Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 1 Instrument Calibration and Atmospheric Corrections Instrument Calibration and Atmospheric Corrections Why calibrate ? – reference data – temporal comparison

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 2 ELM DC or L DC R( ) Band 1Band 2

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 3 Model Based Estimates of R clouds R predicted by model, e.g. Bio-optical model for R( ) as a function of coloring agents ([C], [CDOM], [TSS]) DC or L R( )

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 4 Standard Surfaces Band 1 R( ) DC or L Clouds Deep Vegetation Significant potential for error if only limited samples are available or target, variability is high.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 5 Atmospheric and System Corrections Using Spectral Data (cont’d) Note ELM can also be used with calibrated system – Pros removes atmospheric and sensor artifacts simple and direct if good ground data available

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 6 Atmospheric and System Corrections Using Spectral Data (cont’d) – cons requires large known targets assumes uniform correction across image can introduce sizeable errors if reference reflectance is not well-known or significantly different than target reflectance

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 7 Atmospheric and System Corrections Using Spectral Data (cont’d) calibrating sensors laboratory calibration – spectral calibration – band center – relative spectral response – FW HM – absolute calibration to radiance

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 8 AVIRIS Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) Figure 3 shows a detail of the AVIRIS onboard calibrator which is used for monitoring and updating the laboratory calibration of AVIRIS.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 9 AVIRIS (cont’d) Figure 3. In-flight calibrator configuration

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 10 AVIRIS (cont’d) Figure 1. a) Laboratory spectral calibration set-up.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 11 AVIRIS (cont’d) Figure 1. B) Typical spectral response function with error bars and best fit Gaussian curve from which center wavelength, FWHM bandwidth and uncertainties are derived.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 12 AVIRIS (cont’d) Figure 2. Derived center wavelengths for each AVIRIS channel (bold line), read from left axis, and associated uncertainty in center wavelength knowledge (normal line), read from right axis.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 13 AVIRIS (cont’d) Figure 7. Radiometric calibration laboratory setup.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 14 AVIRIS (cont’d) (a) (b) Figure 5.42 Integrating spheres used for sensor calibration: (a) sphere design, (b) sphere used in calibration of the AVIRIS Sensor. (Image courtesy of NASA Jet Propulsion Laboratory).

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 15 AVIRIS (cont’d) Figure 12. AVIRIS signal-to-noise for the 1995 in- flight calibration experiment.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 16 AVIRIS (cont’d) Figure 13. AVIRIS noise-equivalent-delta-radiance for 1995.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 17 Atmospheric and System Corrections Using Spectral Data (cont’d) radiometric calibration – dark level – intensity std with reflectance panel – transfer through a detector std to sphere – detector stds and spheres – use of onboard reference – (laser line, spectral filters) – use of onboard spectral reference

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 18 Atmospheric and System Corrections Using Spectral Data (cont’d) inflight calibration and generation of model mismatch spectral correction – calibration sites – MODTRAN prediction of sensed radiance

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 19 Adjustments to AVIRIS Data At the start of a flight season, for a surface of known reflectance, predict radiance reaching AVIRIS using MODTRAN convolved with AVIRIS spectral response. Call this L M ( ). N.B. This is for a well-known study site with known radiosonde and optical depth (Langley plot) values. Severe clear, high and dry to minimize errors due to poor characterization of any constituents.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 20 Adjustments to AVIRIS Data (cont’d) Generate a correction vector (1) where L A ( ) is the observed AVIRIS radiance for the target modeled in generating L M. The C M ( ) vector is the residual miscalibration error between MODTRAN and AVIRIS. In particular, any residual spectral miscalibration will be picked up by this process. )( )( )( M A M L L C 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 21 Adjustments to AVIRIS Data (cont’d) Fig. 4. Calibration ratio between AVIRIS and MODTRAN3 derived from the inflight calibration experiment on the 4 th of April 1994.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 22 Adjustments to AVIRIS Data (cont’d) For any spectra predicted by MODTRAN, the equivalent AVIRIS spectra is then given by (2) Furthermore, the onboard calibrator senses slight changes in detectors over time. )()()( MMA CLL 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 23 Adjustments to AVIRIS Data (cont’d) Define a correction vector (3) where L 1 ( ) = lamp radiance at time of inscene correction used to generate equation 1 (Day 1), L 2 ( ) = lamp radiance at time of flight of current interest (Day 2). )( )( )( 2 1 L L C C 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 24 Adjustments to AVIRIS Data (cont’d) To correct AVIRIS radiance on Day 2 to equivalent readings on Day 1, (4) )()()( 21 C CLL 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 25 Adjustments to AVIRIS Data (cont’d) Fig. 5. Calibration ratio of the on-board calibrator signal for the Pasadena flight to the signal for the inflight calibration experiment.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 26 Adjustments to AVIRIS Data (cont’d) So radiance to be compared are (5) or to avoid changing all the image data )()()( vs. )()()( 21 C MMA CLL CLL  

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 27 Adjustments to AVIRIS Data (cont’d) (6) where L A2 is the day 2 radiance that AVIRIS is predicted to observe using ground reflectance estimates and the MODTRAN code. )( vs. )( )()( )( 22 L C CL L C MM A 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 28 Adjustments to AVIRIS Data (cont’d) If we want to correct using MODTRAN then we would want to convert day two spectral radiance to L M values, i.e. )(C )(C)(L )(L M C2 M 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 29 Critical Atmospheric Parameters density of the atmosphere (pressure depth) aerosols type and number water – column water vapor

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 30 Pressure Depth Modtran derived radiance vs. wavelength plots for sensor reaching radiance for different target elevations.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 31 Pressure Depth (cont’d)

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 32 Aerosol Number Density Typical particle size distribution curves for a rural aerosol type. DRY TROPO AEROSOLS RH = 80% TROPO MODEL RH = 95% TROPO MODEL RH = 99% TROPO MODEL

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 33 Modtran derived sensor reaching radiance for identical targets viewed through two atmospheres where only the column water vapor amount differs. Column Water Vapor

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 34 Water Vapor Estimation CIBR (Continuum Interpolated Band Ratio) – spectral prediction of sensed radiance with MODTRAN – computation of a continuum interpolated band ratio – per pixel corrections to reflectance

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 35 A B D C Water Vapor Estimation compare to LUT of MODTRAN predicated C D L L C D L L

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 36 Water Vapor Estimation (cont’d) ATREM – use of bands in ATREM to adjust for material reflectance spectra

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 37 Atmospheric Calibration In general, Scattering dominates below 1 μm; absorption above 1 μm, Top of atm reflectance Tanré 1960 claims (1)

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 38 Atmospheric Calibration rearranging (1) yields: (2)

where A - F are expressed in apparent reflectance (TOA) averaged over a predefined set of AVIRIS bands designed to characterize the absorption feature and its wings. (3) An apparent reflectance spectrum with relevant positions and widths of spectral regions used in three channel rationing being illustrated wavelength Apparent reflectance A B C D E F 0 2

Comparing the average of the mean effective transmission in the two absorption regions with theoretical values predicted using radiation propagation models, you can use LUT to obtain an estimate of water vapor concentration on a pixel-by-pixel basis. Step 1.  from lat, long, T.O.D. and D.O.Y. Step 2.  g calculated based on models and atm path. For  H2O, several spectra computed as function of total column H 2 O range cm. So we end up with many  g spectra. The band ratio transmittances can be calculated for each spectra. Step 3.  a, s,  us and  ud are calculated using 5s (now 6S) which assumes no absorption for these calculations. Step 4.AVIRIS radiance converted to apparent reflectance spectrum (TOA reflectance). Step 5.Calculate channel ratios at 0.94 and 1.14 µm regions using Equation 3 on the results of Step 4. Compare Step 5 to results of Step 2 and estimate column H 2 O and corresponding  g. Step 6.  g from 5 and inputs from 3 and 4 are used with Equation 2 to estimate reflectance spectra.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 41 Band ratio assumes uniform slope in reflectance spectra over 3 bands. This is compensated for vegetation, snow, and ice by adjusting bands to more closely approximate for errors introduced by non linearity. i.e., band ratios use 3 sets of bands, 1 for vegetation, 1 for snow, and 1 for non vegetation or snow.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 42 Atmospheric Calibration Equation 1 can be expressed as: as compared with the manner we normally express radiance if atmosphere is very clear. From radiative transfer  1  2 ( ) are calculated for different H 2 O content.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 43 Atmospheric Calibration

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 44 Atmospheric Calibration wavelength RATIO Ratio of one atmospheric water vapor transmittance spectrum with more water vapor against another water vapor transmittance spectrum with 5% less water vapor.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 45 Atmospheric Calibration wavelength RATIO Ratio of one atmo- spheric transmittance spectrum of CO 2, N 2 0, CO, CH 4, and O 2 in a sun-surface- sensor path with a surface elevation at sea level against another similar spectrum but with a surface elevation at 0.5 km.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 46 Water Vapor Estimation (cont’d) APDA – correction to 940 ratio for upwelled radiance using a column water dependent upwelled radiance

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 47 Water Vapor Estimation (cont’d) APDA Chart

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 48 The APDA Technique The single channel/band Rapda: )LL()LL( )PW(LL R r2,atmr2 r1,atmr1 m,atmm APDA     which can be extended to more channels: im ][jm,atmmjr im, m APDA |)]LL[,]([LIR ]LL[ R   

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 49 The APDA Technique Relate R ratio with the corresponding water vapor amount (PW) Solving for water vapor: )(PW)(- APDAWV eR(PW)        1 APDA )Rln( )R(PW        

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 50 The APDA Technique ))((   PW APDA LnR  )( 1 PW LnR           

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 51 Compute LUT w/ L T (wv,h,  =0.4 and L atm (wv,h,  Calculate R APDA for each MODTRAN run by applying APDA equation to the LUT. Fit ratio values to PW and store the regression parameters. Assume starting PW 1 and subtract height dependent L u from image. Calculate APDA ratio and transform R APDA values to PW 2 using inverse mapping eq. Substitute the L atm in eq. with new PW dpndt values derived from LUT. Calculate RAPDA a 2nd time and trans- form to final PW 3 (x,y). General APDA Procedure

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 52 APDA Solutions Channel #10 from an AVIRIS image of the Los Angeles/Pasadena area. Preliminary water vapor density image generated using the ATREM algorithm (the darker the pixels, the more water vapor).

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 53 APDA Solutions Channel #25 from the cropped AVIRIS image of the Los Angeles/Pasadena area. Preliminary water vapor density image generated using the APDA algorithm (the darker the pixels, the more water vapor).

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 54 Water Vapor Estimation (cont’d) Multi parameter approach – NLLSSF

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 55 Atmospheric Inversion Oxygen - pressure elevation To estimate the effective height (surface pressure elevation) the strength of the oxygen absorption band (760 nm) in the AVIRIS spectrum is fitted to MODTRAN data. 1.To increase sensitivity, average (e.g., 5x5 pixels) to generate AVIRIS spectrum.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 56 Atmospheric Inversion (cont’d) 2. Iteratively predict oxygen spectra in AVIRIS radiance units using pressure elevation. Use non linear least squares to control the iteration process. Parameters adjusted were pressure elevation, reflectance magnitude (a), and reflectance slope (b). )(baR 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 57 Atmospheric Inversion (cont’d) Fig. 4. The fit with residual between the MODTRAN2 nonlinear least square fit spectrum and the AVIRIS measured spectrum for the estimation of surface pressure elevation from the oxygen band at 760 nm.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 58 Atmospheric Inversion (cont’d) The resulting surface pressure elevation can be constrained in subsequent calculations (e.g., aerosol optical depth). Aerosol optical depth - AVIRIS data averaged over 11X11 pixels Select aerosol type in MODTRAN

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 59 Atmospheric Inversion (cont’d) Adjust parameters describing: – aerosol optical depth (visibility parameter) – reflectance magnitude – reflectance spectral slope – leaf chlorophyll absorption (parametric description of location and shape of spectrals feature) Fit run over visible region  veg RbaRγ)( 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 60 Atmospheric Inversion (cont’d) Fig. 7. Spectral fit for aerosols at the Rose Bowl parking lot.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 61 Atmospheric Inversion (cont’d) Fig. 3. The nonlinear least squares between the AVIRIS measured radiance and the MODTRAN2 modeled radiance for estimation of aerosol optical depth. The modeled reflectance required for this fit in the 400 to 600 nm spectral region is also shown as is the resulting AVIRIS calculated reflectance.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 62 Atmospheric Inversion (cont’d) Water vapor determination (940 absorption feature) for each pixel Fits parameters for – column water vapor and – 3 parameters that describe surface reflectance with leaf water. )()( veg RbaR 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 63 Atmospheric Inversion (cont’d) Fig. 7. Fit with residual between the AVIRIS measured radiance and the MODTRAN2 modeled radiance in the 940 nm spectral region for an area of green grass in the Jasper Ridge AVIRIS data set.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 64 Atmospheric Inversion (cont’d) Fig. 8. Surface reflectance with leaf water absorption required to achieve accurate fit between the measured radiance and modeled radiance for the spectrum in Fig. 4.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 65 Atmospheric Inversion (cont’d) The water content, aerosol optical depth, and pressure elevation can all be fixed on a pixel- by- pixel basis and a radiative transfer equation solved of the form.         Sr r r E L g g a s 1 cos 21   

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 66 Atmospheric Inversion (cont’d) where E s is exoatmospheric irradiance,  is solar declination angle, r a is the effective reflectance of the atmosphere, r g is the reflectance of the ground  1 and  2 are sun-target and target-sensor transmissions, S is the single spherical scattering albedo of atmosphere above the target (r g S accounts for multiple scattering adjacency effects).

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 67 Atmospheric Inversion (cont’d) Solving for r g yields S rEL E r aO O g    )/cos( 1 21  

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 68 Non-Linear Least-Squared Spectral Fit (NLLSSF) Technique  g : Lambertian ground reflectance Minimize the difference between the sensor radiance and the MODRAN-derived sensor radiance by changing parameters in the governing radiative transfer equation:           )( ])cos([ g g 2d21OgenvUsensor S1 LELLLLSE   

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 69 NLLSSF Flex Parameters 0.760µm Oxygen Band , ,  surface elevation 0.94µm H 2 O Band water , ,  vapor µm Aerosol Band , ,  visibility

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 70 In the.760µm oxygen band, the target reflectance is assumed linear with In the case of the aerosol and water vapor bands the equation includes a non-linearity for liquid water: NLLSSF Model of Reflectance  =  +  +  (H 2 O l )  =  + 

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 71 Using all Solved Parameters, Invert Governing Radiometric Equation and Calculate Ground Reflectance. Input Constant Parameters (i.e geometry, particle density,etc) General Flow Chart of Algorithm Solve for Total Column Water Vapor Using the.94µm band. Input Image Pixel: Solve for Surface Pressure Depth in.76µm O 2 band. Solve for Atmospheric Visibility Given an Aerosol Type Using.4-7µm bands

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 72 Surface Pressure Elevation

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 73 NLLSSF Curve Fit

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 74 Water Vapor Estimation (cont’d) – Pressure depth 760 feature spectral model prediction and LUT generation model match – amoeba algorithm

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 75 Water Vapor Estimation (cont’d) – aerosol number density/visibility spectral model prediction and LUT generation model match – column water vapor spectral model prediction and LUT generation model match

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 76 Water Vapor Estimation (cont’d) – products reflection spectra water vapor map pressure depth map vegetation moisture map

RIM to generate spectral upwelled radiance estimate Per image or per region model match to spectral estimate of upwelled radiance from RIM Per pixel model over visible region NLLSSF Per pixel atmospheric coefficients for computing inversion equations or APDA per pixel iterative ratio match or Pressure depth (elevation) aerosol number density (visibility) water vapor wavelength Radiance Measured Modeled Residuals local met station visibility radio- sonde or elevation and pressure Per pixel model match on 760nm oxygen feature 6 Per pixel model match on 940nm water feature NLLSSF Radiative Transfer Model MODTRAN

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 78 Estimated image-wide reflectance error for ground targets of 18% reflectance or less.

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 79 Estimated image-wide reflectance error for ground targets of 18% reflectance or less.