Formerly Lecture 12 now Lecture 10: Introduction to Remote Sensing and Atmospheric Correction* Collin Roesler 11 July 2007 *A 30 min summary of the highlights of Howard Gordon’s 9hr Short course Ocean Optics XVI 2002 Do not use any of the figures for any public presentation without Howard’s permission

1970’s Jerlov K d Classification TypeKd(440) Chl. I … III >2.00 … 91.0 >10.00 Variability attributed primarily to chlorophyll. Suggested that the inverse problem to estimate Chlorophyll from L u ( ) should be tractable inf

1970 Clarke, Ewing, Lorenzen Chl < aircraft-based radiometer (305 m) Sargasso to WHOI vertically polarized light 53 o (Brewster’s Angle) to avoid skylight Blue to green ratio Decreased with chl

Coastal Zone Color Scanner launched in Nov 1978 proposed mission was 1 year proof of concept degraded over time (mirrors) lasted until 1986

Coastal Zone Color Scanner 955 km 825 m pixels res.

Coastal Zone Color Scanner measured by sensor atmospheric radiance water-leaving radiance reflected radiance

The atmosphere contributes > 90% to the radiance detected by the satellite-based sensor The Problem measured by sensor atmospheric radiance water-leaving radiance reflected radiance 1% error in atmospheric correction or satellite calibration  10% error in water leaving radiance

The atmosphere contributes > 90% to the radiance detected by the satellite-based sensor The Problem measured by sensor atmospheric radiance water-leaving radiance reflected radiance Atmospheric Correction CZCS Gordon and Clark 1981 First order correction, clear water SeaWiFS Wang and Gordon 1994 Gordon 1997

What is being measured by the satellite sensor? Path radiance, L* –molecular scattering –aerosol scattering –molecular-aerosol multiple scattering white caps, L wc sun glint, L g water leaving radiance, L w

Remotely sensed radiance equation L t = L* r + L* a + L* ra + TL g + tL wc + tL w L* r, Rayleigh molecular scattering, L* a, Aerosol scattering L* ra, Rayleigh-Aerosol multiple scattering L g, sun glint L wc, white caps L w, water leaving radiance T, direct transmittance (~beam attenuation) t, diffuse transmittance

1. Atmospheric Effects (L*, T, t) Gaseous absorption (ozone, water vapor, oxygen) Scattering by air molecules (Rayleigh) Scattering and absorption by aerosols (haze, dust, pollution) Polarization (MODIS response varies w/ signal polarization) Rayleigh (80-85% of total signal) small molecules compared to nm wavelength, scattering efficiency decreases with wavelength as -4 reason for blue skies and red sunsets can be accurately approximated for a given atmospheric pressure and geometry (using a radiative transfer code) Aerosols (0-10% of total signal) particles comparable in size to the wavelength of light, scattering is a complex function of particle size whitens or yellows the sky significantly varies and cannot be easily approximated

1.Atmospheric Effects Direct Transmittance T  L sun (top of atmosphere) = e -   is the optical depth L sun (bottom of atm)  %T

1. Atmospheric Effects A. Absorption (T) Ozone O2O2 Water vapor

1.Atmospheric Effects B. scattering (T, L*) Molecular scattering Aerosol scattering  %T

1.Atmospheric Effects B. scattering (T, L*) i. Rayleigh Hansen and Travis 1974 volume scattering function  ~ b r, (1 + cos 2  ) where b r is the scattering coefficient (~ to air density) The Rayleigh optical depth is given by:  r = ∫ b r (h) dh where h is altitude and the spectral dependence is given by:  r ~ -4 Molecular scattering

1. Atmospheric Effects B. scattering (T, L*) ii. aerosol Use Mie theory to compute the volume scattering function

1. Atmospheric Effects B. scattering (T, L*) ii. aerosol Use Mie theory to compute the volume scattering functions Haze v Water, sea salts

1. Atmospheric Effects B. scattering (T, L*) ii. aerosol  a()a() ~ Phase functions  a()a() ~

1. Atmospheric Effects B. scattering (T, L*) ii. aerosol and the spectral dependence of the optical depth (nm)  (nm) 

1. Atmospheric Effects B. scattering (T, L*) ii. aerosol  a ( ) ~ -a Pacific vs Atlantic aerosol optical depth spectral dependence but generally  a < 0.1 Observations by Smirnov et al. 2002

2. Surface Effects (L g, L wc ) Sun Glint White Caps Corrections based on statistical models (wind & geometry)

3. Water leaving radiance term L a w (0,  ) = t(  ) L w (z,  ) = fcn(L u ) where t(  ) = diffuse transmittance Note that t(  ) is a function not only of the atmospheric composition (i.e. phase function) but also of the radiance distribution, and that t(  ) can be >1.

Up to this point we have L(0,  ) = L* r (0,  ) + L* a (0,  ) + t(  ) L w (z  ) where L r and L a are a function of –incident radiance distribution –respective phase functions –respective optical thicknesses radiance is non-dimensionalized to reflectance  =  L F o  o

Ex. from SeaWiFS (D. Clark) ~0.2 ~ % accuracy in  w requires <0.5% absolute error in  t

Thus far we can do a good job on the Rayleigh contribution, but the aerosols are much more difficult start by defining  (   ) =  a ( )  a (  ) which is independent of aerosol concentration and nearly independent of position over an image (pathlength)

Solving for  w  t( )  w ( ) =  t ( ) –  r ( ) –  a ( ) =  t ( ) –  r ( ) –  (  o )  a ( o ) =  t ( ) –  r ( ) –  (, o ) (  t ( o )-  r ( o ) – t( o )  w ( o ) ) and t( ) is a function of attenuation by  r ( ) x  a ( ) Assumptions 1. aerosol phase functions are strongly peaked 2. aerosols have high single scattering albedo 3. we can find a o for which  w ( o ) = 0, i.e. red s *

Solving for  w   w ( ) = 1 (  t ( ) –  r ( ) –  (, o ) (  t ( o )-  r ( o ) ) t*( ) so we only need to solve for  (   ) where o =670 nm So we have to recall that  w ( ) is directly proportional to the incident radiance distribution the IOPs of the water column  (,  ) =  t ( ) –  r ( ) – t*( )*  w ( )  t (  )-  r (  )

What are the clear water reflectance values?

Gordon and Clark’s (1981) Clear water radiance concept  (520,670) =  t (520) –  r (520) – t*(520)*   t (670)-  r (670) can solve for  (520,670) and  (550,670)  (550,670) =  t (550) –  r (550) – t*(550)*   t (670)-  r (670)

Then calculate  (440,670) by extrapolation  (  o ) = (  o ) n Gordon et al  (  o ) =  a ( )/  a ( o ) ~  a ( )/  a ( o ) ~ (  a1 / o -a2 ) ~ (  o ) n All other terms of  are weakly dependent upon Further, if the aerosol type remains constant over an image, even if the concentration changes,  will be constant over the image and only one n need be used

So the approach is: from pixel geometry, compute  t -  r for each wave band find clear water pixel (chl < 0.25  g/l) use clear water approximations for  w at 520, 550, 670 nm calculate  (520,670) and  (550,670) calculate  (440,670) by extrapolation hold  (  o ) constant for whole image

Example from CZCS

Which lead to the first ocean color pigment climatology

Problems with first order algorithm (CZCS) t*( )  w ( ) =  t ( )–  r ( )–  (,  ) (  t (  )-  r (  )–t*(670)  w (670) ) Check on Assumptions 1.  w (670) =0 and other assumed clear water values are not valid for even moderate chl~1.0 (no clear water pixel) 2.  r ( ) is dependent upon surface atm pressure, ozone 3.  does not really satisfy Angstrom’s Law 4. multiple scattering and polarization in the atmosphere are ignored 5. t* should be replaced by t and is dependent upon aerosol concentration, particularly absorbing aerosols

Problems with first order algorithm (CZCS) Check on Assumptions 1.  w (670) =0 and other assumed clear water values are not valid for even moderate chl~1.0 (use better in water model but NIR wavelengths would be better) 2.  r ( ) is dependent upon surface atm pressure, ozone (see corrections by Gregg et al. 2002) 3.  does not really satisfy Angstrom’s Law (see figures at beginning of lecture, used to define  (  o ) model) 4. multiple scattering and polarization in the atmosphere is ignored

Multiple scattering error in Rayleigh scattering term approaches –5% across a scan line –20% with increasing latitude –greatest for 440 nm, then 670 nm bands need to include the Rayleigh-aerosol multiple scattering term

Problems with first order algorithm (CZCS) Check on Assumptions 1.  w (670) =0 and other assumed clear water values are not valid for even moderate chl~1.0 (use better in water model but NIR wavelengths would be better) 2.  r ( ) is dependent upon surface atm pressure, ozone (see corrections by Gregg et al. 2002) 3.  does not really satisfy Angstrom’s Law (see figures at beginning of lecture, used to define  (  o ) model) 4. multiple scattering and polarization in the atmosphere are ignored (add multiple scattering, polarization terms) 5. t* should be replaced by t and is dependent upon aerosol concentration, particularly absorbing aerosols (still ignore assume aerosols are weakly absorbing)

SeaWiFS

Sensor improvements since CZCS SeaWiFS ~2-4 times more sensitive than CZCS MODIS ~2-4 times more sensitive than SeaWiFS Thus we require significantly improved atm correction to take advantage of added sensitivity e.g.  w (443) N < NE  – Noise equivalent reflectance

First order correction for SeaWiFS Still ignore absorbing aerosols if aerosol is non-abs even up to  a =0.2, it works well when aerosol absorbs, it fails even for low  a

First order correction for SeaWiFS Still ignore absorbing aerosols use multiple scattering for R/A develop look up table for a range of aerosol types  78 = L(765) ~ La+ra(765), L(865) La+ra(865) select aerosol model  AE  correction, Km

First order correction for SeaWiFS Still ignore absorbing aerosols use multiple scattering for Rayleigh use single scattering for aerosol use exponential model for  (   )  ( ,  )

First order correction for SeaWiFS Still ignore absorbing aerosols use multiple scattering for Rayleigh use single scattering for aerosol use exponential model for  (   ) use NIR bands 750 and 865 nm for  w =0 approximation

water P.J. Werdell, 2007

Other issues “augmented reflectance” of white caps contaminates NIR bands, error improved but still needs work with respect to spectral variations [  wc ] N (sr -1 ) Moore, Voss, Gordon 2001

Other issues Earth’s curvature (Ding and Gordon 1994) still not applied to imagery band 7 encompasses an O 2 abs band requires correction (Ding and Gordon 1995), corrected in MODIS  w =0 in NIR

Siegel et al. 2000, relax dark pixel approximation Use iterative approach chl o   w (NIR)  atm corr   w ( ) and chl 1  repeat

Siegel et al. 2000, relax dark pixel approximation

Additional problems in coastal zones high CDM concentrations yield low  w (blue), and thus requires very high accuracy (issue with negative radiances) high sediment loads result in amplified  w (NIR) thus impacting aerosol models (see Gordon et al site-specific approach for coccolithophore bloom; Ruddick et al. 2000) absorbing aerosol (e.g. spectral matching algorithm Gordon et al for dust storm events)

Summary from Howard’s  to  course can get chl or other products with accuracy approaching surface measurements most of the time have methods to deal with some episodic events like dust storms have a reasonable foundation for coastal water algorithms

So say we have the atmospheric correction nailed down and we retrieve water-leaving radiance, L w Variations in the radiance ratios for channels 1 through 3 are interpreted solely as variations in chlorophyll concentration

R 13 R 12 R 23 And the relationship of the radiance ratios to chl… in log-log space over a dynamic range of 0.1 to 100 mg/m 3

SeaWiFS chl algorithm OC4.4 res/oc4_v4_stats_plot_sm.gif

MODIS chl algorithm OC3 R = log10 (R443>R490)/R550 a = [2/830,-2.753,1.457,0.659,-1.403]

A note about SeaWiFS and MODIS SeaWiFs has a routine calibration cycle that MODIS lacks How to account for long term sensor drift –Absolute Calibration –Vicarious Calibration –Use SeaWiFS –Validation

Take Home Messages It is amazing that we can retrieve robust estimates of chlorophyll with better than 1 km resolution from over 800 km above the earth and through the atmosphere that contributes 97% of the observed signal Remote sensing of ocean color works because… –most of the Lw variability in the blue is related to phytoplankton biomass (chl) –we do a pretty good job with atmospheric correction One irony of ocean color remote sensing is that R  bb/a+bb  aphyt  chl then we use chl  IOPs (Hmm) We will talk later about reflectance inversions