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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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

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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

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1001.18 22040

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・ 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