Lecture 3

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					    TransCom 3 Level 2 Base Case
Inter-annual CO2 Flux Inversion Results
                  Current Status

              David Baker, Rachel Law,
             Kevin Gurney, Peter Rayner,
              TransCom3 L2 modelers*,
               and the producers of the
            GLOBALVIEW-CO2 data product

   *(P. Bousquet, L. Bruhwiler, Y-H Chen, P. Ciais, I. Fung,
   K. Gurney, M. Heimann, J. John, T. Maki, S. Maksyutov,
      P. Peylin, M. Prather, B. Pak, S. Taguchi, Z. Zhu)
                      14 June 2004
• TransCom3 and the Level 2 inter-annual
• Inter-annual inversion results
  – Changes in base case since Nov 2002
  – Inter-annual variability (IAV) results
      • Significance: are transport and inversion uncertainties
        small enough to see real IAV?
      • Robustness to set-up: sensitivity to the tightness of the
        ocean prior and to the SEY data uncertainty
• Mean and seasonal flux results
          TransCom3 Background
• In past decade: large spread in regional CO2 flux
  estimates from published inversions!
• Differences in the problem set-up (time span,
  measurement stations, data uncertainties, a priori
  fluxes and flux uncertainties, etc.) cause some of this
  spread. BUT, it was thought that differences between
  transport models might be responsible for the largest
Goal of TransCom3: find the sensitivity of CO2 flux
  inversion results to the transport model used.
[Assumption: no interannual variability in winds; each
  model uses only one year of “typical” winds.]
• ALSO: are there flux results that are robust across all
  (or most) of the transport models?
                        TransCom 3
     Three types of inversions have been done as part of T3
     levels 1 & 2. All use Bayesian synthesis, but make
     different assumptions about the time history of the
     fluxes and use data averaged over different spans.

Inversion Type   Fluxes   Data      References
Long-term mean R          S         Gurney, et al, Nature 415, 626-630
Seasonal         R*12     S*12      Gurney, et al. (2004)
                                    Rayner, et al, Tellus, 51B, 213-232;
Inter-annual     R*12*Y S*12*Y      Bousquet, et al., Science, 290, 1342-46;
R = 22 regions
S = 78 stations (GLOBALVIEW-CO2, 2003)
Y = 15 years (1988-2002) solved for here
        Base Case Assumptions
Nov 2002 [for T3 L3]            June 2004
• 1988-2001 (14 years)          • 1988-2002 (15 years)
                                • GLOBALVIEW- CO2
  (2002), 76 sites [chosen
  to have >68% data               (2003), 78 sites; the
  coverage ]; interpolated        previous 76 +
  data used to fill all gaps.     CPT_36C0 +
• Data uncertainties              HAT_20C0; also
  calculated from GV              SYO_00D0 changed to
  1979-2002 rsd (eGV) as:         SYO_09C0
  e2 = (0.3 ppmv) 2 + eGV2
  [non-seasonal]                • New seasonally- and
                                  data uncertainties
       Base Case Assumptions
Nov 2002 [for T3 L3]     June 2004
A priori fluxes – same   A priori fluxes – Kevin’s
  as in Level 1,           seasonally-varying
  constant across year     ones from the seasonal
A priori flux errors –     inversion
  twice Level 1          A priori flux errors
                           a) Kevin’s seasonally-
                           varying ones
                           b) ditto for land regions,
                           s2 = s2L1 + (0.5 PgC/yr) 2
                           for ocean regions
• Find optimal fluxes x to minimize
                        1                          1
     J  (Hx  z) R (Hx  z)  (x  x ) P (x  x )
                  T                           o T

  x are the CO2 fluxes to be solved for,
  H is the transport matrix, relating fluxes to concentrations
  z are the observed concentrations, minus the effect of
  pre-subtracted tracers (fossil fuel, and seasonal CASA &
  R is the covariance matrix for z,
  xo is an a priori estimate of the fluxes,
  Pxo is the covariance matrix for xo
                 x  (H T R 1H  Pxo1 ) 1 (H T R 1z  Pxo1x o )
                 Px  (H T R 1H  Pxo1 )
Time-dependent basis functions for 13 transport
      models were submitted in Level 2:

•   CSU (Gurney)†             •   MATCH (Law)
•   GCTM (Baker)              •   MATCH (Bruhwiler)
•   GISS-UCB (Fung)           •   NIES (Maksyutov)
•   GISS-UCI (Prather)        •   NIRE (Taguchi)
•   JMA-CDT (Maki)            •   TM2 (LSCE)
•   MATCH (Chen)              •   TM3 (Heimann)
      †   not used here       •   PCTM (Zhu)
12 + 1 – 1 = 12 models used
  Inter-annual Variability (IAV) Results:
               Key Issues
• Is the transport error low enough that key
  features in the inter-annual variability can be
  robustly identified by region? Is the random
  estimation error low enough?
• Is the IAV robust to the basis functions used?
  [Frequency- and SVD-truncation used to test
  this in past; here we examine the effect of a
  tighter ocean prior, and adjusting the data
  error for SEY]
• Where is the variability strongest and most
  robust? What physical mechanisms might
  cause it?
  EUROPE: Monthly Flux

                      12-model median flux

EUROPE: Deseasonalized Flux

                         12-model median flux
 EUROPE: Deseasonalized Flux

EUROPE: Deseasonalized Flux, Mean Subtracted Off     12-model median flux

EUROPE: Deseasonalized Flux, Mean Subtracted Off
          (Summary plot)                           1-sigma internal error

                                      1-sigma model spread
Computation of the inter-annual variability
 (IAV), long-term mean, and seasonality
     from the monthly estimate, xmon

 • xmon = xdeseas + xseas = xmean + xIAV +
 • xdeseas computed by passing a 13-point running mean
   over xmon

 • xseas = xmon - xdeseas     (zero annual mean seasonal

 • xmean = the 1988-2002 mean of xdeseas
 • xIAV = xdeseas - xmean (zero mean, 1988-2002)
 • Corresponding errors also computed
 Chi-square Significance Test
• We try to reject the null hypothesis that the
  estimated IAV is due solely to the combined
  effect of both transport error and random
  estimation error, superimposed on zero IAV
• Compare the variance of xIAV with the
  combined variance the transport and random
  errors: use c2 test (n=14; 15 independent
  years – 1 for mean)
4 cases presented here, to illustrate the impact
of regularization (by tightening the ocean prior),
and sensitivity to SEY:
• Loose ocean: Kevin’s a priori ocean errors
• Tight ocean: s2 = s2Level 1 + (0.5 PgC/yr) 2
• Tight ocean, loose SEY: add 1.5 ppmv in
  quadrature to Seychelles data error, 1988-96
• Tight ocean, loose SEY*: ditto, with an error
  in the a priori uncertainties for May-Nov for
  Region 3 corrected (increased to Kevin’s
Loose ocean errors            <0.00001


  Total Flux (Land+Ocean)

Tight ocean errors            <0.00001


  Total Flux (Land+Ocean)

Tight ocean, loose SEY          <0.00001


    Total Flux (Land+Ocean)

Tight ocean, loose SEY*          <0.00001


     Total Flux (Land+Ocean)

 Loose ocean errors                 <0.00001


                          0.00001         <0.00001

Land & Ocean Fluxes         <0.00001


                           (0.85)      <0.00001
 Tight ocean errors                 <0.00001


                          0.00004        <0.00001

Land & Ocean Fluxes         <0.00001


                           (0.31)      0.0034
Tight ocean, loose SEY                 <0.00001


                            0.000036        <0.00001

Land & Ocean Fluxes            <0.00001


                              (0.38)      0.0062
Tight ocean, loose SEY*                 <0.00001


                             0.000036        <0.00001

Land & Ocean Fluxes             <0.00001


                               (0.37)      0.0057
        Loose ocean errors




        Tight ocean errors




        Tight ocean, loose SEY




        Tight ocean, loose SEY*




                          Loose ocean errors
  <0.00001   <0.00001

 0.0042                               <0.00001

<0.00001     0.053

<0.00001      0.025     <0.00001
                         Tight ocean errors
  <0.00001   0.00016

 0.0055                              <0.00001


<0.00001               <0.00001
                       Tight ocean, loose SEY
  <0.00001   0.00015



<0.00001               <0.00001
                       Tight ocean, loose SEY*
  <0.00001   0.00014



<0.00001               <0.00001


           Loose ocean errors   (0.41)


           Tight ocean errors   (0.155)


           Tight ocean, loose SEY   (0.137)


           Tight ocean, loose SEY*   (0.156)
Loose ocean errors
Tight ocean errors
Tight ocean, loose SEY
Tight ocean, loose SEY*
“But wait – you aren’t allowed to change the data
  errors on SEY just because you don’t like the
    estimate you get for the Tropical Indian!!”
• True, in general, unless you have good reason to
  believe you used overly tight data errors for the site
• Tom Conway, NOAA CMDL (pers. comm., 5/11/04):
   – “Seychelles started out pretty good, but then we had various
     problems over the years. I think the most recent 8 years are
     pretty good again.”
   – “Things look pretty bad again in 1989 and 1990…. `91, `92,
     and `93 look pretty good…”
   – “In 1994… the USAF took over. The samples, most of which I
     believe had been collected near the coast, now were
     collected by USAF personnel at the tracking station (inland).
     This is the period when the sample collectors wrote down
     270° for the wind direction of almost every sample.” [The
     USAF pulled out in 1996, and a measurer trained by CMDL
     began taking samples.]
of our 1992-96
 Mean Fluxes
   (right) to
 Level 1 (left)
Mean Seasonal Cycle

        Prior, no def.
        G04 1992-96
Mean Seasonal Cycle
       G04 1992-96
 Seasonal Cycle
Amplitude [PgC/yr]
• Inter-model differences in long-term mean fluxes are
  larger than in the flux inter-annual variability
• IAV for latitudinal land & ocean partition is robust
  (except for Southern S. America); continent/basin
  partition of IAV in north is of marginal significance; in
  tropics, IAV is significant for the Tropical Pacific and
• The IAV for the 22 regions is significant for only a few
  land regions and about half the ocean regions.
  Probable physical drivers for Tropical Asia (fires) &
  East Pacific (El Niño); other regions less clear…
• Good agreement between the three types of
  inversions (annual-mean, seasonal, inter-annual) in
  mean & seasonality

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