PhD Presentation 1

Slide1 : Heat Transfer and Thermal Power Laboratory Generalized Radiative Transfer Model Including Polarization for Microwave Remote sensing M. Deiveegan Research Scholar Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India Advisors Prof. S. P. Venkateshan Dr. C. Balaji


Slide2 : 2 Organization of Presentation Introduction Forward Model including Effect of Polarization Generation of Atmospheric Profiles Calculation of Interaction Parameters Radiative Transfer Model Validations Parametric studies for Megha Tropiques Forward model for Tropical Cyclones Conclusions


Slide3 : 3 Introduction


Electromagnetic Radiation : 4 Electromagnetic Radiation Microwave Radiation Frequency ~ 0.3 to 300 GHz Wavelength ~1m to 1mm Electric & Magnetic Fields that Simultaneously Oscillate in Planes Mutually Perpendicular to each other and to the Direction of Propagation Through Space. Introduction Illustration:- Remote sensing -Tutorial Participating medium Absorption Scattering Emission Propagation of Radiant energy Basics Applications Remote sensing of Atmosphere Furnace applications Biomedical applications & etc.


Remote Sensing - Introduction : 5 Remote sensing:- Visual, Infrared, Microwave Introduction Passive Sensors Active Sensors Illustration: Remote sensing -Tutorial Sensors:- Active Sensors, Passive Sensors Passive: Measure Natural Radiation Emitted by the Earth and Radiation from other sources Reflected from Earth. Active: Transmit their own Signal and Measure the Energy that is Reflected from the Earth. Why do we need microwave sensors from space? Remote Sensing - Introduction


Atmospheric Parametric Retrievals : 6 Y - Observation vector Z - Modeled vector X - Unknown Parameter Ns- No of freq. bands No- No of observations Objective Function Atmospheric Parametric Retrievals Accuracy of Parametric Retrieval depends on Accurate, Realistic Mathematical Representation of Atmosphere (Forward Model) Accuracy of Inverse Methodology Radiative Transfer Forward Model - Vital part of Parameter Retrieval Forward Model - Radiation Transfer through One-Dimensional Inhomogeneous Absorbing, Emitting & Scattering (Radiative Participating) medium Illustration:- Deiveegan et al., 2006 Introduction New x Ret x (R=0)


Slide7 : 7 Introduction


Slide8 : 8 Introduction – Atmospheric Radiation Atmosphere Modeled as.. Multilayer, Plane Parallel Participating Medium with Absorption, Emission & Scattering. Ocean Surface: Emission, Reflection Gases: (Water vapor, CO2) Emission, Absorption Cloud Liquid Water: Emission, Absorption Cloud Ice Water: Emission, Absorption, Scattering Liquid Hydrometeor: (Rain) Emission, Absorption, Scattering Ice Hydrometeor: Emission, Absorption, Scattering Source of Polarized Signal: Ocean Surface (Reflection) Hydrometers (Scattering) Radiation Interaction with Atmosphere Introduction Illustration: Deiveegan et al., 2006


Introduction – Polarization : 9 Introduction – Polarization Advantages of Polarimetric Measurements: [Mishchenko and Travis, 1997] To Determine Size and Shape of Scattering Particles Experimental Merit:– Highly Accurate Measurements Unpolarized Radiation- Orientation of Electrical Vector Changes Randomly. Polarized Radiation- Vibrations Occur in Single Plane. Polarization - Transforming Unpolarized Radiation into Polarized Radiation. Polarization occurs because of Transmission, Reflection, Refraction & Scattering. Atmosphere- Source of Polarization – Sea surface, Hydrometeors (Rain & Ice) Sensitive to Particle Shape, Size, Distribution Contains information about particles in Atmosphere Introduction Polarization Mathematically Described by 4 Stokes Parameters - I, Q, U, V


Slide10 : 10 Forward Modeling Polarized Microwave Model


Slide11 : 11 Polarization -Direct Problem Steps involved: Mathematical Formulation Algorithm Development Computer Coding (using Compaq Visual Fortran) Validation with other Models & Measurements Parametric Study Accuracy of Forward Model depends on… Realistic Specification of Hydrometeor Sizes, Shapes & Phases encountered in rain clouds. Accurate Generation of Local Optical Properties from vertical hydrometeor profiles. Accuracy and Generality of Radiative Transfer Model. Objectives: To Develop Complete Polarized Vector Microwave Radiative Transfer Model. Forward Model Including Generation of Profiles and Interaction Parameters. To Treat Spherical and Non-Spherical Hydrometeor shape approximations.


Slide12 : 12 Polarization -Direct Problem Atmospheric Parameters Precipitation water (Rain) & Precipitation Ice Cloud Liquid water & Cloud Ice water Atmospheric water vapor & Oxygen Humidity Profile Temperature & Pressure Profile Ocean Surface Parameters Ocean Salinity Sea surface temperature Wind speed in mm/hr in g/m3 in %RH in K & bar in ppt in K in m/s


Slide13 : 13 Generation of the Atmospheric Environment Generation of the Land (or) Open Ocean Surface Environment Generation of the Atmosphere Interaction Parameters Generation of the surface Interaction Parameters Generation of Physical Environment Solution of Vector Radiative Transfer Equation Doubling & Adding Method Generation of Interaction Parameters for Surface & Atmosphere Polarized Microwave Model I II III Polarization -Direct Problem


Slide14 : 14 No. of Layers, Layer Thicknesses Surface level Temperature, Pressure, Humidity, Lapse Rate Artificial Vertical Profiles of Temperature, Pressure, Humidity User defined Hydrometeor Profile Position: Top & Bottom Height Phase: Liquid, Ice Density: in g/m3 (or) mm/hr Interpolation Interface & Layer averaged values of Temperature, Pressure, Humidity, Hydrometeor Measured Vertical Profiles of Temperature, Pressure, Humidity Cloud Analysis Infer Hydrometeor Profile From Measured Temperature, Pressure, Humidity Profile Generation of the Atmospheric Environment Data Two ways to Generate Atmosphere Data Use of External Data Files Definition of an Artificial Atmospheric Profile from Sea Surface Conditions I. Generation of the Environmental Data A B Polarization -Direct Problem


Slide15 : 15 Generation of the Oceanic Environment Data 2-Contributions: Emission from Ocean surface & Reflection of Atmospheric Radiation Reflection mainly determined by Roughness & Foam coverage (Depends on Wind) Ocean Emissivities depends on Dielectric constant of sea water (Depends on Salinity) Sea Surface Temperature (SST) in K, Salinity (SSS) in ppt, Wind Speed in m/s, Artificial Data SST, Salinity, Wind speed Measured SST, Salinity, Wind speed Two ways to Generate Oceanic Surface Data Use of External Data Files Definition of an Artificial Data Generation - Environmental Data continued.. A B Polarization -Direct Problem


Slide16 : 16 Generation of Atmospheric Interaction Parameters Interaction Processes – Absorption, Emission, Scattering Interaction Parameters – Extinction Coefficient, Single Scattering Albedo, Legendre Expansion Coefficients, No. of Legendre terms Required to Calculate Phase Matrix All Interaction Parameters Depend on Frequency, Polarization and Viewing Angle Scattering Calculation – Lorenz Mie Theory & T-Matrix Method Phase Functions – Mie (Legendre Series Approximations)/ Raleigh Drop Size Distribution – Marshall-Palmer, Modified Gamma distributions Type of Water Phase – Liquid & Ice II. Generation of Interaction Parameters Interaction with Gases Liebe (1992) Gases Absorption model Lorenz Mie Scattering T-Matrix Algorithm (Non spherical Particle) Interaction with Hydrometeor Single Scattering Calculation Extinction Coefficient, Single Scattering Albedo, Legendre Expansion Coefficients, No. of Legendre terms Size Distribution, Effective Radius, Radius Range (rmin, rmax) Rain Rate, CLW, T, P From Profile Generation Polarization -Direct Problem


Slide17 : 17 Generation of Ocean surface Interaction Parameters Interaction Processes– Reflection, Emission Interaction Parameters– Bidirectional Reflectivity for each Polarization, Frequency Generation – Interaction parameters continued.. Diffuse Reflection (Angular Independent) Modified Specular Reflection Bidirectional Reflectivity for each Polarization & Frequency Sea surface Temperature Salinity, Wind Speed From Profile Generation Effect of surface roughness Wisler and Hollinger (1977) Parameterization Foam Coverage according to Monahan & O’ Muirchantaigh (1986) Polarization -Direct Problem


Slide18 : 18 Solution of Radiative Transfer Equation Bidirectional Reflectivity for each Polarization & Frequency Extinction Coefficient Matrix, Single Scattering Albedo Matrix, Legendre Expansion Coefficients, No. of Legendre terms Phase Matrix Doubling & Adding Algorithm Layer Information Height, Temperature Collimated Background Radiation Brightness Temperature for Each Frequency & Polarization Doubling & Adding Algorithm – Polarized Model (4-Stokes Parameters) Phase Matrix – 16 Element Matrix Both Solar & Thermal Sources of Radiation considered Randomly Oriented Particle with Any Shape having Plane of Symmetry III. Solution of Vector Radiative Transfer Equation Polarization -Direct Problem


Slide19 : 19 Polarization- Direct Problem Polarized Microwave Model – Over view


Vector Radiative Transfer Equation : 20 Monochromatic Plane parallel Polarized RTE for Randomly Oriented Particles Source of Diffuse Radiation- Thermal Emission + Solar Radiation Diffuse Radiance M- Scattering Matrix μ – Cosine of Zenith angle Φ– Azimuth Angle τ – Optical Depth – Single-scatter Albedo F0–Unpolarized Solar Flux Vector Radiative Transfer Equation The Plane Parallel Solution is Sufficient to Cover most Applications for Radiation Scattering in Planetary Atmospheres Polarization -Direct Problem Why Plane Parallel medium Approximation ? Difference between Polarized and Unpolarized Model


Slide21 : 21 Time averages of real-valued linear combinations of products of field vector components Stokes vectors Direction of propagation ‘ r ’ & polarization state of a plane EM wave Electric field at observation point Stokes Parameters I - Intensity & Q, U, V - polarization state of wave Stokes parameters related by Real numbers Can be measured Simultaneously Polarization -Direct Problem


Slide22 : 22 Doubling & Adding Method I+ -Downward radiance I- -Upward radiance Interaction Principle – Linear interaction of radiation with medium T – Transmission Matrix R – Reflection Matrix S – Source Vector Radiation Emerging from a Layer is Related to Radiation Incident upon the Layer together with Radiation Generated within Layer Three Parts to the Solution Method Conversion of Single Scattering Information to a suitable form Example: Legendre Series in Scattering Angle Angular variation expression Azimuth- Fourier series Zenith- Discretization using Gauss Quadrature Application of Interaction principle in the form of Doubling & adding with Boundary conditions Polarization -Direct Problem


Slide23 : 23 Transformation of Single Scattering Information Doubling & Adding Method continued… Phase Function-Natural Reference Plane (Between Incoming & Outgoing Direction ) Polarized Radiation- Meridian Plane Rotation of the Reference Frame- Has to be Performed Polarization Transformation from Phase Matrix P to Scattering Matrix M Polarization Rotation Matrix Θ – Scattering Angle i1, i2 - Rotation Angle Polarization -Direct Problem


Slide24 : 24 Doubling & Adding Method continued… As a consequence of the Orthogonality of the Legendre polynomials F11 of the phase matrix satisfies the normalization condition Elements of Phase Matrix Randomly-oriented particle with plane of symmetry Polarization -Direct Problem


Slide25 : 25 Fourier Expansion of the Stokes vector and Scattering matrix Fourier series expansion of the Stokes vector and Scattering matrix Useful to Reduce the Number of variables treated at one time Scattering Matrix M Polarization Rotation Explicitly in Azimuth space & then Fourier transform to get Scattering Matrix for each Fourier azimuth mode Doubling & Adding Method continued… Top Surface Boundary: T= 1.0, S = 0, R = 0 Bottom Surface: Specular Surface - Full reflection matrix - Fresnel equations Lambertian- Surface Albedo (Reflectivity) Boundary Conditions Polarization -Direct Problem


Adding Method : 26 Adding Method Doubling & Adding Method continued… Radiance Vector (NStokes ×Nμ) Initialization Initial Layer Optical Depth chosen 10-5 Adding Formula computes properties of common Layer (T) + Downward – Upward 1 Top Layer 2 Bottom Layer T Combined Layer Γ – Multiple Reflection Factor Doubling Method To Combine two Identical layers – To Quickly Build up Initial optical Depth Δτ ; After N steps – 2N Δτ Computes - Upwelling Radiance from Top & Downwelling Radiance from Bottom of Atmosphere Polarization -Direct Problem


Slide27 : 27 Begin with thin layer to assume single scattering. Calculate Reflection and Transmission (R & T) of this layer for every stream. Use adding equations to add layer to itself (Doubling). Outcome is R & T of layer twice as thick. Repeat this until desired optical thickness is obtained for homogeneous layer k. Repeat step 1-4 for layer k+1. Add layers k and k+1 (adding). Repeat step 5-6 for all layers. Algorithm – Adding & Doubling Doubling & Adding Method continued… Polarization -Direct Problem


Slide28 : 28 Including - Generation of Physical Environment, Interaction parameters Two ways to Generate Physical Environment Use of External Data Files Definition of an Artificial Data Capabilities of Present Model Polarized Single Scattering Models - Lorenz Mie Theory, T-Matrix Method Lorenz Mie Theory – Spherical Hydrometeor Approximation T-Matrix Method- Non-Spherical shapes- Oblate (Rain), Chebyshev (Ice) Drop Size Distribution - Marshall-Palmer, Modified Gamma distributions Polarized Sea surface Models - Fresnel, Lambertian Approximation Sea surface Models includes correction for Wind, Foam Both Solar & Thermal Sources of Radiation considered Randomly Oriented Particle with Any Shape having Plane of Symmetry Easy to Couple with any other RTE solution methods like FVM, DOM Accurate & Fast Vector Radiative Transfer Model Polarization -Direct Problem


Slide29 : 29 Limitations of Present Model Effect of Melting layer not considered Polarization -Direct Problem


Slide30 : 30 Validations


Slide31 : 31 Surface without an Atmosphere Calm sea water surface modeled as specular surface at 300 K Complex Refractive Index (3.724-2.212 i) Frequency = 85.5 GHz Validation 1– Specular surface Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation Maximum Error = 0.15 %


Slide32 : 32 Cold Atmosphere – Absorbs & Scatters radiant energy, No Emission Unpolarized collimated beam- net flux Ic=μc π W/m2 Azimuthal=0º , Zenith =78.4º Surface- Diffuse & Reflectance = 0.1, Temperature = 0 K Wavelength = 0.951 μm Validation 2 – Mie Scattering Test Case Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation


Slide33 : 33 Gamma Distribution of Spherical Particle Particle Effective Radius = 0.2 μm, Effective Variance 0.07 Index of Refraction n = 1.44 Atmosphere with Collimated Source of Radiation Properties U ≠ 0, V ≠ 0 Mie scattering test case- Continued.. n (r)– Size Distribution Function r – Particle Radius a, b – Parameters of Gamma Size Distribution Polarization -Direct Problem - Validation


Slide34 : 34 Results of Solar scattering validation case for Φ = 00 Mie scattering test case- Continued.. Stokes Parameter I Stokes Parameter Q Polarization -Direct Problem - Validation


Slide35 : 35 Results of Solar scattering validation case for Φ = 900 Mie scattering test case- Continued.. Stokes Parameter I Stokes Parameter Q Polarization -Direct Problem - Validation


Slide36 : 36 Mie scattering test case- Continued.. Results of Solar scattering validation case for Φ = 900 Stokes Parameter U Stokes Parameter V Polarization -Direct Problem - Validation


Slide37 : 37 Validation 3 – Two layer model with Specular surface Two layer Precipitating Atmosphere – Absorbs, Emits & Scatters Unpolarized, Diffuse, Cosmic black body radiation at 2.7 K Surface- Specularly Reflecting, Index of refraction=(3.724-2.212i) Surface Temperature = 300K Frequency = 85.5 GHz Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation


Slide38 : 38 Two layer validation case- Continued.. Marshall- Palmer Distribution Maximum Diameter 1.0 cm, Absorption by O2, Water Vapor, Cloud Liquid Water is Ignored Atmosphere with only Thermal Sources of Radiation Properties Two Layer Atmosphere U = V = 0 p (d)– Size Distribution Function d – Drop Diameter, (m) N0 - 8.0×106 (m- 4) Rr - Rain Rate (mm/hr ) Polarization -Direct Problem - Validation


Slide39 : 39 Two layer validation case- Continued.. Rayleigh-Jeans approximation Planck function, Output Brightness Temperature Brightness Temperature – Upwelling from Top , Downwelling from Bottom Polarization -Direct Problem - Validation


Slide40 : 40 Validation 4– Two layer model with diffuse surface Two layer Precipitating Atmosphere – Absorbs, Emits & Scatters Unpolarized, Diffuse, Cosmic black body radiation at 2.7 K Surface- Diffuse approximation, Reflectivity= 0.44 Surface Temperature = 300.0 K Frequency = 85.5 GHz Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation


Slide41 : 41 Validation 5 – Comparison with Unpolarized Models Polarization -Direct Problem - Validation


Slide42 : 42 comparison with unpolarized models Continued.. Single scattering calculations: Kummerow (1993) Polarization -Direct Problem - Validation


Slide43 : 43 Present work Kummerow (1993) Single scattering calculation – comparison comparison with FVM Continued.. Polarization -Direct Problem - Validation


Slide44 : 44 Validation 6 – Angular variation of Brightness Temperature Single layer model- Absorption by gases considered, No precipitations Surface- Specular sea surface model Surface Temperature = 300.0 K Salinity = 36 ppt (parts per thousand) Wind speed = 0 m/s Frequency = 89.0 GHz From Ulaby et al. Present work Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation


Slide45 : 45 Validation 7 – Spectral variation of Brightness Temperature Single layer model- Absorption by gases considered, No precipitations Surface- Specular sea surface model Surface Temperature (SST) = 293.0 K Salinity (SSS) = 36 ppt Wind speed = 0 m/s Viewing configuration = 0º , 50º From Ulaby et al. Present work Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation


Slide46 : 46 Validation 8 – Variation of BT with Salinity Single layer model- Absorption by gases considered, No precipitations Surface- Specular sea surface Wind speed = 0 m/s Nadir-viewing configuration Frequency = 1.4 GHz From Ulaby et al. Present work Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation


Slide47 : 47 Validation 9 – Variation of BT with Sea surface Temperature Single layer model- Absorption by gases considered, No precipitations Surface- Specular sea surface Wind speed = 0 m/s Nadir-viewing configuration Frequency = 2.65 GHz From Ulaby et al. Present work Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation


Slide48 : 48 Validation 10 – Comparison with Airborne measurements Measurements by Airborne radiometers 155 m above Bearing sea Single layer 155 m- Absorption by gases considered, No precipitations Surface- Specular sea surface model Sea Salinity = 33 ppt (Assumed) , Sea surface Temperature = 288.0 K (Assumed) Frequency = 37.0 GHz Viewing angle = 380 Webster et al. Polarization -Direct Problem - Validation


Slide49 : 49 Validation 11 – Comparison with Polarimetric K-band Radiometer Measurements by Fully Polarimetric K-band Radiometer (KPR) Fabricated at University of Massachusetts Rough Duct Evaporation campaign during August & September 2001 Sea Salinity = 36 ppt, Sea Surface Temperature = 299.0 K , Wind = 8 m/s Frequency = 18.7 GHz From Juan Pons et al. Max. Error < 3.5% Polarization -Direct Problem - Validation


Slide50 : 50 Validation 12 – Validation with Ground Truth Measurements Sea Salinity = 35 ppt Sea Surface Temperature = 300.0 K Frequencies = 6.6, 10.7, 37.0 GHz Viewing angle = 48.8º 6.6 GHz Error < 4 % 10.7 GHz 37.0 GHz Error < 5 % Error < 12 % Polarization -Direct Problem - Validation


Slide51 : 51 Validation 13 - Validation with GCE Profiles GCE Profiles : Calculated vertical profiles of Rain, Cloud Liquid water, Cloud Ice, Precipitation Ice from Scattered Tropical Convection Experiment Cloud Resolving Model Profiles by Wei-Kuo Tao's Research Group Location: TOGA COARE array (Latitude: -15 to 15; Longitude: 140 to 180) Date: 23 December 1992 Source: Kummerow Research Group TOGA :- Tropical Ocean-Global Atmosphere COARE:- Coupled Ocean-Atmosphere Response Experiment Polarization -Direct Problem - Validation TOGA COARE GCE: Goddard Cloud Ensemble


Slide52 : 52 Validation for Non Raining Atmosphere Wind speed = 0.5 m/s ; SST= 302.4 K ; SSS = 35 ppt No precipitation, only Cloud Liquid Water, Cloud Ice Water, Snow TRMM Data 10.65 Channel is sensitive to Wind speed Polarization -Direct Problem - Validation


Slide53 : 53 Validation for Raining Atmosphere Polarization -Direct Problem - Validation Input Profiles


Slide54 : 54 Wind speed = 18 m/s ; SST = 302.4 ; SSS = 35 ppt Polarization -Direct Problem - Validation


Slide55 : 55 Validation 14 - Validation with TRMM Data Input: Number of Layers: 14 Frequencies: 10.7, 19.4, 21.3, 37.0, 85.5 GHz, Polarization: Vertical, Horizontal (2 Stokes Parameters, only Thermal Source) Number of Quadrature Angles: 12 Profiles of Liquid Cloud, Ice Cloud & Hydrometeors (Liquid & Ice phase) - Taken from TRMM Data Temperature, Pressure and Humidity Profiles – from GCE Profiles Ocean Surface conditions Unknown, Surface Parameters are Assumed SST=302 K, Salinity = 35 ppt, Wind Speed = 18 m/s Output: Vertical, Horizontal Polarized Brightness Temperatures Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE Polarization -Direct Problem - Validation TRMM – Tropical Rain rate Measuring Mission TRMM


Slide56 : Input: TRMM Retrieved Atmospheric Profiles Polarization -Direct Problem - Validation


Slide57 : 57 Brightness Temperature Comparisons Polarization -Direct Problem - Validation


Slide58 : 58 Useful Parametric Studies for MADRAS microwave imager Megha Tropiques


Slide59 : 59 1. Angular variation of Brightness Temperature Single layer model- Absorption by gases considered, No precipitations Surface- Specular sea surface model Surface Temperature = 293.0 K Salinity = 36 ppt Wind speed = 0 m/s Present work Frequencies: 18.7, 23.8, 36.5, 89.0 , 157.0 GHz Polarization-Direct Problem - Parametric study


Slide60 : 60 2. Spectral variation of Brightness Temperature Single layer model- Absorption by gases considered, No precipitations Surface- Specular sea surface model Surface Temperature = 293.0 K Salinity = 36 ppt Wind speed = 0 m/s Present work Frequencies: 18.7, 23.8, 36.5, 89.0 , 157.0 GHz Viewing Angle = 56.0º Polarization-Direct Problem - Parametric study


Slide61 : 61 5 Layer model Absorption by Gases considered. Surface conditions fixed: SST = 297 K, Salinity = 35 ppt, Wind = 10 m/s Frequencies: 18.7, 23.8, 36.5, 89.0 , 157.0 GHz First Layer Rain rate R1 = 0.1 to 50 mm/hr 3. Effect of Rain Cloud Structure on Polarization Rain Structures considered Convective structure Stratiform structure Cirrus Anvil structure Polarization-Direct Problem - Parametric study


Slide62 : 62 Convective Rain structure Vertical distribution of cloud constituents of five layer Cloud model Reference: Determination of precipitation profile from airborne passive microwave radiometer measurement - Kummerow et al. Effect of Cloud Structure- continued.. Polarization-Direct Problem - Parametric study


Slide63 : 63 Convective Rain structure Effect of Cloud Structure- continued.. Polarization-Direct Problem - Parametric study Explain


Slide64 : 64 Stratiform Rain structure Vertical distribution of cloud constituents of five layer Cloud model Reference: Determination of precipitation profile from airborne passive microwave radiometer measurement - Kummerow et al. Effect of Cloud Structure- continued.. Polarization-Direct Problem - Parametric study


Slide65 : 65 Stratiform Rain structure Effect of Cloud Structure- continued.. Polarization-Direct Problem - Parametric study


Slide66 : 66 Cirrus Anvil Rain structure Vertical distribution of cloud constituents of five layer Cloud model Reference: Determination of precipitation profile from airborne passive microwave radiometer measurement - Kummerow et al. Effect of Cloud Structure- continued.. Polarization-Direct Problem - Parametric study


Slide67 : 67 Cirrus Anvil Rain structure Effect of Cloud Structure- continued.. Polarization-Direct Problem - Parametric study


Slide68 : 68 Forward model for Tropical Cyclone (FANOOS, December 2005)


Slide69 : 69 Tropical Cyclone FANOOS - Data Atmosphere – Polarization-case study JAXA/EORC Tropical Cyclone Database FANOOS - continued.. Rainfall Rate & Cloud Image


Slide70 : 70 Forward Model – Inputs Number of Layers: 14 Frequencies: 10.7, 19.4, 21.3, 37.0, 85.5 GHz, Polarization: Vertical, Horizontal (2 Stokes Parameters, only Thermal Source) Number of Quadrature Angles: 12 Profiles of Liquid Cloud, Ice Cloud & Hydrometeors (Liquid & Ice phase) - Taken from TRMM Data Temperature, Pressure and Humidity Profiles – from GCE Profiles Ocean Surface conditions Unknown, Surface Parameters are Assumed SST=300 K, Salinity = 35 ppt, Wind Speed = 18 m/s Total No. of Data Profiles over ocean surface: 28912 No. of profiles with rain rate >0.015 mm/hr : 6815 Output: Vertical, Horizontal Polarized Brightness Temperatures Steps involved Profile Generation Generation of Interaction Parameters Solution of V-RTE


Slide71 : 71 Simulated Brightness Temperature Measured Brightness Temperature (TRMM) 85 GHz, Vertical Polarization Vertical Polarized, 85.5 GHz


Slide72 : 72 Horizontal Polarized, 85.5 GHz Simulated Brightness Temperature Measured Brightness Temperature (TRMM) 85 GHz, Horizontal Polarization


Slide73 : 73 Parity Plot Vertical Polarized, 85.5 GHz Horizontal Polarized, 85.5 GHz Correlation coefficient = 0.839 Correlation coefficient = 0.758


Slide74 : 74 Summary of Results


Slide75 : 75 Comparison with Eddington Model To check the consistency between models, the simulations have also been performed using Eddington model [Kummerow, 1996] TB simulated by both models are agreeing well and are within 5K Low rain rates: TB are High Two models are Indistinguishable Polarization contribution by Spherical Hydrometeors can contribute up to 5 K


Slide76 : 76 Conclusions


Slide77 : 77 Generation of Physical Environment, Interaction parameters Polarized Single Scattering Models - Lorenz Mie Theory, T-Matrix Method Polarized Sea surface Models - Fresnel, Lambertian Approximation Forward Problem presented - Polarized Doubling & Adding Method Brightness Temperature for Vertical, Horizontal Polarization – computed Validation with results available in Literature Accurate & Fast Polarized Radiative Transfer Model 15 Layer- 6 Frequencies (V, H) –12 Quadrature Angles- for 1 Profile: Time Taken 1.2 s Conclusions – Forward Modeling Polarization- Direct Problem Computer Intel Pentium-4, 3.6 GHz RAM - 4.0 GB Software Used Compaq Visual FORTRAN 6.5


Slide78 : 78 Where do we go from here?


Where do we go from here? : 79 Where do we go from here? Using this polarized model (Doubling & Adding) Include Land surface Model To Generate Data base - To perform Parameter Retrieval using Bayesian & ANN.


Slide80 : 80 MICROTROPIQUES code Software used – Compaq Visual Fortran Approximately 6500 lines


Slide81 : 81 Thank you Illustration: NASA webpage


Slide82 : 82 Backup slides


Slide83 : 83 Electromagnetic Radiation - Basics Frequency () - Number of waves (cycles) per second that pass a given point in space Wavelength () - Distance between two consecutive peaks or troughs in a wave [  = C] – Electromagnetic wave travel at the speed of light Wave nature of Radiation: Particulate nature of Radiation : Photons -Radiation can be also described in terms of particles of energy Energy of Photon E = h  , h is Plank’s constant (h = 6.6256x10-34 J s)


Slide84 : 84 Blackbody - Body whose surface absorbs all radiation incident upon it Thermodynamical equilibrium Local Thermodynamical Equilibrium (LTE) Planck function - Intensity emitted by a blackbody having a given temperature Asymptotic behavior of Planck function: Basic Quantities Rayleigh –Jeans Approximations ( λ → ∞ ) Wien's approximation ( λ → 0 ) Intensity (Radiance) -Radiant energy in a given direction per unit time per unit wavelength (or frequency) range per unit solid angle per unit area perpendicular to the given direction


Slide85 : 85 Stefan-Boltzmann law Wien’s displacement law: Kirchhoff’s law: under thermodynamic equilibrium Brightness temperature: Temperature of a blackbody that emits same intensity as measured Specular Surface Diffuse Surface Basic Quantities Reference: First course in Heat Transfer – S. P. Venkateshan


Slide86 : 86 Main Presentation Extinction = absorption + scattering Single scattering albedo = scattering / (absorption + scattering) Radiative Transfer Equation [RTE] Phase Functions Isotropic scattering: Anisotropic scattering: Radiatively Participating Medium Solution Methods Eddington Method Discrete Ordinate Methods – Fiveland et al. Finite Volume Method – Karthikeyan et al.(2003), Swaminathan et al.(2004) Differential Discrete Ordinate Method – Kumar et al., Deiveegan et al.(2006)


Slide87 : 87 Interaction with Single Particle Size parameter Single scattering properties (Extinction, Scattering albedo & Phase matrix) for population of hydrometeors - each layer of the medium Rayleigh Scattering Scattering by Spheres Mie Theory [Exact] Scattering by Non spherical Particles T-Matrix Algorithms [Numerical] Extinction, Albedo for single particle Scattering Phase matrix


Slide88 : 88 Drop size Distribution 88 Single scattering properties depends on Shape Refractive Index Frequency Drop size distribution- Relate individual particles to physical properties of volume Droplets found in cloud – distributed over range of sizes Total number of droplets (per unit volume) Water content of the Cloud (Mass density, g/m3) Cloud – Modified Gamma distribution Precipitation - Marshall Palmer size distribution a, α, , rc = Distribution parameters Rr = Rain rate (mm/hr) α, , rc – values depends types of clouds


Slide89 : 89 Main Presentation Interaction with Group of Hydrometeor Particles For particles with a size-distribution function n (r) Absorption coefficients Scattering coefficients


Slide90 : 90 Main Presentation Interaction with Ocean Surface Ocean surface characterized by Sea Surface Temperature, Salinity & Wind Speed Assumed as a Specular surface - Polarized & Angle Dependent Bidirectional Reflection Matrix Vertical and Horizontal Reflection coefficients [Frenel Reflection] Emission Vector m - Complex index of refraction  - Outgoing Angle


Error due to plane parallel approximation has two very different natures depending on pixel size : 91 Why Plane Parallel medium Approximation ? (H / R) << 1 ; H  Scale Height (~10 km), R Distance from centre of Planet (6380 km) Concentration of Scatterers and Absorbers does not vary in Horizontal Boundary Conditions do not depend on the Horizontal Polarization- Direct Problem Error due to plane parallel approximation has two very different natures depending on pixel size Megha Tropiques & TRMM Sensor Resolutions Main Presentation


Slide92 : 92 Comparison – Polarized, unpolarized models Main Presentation


Slide93 : 93 Transmittance of Atmosphere Characteristics of Atmospheric Gases Atmospheric Gases are Highly selective in their ability to Absorb Radiation. Each Radiatively Active Atmospheric Gas has a Specific Absorption Spectrum. Introduction Main Presentation


Tropical Rainfall Measuring Mission (TRMM) : 94 Tropical Rainfall Measuring Mission (TRMM) Joint mission between NASA and Japan Aerospace Exploration Agency (JAXA). TRMM : 1997 - Present To measure the Rainfall TRMM Instruments TRMM Microwave Imager (TMI) Precipitation Radar (PR) Cloud and Earth Radiant Energy Sensor (CERES) Visible and Infrared Scanner (VIRS) Lightning Imaging Sensor (LIS) TRMM Continued… Illustration: NASA webpage TMI frequencies: 10.7, 19.4, 21.3, 37, 85.5 GHz Main Presentation


Megha Tropiques (MT) : 95 Megha Tropiques (MT) Joint mission between ISRO (India) and CNES (France) To measure the Rainfall TRMM Instruments MADRAS - Microwave Analysis and Detection of Rain and Atmospheric Structures SAPHIR - Sounding Instrument to measure Water Vapor ScaRaB - Scanning Radiative Budget Instrument Illustration: CNES -France MADRAS Main Presentation


Slide96 : 96 Radiative Transfer Models Including Polarization Literature Review


TOGA COARE Experiments : 97 Main Presentation TOGA COARE Experiments Illustration: NASA webpage


Slide98 : 98 Precipitation Characteristics Water in Clouds Emits Radiation, producing Cold areas that can be seen against a Radiatively Cold Background Ice in Clouds Scatters Radiation downward, producing Cold areas that can be seen against a Radiatively Warm Background Introduction Illustration: Deiveegan et al. Main Presentation


Slide99 : 99 Precipitation Characteristics Dominant absorption by water Very little absorption by ice Scattering most prevalent at higher frequencies Ice scattering dominates at higher frequencies Introduction


Slide100 : 100 Precipitation Characteristics TB increases rapidly over the ocean as Cloud Water Increases for Low Rain Rates. Mixture of snow, ice, and rain - Main cause of scattering - Results in Decrease in TB when Rain Rate increases (over land and ocean). Introduction


Slide101 : 101 Wind speed = 0 m/s ; SST = 302.4 ; SSS = 35 ppt Polarization -Direct Problem - Validation


Slide102 : 102 Global Precipitation Mission [GPM] Illustration: NASA webpage Objective of GPM is to develop a scientific understanding of the earth GPM will advance precipitation measurement capability from space through combined use of active and passive remote-sensing techniques. Main Presentation