Bayesian Analysis of the Sheffield Dynamic Global Vegetation Model

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Bayesian Analysis of the Sheffield Dynamic Global
Vegetation Model

• Marc Kennedy,
• Clive Anderson, Stefano Conti, Tony OHagan

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Centre for Terrestrial Carbon Dynamics

• The CTCD
• is a NERC centre of excellence for Earth
  Observation
• made up of groups from Sheffield, York,
  Edinburgh, UCL, Forest Research
• brings together experts in vegetation modelling,
  soil science, earth observation, carbon flux
  measurement and statistics

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Carbon Budget during 1989-98(Gt C y-1
Intergovernmental Panel on Climate Change, 2000)
Fossil fuels, Cement 6.3 0.6
Ocean uptake 2.3 0.8
Increase in atmospheric CO2 3.3 0.2
Land use change 1.6 0.8
Biospheric sink 2.3 1.3
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Centre for Terrestrial Carbon Dynamics

• The CTCD will
• Develop new knowledge about terrestrial carbon
  processes
• Contribute new ways to combine knowledge (expert
  models) with data for carbon accounting
• Account for (and reduce) uncertainty
• Enhance confidence in predictions of the
  evolution of the biosphere under climate change

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Gain
Photosynthesis
Net Ecosystem Production
Loss
Global Carbon Exchange

• Terrestrial carbon source if NEP is negative
• Terrestrial carbon sink if NEP is positive

(gC m-2 yr-1)
Plant respiration
Loss
Soil respiration
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Model-EO Interfaces
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Statistical objectives within CTCD

• Improve the models
• Identify greatest sources of uncertainty
• Combine model information, EO data and other
  information within a coherent Bayesian framework
• Correctly reflect the uncertainty in predictions

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Sheffield Dynamic Global Vegetation Model
GROWTH
Fire
Biomass
Mortality
LEACHED
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SDGVM

• Is a point model
• each pixel represents an area, with associated
  vegetation type / land use
• Vegetation type is described using 17 plant
  functional type parameters
• Still being developed
• improve processes
• change from using monthly to daily data

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Plant Functional Types

• Examples
• Leaf life span
• Leaf area
• Temperature when bud bursts
• Temperature when leaf falls
• Wood density
• Maximum carbon storage
• Xylem conductivity

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Emulator

• We build an emulator for SDGVM
• posterior distribution for the output (NEP),
  conditioned on a set of runs
• fast surrogate model uncertainty
• Maximin Latin hypercube design for inputs
• consider small groups of inputs to vary, others
  fixed at original default values

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Emulator

• Emulator is central for other tools
• Sensitivity analysis
• Uncertainty analysis
• Data assimilation (calibration, correction)
• No additional code runs required for these
• Simple analytical form
• Much more efficient than running the model
• compared with Monte Carlo methods

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Emulator

• Gaussian process prior
• Weak prior information about hyperparameters
• roughness
• precision
• MCMC used to account for posterior uncertainty in
  these parameters

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Model testing Sensitivity analysis

• SA used for model checking and for model
  interpretation
• Calculate main effects of each code input
• average effect of changing the input, other
  inputs integrated out
• Building the emulator has uncovered bugs
• simply by trying different combinations of input
  values

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Prior information

• Plant scientists provided
• selection of potentially influential inputs
• min, max ranges for these inputs
• Uniform priors used
• adequate for testing stage
• when we predict using the final model, we will
  elicit some real priors from the plant scientists

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Main Effect Leaf life span
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Main Effect Senescence Temperature
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Main Effects Soil inputs

• Soil inputs had been fixed in SDGVM
• Output sensitive to sand content, but not clay
  content
• Soil depth has absolutely no effect

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Example use UK carbon balance

• SDGVM run at 15km2 pixels within UK
• Land use inputs from EO data
• Limited met data available
• missing data will be dealt with using a weather
  generator
• Bayesian uncertainty analysis will be used to
  quantify uncertainty on the outputs resulting
  from uncertainty on the inputs

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Summary

• Using a statistical emulator of a model output,
  we can visualise the effect of changing
  individual parameters or pairs of parameters
• Provides a tool for model verification and
  interpretation
• The emulator uses a small number of model runs,
  covering the multidimensional input space, in an
  efficient way
• Identifies the inputs to which the output is most
  sensitive. For these inputs, we should consider
  the uncertainty carefully when we predict the
  output