Nonparametric Regression Splines for Nonparametric Regression Splines for Regional Atmospheric Correction Regional Atmospheric Correction Semih Kuter a Gerhard-Wilhelm Weber b Zuhal Akyürek c Ay � e Özmen b a Çankırı Karatekin University, Faculty of Forestry, Department of Forest Engineering, 18200, Çankırı, Turkey b Middle East Technical University, Institute of Applied Mathematics, 06800, Ankara, Turkey c Middle East Technical University, Faculty of Engineering, Department of Civil Engineering, 06800, Ankara, Turkey
Outline Outline Outline Outline � Introduction ◦ Atmospheric correction, Why? ◦ Atmospheric correction, How? ◦ MARS & CMARS � Study Area, Data Set & Methodology ◦ MARS & CMARS on MODIS Images � Results & Concluding Remarks 2
Atmospheric correction, Why? Atmospheric correction, Why? RS of Earth by space RS of Earth by space-based sensors RS of Earth by space RS of Earth by space-based sensors based sensors based sensors � Measurement of Earth’s surface reflectance from a space-based Remote Sensing space-based Remote Sensing Remote Sensing (RS) platform. Remote Sensing (RS) platform. � Perturbations are introduced by the passage of radiation through the Earth’s atmosphere. 3
Atmospheric correction, How? Atmospheric correction, How? Basic geometry of the problem Basic geometry of the problem Basic geometry of the problem Basic geometry of the problem Sun Sun Satellite • θ s : View zenith angle • θ v : Solar zenith angle • �φ : Relative azimuth • �φ : Relative azimuth Target pixel pixel 4
Atmospheric correction, Why? Atmospheric correction, Why? Factors affecting EM radiation in the atmosphere Factors affecting EM radiation in the atmosphere Factors affecting EM radiation in the atmosphere Factors affecting EM radiation in the atmosphere � Molecular absorption and scattering ◦ ◦ N 2 , O 2 , O 3 , CO 2 , water wapor (RH) etc. Emission Absorption Scattering Emission � Aerosols � Aerosols ◦ Found in the atmospheric boundary layer and transported by wind turbulence and atmospheric convection. � Larger particles ◦ Fog, cloud, rain and snow. � Ionosphere � Ionosphere ◦ Ionization by extreme ultraviolet and X -radiation from the Sun. 5
Atmospheric correction, Why? Atmospheric correction, Why? What is measured by the satellite? What is measured by the satellite? What is measured by the satellite? What is measured by the satellite? � RS satellite measures the top top-of of-atmospheric atmospheric (TOA) reflectance value of the target pixel. � TOA is not the real surface reflectance value of the target pixel, but a perturbed (or distorted) one by the atmosphere. � Dream Dream situation situation : What would be the reflectance value � measured at the satellite level, if there were no atmosphere between the satellite and the target pixel? � Not Not possible possible to to completely completely remove remove the the effect effect of of the the atmosphere. � However, it may be reduced at certain level by using � However, it may be reduced at certain level by using Radiative Radiative Transfer Transfer (RT) models. 6
Atmospheric correction, How? Atmospheric correction, How? Main approaches in atmospheric correction Main approaches in atmospheric correction Main approaches in atmospheric correction Main approaches in atmospheric correction � Absolute atmospheric correction by RT models ◦ ◦ The whole process of atmospheric attenuation is numerically modeled. • • Top Of Atmospheric Top Of Atmospheric (TOA) Reflectance Atmospherically Radiative Transfer (RT) • Temperature corrected reflectance Model • Pressure of the target pixel • • RH RH • Visibility • Angles etc. � Numerous RT models during the last three decades: ◦ ◦ 5S 5S – S imulation of a S atellite S ignal in the S olar S pectrum ◦ ◦ 6S – S econd S imulation of a S atellite S ignal in the S olar S pectrum 6S ◦ ◦ MODTRAN MODTRAN – MOD MOD erate Resolution Atmospheric TRAN TRAN smission ◦ ◦ ◦ ◦ FLAASH FLAASH – F ast L ine-of-sight A tmospheric A nalysis of S pectral H ypercubes 7
Atmospheric correction, How? Atmospheric correction, How? Basic RT equation Basic RT equation Basic RT equation Basic RT equation U H O ρ θ θ ∆ ϕ = ρ + ρ − ρ ( , , ) ( , , ) ( ) ( ) T O O CO T 2 TOA s v g 3 2 2 R R + A R g 2 2 ρ + s T T U ( ) + R A g H O − − ρ ρ 1 1 S S 2 + + s s R A R A � where ◦ ρ s : surface reflectance of the target, ◦ ρ ◦ ρ TOA : TOA reflectance at the satellite level, : TOA reflectance at the satellite level, ◦ θ s and θ v : view zenith angle ( VZA ) and solar zenith angle ( SZA ), ◦ � φ : relative azimuth between the Sun and the satellite direction, ◦ T g : total gaseous transmission, ◦ ρ R : molecular scattering reflectance, ◦ ρ R+A : reflectance of the molecules and aerosols, R+A ◦ T R+A : transmission of the molecules and aerosols, ◦ S R+A : spherical albedo. 8
Atmospheric correction, How? Atmospheric correction, How? Drawbacks of RT models Drawbacks of RT models Drawbacks of RT models Drawbacks of RT models � When working with long time series data acquired by LFOV LFOV ( L arge F ield O f V iew) sensors: LFOV LFOV ( L arge F ield O f V iew) sensors: ◦ Different observational geometry for each pixel, ◦ Atmospheric parameters do not remain constant (or unknown). Operationally Operationally Detailed Detailed RT Codes Detailed Detailed RT Codes Codes Codes too expensive and too expensive and too expensive and too expensive and time consuming time consuming � Processing of a single MSG MSG-SEVIRI SEVIRI image subset: ◦ ◦ Spinning Enhanced Visible and InfraRed Imager ◦ Temporal resolution = 15 min. ◦ 4.4 million pixels for each of the three visible and NIR ◦ 4.4 million pixels for each of the three visible and NIR channels = 20 min. for 6S Backlog develops! Backlog develops! 9
Atmospheric correction, How? Atmospheric correction, How? Alternative to RT codes: SMAC Alternative to RT codes: SMAC SMAC SMAC Alternative to RT codes: Alternative to RT codes: “Simplified Model for “Simplified Model for Atmospheric Correction” Atmospheric Correction” � In the early 90s by H. Rahman & G. Dedieu, � Several hundred times faster than detailed RT codes, � Based on the parametrization of RT equations: ρ ′ ′ ρ ( ) , s ρ θ θ ∆ ϕ = , , s s v ( ) ( ) ′ θ θ + ρ T T T S G s v s ( ( ) ) ( ( ) ) ′ = ′ = ρ ρ ρ ρ θ θ θ θ ∆ ∆ ϕ ϕ − − ρ ρ θ θ θ θ ∆ ∆ ϕ ϕ , , T , , s TOA s v G a s v � where ◦ ρ : surface reflectance ◦ ρ s : surface reflectance ◦ T G : total gaseous transmission, ◦ T( θ s ), T( θ v ) : total downward and upward transmittences, ◦ S : albedo of the land surface, ◦ ρ a : component of measured reflectance produced by the atmosphere . 10
Atmospheric correction, How? Atmospheric correction, How? Alternative to RT codes: SMAC Alternative to RT codes: SMAC SMAC SMAC Alternative to RT codes: Alternative to RT codes: � Input variables for SMAC: TOA reflectance ( ρ TOA ) • Computing Computing • Solar zenith angle ( SZA ) • Viewing zenith angle ( VZA ) surface reflectance surface reflectance • • Solar azimuth angle ( SAA ) Solar azimuth angle ( SAA ) pixel-by pixel-by pixel pixel by-pixel by-pixel pixel pixel • Viewing azimuth angle ( VAA ) • Atmospheric optical depth at Process time for Process time for 550 nm ( τ 550 ) MSG MSG-SEVIRI subset: SEVIRI subset: • Water vapor ( uWV ) • • Ozone content ( uO ) Ozone content ( uO 3 ) only 25 sec. only 25 sec. • Sensor-specific predefined coefficients � Why popular despite its age? � Why popular despite its age? ◦ Atmospheric correction in a short time, ◦ New sensors? No problem… Only the band specific ◦ New sensors? No problem… Only the band specific coefficients need to be updated, ◦ Free and open-source!!! 11
MARS & CMARS MARS & CMARS Multivariate Adaptive Regression Splines Multivariate Adaptive Regression Splines Multivariate Adaptive Regression Splines Multivariate Adaptive Regression Splines � Nonparametric adaptive regression procedure introduced by J. Friedman in 1991. introduced by J. Friedman in 1991. � Expansions of the truncated piecewise linear functions: − τ > τ , , x if x = ( ) − τ x + 0, , otherwise Reflected pair Reflected pair τ τ − − < < τ τ , , , , x x if if x x = ( ) τ − x + 0, . x τ ∈ ℝ otherwise , = = + + ε ε Y Y f f ( ) ( ) � General model: � General model: x x ◦ Y : response variable, ◦ x = (x 1 , x 2 ,…,x p ) T , vector of predictors, ◦ = (x 1 , x 2 ,…,x p ) , vector of predictors, ◦ ε : observation error with zero mean and finite variance. 12
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