Model parameter inversion against Eddy Covariance Data using a Monte Carlo Technique Jens Kattge Wolfgang Knorr Christian Wirth MPI for Biogeochemistry, Jena CCDAS Jena, Germany BGC

Overview Intention Terrestrial Ecosystem Model: BETHY Bayesian approach Metropolis Monte-Carlo method Optimisation setup Results: RMS and Bias Conclusions

CCDAS BETHY+TM2 energy balance/ photosynt. atm. CO 2 Optimized Params + uncert. (58) CO 2 and water fluxes + uncert. 2°x2° Background CO 2 fluxes eddy flux CO 2 & H 2 O Monte Carlo Param. Inversion full BETHY satellite FAPAR CCDAS 1step full BETHY params & uncert. soil water LAI Global Carbon cycle data assimilation system: CCDAS Wolfgang Knorr, Thomas Kaminski, Marko Scholze, Peter Rayner, Ralf Giering, Heinrich Widmann, Christian Roedenbeck, Martin Heimann & Colin Prentice

First attempt: 7 days of hh data Inversion of BETHY model parameters against 7 days of half-hourly Eddy covariance data of NEE and LE at the Loobos site

First Attempt: Loobos BETHY Parameter estimates Relative reduction of uncertainty

Carbon sequestration at the Loobos site during 1997 and 1998 doy

BETHY (Biosphere Energy-Transfer-Hydrology Scheme) NEE = GPP - Raut - Rhet GPP: C3 photosynthesis Farquhar et al. (1980) the Canopy is devided into 3 layers Ecosystem Respiration: autotrophic respiration = f (N leaf, T, frac leaf-plant ) Farquhar, Ryan (1991) heterotrophic respiration = r0*w Q 10 Ta/10 Raich (2002) Stomatal control: stomatal conductance Knorr (1997) Energy and radiation balance: PAR absortion Sellers (1985) diffuse radiation absorption Weiss and Norman (1985) evapotranspiation Penman and Monteith (1965) Timestep: 1/2 hour

23 variable parameters in BETHY assumed a priori uncertainties of parameters: SD = (depending on parameter)

Bayesian approach modelled diagnostics error covariance matrix of observations observations evidence: Likelihood function assumed model parameters a priori error covariance matrix of parameters a priori parameter values prior knowledge: a priori PDF a posteriori probability density function (PDF) normalization constant prior knowledge evidence

Metropolis Monte-Carlo method Monte Carlo sampling of parameter-sets A random walk guided by the metropolis decision Metropolis decision if accept step, if accept step with probability

Figure taken from Tarantola '87 Metropolis Monte-Carlo method

Setup of gap-filling experiment Ecosystem model: BETHY Prior parameter values and uncertainties: Reasonable values and uncertainties (5 -50%) Input data to run BETHY: Latitude, Soil depth, soil type PFFD, Ta, Rh, SWC or Precip FAPAR Observations: 365 days of hh data of NEE and LE 12 days of hh data NEE and LE (represent seasons) Two optimised model run results replicated 50 times to provide data for different gap length scenarios

Results: RMS Antje Moffat, 2006

BIAS per site years Antje Moffat, 2006

BIAS: average over all site years Antje Moffat, 2006

Confidence in half-hourly performance: medium Confidence in daily performance: good Reliability of annual sum: site year bias, most likely due to using 1 set of training data per site and year Conclusions

Optimised model: parameter values Hainich days paraname, parapriori, paramodelmean, paramean, parasdpriori, parasdposteriori, parastep[ipara] aq 3.000e e vcmax 3.500e e ev 5.782e e jmvm 1.740e e gamma 1.830e e kc 4.200e e ec 7.280e e ko 2.700e e eo 3.571e e frd 1.100e e er 3.808e e frl 5.000e e rsoil 2.070e e kw 1.000e e q e e swc 1.000e e fci 8.500e e cw 1.000e e omega 1.600e e av 1.500e e asoil 5.000e e epsa 6.400e e fga 4.000e e lss 1.700e e ls 1.100e e lw 3.000e e