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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 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 computationally intensive to run • No useful observational data to validate LPJ against 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: xt ~ N(t , vt ) Output for past or future year t using run i of GCM I: yit ~ N(zIt , ) Assume conditional independence in both cases Latent trends Model trends in true signal t and GCM biases YIt - t as independent random walks: e.g. t ~ N(t 1 , s t ) 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 Results - temperature NPP 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) Inter-ensemble variability 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 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://www-fis.iarc.fr/bugs/wine/winbugs.jpg] http://mathstat.helsinki.fi/openbugs http://www.mrc-bsu.cam.ac.uk/bugs Bayesian analogue of the DLM z It t bIt t 2t 1 t 2 ~ N (0, ) Problems: Lack of identifiability Bias terms are not really AR(1) bI ,t I bI ,t 1 ~ N (0, I ) A Bayesian ASK-like model M t wI z It bt I 1 zIt 2zI ,t 1 zI ,t 2 ~ N (0, I ) Problems: Lack of fit Unconstrained estimation leads to weights outside range [0,1] bt bt 1 ~ N (0, ) 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? 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 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? Context: the ALARM project Assessing impacts of environmental change upon biodiversity at the European scale Modules: climate change, environmental chemicals, invasive species, pollination Relies heavily upon climate and land use projections Impacts assessed using either via mechanistic models (e.g. LPJ) or through extrapolation from current data Contact us Adam Butler [email protected] Ruth Doherty [email protected] Glenn Marion [email protected]