1. 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 Durham Probabilistic Climate Impacts workshop, September 2006

2. Some background Aims To quantify uncertainties in projections of global and regional vegetation trends for the 21st century from the LPJ ecosystem model, based on future climate uncertainty BIOSS Public 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

3. The 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/

4. Fluxes (daily) Vegetation Dynamics (annual) Drivers

5. LPJ 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

6. LPJ Inputs/drivers Inputs: Soils: FAO global soils dataset: 9 types inc coarse-fine range (CRU) Climate: monthly temperature, precipitation, solar radiation CO 2 : provided for 1901-1998; updated to 2002 from CDIAC Model output scale determined by driving climate Acknowledgements: LPJ code- Ben Smith, Stephen Sitch, Sybil Schapoff CRU data- David Viner (CRU), GCM data (PCMDI)

7. Tropical Broadleaf Evergreen Tree (FPC)

8. C3 Grasses (FPC)

9. Sources 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)

10. LPJ Parameter uncertainty: Zaehle et al. 2005 Latin hypercube sampling Assume uniform PDF for each parameter Exclude 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 parameters Differences in parameter importance in water-limited regions Estimated uncertainty range of modelled results: 61-90: NPP=43.1 –103.3 PgC/yr; cf. 44.4-66.3 Cramer et al. (2001)

11. LPJ Parameter uncertainty: Zaehle et al (2005) NBP = NEE+Biob Uc=full uncertainty range C=excluding unrealistic parameters NPP accounting for parameter uncertainty

12. Increases in 2050s due to increased CO 2 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

13. Future Climate Uncertainty based on IPCC 4 th Assessment GCM simulations

14. IPCC-AR4 simulations

15. GCMs contributing to SRES A2

16. CO 2 concentrations

17. Investigating the effect of Future Climate Uncertainty for LPJ predictions Perform 19 separate runs of LPJ at the global scale one run using CRU data for 1901-2002 at 0.5 o x 0.5 o results from 18 simulations from 9 GCMs for the period 1850-2100 (20 th Century and A2) running at the native scale of each GCM GCMs with multiple ensembles CCCMA-CGCM3, MPI-ECHAM5, NCAR-CCSM3 GCMs with single ensemble member CNRM-CM3, CSIRO-MK3, GFDL-MK2, MRI-CGCM2-3, UKMO-HADCM3, UKMO-HADGEM

18. Global mean temperature anomaly relative to 61-90

19. 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 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

20. Statistical 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

21. Motivating 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

22. Time 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

23. Latent trends Model trends in true signal  t and GCM biases Y It -  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

24. Results - temperature

26. NPP

27. Assumptions 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)

28. Inter-ensemble variability

29. Future 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

30. BUGS 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]

31. Bayesian analogue of the DLM Problems: Lack of identifiability Bias terms are not really AR(1)

32. A Bayesian ASK-like model Problems: Lack of fit Unconstrained estimation leads to weights outside range [0,1]

33. Open questions – 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?

34. Future 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

37. Open 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?

38. Contact us Adam Butler adam@bioss.ac.uk Ruth Doherty ruth.doherty@ed.ac.uk Glenn Marion glenn@bioss.ac.uk