1. Multivariate Data Assimilation of Carbon Cycle Using Local Ensemble Transform Kalman Filter 1 Ji-Sun Kang, 1 Eugenia Kalnay, 2 Junjie Liu, 2 Inez Fung, and 1 Ning Zeng 1 University of Maryland, College Park, Maryland 2 University of California, Berkeley, California

2. Introduction  Anthropogenic emission of CO 2 is increasing  Atmospheric CO 2 variability is relevant to climate  Carbon Sink/Source on the globe: surface fluxes  Estimate surface CO 2 fluxes using Local Ensemble Transform Kalman Filter technique http://svs.gsfc.nasa.gov/vis/a000000/a003300/a003308/index.html http://earthobservatory.nasa.gov/Library/CarbonCycle/carbon_cycle4.html

3. SPEEDY-C & VEGAS with SLand  SPEEDY (Molteni, 2003)  AGCM with T30 resolution (96X48) and 7 layers in vertical  Prognostic variables: U, V, T, q, Ps  Adapted for 6-hr assimilation cycle by Dr. Miyoshi  Added one additional prognostic variable, atmospheric CO 2 : SPEEDY-C  SPEEDY-C coupled with vegetation and soil model  Terrestrial carbon model VEGAS (Zeng, 2005)  Physical land surface model SLand (Zeng et al., 2000a)  Time-varying fluxes of surface CO 2 over land

4.  SPEEDY-C  Nature, including only fossil fuel emission (6 PgC/yr)  Forecast  Simulated Observations  U, V, T, q, Ps: rawinsonde distribution (9% coverage) Observation error: 1m/s for U & V, 1K for T, 0.1g/kg for q, 1hPa for Ps  Atmospheric CO 2 concentration: every other grid (25%) Observation error: 1ppmv  NO observation of CO 2 fluxes (CF)  20 ensemble members, 8% of multiplicative inflation for all the dynamical variables  Initial condition for CF  Close to zero-mean fields  NO a-priori information 1) Perfect Model Simulation

5. Three Types of Data Assimilation  Univariate Data Assimilation [Uncoupled]  Background errors of (CO 2, CF) have NO effect on errors of other atmospheric variables  Multivariate Data Assimilation  Errors of all variables are coupled  One-way Multivariate Data Assimilation U, V, T, q, Ps CO 2, CF U, V, T, q, Ps, CO 2, CF U, V, T, q, Ps U, V U, V, T, q, Ps CO 2, CF U, V, CO 2, CF

6. RMS Error Two-month analysis  Univariate DA  Diverges  Multivariate DA  Better than Univariate DA  One-way multivariate DA  Best performance for CO 2 variables 01JAN01MAR01JAN01MAR 01JAN01MAR01JAN01MAR 01JAN01MAR01JAN01MAR

7. Results: Perfect Model Simulation One-way Multivariate DA Truth Multivariate DA Uncoupled DA [*10 -9 kg/m 2 /s] : Fossil fuel fluxes

8. 2) Imperfect Model: Nature=coupled vegetation model  SPEEDY-C: forecast model  SPEEDY-C coupled with VEGAS and SLand: nature  Surface CO 2 fluxes over land from the coupled model + Prescribed monthly mean of ocean CO 2 fluxes (Takahashi et al., 2002)  One-way multivariate DA with 10% of multiplicative inflation  Initial condition for CF  Adding small random perturbation to randomly chosen 20 CF from nature With model bias, EnKF does not work (climatology of forecast model: significantly different from the nature)

9. Bias Correction  Nature: SPEEDY-C & VEGAS  Forecast: SPEEDY-C  Restart from the nature every six hour  Average the departure of 6-hour forecast for two months  Similar to Danforth et al., 2007 Nature Forecast

10. Results >24 <0.9  No Bias Correction  Bias Correction  Remarkable improvement in the analysis  Especially for the atmospheric variables and atmospheric CO 2 which have observations  CF analysis diverges for two months

11. Inflation  No Bias Correction  Bias Correction  Bias Correction + Different Inflations for CO 2 and CF  Large inflation (150%) for CO 2  Small inflation (5%) for CF Excellent Result

12. Atmospheric CO 2 with Bias Correction with Bias Correction+diff_infl Analysis of atmospheric CO 2 after two months  Bias correction experiment has better result in assimilating atmospheric CO 2  Bias correction + Different inflation experiment still performs well with atmospheric CO 2

13. Surface CO 2 Fluxes with Bias Correction with Bias Correction+diff_infl Analysis of atmospheric CO 2 after two months  Bias correction experiment has divergence in the analysis of surface CO 2 fluxes  Bias correction + Different inflation experiment (large inflation for CO 2, small inflation for CF) works very well in estimating CF under the imperfect model simulation

14. Summary  SPEEDY-C coupled with VEGAS and SLand  Simulated transport of atmospheric carbon dioxide and calculated time-varying fluxes over land in a simple but realistic global model  Three types of data assimilation examined  Multivariate data assimilation is much more effective in estimating surface CO 2 fluxes, even in the absence of observations or prior estimation of surface fluxes  With bias correction and different inflations for CO 2 variables, we could get improvement in the analysis of surface CO 2 fluxes  Adaptive inflation and observation error (Li, 2008)

15. The End Thank you for your attention