Course outline & Intro

1. Course outline & Intro at721

2. 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)

3. 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

4. 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

5. 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)

6. 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.

7. 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

8. RT errors Assumption-based - Plane Parallel vs. 3D/spherical shell atmosphere - Oriented vs. non-oriented particles Calculation-based • Zenith/azimuthal resolution (“streams”) • Neglect of polarization (very common) • Truncation of phase function

9. 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.

10. 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

11. 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)

12. 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

13. 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?

14. The OCO-2 retrieval: Forward Model Components • 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 • 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 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.

15. 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)

16. Class Topics • Introduction (1 class) • 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) • 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 • Instrument Models (1 week) • 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 • Class Project Presentations (1 week)

17. Optical Properties?1: Index of Refraction

18. Optical Properties: Gas Absorption Desired Quantity: Absorption Cross-section per molecule (m^2) Function of temperature, pressure, h2o concentration.

19. 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 = σeN(z) Δz • Scattering Cross Section : σs = σeϖ0 • Backscattering Cross Section: Cb = σeϖ0 P(Θ=180o)

20. Single-scattering regimes

21. 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!

22. Rough surfaces: Specular vs. Lambertianincident radiation can be reflected into any direction, but amount depends on surface

23. Radiative Transfer

24. (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.

25. 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

26. 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

27. The different spectral regions provide different signatures of the Earth below Smoke - small part. Shadow Grass Lake Fire Hot Area Cloud Soil Smoke - large part. AVIRIS spectral movie from 0.4 to 2.4 microns Fire scene

28. FUV 0.1um 10 um ‘window’ Emission by high clouds, upper trop water vapor Scattering by clouds, aerosol, surface Emission by clouds, surface Scattering by molecular atmosphere 6.3 um water vapor 0.6 um visible Penetration 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 FUV 0.1um 10 um ‘window’ 6.3 um water vapor 0.6 um visible

29. Non-uniqueness and Instability Estimation ‘metric’ of length (e.g. least squares) Cost Function:  = M [y-f(x)] measurement Prediction of measurement UnconstrainedConstrained  = M [y-f(x)] + (x) M M x1 x1 C x2 x2 Solution space non-unique C(x)= initial or a priori constraint

30. Information content background Information is an augmentation of existing knowledge thus it is a relative concept We start with some ‘knowledge base’ P(xa) Sa we propose that the measurement has added information if the ‘volume’ of the distribution is reduced - so Sx/Sa characterizes infoirmation P(xy) Sx

31. Shannon’s measure of information Entropy 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