Radiometric and Atmospheric Correction Lecture 3 Prepared by R. Lathrop 10/99 With slide by Z. Miao Revised 1/09

Where in the World?

RS Applications to Disaster Response: Haiti Matterhorn by apanotous

Data-to-Information Conversion Statement of problem Signal (W m-2) Dt (Time) Julian day Data collection At-satellite radiance signal Remote sensing process Data-to-Information Conversion Image presentation Radiometric correction Spectral or histogram enhancement (e.g., LUT stretch) Signal (W m-2) Dt (Time) Julian day As for remote sensing data processing, there are four major steps: Statement and definition of your problem; data collection; Data-to-information conversion which is one of the most important processes; and information presentation. For data-to-information, we already studied image display and spectral enhancement (Lookup-stretch ) in last lecture and lab. Today we will go through radiometric and atmospheric correction of image. Analog-to-DN conversion DN (Brightness value) 255 # of pixels # of pixels DN (Brightness value) 255 etc. Target surface reflectance signal

Learning objectives Remote sensing science concepts Math Concepts Basic interactions between EMR & earth surface and atmosphere The differences between DN values, radiance and reflectance, at-satellite and surface radiance Principle of conservation of energy Radiometric Correction Atmospheric correction: need for and basic overview of techniques Terrain correction: need for and basic overview of techniques Math Concepts Analog-to-DN and DN-to-radiance conversion response function Linear regression analysis for scene-to-scene normalization Skills Applying radiometric response functions Determining best-fit relationships using linear regression for simple atmospheric correction

Radiometric correction Radiometric correction: to correct for varying factors such as scene illumination, azimuth, elevation, atmospheric conditions (fog or aerosol), viewing geometry and instrument response. Objective is to recover the “true” radiance and/or reflectance of the target of interest When the emitted or reflected electro-magnetic energy is observed by a sensor on board an aircraft or spacecraft, the observed energy does not coincide with energy emitted or reflected from the same object observed from a short distance. This is due to sun’s azimuth and elevation, atmospheric conditions (fog or aerosols), sensor’s response.

Analog-to-digital conversion process A-to-D conversion transforms continuous analog signal to discrete numerical (digital) representation by sampling that signal at a specified frequency Continuous analog signal As we know, remote sensor record in analog format or directly in digital number (with digital camera). For analogy sensor, we should converse analog signal to DN(i.e., brightness value). Discrete sampled value Radiance, L dt Adapted from Lillesand & Kiefer

Units of EMR(electro-magnetic radiation) measurement Irradiance - radiant flux incident on a receiving surface from all directions, Energy per unit surface area, W m-2 Radiance - radiant flux emitted or scattered by a unit area of surface as measured through a solid angle, W m-2 sr-1 µm-1(energy (Watt) per unit area (square meter) per solid angle per unit wavelength (µm-1)) Reflectance - fraction of the incident flux that is reflected by a medium Here we want to clear three definitions: irradiance, radiance and reflectance. Irradiance is radiant flue incident on an object of interest. Radiance is radiant flux emitted or scattered by a unit area of surface. Unit of radiance and reflectance is w m-2 sr-1 um-1. The difference between radiance and reflectance are that reflectance is part of incident radiant flux. Solid angle: an angle formed by three or more planes intersecting at a common point.

For today’s lecture, we’ll use Landsat imagery for our examples For more info, go to: http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_toc.html

Radiometric response function Conversion from radiance (analog signal) to DN follows a calibrated radiometric response function that is unique for channel Inverse relationship permits user to convert from DN back to radiance. Useful in many quantitative applications where you want to know absolute rather than just relative amounts of signal radiance Calibration parameters available from published sources and image header We use a calibrated radiometric response function to convert radiance to DN. Of course, we are able to use inverse relationship to convert DN back to radiance.

Radiometric response function Radiance to DN conversion DN = G x L + B where G = slope of response function (channel gain) L = spectral radiance B = intercept of response function (channel offset) DN to Radiance Conversion L = [(LMAX - LMIN)/255] x DN + LMIN where LMAX = radiance at which channel saturates LMIN = minimum recordable radiance We use the linear to convert radiometric response function to DN or from DN to L.

Radiometric response function Spectral Radiance to DN DN to Spectral Radiance 255 Lmax Slope = channel gain, G DN L Slope = (Lmax – Lmin) / 255 DN to spectral radiance: slope=(Lmax-Lmin)/255. Lmin Lmin L Lmax DN 255 Bias = Y intercept

High vs. Low Gain Dynamic Ranges Some sensors such as Landsat ETM can operate under high gain settings when image brightness is low or low gain when image brightness is high Some sensor can change gain (slope of radiance to DN) values based on image brightness. http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter6/chapter6.html

Radiometric response function Example: Landsat 5 Band 1 From sensor header, get Lmax & Lmin Lmax = 15.21 mW cm-2 sr-1 um-1 Lmin = -0.15200000 mW cm-2 sr-1 um-1 L = -0.15200000 + ((15.21 - 0.152)/255) DN L = -0.15200000 + (0.06024314) DN If DN = 125, L = -0.15200000 + (0.06024314) 125 L = -0.15200000 + 7.53039 L = 7.37839 mW cm-2 sr-1 um-1

Radiometric response function Example: Landsat 7 Band 1 Note that Landsat Header Record refers to gain and bias, but with different units (i.e., W m-2 sr-1 µm-1, rather than mW m-2 sr-1 µm-1) 1 W m-2 sr-1 µm-1= 0.1 mW cm-2 sr-1 µm-1 L = Bias + (Gain* DN) Unit conversion: 1 W m-2 sr-1 µm-1 = 1000 mW/10000cm2 sr-1 µm-1= 0.1 mW cm-2 sr-1 µm-1 If DN = 125, L = ? Landsat Science Data User’s Handbook ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter1

DN-to-Radiance conversion Example: Landsat ETM Band Gain Bias 1 0.7756863 -6.1999969 2 0.7956862 -6.3999939 3 0.6192157 -5.0000000 4 0.6372549 -5.1000061 5 0.1257255 -0.9999981 6 0.0437255 -0.3500004 Note that Landsat Header Record refers to gain and bias, but with different units (W m-2 sr-1 um-1)

Radiometric response function Example: Landsat 7 Band 1 Note that Landsat Header Record refers to gain and bias, but with different units (W m-2 sr-1 µm-1) Gain = 0.7756863 W cm-2 sr-1 µm-1 Bias = -6.1999969 W cm-2 sr-1 µm-1 L = -6.1999969 + (0.7756863) DN If DN = 125, L = 90.76079 W m-2 sr-1 µm-1 Same 9.076079 mW cm-2 sr-1 µm-1 Landsat Science Data User’s Handbook ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

Radiometric response function Example: Landsat 5 Thermal IR Gain = 0.005632 mW cm-2 sr-1 um-1 Bias = 0.1238 mW cm-2 sr-1 um-1 L = 0.1238 + (0.005632) DN To convert to at-satellite temperature (o K): T = 1260.56 / loge [(60.776/L) + 1] Remember 0oC = 273.1K For more details see Markham & Barker. 1986. EOSAT Landsat Technical Notes v.1, pp.3-8.

Radiometric response function Example: Landsat 7 Thermal IR For High Gain Band 6: MIN = 3.2; LMAX = 12.65 Gain = 0.037059 W m-2 sr-1 mm-1 Bias = 3.2W m-2 sr-1 mm-1 L = 3.2 + (0.03706) DN To convert to at-satellite temperature (o K): T = 1282.71 / loge [(666.09/L) + 1] Remember 0oC = 273.1K Next slides we will show the results. For more details see Markham & Barker. 1986. EOSAT Landsat Technical Notes v.1, pp.3-8.

Oyster Creek Nuclear Plant, NJ Thermal plume Landsat ETM Dec 1, 2001 What’s the temperature difference between the plume and ambient Barnegat Bay waters? High gain B6 Plume DN = 133 Bay DN = 118

What’s the Temperature difference between plume and ambient bay? L = 3.2 + (0.03706) DN Plume DN = 133 L = 8.13 Bay DN = 118 L = 7.57 T (oC)= {1282.71 / loge [(666.09/L) + 1]} – 273.1 Plume Temperature = 17.2 oC Ambient Bay temperature = 12.7 oC Remember this is the uncorrected at-satellite temperature, but the relative temperature difference of approx 4.5 oC should be valid Radiance signal of an object of interest on the ground should be higher than at-satellite signal. For more details see. http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11/chapter11.html

At-Satellite Reflectance To further correct for scene-to-scene differences in solar illumination, it is useful to convert to at-satellite reflectance. The term “at-satellite” refers to the fact that this conversion does not account for atmospheric influences. At-Satellite Reflectance, pl = (p Ll d2 ) / (ESUNl cosq) Where Ll = spectral radiance measured for the specific waveband q = solar zenith angle ESUN = mean solar exoatmospheric irradiance (W m-2 um-1), specific to the particular wavelength interval for each waveband, consult the sensor documentation. d = Earth-sun distance in astronomical units, ranges from approx. 0.9832 to 1.0167, consult an astronomical handbook for the earth-sun distance for the imagery acquisition date

Solar zenith vs. elevation angle At-satellite reflectance Tangent plane Ground reflectance Zenith angle Solar elevation angle = 90 - zenith angle Zenith: the point on the celestial sphere that is directly above the observer. http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter6/chapter6.html

Solar Zenith angle qo = 0 qo = 60 qo = solar zenith angle qo = 0 cosqo = 1 As qo cosqo zenith angle Tangent line Solar elevation angle = 90 - zenith angle =30 If zenith angle=60, solar elevation angle=30. Note that the sum of zenith and solar elevation angle is always equal to 90. Note zenith angle is different from azimuth angle. N Azimuth angle

At-Satellite Reflectance Example: Landsat 7 Band 1 If Acquisition Date = Dec. 1, 2001 At-Satellite Reflectance = ?

We can use the website to get altitude/azimuth table. http://aa.usno.navy.mil/data/docs/AltAz.html

Table 11.4 Earth-Sun Distance in Astronomical Units Julian Day Distance 1 .9832 74 .9945 152 1.0140 227 1.0128 305 .9925 15 .9836 91 .9993 166 1.0158 242 1.0092 319 .9892 32 .9853 106 1.0033 182 1.0167 258 1.0057 335 .9860 46 .9878 121 1.0076 196 1.0165 274 1.0011 349 .9843 60 .9909 135 1.0109 213 1.0149 288 .9972 365 .9833 This is the earth-sun distance in Astronomical Unit. Landsat Science Data User’s Handbook ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

Solar Spectral Exoatmospheric Irradiances(ESUN): Landsat ETM Watts m-2 um-1 Band 1 1969.0 Band 2 1840.0 Band 3 1551.0 Band 4 1044.0 Band 5 225.70 Band 7 82.07 Band 6 1368.0 Landsat Science Data User’s Handbook ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

At-Satellite Reflectance Example: Landsat 7 Band 1 The equation for converting radiance to reflectance: pl = (p Ll d2 ) / (ESUNl cosq) Dec. 1, 2001  Julian Day = 335 Earth-Sun d = 0.986 ESUNl = 1969.0 Cosq = Cos(63.54) = 0.44558 Ll = 90.76079 W m-2 sr-1 um-1 pl = (3.14159*90.76079*0.9862)/(1969.0*0.44558) pl = 277.20558/877.34702 = 0.31596. pl=surface target reflectance at a specific wavelength. The equation may be used to convert radiance to reflectance.

Landsat Reflectance Conversion: ERDAS Imagine module Erdas Imaging offers a tool to caclulate landsat reflectance conversion.

Atmospheric Correction

Path radiance and target radiance Target Reflectance (BRDF) Surround Reflectance Multiple Scattering Direct Solar Irradiance Adjacency Effect Sky Path Radiance (Single scattering) Path Radiance Path radiance is radiance imposed by atmosphere.

Basic interactions between EMR and the atmosphere Scattering, S Absorption, A Transmission, T Incident E = S + A + T Within atmosphere, determined by molecular constituents, aerosol particles, water vapor Atmosphere composite, aerosol particule and water vapor affect radiation reflectance.

Atmospheric windows Specific wavelengths where a majority of the EMR is absorbed by the atmosphere Wavelength regions of little absorption known as atmospheric windows Transmittance (%) Some specific wavelength is of little absorption known as atmospheric windows. The atmospheric window lies approximately at wavelength of infrared radiation between 8 and 15 micrometers. Graphic from http://earthobservatory.nasa.gov/Library/RemoteSensingAtmosphere/

From Shaw, G. A. and H. K. Burke. Spectral Imaging for Remote Sensing

Atmospheric interference with EMR Shorter wavelengths strongly scattered, adding to the received signal Longer wavelengths absorbed, subtracting from the received signal Signal decreased by absorption Signal increased by scattering 0.4 0.5 0.6 0.7 0.8 1.1 um Ref Longer wavelengths is absorbed more by atmosphere. So at-satellite signal is decreased comparing ground signal. Short wavelength strongly scattered, at-satellite signal is increased. All of these interference are noise. We better remove it. Adapted from Jensen, 1996, Introductory Digital Image Processing

Atmospheric Interference Interaction of the atmosphere with reflected/emitted ENMR can add noise to the signal. Noise: extraneous unwanted signal response Want high signal-to-noise ratio Over low reflectance targets (i.e. dark pixels such as clear water) the noise may swamp the actual signal Atmospheric interference on reflectance is noise. So, we want signal-to-noise ratio as high as possible. True Signal Observed Signal Noise +

Atmospheric correction Atmospheric correction procedures are designed to minimize scattering & absorption effect due to the atmosphere Scattering increases brightness. Shorter wavelength visible region strongly influenced by scattering due to Rayleigh, Mie and nonselective scattering Absorption decreases brightness. Longer wavelength infrared region strongly influenced by water vapor absorption. Atmospheric correction is designed for minimizing scattering and absorption effect due to atmosphere. Generally, shortwave band is increased by scattering, and longer wave band is reduced by absorption.

Satellite Received Radiance Total radiance, Ls = path radiance Lp + target radiance Lt Ideally, we want to get target radiance as more as possible. Target radiance, Lt = 1/p RTqu (E0 deltalTqo cosqo deltal+ Ed) Where R = average target reflectance qo = solar zenith angle Qu = nadir view angle Tqo = atmospheric transmittance at angle q to zenith E0l = spectral solar irradiance at top of atmosphere Ed = diffuse sky irradiance (W m-2) Delta l = band width, l2 – l1

Atmospheric correction techniques Absolute vs. relative correction Absolute removal of all atmospheric influences is difficult and requires a number of assumptions, additional ground and/or meteorological reference data and sophisticated software (beyond the scope of this introductory course) Relative correction takes one band and/or image as a baseline and transforms the other bands and/or images to match

Atmospheric correction techniques: Histogram adjustment Histogram adjustment: visible bands, esp. blue have a higher MIN brightness value. Band histograms are adjusted by subtracting the bias for each histogram, so that each histogram starts at zero. This method assumes that the darkest pixels should have zero reflectance and a BV = 0.

Atmospheric correction techniques: Dark pixel regression adjustment Select dark pixels, either deep clear water or shadowed areas where it is assumed that there is zero reflectance. Thus the observed BV in the VIS bands is assumed to be due to atmospheric scattering (skylight). Regress the NIR vs. the VIS. X-intercept represents the bias to be scattered from the VIS band (visible band). For, histogram adjustment, we should select dark pixels, e.g., deep clear water or shadowed areas. Then the BV at dark pixels will be set to 0

Atmospheric correction techniques: Scene-to-scene normalization Technique useful for multi-temporal data sets by normalizing (correcting) for scene-to-scene differences in solar illumination and atmospheric effects Select one date as a baseline. Select dark, medium and bright features that are relatively time-invariant (i.e., not vegetation). Measure DN for each date and regress. DB b1, t2 = a + b DN b1, t1 Another correction method is scene-to-scene normalization. As for scene-to-scene normalization, we should select one date as a baseline. Then select dark, medium and bright features that are relatively time-invariant and make regression for those features. We talk more detail in the lab class.

Scene-to-Scene Normalization Example: Landsat 5 vs Landsat 7 Landsat 7: Sept 01 Landsat 5: Sept 95

Scene-to-Scene Normalization Example: Landsat 5 vs Landsat 7 Landsat 5: Sept 95 Landsat 7: Sept 99 & 01 99 R2 = 0.971 01 R2 = 0.968 99 R2 = 0.932 01 R2 = 0.963

Scene-to-scene normalization: work flow NOTE: the selected features of the two images must correspondingly come from SAME locations.

Hyperspectral Image Cube From Shaw, G.A. and H.K. Burke. Spectral Imaging for Remote Sensing. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.69.1178&rep=rep1&type=pdf.

Atmospheric correction: absolute MODTRAN (Moderate resolution TRANsmission model) predicts the atmospheric emission, thermal scatter, and solar scatter for arbitrary, refracted paths above the curved earth, incorporating the effects of molecular absorbers and scatterers, aerosols and clouds. FLAASH (Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes) handles data from a variety of hyper- and multi-spectral imaging sensors, supports off-nadir as well as nadir viewing, and incorporates algorithms for water vapor and aerosol retrieval and adjacency effect correction. Based on MODTRAN. Marketed by Spectral Sciences Inc. http://www.spectral.com/remotesense.shtml AVIRIS after AVIRIS before

FLAASH Fast Line-of-Sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) approach From Shaw, G.A. and H.K. Burke. Spectral Imaging for Remote Sensing. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.69.1178&rep=rep1&type=pdf.

FLAASH Fast Line-of-Sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) approach Employs a band ratio technique to quantify the effect of water vapor on hyperspectral measurements. Involves comparing ratios of radiance measurements made near edges of known atmospheric water-vapor absorption bands in order to estimate the column water vapor in the atmosphere on a pixel-by-pixel basis. Look-up tables, indexed by measured quantities in the scene, combined with other information such as the solar zenith angle, are used to estimate reflectance across the scene, without resorting to reference objects within the scene. From Shaw, G.A. and H.K. Burke. Spectral Imaging for Remote Sensing. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.69.1178&rep=rep1&type=pdf.

Terrain Shadowing USGS DEM Landsat ETM Dec 01 Since terrain shadow can affect target reflectance, we should do terrain shadow correction sometimes. Solar elevation = 26.46 Sun Azimuth = 158.78

Terrain correction To account for the seasonal position of the sun relative to the pixel’s position on the earth (i.e., slope and aspect) Normalizes to zenith (sun directly overhead) Lc = Lo cos (Qo) / cos(i) where Lc = slope-aspect corrected radiance Lo = original uncorrected radiance cos (Qo) = sun’s zenith angle cos(i) = sun’s incidence angle in relation to the normal on a pixel (i = Qo-slope) By accounting for the seasonal position of the sun relative to the pixels’s position on the earth, we normalize sun position zenith.

Cosine Terrain correction Sensor Qo Sun Lc = Lo cos (Qo) / cos(i) i 90o Terrain: assumed to be a Lambertian surface Adapted from Jensen

Terrain correction Terrain Correction algorithms aren’t just a black box as they don’t always work well, may introduce artifacts to the image Example: see results on right from ERDAS IMAGINE terrain correction function appears to “overcorrect” shadowed area

Summary The differences between DN values, radiance and reflectance, at-satellite and surface radiance; Analog-to-DN and DN-to-radiance conversion response function; Radiometric Correction; Atmospheric correction, e.g., scene-to-scene normalization.

Data-to-Information Conversion Statement of problem Signal (W m-2) Dt (Time) Julian day Data collection At-satellite radiance signal Remote sensing process Data-to-Information Conversion Image presentation Radiometric correction Spectral or histogram enhancement (e.g., LUT stretch) Signal (W m-2) Dt (Time) Julian day As for remote sensing data processing, there are four major steps: Statement and definition of your problem; data collection; Data-to-information conversion which is one of the most important processes; and information presentation. For data-to-information, we already studied image display and spectral enhancement (Lookup-stretch ) in last lecture and lab. Today we will go through radiometric and atmospheric correction of image. Analog-to-DN conversion DN (Brightness value) 255 # of pixels # of pixels DN (Brightness value) 255 etc. Target surface reflectance signal

Homework Landsat TM Thermal IR calibration; Reading Ch. 6; ERDAS Field Guide Ch. 5: 132-135.