1. 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

2. 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

3. 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)

4. Satellite to retrieve CO 2 and CH 4 column density will be launched next year in Japan. GOSAT Greenhouse gases Observing SATellite Column density z: altitude A v : Avogadoro’s number P(z): Pressure R: Gas constant T(z): Temperature Orbit

5. It is important to clear the accuracy of the retrieved CO 2 and CH 4 column density. In this study The method to evaluate the accuracy of the retrieved CO 2 column density from GOSAT is shown. Retrieved CO 2 column density is represented as

6. Contents in the following this presentation 1. Observation overview by GOSAT and introduction of noise factors 2. Retrieval process of CO 2 column density 3. Evaluation method and results of the retrieved CO 2 column density using ANOVA in experimental design We applied analysis of variance (ANOVA) in experimental design to evaluate the accuracy of the retrieved CO 2 column density.

7. Observation bands Sensor FTS (Fourier Transform Spectroscopy) FTS sensor can obtain spectrum with high wave-number resolution. CO 2 absorption line Sampling laser Incident radiance Amp ADC Detector CCD camera FTS

8. Data handling facility signal (Interferogram) spectrum x F(x): Retrieval process noise in sensor CO 2 column density noise; uncertainty factors

9. CO 2 column density F(x): Retrieval process Temperature profile different Data handling facility noise uncertainty factor

10. Rodgers’s method Fixed mirror Moving mirror Detector Electric filters ADC Optical filter SpectrumColumn density Sensor E) Quantized noise F) Sampling jitter FT C) Shot noise D) Detector noise Data handling facility A) Temperature profile B) Water vapor amount profile G) Aerosol optical depth FTR Incident radiance noise: uncertainty factor FTS Rodgers’s method

11. Spectrum → CO 2 density Rodgers’s method i: iteration number x: Vector of CO 2 density (x 1,x 2, ・・・,x L ) y: Observed spectrum S e : Covariance of the observing error S a : Covariance of the error of prior density F(x): Theoretical spectrum as x K: Jacobian (=∂F(x)/ ∂x l )

12. Solar zenith angle 30 degree Satellite zenith angle 0 degree Ground surface albedo 0.3 Atmospheric condition US standard model Cloud none 25 layers 115km

13. · 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 CO 2 column density is evaluated by analysis of variance (ANOVA) in experimental design. · The retrieval accuracy is evaluated by ANOVA using results of experiments.

14. 1.Levels for each error factors are set 2.Retrieved CO 2 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 CO 2 column density is evaluated by analysis of variance.

15. Level Noise factor+10 ATemperature-2K+2K0K BWater vapor amount-10%+10%0% CShot noiseNoneExisted DDetector noiseNoneExisted ESampling jitterNoneExisted FQuantization noiseNoneExisted GAerosolNoneExisted 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.

16. Initial model Assume that retrieved CO 2 column density y come from the following regression model. α, β, γ, δ, ε, ζ, and η are the differential effect on the retrieved CO 2 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.

17. 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.ABC 1 2 +1 3 +1 4

18. Test No.y[×10 21 /cm 2 ]ABCDEFG 18.101756 +1 28.035052 +1 38.10213+1 +1 48.172004+1 +1 58.1360740 +1 68.0698670+1 78.205764+1 +1 88.272321+1+1 +1 98.339642+1 +1+1 108.272128+1 +1 118.240303+10 +1 128.306145+10 +1 138.1842480 +1 148.1180270+1 158.1849580+1 168.2545120+1 17 8.15396500 188.22024400+1 A: Temperature profile B: Water vapor amount C: Shot noise D: Detector noise E: Sampling jitter F: Quantization noise G: Aerosol noise

19. FactorS [×10 40 ] φ V [×10 40 ]F-value A6.451 8.35 B1.521 1.97 C0.011 D 1 E 1 F1.601 2.07 G0.671 0.87 Error7.73100.77 Total18.0117 Initial model A: Temperature profile B: Water vapor amount C: Shot noise D: Detector noise E: Sampling jitter F: Quantization noise G: Aerosol noise S: sums of squares,φ: degrees of freedom, V: mean squares Results Final model Facto r S [×10 40 ] φ V[×10 40 ]F-value A6.451 10.72 B1.521 2.53 F1.601 2.66 Error7.73140.60 Total18.0117 Results

20. ・ We denote the evaluation method of the retrieved CO 2 column density using analysis of variance. ・ Since it takes much time to retrieve CO 2 column density, it is difficult to evaluate the retrieved CO 2 column density by much times experiments. Therefore, the denoted method is efficient since evaluation can be done by the minimum number of experiments