Vertical Weighting Functions & Validation of
Satellite Retrievals
Chris Barnet
NOAA/NESDIS/STAR
(the office formally known as ORA)
University of Maryland, Baltimore County (Adjunct Professor)
AIRS Science Team Member
NPOESS Sounder Operational Algorithm Team Member
GOES-R Algorithm Working Group – Chair of Sounder Team
NOAA/NESDIS representative to IGCO
July 27, 2006
MSRI-NCAR Summer Workshop on
Data Assimilation for the Carbon Cycle
Outline for Todays’s Lecture
• A question from yesterday.
– What are they.
– How are they used.
• Validation Techniques.
– Discussion of observation types (mostly references).
– Comparisons of CH4 and CO2 product with in-situ.
• Summary of some papers on using AIRS CO2
products in carbon assimilation systems.
• Trace gas product correlations – A better way to use
AIRS data?
2
A Question From Jeremy
1. What does the K matrix look like for
temperature and moisture?
2. Why is there more vertical information
about temperature than CO2?
3
Example of T(p) & q(p) Channel
Kernel Functions
AIRS 15 µm (650-800 cm-1) band
AIRS 6.7 µm (1200-1600 cm-1) band
K = dR/dT
K = dR/dq
4
Brightness Temperature (K)
Weak Lines (Water & CO2) in Window
Region Sound Boundary Layer Temperature
Texas
Spikes down Cooling with height
(No inversion)
Spikes up Heating with height
Ontario
(low-level inversion)
5
Example of 15 µm spectrum with “inbetween” the lines marked with blue dots
Lines up (in emission): T(z)
increases with altitude
Lines down (in absorption):
T(z) decreases with altitude
6
From Yesterday: K = dR/dCO2
Polar
Mid-Latitude
Tropical
TPW = 0.5 cm
TPW = 1.4 cm
TPW = 2.5 cm
Isothermal vertical
structure weakens
sensitivity
moisture optical
depth pushes peak
7
sensitivity upwards
Why are CO2 channel functions broad & all at the same
altitude while T(p) functions have profile information?
• Spectroscopy: The CO2 lines are strong narrow lines. Temperature
affects the width (and hence the channel transmittance) while # of
CO2 molecules affects the strength. Once the line is saturated (near
the surface, where p is large) we loose sensitivity.
• Radiative transfer: The temperature enters both in the absorption
coefficient and in the Planck function.
8
Why is CH4 considered to be
25x more powerful as a
greenhouse gas than CO2?
9
Why is CH4 considered to be 25x more
powerful as a greenhouse gas than CO2?
• At 380 ppm the CO2 lines are saturated and
as CO2 increases the absorption of energy
changes as the log(N).
• CH4 is 1.8 ppm and the lines are not
saturated. As the amount of CH4 changes
the absorption is linear w.r.t # of molecules.
10
Retrieval Averaging Functions
See
1)Rogers 2000, pg. 43-44 &
pg. 83-85
2)Rodgers and Conner 2003
3) My notes – section 8.12.1
11
Retrieval Vertical Weighting
Functions
• Our Retrieval Equation Can Be Written As
• Note that this equation is really a weighting average of
the state determined via radiances and the a-priori.
– The radiance covariance can be written as KTN-1K, in
geophysical units, and
– The product covariance is given by [KTN-1K + C-1]-1
12
We can derive the Averaging
Function our minimization equation
• We can linearize the retrieval about the “truth” state
• And simplify by replacing the region highlighted in
green above with the variable G
13
Computing the Vertical Averaging
Function
• The vertical averaging function is the amount of the
answer that came from the radiances
• And I-A is the amount that came from the prior
Retrieval covariance
Inverse of a-priori
14
covariance
Value of the Vertical Averaging
Function
• A is the retrieval weighing of the channel kernel functions (think
of a retrieval as an integrator of data)
• A tells you how much the observations were believed.
• I-A tells you how much of the a-priori was believed.
• When comparing other measurements (such as high vertical
resolution sondes or aircraft) the validation measurements
– Must have similar vertical smoothing
– Should be “degraded” by the fraction of the prior that entered the solution
(i.e., we know we can’t measure 100%)
• When using AIRS products the A maxtrix
– Tells you the vertical correlation between parameters
– Tells you how much to believe the product and where to believe the
product.
– You can remove our a-priori assumptions and substitute your own.
15
We can use averaging function to optimally
smooth the truth for comparisons
Aj,j
retrieval
“convolved
truth”
a-priori
“truth”
This retrieval is
only believed at
the 50% level
16
Application of Vertical Averaging
Functions with modeled CO2
• Comparison of CO2
product and Kawa 2004
model for April 2005
• At first glance it looks like
the retrieval and model do
not agree.
• But if we “degrade” the
model with the retrieval apriori they agree quite well.
• To use AIRS products to
nudge an assimilation, the
vertical weighting function
tells the model when and
where to believe the AIRS
products.
17
Or We Can compute a Averaging
Function via Brute Force
1.
2.
3.
4.
Start with the retrieval state, X0
Perturb X0 in some atmosphere layer by Xk
Compute change in radiance, R(X0+Xk)-R(X0)
Compute a new retrieval, Xk, using the perturbed
radiance.
5. Xk-X0 is the jth column of Akj
6. Goto Step 1 and compute another row of A
This method has the advantage that the entire
system, including cloud correction and multipleinteracting and non-linear retrieval steps can be
analysed.
18
The “Brute Force” Averaging provided a
Sanity test for Internal Averaging Functions
Ajk & trace{A} via Brute Force for T(p)
A = G*K
19
Validation
20
“what is truth”
• Compare to ECMWF & NCEP Models (e.g., See Susskind, 2005)
– Can compare complete global dataset
– Differences can be model or retrieval errors
– Implicitly validating against all other instruments (space-borne, sondes, buoy’s
etc.) used in analysis
• Compare to Radiosondes, Ozonesondes (e.g., See Tobin, 2006, Divakarla,
2006)
– Only a couple hundred “dedicated” sondes are flown per year. Usually we fly
2 sondes so we can see lower and upper air at overpass time.
• Sondes can take 1-2 hours to ascend
• Sondes can drift up to 100’s of km’s
– A few hundred sondes are launched globally per day that are within 300 km
and +/- 1 hour of our overpass.
• Different sonde instruments, quality of launches, etc.
• In-situ intensive experiments with sondes, aircraft and LIDAR.
– Have participated in INTEX-NA6 AEROSE, START, MILAGRO, INTEX-B,
AMMA
21
An example of things that go wrong
with “truth”
These 2 sondes were
launched 1.5 hours
apart from same
location.
22
Example of Validation of
Methane Products from AIRS
with ERSL/GMD surface
flasks and aircraft
23
Also providing the vertical information
content to understand CH4 product
AIRS mid-trop measurement
column
Fraction Determined from
AIRS Radiances
CH4 total column f/ transport model
(Sander Houweling, SRON)
Peak Pressure of AIRS
Sensitivity
24
Comparison of CH4 product &
ESRL/GMD Continuous Ground Site
Barrow
Alaska
3deg. x 3deg.
gridded retrieval
averaged over 60-70
lat, & -165 to -90
lng
25
Comparisons of AIRS product to
ESRL/GMD Aircraft Observations
ESRL/GMD
aircraft profiles
are the best
validation for
thermal
sounders since
they measure a
thick
atmospheric
layer.
26
ESRL/GMD Flask Data from Poker Flats,
Alaska: Seasonal cycle is a function of altitude
7.5 km
385 mb
5.5 km
500 mb
1.5 km
850 mb
Surface Flasks
(Barrow)
27
We need to determine how much of our
CH4 signal is from stratospheric air
Dobson-Brewer circulation
UT/LS region in
high latitudes
has “older” air.
Can depress high latitude,
high altitude methane
signals in winter/spring
time-frame.
We will
explore tracer
correlations to
unravel surface
vs
stratospheric
sources.
(working w/ L.
Pan, NCAR)
28
Example of Validation of
Carbon Dioxide Products from
AIRS with ESRL/GMD
Marine Boundary Layer and
Aircraft Products and
Japanese Commercial Aircraft
29
Also providing the vertical information content
& comparing CO2 product with models
AIRS mid-trop
measurement column
CO2 Transport Model
Randy Kawa (GSFC)
Fraction Determined
from AIRS Radiances
Averaging Function
Peak Pressure
30
Preliminary Comparisons
to ESRL/GMD aircraft
•
Comparison of AIRS &
ESRL/GMD observations..
•
•
•
•
•
•
Usually  5 hour time
difference
Limit retrievals within 200
km of aircraft.
Spot vs. regional sampling
Retrieval is average of
“good” retrievals
• 3 – 50 ret’s are used in
each dot.
 = ± 3.1 ppmv,
correlation = 0.83
Investigation of outliers is
in-work.
31
Comparisons to JAL aircraft
observations & ESRL/GMD MBL model
ESRL/GMD Marine
Boundary Layer
Model (surface
measurement)
AIRS CO2
retrieval from
GRIDDED dataset
– mid-trop thick
layer measurement
Matsueda et al.
2002 aircraft –
single level
measurement
JAL Aircraft data provided by H. Matsueda
32
Same as before, but in-situ
CO2 adjusted by a-priori in retrieval
In-situ data is adjusted by
the % of a-priori in our
regularized retrieval.
This depresses the
seasonal amplitude of the
in-situ data and is a
gauge of our retrieval
performance.
Differences should exist
between single level
(surface or altitude)
observations and AIRS
thick layer observations.
JAL Aircraft data provided by H. Matsueda
33
Again, to what extent does
stratospheric age of air play a role?
Surface measurements (dashed line)
and model of 500 mb concentration
(solid line) can differ by 5 ppm
(NOTE: Vert. Scale is 350-385 ppm)
2000
2002 2004
Brewer-Dobson effect has altitude,
latitude, and seasonal variation with a
maximum in northern winter/spring.
Model runs of Brewer-Dobson
circulation effect are courtesy of
Run-Lie Shia, Mao-Chang Liang,
Charles E. Miller, and
Yuk L. Yung, California Inst. Of
Technology & NASA Jet
Propulsion Lab.
34
Example of Validation of CO2
measurements with Models
35
Chevallier, Engelen & Peylin,
GRL, 2005
• Compared CO2 derived from ECMWF
4DVAR analysis of 18 AIRS channels (R.
Engelen’s CO2 product) vs Laboratoire de
Météorologie Dynamique (LMDZ) GCM
driven by surface flux climatology
– Large systematic differences at high latitudes
– Significant sea/land contrast
– Use of a constant averaging kernel may contribute
to biases.
36
Chevallier (continued)
37
Tiwari, et al., JGR 2006 (in press)
• CO2 flux estimates of Rodenbeck 2003 used as boundary
conditions for TM3 (4x5 deg, 19 , NCEP winds) & LMDZ
(2.5x3.75 deg, 19 , ECMWF winds)
– Averaged monthly fluxes for 1993-2001 and used as driver of transport
for 2000-2003
– Spun up model from Jan. 2000-Dec. 2002
• Compared to R. Engelen’s product to explore two potential
pathways for transport of CO2
– North hemisphere mid-lat air laden w/ fossil fuel via northern high
latitudes along upward sloping constant pot. Temp surfaces.
– Dispersal of CO2 laden air in the PBL toward the tropics and
subsequent upwards via deep convection.
• Conclusions
– Models agree with each other more than with retrievals.
– Hovmoeller diagrams (time vs latitude) show that models transport the
CO2 via the northern pathways whereas in the retrievals the CO2
shows up instantaneously.
38
– More work is needed.
Tiwari: Comparison of Models and
R.Engelen’s AIRS CO2 Product
39
Tiwari: Comparison of Models and
R.Engelen’s AIRS CO2 Product
40
Both of These Studies Have Caveats
• Used a constant averaging
function that is probably
too high.
• Noted land/sea boundaries
were evident in product.
• Used the ECMWF derived
CO2 that
– Only uses 18 channels
– Uses ECMWF 4DVAR
analysis that already has
used AIRS radiance data.
– Uses internal clear flag that
appears to select too many
cases as clear.
41
Can we “Validate” our
Product Using Atmospheric
Correlations
Or
Can AIRS product
correlations have scientific
value
42
Suntharalingam, Jacob, Palmer, Logan,
Yantosca, Xiao and Evans 2004
Biofuel & biomass would be low numbers  10-12
Biosphere would be very large numbers  800-1000
Fossil fuel would be  25 w/o CO controls,  100 with
43
Pan, Wei, Kinnison, Garcia, Wuebbles,
and Brasseur (submitted to JGR)
• Using aircraft measurements of O3, CO,
and H2O in the upper troposphere/lower
stratosphere to validate MOZART-3 &
WACCM3 model.
– Chemical discontinuity at tropopause caused by
changes in thermal and dynamic fields (BrewerDobson circulation)
44
Pan et al, 2006: Example of ER-2
Observations
Profiles from 38 ER-2 flights from approximately 5-18
km near Fairbanks Alaska (65N, 147W)
45
O3,CO correlations
Green cases: below
thermal tropopause
Red cases: above
thermal tropopause
Case.1 MOZART-3
w/ ECMWF Op
winds
Case.2 MOZART-3
w/ ECMWF Exp471
winds
Case.3 WACCM3
46
O3,H2O Correlations
Green cases: below
thermal tropopause
Red cases: above
thermal tropopause
Case.1 MOZART-3 w/
ECMWF Op winds
Case.2 MOZART-3 w/
ECMWF Exp471 winds
Case.3 WACCM3
47
So How Does This Relate to AIRS
measurements?
• We are collaborating with Laura Pan (NCAR) to
compare AIRS products with Aircraft Products
• We are computing correlations of AIRS products
to see if we can distinguish air mass types.
– Can we identify cases affected by Brewer-Dobson
circulation and improve our ESRL/GMD & Matsueda
comparisons?
– Can we identify biomass regions and chemical
conversion of CO?
48
Preliminary Analysis Looks
Promising
49
Example of pollution events
Domes of CO2 over cities?
Balling et al. , 2001
Idso et al. 2001
50
So maybe the utility of thermal
sounders has yet to be exploited
• AIRS has measured global tropospheric CO2 & CH4 for the first
time.
• AIRS has a unique capability to intercompare tropospheric
products of temperature, water, O3, CO, CH4, and CO2.
• We expect to learn new things from this dataset.
• We are exploring diurnal signals and hope to identify large
pollution or biosphere events over the lifetime of these instruments.
• We are exploring the use of trace gas correlations within the AIRS
products.
• We want to work with transport modelers to compare our product
to a realistic emission scenario for CO2 with proper vertical
weighing functions.
• Other ideas?
51
References
AIRS Instrument & Retrieval Algorithms
•
Aumann, H.H., M.T. Chahine, C. Gautier, M.D. Goldberg, E. Kalnay, L.M. McMillin, H.
Revercomb, P.W. Rosenkranz, W.L. Smith, D.H. Staelin, L.L. Strow and J. Susskind 2003.
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•
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cover. J. Geophys. Res. v.111 doi:10.1029/2005JD006272, 19 pgs. {PDF FILE =
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•
Susskind, J., C.D. Barnet and J.M. Blaisdell 2003. Retrieval of atmospheric and surface
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•
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52
References
Analysis of AIRS C products
•
Barkley, M.P., P.S. Monks and R.J. Engelen 2006. Comparison of SCIAMACHY
and AIRS CO2 measurements over North America during the summer and
autumn of 2003. Geophys. Res. Lett. (in press). {PDF FILE = grl_fsi_v1.pdf}
•
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the estimation of CO2 sources and sinks. Geophys. Res. Lett. v.32 L23801
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•
Tiwari,Y.K., M. Gloor, R.J. Engelen, F. Chevallier, C. Rodenbeck, S. Korner, P.
Peylin, B.H. Braswll and M. Heimann 2006. Comparing CO2 retrieved from
AIRS with model predictions: implications for constraining surface fluxes and
lower to upper tropospheric transport. J. Geophys. Res. (in press).
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53
References
AIRS Trace Gas Algorithms
•
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•
Crevoisier, C., S. Heilliette, A. Chedin, S. Serrar, R. Armante and N.A. Scott 2004. Midtropospheric CO2
concentration retrieval from AIRS observations in the tropics. Geophys. Res. Lett. v.31 p.17106-17110.
doi:10.1029/2004GL020141 {PDF FILE = 2004GL020141.pdf}
•
Crevoisier, C., A. Chedin and N.A. Scott 2003. AIRS channels selection for CO2 and other trace gases
retrieval. Quart. J. Roy. Meteor. Soc. v.128 p.2719-2740. doi:10.1256/qj.02.180 {PDF FILE =
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•
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within an operational 4D-Var data assim. system: Results and Validation. J. Geophys. Res. v.110 D18305
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•
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with respect to CO2. J. Appl. Meteor. v.43 p.373-378. {PDF FILE = Engelen_jap2004.pdf}
•
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54
References
Averaging Functions & Validation
•
Divakarla, M.G., C.D. Barnet, M.D. Goldberg, L.M. McMillin, E. Maddy, W.W. Wolf, L. Zhou and X. Liu 2006. Validation of
Atmospheric Infrared Sounder temperature and water vapor retrievals with matched radiosonde measurements and forecasts. J.
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•
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•
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•
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•
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•
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•
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•
Tobin, D.C., H.E. Revercomb, R.O. Knuteson, B.L. Lesht, L.L. Strow, S.E. Hannon, W.F. Feltz, L.A. Moy, E.J. Fetzer and T.S.
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55
References
Circulation & Gas Correlations
•
Shia, R.L., M.C. Liang, C.E. Miller and Y.L. Yung 2006. CO2 in the upper
troposphere: influence of stratosphere-troposphere exchange. Geophys. Res.
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•
Palmer, P.I., P. Suntharalingam, D.B.A. Jones, D.J. Jacob, D.G. Streets, Q. Fu,
S.A. Vay and G.W. Sachse 2006. Using CO2:CO correlations to improve
inverse analyses of carbon fluxes. J. Geophys. Res. v.111 D12318
doi:10.1029/2005JD006697, 11 pgs. {PDF FILE = 06jgr_palmer_co_co2.pdf}
•
Suntharalingam, P., D.J. Jacob, P.I. Palmer, J.A. Logan, R.M. Yantosca, Y.
Xiao and M.J. Evans 2004. Improved quantification of Chinese carbon fluxes
using CO2/CO correlations in Asian outflow. J. Geophys. Res. v.109 D18S18
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56
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CO2 Domes, Fossil Fuel Use
•
Balling Jr., R.C., R.S. Cerveny and C.D. Idso 2001. Does the urban CO2 dome of
Phoenix, Arizona contribute to its heat island? Geophys. Res. Lett. v.28 p.45994601. {PDF FILE = 2000GL012632.pdf}
•
Idso, C.D., S.B. Idso and R.C. Balling Jr. 2001. Intensive two-week study of an
urban CO2 dome. Atmospheric Environment v.35 p.995-1000. {PDF FILE =
01_idso_domes.pdf}
•
Deffeyes, Kenneth 2005. Beyond oil: The view from Hubbert's peak. Hill and
Wang, (div of Farrar, Straus and Giroux) NYC 202 pgs.
•
Deffeyes, Kenneth 2001. Hubbert's peak: the impending world oil shortage.
Princeton University Press 208 pgs.
•
Eshel, G. and P.A. Martin 2006. Diet, energy, and global warming. Earth
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•
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57