Ji-Sun Kang. Pr. Eugenia Kalnay (Chair/Advisor) Pr. Ning Zeng (Co-Chair) Pr. Brian Hunt (Dean s representative) Pr. Kayo Ide Pr.

Transcription

1 Carbon Cycle Data Assimilation Using a Coupled Atmosphere-Vegetation Model and the LETKF Ji-Sun Kang Committee in charge: Pr. Eugenia Kalnay (Chair/Advisor) Pr. Ning Zeng (Co-Chair) Pr. Brian Hunt (Dean s representative) Pr. Inez Fung Pr. Kayo Ide Pr. Ross Salawitch

2 Introduction Time series of atmospheric CO 2 (ppm) (from Samiento et al., 2002) Substantial ti increase of atmospheric CO 2 caused dby human activities Radiative properties of CO 2 result in global warming 2

3 Introduction ator /Librar /CarbonC c cle4 html Increase rate of atmospheric CO 2 : about half of the increase rate of anthropogenic CO 2 emission + a strong variability according to climate Missing carbon : surface CO 2 sources and sinks Not enough knowledge about surface CO 2 fluxes on the globe 3

4 Observations Direct observation of surface CO 2 fluxes: FLUXNET Representative of small local area from m 2 to km 2 Flask measurement of atmospheric CO 2 : ESRL/NOAA GLOBALVIEW-CO 2 High precision information Spatially sparse and temporally heterogeneous CO 2 -dedicated satellite: OCO, GOSAT FLUXNET 4

5 Previous Methods on CO 2 Sources/Sinks Inversion methods Inverse of transport model: difficult and ill-posed Computationally impractical for high-density data Data assimilation il studies 4D-Var (Baker et al., 2006) EnKF (Peters et al., 2005; Feng et al., 2008) J 2 1 { M( S) O} ( S S σ o σ S 0 0 = 2 ) 2 Minimizing the difference between the simulated CO 2 concentration and the observed CO 2, prior errors of CO 2 variables Atmospheric CO 2 observation, O Transport model, M a-posteriori estimate, S Require a prior estimate of surface CO 2 flux fields Don t account for the transport errors in the wind fields A-priori fields of surface CO 2 fluxes, S 0 5

6 Objectives Explore the feasibility of estimating surface CO 2 fluxes by assimilating remotely sensed atmospheric CO 2 observations using the LETKF (Hunt et al., 2007) Consider transport errors in estimating surface CO 2 fluxes No a-priori information for surface CO 2 fluxes Carbon Data Assimilation with a Coupled Ensemble Kalman Filter Supported by Climate Change Prediction Program in Department of Energy Simulation mode (SPEEDY) Develop new methodologies University of Maryland Prof. Eugenia Kalnay Realistic System (LETKF/CAM) Assimilating real observation of GOSAT & AIRS UC Berkeley Prof. Inez Fung 6

7 Development of New Models for Simulation and Assimilation of CO 2 SPEEDY-C Coupled SPEEDY-C Ct to VEGAS and dsl SLand

8 SPEEDY-C SPEEDY (F. Molteni, 2003) (Simplified Parametrizations, primitive-equation DYnamics) General Circulation Model of the Atmosphere Spectral model with T30 resolution (96X48) Seven layers in the vertical Prognostic variables: U, V, T, q, Ps Adapted for 6hr assimilation cycle by Dr. Takemasa Miyoshi I added an additional prognostic variable, CO 2 No feedback between CO 2 and radiative properties in SPEEDY-C CF 8

9 Performance of SPEEDY-C SPEEDY-C NCAR CCM Atmospheric CO2 Vertical cross-section Atmospheric CO2 On surface layer 9

10 SPEEDY-VEGAS Coupled SPEEDY-C withvegaswithsland SLand VEGAS (dynamic terrestrial carbon model, Zeng et al., 2005) SLand (simple physical land model, Zeng et al., 2000) Heat, water, and energy fluxes are obtained through h coupling 10

11 Spin-up p of coupled SPEEDY-VEGAS Offline simulation of Land-Vegetation model forced by SPEEDY climatology for 600 years Online simulation of Atmosphere-Land-Vegetation model for 30 years Equilibrium state of atmosphere, land, and vegetation Net Ecosystem Productivity, NEP (Gt/yr) 11

12 Carbon fluxes in SPEEDY-VEGAS Winter Summer Vegetation uptakes atmospheric CO 2 during growing season Land surface releases CO 2 into the atmosphere during decaying season 12

13 Summary of Models For Observing System Simulation Experiments (OSSEs), we have developed two models SPEEDY-C SPEEDY-VEGAS Despite the simplicity of models, the performance of ftwo systems is good enough hfor this study 13

14 Three Types of Analysis in LETKF Carbon-Univariate Data Assimilation Multivariate Data Assimilation 1-way Multivariate Data Assimilation

15 Local Ensemble Transform Kalman Filter (LETKF, Hunt et al. 2007) Observations y o, R Ensemble Forecasts x b(i), P b LETKF x a(i), P a Ensemble analyses Analysis (1- K) background + K obs K (Kalman gain) is determined by the error statistics of ensemble forecast and observations EnKF provides background and analysis uncertainty estimation in every analysis step (P b, P a ) LETKF assimilates the observations locally 15

16 How to update surface CO fluxes 2 X b * X = CF : model state vector (u, v, T, q, Ps, CO 2 ) :surfaceco CF 2 flux State space augmentation (Friedland, 1969) Append CF (surface CO 2 fluxes here) Update CF as part of the data assimilation process According to variables included in X * Carbon-Univariate Data assimilation: X * =(C) T Fully multivariate Data Assimilation: X * =(U, V, T, q, Ps, C) T 1-way multivariate Data Assimilation: X * =(U, V, C) T 16

17 Carbon-Univariate Data Assimilation U C CF T V Ps q Background Error Covariance Matrix, P b CF C U V T q Ps Update U, V, T, q, Ps X b C = CF Errors of carbon variables are correlated NO correlation between errors of CO 2 variables and atmospheric variables C-Univariate analysis cannot deal with CO 2 transport errors 17

18 Multivariate Data Assimilation C CF U T V Ps q Background Error Covariance Matrix, P b CF C U V T q Ps Update U, V, T, q, Ps, C, CF X b * X = CF X * =(U,V,T,q,Ps,C) CF=surface carbon flux Errors of all variables are coupled Errors of CO 2 variables correlated with errors of all atmospheric variables (U, V, T, q, Ps) This includes the error correlation between CO 2 variables and (T, q, Ps), which is not physical and introduces sampling errors 18

19 1-way Multivariate Data Assimilation U C CF T V Background Error Covariance Matrix, P b CF C Update CF & C U V T q Ps X * X * (U V C) = CF X b X * =(U, V, C) CF=surface carbon flux In the analysis for CO 2 variables, errors of wind fields are coupled Wind field is NOT affected by these two carbon variables Ps q Update U, V, T, q, Ps 19

20 Model is perfect! ect Errors (forecast) = initial condition error + observation error Using the same model for nature run and forecast 1) Perfect Model Experiments Carbon-Univariate Data Assimilation Multivariate Data Assimilation 1-way Multivariate Data Assimilation

21 Experimental Design SPEEDY-C: nature run & ensemble forecast Nature: only fossil fuel emission (6PgC/yr; Andres et al., 1996) Persistence forecast of surface CO 2 fluxes Simulated Observations U, V, T, q, Ps: rawinsonde distribution 9% grid coverage in the horizontal Observation errors: U, V 1m/s, T- 1K, q 0.1g/kg, Ps 1hPa Atmospheric CO 2 concentration: at every four grid points 25% grid coverage in the horizontal Observation errors: 1 ppmv ALL LEVELS experiment: observations at every level NO observations of CO 2 flux on the surface 21

22 Experimental Design Observation stations for atmospheric variables ( ), and atmospheric CO 2 (+) Multiplicative inflation: 5% 20 ensemble members 22

23 Initial Conditions for CO 2 True state of atmospheric CO 2 True state of surface CO 2 fluxes Random initial condition Random initial condition No a-prior information! 23

24 Results U V Time series of RMS errors Carbon-univariate DA Filter divergence! Fully multivariate DA Error correlations between CO 2 and T, q, Ps introduce sampling errors 1-way Multivariate DA T q Best system for CO 2 C CF variables 24

25 Analysis of surface CO fluxes 2 After two months of analysis Truth C-univariate DA Multivariate DA 1-way multivariate DA 25

26 OCO+AIRS & OCO Experiments OCO was most sensitive to the CO 2 concentration in the lower troposphere CO 2 retrievals from AIRS have the largest sensitivity in the upper troposphere We assumed that there are observations of CO 2 concentration at only two layers of σ=0.95 & σ=0.34 (OCO+AIRS), or only at σ=0.95 (OCO) 26

27 Results from 1-way multivariate DA After two months of analysis True state t of surface CO 2 fluxes ALL LEVEL experiment OCO+AIRS experiment OCO experiment 27

28 Summary of perfect model experiments Carbon-univariate data assimilation It failed! Multivariate data assimilation Better than the C-univariate DA Unphysical correlation of CO 2 variables with (T, q, Ps) introduces spurious signals around the major source regions 1-way multivariate i t data assimilation il Best performance OCO+AIRS and OCO experiments Surface CO 2 fluxes are analyzed well if the observation of CO 2 concentration is sensitive to the values near the surface 28

29 Model is not perfect in reality! Errors in the forecast = initial condition error + observation error + model error 2) Imperfect Model Experiments Bias Correction Adaptive inflation i

30 Imperfect Model Experimental Design NATURE RUN: SPEEDY-VEGAS Evolving CO 2 fluxes over land every 6 hour Monthly ocean CO 2 fluxes of -2PgC/yr (Takahashi et al., 2002) ENSEMBLE FORECAST: SPEEDY-C 1-way multivariate data assimilation with 8% inflation Truth of CF at the initial time Random initial condition 30

31 Correction of Model bias Systematic errors of the model cannot be neglected (the climatology of the forecast model is significantly different from that of the nature run) Low-dimensional method (LDM, Danforth et al., 2007) Forecast Nature 6hr Make a series of 6-hour forecasts Average out the forecast errors for two months Subtract the mean from the forecast every analysis step Bias correction applied to the meteorological variables, NOT CO 2 variables 31

32 Results U V Without bias correction Errors grow with time due to the model bias With bias correction Atmospheric variables are much better Still, it fails for surface CO 2 fluxes T q C CF 32

33 Adaptive Inflation Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter (Li et al., 2009) Based on the innovation statistics: O-B, O-A, A-B Inflation estimation relies on the accuracy of the observation error statistics estimate the inflation factor and observation errors simultaneously Inflation for meteorological o og variables and CO 2 variables for each vertical level For the lowest layer s CO 2, different inflation is estimated over land and over ocean 33

34 Adaptive inflation for surface CO 2 fluxes p 2 For surface CO 2 fluxes, Ensemble forecast Analysis at t=t i t i t Inflation = (ensemble spread of forecast)/(ensemble spread of analysis) Estimate the inflation adaptively at every grid point 34

35 Estimation of observation errors 2.5 C_z2 C_z3 C_z4 C_z5 C_z6 C_z7 U_z1 U_z2 U_z3 U_z4 U_z5 U_z6 U_z7 V_z1 V_z2 V_z3 V_z4 V_z5 V_z6 V_z7 observation errors Estimated Initial guess: twice the true value True value analysis steps 35

36 RMS errors U V With a fixed inflation With the adaptive inflation Surface CO 2 flux analysis improves significantly Atmospheric variables and atmospheric CO 2 also improve T q C CF 36

37 Analysis of surface CO fluxes 2 After two months of data assimilation Truth NO bias correction, NO adaptive inflation With bias correction, NO adaptive inflation With bias correction+ adaptive inflation 37

38 Why adaptive inflation is so important? land ocn+ice lev2 lev3 lev4 lev5 lev6 lev Lowest layer s CO 2 inflation Upper level s CO 2 inflation inflation Estimated i Over land inflation Estimated i Over ocean analysis steps analysis steps Inflation for the lowest layer s CO 2 Large over the land Variability of surface CO 2 fluxes over the land Other inflation factors are similar to what we used before 38

39 Why adaptive inflation is so important? Inflation for surface CO 2 fluxes Average of estimated inflation for two months of analysis Maximum inflation is less than 10% Relatively large inflation appears over the area where the surface CO 2 flux signals are significant 39

40 Summary of the imperfect model experiments Carbon cycle data assimilation under the imperfect model assumption Bias correction: o large improvements e But, fails for surface carbon fluxes We applied the advanced technique of adaptive inflation introduced by Li et al., 2009 Adaptive inflation gives excellent analysis of surface CO 2 fluxes Also provides an accurate estimate of observation errors 40

41 3) Perfect Model Experiments with Adaptive Inflation Technique Carbon-Univariate data assimilation 1-way multivariate li i data assimilation il i

42 Impact of adaptive inflation Fixed inflation C-Univariate DA w/ fixed inflation C-Univariate DA w/ adaptive inflation 1-way mult DA w/ adaptive inflation Adaptive inflation Significant improvement on the C-univariate data assimilation Carbon-Univariate DA has even better analysis of CF than the 1-way multivariate DA! 42

43 Estimated Adaptive Inflation CO2lev1 CO2lev2 CO2lev3 CO2lev4 CO2lev5 CO2lev6 CO2lev Atmospheric CO 2 inflation Surface CO 2 flux inflation Estimate ed inflation Analys is steps Analysis steps Estimated_Obs_err Inflation of atmospheric CO 2 should be large at the early stage of analysis Random initial condition Inflation for the surface CO 2 fluxes should be small (< 1% ) 43

44 Analysis of Surface CO fluxes 2 Truth Results from both are good But, 1-way multivariate DA has spurious signals Negative impact of error correlation between surface CO 2 flux and wind 1-way multivariate DA C-univariate DA 44

45 Summary of perfect model experiments with adaptive inflation Carbon-univariate analysis becomes even better than the 1-way multivariate DA Relatively large inflation at the early stage of the analysis is necessary due to the random initial condition Inflation for the surface CO 2 fluxes need to be small We found that the correlation of errors between wind and surface CO 2 fluxes may not be as useful as we had originally thought This gives a new idea for next improvement! 45

46 4) New Approach in Multivariate Data Assimilation System We found that surface carbon should not be correlated with wind

47 New 1-way Multivariate Data Assimilation CF C U V T q Ps T V U C CF Ps q Update CF & C Update U, V, T, q, Ps Analysis of atmospheric variables are the same as before (green box) The error of the wind fields is coupled with the atmospheric CO 2, not with surface CO 2 flux Variable localization Schematic plot of Background Error Covariance Matrix 47

48 Perfect model experiments (a) Truth (b) C-univariate DA (c) 1way_variable localization (d) 1way multivariate DA [old] 48

49 Imperfect model experiments Truth C-univariate DA 1-way multivariate DA [old] 1-way [variable localization] 49

50 Conclusions on variable localization New concept of multivariate data assimilation was developed ( variable localization ) The system controls the correlation of errors among the variables Uncertainty of wind is helpful for the analysis of atmospheric CO 2, but not for the surface CO 2 flux New 1-way multivariate data assimilation has the best result in the analysis of surface CO 2 fluxes Remaining problem: Hot spots over the Southern Hemisphere 50

51 Summary and Future Work Development of Models Univariate vs. Multivariate Analysis Bias Correction and Adaptive Inflation Variable Localization Future Plans

52 Summary For OSSEs, two models were developed SPEEDY-C SPEEDY-VEGAS Three types of data assimilations were examined Carbon-univariate DA Fully multivariate DA 1-way multivariate DA Bias correction Adaptive inflation and observation error estimates Variable localization 52

53 Summary of Progress Imperfect model experiments CTRL adaptive_infl Variable localization Truth Bias correction +bias correction +adaptive inflation +variable localization 53

54 Future Plans Remaining problem: hot spots Produced by the model bias of atmospheric CO 2 which we did not correct Bias correction requires a reanalysis There is no CO 2 reanalysis that can be used for bias estimate Another method for correcting bias is necessary Analysis increments are promising for this No bias correction of atmospheric CO 2 Bias correction of atmospheric CO 2 54

55 Future Plans Assimilating column-integrated observation of CO 2 Methodologies developed in this study will guide the state-of-art art data assimilation system for the carbon cycle (LETKF/CAM3.5 at UC Berkeley) 55

56 Thank you for your attention

57 Inflation Ensemble forecast tends to underestimate the uncertainty in practice Analysis overfits the background state estimate and gives too small weight to the observations Inflate the background covariance every data assimilation cycle to increase model error covariance Manually tuning the inflation parameter Too expensive 57

58 Local Ensemble Transform Kalman Filter (LETKF, Hunt et al. 2007) y = H Y X x x b( i) b( i) [ g ] [ g ] [ g ] { b( i) b y } b [ g ] = [ g ] y[ g ] { b( i) b x } b [ g ] = [ g ] x[ g ] a X a b b = x + X K( y b ~ = X ( k 1) P ~ Kalman gain, K o y b ) (1-K) fcst+k obs 1 a [ ] 2 Observations y o, R Ensemble Forecasts x b(i), P b LETKF x a(i), P a ~ K [ ] b T 1 b 1 b T 1 ( HX ) R ( HX ) + ( k 1) I ( HX ) = R ~ a b T 1 b 1 P [( HX ) R HX + ( k 1) ] 1 = I 58