Using data assimilation to improve understanding and forecasts of the terrestrial carbon cycle Mathew Williams School of GeoSciences, University of Edinburgh And National Centre for Earth Observation

Source: CD Keeling, NOAA/ESRL Sampling at 3397 meters, well mixed free troposphere

GPP R H 60 o R A Source: Schlesinger (1997), Schimel et al. (1995), Reeburgh (1997) THE BIOLOGICAL GLOBAL CARBON CYCLE (1750) Pools (billions of tonnes C) & fluxes ( billions of tonnes C yr -1 ) Soils 1580 Atmosphere 540 Deep ocean DOC 700 DIC Surface DOC 40 POC 7 Sediments 75,000,000

? GPP R H Net destruction of vegetation R A Source: Schlesinger (1997), Schimel et al. (1995), Reeburgh (1997) THE MODERN GLOBAL CARBON CYCLE (2000) Pools (billions of tonnes C) & fluxes ( billions of tonnes C yr -1 ) Soils 1580 Atmosphere 720 (+3.2/yr) Unattributed C sink 1.6 Deep ocean DOC 700 DIC Surface DOC 40 POC 7 Sediments 75,000,000

Friedlingstein et al 2006: C4MIP Intercomparison of 11 coupled carbon climate models

Problems with models Poor parameterisation Inaccurate initial conditions Missing processes Solution: make and break models with observations?

Space (km) time s hr day month yr dec Flask Site Time and space scales in ecological processes Physiology Climate change Succession Growth and phenology Adaptation Disturbance Photosynthesis and respiration Climate variability

OCO Space (km) time s hr day month yr dec Flux Tower Aircraft Flask Site Flask Site Field Studies MODIS Time and space scales in ecological observations Tall tower

Observing networks: Flask [CO 2 ]

Observing networks: CO 2 Fluxes FluxNet - ~200 eddy covariance systems

Source: Wofsy et al, Harvard Forest LTER Hourly data ~5 m above canopy

Tall Tower ‘Angus’ CO 2 CH 4 N 2 O SF 6 CO H Rn at 222 m at 50 m  T and RH at 220,100, 50 and 5 m agl  P, u and wind direction at 5 m agl  Li-7000  Agilent 6890 FID & ECD  TGA3  ANSTO Radon Photo: T Hill & T Wade

Landscape and regional ecology

Barkley et al, [2006] SCIAMACHY CO 2 [P Monks] MODIS EVI [NASA] Airborne LIDAR biomass [C Nichol] A range of Earth observation data

Improving estimates of C dynamics MODELS OBSERVATIONS FUSION ANALYSIS MODELS + Capable of interpolation & forecasts - Subjective & inaccurate? OBSERVATIONS +Clear confidence limits - Incomplete, patchy - Net fluxes ANALYSIS + Complete + Clear confidence limits + Capable of forecasts

GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Modelling C exchanges

GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Photosynthesis & plant respiration Phenology & allocation Senescence & disturbance Microbial & soil processes Climate drivers Non linear functions of temperature Simple linear functions Feedback from C f

Exploring model behaviour  Sensitivity to initial conditions  Parameter sensitivity  Steady state solutions  A master’s study by Tom Ilett – Supported by Sarah Dance, Jon Pitchford, Nancy Nichols

Sensitivity of pools and NEE to altered initial conditions of C f

C r - roots C w - wood C lit - litterC som – soil organic matter NEE sensitivity to varying initial conditions over 3 years

Parameter details Parameter sensitivity

The steady state solution For  C f = 0 The equilibria for the other stocks are linear functions of G and C f Assume climate inputs are constants

There are three fixed points for GPP and C f, for C f  0; 50; 450.

Equilibrated values of other C stocks Equilibrium value (gC m -2 ) Time to equilibrium (yrs) G*10.8 gC m -2 d -1 C f* 450<12 C r* 290<12 C w* 37, C lit* 210<12 C som* 230,

NEE trajectories 12 yrs250 yrs2000 yrs Evolution of NEE  0, time constant depends on stabilisation of C som

Relationship between GPP, C f and time – an indicator of phenology?

Convergence to attracting orbit for a 15 year projection. Trajectories become darker as time progresses – final year is a black line

Combining models and observations  Are observations consistent among themselves and with the model?  What processes are constrained by observations?

The Kalman Filter MODEL AtAt F t+1 F´ t+1 OPERATOR A t+1 D t+1 Assimilation Initial stateForecast Observations Predictions Analysis P Ensemble Kalman Filter Drivers

Data brings confidence Williams et al, GCB (2005)  = observation — = mean analysis | = SD of the analysis

Reflex experiment  Objectives: To compare the strengths and weaknesses of various model-data fusion techniques for estimating carbon model parameters and predicting carbon fluxes.  Real and synthetic observations from evergreen and deciduous ecosystems  Evergreen and deciduous models  Multiple MDF techniques

ParticipantName – type of methodology CodePriorInitial poolsConvergence tests Number of parameter sets produced Number of model iterations Programming language E1 (stage 1) MCMC Metropolis, then EnKF UniformParameters to be estimated Gelman and Rubin (1992) ~400000~ Fortran E1 (stage 2) Evensen (2003) PDFs from stage 1 n/aState only8000Fortran E2Ensemble Kalman filter Evensen (2003) gaussian Cr=Cfmax, Clit=0.5Cfmax, Clab=0.5Cfmax n/a - ran EnKF 2 times with reinitialisation ~ Fortran90 U1Unscented Kalman filter Gove & Hollinger (2006) gaussian From M3n/a R G1Genetic algorithmBased on Haupt and Haupt (2004) uniform Tuned with parameters n/a ~100000Fortran90 M1MCMC – Metropolis Included in calibration visual Fortran M2MCMC – MetropolisMCMC1uniform Parameters to be estimated Visual comparison of parameter PDFs from 2 chains Fortran M3Simulated annealing-Metropolis SAMuniform Parameters to be estimated none1000~250000Fortran M4MCMC – MetropolisMCMC3uniform Spinup to equilibrium of total C Heidelberger and Welch (1983) 80000~300000R M5Multiple complex MCMC – Metropolis SCEMuniform Parameters to be estimated Gelman and Rubin (1992) ~ Matlab Algorithms in the Reflex Experiment

Parameter constraint Consistency among methods Confidence intervals constrained by the data Consistent with known “truth” “truth”

Parameter retrieval for EV ID Paramd1d2d3DRankBias p1T d p2F g B p3F nf A p4F nrr p5T f A p6T w * p7T r p8T l p9T s * p10E t p11P r B Mean d1.Consistency among methods:  (m 1,…,m 9 )/(p max -p min ) d2. CIs constrained by the data:  (CI 1,…,CI 9 )/(p max -p min ) d3.Consistent with truth:|t-  (m 1,…,m 9 )|/(p max -p min ) m i =estimate by method i, p=prior, t=truth. D =  (d 1,d 2,d 3 ). A, B indicate correlations

Parameter summary  Parameters closely associated with foliage and gas exchange are better constrained  Parameters for wood and roots poorly constrained and even biased  Similar parameter D values for synthetic and true data  Correlated parameters were neither better nor worse constrained

Testing algorithms & their confidence Fraction of successful annual flux tests (3 years x 2 sites, n=6) Confidence interval (gC m -2 yr -1 ) GPP ReRe NEE

Problems with soil organic matter…

And with woody C

State retrieval summary  Confidence interval estimates differed widely  Some techniques balanced success with narrow confidence intervals  Some techniques allowed large slow pools to diverge unrealistically

Conclusions  Attractor analysis is a useful technique for understanding C models  Model data fusion provides insights into information retrieval from noisy and incomplete observations  Challenges and opportunities: – introducing stochastic forcing – Linking other biogeochemical cycles – Designing optimal sensor networks – Theoretical understanding of plant process

Thank you

Time (days since 1 Jan 2000) Williams et al GCB (2005)  = observation — = mean analysis | = SD of the analysis

Time (days since 1 Jan 2000) Williams et al GCB (2005) = observation — = mean analysis | = SD of the analysis