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Data-model assimilation for manipulative experiments. Dr. Yiqi Luo Botany and microbiology department University of Oklahoma, USA. Manipulative experiments. More manipulative experiments under planning by NEON and DOE. What is the nature of manipulative experiments?.

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## Data-model assimilation for manipulative experiments

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**Data-model assimilation for manipulative experiments**Dr. Yiqi Luo Botany and microbiology department University of Oklahoma, USA**Manipulative experiments**More manipulative experiments under planning by NEON and DOE**How can we extrapolate results from the Duke FACE experiment**to predict long-term, large-scale change**CO2**CO2 CO2 CO2 GPP CO2 Fine roots (X3) Leaves (X1) Wood (X2) Surface metabolic leaf litter (X4) Soil metabolic root litter (X7) CO2 CO2 CO2 Surface microbes (X9) Wood litter (X6) Soil microbes (X10) CO2 CO2 CO2 Soil structural root litter (X8) Surface structural leaf litter (X5) CO2 CO2 CO2 Slow SOM (X11) CO2 CO2 Passive SOM (X12) CO2**Observed C and N dynamics in FACE experiments are not**applicable to natural ecosystems in response to a gradual CO2 increase. Luo and Reynolds 1999**Hui et al. 2002**Luo 2001 Results of manipulative experiments can not be simply extrapolated to predict ecosystem responses to global change in the real world**Luo and Reynolds (1999)**“Rigorous analysis of (results from) step experiments requires not only statistical but also other new approaches, such as deconvolution and inverse modeling”**Data-model assimilation at Duke FACE**• Tool development • Deconvolution (Luo et al. 2001) • Adjoint function (White and Luo. 2002) • Stochastic inversion, Xu et al. 2006 • Step-wise inversion, Wu et al. (in review) • Linear, nonlinear, ensemble Kalman Filter (Gao et al. see poster) • Applications • Soil C processes: Luo, et al. 2001 • Transfer coefficients: Luo, et al. 2003 • Uncertainty analysis, Xu et al. 2006 • Forecasting of carbon sequestration**Error distribution**Norman Distribution Double exponential distribution Frequency Observation error (umol m-2 s-1) Frequency Relative uncertainty (%) Frequency Hour Day Month Year Framework for Uncertainty analysis Measurement errors Stochastic inversion Variability in estimated parameter values Forward model Uncertainty in model predictions**Tree biomass growth**Soil respiration Soil carbon Litter fall Multiple data sets Foliage biomass**Mathematical and statistical procedure**1. Matrix to describe C flow GPP CO2 Leaf (X1) Wood (X3) Root (X2) 2. Mapping functions Qj(A)(t) = qj(A)(t) • X(A)(t) Metabolic litter (X4) Structure litter (X5) 3. Cost function CO2 Microbes (X6) CO2 CO2 CO2 CO2 CO2 Slow SOM (X7) 4. Search method CO2 MCMC– Metropolis-Hastings algorithm Passive SOM (X8)**Criteria I: Data-model fitting**Luo et al. 2003, GBC**Criteria II: Probability Distribution**Prior knowledge Posterior distribution Well-constrained Inverse model Edge-hitting Observed Data No-information**Multiple data sets**Stochastic inversion Variability in estimated parameter values Uncertainty analysis Variability in estimated parameter values Xu et al. 2006, GBC**ln (Y)=0.966 ln (X) + 0.215**R2= 0.969 Luo et al. 2003, GBC**Multiple data sets**Stochastic inversion Variability in estimated parameter values Forward model Uncertainty in model predictions Xu et al. 2006, GBC Model predictions**Estimated initial values of pools and residence times to**partition C sink to two components caused by climate change and forest regrowth**Applications**• Magnitudes (50%, 100%, and 200%) of measurement errors (Weng et al. poster) • Distributions (Normal vs. double exponential) of measurement errors of eddy-flux data (Liu et al. in review) • Different assimilation algorithms (least squares, maximal likelihood, and Kalman filter (Gao et al. poster) • Continental analysis on residence times (Tao Zhou et al. in review), Q10 values (Tao Zhou et al. in review, and their uncertainties (Xuhui Zhou et al. poster) Uncertainty Analysis Measurement errors Stochastic inversion Variability in estimated parameter values Forward model Uncertainty in model predictions**Data from manipulative experiments can not be directly**extrapolated to the real world. We have to extract information from data on fundamental processes • Model assimilation of multiple data sets is one of the best approaches to synthesis of experimental results with processing thinking and can better balance evidence from different lines. Summary**Acknowledgement**Data from the Duke FACE Schlesinger Ellsworth Finzi DeLucia Katul Oren Idea and math development Luther White James Reynolds S. Lakshmivarahan Dafeng Hui Tao Xu Tao Zhou Ensheng Weng Chao Gao Ensheng Weng Li Zhang Min Liu Financial support DOE TCP NSF http://bomi.ou.edu/luo

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