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Case studies in Gaussian process modelling of computer codes for carbon accounting

Case studies in Gaussian process modelling of computer codes for carbon accounting. Marc Kennedy , Clive Anderson, Stefano Conti, Tony O’Hagan. Talk Outline. Centre for Terrestrial Carbon Dynamics Computer Models in CTCD Bayesian emulators Case Study 1 : SPA Case Study 2 : SDGVM.

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Case studies in Gaussian process modelling of computer codes for carbon accounting

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  1. Case studies in Gaussian process modelling of computer codes for carbon accounting Marc Kennedy, Clive Anderson, Stefano Conti, Tony O’Hagan

  2. Talk Outline • Centre for Terrestrial Carbon Dynamics • Computer Models in CTCD • Bayesian emulators • Case Study 1: SPA • Case Study 2: SDGVM

  3. 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

  4. Gain Photosynthesis Net Ecosystem Production Loss • Terrestrial carbon source if NEP is negative • Terrestrial carbon sink if NEP is positive Plant respiration Loss Soil respiration

  5. Computer Models in CTCD • SPA • Simulates plant processes at 30-minute time intervals • ForestETP • Stand scale • Localised modelling • SDGVM • Global scale • Coarse resolution

  6. Statistical objectives within CTCD • Contribute to the development of these models • through model testing using sensitivity analysis • Identify the greatest sources of uncertainty • Correctly reflect the uncertainty in predictions • Uncertainty analysis: propagating the parameter uncertainty through the model

  7. Bayesian Emulation of Models • Model output is an unknown function of its inputs • Convenient prior is a Gaussian process • Run code at set of ‘well chosen’ input points • Obtain posterior distribution • The emulator is the posterior distribution of the output • Fast approximation • Measure of uncertainty • Nice analytical form for further analysis

  8. Case study 1: Soil Plant Atmosphere (SPA) Model • SPA is a fine scale model created by Mat Williams • Aggregated SPA outputs were used to create the simpler up-scaled model (ACM: the Aggregated Canopy Model) by fitting a set of simple equations with 9 parameters • Can an emulator do any better than ACM as an approximation to SPA?

  9. ACM vs. Emulator for predicting SPA • Bayesian emulator created using only 150 of the total 6561 points used to create ACM • Predicted remaining 6411 SPA points using emulator and ACM • Compare Root Mean Square Errors (RMSE)

  10. RMSE = 0.726 using ACM RMSE = 0.314 using emulator SPA Predictions ACM Predictions Emulator Predictions

  11. Case Study 2: Sheffield Dynamic Global Vegetation Model • SDGVM is a point model • each pixel represents an area, with an associated vegetation type / land use • Vegetation type is described using 14 plant functional type parameters • SDGVM is constantly being developed • To improve process modelling • To incorporate more detailed driving data

  12. Plant Functional Type inputs Examples: • Leaf life span • Leaf area • Temperature when bud bursts • Temperature when leaf falls • Wood density • Maximum carbon storage • Xylem conductivity • Emulator will allow small groups of inputs to vary, others fixed at original default values

  13. Soil inputs • Soil clay % • Soil sand % • Soil depth • Bulk density

  14. Run code 24.259 14.24 18.384 36.204 -3.214 1.774 254.0 6.304346 7.913044 20.28985 6.521775 330.0 8.739128 8.173912 13.4058 19.56525 326.0 8.30435 5.56522 7.971025 50.000023 145.0 5.521742 5.043478 0.72465 33.695625 236.0 9.43478 8.782606 1.08695 75.0 123.0 9.608696 9.478258 21.0145 71.739151 Emulator for SDGVM • Built an emulator for the NEP output of SDGVM • 80 runs in the 5-dimensional input space were used as training data • A maximin Latin hypercube design was used to ensure even coverage of the input space. Plant scientists specified the ranges … …

  15. Model testing: Sensitivity analysis • We use sensitivity analysis for model checking and for model interpretation • Calculate main effectsof each code input • How does output change if we vary the input, averaged over other inputs? • Building the emulator has uncovered bugs • simply by trying different combinations of input values

  16. Main Effect: Leaf life span

  17. Main Effect: Leaf life span (updated)

  18. Main Effect: Senescence Temperature

  19. Main Effects: Soil inputs • Soil inputs had been fixed in SDGVM • Output sensitive to sand content, but not clay content, over these ranges • More detailed soil input data are now used

  20. Bulk density Bulk density Before… After… Error discovered in the soil module NEP 80 60 40 20 0 -20 0 500000 1000000 1500000

  21. SDGVM: new sensitivity analysis • We initially analysed uncertainty in the NEP output at a single test site, using rough ranges for the 14 plant functional type parameters • Assumed default (uniform) probability distributions for the parameters • The aim here is to identify the greatest potential sources of uncertainty

  22. NEP (g/m2/y) NEP (g/m2/y)

  23. Leaf life span 69.1% Water potential 3.4% Maximum age 1.0% Minimum growth rate 14.2%

  24. Plant Functional Type parameters • Uncertainty is driven by just a few key parameters • Maximum age • Leaf life span • Water potential • Minimum growth rate • The next step was to refine the rough probability distributions for these parameters

  25. Elicitation • We elicited formal probability distributions for the key parameters • based on discussion with Ian Woodward • representing his uncertainty about their values within the UK • noting that each really applies as an average over the species actually present in a given pixel

  26. Leaf life span (days) Minimum growth rate (m) Maximum age (years) Water potential (M Pa)

  27. Uniform probability distributions Refined probability distributions Leaf life span 69.1% Water potential 3.4% Maximum age 1.0% Minimum growth rate 14.2% Mean NEP = 174 gCm-2 Std deviation = 14.32 gCm-2 Mean NEP = 163 gCm-2 Std deviation = 12.65 gCm-2

  28. Uncertainty analysis at sample sites • We computed uncertainty analyses on NEP outputs from SDGVM for 9 sites/pixels Stockten on the Forest (Nr York) Milton Keynes Barnstaple (Devon) Keswick (Lake District) Lowland (Scotland) Dartmoor New Forest (Hampshire) Kielder S. Ballater (Scotland) 20 70 120 170 220 270 NEP

  29. Uncertainty is clearly substantial, even when we only take account of uncertainty in these parameters • The most important parameter is minimum growth rate, which accounts for typically at least 60% of overall NEP uncertainty • This suggests targeting this parameter for research • Seeding density?

  30. Ongoing work • We need to estimate uncertainty in the overall UK carbon budget • Developing new theory for aggregating uncertainty over many pixels • Windows software will be made available later this year www.shef.ac.uk/st1mck

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