .............................. ........... . .. ................... ....... . ... ..... α Band 1 (Blue) Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) 11. Generate HOT Image and determine the HOT values for clear areas and hazy areas (Not the same image as in the previous slide) Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) 12. Plot histogram for different HOT levels for clear and hazy areas Clear areas Increasing HOT = > Increasing Haze Haze areas Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) 14. Estimate radiometric adjustment using a method similar to “dark object subtraction” to normalize the image to the radiometric level of the clearest areas. DN 13. Plot histogram lower bound versus HOT for bands TM1–TM3 Clear pixel From Step 13 plot, note that, for Band TM 1 (Blue), the histogram lower bound for clear pixels (i.e., HOT= 30) is approximately 20 DNs. Consider a hazy pixel with an observed HOT level of 40. It is a member of a histogram with a lower bound 27. This implies that this hazy pixel should have its band 1 DN level reduced by 7 during the radiometric adjustment phase. This procedure can be used to adjust all bands for which the histogram analysis has been done. Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT) Results Advantages and disadvantages of image-based techniques?? Model-based atmospheric corrections – Absorption Transmittance (T): T Transmitte d radiation Incident radiation I Io L Absorbance (A): 1 A log T 1 log 10 T or for gases A ln ln T T Beer’s Law: For monochromatic plane-parallel light entering a medium perpendicular to the surface of the medium: c - molar concentration; L- light path length, and A cL α - molar absorption coefficient for the medium 10 T 1 If L 1 cm , then A c or c A / A cL and A ln T T e Hence Beer’s law can be used to estimate concentrations cL Molar absorption coefficient is sometimes called molar extinction coefficient – however, this is only in the idealized case when scattering is zero. Model-based atmospheric corrections Molar absorption coefficient, extinction coefficient and attenuation coefficnet T e cL => in the absence of scattering. However, transmittance is function of absorptance + scattering, hence we need to define a new term, called “optical depth (or optical thickness, τ) ”, as a measure of transmittance. Optical depth is defined as the negative natural logarithm of the fraction of radiation that is not scattered or absorbed on a path. Hence optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of path length, and approaches zero as the path length approaches zero. Hence, optical depth is conceptually I analogous to absorbance, but not the same. ln ln T T e Includes both absorbance and scattering IO cL ε – extinction (or attenuation) coefficient Optical thickness or Optical depth Optical thickness (δ) has three components: Molecular scattering aerosol Molecular absorption Optical thickness due to molecular scattering by atmospheric gases • Mainly affects shorter wavelengths Optical thickness due to molecular absorption by atmospheric gases • Mainly due to 7 gases: water vapour (H2O), carbon dioxide (CO2), ozone (O3), nitrous oxide (N2O), carbon monoxide (CO), methane (CH4) and oxygen (O2) • Water vapour absorption is significant and varies with time and space. Optical thickness due to atmospheric aerosol Aerosol scattering is significant and varies with time and space. Optical depth due to molecular absorption by atmospheric gases Optical depth due to molecular scattering and absorption by atmospheric gases Rayleigh Scattering Strong water vapor bands are located near 1.38 and 1.88 micron. No signals are detected under clear sky conditions. Strong water vapor bands are located near 1.38 and 1.88 micron. No signals are detected under clear sky conditions. Radiance spectrum over a pixel (mineral Kaolinite) Reflectance spectrum of Kaolinite after atmospheric corrections Ground pixel reflectance is given by: R ( L Sensor L path ) d 2 E sun cos 0 T o What is known? • Sun-earth distance • Radiance at the sensor • Zenith angle • Incoming solar spectral irradiance What is unknown? • Path radiance • Transmittance Radiative transfer codes are used to estimate the unknowns Radiative Transfer • The physical phenomenon of energy transfer in a medium • In our case, it refers to electromagnetic radiation in the atmosphere • The propagation of the radiation through the atmosphere is affected by the processes of absorption and scattering, as well as atmospheric emissions • The equations of radiative transfer describe the interactions mathematically However, we need not worry about radiative transfer equations – leave that to atmospheric physicists - because computer codes are available that can model the atmospheric transmission of solar radiation using radiative transfer equations. However we need to worry about providing input variables to the equations. Radiative Transfer codes • MODTRAN (Moderate resolution atmospheric transmission) • 6SV (Second Simulation of a Satellite Signal in the Solar Spectrum) • DISORT (Discrete Ordinates Radiative Transfer Program for a Multi-Layered Plane-Parallel Medium) Radiative transfer codes simulate the Path Radiance (Lpath) and atmospheric transmittance (Tθ), based on user provided values for different atmospheric parameters. Atmospheric correction algorithms Atmospheric correction algorithms are used for estimating the values of atmospheric parameters, based on a user provided inputs. Main algorithms are (all commercial) •ATmospheric CORrection (ATCOR) : PCI Geomatica, ERDAS • ATmosphere REMoval (ATREM) • Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) (ENVI) Flow chart of radiative-transfer based models AC algorithm Key atmospheric parameters AC - Atmospheric correction RT - Radiative Transfer RT Code LUTs AC algorithm Atmospheric parameters to be input to Radiative Transfer codes for simulation of path radiance and transmittance INPUTS TO RADIATIVE TRANSFER MODELS: • Solar azimuth • Location • Wavelength (bands) • Ground elevation • Sensor view angle • Atmospheric optical depth WITH ABOVE PARAMETERS, RADIATIVE TRANSFER MODELS SIMULATE PATH RADIANCE AND TRANSMITTANCE FOR ESTIMATING SURFACE REFLECTANCE Estimation of atmospheric optical depth Atmospheric optical depth A. Due to molecular scattering by gases B. Due to molecular absorption by gases C. Due to absorption and scattering by aerosols Since optical depth is a function of concentration: cL We need to estimate the concentration of the seven important gases (O2, O3, N2O, CO2, CO, CH4, H2O) + aerosols in the direction of solar incidence. PROBLEM: Atmosphere is not homogenous, vertically or horizontally: Not realistically possible to measure concentrations of all of the above gases and aerosols over the entire atmospheric column (at least up to 100 km height) for every pixel. PRACTICAL SOLUTION USED IN ALL ALGORITHMS: • Define standard atmospheres • mid-latitude summer atmosphere • US standard atmosphere 1976 • standard tropical atmosphere • desert tropical (arid) atmosphere • fall (autumn) atmosphere • mid-latitude winter • subarctic winter • Vertically profile different standard atmospheres at a number of locations for: • air pressure, • air temperature, • Gaseous concentrations (except H2O) • τ due to aerosols? • τ due to water vapour? The unkown parameters ….. • Aerosol type and concentration • Water vapour concentration Water vapour concentration Must have bands in one of the following bands: •1050-1210 nm (for the 1135 nm water feature) •870-1020 nm (for the 940 nm water feature) •770-870 nm (for the 820 nm water feature) The band depth can be used to estimate the water vapor content (pixel wise) Aerosol : nature and concentration δAerosol≈εAerosolCAerosol • For εAerosol • Estimate from visibility: • Get the user input for visibility • Use Koschmieder equation (VIS = 3.912/ε) to estimate extinction coefficient from visibility (Aerosol optical depth not critical if the visibility is high, that is >40 km) • For CAerosol • Concentration difficult to estimate for every atmospheric condition, therefore standard types are used: - rural, urban, desert, maritime • The concentration of aerosols measured for different visibility ranges and different aerosol types, and are stored in lookup tables • Typical user inputs values are: •sensor type (LANDSAT/ASTER/etc etc) •solar azimuth • sensor viewing angle • Latitude-Longitude • standard atmosphere in the image • visibility • aerosol type • average ground elevation • Water vapour absorption channels (if the sensor type is provided, this is taken from the header file) ATCOR-2 LUT derived using MODTRAN The catalogue (LUT) consists atmospheric correction functions for: 1. Different standard atmospheres (altitude profile of pressure, air temperature, gases concentration) • mid-latitude summer atmosphere 2. 3. 4. 5. 6. 7. • US standard atmosphere 1976 • standard tropical atmosphere • desert tropical (arid) atmosphere • fall (autumn) atmosphere • mid-latitude winter • subarctic winter. Different aerosol types: rural, urban, desert, maritime Different aerosol concentrations (aerosol optical depth) defined by the visibility. The range provided is 5-40 km, calculated values are: 5, 7, 10, 15, 23, 40 km. Values for 4 and 80 km are obtained by linear extrapolation. The conditions range from hazy to very clear. Water vapour concentrations (calculated from absorption bands depths – optionally user defined) Different ground elevations ranging from 0 to 1 km (calculated values are for 0, 0.5, and 1km ASL; other values interpolated.) Solar zenith angles ranging from 0o - 70o in the steps of 10o Different functions for each sensor and each band - the atmospheric correction functions depend on the spectral response of the sensor, thus there are different functions for each sensor and each band The above parameters can be specified by the user, or are read from the image header. For illustration - in ATCOR-2, the number of entries in the look-up tables for the six reflective bands of Landsat TM is about 9000, i.e. 12 x 7 x 6 x 3 x 6 = 9072, including 12 atmospheres, 7 solar zenith angles, 6 visibilities, 3 ground elevations, and 6 bands. Measured atmospheric data can also be used to calculate new files of look-up tables for the catalogue. After estimation of path radiance, global flux and atmospheric transmission, apply the following equation to derive surface reflectance { d ( c 0 c1 * DN ) L path } 2 R T o E g Bidirectional Reflectance Distribution Function Bidirectional Reflectance Distribution Function Bidirectional Reflectance Distribution Function Bidirectional Reflectance Distribution Function The bidirectional reflectance distribution function (BRDF) is a theoretical concept that describes the relationship between 1) the geometric characteristics of the solar irradiance, and 2) the remote sensing system viewing geometry; hence the bidirectional terminology (Sandmeier, 1996; Jensen, 2000) f ( i , i ; r , r ; ) dL ( i , i ; r , r ; ) dE ( i , i ) Bidirectional Reflectance Distribution Function Very difficult to acquire BRDF information about a surface because a) the Sun is constantly moving across the sky, and/or b) it is difficult to acquire multiple images of the terrain from various angles of view in a short period of time. This problem resulted in the invention of the goniometer; a specialized instrument that measures spectral reflectance in a specified number of directions distributed throughout the hemisphere above a particular surface in a very short time (5-10 minutes), allowing scientists to generate a useful BRDF for that surface. Bidirectional Reflectance Distribution Function Bidirectional reflectance factor (R) R ( i , i ; r , r ; ) dL ( i , i ; r , r ; ) dL ref ( i , i ; r , r ; ) dLr is the energy reflected from a surface in a specific direction divided by the radiance dLref , reflected from a loss-less Lambertian reference panel measured under identical illumination geometry. The Rref is a calibration coefficient determined for the spectral reflectance panel used. The bidirectional reflectance factor (R) is then normalized to an anisotrophy factor (ANIF) to analyze the spectral variability in BRDF data. The ANIF is calculated by normalizing bidirectional reflectance data R to nadir reflectance, Ro using the equation (Sandmeier et al., 1998a; Sandmeier and Itten, 1999) ANIF ( i , i ; r , r ; ) R ( i , i ; r , r ; ) Ro ( ) Bidirectional Reflectance Distribution Function (Jensen and Schill, 2000) Atmospheric absorption Zenith angle (Sun zenith angle 75 degrees) -75o Reflectance -45o -15o 0o 15o 45o 75o Wavelength Bidirectional Reflectance Distribution Function (Jensen and Schill, 2000) Atmospheric absorption Azimuth angle Reflectance 0o 30o 60o 90o 150o 270o Wavelength Bidirectional Reflectance Distribution Function Bidirectional reflectance factor (R) An understanding of BRDF is needed in remote sensing to correct for Sun illumination angle and sensor viewing angle effects for • Mosaicking images, • Deriving albedo, • Improving land cover classification accuracy, • Enhancing cloud detection, and • Correcting for atmospheric conditions • To identify bands that are least impacted by BRDF, recognize optimal sun/sensor angle-of-views (Myneni et al., 1995; Woodcock et al., 1997). Bidirectional Reflectance Distribution Function The accurate computation of BRDF required for: • Making corrections to reflectance measurements of features measured from nadir or off-nadir pointing remote sensing systems. • To identify bands that are least impacted by BRDF, recognize optimal sun/sensor angle-of-views, and provide insight into radiometrically adjusting remotely sensed data to minimize BRDF effects.