Statistical approach

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:

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 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 - 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

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

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]

Bayesian 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 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 – 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

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?

Contact us

Adam Butler [email protected]

Ruth [email protected]

Glenn [email protected]