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Impact of climate uncertainty upon trends in outputs
generated by an ecosystem model
Adam Butler & Glenn Marion, Biomathematics & Statistics Scotland
•
Ruth Doherty, Edinburgh University•
Jonathan Rougier,University of DurhamProbabilistic Climate Impacts workshop,
September 2006
Some backgroundSome background
AimsTo quantify uncertainties in projections of global and regional vegetation trends for the 21st century from the LPJ ecosystem model, based on future climate uncertainty
BIOSSPublic body providing quantitative consultancy & research to support biological science
Funded by ALARM: a 5 year EU project to assess risks of environmental change upon European biodiversity
The Impacts model: LPJThe Impacts model: LPJ
“The Lund-Potsdam-Jena Dynamic Global Vegetation Model (LPJ) combines process-based, large-scale representations of terrestrial vegetation dynamics and land-atmosphere carbon and water exchanges in a modular framework…”
http://www.pik-potsdam.de/lpj/
Fluxes(daily)
VegetationDynamics (annual)
Drivers
LPJ Vegetation Model simulationsLPJ Vegetation Model simulations
Driven by climate and soils inputs LPJ simulates:
Daily: carbon and water fluxes
Annually: vegetation dynamics and competition amongst 10 Plant Functional Types (PFTs)
Average grid-cell basis with a 1-year time-step
Spin-up period of 1000 years to develop equilibrium
vegetation and soil structure at start of simulation
LPJ Inputs/driversLPJ Inputs/drivers
Inputs:Soils: FAO global soils dataset: 9 types inc coarse-fine range (CRU)Climate: monthly temperature, precipitation, solar radiation
CO2: provided for 1901-1998; updated to 2002 from CDIAC
Model output scale determined by driving climate
Acknowledgements:LPJ code- Ben Smith, Stephen Sitch, Sybil SchapoffCRU data- David Viner (CRU), GCM data (PCMDI)
Tropical Broadleaf Evergreen Tree (FPC)Tropical Broadleaf Evergreen Tree (FPC)
C3 Grasses (FPC)C3 Grasses (FPC)
Sources of LPJ Model UncertaintySources of LPJ Model Uncertainty
Model inputs: future climate uncertainty
Representation of mechanisms driving model processes (Cramer et al. 2001; Smith et al. 2001- tests different formulations of relevant processes)- generally use most up-to date formulations from literature
Parameters within the model (Zaehle et al. 2005, GBC)
LPJ Parameter uncertainty: LPJ Parameter uncertainty: Zaehle et al. 2005Zaehle et al. 2005
Latin hypercube sampling Assume uniform PDF for each parameterExclude unrealistic parameter combinations
Simulations at sites representing major biomes (81)
400 model runs (61-90 CRU climatology and HadCM2 1860-2100)
Identified 14 functionally important parametersDifferences in parameter importance in water-limited regionsEstimated uncertainty range of modelled results:
61-90: NPP=43.1 –103.3 PgC/yr; cf. 44.4-66.3 Cramer et al. (2001)
LPJ Parameter uncertainty:LPJ Parameter uncertainty:Zaehle et al (2005)Zaehle et al (2005)
NBP = NEE+BiobUc=full uncertainty rangeC=excluding unrealistic
parametersNPP accounting
for parameter uncertainty
Increases in 2050s due
to increased CO2 and
WUE, thereafter a
decline
Parameter uncertainty
increases in the future
Uncertainty estimates in
NBP/NPP comparable to
those obtain from
uncertainty amongst 6
DGVMs
Future Climate Uncertainty Future Climate Uncertainty based onbased on
IPCC 4IPCC 4thth Assessment GCM Assessment GCM simulationssimulations
IPCC-AR4 simulationsIPCC-AR4 simulations
GCMs contributing to SRES A2GCMs contributing to SRES A2
COCO22 concentrations concentrations
Investigating the effect of Future Investigating the effect of Future Climate Uncertainty for Climate Uncertainty for
LPJ predictions LPJ predictions
Perform 19 separate runs of LPJ at the global scaleone run using CRU data for 1901-2002 at 0.5o x 0.5o
results from 18 simulations from 9 GCMs for the period 1850-2100 (20th Century and A2) running at the native scale of each GCM
GCMs with multiple ensemblesCCCMA-CGCM3, MPI-ECHAM5, NCAR-CCSM3
GCMs with single ensemble memberCNRM-CM3, CSIRO-MK3, GFDL-MK2, MRI-CGCM2-3, UKMO-HADCM3, UKMO-HADGEM
Global mean temperature anomalyGlobal mean temperature anomaly relative to 61-90 relative to 61-90
Net Primary Production
Net Ecosystem Production
Plant Functional Type
Heterotrophic respiration
Vegetation carbon
Soil carbon
Fire carbon
Run-off
Evapotranspiration
For each grid cell LPJ produces annual values for:
LPJ OutputsLPJ Outputs
…we focus on globally averaged values of these variables…
Net Primary Production
Net Ecosystem Production
Plant Functional Type
Heterotrophic respiration
Vegetation carbon
Soil carbon
Fire carbon
Run-off
Evapotranspiration
Statistical approachStatistical approach
• Statistical post-processing of LPJ output
• Analyse trends in global annual mean NPP based on outputs from 19 runs of the LPJ model
• Runs forced using a total of 18 ensembles from 9 GCMs, and using gridded CRU data
• Analysis (partially) deals with climate uncertainty, but does not deal with parameter or structural uncertainties in the LPJ model
Motivating factorsMotivating factors
• Statistical pre-processing of LPJ inputs is tough: would need to describe month-to-month trends in three climate variables for each location
• GCMs are each run at different spatial resolutions, all of which differ from the resolution of the CRU data
• LPJ is fairly computationally intensive to run
• No useful observational data to validate LPJ against
Time series modelTime series model
Use a hierarchical time series model to draw inferences about “true” response of LPJ model to projected climate changes based on the 19 runs
Output from past year t using CRU data:
Output for past or future year t using run i of GCM I:
Assume conditional independence in both cases
),(N~ ttt vx
),N(~ Itit zy
Latent trendsLatent trends
Model trends in true signal t and GCM biases YIt - t
as independent random walks: e.g.
allows process variability to change linearly over time
Can fit as a Dynamic Linear Model using the Kalman filter – easy to implement in R (sspir package)
Parameter estimation by numerical max likelihood
),(N~ 1 tstt
Results - temperatureResults - temperature
NPPNPP
AssumptionsAssumptions
• Observational errors are IID and unbiased
• Inter-ensemble variabilities for a given GCM are IID
• Random walk model can provide a good description of actual trends
• Levels of variability do not change over the course of the runs (except for a jump at present day)
Inter-ensemble variabilityInter-ensemble variability
Future work - methodologyFuture work - methodology
Explore impacts of making different assumptions about the biases in the GCM responses
Explore impacts of varying levels of inter-ensemble variability and observation error
Explore links between this and a regression-based (ASK-like) approach
Deal with uncertainty in estimation of parameters in time series model – e.g. a fully Bayesian analysis
Apply analysis to output from newer version of LPJ
Apply a similar analysis at the regional scale
Extend approach to other variables, especially PFT
Incorporate information on multiple scenarios
BUGSBUGS
BUGS: free software for fitting a vast range of statistical models via Bayesian inference
Provides an environment for exploring the impacts of different assumptions
Allows for the use of informative priors http://mathstat.helsinki.fi/openbugs
http://www.mrc-bsu.cam.ac.uk/bugs
[http://www-fis.iarc.fr/bugs/wine/winbugs.jpg]
Bayesian analogue of the DLMBayesian analogue of the DLM
IttIt bz
),0(~2 21 Nttt
),0(~1,, ItIItI Nbb Problems:Lack of identifiabilityBias terms are not really AR(1)
A Bayesian ASK-like modelA Bayesian ASK-like model
t
M
IItIt bzw
1
),0(~2 2,1, ItItIIt Nzzz
),0(~1 Nbb tt Problems:Lack of fitUnconstrained estimation leads to weights outside range [0,1]
Open questions Open questions – statistical methodology– statistical methodology
• What assumptions can we make about the biases in GCM responses and in the observational data?
• How reasonable is the assumption that future variability is related to past variability, and how far can we weaken this assumption?
• How should we best deal with small numbers of ensembles & unknown levels of “observational error”? Can we ellicit more prior information?
Future work - applicationFuture work - application
Apply analysis to output from newer version of LPJ
Apply a similar analysis at the regional scale
Extend approach to other variables, especially PFT
Analyse outputs from multiple SRES scenarios
Open questions - applicationOpen questions - application
Should LPJ be run at the native spatial scale of the data/GCM that is being used to force it ?
LPJ includes stochastic modules – switched off here, but how could we best deal with these…?
For a limited number of runs what experimental design would enable us to best reflect the different elements of climate and impact uncertainty?
