Using data assimilation to improve estimates of C cycling Mathew Williams School of GeoScience, University of Edinburgh

DATA MODELS DATA +Direct observation, good error estimates -Gaps, incomplete coverage MODELS +Knowledge of system evolution -Poor error estimates Terrestrial Carbon Dynamics MODEL-DATA FUSION

Soil chamber Eddy fluxes Litterfall Autotrophic Respiration Photosynthesis Soil biota Decomposition CO 2 ATMOSPHERE Heterotrophic respiration Litter Soil organic matter Leaves Roots Stems Translocation Carbon flow Litter traps Leaf chamber

Time update “predict” Measurement update “correct” A prediction-correction system Initial conditions

Ensemble Kalman Filter: Prediction ψ is the state vector j counts from 1 to N, where N denotes ensemble number k denotes time step, M is the model operator or transition matrix dq is the stochastic forcing representing model errors from a distribution with mean zero and covariance Q error statistics can be represented approximately using an appropriate ensemble of model states Generate an ensemble of observations from a distribution mean = measured value, covariance = estimated measurement error. d j = d +  j d = observations  = drawn from a distribution of zero mean and covariance equal to the estimated measurement error

Ensemble Kalman Filter: Update H is the observation operator, a matrix that relates the model state vector to the data, so that the true model state is related to the true observations by d t = H ψ t K e is the Kalman filter gain matrix, that determines the weighting applied to the correction  f = forecast state vector  a = analysed estimate generated by the correction of the forecast

Ponderosa Pine, Oregon,

GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Temperature controlled 6 model pools 10 model fluxes 9 rate constants 10 data time series R total & Net Ecosystem Exchange of CO 2 C = carbon pools A = allocation L = litter fall R = respiration (auto- & heterotrophic)

Setting up the analysis  The state vector contains the 6 pools and 10 fluxes  The analysis updates the state vector, while parameters are unchanging during the simulation  Test adequacy of the analysis by checking whether NEP estimates are unbiased

Setting up the analysis II  Initial conditions and model parameters – Set bounds and run multiple analyses  Data uncertainties – Based on instrumental characteristics, and comparison of replicated samples.  Model uncertainies – Harder to ascertain, sensitivity analyses required

Multiple flux constraints R a = 0.47 GPP Williams et al. 2005

A f = 0.31 A w =0.25 A r =0.43 Turnover Leaf = 1 yr Roots = 1.1 yr Wood = 1323 yr Litter = 0.1 yr SOM/CWD =1033 yr Williams et al. 2005

Data brings confidence

Parameter uncertainty  Vary nominal parameters and initial conditions ±20%  Generate 400 sets of parameters and IC’s, and then generate analyses  Accept all with unbiased estimates of NEP (N=189)  The mean of the NEE analyses over three years for unbiased models (-421±17 gC m -2 ) was little different to the nominal analysis (  419±29 g C m -2 )

Discussion  Analysis produces unbiased estimates of NEP  Autocorrelations in the residuals indicate the errors are not white  Litterfall models over simplified  Relative short time series and aggrading system  Next steps: assimilating EO products, and long time series inventories

Acknowledgements: Bev Law, James Irvine, + OSU team

Heterotrophic and autotrophic respiration Fraction of total respiration R a = 42% R h = 58%