Post on 04-Jan-2016
transcript
An evaluation method of the retrieved physical quantity deriving from the satellite remote sensing using analysis of variance in experimental design
Mitsuhiro TOMOSADA
Hiroe TSUBAKI
In resent year, global warming becomes serious problem.
· The changes of density for greenhouse gases are necessary to investigate to take measures.
· It is necessary to take measures immediately.
Global mean surface temperature anomaly 1850 to 2006 relative to 1961–1990
Satellite remote sensing is able to observe almost all over the world.
However, the number of observing stations of greenhouse gases are very few.
Map of ground-based in-situ sampling stations (WMO/GAW Report No.140)
Satellite to retrieve CO2 and CH4 column density will be launched next year in Japan.
GOSAT Greenhouse gases Observing SATellite
zv dzzT
zPzx
R
A0 )(
)()(
Column density
z: altitude Av: Avogadoro’s numberP(z): Pressure R: Gas constantT(z): Temperature
Orbit
It is important to clear the accuracy of the retrieved CO2 and CH4 column density.
In this study The method to evaluate the accuracy of the retrieved CO2 column density from GOSAT is shown.
yy ˆ
yy
Retrieved CO2 column density is represented as
Contents in the following this presentation
1. Observation overview by GOSAT and introduction of noise factors 2. Retrieval process of CO2 column density 3. Evaluation method and results of the retrieved CO2 column density using ANOVA in experimental design
We applied analysis of variance (ANOVA) in experimental design to evaluate the accuracy of the retrieved CO2 column density.
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Wavenumber [/cm]
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Sensor FTS (Fourier Transform Spectroscopy)
FTS sensor can obtain spectrum with high wave-number resolution.
CO2 absorption line
Samplinglaser Incident
radiance
Amp ADC
Detector
CCD camera
FTS
Data handling facility
signal (Interferogram)
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spectrum
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F(x): Retrieval process
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noise in sensor
CO2 column density
noise; uncertainty factors
CO2 column density
F(x): Retrieval process
Temperature profile
Temperature profiledifferent
Data handling facility
noiseuncertainty factor
Rodgers’s method
Fixed mirror
Moving mirror
Detector
Electric filters
ADC
Optical filter
Spectrum Column density
Sensor
E) Quantized noiseF) Sampling jitter
FT
C) Shot noiseD) Detector noise
Data handling facility
A) Temperature profileB) Water vapor amount profileG) Aerosol optical depth
FTR
Incident radiance
noise: uncertainty factor
FTS
Rodgers’s method
aiaieTii
Tiaii F xxSxySKKSKSxx
11111
1
Spectrum → CO2 density
Rodgers’s method
i: iteration numberx: Vector of CO2 density (x1,x2, ・・・ ,xL)y: Observed spectrumSe: Covariance of the observing errorSa: Covariance of the error of prior densityF(x): Theoretical spectrum as xK: Jacobian (=∂F(x)/ ∂xl)
Solar zenith angle 30 degreeSatellite zenith angle 0 degreeGround surface albedo 0.3Atmospheric condition US standard modelCloud none
25 layers
115km
· Experiments are designed by the implemental of a level-combination in the experimental environment.
Experimental design has applied in manufacturing, finance, social sciences, biology, chemistry, and a multitude of other areas.
· The design of experiment is based on an ANOVA model (a regression model)
The accuracy of CO2 column density is evaluated by analysis of variance (ANOVA) in experimental design.
· The retrieval accuracy is evaluated by ANOVA using results of experiments.
1. Levels for each error factors are set
2. Retrieved CO2 column density is modeled.
3. Experiments are designed based on the set levels of factors, orthogonal design table is built.
4. Experiments are run following the orthogonal design table.
5. Accuracy of an retrieved CO2 column density is evaluated by analysis of variance.
Level
Noise factor -1 +1 0
A Temperature -2K +2K 0K
B Water vapor amount -10% +10% 0%
C Shot noise None Existed
D Detector noise None Existed
E Sampling jitter None Existed
F Quantization noise None Existed
G Aerosol None Existed
Table of levels
Levels are used in the ANOVA model where the experimenter wants to test whether the response y has a significant difference among the levels.
ey Initial model
Assume that retrieved CO2 column density y come from the following regression model.
α, β, γ, δ, ε, ζ, and η are the differential effect on the retrieved CO2 column density due to the temperature profile (A), the water vapor amount profile (B), the shot noise (C), the detector noise (D), the sampling jitter (E), the quantization noise (F), and aerosol optical depth (G).μ is the overall mean of the process, e is a random error component.
Orthogonal design table is represented the design of experiments as table.
A design of experiments is a set of level-combinations with main purpose of estimating main effects. Design table is a matrix such that · each entry in each column appears equally · each entry-combination in any two columns appear equally entry: level of factor or some interactions of the factor
Factor
Test No. A B C
1 -1 -1 -1
2 -1 +1 +1
3 +1 -1 +1
4 +1 +1 -1
Test No. y[×1021/cm2] A B C D E F G
1 8.101756 -1 -1 -1 -1 -1 +1 +12 8.035052 -1 -1 +1 +1 +1 -1 -13 8.10213 -1 +1 -1 -1 +1 -1 -14 8.172004 -1 +1 +1 +1 -1 +1 +15 8.136074 -1 0 -1 -1 -1 -1 +16 8.069867 -1 0 +1 +1 +1 +1 -17 8.205764 +1 -1 -1 -1 +1 +1 -18 8.272321 +1 -1 +1 +1 -1 -1 +19 8.339642 +1 +1 -1 -1 +1 -1 +1
10 8.272128 +1 +1 +1 +1 -1 +1 -111 8.240303 +1 0 -1 -1 -1 +1 -112 8.306145 +1 0 +1 +1 +1 -1 +113 8.184248 0 -1 -1 -1 +1 +1 +114 8.118027 0 -1 +1 +1 -1 -1 -115 8.184958 0 +1 -1 -1 -1 -1 -116 8.254512 0 +1 +1 +1 +1 +1 +117 8.153965 0 0 -1 -1 -1 -1 -118 8.220244 0 0 +1 +1 +1 +1 +1
A: Temperature profile B: Water vapor amount C: Shot noise D: Detector noiseE: Sampling jitter F: Quantization noise G: Aerosol noise
221 /101872.8 cmy
Factor S [×1040] φ V [×1040] F-valueA 6.45 1 6.45 8.35 B 1.52 1 1.52 1.97 C 0.01 1 0.01 0.01 D 0.01 1 0.01 0.01 E 0.01 1 0.01 0.01 F 1.60 1 1.60 2.07 G 0.67 1 0.67 0.87
Error 7.73 10 0.77 Total 18.01 17
ey Initial model
A: Temperature profile B: Water vapor amount C: Shot noise D: Detector noiseE: Sampling jitter F: Quantization noise G: Aerosol noise
S: sums of squares ,φ: degrees of freedom, V: mean squares
Results
Final modeley
Factor
S [×1040] φ V[×1040] F-value
A 6.45 1 6.45 10.72 B 1.52 1 1.52 2.53 F 1.60 1 1.60 2.66
Error 7.73 14 0.60 Total 18.01 17
Results
][/1003.117
1001.18 22040
cmy
・ We denote the evaluation method of the retrieved CO2 column density using analysis of variance.
・ Since it takes much time to retrieve CO2 column density, it is difficult to evaluate the retrieved CO2 column density by much times experiments. Therefore, the denoted method is efficient since evaluation can be done by the minimum number of experiments