NASA Graduate Student Fellowship
in Earth Systems Science Proposal
Retrieval of carbon dioxide information
from AIRS and OCO data using novel
techniques
Daniel R. Feldman
California Institute of Technology
1200 E. California Blvd., MC 138-78
Pasadena, CA 91125
Faculty Advisor:
Yuk Yung
March 16, 2004
Abstract:
Atmospheric remote sensing data from nadir and limb sounding high-resolution infrared satellite
measurements will dramatically increase knowledge of the spatial and temporal distribution of
carbon dioxide (CO2) and other trace gases. The goal of this research is to use multiple satellite
data sets to compile a spatial distribution of monthly-averaged column CO2 concentrations with
sufficient accuracy to allow for improved carbon source-sink inversions. Data from
Atmospheric Infrared Sounder (AIRS) and the Orbiting Carbon Observatory (OCO, schedule
launch: August, 2007) will be used. Preliminary results suggest that such retrievals are possible
but many complicating factors must be addressed and data validation is required. Consequently,
this research proposes to develop a retrieval and validation system for AIRS data which will
improve OCO retrievals. Such a system may allow source-sink inversion codes to identify the
basis of the discrepancy in carbon cycle budgets and to forecast future atmospheric CO2 with
greater confidence.
1
Introduction:
Understanding the global distribution of carbon dioxide is of critical importance for
predicting and perhaps mitigating the extent and severity of global warming. The primary
motivation behind the drive to understand the spatial distribution of carbon dioxide (CO2) is the
identification of this greenhouse gas's sources and sinks, which may ultimately determine the
course of climate change in the coming decades.1 There are serious policy implications
contingent upon the severity of the incipient global warming, 2 as current model estimates of
climate change predict an increase of between 1.4 and 5.8 C by the end of this century.
Moreover, the warming rates may differ substantially for different regions and higher latitudes
are predicted to warm at rates much higher than the global average.3 Heightened levels of CO2
contribute substantially to this climate change and so understanding the sources and sinks of this
greenhouse gas is of singular importance to predicting the course of global warming. The
current network of CO2 measurements from ground and aircraft data maintained by NOAA’s
Climate Monitoring Diagnostics Laboratory (CMDL) has been able to record background levels
of CO2 successfully. However, the CMDL network is too sparse to provide the data density
needed to infer CO2 fluxes on regional and sub-regional scales.4 For example, the tabulation of
anthropogenic carbon outputs and natural sinks cannot account for the “missing” carbon sink of
1.7 Pg/yr, which represents over one-sixth of the anthropogenic output.5 It has been proposed
that this discrepancy can be addressed with satellite measurements of sufficient resolution and
accuracy.6 As seen in Figure 1, satellite measurements can outperform the CMDL network
because they acquire much more data with uniform spatial sampling with standardized global
sampling. Therein lies the drive for the Orbiting Carbon Observatory (OCO) instrument, which
aims to measure CO2 column abundance to within 0.3% of the true value.7 Nevertheless, it may
be possible to use data from the operational Atmospheric Infrared Sounder (AIRS) instrument to
provide auxiliary CO2 information to assist in the algorithm improvement for the OCO and to
create an independent source of CO2 data. As part of my doctoral thesis, I plan to use both sets of
satellite measurements to fortify the CO2 mapping efforts and carefully integrate the data
products to improve the accuracy of what is delivered to the source-sink inversion algorithms.
With monthly-averaged CO2 data at better than 2.5 ppmv accuracy for a 5° latitude by 5°
longitude grid, the source-sink inversions will be able to reduce uncertainties in the forecast of
future atmospheric CO2 levels.
Background:
The Atmospheric Infrared Sounder (AIRS) instrument has been operational since
November 2002 and was primarily designed as a satellite to improve weather forecasting.8 The
spacecraft travels in a sun-synchronous orbit with a 1:30 PM local crossing at a nominal altitude
of 705 km and uses a highly-advanced grating spectrometer to acquire thermal emission data in
2378 spectral channels between 650 and 2500 cm-1 (3.7 to 15.4 m). The instrument also has a
4-channel visible/near-infrared module that senses between 0.4 and 1.0 m. It has previously
been suggested that AIRS spectral data in the two strong CO2 bands (667 cm-1 and 2350 cm-1)
could be used to retrieve CO2 abundances,9 although the estimated accuracy is only several ppmv
for a single sounding.10 Because the CO2 bands being measured are completely saturated, AIRS
data is a first sensitive to temperature which is not itself known with great accuracy. Therefore,
2
the retrieval algorithm must find a way to constrain the temperature appropriately so that desired
accuracy may be achieved.
The OCO instrument is scheduled to launch in August, 2007 and is being designed and
developed to measure the dry column-averaged abundance of carbon dioxide at a fine resolution
in the lower troposphere.11 OCO will measure sunlight reflected from the earth's surface.
Spectra recorded in three near-infrared channels will maximize measurement sensitivity to CO2
concentrations near the surface . The 1.61 m band will measure CO2 absorption in an undersaturated line while the 2.06 m will provide some CO2 information but will be primarily used to
characterize aerosols for each sounding. In order to provide a pressure metric, OCO will also
measure oxygen, which exhibits a particularly uniform profile concentration, using the O2 Aband at 0.76 m. The aim of this research is to map the data to a 1° latitude by 1° longitude grid
with an accuracy of 0.3% for monthly mean column averaged dry-air mole fraction of CO2.12
Due to the nature of the radiance being measured, OCO is more sensitive to the lower
troposphere, while AIRS gathers more information in the middle and upper troposphere (refer to
Figure 2). Therefore, the data may be complementary and it may be possible to integrate the
data sets and make the CO2 retrieval system more robust.
Radiative Transfer and Inversions:
Retrieving gas concentration values from remote sensing measurements is a very
challenging task and has been the subject of much recent research.13 Measurements made from a
satellite platform in a non-scattering atmosphere can be modeled using the equation of radiative
transfer for a plane-parallel atmosphere as shown in equation (1):

I TOA (  , )  Bs ( (0), )T (0, z,  )   B( ( z ' ), )
0
T ( z ' ,0,  )
d z'
z '
(1)
where I is the specific intensity of radiation, or radiance, at wavenumber measured by the
satellite with a solar zenith angle whose cosine is equal to , Bs((0),) is the Planck emission at
wavenumber from the surface at temperature (0), (z') represents the temperature at height z',
and T(z',z, ) is the transmission between z' and z at wavenumber 
If the atmospheric temperature profile were known exactly and there were no internal
sources of radiation, it would be possible to invert equation (1) to find the gas concentrations of
species that absorb at the wavelength of interest. However, there are several factors which
greatly complicate the retrieval process. First, equation (1) is often ill-conditioned. Second,
there is no analytic form that describes the complete atmospheric state and its absorption and
emission characteristics, so discrete methods must be employed. Third, the equation of radiative
transfer is only linear under select circumstances, requiring the employment of nonlinear
methods. Finally the most confounding factor of remote sensing retrievals is that the
measurement vector, which is a vector of radiance values that define the spectrum, does not
uniquely determine the state vector, so a correct retrieval is not guaranteed.
Nevertheless, it is possible to use ancillary data and a careful analysis of the information
content of the measurements to obtain a maximum likelihood profile. Several techniques have
been developed to address the difficulties associated with atmospheric remote sensing retrieval.
These techniques solve the inverse problem based on the Optimal Estimation Theory as
described by Rodgers.14 Such algorithms rely heavily on a forward model, which is sufficient to
3
reproduce top-of-atmosphere radiances for a given state vector. The inversion techniques start
with an a priori estimate of the state vector and then iterate a recursive zero-finding method by
adding an update value  to find a state that closely simulates the measurement vector. This  is
a function of the current state xi, the a priori state xa, the measurement y, the forward model
evaluated at the current state F(xi), the Jacobian matrix of the forward model with respect to the
state vector K, the covariance matrix of the state vector Sa , and the covariance matrix of the
measurement vector S.
One useful technique called the Levenberg-Marquardt revised method (L-Mr) combines
the Gauss-Newton and steepest-descent methods using a hybridization parameter i. By
judiciously updating the i parameter, it is possible to approach a solution without excessive
iteration and with reasonable accuracy. The original Levenberg-Marquardt method was prone to
numerical instability, leading to the development of a revised method15 which is described by
equation (2):


T 1
T 1
1
x i1  x i  1  i S1
a  K i S K i  * K i S K i * y  F x i  S a * x i  x a 
1
(2)
where the L-Mr allows for multiple updates to the weighting function matrix.
In order to test the improvement that each iteration of the L-Mr adds to the previous
 estimate, a cost-function test is commonly used. The cost-function, or test, is a measure of the
probability that the measurement vector from the current iterative state of the L-Mr is not
significantly different from the actual measurement. Additionally, the algorithm analyzes the
information content introduced by the retrieval algorithm and determines if that information has
been effectively incorporated into the updated state.
Current State of Research:
Preliminary retrieval algorithms have been developed for both the AIRS and OCO
instruments. An initial analysis of the information content from the AIRS Radiative Transfer
Algorithm (AIRS-RTA)16 data suggests that the proposed retrieval scheme is indeed feasible.
Single species test-case retrievals of temperature and CO2 have been conducted successfully but
the question of retrieval precision remains. Regrettably, sensitivity tests have shown that the
AIRS-RTA cannot describe many of the spectral features of the ν3 band of CO2 leading us to
work with the Fast Atmospheric Signature Code17 which is a line-by-line code than can also
model aerosol and cloud effects.
A retrieval algorithm for the OCO instrument has been developed in part by Professor
Yung’s student, Vijay Natraj, and it is available to me. In selected scenarios, the algorithm was
able to retrieve surface pressure and column averaged dry-air mole fraction of CO2 with the
desired accuracy. The algorithm uses the Discrete Ordinate Radiative Transfer code as its
forward model which is accurate but computationally-expensive code.18 Other forward models
including LIDORT19 and SMART (Spectral Mapping Atmospheric Radiative Transfer by D.
Crisp) may cut down computation time. Currently, a complete retrieval code is still being
developed by the OCO Science Team which is based at the Jet Propulsion Laboratory (JPL).
Over the course of my research as a doctoral student at Caltech, I have found that the
presence of JPL to be absolutely invaluable. Both the AIRS and OCO projects will be carried
from inception to completion at JPL and the scientists and engineers that manage and advise
these projects are well-qualified to help me in the course of my studies. For the AIRS data, Dr.
4
Luke Chen and Dr. Moustafa Chahine at JPL will be very helpful, as both bring great expertise
to bear on the retrieval problem. For the OCO project, I have been and will continue to be
working with the OCO science team on algorithm development which includes weekly meetings
at JPL. So far, the work with JPL scientists and engineers has been very illuminating and
exciting, and as a result, my faculty advisor and I spend a significant amount of time at JPL. The
laboratory’s proximal location to Caltech affords me the ability to meet regularly with experts in
my field and I look forward to continuing to do so.
Proposed Work:
Both the AIRS and OCO retrieval algorithms need to be improved. Currently, I perform
ancillary work for the OCO retrieval algorithm but I am developing my own retrieval algorithm
for AIRS data. Consequently, I am focusing most of my current efforts on building those
algorithm components necessary for the AIRS retrieval.
At this time, the AIRS retrieval is at this time a standard implementation of Optimal
Estimation Theory but it will incorporate several novel methods that may improve precision.
First, various meteorological data reanalyses including those performed by NCEP20 and
ECMWF21 will be used to create climatological mean values and covariance matrices for most
components of the state vector on a latitude, longitude, and altitude grid. While climatological
data is sufficient for upper atmospheric layers, it is inadequate to describe surface characteristics.
As a result, real-time ECMWF surface data will be incorporated into the a priori state vector.
There is no such reliable CO2 information in the climatology data, so the results of a chemicaltransport model will be used to create a climatology that has some bearing on actual carbon
dioxide profiles.22
The AIRS retrieval will not use a simple conjugate-gradient technique to retrieve the state
vector. We have shown that there are many local minima which closely describe the state
vector; therefore, a simple nonlinear zero-finding iteration method will probably be unable to
find the most-likely state vector given a complicated state space. We plan to test other nonlinear
zero-finding techniques even though some are very computationally-intensive. It is unclear
whether the method of Monte Carlo simulated annealing will converge in a reasonable amount of
computation time, so we are currently interested in testing a basin-hopping method for global
optimization. This latter technique, if implemented properly, may be able to avoid local minima
while still performing a limited number of forward model calculations.
The AIRS retrieval algorithm that we develop will need to pass a series validation tests
by June, 2004 before it can be implemented. In the first test, we will compare both measured
and calculated spectra during the spring and the fall for a site in the northern hemisphere over the
ocean in the absence of sunlight. We expect a detectable difference in the spring and fall spectra
that correspond to expected CO2 changes. Next, we will compare the monthly-mean measured
and calculated spectra for cloud-cleared nighttime scenes over a site in the northern Pacific and a
site in the southern Pacific. Again, we expect to be able to detect the sharp meridional gradient
in CO2 concentration across the equator over the Pacific Ocean.
Over the summer, the AIRS code will be tested and adapted for a wide variety of
atmospheric scenarios. First, it will be improved to accommodate “popping” (a phenomenon
whereby individual AIRS channels exhibit excess random noise) and noisy channels. Next, a
subroutine will be developed to determine the appropriate bases for the state and measurement
spaces. Also, the algorithm will need to be modified to account for topography and sub-tropical
and temperate regions, where carbon dioxide sources and sinks may change rapidly.23
5
Once an adequate retrieval code is prepared, its performance must be verified using more
accurate carbon dioxide measurements from other sources. Validation methods including
ground-based testing facilities,24 aircraft measurements,25 and solar FTIR spectroscopy26 can all
measure CO2 over a limited spatial scale with accuracy well in excess of that possible from AIRS
or even OCO. Given the results of the information content analyses for AIRS and OCO, we
expect both retrieval algorithms to improve upon a priori CO2 values. Therefore, if the retrieval
code does not perform to our specifications, the choice of measurement and state bases or a
priori constraints may have to be recalibrated. If recalibration fails, we may need to develop a
system for continuous integration of ground-validation data.
Several groups are currently working on CO2 retrieval from AIRS data and but have not
surmounted the difficulties associated with the problem specifications. In particular, the retrieval
scheme must choose the most effective state and measurement spaces, and it must address the
effects of cloud contamination and uncertainties in profile temperature.
Because the ν2 and ν3 bands of CO2 are so saturated, satellite radiance measurements are
first sensitive to temperature. Therefore, uncertainty in profile temperature on the order of 0.5 K
may have a confounding effect on the CO2 retrieval. Fortunately, ECMWF real-time and
reanalysis data set may provide this level of accuracy. However, the presence of clouds will lead
to significant temperature profile uncertainty. One solution to the cloud-cover problem is simply
to excise those spectra for which there is significant cloud cover, but this technique is done at the
expense of lost carbon dioxide information. There are many ground prints that experience
persistent cloud-cover. Therefore, we will analyze to what extent some of these cloudcontaminated pixels can be retained and while still contributing to increased knowledge of
carbon dioxide spatial distribution information.
Once both the OCO retrieval algorithm and the AIRS retrieval algorithm have been made
robust, they will be integrated to form a generalized CO2 retrieval scheme. The specifics of this
integration remain to be determined, but once the retrieval codes are operational, results will be
delivered to the source-sink inversion codes. These codes will identify the missing regionalscale carbon sinks and ultimately improve the forecast of future CO2 levels.
Figures:
0.6
A) Flask
0.0
1.2
0.6
Flux Retrieval Errors
(GtC/yr/region)
1.2
B) Satellite
0.0
Fig. 1: Carbon flux errors for 26 continent/oceanbasin-sized zones retrieved from inversion studies. A)
Studies using data from CO2 stations produce flux
residuals that exceed 1 GtC/yr in some zones. B)
Inversion tests using global XCO2 pseudo-data with 1
ppm accuracy reduce the flux errors to <0.5
GtC/yr/zone19.
Fig. 2: A comparison of the averaging kernels
(matrix which provides approximate linear
mapping of measurement space to state space)
for column CO2 soundings using NIR
absorption of reflected sunlight and thermal
IR emission.
6
References:
1
IPCC (2001). Intergovernmental Panel on Climate Change Assessment: Climate Change: The Scientific Basis.
Third Assessment: Chapter 3. <http://www.grida.no/climate/ipcc_tar/wg1/>
2
Ibid: Chapter 9 and Summary for Policymakers.
3
Ibid: Chapter 9.
4
Rayner, P. J., D. M. O'Brien (2001). "The utility of remotely sensed CO 2 concentration data in surface source
inversions." Geophysical Research Letters. 28 (12): 175-178.
5
Schimel, D.S., et al. (2001). “Recent patterns and mechanisms of carbon exchange by terrestrial ecosystems.”
Nature. 414 (6860): 169-172.
6
O’Brien, D.M., Rayner, P.J. (2002). “Global Observations of the carbon budget: CO 2 column from differential
absorption of reflected sunlight in the 1.6 µm band of CO 2.” Journal of Geophysical Research. 107 (D18), ACH
6(1-16).
7
Crisp, D., et al. (2002). “The Orbiting Carbon Observatory (OCO) Mission”
<http://oco.jpl.nasa.gov/pubs/OCO_Cospar_2002_final.pdf>
8
Aumann, H. H., M. T. Chahine, et al. (2003). "AIRS/AMSU/HSB on the aqua mission: Design, science objectives,
data products, and processing systems." IEEE Transactions on Geoscience and Remote Sensing. 41 (2): 253-264.
9
Ibid.
10
Fishbein, E., et al. (2003). “Formulation and Validation of Simulated Data for the Atmospheric Infrared Sounder
(AIRS).” IEEE Transactions on Geoscience and Remote Sensing. 41 (2): 314-329.
11
Kuang, Z. M., et al. (2002). "Spaceborne measurements of atmospheric CO2 by high-resolution NIR spectrometry
of reflected sunlight: An introductory study." Geophysical Research Letters. 29 (15): 1716-1719.
12
Crisp, D., et al. (2002). “The Orbiting Carbon Observatory (OCO) Mission”
<http://oco.jpl.nasa.gov/pubs/OCO_Cospar_2002_final.pdf>
13
Milman, A.S. (1999). Mathematical Principles of Remote Sensing: Making Inferences from Noisy Data.
Chelsea, MI: Sleeping Bear Press, Ch. 10-13.
14
Rodgers, C. D. (2000). Inverse Methods for Atmospheric Sounding: Theory and Practice. London, World
Scientific.
15
Fletcher, R. Practical Methods of Optimization. Chichester, New York: John Wiley & Sons, 1987.
16
Strow, L. L., et al. (2003). "An overview of the AIRS radiative transfer model." IEEE Transactions on Geoscience
and Remote Sensing. 41 (2): 303-313.
17
Smith, H.J.P. et al. (1978) “FASCODE- Fast Atmospheric Signature Code (Spectral Transmittance and
Radiance).” Air Force Geophysics Laboratory Technical Report. AFGL-TR-78-0081, Hanscom AFB, MA.
18
Spurr, R.J.D., et al. (2001) “A linearized discrete ordinate radiative transfer model for atmospheric remotesensing retrieval.” Journal of Quantitative Spectroscopy and Radiative Transfer. 68 (6): 689-735.
19
Ibid.
20
Kalnay, E., et al. (1996). “The NCEP/NCAR 40-year reanalysis project.” Bulletin of the American
Meteorological Society. 77 (3): 437-471.
21
Simmons, A.J., et al. (2001). “The ERA-40 Project Report Series No. 1” Proceedings of Workshop on ReAnalysis 2001. http://www.ecmwf.int/publications/library/ecpublications/_pdf/ERA40_PRS_1.pdf
22
Olsen, S.C., et al. (2004). “Differences between surface and column atmospheric CO 2 and implications for
carbon cycle research.” Journal of Geophysical Research-Atmospheres. 109 (D2): art. No. D02301.
23
Bousquet, P., et al. (2000). “Regional Changes in Carbon Dioxide Fluxes of Land and Oceans Since 1980”
Science. 290 (5495), 1342-1346.
19
Rayner, P. J. and D. M. O'Brien (2001). "The utility of remotely sensed CO 2 concentration data in surface source
inversions." Geophysical Research Letters. 28 (12): 175-178.
24
GLOBALVIEW-CO2 (2003). Cooperative Atmospheric Data Integration Project - Carbon Dioxide. CD-ROM,
NOAA/CMDL, Boulder, Colorado. [Also available on Internet via anonymous FTP to ftp://ftp.cmdl.noaa.gov,
Path: ccg/co2/GLOBALVIEW].
25
Anderson, B. E., et al. (1996). “Airborne Observations of the Spatial and Temporal Variability of Tropospheric
Carbon Dioxide.” Journal of Geophysical Research. 101 (D1), 1985-1997.
26
Yang, Z. et al. (2002). “Atmospheric CO2 retrieved from ground-based near IR solar spectra.” Geophysical
Research Letters. 29 (9): 53
7