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

1
Case studies in Gaussian process modelling of
computer codes for carbon accounting

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

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 0.314 using emulator
RMSE 0.726 using ACM
SPA Predictions
Emulator Predictions
ACM 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
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 effects of 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
(No Transcript)
21
Error discovered in the soil module
NEP
80
60
40
20
0
-20
0
500000
1000000
1500000
22
(No Transcript)
23
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

24
NEP (g/m2/y)
NEP (g/m2/y)
25
Leaf life span 69.1
Water potential 3.4
Maximum age 1.0
Minimum growth rate 14.2
26
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

27
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

28
Leaf life span (days)
Minimum growth rate (m)
Maximum age (years)
Water potential (M Pa)
29
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
30
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
31

• 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?

32
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