model parameter inversion against eddy covariance data using a monte carlo technique jens kattge...
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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