Sensitivity Analysis of Fourier Transformation Spectrometer: Fts against Observation Noise on Retrievals of Carbon Dioxide and Methane

—Sensitivity analysis of Fourier Transformation Spectrometer: FTS against observation noise on retrievals of carbon dioxide and methane is conducted. Through experiments with real observed data and additive noise, it is found that the allowable noise on FTS observation data is less than 2.1x10-5 if estimation accuracy of total column carbon dioxide and methane is better than 1(%).


INTRODUCTION
Greenhouse gases Observing SATellite: GOSATcarries TANSO CAI for clouds and aerosol particles observation of mission instrument and TANSO FTS 1 : Fourier Transformation Spectrometer 2 for carbon dioxide and methane retrieving mission instrument [1].In order to verify the retrieving accuracy of two mission instruments, ground based laser radar and TANSO FTS are installed.The former is for TANSO CAI and the latter is for FTS, respectively.One of the other purposes of the ground-based laser radar and the ground-based FTS is to check sensor specifications for the future mission of instruments to be onboard future satellite with extended mission.Although the estimation methods for carbon dioxide and methane are well discussed [2]- [6], estimation method which takes into account measurement noise is not analyzed 1 http://www.jaxa.jp/projects/sat/gosat/index_j.html 2 http://ja.wikipedia.org/wiki/%E3%83%9E%E3%82%A4%E3%82%B1%E3%83%AB%E3%82%BD%E3%83%B3%E5%B9%B2%E6%B8%89%E8%A8 %88 yet.Therefore, error analysis for additive noise on estimation accuracy is conducted.
In order to clarify requirement of observation noises to be added on the ground-based FTS observation data, Sensitivity analysis of the ground-based FTS against observation noise on retrievals of carbon dioxide and methane is conducted.Experiments are carried out with additive noise on the real acquired data of the ground-based FTS.Through retrievals of total column of carbon dioxide and methane with the noise added the ground-based FTS signals, retrieval accuracy is evaluated.Then an allowable noise on the ground-based FTS which achieves the required retrieval accuracy (1%) is reduced.
The following section describes the proposed sensitivity analysis followed by some experiments.Then concluding remarks with some discussions is followed by.

A. Ground-based FTS
Figure 1 shows schematic configuration of the groundbased FTS which is originated from Michelson Interference Measurement Instrument.Light from the light source divided in to two directions, the left and the forward at the dichotic mirror of half mirror.The left light is reflected at the fixed hold mirror and reaches to the half mirror while the forward light is reflected at the moving mirror and reaches at the half mirror.Then interference occurs between the left and the forward lights.After that interference light is detected by detector.Outlook of the ground-based FTS is shown in Figure2.www.ijacsa.thesai.org

B. Principle for Carbon Dioxide and Methane Retrievals with TANSO FTS Data
Figure 4 shows a principle of the retrieval method for atmospheric continuants using GOSAT/TANSO data.Figure 4 (a) shows Top of the Atmosphere: TOA radiance in the wavelength ranges from 500 to 2500nm (visible to shortwave infrared wavelength regions).There are three major absorption bands due to oxygen (760-770nm), carbon dioxide and methane (1600-1700nm), and water vapor and carbon dioxide (1950-2050nm) as shown in Figure 4 (b), (c), and (d), respectively.These bands are GOSAT/TANSO spectral bands, Band 1 to 3, respectively.In addition to these, there is another wide spectrum of spectral band, Band 4 as shown in Figure 4(e) which covers from visible to thermal infrared regions.. www.ijacsa.thesai.org

A. Ground-based FTS Data Used
The ground-based FTS data used for experiments are acquired on November 14 and December 19 2011.Figure 5 shows the interferograms derived from the acquired the ground-based FTS data.

B. Experimental Method
Observation noise is included in the observed interferograms.In addition to the existing noise, several levels of additional noises which are generated by random number generator of Messene Twister with zero mean and several standard deviations is added on to the iterferograms as shown in Figure 6.

C. Experimental Results(Noise Added Interferograms and
Fourier Spectra) Figure 7 shows noise added interferograms and the Fourier spectra derived from the noise added interferograms.Added noises ranges from 0 to 1x10 -3 .1/1000 of standard deviation of noise (zero mean) against signal level is added to the single channel of signal level in maximum.Vertical axis shows signal level and horizontal axis shows optical pass length difference for Figure 7    From these figures, it is concluded as follows, Allowable retrieval errors for methane and carbon dioxide are 0.02 ppm and 4 ppm, respectively.Therefore, acceptable noise level on FTS interferogram is less than 2.1 x 10 -5 .
IV. CONCLUSION Sensitivity analysis of Fourier Transformation Spectrometer: FTS against observation noise on retrievals of carbon dioxide and methane is conducted.Through experiments with real observed data and additive noise, it is found that the allowable noise on FTS observation data is less than 2.1x10 -5 if estimation accuracy of total column carbon dioxide and methane is better than 1% (allowable retrieval errors for methane and carbon dioxide are 0.02 ppm and 4 ppm, respectively.These correspond to 1% error for both methane and carbon dioxide retrievals).

Figure 3 (
Figure 3 (a) shows an example of the interferogram 3 (interference light detected by the detector of the ground-based FTS).By applying Fourier Transformation to the interferogram, observed Fourier spectrum is calculated as shown in Figure 3 (b).When the ground-based FTS observes the atmosphere, the observed Fourier spectrum includes absorptions due to atmospheric molecules and aerosol particles.By comparing to the spectrum which is derived from the radiative transfer code with atmospheric parameters, atmospheric molecules and aerosol particles are estimated.

Figure 1 Figure 2 Figure 3
Figure 1 Michelson Interference Measurement Instrument

Figure 4
Figure 4 Example of TOA radiance and absorption bands as well as spectral bands of GOSAT/TANSO instrument III.EXPERIMENTS

Figure 5
Figure 5 Example of interferograms used for experiments.

Figure 6
Figure 6 Method for adding the noises to the acquired interferograms (a), (c), (e), (g), (i), (k), and (m) while vertical axis shows Fourier spectrum (amplitude) and horizontal axis shows frequncy (or wave number) for the rest of Figure 7. www.ijacsa.thesai.orgAs shon in Figure 7, Fourier spectra is degrading in accordance with incresing of noise obviously.Although the additive noises are not clearly seen, it is slightly recognizable the noise through comparison between Figure (b) and (o).

Figure 7
Figure 7 Noise addediInterferograms and Fourier spectrum derived from the interferograms D. Experimental Results (Retrieval Error) Figure 8 (a) shows methane retrieved results.Horizontal axis shows standard deviation of additive noise and vertical axis shows retrieved methane amount in unit of ppm (percent per million).Figure 8 (b) shows retrieved error (retrieved methane amount from noise added interferogram minus retrieved methane amount from noise free interferogram).Meanwhile, Figure8(c) shows carbon dioxide retrieved results.Horizontal axis shows standard deviation of additive noise and vertical axis shows retrieved carbon dioxide amount in unit of ppm (percent per million).Figure8 (d)shows retrieved error (retrieved methane amount from noise added interferogram minus retrieved carbon dioxide amount from noise free interferogram).GFIT of retrieval software code is used for both estimations of total column carbon dioxide and methane contents in the atmosphere[6].

Figure 8
Figure 8 Retrieved carbon dioxide and methane amount with noise added and noise free iterferograms together with retrieved errors.