Transcript Uncertainty in environmental modelling: carbon flux

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
Slide 1
This talk
 Carbon flux in England and Wales
 Sources of uncertainty
 Dealing with uncertainty
 Results (so far)
 Further research
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Slide 2
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).
mucm.group.shef.ac.uk
Slide 3
NBP in pictures
Vegetation
extracts carbon
from the
atmosphere.
This is given as
GPP.
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Slide 4
NBP in pictures
Vegetation and
soil respire; this
adds carbon
back into the
atmosphere.
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Slide 5
NBP in pictures
Disturbances
can negatively
affect this
process.
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Slide 6
NBP in pictures
Disturbances
can negatively
affect this
process.
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Slide 7
NBP in pictures
NBP = GPP – plant respiration
– soil respiration – disturbances
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Slide 8
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.
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Slide 9
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.
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Slide 10
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.
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Slide 11
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.
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Slide 12
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.
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Slide 13
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.
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Slide 14
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.
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Slide 15
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
proportion of PFT t at site i.
is the
 Uncertainty about the simulator and its inputs
must be propagated through this sum.
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Slide 16
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)
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Slide 17
Uncertainty in moving from 33 to
707 sites
 Sample sites:
varied climatic conditions
cover the whole region adequately
wide range of land cover types
different inter-site distances
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Slide 18
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.
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Slide 19
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 nonsample 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.
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Slide 20
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.
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Slide 21
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
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Slide 22
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.
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Slide 23
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.
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Slide 24
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.
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Slide 25
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………………………………..
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Slide 26
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)
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Slide 27
Results
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
0.00
0.00
0.29
0.32
PFT
Covariance
Total
7.55
0.02
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Slide 28
NBP results in colour
Mean (gC/m2)
Standard deviation (gC/m2)
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Slide 29
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….
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Slide 30
Uncertainty in the land cover map
 We used:
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Slide 31
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.
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Slide 32
Uncertainty in SDGVM’s connection
with reality
 SDGVM is a perfect representation of reality.
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Slide 33
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.
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Slide 34
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
mucm.group.shef.ac.uk
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