ATBD - GHG-CCI

ESA Climate Change Initiative (CCI) 

Algorithm Theoretical Basis Document 

Version 2 (ATBDv2) – UoL-FP 

for the Essential Climate Variable (ECV) 

Greenhouse Gases (GHG) 

Page 1 

Version 2 – Draft 1 

18 March 2013 



Version 2 (ATBDv2) 

- 

The University of Leicester Full- 

Physics Retrieval Algorithm for the 

retrieval of XCO 2 and XCH 4 



Written by: 

GHG-CCI group at University of Leicester 

Lead author: R. Parker, University of Leicester, UK






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18 March 2013 

Change log: 

Version Nr. Date Status Reason for 

change 

Version 2 – Draft 1 18. Mar. 2013 First Draft based on existing 

UoL ATBD 

New document. 

Version 2 - Final 12. Aug. 2013 Final Final version






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18 March 2013 

University of Leicester 

Level 2 Retrieval 

Algorithm Theoretical 

Basis 

Robert Parker 

Hartmut Boesch 

Austin Cogan 




Version 2.0, Revision 1. 

18 th March, 2013 

Earth Observation Science 

Department of Physics and Astronomy 


Leicester, UK






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Document History: 

Version Revision Date Description/Comments 

1.0 1 28/6/2011 Initial version of ATBD 

2.0 1 18/03/2013 Updated for Version 4.0 of GOSAT retrievals 

The research described in this document was carried out at the University of Leicester, 

Leicester, UK. 

Copyright 2013. All rights reserved.






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Table of Contents 

1 Introduction ...................................................................................................................... 7 

1.1 Purpose .................................................................................................................... 7 

1.2 Scope ....................................................................................................................... 7 

2 GOSAT Overview ............................................................................................................ 7 

2.1 Objectives ................................................................................................................. 7 

2.2 Measurement Approach ........................................................................................... 8 

2.3 Instrument Characteristics ........................................................................................ 8 

2.3.1 Observing Modes ............................................................................................ 10 

2.3.2 Data Product Delivery ..................................................................................... 10 

2.4 L1B Processing ...................................................................................................... 11 

2.4.1 Radiometric Calibration ................................................................................... 11 

2.4.2 Noise ............................................................................................................... 11 

3 Algorithm Description ..................................................................................................... 11 

3.1 Algorithm Overview ................................................................................................ 11 

3.2 Forward Model ........................................................................................................ 13 

3.2.1 Solar Model ..................................................................................................... 13 

3.2.2 Radiative Transfer ........................................................................................... 13 

3.2.3 Instrument Model ............................................................................................. 14 

3.3 State Vector ............................................................................................................ 16 

3.3.1 Description of Carbon Dioxide Retrievals ........................................................ 16 

3.3.2 Description of Full-Physics Methane Retrievals .............................................. 20 

3.3.3 Description of Proxy Methane Retrievals ....................................................... 21 

3.4 Screening ............................................................................................................... 23 

3.4.1 Pre-Processing Screen ................................................................................... 23 

3.4.2 Cloud Screen ................................................................................................... 23






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3.4.3 Post-Processing Screen .................................................................................. 23 

4 References .................................................................................................................... 25 

APPENDICES ....................................................................................................................... 27 

Appendix A Acronyms .................................................................................................... 27 

Appendix B OCO ATBD ................................................................................................. 27 

LIST OF FIGURES 

Figure 2-1. TANSO-FTS instrument design showing the major optic components and optical 

path [Kuze, 2011]. 

Figure 2-2. Diagram illustrating the observation points of GOSAT in 5-point mode 

[Hamazaki, 2006]. 

Figure 3-1. ILS used in the retrievals for each GOSAT spectral band with different 

wavenumbers given. 

Figure 3-2. Validation of a priori surface pressure with in-situ ground based measurements 

from ARM instruments in Southern Great Plains/USA and Black Forest/Germany. 

Figure 3-3. Gaussian profiles based on the height and thickness described for various 

regions by Eguchi et al, 2007. 

Table 3-1. State Vector for CO 2 retrievals. 

Table 3-2. State Vector for CH 4 retrievals. 

LIST OF TABLES 

Table 3-3. Description of additional parameters used in the Carbon Dioxide post-processing 

screen.






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1 Introduction 

1.1 Purpose 

This Algorithm Theoretical Basis (ATB) document describes the algorithm used to retrieve 

the column averaged dry air mole fraction of carbon dioxide, X CO2 , and of methane, X CH4 , as 

well as other quantities included in the Level 2 Product generated from GOSAT spectra. This 

document explains the sources of input data required for the retrievals and the physical 

theory and mathematical background that underlies the information within the retrievals. 

Additionally, this document provides details of the retrievals implementation, assumptions 

and limitations of the approach used. 

1.2 Scope 

This document covers the algorithm theoretical basis for the parameters of the Level 2 

Products that are routinely retrieved at the University of Leicester. Section 1 provides the 

purpose and scope of the document. Section 2 explains the mission and instrument. Section 

3 describes the processing and algorithm and section 4 gives the references for publications 

cited in the document. 

2 GOSAT Overview 

2.1 Objectives 

Human activities such as fossil fuel combustion or land use change have led to a dramatic 

increase in atmospheric CO 2 concentrations from a pre-industrial level of 280 parts per 

million (ppm) to more than 386 ppm today. Atmospheric levels of methane (CH 4 ) have risen 

also dramatically over the last 300 years from 400-700 parts per billion (ppb) to 1774 ppb 

[IPCC, 2007]. Networks of surface in situ greenhouse gas sensors provide accurate 

measurements of the global greenhouse gas concentrations and their large scale temporal, 

seasonal and latitudinal variations. However, these are too sparse to allow the establishment 

of sub-continental carbon budgets and key questions remain unresolved, limiting the 

accuracy of future climate change forecasts and the ability to manage future levels of 

atmospheric CO 2 and CH 4 . Satellites observations, if acquired with high accuracy and 

precision, have the potential to overcome such limitations by providing globally denselysampled 

datasets of column CO 2 and CH 4 . 

The first observations of greenhouse gases from a dedicated satellite sensor are now 

available with the launch of the Japanese Greenhouse gas Observing SATellite (GOSAT) on 

23 January 2009. GOSAT provides global measurements of total column CO 2 and CH 4 from 

its shortwave infrared (SWIR) bands and of mid-tropospheric sub-columns from its thermal- 

IR bands. The mission aims; to monitor the density of greenhouse gases precisely and 

frequently worldwide, to study the absorption and emission levels to greenhouse gases per 

continent or large country over a certain period of time, and to develop and establish 

advanced technologies that are essential for precise greenhouse gas observations.






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2.2 Measurement Approach 

The Greenhouse Gases Observing SATellite (GOSAT) project was developed jointly by the 

Japan Aerospace Exploration Agency (JAXA), the National Institute for Environmental 

Studies (NIES) and the Ministry of Environment (MOE) with the primary aim to estimate 

emissions and absorptions of greenhouse gases with an increased accuracy on a subcontinental 

scale and to provide the environmental administration with an assessment of 

forest carbon balances, regional emissions and absorptions. Research using GOSAT may 

provide an increased understanding of the global distribution and temporal variations of 

greenhouse gases. This could develop our knowledge of the carbon cycle on a global scale 

and its influence on the climate, which is essential for the prediction of climate change and 

its possible impacts. Additionally, it aims to lead to new developments in both Earth 

observation satellite technologies and the approach of greenhouse gas measurements. 

GOSAT was successfully launched on the 23rd January 2009 by JAXA's H-IIA rocket and 

was the first dedicated greenhouse gas satellite. Onboard GOSAT is the Thermal And Nearinfrared 

Sensor for carbon Observation (TANSO) instrument which composes of two 

sensors; a Fourier Transform Spectrometer (FTS) that is used to measure greenhouse 

gases, and a Cloud and Aerosol Imager (CAI) that provides information about the scene, 

such as cloud and aerosol quantities. Both sensors are kept looking towards the Earth's 

geocentric direction by a three-axis attitude control system. The power required for this as 

well as the sensors operation is gained from two solar paddles which face the Sun. The 

satellite has a Sun synchronous orbit, optimising the power supply, and is quasi-recurrent 

with 14 + 2/3 revolutions per day. 

2.3 Instrument Characteristics 

TANSO-FTS comprises of three units; an electronic circuit unit, a control unit and an optical 

unit. The electronic unit is composed of a main and a redundant digital processing circuit that 

functions as a data processor, data-telemetries-commands-transmission interface with the 

satellite bus system and includes the temperature controller. The control unit acts as a 

controller for the cooling machine, the electronic cooling machine, the optical path switcher 

and solar irradiance diffusing board. It also functions as a driver and controller of the 

interferometer and the pointing mechanism. The optical unit contains the pointing 

mechanism (with redundancy), the blackbody diffusing board, the solar irradiance diffusing 

mechanism, the optical path switcher, monitoring camera, Fourier interferometer, relay and 

band splitting optics, the detector optics, analogue processing circuit and the cooling 

machine. 

The interferometer, based on the original Michelson interferometer, is a device that can 

divide a beam of radiation into two separate paths and then recombine these after a path 

difference has been introduced. This creates a condition whereby interference between to 

two beams can occur. The intensity variations of the resulting beam is measured as a 

function of path difference by the detector.






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Figure 2-1. TANSO-FTS instrument design showing the major optic components and optical 

path [Kuze, 2011]. 

The interferometer used by TANSO-FTS is of double pendulum type as shown in Figure 2-1. 

It uses corner cube mirrors which are statically aligned with each other and the rotary motor 

to maximise modulation efficiency with the minimum optical shear. These are attached to a 

swing arm that is moved by the rotary motor with less than 1% speed stability, creating 

uniform frequency of the output modulated signal. The rotary speed is required to take four 

seconds in order to achieve a small enough sampling electrical bandwidth and the 

necessary signal to noise ratio (SNR). This is used as the nominal time for interferogram 

acquisition, although TANSO-FTS is also capable of faster scanning modes that allow 

denser observations but at the expense of SNR. Between the mirrors is a beam splitter, 

where a beam of radiation from an external source can be partially reflected to one mirror 

and partially transmitted to the other mirror. Once reflected from the mirrors both beams 

return to the beam split and are partially reflected, transmitted and interfere. Due to the effect 

of interference, the intensity of each beam reaching the detector depends on the optical path 

difference (OPD) of the two beams. The OPD created are +/- 2.5 cm, four times as long as 

the mechanical motion, and are obtained to make both the real and imaginary spectra for 

suitable phase correction. The width of the beam splitter was selected to be larger than the 

maximum OPD to try to reduce the effects of channelling. The resulting light is reflected from 

a collecting mirror towards a circular slit, which due to its physical geometry forces the 

different spectral bands to be adequately aligned. The circular slit's geometry was designed 

to provide the maximum efficiency while maintaining within the maximum IFOV divergence 

for band 2 for 0.2 cm-1 spectral resolution. This defines the instantaneous field of view 

(IFOV) to be 15.8 mrad, equivalent to 10.5 km projected onto the surface of the Earth. The 

narrowed light passes to a collimating mirror and is then split through dichroic filters for each 

band in series. To minimize the background TIR, these filters transmit longer wavelength 

light and reflect shorter wavelength light. This minimizes the polarization sensitivity of the 

shorter wavelengths which then travel though a narrow band-pass filter. These are divided






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by a beam splitter into two polarizations that are then measured by two detectors. The bandpass 

filters are fixed to reduce channelling, to decrease stray light and to discard shorter 

wavelength light to evade aliasing (indistinguishable signals). While band 1 is measured by 

two Si detectors, both bands 2 and 3 are measured using InGaAs detectors that are nonbiased 

and cooled to -40 degrees C using thermoelectric coolers which minimizes dark 

currents. The TIR light is observed by a Photo-Conductive (PC) HgCdTe (MCT) detector that 

is cooled to 70 K using a pulse tube cooler with low vibration, which does not influence the 

interferogram. 

2.3.1 Observing Modes 

GOSAT TANSO-FTS nominally performs a cross-track scanning pattern where the number 

of lattice points can be varied from one to nine points per one cross-track scan, until August 

2010 5-points was used and afterwards 3-points have been used to reduce pointing errors 

caused by vibrations. Additionally, it can measure in specific observation mode which 

provides targeted observations for validation and experimental purposes. It can also 

measure over the ocean using the sun glint mode, whereby the along-track and cross-track 

mechanism can be used to point at the angle where the sun light is reflected off of the waves 

of the ocean causing the radiance to be very high. This overcomes the difficulty of 

measuring SWIR over the ocean that has a very low albedo, hence a low radiance that is 

hard to measure. The fourth instrument channel measures the thermal infrared (TIR) region 

that allows vertical profiling over both land and ocean. The instrument uses a solar 

irradiance calibration for the SWIR observations and a blackbody calibration for the TIR 

observations. It also performs deep-space and lunar calibrations for both SWIR and TIR 

bands. 

Figure 2-2. Diagram illustrating the observation points of GOSAT in 5-point mode 

[Hamazaki, 2006]. 

2.3.2 Data Product Delivery 

The GOSAT L1B data is downloaded via the GUIG and stored at the University of Leicester, 

where it is backed up and processed to provide radiometrically calibrated radiances with 

derived a priori values. Each observation is then processed further to estimate the column 

averaged dry air mole fraction of CO 2 and CH 4 (Level 2 Product), along with a number of






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other parameters such as surface pressure, temperature, water vapour, albedo, aerosol 

profiles, cirrus profile, CO 2 column averaging kernels, and a number of quality control 

products. 

2.4 L1B Processing 

2.4.1 Radiometric Calibration 

Firstly, the TANSO-FTS Radiometric Conversion coefficients for each band supplied via 

GUIG are applied to the GOSAT L1B SWIR spectral radiance. This converts the spectra 

from arbitrary units to radiance in W/cm 2 /Sr/cm -1 and these coefficients were derived by 

JAXA from pre-flight test results. Additionally, these coefficients correct the absorption 

effects of H 2 O, O 2 and CO 2 in gain H and the channelling around the detector optics of Band 

2 S polarisation are corrected. These coefficients are first interpolated onto the same 

wavenumber grid as the spectra and are then the spectral radiance is multiplied by them. 

Secondly, the radiances are multiplied by a radiance correction factor (1/degradation) in 

each band and polarisation with respect to time to correct the degradation in the solar 

diffuser. These factors are based on Yoshida et al., 2012. 

2.4.2 Noise 

The noise for each SWIR band and polarisation can be estimated by taking standard 

deviation of the out of band radiance characteristics of the GOSAT L1B spectra and 

multiplying with the radiometric calibration and degradation correction. The polarisations of 

the noise for each band are combined to give the noise for each band, using: 

3 Algorithm Description 

3.1 Algorithm Overview 

The UoL-FP retrieval algorithm is based on the algorithm that was developed to retrieve X CO2 

from a simultaneous fit of the near-infrared O 2 A Band spectrum at 0.76 µm and the CO 2 

bands at 1.61 and 2.06 µm as measured by the OCO-2 instrument. While the algorithm was 

developed to retrieve X CO2 from OCO and OCO-2 observations, it was designed to be 

adaptable to analyze data from other instruments for algorithm testing and validation. The 

algorithm has already been successfully used to retrieve XCO2 and XCH4 from observations 

from SCIAMACHY, GOSAT, and ground-based Fourier Transform spectrometers (FTS) 

(Parker et al., 2011), (Crisp et al., 2012), (Boesch et al., 2006) and to carry out retrievals 

simulations for OCO and OCO-2, GOSAT, Sentinel 5 (ESA CAMELOT project) or CNES 

Minicarb (Boesch et al., 2011, O’Dell et al., 2012).






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The retrieval algorithm uses an iterative retrieval scheme based on Bayesian optimal 

estimation to estimate a set of atmospheric/surface/instrument parameters, referred to as the 

state vector x, from measured, calibrated spectral radiances. 

The forward model describes the physics of the measurement process and relates 

measured radiances to the state vector x. It consists of a radiative transfer (RT) model 

coupled to a model of the solar spectrum to calculate the monochromatic spectrum of light 

that originates from the sun, passes through the atmosphere, reflects from the Earth’s 

surface or scatters back from the atmosphere, exits at the top of the atmosphere and enters 

the instrument. The top of atmosphere (TOA) radiances are then passed through the 

instrument model to simulate the measured radiances at the appropriate spectral resolution. 

The forward model employs the LIDORT radiative transfer model combined with a fast 2- 

orders-of-scattering vector radiative transfer code (Natraj et al., 2008). In addition, the code 

uses the low-streams interpolation functionality (O'Dell , 2010) to accelerate the radiative 

transfer component of the retrieval algorithm. 

The inverse method employs the Levenberg-Marquardt modification of the Gauss-Newton 

method to find the estimate of the state vector with the maximum a posteriori probability, 

given the measurement y (Connor et al., 2008, Rodgers, 2000). The state vector will 

typically include a CO 2 (or CH 4 ) profile together with non-CO 2 state vector. After this iterative 

retrieval process has converged to a solution, the error covariance matrix Ŝ 

and the averaging kernel matrix A 

are calculated using the a priori covariance matrix S a and the measurement covariance 

matrix S ε . X CO2 is inferred by averaging the retrieved CO 2 profile, weighted by the pressure 

weighting function, h, such that 

The associated column averaging kernel for a level j is then given by 

and the variance of X CO2 by






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The main parameters for the characterization of the X CO2 retrieval that are calculated by the 

retrieval algorithm are the a posteriori X CO2 retrieval error given by the square root of the 

variance σ XCO2 and the column averaging kernel a CO2 . 

3.2 Forward Model 

3.2.1 Solar Model 

The monochromatic TOA spectrum calculated by the RT code is multiplied with a synthetic 

solar spectrum, which is calculated with an algorithm based on an empirical list of solar line 

parameters [G. Toon, private communication]. The solar line list covers the range from 550 

to 15,000 cm -1 and is derived from FTS solar spectra: Atmospheric Trace Molecule 

Spectroscopy (ATMOS), MkIV balloon spectra for the range 550–5650 cm -1 , and Kitt Peak 

ground-based spectra for 5000–15,000 cm -1 . The solar model includes both disk center and 

disk integrated line lists. 

3.2.2 Radiative Transfer 

The radiative transfer module (RTM) encapsulates all the physics associated with the 

modification of the solar radiation during its passage through the atmosphere and reflection 

by the surface. The RTM calculates the top-of-atmosphere Stokes parameters I, Q, and U 

on a high resolution 0.01 cm -1 wavelength grid. The Stokes parameter V, representing 

circularly polarized radiation, is ignored as it is generally negligible and most instruments. 

The solar spectrum multiplies the high-resolution Stokes vectors calculated by the RT model, 

which are initially dimensionless reflectance, to give them the proper radiance units. 

A fully-polarimetric vector calculation of radiative transfer (RT) would be desirable to 

calculate the Stokes vector at each monochromatic wavelength. However, at 0.01 cm¡1 

resolution, this would lead to tens of thousands of computationally expensive RT calculations 

per forward model run. We therefore adopt an approximate approach called “Low Streams 

Interpolation” (LSI), which is described fully in (O’Dell, 2010) and references therein. 

Rather than performing full-accuracy calculations with a large number of angular streams at 

all monochromatic wavelengths, such calculations are only performed at a few tens of 

wavelengths. Very fast, low accuracy calculations are performed at all the monochromatic 

wavelengths; these are combined with the small number of high accuracy calculations to 

provide an estimate of the Stokes vector at each monochromatic point. 

Monochromatic RT calculations are made using a combination of a fast single-scattering 

model (Nakajima and Tanaka, 1988), the LIDORT scalar multiple-scattering model (Spurr et 

al., 2001), and a second-order-of-scattering polarization model called 2OS (Natraj and Spurr, 

2007). Neglecting higher orders of scattering for Q and U is shown to lead to radiance errors 

on the order of 20% or less of the expected OCO instrument noise, and XCO2 errors 

typically on the order of a few tenths of a ppm or less (Natraj et al., 2008). The LSI method 

has radiance errors typically less than a tenth of a percent (O’Dell, 2010). 

LIDORT






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The Full Physics algorithm uses LIDORT (Spurr et al., 2001, Spurr, 2002) to solve the 

radiative transfer equation (RTE). LIDORT is a linearized discrete ordinate radiative transfer 

(RT) model that generates radiances and Jacobians (derivatives of the radiance with respect 

to atmospheric and surface properties) simultaneously. The Jacobians are computed by an 

internal perturbation analysis of the complete discrete ordinate solution to the RTE. LIDORT 

is a quasispherical model; the direct beam and line of sight attenuations are treated for a 

curved atmosphere while the multiple scattering considered to be locally plane parallel. 

Two Orders of Scattering (2OS) Model 

Since multiple scattering is depolarizing, it is reasonable to expect that the polarization could 

be accounted for by a low-order scattering approximation. Natraj and (Spurr , 2007) 

extended the scalar (Kawabata and Ueno, 1988) model to compute the first two orders of 

scattering (2OS) for vertically inhomogeneous scattering media with polarization included. 

To enable accurate computations for a large range of solar viewing angles, atmospheric 

transmittances for the incoming solar beam are treated for a curved spherical-shell 

atmosphere (Spurr, 2002). For glint and nadir modes of operation, there is also a correction 

for the sphericity along the line of sight. Polarization induces a change in the intensity; to 

account for this, we compute a correction to the scalar intensity. The 2OS model 

simultaneously computes both the simulated backscatter radiance (and intensity correction) 

and any number of associated weighting functions (partial derivatives of the radiance with 

respect to retrieved and other atmospheric and surface properties). The 2OS computation is 

an order of magnitude faster than a full multiple scattering scalar calculation and two orders 

of magnitude faster than a vector multiple scattering computation. 

3.2.3 Instrument Model 

The instrument model convolves the monochromatic radiance spectrum with the instrument 

lineshape function (ILS). As described in (Boesch et al., 2006), the instrument model can 

also simulate continuum intensity scaling, zero-level offsets and channeling effects. The 

instrument model performs these actions and is described below. Additionally, the steps 

taken to calibrate the measured spectra are also described. 

3.2.3.1 Pixel-Wavelength Mapping 

The dispersion gives the pixel-wavelength mapping and consists of two parameters for each 

band; the start wavenumber W and the wavenumber increment D needed to reach the next 

pixels wavenumber. The wavenumber ν for detector pixel i and spectrometer k is given by 

The dispersion is described in detail in section 3.3.1.7.






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3.2.3.2 Instrument Lineshape Function (ILS) 

To describe the response of the instrument to light with wavelength an instrument line shape 

function (ILS) is used, which is obtained from the JAXA ILSF model. This model is evaluated 

with the parameter adjustment by using the GOSAT pre-flight test results. Band 1 has the 

ILS provided for both polarisations due to band 1 being sensitive to displacement of the 

optical axis with its shorter wavelengths, whereas bands 2 and 3 have accurate alignment. 

The ILS model gives the ILS for three different wavelengths in band 1 and four different 

wavelengths in bands 2 and 3, which are interpolated between. 

Figure 3-1. ILS used in the retrievals for each GOSAT spectral band with different 

wavenumbers given. 

The ILS model provided by JAXA can be seen in figure 3-1, which gives the ILS function for 

50 wavenumbers. However, to optimise the retrieval we implement only the centre 20 

wavenumbers with little reduction of accuracy. 

3.2.3.3 Zero-level Offset 

A zero-level offset parameter is retrieved to scale the intensity in the O2-A band. 

For further details see section 3.3.1.7 

3.2.3.4 Polarisation 

The polarisation option is currently turned off but the OCO Full Physics Algorithm has the 

option to enable this in the future if necessary.






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3.3 State Vector 

3.3.1 Description of Carbon Dioxide Retrievals 

The retrievals for Carbon Dioxide use a state structure that represents the atmosphere, 

surface and instrument. The state structure presently consists of 97 state vector elements as 

shown in Table 3-1. 


Description Parameters Number of Elements 

Aerosols 3 x 20 levels 60 

CO 2 20 levels 20 

Albedo 2 x 3 bands 6 

Dispersion 2 x 3 bands 6 

Zero-Level Offset 1 1 

Surface Pressure Scalar 1 

Temperature Scalar 1 

Water Vapour Scalar 1 

CH 4 Scalar 1 

Total 97 

The following sub-sections describe the a priori value and corresponding uncertainties of 

each state vector quantity. 

3.3.1.1 Profile of Carbon Dioxide Concentration 

The CO 2 a priori profile is obtained from 3 hourly model 3.75 degree longitude by 2.5 degree 

latitude gridded LMDZ 2009 CO 2 fields. The model CO 2 has a model run initialisation offset 

applied of 333 ppm as well as an additive correction of 18.246352 ppm which was derived 

by a comparison of the XCO 2 computed from the model fields to the NOAA Mauna Loa 

XCO 2 observations. The CO 2 profile is interpolated with latitude, longitude and time to the 

specific location desired. Additionally, the CO 2 is incremented according to yearly global CO 2 

increases by NOAA.






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3.3.1.2 Methane Concentration 

The a priori profile of CH 4 is acquired from a TM3 model run (Sander Houweling, personnel 

communication) and is interpolated to the desired latitude, longitude and time. This is only 

retrieved as a scalar, assuming the profile shape to be true. 

3.3.1.3 Surface Pressure 

Both under-constrained and over-constrained retrieval scenarios rely on the use of a priori 

information to constrain the solution to be physically reasonable. In order to perform retrievals the a 

priori need to be well constrained. In particular, it is most important that the surface pressure is well 

constrained since this can have the largest effect on the spectral lines retrieved. The European 

Centre for Medium-Range Weather Forecasts (ECMWF) is an assimilation model that uses 

observations from surface buoy and satellite measurements [ECMWF Technical Notes, 2008]. 

ECMWF provide atmospheric profiles of pressure, temperature and specific humidity on a 1.125 

degree by 1.125 degree global grid with 91 levels. Given the latitude, longitude and altitude of a site 

of interest the surface pressure can be determined from these profiles. ECMWF provide potential 

data for the lowest level of the same grid, which can be used to find the geopotential height of each 

grid point level as: 

where gravity, g, is calculated as a function of latitude and approximate altitude. Taking the four 

surrounding grid points of the site of interest, the pressure, P, at the site altitude can be found for 

each grid point by using the hydrostatic equation: 

where P 0 is the pressure of the grid point level lower than the site altitude, Z is the difference in 

altitude between the grid point level and the site altitude and Z 0 is the scale height defined as: 

where R is the ideal gas constant, T is the average temperature across the differential, M is the 

Molar mass of wet air and g is the gravitational acceleration as a function of latitude and altitude. 

The Molar mass of wet air can be calculated by: 

where SH is the ECMWF specific humidity, ρ d is the dry air mass and ρ w is the mass of wet air. The 

site altitude can be obtained from a global digital elevation model with a horizontal grid spacing of 

30 arc seconds named GTOPO30 provided by the U.S. Geological Survey. Note, that in the case that






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the site altitude is lower than the lowest level of a grid point the pressure is calculated with respect 

to the lowest level, where the temperature and molar mass are extrapolated downwards based on 

the lapse rate and gradient of the 5 lowest levels above, respectively. The surface pressure for the 

site can then be resolved by interpolating the pressures with latitude, longitude and time. 

To validate the surface pressure two sites were chosen; Southern Great Plains (SGP)/USA, 

and Black Forest/Germany, which are flat and mountainous in topography respectively. The 

Atmospheric Radiation Measurement (ARM) program has a central facility in SGP which 

takes in situ ground based measurements of surface pressure using the Temperature, 

Humidity, Wind and Pressure Sensors (THWAPS) instrument. Figure 3-3 shows that the 

surface pressure determined is within 1 hPa of THWAPS observations. Surface Pressure 

observations were also made by the ARM mobile facility that visited Black Forest, Germany, 

in 2007 with the Surface Meteorological Instrument (MET). Figure 3-2 illustrates that over a 

mountainous topography the surface pressure can still be resolved to within 1 hPa. Hence, 

the surface pressure a priori can be constrained to less than 0.1%, although we use a 1- 

sigma error of 4 hPa on the a priori surface pressure estimate to allow for more difficult 

topographies. 

Figure 3-2. Validation of a priori surface pressure with in-situ ground based measurements 

from ARM instruments in Southern Great Plains/USA and Black Forest/Germany. 

3.3.1.4 Temperature and Water Vapour 

The ECMWF specific humidity data can be used to generate water vapour volume mixing 

ratio profiles using the equation: 

where R d and R w are the gas constants in dry and wet air respectively. ECMWF also 

provides temperature profiles which, along with the H2O VMR , are interpolated with latitude,






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longitude and time to the specific observation. A constant O 2 VMR profile of 0.2095 is also 

used as a priori. We have assumed the temperature and H 2 O profiles are correct but allow 

the retrieval to scale them. 

3.3.1.5 Aerosol Profiles 

Aerosols are currently poorly characterized and little data is available. Therefore the same a 

priori for aerosol is used for all retrievals and a large a priori covariance (50 times the 

standard deviation of an aerosol profile) is used to allow a large flexibility and force the 

retrieval to rely more on the measurement in order to determine the parameter. Three 

atmospheric extinction profiles are used. Two of these profiles are the same shape, 

Gaussian profile with a 2 km height and 2 km width, and have a total column aerosol optical 

depth of 0.05 each. The only difference between these profiles are the aerosol properties 

used for each; based on Kahn et al, 2001, one uses classification 4b and the other uses 

classification 5b. Therefore providing one profile designed for carbonaceous and dusty 

environments and the other profile for carbonaceous and sooty environments. The third 

profile cases allows for the possibility of a cirrus cloud and is based on the height and 

thickness described in Eguchi et al, 2007. A Gaussian profile of 0.05 optical depth was 

created for each of the latitude regions described using the height and thickness given and 

then a look up table based on every 1 degree of latitude was created globally by 

interpolating between these regions with respect to latitude. Each retrieval uses the cirrus 

profile defined in the look up table that is closest to that retrievals specific latitude. The cirrus 

properties are constructed from ice cloud models based on the Baum models and an 

effective radius of 60 μm is used always. 

Figure 3-3. Gaussian profiles based on the height and thickness described for various 

regions by Eguchi et al, 2007.






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3.3.1.6 Surface Properties 

The albedo is calculated from the spectral continuum from the GOSAT L1B using the 

reflectivity: 

where SZA is the solar zenith angle and the Solar radiance and observed GOSAT radiance 

are given by S Solar and S GOSAT respectively. The retrieval uses two albedo parameters for 

each spectral band, giving the albedo for the centre wavelength of the band and the slope of 

the albedo. The slope of the albedo is set to zero in the a priori. The covariance for albedo is 

completely open and the slope a priori error is set so that the band edges can vary by 50%. 

3.3.1.7 Instrument Properties 

The dispersion is given in the GOSAT L1B data but requires adjusting in all SWIR bands. 

This adjustment can be calculated by the difference of the spectra away from a well known 

single strong Fraunhofer line (12985.163 cm -1 ) in the O 2 A band. Additionally, the O 2 A band 

dispersion requires shifting one spectral point lower to become approximately correct. It 

should be understood that although all SWIR band's dispersions are adjusted they are only 

approximate and require the dispersion to be retrieved. 

In addition to dispersion, the zero-level offset is retrieved in the O 2 A Band in order to scale 

the intensity. 

3.3.2 Description of Full-Physics Methane Retrievals 

The Full-Physics Methane retrieval is similar to the CO 2 retrieval described in Section 3.3.1 

with the target retrieval species changed from CO 2 to CH 4 . 



Aerosols 3 x 20 levels 60 

CH 4 20 levels 20 

Albedo 2 x 3 bands 6 

Dispersion 2 x 3 bands 6 

Zero-Level Offset 1 1 

Surface Pressure Scalar 1






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CO 2 Scalar 1 

Total 97 

3.3.2.1 Profile of Methane Concentration 


communication) and is interpolated to the desired latitude, longitude and time. 


Same as Section 3.3.1.1 




Same as section 3.3.1.4 







3.3.3 Description of Proxy Methane Retrievals 

For our GOSAT CH 4 retrieval, we have adopted the CO 2 proxy method of (Frankenberg et 

al., 2006). CO 2 is known to vary in the atmosphere much less than CH 4 and as the CO 2 

absorption band is spectrally close to that of CH 4 we can use the CO 2 as a proxy for the light 

path to minimize common spectral artefacts due to aerosol scattering and instrumental 

effects (Frankenberg et al, 2008, ,Butz et al, 2010). CH 4 and CO 2 retrievals are carried out 

sequentially with channels at 1.65 µm and 1.61 µm respectively. In order to obtain a volume 

mixing ratio (VMR) of CH 4 , it is necessary to multiply the X CH4 /X CO2 ratio by a model X CO2 . We 

obtain the CO 2 VMRs from the LMDZ model (Chevallier et al. 2010), convolved with scenedependent 

instrument averaging kernels obtained from the GOSAT CO 2 retrieval.






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The state vector of our retrieval consists of a 20-level profile for CH 4 and CO 2 VMRs, scaling 

factors for H 2 O VMR and temperature profiles, surface albedo and a spectral shift/stretch. 

Table 3-3. State Vector for CH 4 retrievals. 


CH 4 20 levels 20 

Albedo 4 4 

Dispersion 2 2 



CO 2 Scalar 1 

Total 29 

The following sub-sections describe the a priori value and corresponding uncertainties of 

each state vector quantity. 

3.3.3.1 Profile of Methane Concentration 


communication) and is interpolated to the desired latitude, longitude and time. 






Same as section 3.3.1.4 


The aerosol profile is based upon the GEMS/MACC aerosol model, interpolated to the 

time/location of the GOSAT sounding. 


A 3 rd order polynomial is retrieved for the albedo to allow for a spectrally dependent albedo. 


Same as Section 3.3.1.7






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3.4 Screening 

3.4.1 Pre-Processing Screen 

The GOSAT L1B soundings are screened initially to filter out any observations where the 

signal to noise (SNR) is < 50, if the sounding is over ocean and if a sounding contains any 

invalid L1B data. 

3.4.2 Cloud Screen 

One major disadvantage of using SWIR observations is that the iFOV must be free of thick 

clouds as these will cause irradiation to be reflected towards the satellite from a higher 

altitude, that of the cloud, rather than the Earth's surface. Therefore, a cloud screen is 

necessary to filter out exposures where thick clouds are within the iFOV. When irradiation 

gets reflected towards the satellite from a thick cloud the effective surface is that of the cloud 

rather than the Earth's surface. This results in the actual surface pressure being that at the 

cloud altitude, which typically is significantly lower than that at the Earth's surface pressure. 

An estimate of the actual surface pressure can be obtained by performing O 2 A band 

retrievals where the surface pressure is retrieved. We implement a super fast O 2 retrieval by 

using a small spectral window (13056 to 13074.8 cm -1 ). If the retrieved surface pressure is 

compared to the a priori surface pressure then the difference in surface pressure can be 

determined. Since the a priori surface pressure is well constrained, a surface pressure 

difference of greater than 30 hPa would normally only occur if a thick cloud is present in the 

iFOV, thus the exposures can be cloud screened using this method. 

3.4.3 Post-Processing Screen 

3.4.3.1 Carbon Dioxide Screen 

The CO 2 is post-screened based on the algorithm convergence criteria as above (i.e. 

outcome =1 or 2) as well as on the normalised CHI-Squared value for each spectral band. 

Currently a threshold of 0 < CHI-Square Band 1 < 1.3, 0.6 < CHI-Square Band 2 < 1.5 and 

0.4 < CHI-Square Band 3 < 1.5 is used. In addition to these screens we also presently filter 

on a number of other parameters to reduce the 

Additionally, these full physics retrievals are subjected to spectral interference from aerosols 

and clouds and topographic assumptions of the a priori, therefore we apply a number of 

extra screens to reduce these effects as explained in the table below. 

Table 3-4. Description of additional parameters used in the Carbon Dioxide post-processing 

screen. 

Parameter 

Minimum 

Threshold 

Maximum 

Threshold 

Explanation 

Saturation Test Band 2 

Polarisation P 

0 3.5x10 -5 Instrument saturation Flag determined from L1B 

radiance.






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18 March 2013 

Saturation Test Band 2 

Polarisation S 

Number of Cross Track 

Points 

Cross Track Angle Error 

(Degrees) 

Along Track Angle Error 

(Degrees) 

0 4.0x10 -5 Instrument saturation Flag determined from L1B 

radiance. 

-1 10 Filters out invalid cross-track values. 

-0.007 0.007 Reduce geolocation uncertainty. 

-0.05 0.05 Reduce geolocation uncertainty. 

A Posterior Error (ppm) 0 1.6 Filters out significantly poor retrievals. 

Retrieved AOD Aerosol 

profile 1 

Retrieved AOD Aerosol 

profile 2 

0 0.15 Removes any soundings with high AOD. 

0 0.15 Removes any soundings with high AOD. 

Retrieved AOD Total 0 0.2 Removes any soundings with high AOD. 

Albedo band 1 0 0.45 Removes high-albedo cases (High-gain only) 

CO2 Ratio 0.96 1.01 Ratio between band 2 and band 3 CO2 

H2O Ratio 0.96 1.2 Ratio between band 2 and band 3 H2O 

Aerosol Ratio 0 3 Ratio between Aerosol 1 and Aerosol 2 AOD 

It should be noted that all the screen criteria for CO 2 are still under development and may 

change in the future. 

3.4.3.2 Methane Full-Physics Screen 

Currently the methane full-physics post-screen is the same as the CO2 post-screen as 

described in Section 3.4.3.1 but updates are expected as the retrieval is further developed. 

3.4.3.3 Methane Proxy Screen 

The methane is post-screened based on the algorithm convergence criteria as above (i.e. 

outcome =1, cost_div = F, conv_flag = T) as well as on the normalised CHI-Squared value 

for both the CO 2 and CH 4 . Currently a threshold of 0.4 < CHI-Square CH 4 < 3.0 and 0.4 < 

CHI-Square CO 2 < 2.0 . Currently all soundings below 60°S are also removed (i.e. 

Antarctica).






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APPENDICES 

Appendix A 

ARM 

AOD 

CO 2 

CH 4 

ECMWF 

FTS 

GOSAT 

H 2 O 

iFOV 

ILS 

Km 

LMDZ 

O 2 

OCO 

ppm 

TANSO 

VMR 

Acronyms 

Atmospheric Radiation Measurement program 

Aerosol Optical Depth 

Carbon Dioxide 

Methane 

European Centre for Medium Range Weather Forecasting 

Fourier Transform Spectrometer 

Greenhouse gases Observing SATellite 

Water 

Instantaneous Field of View 

Instrument Line Shape 

Kilometer 

Laboratoire de Météorologie Dynamique general circulation model 

Oxygen 

Orbiting Carbon Observatory 

Parts per million 

Thermal And Near infrared Sensor for carbon Observations 

Volume Mixing Ratio 

Appendix B 

OCO ATBD 

The latest version of the OCO-2 Level 2 Full Physics Retrieval Algorithm Theoretical Basis is available 

via http://disc.sci.gsfc.nasa.gov/acdisc/documentation/ACOS.shtml

ATBD - GHG-CCI

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