4. Retrieval - Principle and Method
4.1 SMILES observation species
4.2 Forward model development
4.3 Retrieval algorithm
4.4 Error analysis
4.5 SMILES observation capability

SMILES observations

Observation species

Standard Products••••

O3, HCl, ClO
HO2, HOCl
O3 isotopes, BrO
HNO3, CH3CN

Research Products• UT/LS region (O3, HCl, CH3CN)• Upper stratosphere and lower mesosphere (O3, HCl, HO2)
• UTH, Cirrus Cloud• H2O2• Isotope species of HCl, and CH3CN• Mass-Independent Fractionation of Ozone isotopesObservation species

SMILES observation altitude range
Observation Altitude Range

Observation Species
Observation
altituderange

Species

MesosphereO3, H37Cl, H35Cl, wind,
OOO18 HO2, OOO17, ClO
H2O2(medium/lowSNR)

Stratosphere(high SNR)

Stratosphere

理科年表CD－ROM2004（丸善）より

O3, H37Cl, H35Cl, H2O, ClO
Temp, Pointing offset(medium/lowSNR)

wind, HOCl, N2O, CH3CN,
OOO18, OOO17 HNO3,HO2, BrO, H2O2, SO2

UT/LS

H2O, Ice water content, O3

Observation species

Observation frequency and spectrum

SMILES has 3 observation frequency bands.
Simulated Observation Spectrum are shown with eachmolecule and at each tangent height.

- 2 spectrometer of 1200 MHz bandwidth- 1.8MHz resolution

Observation species

Products by JEM/SMILES experiment
Processingmodes

Band A

Band B

Band C

Stratospherichigh SNR
10-60 kmO3, H37Cl, H2O,Temp, Pointing
offsetO3, H35Cl, H2O,Temp, Pointing
offset

H2O, ClO

Stratosphericwind, HOCl,
medium/low SNR CH3CN, OOO18,
10-60 km
HNO3, BrO,H2O2, SO2wind, N2O,
OOO18, HO2,HNO3, SO2

O3, OOO18,
OOO17, HO2,HNO3, BrO

MesosphericO3, H37Cl, wind,medium/low SNR OOO18, H2O2
50-90 kmO3, H37Cl, wind,
HO2, , OOO18,
OOO18, HO2, SO2 OOO17, ClO

UT/LSExtremely Low
SNR

H2O, Ice water content, O3
H2CO, HOBr,
ClONO2, OClO,ClOOCl, H2SO4

CH3Cl, H2CO,HOBr, ClONO2,OClO, ClOOCl

COF2, ClONO2,NO2, OClO,ClOOCl

blue: single scan, red: daily average, green: monthly average, black: very challenging

Forward model development

System model

Forward model
1) radiative transfer model2) Sensor model

L1 Data = S + Bmole + TsysS:
Signal from purpose molecule in the atmosphere
B: Background Base line from molecules (O3, H2O, N2, O2, etc.)
moleTsys: System noise(Tant, Topt, Trx) + Side lobe

L1 dataTemperature calibration

hot loademissionemissionfrom side lobe

Tant
Topt

Tant
Topt

Trx

Trx

Hot load～300K
absorberCold load
2.7K
backgroundswitch

T b*Signal
BmoleTantTopt
Trx

Signal oflimb observation

optics loss

SignalBmoleemission
from side lobe
Tsys (Tant , Topt ,Trx)
Tant:antenna noise temperature
Topt: optics noise temperature
Trx: receiver noise temperature

Forward model development

Radiative transfer process in the atmosphere
Limb sounding geometry (without refraction)
Radiative trans. eq. for the pencil beam
sfar

zT

AtmosphereEarthdsz

snear

SMILESzmax{Tδυ ( snear ) = Tδv ( s far ) exp − ∫+∫snearsfarRe
Integration pathsnearsfarkυ ( s )ds{kυ ( s)Te ( s ) exp − ∫snears}}kυ ( s)ds ds

where, v is the frequency, Te in the brightness
temperature of the atmospherek is the line absorption for the molecular labeled
by i is given byx a ( si ) P( si ) aαν ( si ) + k air (si )kT ( si )akν ( si ) = ∑Items included- Atmospheric Refraction is included- Line shape function is used the Voight functions for the each pressure.
- Continuum Liebe MPM89 for operational code, SMILES continuum for research code
- 2 dimension integrals are possible for the atmospheric models in research code
- Scattering calculation included in research codeForward model development

Radiative transfer calculation including
cloud cases for research products

Forward model development

An example: Ice cloud effects in the UT/LS
An example of spectral cloud effects
O3ClO

Example: Effects of cirrus in different
ice water path on SMILES spectra(SetUp: tropical standard atmosphere, cirrus 12-13km,
effective size 12mm, 4km tangent altitude)

Forward model development

Radiative transfer calculation in the atmosphere

Atmospheric Continuum
in SMM region
Difference of absorptionof the several models are
more than 50%Forward model development

Continuum model applicable to SMILES

Laboratory Experiment of water vapor
TDS spectrometer + SMILES SIS spectroscopyForward model development

Continuum model applicable to SMILES
Laboratory Experiment of water vapor
TDS spectrometer + SMILES SIS spectroscopyForward model development

Summary of SMILES
molecular spectroscopic data
Freq. (GHz)γnCurrent Accuracy Required Accuracy

O3625.372 2.99

0.75

4%

H35Cl

650. 732 --625.919 3.41--0.73--4%by the error analysis

1%2 Yamada and Amano

1%1%12212
3
done Yamada and Amano
311 Yamada and Amano (一部）
done Yamada and Amano
done Yamada and Amano111-(Pressure Shift δ0(MHz/Torr)=0.146, s=0.4047, χ=0.3763) 17.8%

H37Cl
ClO
HO2

624.978 --649.451 2.782
625.660 --649.702 3.51
H2O2625.04 3.78
HOCl
625.076 --O3isotopes Many
BrO
624.768 3.05
650.179 3.03
HNO3
624.484 --624.776 --625.345 --650.288 --CH3CN
624.819- --624.926 -----0.86--0.63------0.80
0.80-------------

--3%
--4%
------3%3%-------------

Priority

1%
3%
3%
3%3%
0.5%
5%
5%
3%
3%
3%
3%
3%
3%

Instrumental detail
Radiative transfer
calculation

Brightness temperature
At the tangent height 1

Brightness temperature
At the tangent height 2

T[K]Forward model development

Doppler shift

Re + zT，Re=Earth’s radius
Re + z ISS⎛ v ⎞f D = ⎜1 + D ⎟ fc ⎠⎝vD = vISS ⋅ cos φ ⋅Doppler shift

K→ Watt/Hz

P = kT k: boltzmann coefficient
P[Watt/Hz]

Hot load

Brightness temperature
At the tangent height 3

Antenna
Optical lossOptical loss

P out = Pin ⋅10G /10

Standing wave

Standing wave

Pout = Pin | 1 + A1e− B1 cf i+ A2 e

Cold sky

SSB filter

Hot loadUSB

SSB filter functions

1( 2 N + 1 2)
{1 ± cos(πf rf )}
2f L0
N:整数
Power with transmittance： P ( f rf ) = t ( f rf ) P in ( f rf )t=transmittance （＋：USB, －：LSB)：

Power at frequency fif： Pout ( f if 1 ) = P ( f L 0 + f if 1 ) + P ( f L 0 − f if 1 )LSB− B2 cf i 2|

Forward model developmentInstrumental detail (continued)
USB

Data interpolation
1ch is divided by N

For AOS channel response function

P out = Pin + Pnoise

LSBnoise(1)Pnois= constant⎧ ( f − f0 )2 ⎫1exp ⎨−⎬
channel response function： R ( f 0 , f ) =2σ 2 ⎭
2πσ⎩(Gaussian)
AOS

Frequency conversion
gain

P out = Pin ⋅10

f if 2 =| f if 1 − f L 02 |G / 10Power withchannel response function
Poewer for 1ch：

AOSi max

P ( f ) = ∑ Pf i R ( f i , f )1Pch = ∫ch _ hch _ lP ( f )df※ Pfi, fi = Power and freqquency at the data number i
imax number of data
ch_h, ch_l upper/lower limit of channel frequency

standing wave
P[Watt]T[K]P out = Pin + Pnoise

noise(2)USB, LSB loop

Brightness temperature
calibration

Tobs [K ] =Frequency
calibration

Pobs − Pcold(Thot − Tcold ) + Tcold
Phot − Pcold

Doppler correction⎛ v ⎞f = f D ⎜1 + D ⎟c ⎠⎝※ Pobs, Pcold, Phot Signal power from observation、cold sky, Hot load
Tcold, Thot temperature at cold sky, Hot loadTangent height, cold load，hot loadの loop

outputRetrieval algorithm

Retrieval
Optimal Estimation Method– Linear least-squares method, allowing « a priori » knowledge tobe taken into account– Atmospheric parameters x estimated by minimising χ2 :

χ2 = [y-F(x,b)]T • Sy-1 • [y-F(x,b)] + (x-x0)T • Sx0-1 • (x-x0)
measurement spaceparameter spacey:spectral measurements
F(x,b) : forward modelb:
model parameters (spectroscopy, instrument)« a priori » parameter vector
x0 :– Weights: Measurement and « a priori » covariance matrices Syand SX0– Diagnostics: Error covariance and averaging kernel matrices

Non-linear retrieval

Retrieval algorithm

Non-linear retrieval

iterative Levenberg-Marquardt regularisation

OEM with Levenberg-Marquardt iteration scheme:-1

xi+11= x0 + ( KiTSy-1Ki + Sx0-1 + γ U ) • { KiTSy-1 • ( [y - F(xi, b)] + Ki [xi - x0] ) + γ U [xi-x0] }Di : contribution function matrix
y:F(x,b) :b:xi , x 0 :Sx0, Sy, :spectral measurementsforward model
model parameters (spectroscopy, instrument)
parameter and « a priori » parameter vector« a priori » and measurement covariance matrix

Sb, Kb = ( ∂F / ∂b ) :model parameter error covariance and weighting function matrices

K = ( ∂F / ∂x ) :γ:
U:weighting function matrix
Marquardt parameter. Convergence: γ → 0 !
scaling matrix

Algorithm development for
operational code

Retrieval algorithm- Algorithms have been studied by NICT, Bremen university, and JAXA.
- In 2006, JAXA started the development of Operational Retrieval
Code (ORC), and related algorithm studies- Retrieval procedure based on:=> Optimal Estimation Method
look for a solution in the vicinity of an a priori
value of the retrieved parameters=> Levenberg-Marquardt iterative scheme for non
linear inversion of strong lines- Retrieved parameters:=> Vertical distribution of the species VMR=> Temperature distribution=> Scan altitude offset + baseline parameters

Error analysis

Error estimations
Retrieval Errors : S
Stotal= Sstatistic + Snull + Smodel

A=DK: averaging kernel matrix

Sstatistic= D Sy DT: statistical error

Snull= (A - U) Sx0 +(A - U)T: smoothing error

Smodel= (D Kb) Sb (D Kb)T

: model parameter error

Model parameter errors
Factors in model parameter errors
1. Calibration knowledge
2. Side Band knowledge
3. Antenna Pattern knowledge
4. Pointing knowledge
5. Spectroscopic parameter knowledge
6. AOS response function knowledge

Error analysis

Precision and accuracy
An example for O3
1. Calibration knowledge(SW: Standing wave,
GTV: time variation of the gain)
2. Side Band knowledge(SSB: SSB filter ratio)
3. Antenna Pattern knowledge(Antenna: Antenna pattern)
4. Pointing knowledge(THRE: Tangent height random error)
5. Spectroscopic parameter knowledge(PB: Pressure broadening error)
6. AOS response function knowledge(AOS: error from spectrometer)

Error analysis

Examples for error estimations
StotalO3Error analysis= Sstatistic + Snull + Smodel
ClO

HO2

Error analysis

Tangent point retrieval and its error“Altitude scan off-set” canbe retrieved.
→ improved to operational
processing in JAXA.
“Pointing random error” is amajor source of the error inO3, HCl, and ClO retrieval.
What can we do for that?

Error analysis

Tangent height retrieval- Work still in progress but first results are promising.
- Tangent height retrieval improved the retrieval errorof Ozone, HCl, significantlyOzone (mid-latitude scenario)
Observable Altitude region:
Altitude resolution:

Band A

Observation capability

11 - 91km (tropopause 12km)
2.1km-6.2 km

Band B

Band CBandC ClO (mid-latitude scenario)

Observable Altitude region:

24-63km

Altitude resolution:

3.5-8.1km

Observation capability

H2O (mid-latitude scenario)
Observable Altitude region:
Altitude resolution:

Band A

Observation capability

8 - 37km (tropopause 12km)
2.4km-5.8 km

Band B

Band CJEM/SMILES observation

Observation capability