Model parameter inversion against Eddy Covariance Data using a Monte Carlo Technique

Jens Kattge

Wolfgang Knorr

Christian Wirth

MPI for Biogeochemistry, Jena

CCDAS

Jena, Germany18.09.2006

BGC

Overview

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

CCDASBETHY+TM2

energy balance/photosynt.

atm. CO2

Optimized Params+ uncert. (58)

CO2 and waterfluxes + uncert.

2°x2°

BackgroundCO2 fluxes

eddy flux CO2 & H2O

Monte CarloParam. Inversion

full BETHY

satelliteFAPAR

CCDAS 1stepfull BETHY

params& uncert.

soil waterLAI

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 (Nleaf, T, fracleaf-plant) Farquhar, Ryan (1991)

heterotrophic respiration = r0*wQ10 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 = 0.05-0.5 (depending on parameter)

photosynthesis αq quantum efficiency of photon capture Vcmax maximum carboxylation rate at 25 °C EVm activation energy of VcmaxrJmVm ratio of Jmax to Vcmax at 25 °CΓ*25 CO2 compensation point without dark resp. at 25 °CKC25 Michaelis Menten constant for carboxylation at 25 °CEKc activation energy of KCKO25 Michaelis Menten constant for oxygenation at 25 °CEKo activation energy of KO

carbon balance fRd ratio of leaf dark respiration at 25 °C and Vcmax ERd activation energy of leaf dark respirationfR,leaf ratio of canopy to total plant respirationRhet0 heterotrophic respiration at 0 °C and field capacity κ soil moisture factor of heterotrophic respiration Q10 temperature dependency of heterotrophic respiration

stomatal control wpwp soil water content at permanent wilting pointfCi non water limited ratio of Ci,0 and Ca cw maximum water supply rate of root system

energy and radiation balance ω single scattering albedo of leaves av albedo of close vegetation surface cover as fraction of solar rad. abs. by soil under close canopy εs sky emissivity factor ga,v vegetation factor of atmospheric conductance

Bayesian approach

€

L(r m ) = k2 *exp -

1

2[

r f (

r m ) −

r f 0]t C f

-1[r f (

r m ) −

r f 0]

⎧ ⎨ ⎩

⎫ ⎬ ⎭

modelled diagnostics

error covariance matrixof observations

observations

• evidence: Likelihood function

€

ρ(r m ) = k1 *exp -

1

2(

r m −

r m 0)t Cm

-1 (r m −

r m 0)

⎧ ⎨ ⎩

⎫ ⎬ ⎭

assumedmodel parameters

a priori error covariance matrixof parameters

a prioriparameter values

• prior knowledge: a priori PDF

€

σ(r m ) = k * ρ (

r m ) * L(

r m )

• 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

€

ρ(pi+1) /ρ (pi) ≥1

€

ρ(pi+1) /ρ (pi)

€

ρ(pi+1) /ρ (pi) <1

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 PrecipFAPAR

Observations: 365 days of hh data of NEE and LE12 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

€

BE =1

N( pi

i=1

N

∑ − oi)

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 2000 365 days

• paraname, parapriori, paramodelmean, paramean, parasdpriori, parasdposteriori, parastep[ipara]• • aq 3.000e-01 3.264e-01 0.084 0.100 0.031 0.120• vcmax 3.500e-05 3.725e-05 0.062 0.500 0.027 0.180• ev 5.782e+04 5.818e+04 0.006 0.050 0.028 0.260• jmvm 1.740e+00 1.744e+00 0.002 0.020 0.013 0.220• gamma 1.830e-06 1.771e-06 -0.034 0.050 0.048 0.270• kc 4.200e-04 4.069e-04 -0.033 0.050 0.053 0.200• ec 7.280e+04 6.745e+04 -0.077 0.060 0.042 0.270• ko 2.700e-01 2.725e-01 0.008 0.070 0.050 0.240• eo 3.571e+04 3.833e+04 0.068 0.100 0.076 0.280• frd 1.100e-02 7.231e-03 -0.343 0.100 0.076 0.230• er 3.808e+04 3.754e+04 -0.015 0.050 0.047 0.240• frl 5.000e-01 7.082e-01 0.416 0.100 0.075 0.230• rsoil 2.070e+00 1.854e+00 -0.110 0.100 0.027 0.100• kw 1.000e+00 1.025e+00 0.022 0.050 0.073 0.240• q10 1.720e+00 1.556e+00 -0.101 0.050 0.019 0.180• swc 1.000e+01 3.092e+00 -1.181 0.250 0.120 0.120• fci 8.500e-01 8.285e-01 -0.025 0.010 0.008 0.200• cw 1.000e+00 6.365e-01 -0.452 0.250 0.013 0.080• omega 1.600e-01 1.605e-01 0.003 0.020 0.015 0.260• av 1.500e-01 3.202e-01 0.752 0.150 0.108 0.240• asoil 5.000e-02 9.734e-02 0.606 0.250 0.349 0.250• epsa 6.400e-01 4.129e-01 -0.439 0.050 0.028 0.130• fga 4.000e-02 3.994e-02 -0.003 0.050 0.060 0.280• lss 1.700e+00 1.643e+00 -0.034 0.500 0.018 0.010• ls 1.100e+02 1.148e+02 0.043 0.500 0.003 0.010

• lw 3.000e+02 2.965e+02 -0.012 0.500 0.002 0.010