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Understanding Monte Carlo Experiment and succeding investigations Zoltán Barcza, Ferenc Horváth Department of Meteorology, Eötvös Loránd Universtiy, Budapest MTA ÖK Institute of Ecology and Botany, Vácrátót Budapest of May, 2014

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BOX WROTE THAT „Essentially, all models are wrong, but some are useful" Monte Carlo Experiment Monte Carlo Experiment

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Biome-BGC Monte Carlo Experiment SpinUp ININormal INIOUTPUT daily monthly avg annual avg annual sum METDATA for SpinUp METDATA for Normal CO 2 (optional) NDEP (optional) EPC - ecophysiology SITE parameters MANAGEMENT (opt.) MORTALI TY (opt.) GROUNDWATER (opt.) MCE INI – parameter randomization

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Biome-BGC Monte Carlo Experiment QUESTIONS: 1. WHAT DO I WANT TO RANDOMIZE? 2. HOW SHOULD I DEFINE PARAMETER INTERVALS?

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Biome-BGC Monte Carlo Experiment 1. WHAT DO I WANT TO RANDOMIZE? We should only fix parameters which are measured locally (we ‘believe’ in these parameters). But: consider structural problems that can cause bias in the parameter values! MAIN ISSUE WITH PARAMETER ESTIMATION [CALIBRATION, OPTIMIZATION]: THE MODEL IS HIGHLY NON-LINEAR, AND HAS A LARGE DEGREE OF FREEDOM.

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Biome-BGC Monte Carlo Experiment 1. OK, BUT WHAT DO I WANT TO RANDOMIZE? Typically the steps are: a)sensitivity analysis – use as many parameters as possible, and check the effect of parameter variability on the results. b)parameter estimation [optimization] – restrict the number of parameters to decrease the degree of freedom [literature also suggests that the number of parameters than can be estimated is quite low]

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Biome-BGC Monte Carlo Experiment 2. HOW SHOULD I DEFINE PARAMETER INTERVALS? Parameterization of Biome-BGC: must read White et al. 2000:

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Biome-BGC Monte Carlo Experiment White et al: 85 pages, vast amount of data

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Biome-BGC Sensitivity Analysis OUTPUT VARIABLES = f (params)

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Sensitivity analysis Parameter interval is critical. Investigated output is critical. Possible configurations: -wide parameter interval -small interval, e.g. 1% of total interval, around mean Note: check the sensitivity of the model to output which is interesting in your work! Slowly and quickly changing fluxes/pools are driven by different parameters….

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Biome-BGC Generalized Likelihood Uncertainty Estimation (GLUE) LHOOD MISFIT ‘BEST’ ? OBSER- VATION DATA

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0. maximum root depth 1. symbiotic+asymbiotic fixation of N 2. annual whole-plant mortality fraction 3. new fine root C : new leaf 4. current growth proportion 5. C:N of leaves 6. canopy light extinction coeff 7. canopy average specific leaf area 8. fraction of leaf N in Rubisco 9. maximum stomatal conductance Oensingen

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Equifinality We have to learn to live together with equifinality…

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GLUE Parameter uncertainty [confidence interval] can be calculated. Additionally, uncertainty of the calibrated model can be estimated if we run the model with the retained parameter sets, or with a subset of the best parameter settings. Parameter estimation can be performed for multiple years, for multiple sites, but it can also be performed for individual years… All depends on the scientific question that we want to answer.

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