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Uncertainty in environmental modelling: carbon flux calculations for England and Wales. Marc Kennedy, Clive Anderson, Anthony O’Hagan, Mark Lomas, Ian Woodward, Andreas Heinemayer and John Paul Gosling. This talk. Carbon flux in England and Wales Sources of uncertainty - PowerPoint PPT Presentation
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Slide 1
Marc Kennedy, Clive Anderson, Anthony O’Hagan, Mark Lomas, Ian Woodward, Andreas Heinemayer and
John Paul Gosling
Uncertainty in environmental modelling: carbon flux calculations
for England and Wales
Slide 2mucm.group.shef.ac.uk
This talkCarbon flux in England and WalesSources of uncertaintyDealing with uncertaintyResults (so far)Further research
Slide 3mucm.group.shef.ac.uk
Carbon Flux Carbon flux (CF) is the exchange of carbon
between the land (vegetation and soils) and the atmosphere.
Gross primary production (GPP) is a measure of photosynthetic fixation by vegetation of CO2.
Net biome productivity (NBP) is the net uptake of carbon by the land (i.e. vegetation and soil).
Slide 4mucm.group.shef.ac.uk
NBP in pictures
Vegetation extracts carbon
from the atmosphere.
This is given as GPP.
Slide 5mucm.group.shef.ac.uk
NBP in pictures
Vegetation and soil respire; this
adds carbon back into the atmosphere.
Slide 6mucm.group.shef.ac.uk
NBP in pictures
Disturbances can negatively
affect this process.
Slide 7mucm.group.shef.ac.uk
NBP in pictures
Disturbances can negatively
affect this process.
Slide 8mucm.group.shef.ac.uk
NBP in pictures
NBP = GPP – plant respiration – soil respiration – disturbances
Slide 9mucm.group.shef.ac.uk
Previous attempts to quantify CF
Some studies have focused on particular plant functional types, e.g. woodland, and particular areas of the UK.
Others have tried to quantify it in extremely small areas with respect to England and Wales.
Dynamic vegetation models (DVMs) have been employed to calculate CF as have techniques of inversion on the atmospheric CO2 levels.
Slide 10mucm.group.shef.ac.uk
What do we want to know about?
What was the NBP for England and Wales in the year 2000?
Not just a guess – even if it is a well educated guess using sophisticated models and super computers.
A mean for NBP AND a measure of our uncertainty.
Slide 11mucm.group.shef.ac.uk
Our results
Mean NBP of 7.55 MtC A standard deviation of 0.56 MtC for NBP
Basic idea: Use a simulator of the physical
processes (or computer code) to inform us about the actual NBP value.
Slide 12mucm.group.shef.ac.uk
SDGVM
The simulator we used for this study was the Sheffield Dynamic Global Vegetation Model (SDGVM).
The simulator can be represented as a function:
η(X) = Y
where X is a vector of inputs and Y is the model output.
Slide 13mucm.group.shef.ac.uk
Where does the uncertainty come from? We consider two main sources of uncertainty:
we do not know η(X) for every possible X therefore we are uncertain about η(.),
we do not know the correct values of X for the simulator.
Slide 14mucm.group.shef.ac.uk
Uncertainty in computer code outputs – a GP model Our prior uncertainty about the simulator is
given by a Gaussian process:
These beliefs are updated using training data from the simulator.
Slide 15mucm.group.shef.ac.uk
Uncertainty in computer code outputs – what does SDGVM give us? England and Wales is divided into squares
with 1/6th of a degree length. We consider NBP for the situation where each square is
completely covered by Grassland Crops Deciduous broadleaf trees Evergreen needle leaf trees
Essentially, we have a function that represents SDGVM for each PFT at each site.
Slide 16mucm.group.shef.ac.uk
Uncertainty in computer code outputs – aggregation of outputs We are interested in the total NBP for England
and Wales in the year 2000, which is given by:
where is the area of site i and is the proportion of PFT t at site i.
Uncertainty about the simulator and its inputs must be propagated through this sum.
Slide 17mucm.group.shef.ac.uk
Uncertainty in computer code outputs – computational restrictions Using an emulator allows us to run just the
simulator a fraction of the times in comparison to a Monte Carlo method.
However, to emulate well, we need approximately 900 simulator runs per site.
707 * 900 simulator runs = 636300 simulator runs (This would take about 440 days as one
simulator run takes approximately 1 min)
Slide 18mucm.group.shef.ac.uk
Uncertainty in moving from 33 to 707 sites
Sample sites: varied climatic conditionscover the whole region adequately
wide range of land cover typesdifferent inter-site distances
Slide 19mucm.group.shef.ac.uk
Uncertainty in moving from 33 to 707 sites - kriging We cannot simply interpolate across the whole
of England and Wales using some standard regression technique as we wish to capture all our uncertainty.
Kriging has been about for many years in geostatistics, and it is analogous to the Gaussian process techniques we use to model the simulator.
Slide 20mucm.group.shef.ac.uk
Uncertainty in moving from 33 to 707 sites - kriging We want to report mean NBP and its variance
for each site. We get a posterior mean value for the non-
sample sites. We also get a measure of our about NBP
uncertainty at each non-sample site.
In order to perform kriging, we must specify a spatial correlation structure. This can be done in a fully probabilistic manner; however, we actually just estimated the covariograms using the sample sites.
Slide 21mucm.group.shef.ac.uk
Uncertainty in computer code inputs
Our uncertainty in the simulator inputs drives some of our uncertainty about the simulator output.
Y = η(X)
Effort must be made to accurately elicit our beliefs about X.
Slide 22mucm.group.shef.ac.uk
Uncertainty in computer code inputs – parameter types There are three main parameter types that
SDGVM uses: Plant inputs
There are 4 plant functional types (PFTs): grassland, crop, deciduous broad leaf and evergreen needle leaf.
Soil inputs These are location specific, i.e. what are
the average soil characteristics at that particular site.
Climate data
Slide 23mucm.group.shef.ac.uk
Uncertainty in computer code inputs – sensitivity analysis We use sensitivity analysis techniques that
exploit properties of the Gaussian process model to establish which simulator inputs actually have an impact on NBP.
We then spent time eliciting expert beliefs about those important inputs.
This exercise led to many adjustments to the simulator as we explored parts of the input space the simulator builders had never considered.
Slide 24mucm.group.shef.ac.uk
Uncertainty in computer code inputs – soil parameters Soil texture and bulk density parameters must be
specified for each simulator run.
The important soil parameters were found to be sand percentage, clay percentage and bulk density.
We use the same soil parameters for each PFT.
For each of the sample sites, soil data were available at 1 km2 resolution, giving a number of observations of the relevant parameters for each site.
Slide 25mucm.group.shef.ac.uk
Uncertainty in computer code inputs – plant parameters Different numbers of plant-type inputs were
found to be important for each PFT.
There was not the same kind of data available as there was for the soil parameters.
The plant parameters were assumed to be the same across England and Wales.
We elicited distributions for these from an expert.
Slide 26mucm.group.shef.ac.uk
Uncertainty in computer code inputs – climate forcing data For SDGVM, the climate inputs are interpolated
climate records or climate models.
In this study, monthly temperature, precipitation, air humidity and cloudiness for the year 2000 from the CRU/UEA dataset were used.
Monthly data are downscaled to a daily time-step with a weather generator.
The climate data is assumed to be known with no uncertainty………………………………..
Slide 27mucm.group.shef.ac.uk
Uncertainty in computer code inputs – sensitivity analysis
Expected output for each input after integrating out uncertainty from other inputs.
This is for DcBl at site 3 (Middlesbrough area)
Slide 28mucm.group.shef.ac.uk
Results
PFT Mean (MtC)Interpolation
variance (MtC2)
Variance from input uncertainty
(MtC2)
Total Variance
(MtC2)
Grassland 4.64 0.01 0.26 0.27
Crops 0.45 0.01 0.02 0.03
DcBl 1.68 0.00 0.01 0.01
EvNl 0.78 0.00 0.00 0.00
Covariance 0.00 0.00
Total 7.55 0.02 0.29 0.32
Slide 29mucm.group.shef.ac.uk
NBP results in colour
Mean (gC/m2) Standard deviation (gC/m2)
Slide 30mucm.group.shef.ac.uk
Our results vs. previous results
Previous attempts have been limited to specific areas within what we have covered in this analysis.
We have expressed a measure of uncertainty about NBP and not just given a point estimate.
But our results are far from being perfect….
Slide 31mucm.group.shef.ac.uk
Uncertainty in the land cover map
We used:
Slide 32mucm.group.shef.ac.uk
Uncertainty in the climate forcing data We used observed climate data to drive
SDGVM.
Observed data taken as being known.
We had to move from monthly to daily data on precipitation using a simple stochastic model –a first order Markov chain for the sequence of wet and dry days and then the amount drawn from a gamma distribution.
Slide 33mucm.group.shef.ac.uk
Uncertainty in SDGVM’s connection with reality SDGVM is a perfect representation of reality.
Slide 34mucm.group.shef.ac.uk
Uncertainty in SDGVM’s connection with reality SDGVM is a perfect representation of reality.
I think not!
We have to think about model discrepancy.
This is extremely difficult especially when we have no data on the same scale on which we are modelling.
Slide 35mucm.group.shef.ac.uk
References Kennedy, M.C., Anderson, C.W., O'Hagan, A., Lomas,
M.R., Woodward, F.I., Heinemeyer, A. and Gosling, J.P. (2006). Quantifying uncertainty in the biospheric carbon flux for England and Wales. To appear in J. R. Statist. Soc. Ser. A.
Gosling, J.P. and O’Hagan, A. (2006). Understanding the uncertainty in the biospheric carbon flux for England and Wales. Research report 567/06, Department of Probability and Statistics, University of Sheffield, Sheffield, UK.
Both of these and software to help you get started with UA and SA for computer models can be found on:
www.tonyohagan.co.uk