Download - Course outline & Intro
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Course outline & Intro
at721
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On the website:“Theoretical Topics In Radiative Transfer”
In Reality:“Construction of forward models of atmospheric remote sensing instruments, and their application to inverse techniques”
Bigger Picture Questions• Forward Modeling: How can we simulate different instruments,
in order to understand their sensitivity to different atmospheric (or surface) variables we care about?
• Inverse Modeling: How can we estimate atmospheric or surface variables from remote sensing observations? (i.e. radiances)
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Example: passive microwave ocean retrievals
• State: (ask students)– Surface Wind– water vapor path– Cloud liquid water path– Precip
• Observations:– Passive microwave at different frequencies /
polarizations
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• MODEL:– State Synthetic Observations
Best Match leads to our “best-guess answer”What are the known sources of error? (Ask Students)• Instrument noise• Errors in non-retrieved parameters
– (e.g., temperature profile, cloud fraction)• Forward model errors
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Before forward model errors, what goes into a typical forward model?
• Ie, how go from state to synthetic observations? (Ask Students)
Three Main Pieces:– Physical Optical properties– Radiative transfer (Radiances or TBs typically)– Instrument model (spectral response, spatial
response, polarization response)
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Sources of Forward model error?
• Physical assumptions: (Ask students)– “Ice is spherical” (mie theory applies)– No ice is present– No water-leaving radiances– Structure of cloud profile– Cloud is plane parallel– Etc.
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Errors in optical properties calculations
– Calculation of scattering properties of non-spherical aerosols
– Gas absorption spectroscopy– Water vapor continuum absorption– Surface reflectance parameterization (lambertian,
cox-munk, polarization?)– Imperfect / approximate SS calculations
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RT errorsAssumption-based
- Plane Parallel vs. 3D/spherical shell atmosphere
- Oriented vs. non-oriented particlesCalculation-based• Zenith/azimuthal resolution (“streams”)• Neglect of polarization (very common)• Truncation of phase function
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Assumptions vs. calculations
• In most cases, calculations can be made nearly perfect given sufficient computing power (though usually not practical)
• Physical / optical / RT assumptions usually dominate errors (“ice is spherical”) rather than 2 vs. 16 streams, e.g.
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Primary Focus of this class• How to construct forward models for a range of remote
sensing problems?
• Forward models can help with many things:– Sensitivity studies– Instrument / mission design– Training look-up based retrieval algorithms– Virtually all retrieval schemes– Testing retrieval schemes (usually with more accurate forward
model)– “Direct Radiance” Data Assimilation
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Secondary focus • How might different types of forward model errors affect
retrieval errors? This generally requires a full treatment of inverse theory.
• How can we use forward models to assess the sensitivity of different observations to different physical variables? (dy/dx)
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Identify primary forward model components
– Thermal infrared temperature retrievals– Vis/NIR Aerosol retrievals over land– Cloud Optical depth / Re retrieval (a la MODIS)– Sea ice retrievals
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Thermal IR Temperature RetrievalsForward model components
• Temperature-dependent abs. coefficient calculator for target gas
• Abs coeff for other gases• Surface Emissivity model (perhaps very simple, like
0.98)• RT model to simulate TBs at TOA at an arbitrary zenith
angle• Instrument Model! How does the instrument respond
spectrally? Is monochromatic good enough? Integrate across a small piece of spectrum?
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Solar Model:• Continuum: Fit to SolSpec• Disk-Integrated Linelist (G. Toon)• Sun-Earth Doppler shift included
Instrument Model:• Spectral Dispersion• Tabulated ILS • Earth-Instrument Doppler shift included• Explicit Treatment of Polarization Angle
Atmospheric/Surface Properties• Hi-resolution points at 0.01 cm-1 spacing• Rayleigh Scattering (fully polarized)• Spectroscopy: New Line Parameters + Line Mixing + Non-Voigt Line Shapes• Aerosol/Cloud properties: single scattering properties at band endpoints• Lambertian land surface• Fully polarized Cox-Munk ocean surface model
Atmospheric Radiative Transfer• Scalar multiple-scattering code• Exact first order of scattering • 2OS polarization correction• “Low-Streams Interpolator” acceleration method
Jacobians:• Analytic derivatives calculated for all SV elements.
The OCO-2 retrieval: Forward Model Components
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Eg: MODIS
• MODIS cloud retrievals– Temperature profiles (assumed?)– Solar model– Physical cloud model
• Vertically homogeneous or not?• Particle size distribution• Calculation of Index of Refraction• Cloud Phase
– Surface albedo (from previous clear-sky obs)
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Class Topics1. Introduction (1 class)2. Physical to Optical Properties (3 weeks)
• Geometry / scattering angle• Phase Function expansion• Single scattering / Mie theory• Non-spherical particles• Combination of optical properties• Surfaces (Cox-Munk, Lambertian)
3. Radiative Transfer (6 weeks)• Stokes Parameters, Polarization• The general RT equation & component terms• Nonscattering (emission-only) RT• Scattering Techniques
• Single-scattering approximation• Multiple scattering techniques
• Polarized RT• Fast techniques for non-monochromatic channels
4. Instrument Models (1 week)5. Inverse theory (3 weeks)
• Problem set-up• Sensitivity studies; the Jacobian• Baye’s theorem• Cost Functions & Covariance matrices• Solution for Gaussian statistics & linear problem• Solution diagnostics• Nonlinear solution techniques• Information theory / channel selection
6. Class Project Presentations (1 week)
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Optical Properties?1: Index of Refraction
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Optical Properties: Gas Absorption
Desired Quantity:Absorption Cross-
section per molecule (m^2)Function of
temperature, pressure, h2o concentration.
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Optical properties: Particle “single scattering properties”
• Extinction Efficiency Qe or Cross section σe
• Single Scattering Albedo ϖ0
• Phase Matrix (a 4x4 Quantity) P(Θ)– Intensity phase function P(Θ) is the (1,1) component– Asymmetry parameter g is sometimes used as a simple substitute
Derived Quantities:– Extinction Cross Section σe = Qe π r2
– (extinction) Optical Depth: τ = σe N(z) Δz– Scattering Cross Section : σs = σe ϖ0
– Backscattering Cross Section: Cb = σe ϖ0 P(Θ=180o)
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Single-scattering regimes
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Optical Properties: Surface reflectance
• Absorptivity (may be internally transmitted)
• Emissivity (=Absorptivity)
• Reflectivity = Albedo = 1 – Emissivity
• Bidirectional Reflectance Distribution Function (BRDF) How light incident on surface can be
reflected differently into ALL outgoing angles!
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Rough surfaces: Specular vs. Lambertianincident radiation can be reflected into any direction, but amount depends on
surface
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Radiative Transfer
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(Scalar) Radiative Transfer
extinction Scattering Source Emission Source
Very hard to Solve generally, and this doesn’t even include polarization!Special Cases:• Plane Parallel: can ignore 3D nature of the problem. This is a huge
assumption but often can be justified.• Scattering not important : Equation becomes (almost) trivial and is
simple to code• Single-scattering only : Equation becomes relatively simple (especially in
1D)• Strong multiple scattering: Directional dependence is weak, can invoke
certain approximations.
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RT Topics
• Emission-only• Single-scattering• Quadrature Schemes
– “Discrete Ordinates” (DISORT)– Adding-Doubling– Successive orders of Scattering– Similarity Transformations (“Delta Scaling”)
• Monte Carlo Techniques• Polarized RT
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Instrument Modeling Topics
• Spectral Response Function (how does it accept light spectrally). Ie “wavelength”
• Spatial Response Function (ie footprint size)• Polarization response
– Intensity only?– Single or multiple polarizations?
• Noise model– Often needed for inverse models
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AVIRIS spectral movie from 0.4 to 2.4 microns Fire scene
Smoke - small part.
CloudHot Area
Smoke -large part.
Fire
Shadow
GrassLake
Soil
The different spectral regions provide different signatures of the Earth below
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10 um ‘window’
6.3 um watervapor
0.6 um visible
FUV 0.1um
Penetration
10 um ‘window’
6.3 um watervapor
0.6 um visible
FUV 0.1um
Emission by clouds, surface
Emission by high clouds, upper trop water vapor
Scattering by clouds, aerosol, surface
Scattering by molecular atmosphere
We are going to create a model in this class that will allow you model the flow of radiation through the atmosphere from the UV to the microwave
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Non-uniqueness and Instability Estimation
Cost Function: = M [y-f(x)]
measurement Prediction of measurement
‘metric’ of length (e.g.least squares)
Unconstrained Constrained
x2
x1
Solution space non-unique
x2
x1
= M [y-f(x)] + (x)
M M
C
C(x)= initial or a priori constraint
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Information content background
Information is an augmentation of existing knowledge thus it is a relative concept
P(xa) Sa
P(xy) Sx
we propose that the measurement has added information if the ‘volume’ of the distribution is reduced - so Sx/Sa characterizes infoirmation
We start with some‘knowledge base’
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Shannon’s measure of informationEntropy is a measure of the # of distinct states of a system, and thus a measure of information about that system. If the system is defined by the pdf P(x), then
In our context, information is the change (reduction) in entropy of the ‘system’ after a measurement is made
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